Tracers in the Oil Field (Developments in Petroleum Science)

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D e v e l o p m e n t s in P e t r o l e u m Science, 43

tracers in the oil field

BERNARD ZEMEL

The University of Texas at Austin, Center for Petroleum and Geosystems Engineering, Austin, TX 78712, USA

ELSEVIER

SCIENCE

Amsterdam - Lausanne - New York-

Oxford - Shannon - Tokyo

1995

ELSEVIER SCIENCE B.V. Sara B urgerhartstraat 25 P.O. Box 211, 1000 AE Amsterdam, The Netherlands

ISBN: 0-444-88968-X

9 1995 Elsevier Science B.V. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Science B.V., Copyright & Permissions Department, P.O. Box 521, 1000 AM Amsterdam, The Netherlands. Special regulations for readers in the USA - This publication has been registered with the Copyright Clearance Center Inc. (CCC), Salem, Massachusetts. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the USA. All other copyright questions, including photocopying outside of the USA, should be referred to the publisher. No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. This book is printed on acid-flee paper. Printed in The Netherlands

This work is dedicated to my wife, Jane, with gratitude for her understanding and patience during its preparation.

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TABLE Preface

OF

CONTENTS

............................................................................................................................... x v ~

Acknowledgments

...........................................................................................................

~dx

C r e d i t s .................................................................................................................................

xm

Chapter

One: Radioactivity

Basics

I N T R O D U C T I O N ............................................................................................................... I s o t o p e s a n d n u c l e a r s t r u c t u r e ...............................................................................

1 1

R A D I O A C T I V I T Y .............................................................................................................. Activity a n d half-life .................................................................................................. S t a t i s t i c s of c o u n t i n g ................................................................................................ S t a t i s t i c s of c o u n t i n g zero, s i g n a l vs. n o i s e ................................................. S e q u e n t i a l r a d i o a c t i v e d e c a y ................................................................................... R a d i o a c t i v e e q u i l i b r i u m ............................................................................................ N u c l e a r d e c a y p r o c e s s e s .......................................................................................... B e t a d e c a y ......................................................................................................... A l p h a d e c a y ....................................................................................................... G a m m a r a y e m i s s i o n ...................................................................................... N e u t r o n s o u r c e s ............................................................................................... C h a r a c t e r i s t i c e n e r g y ............................................................................................... D e c a y s c h e m e s .................................................................................................

3 3 5 5 6 7 9 10 11 12 12 14 15

I N T E R A C T I O N S O F R A D I A T I O N W I T H M A T T E R ................................................ A l p h a p a r t i c l e s a n d o t h e r p o s i t i v e l y c h a r g e d ions .............................................. B e t a p a r t i c l e s a n d p o s i t r o n s ................................................................................... G a m m a r a d i a t i o n ( a n d x-rays) ................................................................................ P h o t o e l e c t r i c a b s o r p t i o n (x) ............................................................................ C o m p t o n s c a t t e r i n g ((~) ................................................................................... P a i r p r o d u c t i o n (~) ............................................................................................ G a m m a r a y a t t e n u a t i o n .......................................................................................... C o l l i m a t e d b e a m s a n d s o u r c e g e o m e t r y ...................................................... D i s t r i b u t e d s o u r c e s a n d d e t e c t o r s ................................................................ N e u t r o n r e a c t i o n s w i t h m a t t e r ............................................................................... E l a s t i c collisions ( m o d e r a t i n g ) ....................................................................... N e u t r o n a b s o r p t i o n .......................................................................................... A t t e n u a t i o n of n e u t r o n s in m a t t e r ...............................................................

18 18 19 19 20 20 21 22 23 26 29 30 30 32

S O U R C E S O F R A D I O A C T I V E M A T E R I A L .............................................................. P r i m o r d i a l s o u r c e s ..................................................................................................... M a n m a d e m a t e r i a l s .................................................................................................. C o s m i c r a d i a t i o n ........................................................................................................

33 34 35 36

R E F E R E N C E S ................................................................................................................... 37

viii

Tracers in the Oil Field

Chapter Two: Measurements and Applications I N T R O D U C T I O N ............................................................................................................... 3 9 R A D I A T I O N D E T E C T I O N A N D M E A S U R E M E N T ................................................ I n t e r a c t i o n of r a d i a t i o n w i t h m a t t e r ...................................................................... Efficiency a n d g e o m e t r y of d e t e c t i o n ..................................................................... S i g n a l - t o - n o i s e r a t i o ..................................................................................................

39 39 40 40

C H A R G E C O L L E C T I O N I N G A S C O U N T E R S ........................................................ T h e effect of a n i m p r e s s e d v o l t a g e ......................................................................... P u l s e c o u n t i n g a n d c u r r e n t c o u n t i n g ..................................................................... I o n c h a m b e r ................................................................................................................ P r o p o r t i o n a l c o u n t e r ................................................................................................. G e i g e r - M u e l l e r c o u n t e r ............................................................................................. C o u n t e r p l a t e a u vs. p u l s e - h e i g h t p l a t e a u ............................................................

41 42 43 44 45 46 47

C O U N T I N G S Y S T E M S .................................................................................................... S i m p l e c o u n t e r s ......................................................................................................... C o u n t e r s m e a s u r i n g e n e r g y .................................................................................... B a c k ~ o u n d r e d u c t i o n ......................................................................................

48 48 49 50

S C I N T I L L A T I O N D E T E C T O R S ................................................................................... T h e p h o t o m u l t i p l i e r t u b e .......................................................................................... T h e NaI(T1) d e t e c t o r ................................................................................................. O p e r a t i o n of d e t e c t o r ....................................................................................... E n e r g y s p e c t r u m f r o m NaI(T1) c r y s t a l ....................................................... S p e c t r u m a n a l y s i s ........................................................................................... L i q u i d s c i n t i l l a t i o n c o u n t e r s ..................................................................................... A q u e o u s s o l u t i o n s of b e t a e m i t t e r s .............................................................. C o u n t e r o p e r a t i o n ............................................................................................

51 52 53 53 55 56 58 58 59

S O L I D S T A T E I O N I Z A T I O N D E T E C T O R S ............................................................... D i o d e d e t e c t o r s ........................................................................................................... G e r m a n i u m d e t e c t o r s ............................................................................................... T h e r m o l u m i n e s c e n t d o s i m e t e r s (TLD's) ...............................................................

63 63 64 64

N E U T R O N D E T E C T O R S ................................................................................................ 6 5 COUNT RATE METERS, MULTICHANNEL ANALYZERS, A N D S C A L E R S .................................................................................................................. A n a l o g c o u n t r a t e m e t e r s ........................................................................................ M u l t i c h a n n e l a n a l y z e r s ............................................................................................ P u l s e - h e i g h t a n a l y z e r m o d e ........................................................................... M u l t i c h a n n e l s c a l e r m o d e ............................................................................... M a r i n e l l i b e a k e r s .......................................................................................................

65 65 67 68 69 70

C O U N T I N G R A D I O A C T I V E A T O M S .......................................................................... 7 0 A c c e l e r a t o r m a s s s p e c t r o m e t r y ............................................................................. 71 R e s o n a n c e ion s p e c t r o m e t r y ................................................................................... 71 U S E F U L N U C L E A R P R O C E D U R E S ......................................................................... 71 I s o t o p e g e n e r a t o r s .................................................................................................... 71

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A d v a n t a g e s ....................................................................................................... P r o c e d u r e s ........................................................................................................ B i o m e d i c a l b a s e ............................................................................................... I s o t o p e d i l u t i o n p r o c e d u r e s ..................................................................................... M a s s m e a s u r e m e n t s ...................................................................................... V o l u m e m e a s u r e m e n t s .................................................................................. F l o w - r a t e m e a s u r e m e n t s .............................................................................. A c t i v a t i o n a n a l y s i s ..................................................................................................

71 72 73 74 75 75 76 77

D O S I M E T R Y ...................................................................................................................... D o s i m e t r y u n i t s ........................................................................................................ D o s e c a l c u l a t i o n s ...................................................................................................... E s t i m a t e d e x t e r n a l d o s e f r o m a p o i n t g a m m a s o u r c e ............................. E s t i m a t e d i n t e r n a l d o s e f r o m i n g e s t e d b e t a s o u r c e .................................

78 78 79 79 79

L I C E N S I N G A N D C O N T R O L O F R A D I O A C T I V E M A T E R I A L .......................... 81 R a d i a t i o n p r o t e c t i o n : A L A R A a n d M P C .............................................................. 83 R E F E R E N C E S ..................................................................................................................

85

Chapter Three: I n t e r w e l l W a t e r Tracers I N T R O D U C T I O N .............................................................................................................. 8 9 F U N C T I O N S O F A W A T E R F L O O D I N G T R A C E R ................................................. H i s t o r y a n d d e v e l o p m e n t ........................................................................................ R e s e r v o i r c o n s t r a i n t s .............................................................................................. T r a c e r e x c h a n g e .............................................................................................. T r a c e r r e a c t i o n ................................................................................................ T r a c e r m a t e r i a l s for i n t e r w e l l u s e ................................................................ R a d i o a c t i v e a n d u n t a g g e d c h e m i c a l t r a c e r s .......................................................

89 90 90 91 91 92 92

R A D I O A C T I V E L Y T A G G E D T R A C E R S F O R W A T E R F L O O D S ......................... 9 3 R a d i o a c t i v e t r a c e r s a v a i l a b l e for field u s e ........................................................... 9 3 H e x a c y a n o c o b a l t a t e i o n s .............................................................................. 9 4 T r i t i a t e d w a t e r ................................................................................................. 9 4 O t h e r a n i o n i c c o m p l e x e s ................................................................................ 9 5 S p e c i a l t y t r a c e r s ............................................................................................. 9 5 T r a c e r q u a l i t y c o n t r o l .............................................................................................. 9 6 T r a c e r p r e p a r a t i o n ................................................................................................... 9 8 T r i t i a t e d w a t e r ................................................................................................. 9 8 H e x a c y a n o c o b a l t a t e s ..................................................................................... 9 8 T h i o c y a n a t e ion ............................................................................................... 9 9 F i e l d t r a c e r v e r i f i c a t i o n .................................................................................. 9 9 T r a c e r i n j e c t i o n p r o c e d u r e s ........................................................................... 1 0 0 F i e l d t r a c e r d e s i g n ..................................................................................................... 1 0 3 T o t a l d i l u t i o n field t r a c e r m o d e l .................................................................... 1 0 3 A b b a s z a d e h - B r i g h a m m o d e l ......................................................................... 1 0 5 T r a c e r a n a l y s e s : s e n s i t i v i t y , d y n a m i c r a n g e , a n d s e l e c t i v i t y ................ 1 0 5 A n a l y t i c a l s t r a t e g i e s ................................................................................................ 1 0 7

Tracers in the Oil Field

I o n e x c h a n g e c h r o m a t o g r a p h y ..................................................................... 1 0 8 C l a s s i c a l l i q u i d c h r o m a t o g r a p h y .................................................................. 1 0 9 N O N R A D I O A C T I V E L Y T A G G E D T R A C E R S F O R W A T E R F L O O D S ............... C h e m i c a l t r a c e r s a v a i l a b l e ..................................................................................... P o t e n t i a l t r a c e r s ....................................................................................................... A n a l y t i c a l m e t h o d s .................................................................................................. I o n c h r o m a t o g r a p h y ....................................................................................... M i n i m u m d e t e c t i o n l i m i t s ..............................................................................

114 115 116 117 118 124

T R A C E R S A M P L I N G A N D A N A L Y S I S I N T H E F I E L D ....................................... C o n v e n t i o n a l field s a m p l i n g .................................................................................... C o n t i n u o u s t r a c e r a n a l y s i s in t h e field ................................................................. A d d i t i v e p r o c e d u r e ........................................................................................... D i f f e r e n t i a l p r o c e d u r e s ...................................................................................

125 125 126 127 130

R E F E R E N C E S .................................................................................................................. 1 3 1

Chapter Four: Field Examples and Data Analysis I N T R O D U C T I O N .............................................................................................................. 13 7 W a t e r f l o o d l i t e r a t u r e ................................................................................................ 1 3 7 F I E L D T R A C E R R E P O R T S ........................................................................................... C o r r e l a t i o n o f t r a c e r d a t a w i t h field m e a s u r e m e n t s ......................................... N o r t h W e s t f a u l t block ................................................................................... F l o w m e c h a n i s m s ..................................................................................................... E k o f i s k field ...................................................................................................... G u l f a k s field ...................................................................................................... P h y s i c a l m o d e l of t r a c e r m o v e m e n t ..................................................................... A p p l i c a t i o n s of t h e B r i g h a m m o d e l .............................................................. S i m u l a t i o n of a t r a c e r p u l s e ................................................................................... Big M u d d y field t e s t s ....................................................................................... R a n g e r field t r a c e r t e s t s ................................................................................ N i i t s u oilfield t r a c e r s ....................................................................................... M a l j a m a r u n i t t r a c e r s .................................................................................... ......... C a t i o n i c r e s e r v o i r .....................................................................................................

138 138 139 141 141 142 145 146 148 150 153 159 163 164

V O L U M E T R I C A N A L Y S I S O F F I E L D T R A C E R D A T A ........................................ B a s i c a s s u m p t i o n s ................................................................................................... T r a c e r r e s p o n s e c u r v e s ........................................................................................... L a n d m a r k s ....................................................................................................... C u r v e n o i s e ....................................................................................................... T r a c e r r e s p o n s e a n a l y s e s u s i n g m o m e n t s .......................................................... M o m e n t a n a l y s e s ............................................................................................ F i r s t m o m e n t ................................................................................................... E x t r a p o l a t i o n of i n c o m p l e t e d a t a ................................................................. S e c o n d m o m e n t ............................................................................................... D i s t r i b u t i o n of i n j e c t e d w a t e r b e t w e e n p r o d u c e r s .............................................. M a s s b a l a n c e in w a t e r f l o o d t r a c e r s .............................................................

165 166 166 167 167 168 168 169 169 171 171 172

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S w e p t p o r e v o l u m e f r o m f i r s t m o m e n t ....................................................... 1 7 2 F i e l d r e s u l t s , N o r t h W e s t f a u l t block .................................................................... 1 7 6 F i e l d d e s c r i p t i o n ............................................................................................... 1 7 6 C a l c u l a t i o n m e t h o d s ................................................................................................ 1 7 8 W a t e r p r o d u c t i o n a t w e l l M-10 f r o m M-03 ................................................ 1 7 9 W a t e r p r o d u c t i o n f r o m M - 0 3 to M - 2 3 ....................................................... . 1 8 1 S w e p t p o r e v o l u m e c a l c u l a t i o n s f r o m M - 0 3 to M - 2 3 ............................. . 1 8 1 S w e p t p o r e v o l u m e c a l c u l a t i o n s f r o m M - 0 3 to M - 1 0 ............................. 91 8 3 P r o d u c t i o n r e s p o n s e a n d s w e p t v o l u m e s f r o m M - 1 4 ............................. 91 8 4 R E F E R E N C E S .................................................................................................................

91 8 6

Chapter Five: Unconventional Waterflood Tracing I N T R O D U C T I O N .............................................................................................................. 1 9 1 R E S I D U A L O I L M E A S U R E M E N T S B Y T R A C E R S ............................................... 1 9 1 M e t h o d s i n u s e ........................................................................................................... 1 9 2 P a r t i t i o n i n g t r a c e r s .................................................................................................. 1 9 2 T r a c e r m e t h o d ........................................................................................................... 1 9 2 P r i n c i p l e s ........................................................................................................... 1 9 3 E q u a t i o n s .......................................................................................................... 1 9 3 D i s t r i b u t i o n coefficients ................................................................................. 1 9 5 E q u i l i b r i u m c o n d i t i o n s .................................................................................... 1 9 9 S i n g l e - w e l l t r a c e r t e s t for r e s i d u a l oil .................................................................... 2 0 1 S y m m e t r y p r o b l e m ......................................................................................... 2 0 1 A s y m m e t r y s o l u t i o n ....................................................................................... 2 0 2 F i e l d p r o c e d u r e s ............................................................................................... 2 0 4 T w o - w e l l t r a c e r t e s t ( T W T T ) for r e s i d u a l oil ....................................................... 2 0 7 R e s e r v o i r c o n d i t i o n s for t w o - w e l l t r a c e r t e s t ............................................. 2 0 8 T w o - w e l l t r a c e r t e s t s for r e s i d u a l oil: F i e l d r e s u l t s ................................... 2 0 9 O B S E R V A T I O N W E L L S ................................................................................................ 2 1 5 A d v a n t a g e s a n d d i s a d v a n t a g e s ............................................................................. 2 1 5 L o g g i n g o b s e r v a t i o n w e l l s ....................................................................................... 2 1 6 R e q u i r e m e n t s a n d l i m i t a t i o n s ....................................................................... 2 1 6 C o m p a r i s o n w i t h w a t e r f l o o d t r a c i n g ........................................................... 2 1 7 S u i t a b l e t r a c e r s ............................................................................................... 2 1 7 T r a c e r d e t e c t i o n ............................................................................................... 2 1 7 W e l l field e x p e r i e n c e ........................................................................................ 2 1 8 D e s i g n of a l o g g i n g o b s e r v a t i o n w e l l t r a c e r t e s t ................................................. 2 2 2 T e s t d e s i g n f a c t o r s .......................................................................................... 2 2 4 D i l u t i o n of t r a c e r p u l s e ................................................................................... 2 2 5 T r a c e r r e s p o n s e a t o b s e r v a t i o n w e l l ........................................................... 2 2 6 O t h e r field t r a c e r t e s t s ................................................................................... 2 2 7 S a m p l i n g o b s e r v a t i o n w e l l s .................................................................................... 2 3 0 M o n i t o r i n g t r a c e r s i n j e c t e d a t a n o b s e r v a t i o n w e l l ............................................ 2 3 2 INTERWELL

R E A C T I O N S ........................................................................................... 2 3 4

Tracers in the Oil Field

C o n v e r s i o n of i n j e c t e d s u l f a t e ion to h y d r o g e n sulfide ....................................... 2 3 4 FLOW THROUGH DOWNHOLE

F R A C T U R E S .................................................................................

INJECTION

237

A N D S A M P L I N G ........................................................... 2 3 8

R E F E R E N C E S ..................................................................................................................

239

Chapter Six: Interwell Gas Tracing I N T R O D U C T I O N ..............................................................................................................

243

G A S T R A C E R S F O R O I L F I E L D U S E ........................................................................ C h e m i c a l a n d p h y s i c a l r e s t r a i n t s ......................................................................... H i s t o r y a n d d e v e l o p m e n t ........................................................................................ G a s t r a c e r s u s e d for i n t e r w e l l t e s t s .............................................................

243 243 244 244

N O N I D E A L B E H A V I O R O F G A S T R A C E R S ........................................................... P a r t i t i o n of g a s t r a c e r s a n d i n j e c t e d g a s velocities ............................................ T r a c e d g a s p r o c e d u r e s ............................................................................................. P r e s s u r e m a i n t e n a n c e ................................................................................... S o l v e n t flooding ................................................................................................ R e s i d u a l oil ........................................................................................................

246 246 249 249 249 249

F I E L D P R O C E D U R E S .................................................................................................... T r a c e r p r o c e d u r e s a n d d e s i g n ................................................................................. D i l u t i o n v o l u m e s .............................................................................................. S a m p l i n g a n d a n a l y s i s ............................................................................................. T r a c e r s a m p l i n g ............................................................................................... N o n r a d i o a c t i v e t r a c e r a n a l y s i s .................................................................... A n a l y s i s of r a d i o a c t i v e t r a c e r s ..................................................................... O n - l i n e t r a c e r a n a l y s i s ................................................................................... V e r i f i c a t i o n of t r a c e r s .....................................................................................

250 250 250 251 251 252 253 254 255

F I E L D T R A C E R T E S T S ................................................................................................. G a s t r a c i n g a n d r e s e r v o i r d e s c r i p t i o n ................................................................... C o a l i n g a field .................................................................................................... D u a l c o m p l e t i o n well ....................................................................................... R e s i d u a l oil i n t h e g a s cap ....................................................................................... L a n d m a r k m e t h o d for r e s i d u a l oil ................................................................ S o l v e n t injection (MI) t r a c i n g ................................................................................. P h a s e b e h a v i o r ................................................................................................ F i e l d t e s t r e s u l t s ....................................................................................................... R a i n b o w K e g R i v e r B pool ............................................................................. S o u t h S w a n H i l l s M I flood ............................................................................. M i t s u e M I flood ................................................................................................ J u d y C r e e k M I flood ........................................................................................ F e n n - B i g V a l l e y M I flood ................................................................................

255 255 256 257 258 258 264 264 265 265 268 270 273 274

S T E A M T R A C I N G ............................................................................................................ 2 7 5 S t e a m b e h a v i o r ......................................................................................................... 2 7 6 G a s t r a c e r s for s t e a m ( v a p o r ) ...................................................................... 2 7 6

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W a t e r t r a c e r s for c o n d e n s a t e ....................................................................... 2 7 7 S t e a m t r a c e r i n j e c t i o n .................................................................................... 2 7 7 T r a c e r field r e s u l t s .................................................................................................... 2 7 7 T i a J u a n a & J O B O s t e a m d r i v e s ................................................................. 2 7 7 M i d w a y S u n s e t s t e a m pilot ........................................................................... 2 7 8 K e r n R i v e r s t e a m flood ................................................................................... 2 7 8 P e a c e R i v e r s t e a m p i l o t ................................................................................. 2 7 8 S a m p l e collection a n d a n a l y s i s ..................................................................... 2 8 2 GAS TRACING IN UNCONVENTIONAL

RESERVOIRS

.................................... 2 8 4

R E F E R E N C E S .................................................................................................................. 2 8 5

Chapter Seven: Downhole Tracers I N T R O D U C T I O N .............................................................................................................. 2 9 3 T r a c e r d e t e c t i o n i n t h e b o r e h o l e ............................................................................ 2 9 3 F A S T N E U T R O N A C T I V A T I O N O F T R A C E R S ...................................................... 2 9 5 L e a k s b e h i n d c a s i n g ................................................................................................. 2 9 5 O x y g e n a c t i v a t i o n log ............................................................................................... 2 9 5 C o n t i n u o u s n e u t r o n a c t i v a t i o n ..................................................................... 2 9 7 S h o r t p u l s e n e u t r o n a c t i v a t i o n ..................................................................... 2 9 8 O t h e r f a s t n e u t r o n a c t i v a t i o n s .............................................................................. 3 0 6 F a s t n e u t r o n a c t i v a t i o n of b a r i u m .............................................................. 3 0 6 D r i l l i n g m u d b e h i n d c a s i n g ............................................................................. 3 0 6 L O G - I N J E C T - L O G T R A C E R P R O C E D U R E S .......................................................... 3 0 7 R e s i d u a l oil b y n e u t r o n - a c t i v a t e d b r i n e t r a c e r ................................................... 3 0 8 W a t e r s a t u r a t i o n b y n e u t r o n - a c t i v a t e d b o r o n t r a c e r ....................................... 3 1 0 R a d i o a c t i v e t r a c e r s ......................................................................................... 3 1 0 R A D I O A C T I V E T R A C E R S F O R W E L L T R E A T M E N T D O W N H O L E ............... 3 1 1 S t i m u l a t i o n t r e a t m e n t ................................................................................... 3 1 2 C o n t r o l t r e a t m e n t ........................................................................................... 3 1 2 T r a c e r s u s e d for w e l l t r e a t i n g ....................................................................... 3 1 2 S p e c t r a l g a m m a r a y a n a l y s e s ............................................................................... 3 1 3 N a I s c i n t i l l a t i o n d e t e c t o r s ............................................................................. 3 1 3 D e c o n v o l u t i o n of g a m m a s p e c t r a ................................................................ 3 1 4 D e p t h of t r e a t m e n t p e n e t r a t i o n f r o m t r a c e r d a t a ............................................. 3 1 9 P r i n c i p l e s of m e a s u r e m e n t ............................................................................ 3 1 9 D o w n h o l e m e a s u r e m e n t s w i t h l o g g i n g tools .............................................. 3 2 0 D o w n h o l e t r a c e r p r o c e d u r e s ................................................................................... 3 2 2 D o w n h o l e t r a c e r t e s t d e s i g n .......................................................................... 3 2 2 F i e l d e x a m p l e s ........................................................................................................... 3 2 6 H y d r a u l i c f r a c t u r e t r a c i n g ............................................................................. 3 2 6 T a g g e d g r a v e l p a c k t r a c i n g ........................................................................... 3 2 7 T a g g e d d i v e r t e r s a n d m u l t i s t a g e acid t r e a t m e n t ...................................... 3 2 8 D i r e c t i o n a l o r i e n t a t i o n a t t h e b o r e h o l e ................................................................. 3 2 8 F o c u s i n g c o l l i m a t o r ......................................................................................... 3 3 1

xiv

Tracers in the Oil Field

A n o m a l o u s b a c k g r o u n d i n t e r f e r e n c e : R a d i o a c t i v e scale .................................. 3 3 2 O T H E R G A M M A - R A Y T R A C E R M E T H O D S ............................................................ 3 3 3 C e m e n t b e h i n d casing .............................................................................................. 3 3 3 W e l l t r a c e r m e t h o d ................................................................................................... 3 3 6 P R O D U C T I O N L O G G I N G .............................................................................................. W a t e r injection logging ............................................................................................. T r a c e r loss log .................................................................................................. Velocity shot log ............................................................................................... T r a c e r dilution logging P u l s e m e t h o d .................................................................................................... C o n t i n u o u s m e t h o d ......................................................................................... P r o d u c t i o n logging for gas: Field s t u d y ........................................................ P r o d u c t i o n logging w i t h isotope g e n e r a t o r s ......................................................... A v a i l a b l e isotope g e n e r a t o r s ......................................................................... I s o t o p e g e n e r a t o r s for d o w n h o l e logging ..................................................... C o n t i n u o u s t r a c e r p r o d u c t i o n f r o m a n isotope g e n e r a t o r ....................... Injection logging of s t e a m wells .............................................................................. Field injectivity profile m e a s u r e m e n t s ........................................................ S t e a m t r a c e r s u r v e y e v a l u a t i o n .................................................................. I n j e c t e d s t e a m q u a l i t y ....................................................................................

336 337 338 342 344 345 348 349 352 352 353 355 357 358 359 361

B O R E H O L E P R O C E S S E S ............................................................................................. M u d w a t e r i n v a s i o n .................................................................................................. H y d r a u l i c b e h a v i o r of m u d ............................................................................ Drill-bit w e a r ..............................................................................................................

362 362 364 364

R E F E R E N C E S .................................................................................................................. 3 6 5

Chapter Eight: Tracers in Facility Operations I N T R O D U C T I O N .............................................................................................................. 3 7 1 F L O W - R A T E M E A S U R E M E N T ................................................................................... I s o t o p e d i l u t i o n .......................................................................................................... C o n t i n u o u s injection m e t h o d ......................................................................... P u l s e injection m e t h o d s .................................................................................. P u l s e velocity .............................................................................................................

371 372 372 373 378

F L O W - R A T E A P P L I C A T I O N S ..................................................................................... Single- a n d m u l t i p h a s e flow .................................................................................... S l u d g e in pipes ........................................................................................................... L i n e m e t e r i n g by t r a c e r ........................................................................................... L i n e m e t e r i n g w i t h isotope g e n e r a t o r s ........................................................ O t h e r isotope g e n e r a t o r s for flow m o n i t o r i n g ............................................

379 379 382 382 384 386

F L O W R E G I M E I N P I P E A N D G A T H E R I N G L I N E S ............................................ S i n g l e - e n e r g y g a m m a - r a y t r a n s m i s s i o n .............................................................. S i n g l e - e n e r g y g a m m a for t h r e e - p h a s e flow ................................................ D u a l - e n e r g y g a m m a for t h r e e - p h a s e flow ...........................................................

387 387 388 389

T a b l e of C o n t e n t s

xv

T h r e e - p h a s e s a t u r a t i o n s ............................................................................... 3 8 9 D u a l - d e t e c t o r d u a l - e n e r g y s y s t e m s for t h r e e - p h a s e flow ................................. 3 9 2 G a m m a - r a y b a c k - s c a t t e r ....................................................................................... 3 9 4 T h r e e - p h a s e s a t u r a t i o n s ............................................................................... 3 9 4 P i p e l i n e w a l l s .................................................................................................... 3 9 4 N e u t r o n m e t h o d s ...................................................................................................... 3 9 5 C o m b i n e d m e t h o d s ................................................................................................... 3 9 6 UNDERGROUND G A S S T O R A G E .............................................................................. 3 9 6 T r a c e r s for u n d e r g r o u n d g a s s t o r a g e .................................................................... 3 9 6 P r o c e d u r e s i n c u r r e n t u s e .............................................................................. 3 9 7 K r - 8 5 for p r e t e s t of s t o r a g e i n t e g r i t y ................................................................... 3 9 7 H y d r o g e n t r a c e r for g a s m i x i n g in u n d e r g r o u n d s t o r a g e ................................... 3 9 8 T r o u b l e s h o o t i n g w i t h t r a c e r s ................................................................................. 3 9 9 O I L , W A T E R , A N D G A S S E P A R A T O R S .................................................................... 4 0 0 R e s i d e n c e t i m e d i s t r i b u t i o n (RTD) i n o i l / w a t e r s e p a r a t o r s .............................. 4 0 0 O i l / w a t e r s e p a r a t o r s ....................................................................................... 4 0 0 H y d r a u l i c b e h a v i o r of A P I s e p a r a t o r .......................................................... 4 0 1 H y d r a u l i c b e h a v i o r of oilfield s e p a r a t o r s .................................................... 4 0 2 E R O S I O N A N D C O R R O S I O N ....................................................................................... 4 ! 1 C o r r o s i o n a n d e r o s i o n m o n i t o r i n g .......................................................................... 4 1 1 C o r r o s i o n c o u p o n s ........................................................................................... 4 1 1 O t h e r c o r r o s i o n a n d e r o s i o n d e t e c t i o n p r o c e d u r e s .................................... 4 1 2 C o r r o s i o n t r e a t i n g ..................................................................................................... 4 1 3 S C A L E M O N I T O R I N G A N D T R E A T M E N T ............................................................. 4 1 4 T a g g e d s c a l e i n h i b i t o r s ............................................................................................ 4 1 5 PIPELINE

L E A K S ........................................................................................................... 4 1 6

ENVIRONMENTAL P R O B L E M S ................................................................................ 4 1 7 N a t u r a l l y O c c u r r i n g R a d i o a c t i v e M a t e r i a l ( N O R M ) ......................................... 4 1 7 O t h e r e n v i r o n m e n t a l c o n c e r n s .............................................................................. 4 1 8 Oil spills a n d oily w a t e r ................................................................................... 4 1 8 Drilling fluids ..................................................................................................... 4 1 9 O t h e r t r a c e r a p p l i c a t i o n s .............................................................................. 4 1 9 R E F E R E N C E S .................................................................................................................. 4 2 0

Appendix:

Analytical Flow Model for Design and Analysis of Tracer Pulse Tests

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

427

I N T R O D U C T I O N .............................................................................................................. 4 2 9 A n a l y t i c a l b a s e for t r a c e r m o v e m e n t .................................................................. 4 2 9 A R E A L D I L U T I O N F R O M P A T T E R N G E O M E T R Y ............................................... 4 3 1 P a t t e r n b r e a k t h r o u g h c u r v e for a f i v e - s p o t ........................................................ 4 3 1 D i s p l a c e m e n t of o n e fluid b y a n o t h e r .......................................................... 4 3 1 D i s p l a c e m e n t of a s m a l l s l u g ........................................................................ 4 3 2 G e n e r a l p a t t e r n b r e a k t h r o u g h c u r v e s ................................................................. 4 3 3

xvi

Tracers in the Oil F i e l d

C o r r e l a t i o n of p a t t e r n b r e a k t h r o u g h curves ....................................................... 4 3 4 A R E A L D I L U T I O N BY M I X I N G E F F E C T S .............................................................. Mixing in porous m e d i a ............................................................................................ F u n d a m e n t a l s .................................................................................................. Mixing in l i n e a r s y s t e m s ................................................................................ Mixing w i t h i n a s t r e a m t u b e ..........................................................................

436 436 436 437 438

TRACER RESPONSE FROM DEVELOPED HOMOGENEOUS P A T T E R N S ........................................................................................................................ F o r m u l a t i o n ............................................................................................................... C o r r e l a t i o n of t r a c e r p r o d u c t i o n curves ............................................................... Adsorption a n d decay ...............................................................................................

440 440 441 443

T R A C E R F L O W I N I R R E G U L A R A N D O P E N P A T T E R N S ................................ 4 4 6 T R A C E R R E S P O N S E I N L A Y E R E D R E S E R V O I R S ............................................. L a y e r i n g ...................................................................................................................... C o m p u t a t i o n of t r a c e r r e s p o n s e from a l a y e r e d r e s e r v o i r ...................... N u m e r i c a l e x a m p l e of l a y e r e d r e s p o n s e c o m p u t a t i o n ............................. H e t e r o g e n e i t y definition by layers ........................................................................ S t a t i s t i c a l b a c k g r o u n d ................................................................................... D y k s t r a - P a r s o n s coefficient to c h a r a c t e r i z e l a y e r i n g h e t e r o g e n e i t y .......................................................................... C o n s t r u c t i o n of l a y e r s u s i n g D y k s t r a - P a r s o n s coefficient, VDP ...................................................................................... N u m e r i c a l e x a m p l e of l a y e r construction from VDP ................................

448 448 448 449 450 450

D E C O N V O L U T I O N O F T R A C E R B R E A K T H R O U G H DATA .............................. N o n l i n e a r regression ................................................................................................ I n t e r p r e t a t i o n of Loco field t r a c e r test ................................................................. A d j u s t m e n t s for o p e n p a t t e r n ...................................................................... L a y e r a n a l y s i s by n o n l i n e a r r e g r e s s i o n ...................................................... A r e a l h e t e r o g e n e i t i e s ...............................................................................................

454 454 456 457 458 461

D E S I G N O F T R A C E R T E S T S ....................................................................................... Design b a s e d on a single layer ................................................................................ D e s i g n b a s e d u p o n l a y e r i n g .................................................................................... D e s i g n b a s e d on t h e D y k s t r a - P a r s o n s VDP coefficient ....................................

462 462 463 466

451 452 453

D E R I V A T I O N O F P A T T E R N B R E A K T H R O U G H C U R V E S ............................... 4 6 6 N O M E N C L A T U R E .......................................................................................................... 4 6 8 S Y M B O L S .......................................................................................................................... 4 7 0 E R R O R F U N C T I O N S ...................................................................................................... 4 7 1 R E F E R E N C E S .................................................................................................................. 4 7 2 I n d e x ................................................................................................................................... 4 7 5

PREFACE Most of the applications of tracers to oilfield operations have occurred within the past forty years. Throughout most of this period, I have been an active participant in these applications and have observed the development of m a n y innovative and useful techniques. Unfortunately, perhaps due to the n a t u r e of this competitive industry, a good deal of the work is poorly documented, if at all, in the open literature. In addition, available literature is widely dispersed and the small service companies t h a t have supported much of this effort are disappearing from the scene. As a result, much of this knowledge passes only by word of mouth among an ever-decreasing set of providers. This book is an attempt to fill the void and make the technology more available to current users in the oil field. The initial expansion of tracer applications in the oil field was based on radioactive tracers, much of it a consequence of the Atoms-for-Peace programs following the nuclear developments of World War II, and depended on a multitude of small service companies for support. In the intervening years, developments in analytical chemistry have expanded the use of nonradioactive tracers in biomedicine and other fields, but very little of this has made its way to the oil field. Because there is so little knowledge among oilfield personnel about either of these, I have included enough background material for both kinds of tracers to enable a field engineer to evaluate their application to field problems. The computer revolution of recent years has added a dimension to tracer technology and has placed new emphasis on mathematical modeling and computer simulation of tracer-response curves. Unfortunately, there is little communication between those who design and perform the tracer tests in the oil field and those who model them. This often results in a poorly designed test, in modelers who do not u n d e r s t a n d the significance of the field data they model, and in practitioners concerned only with a qualitative aspect of the test. This book is primarily concerned with field and laboratory test procedures; however examples of computer modeling of oilfield tracer tests described in the literature are included. I have emphasized quantitative aspects of tracer tests, with regard both to field practice and to data analysis, and I anticipate a future in which most tracer design and analysis will also involve computer simulation. Tracers have been used to study a very broad range of topics in the oil field. It is not possible in a book of this kind to touch on all of them or to dwell equally on all the topics chosen. Some topics are a m a t t e r of personal choice, but most were chosen for their applicability to modern field usage, and because they provide the most quantitative information. This book is about field applications, and where possible, the tracer applications discussed here are illustrated by data from field tests t h a t have been reported in the open literature, or for which permission to publish has been received from the sponsoring company. I have freely taken tracer applications from other disciplines wherever they provide a useful procedure for oilfield use. While this book is not concerned with

ooo

XVI]I

Tracers in the Oil Field

oilwell logging as such, those areas of oilfield logging that use tracer techniques have been included and placed in context with other oilfield tracer methods. The use of radiation from radioactive sources for monitoring flowrates and measuring fluid saturations in pipes and tubulars is also included here because it is so intimately tied up with tracer measurements. Two tracer applications used in the biomedical field offer an advantage over current techniques used in the oilfield, and are therefore included here: 1) the use of short-lived radioactive tracers from isotope generators down hole to monitor tracers in the neighborhood of the borehole; and 2) the use of a focusing collimator for imaging radioactively tagged treatments inside the borehole. J u s t as oilfield tracer applications have roots in hydrology, g r o u n d w a t e r studies, chemical reactor engineering, civil engineering, sanitation, environmental studies, and many other, disciplines, many of the procedures developed in the oil field are applicable to equivalent studies in these disciplines. An example is the use of partitioning tracers in locating and removing nonaqueous toxic substances from the ground by Dr. Gary Pope and his co-workers. This technique was designed to measure residual oil in the reservoir. Laboratory tests and computer simulations at The University of Texas at Austin have demonstrated the suitability of the technique for monitoring the amount and location of these toxic nonaqueous fluids in the near subsurface. The efficacy of such tertiary oilfield recovery methods as surfactant flooding for removing these materials has also been demonstrated. The design of a tracer test is often an educated guess based upon empirical factors, and the produced data are frequently used only for qualitative observation. An analytical method for designing a waterflood tracer test and analyzing the tracer response data from the field was introduced by Brigham and Smith in 1964 and has since been modified by Abbaszadeh and Brigham. The method has been described in the literature, but the mathematical language has kept its applications from being widely used. An appendix written by Dr. Abbaszadeh has been added to this text to clarify this method for designing a field tracer test and analyzing the tracer response curves from the test.

Bernard Zemel Austin, Texas September 12, 1994

ACKNOWLEDGMENTS I wish to t h a n k both the Center for Petroleum and Geosystems Engineering and the Department of Petroleum and Geosystems Engineering at The University of Texas at Austin for granting me the privilege of a Visiting Scholar position during the preparation of this book. The preparation of a camera-ready manuscript would have been far more difficult without the aid of departmental facilities and my many discussions with faculty and staff members. I am particularly beholden to Dr. Gary Pope for his encouragement during the writing of this work and for our many discussions about tracers in the oil field. I must also express my appreciation for the computer simulations of tracer movement in the reservoir performed by Dr. Pope and his student Vichai Maroongroge, which have clarified my understanding of the functions of a tracer test. I wish to thank the following people who have taken the time to read and return critical reviews of various sections of this book: Dr. Harry Deans of the University of Wyoming, and Krishan Malik, Dr. Dan Hill, Dr. Henry Dunlap, Dr. Larry Lake, Dr. Augusto Podio, and Dr. John C. Reis of The University of Texas at Austin. Thank are due both to Shell Development Co. and to BP Exploration for permission to share the results of unpublished work with which I was involved. This has enabled me to illustrate some useful unconventional tracer procedures. I also wish to thank those oilfield people, too numerous to mention here, who have shared information on field tracer applications over the years. I would like to extend special thanks to Larry Taylor of True Tag, Larry Gadeken of Haliburton, Wally Loder of Tracer Tech International, Roy Dobson and Dave Ferguson of Tracerco, Andy Carmichael of Teledyne Isotopes, and Gordon Tinker. Equally important are Mike Prats and Philip Clossman, who are responsible for my starting this book. Finally, I wish to t ha nk my editor and book designer, Jane Chamberlain of Pangloss Publishing, for her careful pruning of the language and the many hours she spent laying out the pages in a Macintosh program never intended for this purpose.

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CREDITS Since this is a book on field tracer applications, it contains illustrations and tables describing these applications. Many of these have been taken from copyrighted material published in the oilfield literature, in subsidiary texts, in the commercial literature, and from unpublished company reports. The cooperation of the publishers in granting permission to use this material is appreciated and acknowledged below, as is that of the sponsoring companies allowing the use of unpublished company reports. Illustrations from government documents and other public sources are not listed here but are noted and referenced in the text. The illustrations and tables used from these sources are noted where they appear in the text, and sources are listed with the references at the end of each chapter. Credits for these sources are given below in the following order: 1) the oilfield literature as described in journals and society presentations or taken from unpublished company reports by permission of the sponsoring company; 2) texts on basics of tracer properties or applications; and 3) commercial suppliers of services or materials used in tracer tests. The following copyrighted 9 material is reproduced by permission from the Society of Petroleum Engineers (SPE). It includes preprints of presentations at meetings and papers from SPE journals. Figures are cited in order of appearance: 3.2, 4.1, 4.2, 4.3, 4.6, 4.7, 4.11, 4.12, 4.13, 4.15, 4.16, 4.17, 4.18, 5.2, 5.11, 5.14, 5.15, 5.16, 5.18, 5.19, 5.20, 5.21, 6.1, 6.7, 6.8, 6.12, 6.13, 6.14, 7.1, 7.2, 7.3, 7.5, 7.6, 7.7, 7.14, 7.15, 7.16, 7.19, 7.20, 7.21, 7.23, 7.25, 7.26, 7.30, 7.31, 7.33, 8.6, 8.7, 8.8, 8.16, 8.17, 8.18, 8.19, 8.20, 8.21, and 8.22. The following copyrighted 9 material is reproduced by permission of the Petroleum Society of CIM: Table 5.2, Figs. 5.10, 6.2, 6.3, 6.4, 6.5, 6.9, 6.10, and 6.11. The following figures are reproduced from journals and other compendia with permission from the copyright owner: Fig. 1.14 from Geophysics, 9 the Society of Exploration Geophysicists Fig. 1.15 from Nucleonics, 9 McGraw Hill Publishing Co. Fig. 3.5 from Journal of Chromatography, 9 Elsevier Science Ltd., Kidlington, UK, Pergamon Press Fig. 3.6 from Journal of Chromatography, 9 Elsevier Science Ltd., Kidlington, UK, Pergamon Press Figs. 4.4 and 4.5 from the International Energy Agency for permission to use material 9 from the Symposium on Reservoir Engineering, Paris (1990) Figs. 4.8, 4.9, 4.10, 4.14, and 5.12 from The Journal of Petroleum Engineering Science, 9 Elsevier Science Publishers Figs. 7.4 and 7.17 from The Analyst and SPWLA Symposia, 9 Society of Professional Well Logging Analysts

x~

Tracers in the Oil Field

Fig. 7.11 from the International Symposium on Exploration of Energy and Natural Resources, Vienna, 9 International Atomic Energy Agency Fig. 7.27 from Formation Evaluation Symposium, 9 Canadian Well Logging Society Fig. 8.9 from Nucleonics, 9 McGraw Hill Publishing Co. Figs. 8.12, 8.13, 8.14 from Nuclear Geophysics, 9 Elsevier Science Ltd., Kidlington, UK, Pergamon Press Fig. 8.25 from the Proceedings of the Twenty Fourth Annual Meeting (1977) 9 Southwest Petroleum Short Course Assoc. The following figures, tables and other stated material from previously unpublished works are reproduced with permission as follows: Figs. 4.22, 4.23, 4.24, 4.25, 4.26, 4.27, 5.4, Table 5.1 and associated text, BP Exploration Co. Figs. 3.10, 5.23 and associated text, Shell Development Co. The following figures are reproduced with permission from the copyright owner from the specified texts: Fig. 1.1, R.D. Evans, The Atomic Nucleus, 9 Krieger Publishing Co., Malabar, Florida Figs. 1.1, 1.2, and 1.16, Treatise on Analytical Chemistry, Elving and Kolthoff (eds.), Part 1, 14, sect. K, chap. 1, 9 John Wiley & Sons, New York Figs. 1.17 and 2.22, Ehmann, W.D., and Vance, D.E., Radiochemistry and Nuclear Methods of Analysis, 9 John Wiley & Sons, New York Fig. 2.3, Knoll, G.F., Radiation Detection and Measurement, 9 John Wiley & Sons, New York Fig. 2.20, Tsoulfanidis, N., Measurement and Detection of Radiation, 9 Hemisphere Publishing Corp., Washington, D.C. Fig. 7.18, Hine, G.J., and Sorensen, J.A., eds., Instrumentation in Nuclear Medicine, vol.2, chap. 1., 9 Academic Press, New York Fig. 8.24, Levenspiel, O., Chemical Reaction Engineering, 9 John Wiley & Sons, New York The following figures are reproduced from the specified texts with permission from the commercial supplier holding the copyright: Fig. 2.10, The RCA Photomultiplier Manual, 9 1970 Burle Industries, Tube Products Division Figs. 2.14, 2.15, 2.16, Workshop Manuals, 9 Packard Instrument Co, Meriden, Connecticut

Credits

xxifi

Fig. 2.17, Instrument Manual, 9 Beckman Instruments, San Diego, California Figs. 5.6, 5.7, and 5.8, Determination of Residual Oil Saturation, 9 Interstate Oil Compact Commission, Oklahoma City, Oklahoma Figs. 7.10, 7.12, 7.24, 9 Schlumberger Logging Co., Houston, Texas Fig. 7.13, 9 Haliburton Logging Co.

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Tracers in the Oil Field

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CHAPTER 1

RADIOACTIVITY BASICS

INTRODUCTION Modern applications of radioactivity and radioactive tracers to industrial and commercial problems stem largely from the nuclear developments associated with the atomic bomb and subsequent "Atoms for Peace" programs in the United States and elsewhere after World War II. Successful applications of nuclear technology were noted especially in the fields of medicine and oil exploration. During this time the use and development of nuclear logging tools expanded greatly. Radioactive tracers were also applied to virtually every phase of oil production both in the laboratory and in the field, and small companies offering m a n y types of radioactive services proliferated. To a lesser extent, these tracer studies are still going on, most of them in the medical area. While radioactivity is certainly not a requirement for a tracer, most of the open forums devoted to tracer applications at this time are those sponsored by nuclear societies such as the International Atomic Energy Agency (IAEA) and the American Nuclear Society. This chapter is concerned with the basic principles and definitions required to apply radioactivity and the use of radioactive tracers to oilfield problems. This work will not cover considerations of nuclear structure or aspects of nuclear physics and chemistry that have no significant bearing on the use of radioactivity in the oil field. For readers in search of further information on these topics, m a n y excellent references are available, a few of which are listed at the end of this chapter. We will emphasize aspects of radioactivity relevant to current oilfield practice, including some t h a t may not be in current use but have a demonstrated utility in this area.

Isotopes a n d n u c l e a r s t r u c t u r e All m a t t e r is composed of elements, which are composed of atoms. An atom consists of a small, positively charged nucleus balanced by a distribution of surrounding orbital electrons of negative charge. The atoms of each element differ in their nuclear properties. While avoiding discussion of nuclear structure, we can t r e a t the nucleus as being composed of neutrons and protons. The neutron is a heavy particle t h a t carries no charge, whereas the proton is a heavy particle with a single positive charge. Any given species of atom or nuclide has a nucleus composed of a certain n u m b e r of neutrons (N) and protons (P). The number of protons in the nuclide is the atomic n u m b e r (Z), which determines the extra nuclear electrons of the atom and its chemical nature. The sum of the neutrons and protons in the nucleus (N+P) is the atomic mass (M).

2

Chapter I

The elements are arranged in periodic tables according to their atomic n u m bers. For each nuclide of a given atomic n u m b e r there can, however, be different n u m b e r s of neutrons. Atoms with the same atomic n u m b e r but different n u m b e r of n e u t r o n s in the nucleus are called isotopes. Isotopes of an element all have the same chemical properties and occupy the same place in the periodic table but differ in their atomic weight. The fractional atomic weights listed in the periodic table are the weighted average of the atomic masses of the n a t u r a l l y occurring isotopes. Conventional s h o r t h a n d for expressing the atomic weight of an isotope is mz I, where I is the common n a m e of the element and m is the mass. Since z is the atomic number, which defines the common name given to I, it is r e d u n d a n t and normally omitted. Thus hydrogen of mass 3 is written as 3H. In this text we will also use the designation H-3 or hydrogen-3 as an equivalent form. H-3 also carries the common name of tritium and is abbreviated as (T). A consequence of Einstein's special theory of relativity is the r e l a t i o n s h i p between mass (M) and energy (E) given by the expression: E=MC 2

(1.1)

where C is the velocity of light. The atomic mass unit (amu) is based upon the mass assigned to the carbon isotope 12C, which is given a value of exactly 12. The SI unit for energy is the joule (j); however the unit traditionally and most widely used for energy in nuclear studies is the electron volt (eV). This is defined as the energy gained by an electron when it is accelerated through a potential difference of one volt. A multiple frequently used is the mega electron volt (MeV), which is equal to 106 eV. Based upon these units: TABLE 1.1 Mass conversion units Unit

Abbreviation

joules

MeV

electron volt

eV

1.602 x 10 -19

10~

atomic mass unit

amu

1.492 x 10 -10

931.5

8.170 x 10 -14

0.51

electron rest mass

It should be noted t h a t the m e a s u r e d mass of a nucleus is always smaller t h a n the combined mass of its component neutrons and protons. This difference is called the mass defect. Its energy equivalent is called the binding energy, and is a m e a s u r e of the stability of the nucleus. Nuclear reactions always result in the emission or absorption of energy, calculated from the difference between the masses of the products and those of the reactants.

Radioactivity Basics RADIOACTIVITY Some combinations of protons and neutrons result in unstable nuclei. Such nuclides undergo spontaneous disintegration with time. This decay, accompanied by the emission of nuclear particles and/or electromagnetic radiation, is termed radioactivity. Emission of particles from the nucleus also results in the formation of a new nuclide if there is a net change in the n u m b e r of protons in the new nucleus as a result of the decay. Statistically, decay of a given radioactive nucleus is a random, unpredictable event; however if a sufficient number of radioactive nuclides is present, the rate of decay, dN/dT, becomes proportional to the number of nuclides (N) present. The greater the number of radioactive nuclides, the more closely this rule is followed. The rate of decay per unit time, dN/dt, is a m e a s u r e of the a m o u n t of radioactivity (A) present and has the dimensions of events per second. This is shown below, where k is a proportionality constant, known as the decay constant, which is specific to each isotope.

dN

A = -d-~-= LN

(1.2)

Activity and half-life In modern (SI) nomenclature, the basic unit for the amount of radioactivity present, A, is the becquerel (Bq), which is equal to a decay rate of one disintegration per second (dps). An older unit still widely used in the industry is the curie (Ci), which is equal to 3.7 x 1010 dps. The Bq and the Ci are normally used in multiples and submultiples, respectively, of these units as can be seen in Table 1.2. TABLE 1.2 Unit multipliers Prefix

Symbol

Multiple

femto pico nano micro milli kilo mega giga tera

f p n ~t m k M G T

10-15 10 -12 10-9 10-6 10-3 10 3 10 6 109 1012

Example fj = femtojoule pCi = picocurie nCi = nanocurie ~tSv = microsievert mGy = milligray kr = kilorad MBq = megabecquerel GeV = gigaelectron volt TBq = terabecquerels

4

Chapter i

These multiples are important in a wide variety of nuclear units, such as electron volts (eV), sieverts, grays, etc., as well as non-nuclear units such as joules, seconds, and grams. All of these units will be discussed as they arise in appropriate sections of chapters I and 2. Integration of Eq. (1.2) above yields the standard equation for the exponential decay of radioactivity. Here N O is the n u m b e r of radioactive atoms p r e s e n t at zero time, )~ is the decay constant, and N is the n u m b e r r e m a i n i n g at a subsequent time: N = N o r ~t

(1.3)

The average life expectancy (x) of any radioactive species can be calculated from the first m o m e n t of the probability, e -xt, t h a t the nucleus will survive the time, t, and is given by: 1 t =-

(1.4)

Radioactive decay r a t e s are normally t a b u l a t e d in t e r m s of half-life, t 1/2 r a t h e r t h a n decay constant, where t l/2 is the time required for the activity of a given nuclear species or nuclide to decrease to h a l f of its original value. By substituting the half-life t 152 for t in Eq. (1.3), =

In 2 tm

(1.5)

Hence, if the n u m b e r of half-lives, h = t/t 1/2, N = N02 -h

(1.6)

This is a convenient method to calculate decay in terms of powers of 2. The half-life is specific to each radionuclide. Thus, a curie (37 GBq) of tritium w i t h a half-life of 12.6 years would decay to h a l f t h a t value in 12.6 years, w h e r e a s a curie of carbon-14 (14C) would require 5700 years to decrease to onehalf its value. TABLE 1.3 Confidence level as a function of standard deviation Deviation (units of s ) 0

Confidence level (%) 0 68

2a 3a

95 99

Radioactivity Basics

Statistics of counting The equation of radioactive decay can be derived from simple probability theory since the time of decay for any single atom is unpredictable. For a given nuclide, the chance of a decay occurring in a given time is described by the binomial distribution. This is a distribution t h a t for most nuclear counting can be approximated by the simpler Poisson distribution, an approximation of the binomial distribution characterized by a low probability of success. It assumes a relatively large n u m b e r of active atoms, which are counted for a time which is short compared to their half-life. This is the usual situation for most counting experiments. If p(m) is the probability of collecting m events, when M is the m e a n n u m b e r expected, then the Poisson distribution is given by: Mm p(m) = ~ e -M

(1.7)

It can be shown t h a t this is a single p a r a m e t e r distribution: i.e., a single value, m, provides both an estimate of the mean, M, and of the predicted variance, ~2. Thus M is equal to m, with a standard deviation given by ~ = ~]m. If, for example, we record 100 disintegrations, this is a good estimate of the "true" (expected) value, with a standard deviation of ~] 100 = 10. For more t h a n about 20 events, the Poisson distribution can be replaced by the normal (Gaussian) distribution. This is the standard, symmetrical, bell-shaped curve. For this distribution there is a 68 percent confidence level t h a t the m e a s u r e d count will not differ from the "true count" by more t h a n one s t a n d a r d deviation, ~. The confidence level for other values of ~ is given in Table 1.3 above. It is important to remember t h a t the single p a r a m e t e r of the Poisson distribution still holds here although it is not generally true for Gaussian distributions. Most oilfield tracer data are reported in terms of a confidence level. STATISTICS OF COUNTING ZERO, SIGNAL VS. NOISE We do not live in a radiation-free environment. As will be discussed later in this chapter, there are m a n y naturally occurring and m a n m a d e sources of radiation. As a result, when radioactive material is m e a s u r e d by a counter, the total n u m b e r , Nt, of radioactive atoms counted includes a b a c k g r o u n d component, Nb, due to radiation from the environment. This b a c k g r o u n d radioactivity must be subtracted from the measured activity in order to arrive at a true value. Since radioactivity is a statistical, fluctuating phenomenon, it is important in most applications to have a criterion for knowing when there is a significant a m o u n t of radioactivity present in a sample in the presence of a radioactive background. If Nt r e p r e s e n t s the total n u m b e r of radioactive events counted and Nb represents the background count, then the net count, Nn, is given by:

6

Nn = N t - Nb

Chapter I

(1.8)

The variance of either the sum or the difference of two statistically random quantities is equal to the sum of the variances. Since the variance, ~2(N) = N, the standard deviation ~(Nn), of Nn is given by: ~(Nt + Nb) = ~] ~2(Nt ) + ~2(Nb)= ~]Nt + Nb

(1.9)

As the number of radioactive atoms being counted approaches zero, Nt approaches Nb, and in the limit, the error in determining zero is proportional to the square root of the background. For a 95 percent confidence level, this is given by 2g: 2(~N(0) = 2~]2NB

(1.10)

Since radioactivity is measured as a counting rate, R = N/t, where N is the number of events per unit time t, the error of determining zero count rate is given by: 2~R(0) = ~]2RB

(1.11)

where R B is the background counting rate. This is an important number since, all other things being equal, it is a measure of the lowest detectable activity in a given counter and is the noise level that the counting signal must overcome. Other factors affecting this number will be discussed as they arise in chapters 1 and 2.

Sequential radioactive decay In any mixture of unrelated radioactive materials, the total activity is the sum of the individual activities. This total activity decreases as each of the separate activities decays exponentially according to its own half-life, and there are no special relationships between them. In a sequential decay, however, decay of a radioactive isotope results in the formation of a second radioactive isotope rather than a stable isotope. Thus, if N 1 is the (original) parent isotope, then N2 is the number of atoms of the daughter isotope produced by decay of the parent N 1. The rate of formation of N2 by decay of its parent is equal to NI~I. The rate of loss of N2 by its own decay rate is N2~2; hence the net rate of growth of N2 is given by the difference, as shown in Eq. (1.12). dN2 = ~,IN1- ~2N2 dt

(1.12)

Radioactivity Basics

This is a linear, first-order differential equation. The solution is demonstrated in many textbooks on radioactivity and is given below, where N(0)2 refers to the amount (if any) of N2 present initially: ~ NI[e-A1 t _ e-;t2 t ]+ N(0)2 e-;t2t N2 = ~2_~ 1

(1.13)

This can also be expressed in terms of half-lives, letting Ti represent the halflife of species i and h = t ~ i , the number of half-lives elapsed, as follows: T1 N112 -hi - 2 -h2 ]+ N(0)2 -h2 N2 = T 2 - T'-------~

(1.14)

Radioactive equilibrium When the parent half-life is shorter than that of the daughter, there can be no equilibrium. The parent simply decays away, leaving only the daughter activity. If the parent half-life is longer than the daughter half-life, the two will ultimately reach an equilibrium wherein the exponential portion becomes negligible. At radioactive equilibrium, then, Eq. (1.13) reduces to: N2 = ~ N 1 ~2 -~,1

(1.15)

This is called transient equilibrium. Here both parent and daughter decay with the half-life of the parent. The growth and decay of the daughter as the parent decays is shown in Fig. 1.1 (Lieser, 1986). It should be noted that the total activity is always the sum of both activities. If the daughter activity is separated from the parent, it will decay at its own decay rate as shown. The rate at which new daughter activity grows in and reaches equilibrium with the parent is given by the exponential factor [ 2-hl - 2 - h 2 ] of Eq. (1.14). The total activity is sum of the two activities. When the parent half-life is so much longer than its daughter's that it does not show decay through many daughter half-lives, the decay of the parent can be ignored. This is a limiting case of the transient equilibrium described above, known as secular equilibrium, shown in Fig. 1.2 (Lieser, 1986). Since k 1 is negligible compared to k2, Eq. (1.13) simplifies to: ~'IN (1- e "~'2t N2= ~22 1 )

(1.16/

For a time, t, that is long compared to daughter half-life ~2, this reduces to: N2 = ~; N1 ~2

hence A1 = A2

(1.17)

8

Chapter i

The growth of the daughter activity is derived from Eq. (1.12) and given by the expression: N2=~22~1N I ( I _ e-k2t ) (1.18)

Total activity = A + A 1 2 io + .....

/

"~ <

3

Decay of separated daughter

i

10,

,021[ 0

Daughter A 2 growing in

parent A 1

Time in half-lives

Figure 1.1. Transient equilibrium The rate of growth of the activity is given by (1 - e-~2t). This factor plays an important role in many nuclear reactions of interest in the oil field. It is also known as the saturation factor. In these equilibria, if the daughter is separated from the parent, it immediately begins to decay at its own half-life, T2, as shown in the figures. A new daughter then begins to grow in from the parent activity and continues until equilibrium is reestablished. The formation of daughter activities is not limited to a single generation but may go on for many generations of radioactivity (Bateman, 1910). Principal examples of a long sequence of radioactive generations are the uranium and thorium series. The uranium series is illustrated in Fig. 1.17. The gamma emission from these naturally occurring radioactive series (plus potassium) is the major source of gamma radiation in the wellbore. The two kinds of radioactive equilibria described above are important in accounting for the naturally occurring radioactive chains. They have an additional importance in the development of isotope generators described in a later chapter.

Radioactivity Basics

Total activity = A 1+ A 2 @ _

.

.

.

.

4

/

nt activity, A 1

'~ 103t ~, ~

Decay of

Daughter activity, A 2 growth 2 10-

,

~

,

~separated ~ daughter '~

,

,

,

,

,

Time in half-lives

Figure 1.2. Secular equilibrium

N u c l e a r decay processes We described the nucleus in terms of neutrons and protons. The proton has a mass of about one atomic unit and carries a positive charge. Outside the nuclear environment, the proton exists as a stable e n t i t y - the hydrogen ion. The neutron also has a mass of one unit but carries no charge. It can also exist outside of the nucleus but it is u n s t a b l e with respect to decay and m a y react w i t h other nuclei in the neighborhood. In a v a c u u m it decays w i t h a half-life of about 11 m i n u t e s to a proton plus an electron. An electron emitted from a nucleus is called a beta particle. It carries a negative charge and has no significant mass. By i n t e r n a t i o n a l convention, nuclear reactions are always w r i t t e n w i t h the mass (N + P) of each species at the top left and the charge carried at the bottom left of the e l e m e n t symbol. In writing the equation for a n u c l e a r reaction, the total charge on each side of the equation m u s t balance, as m u s t the total mass on each side of the equation. This is shown in the equation for n e u t r o n decay below, w h e r e a n e u t r o n with zero charge and mass of 1 decays to a proton h a v i n g a mass of 1 and a charge of +1, plus a ~ particle whose mass is zero and charge is

10

Chapter i

-1. In nuclear reactions the neutron is written as n to avoid confusion with N, the symbol for nitrogen:

1 On - - >

o p+_113

The decay of radioactive nuclei can take place by several mechanisms t h a t m a y not be m u t u a l l y exclusive. In the oil industry we are normally concerned with only two of these, beta decay and alpha decay. An additional decay path of interest is spontaneous fission, which is the only practical decay path resulting in neutron emission. BETA DECAY The three processes classified under beta decay are beta particle emission, positron emission, and electron capture. Beta particle emission This is the conventional emission of a negative beta particle. Negative beta particle (-~) decay of the radioactive nucleus results in a new nucleus with essentially the same mass but with an increase of one in atomic number. For example, carbon-14 decays by beta emission with a half-life of 5700 years. In the process the atomic number is increased by one, hence carbon-14 is t r a n s m u t e d to nitrogen-14. As shown below, the masses on both sides of the equation add up to 14 and the charges add up to 6 on each side.

14o .14

+

Positron emission This is the emission of an anti-electron (+~). An antiparticle is associated with most of the subnuclear particles. The antiparticles have most of the same properties as their coparticles but have an opposite charge or other opposite nuclear property. While antiparticles include both antiprotons and antineutrons, the only one of significance to oilfield tracer work is the antielectron, which has a positive charge and is called a positron. Positron emission is a common form of beta decay. Particles and antiparticles cannot coexist. They annihilate each other when they come in contact and are converted to a penetrating form of radiation called annihilation radiation. The annihilation of a positron with an electron results in the formation of two g a m m a rays, emitted 180 ~ apart. Each g a m m a ray has the mass-equivalent energy of an electron or 0.51 MeV, as shown in Table 1.1, and illustrated in Fig. 1.3. The elimination of a positron from a nucleus because of radioactive decay requires the same kind of charge balance as electron decay, except t h a t it is

11

Radioactivity Basics

opposite in sign. This results in the formation of a new element having the same mass but with a decrease of one in atomic number. Thus 22Na decays by positron emission with a half-life of 2.26 years. The 22Na being t r a n s m u t e d to 22Ne: 22 22 0 11Na --> lONe ++1

Electron capture (ec) The third form of beta decay is an alternative to positron emission and has the same effect on the charge balance. In electron capture, an inner orbital electron from the atom, usually a K or L electron, is captured by the nucleus. A proton is then converted to a neutron, resulting in a new nucleus having the same mass with a decrease of one unit in atomic number. It differs from positron emission in t h a t there is no annihilation radiation associated with it. Instead, monoenergetic X-rays characteristic of the captured orbital electron are generated from the extra nuclear part of the atom. 22Na decays principally by positron emission, but 10 percent of the nuclei decay instead to an excited state of 22Ne by electron capture: 22 0 22 11Na + -le --> 10Ne

T= 0.51 MeV o=

180

T= 0.51 MeV

Figure 1.3. Positron annihilation

ALPHA DECAY An alpha particle is identically a helium nucleus emitted from a radioactive nucleus. It has a mass of 4 atomic units and a charge of plus 2. It is the principal mode of decay for elements of atomic number greater than 82 and is involved in the natural occurrence of uranium and thorium chains in the ground. Alpha decay results in t r a n s m u t a t i o n of the radionuclide to a n e w e l e m e n t whose atomic n u m b e r is lower by 2 units and whose mass is lower by 4 mass units t h a n the original nucleus, as shown below.

12

Chapter I

234 4 238V --'Y Wh + 2He 92 90 This is the predominant decay path for all the naturally occurring radioactive series. The series of isotopes in secular equilibrium with the p a r e n t U-238 is illustrated in Fig. 1.17, shown later in this chapter. In this figure of atomic number vs. atomic mass, alpha decay moves the atomic number down 2 units and decreases the atomic mass by 4 units as shown by the arrow. G A M M A RAY EMISSION

G a m m a radiation (and internal transition) normally occurs as a m e a n s of deexcitation of an activated nuclear state induced by beta or alpha decay. It is not a primary m o d e of decay and usually shares the half-life of the particle decay mode, although in some case the activated state m a y have an extended half-life.

De-excitation by gamma emission In the course of the alpha and beta decay processes indicated above, new elements are formed, most of which are left in an excited (nuclear) state. Usually these excited states decay to the ground state almost instantly (with less t h a n a picosecond's delay) with the emission of penetrating electromagnetic radiation called g a m m a rays. There may even be several excited states, each resulting in its own g a m m a ray emission. Occasionally there is a significant half-life of decay from the excited state due to a forbidden transition. Such excited states are called isomers and are designated by the symbol (m) following the mass number, e.g., 137mBa. They have the same mass and atomic n u m b e r but a different half-life from the associated beta or alpha decay.

De-excitation by internal transition (it) In this alternative to de-excitation by g a m m a emission for some excited states, the excess nuclear energy is transferred directly to an orbital electron, which is emitted from the atom as a free electron. This results in a monoenergetic electron with the characteristic energy of the transition less the binding energy of the electron. It is accompanied by x-radiation emitted by the atom as these electron shells are filled up. G a m m a radiation differs from X-radiation only in that it is emitted from the nucleus r a t h e r t h a n from interactions with the extranuclear electrons. G a m m a radiation is more energetic as well, although there is a small region of energy where the rays overlap. X-rays usually range from 100 eV to about 100 keV, whereas gamma radiation ranges from about 10 keV to 100 MeV. NEUTRON

SOURCES

Neutrons are not emitted as a means of de-excitation byany of the radioisotopes having a practical half-life. They are generated as a byproduct in

Radioactivity Basics

13

nuclear fission reactions, by nuclear interactions with charged particles, and by nuclear interactions with gamma rays.

Fission Fission is a procedure whereby the nucleus breaks up into two large fragments, which break down further into smaller nuclides by various decay processes (mostly beta decay) and the emission of neutrons. Associated with fission and the subsequent processes is the release of a large amount of energy. M a n y of the t r a n s u r a n i c elements are subject to spontaneous fission as a means of de-excitation. 252Cf is the only practical neutron source of this type. It is a transuranic element t h a t decays primarily by alpha decay with a half-life of 2.65 years. Approximately 3.1 percent of the 252Cf decays by spontaneous fission accompanied by the emission of neutrons. This very compact portable source of neutrons produces about 2.3 x 106 neutrons/second/~gm of californium. Fission of u r a n i u m and plutonium isotopes in nuclear reactors is the largest source of available neutrons. In these reactions a controlled chain reaction maintains an excess of neutrons in the reactor. Most available reactors are small research reactors, m a n y of the swimming pool type. These are not portable in any sense of the word but do constitute a commercial source for m a n y radioactive isotopes and are used for activation analyses. They offer neutron fluxes in the order of 1012 to 1015 neutrons/second/cm 2.

Beryllium alpha reactions Most a particles lose energy by reaction with the atomic electrons, however a small fraction of the alphas overcome the nuclear barriers to react with a target nucleus, providing one of the means of making portable neutron generators. Such sources are generally referred to as chemical neutron sources. In particular, the reaction of alpha particles with beryllium is a useful method for g e n e r a t i n g neutrons by the following reaction: 9 12 1 He + 4Be --~ 6 C + oN + 5.71MeV The interaction of particles with a nucleus is normally written in an abbreviated form. For example, the above reaction can be expressed as 9Be(a,n)12C. The first symbol, 9Be, represents the target material; the photon or particle reaction is indicated by the parenthesis, (a,n), where an alpha particle enters the t a r g e t nucleus and a neutron leaves it; the last symbol shows the conversion product of the t a r g e t material 12C. The energy of the reaction is 5.71 MeV. A n u m b e r of such sources are in use in the petroleum industry for downhole neutron generation. Several t r a n s u r a n i c alpha sources are used for this purpose. 239Pu, 238Pu, and 241Am are widely used, under the acronyms PUBE and AMBE. The probability of alpha interaction with the Be is maximized by using an alloy of the transuranic element with beryllium.

14

Chapter i

Particle accelerators A second nuclear interaction for generating neutrons is the 3H(2H,n)4He reaction. This is often written as T(D,n)a, where D stands for deuterium and T for tritium, and represents the reaction: 2 H + 3 H --~ 4He + n For the reaction to take place, the deuterium need only be accelerated to an energy of 100 to 300 keV. This can be done using a relatively simple static generator, which can be small enough to go down hole in an oil well. The reaction, which produces 14 MeV neutrons, has a great advantage over chemical neutron sources in t h a t it can be pulsed and turned on and off at will. It has become a major tool for use in borehole logging.

Other neutron-forming reactions In addition to the reactions indicated above, a variety of other (a,n) and (7,n) "chemical" neutron sources have been developed; however the ones discussed earlier are most common. These are portable sources that may be used in the laboratory, taken to the field or even in many cases used down hole. Neutrons are i m p o r t a n t in direct and indirect tracer applications because of their ability to undergo reactions with m a n y materials of interest in the oil field. C h a r a c t e r i s t i c energy The emission of radiation from the nucleus is always associated with a discrete energy, Q, which is characteristic of the nuclear transition. The alpha particles emitted from the nucleus, as well as the g a m m a rays emitted from the subsequent excited nuclei, are emitted with a characteristic energy, Q. Beta particles (both negative and positive) appear to be exceptions, showing instead a continuous spectrum of energies. A plot of beta energy versus the n u m b e r of beta particles having t h a t energy for a given nuclide extends from zero energy to a maximum energy Emax. A typical beta spectrum is shown in Fig. 1.4. This continuous energy spectrum is due to the simultaneous emission of a neutrino with each beta. The characteristic energy is shared between the two. Neutrinos, having no charge and virtually n o mass, are measurable only with great difficulty. As a result we obtain only the beta part of the spectrum. The characteristic energy of the emitted beta particle is, however, given by the maxim u m energy, Emax, of the spectrum. This energy is tabulated as the beta energy for a given isotope. The average energy of the beta emission is about 1/3 of the m a x i m u m energy. As illustrated for tritium in the figure above, the m a x i m u m energy is 18 keV and the mean energy, Eave, is 6 keV. The only radioactive sources of monoenergetic electrons are those emitted by isotopes undergoing internal transition. Positrons have a similar type of spectrum, except t h a t after m a n y collisions they undergo annihilation.

15

Radioactivity Basics

m

0.8 0.6

N(E)

Emax

0.4 0.2 0

0

3

6

9

12

15

18

Energy, keV

Figure 1.4. Tritium beta energy spectrum DECAY SCHEMES The decay schemes for all of the normally available isotopes are published in m a n y compendia, which present the information in different ways. References to some of these compilations are given at the end of this chapter. One kind is a tabular listing of each isotope, giving pertinent properties such as half-life, mode of decay and all the emitted radiation. Another shows detailed two-dimensional decay schemes. A collection of such (simplified) beta decay schemes for some common tracer materials is shown in Fig. 1.5. Beta decay is often accompanied by g a m m a radiation from the produced isotope, each g a m m a ray having a characteristic energy. Thus, from Fig. 1.5, cobalt60 undergoes negative beta decay to an excited state of (stable) Ni-60. The cobalt60 emits two g a m m a rays in cascade; one g a m m a ray of 1.173 MeV in going to a lower excited state, and a second g a m m a ray of 1.332 MeV in going from this excited state to the ground state. A total of two gamma rays are emitted with each beta particle. The decay schemes in the figure illustrate m a n y of the reactions discussed earlier. Nuclear structures can be quite complex, and different decay processes may go on simultaneously. Naturally occurring K-40 shown in this figure undergoes two such decay processes, each with its own decay probability, leading to different decay products. In addition, there are periodic charts t h a t show all of the isotopes in a twodimensional a r r a y where the number of protons, Z, per nuclide is plotted against the n u m b e r of neutrons, N = A-Z. A roughly 45-degree line drawn through the such charts passes t h r o u g h the stable isotopes. Nuclides with an excess of neutrons with respect to this line decay by beta (-) decay; those with an excess of protons decay by electron capture or positron decay, as shown in Fig. 1.6. These

16

Chapter I

are large wall charts t h a t are not easy to reproduce in this space. The nuclear properties of each isotope are shown within its designated square in the chart. This includes the decay modes, half-lives, and radiation emitted for the radionuclides, and other nuclear properties for the stable isotopes. A small section of such a chart is shown in Fig. 1.7. The chart makes it easy to see the effect of a variety of nuclear interactions with a given isotope. The probability of any given reaction is a function of the energy of the incident particle or ray. Most nuclear interactions of positively charged particles, fast neutrons, and g a m m a rays have energy thresholds below which no reaction takes place. A typical view for the products from nuclear reactions with a given isotope is shown in Fig. 1.8. The likelihood of each reaction depends upon its specific probability at the energy of the incident particle.

6000 T = 5.26 years

5700 T = 270 days 27

27

.

~

0.136 MeV

2.505 MeV !

= 1.173 MeV ~,1.332 MeV y1 l 60Ni ~ 0 MeV y2

y2 = 1.332 MeV

(11%) 59Fe

137

C T = 5730 years

Cs T=27years

(6.5%)~ ~ ( 9 3 " 5 % )

~~

37mga T= 2.7 minutes 137ga ~ 0.662 MeV

0 MeV

1.406 MeV

4~

J~Y

$3 (9%)

4~

T = 1.26 x 109years

~'~' (11%)

40CaN-(89%)

Figure 1.5. Nuclear energy levels

Radioactivity Basics

17

100 8O

e.c, 13+

~ 60: 40 20 J

J

/

/.~_

J

J

~

J

20 4b 6b 8b 16o 12o 14o Neutrons

Figure 1.6. Nuclear chart showing nuclear stability line

C9 127 m s

C10

B8

B9

B10

Be8

Be9

-19 174 m s 10 s e c

4 3 He3

Be 6

Be 7

Cll

19.4 s 20.4 m

-21

-16 10 sec 53.3 d 10 s e c

Li 5

-21

Li 6

Li 7

He5

He6

840ms

10 sec

He 4

Li 8

-21

He7

lO see 805 ms short Z

H1

H2

H3

3

4

12.3 Y

1 N

2 v

Figure 1.7. Nuclear chart, partial display

5

18

Chapter I

a, 3n

2n

0~, n

P,T n, 2n He 3 n

a, np

T,R n, 2n

original nucleus

d,p n, T

t, np

T,np

T,P

n,p

p, n

n, cz

t, n

Hea, p

n, He 3

Figure 1.8. Nuclear reactions from chart

I N T E R A C T I O N S OF R A D I A T I O N WITH M A T T E R

The particles and radiation emitted during radioactive decay interact with the surrounding matter in many ways before they are absorbed. The reactions they undergo in the course of these interactions, including those leading to detection, are at the heart of the applications of such tracer materials to any problem.

Alpha particles and other positively charged ions Alpha particles are helium nuclei, ~He, which are emitted by radioactive decay with energies mostly in the range of 4 to 6 MeV. As they move through matter, they lose most of their energy by coulombic interaction with the intervening electrons. The travel path is very short and straight. A 6 MeV alpha particle has a range in air of about 4.5 centimeters. For most alpha emitters, particles not at the surface are absorbed in the emitter. A small fraction of the alpha particles can react with the nucleus in the (a,n) reaction described earlier. At a high enough energy, many positive ions become capable of reacting with nuclei directly. The ions are raised to high energy by accelerators designed for this purpose. Protons, in particular, are accelerated to high energies in cyclotrons

Radioactivity Basics

19

and other machines, where they are a source of radioactive species not otherwise available.

Beta particles and positrons Negative and positive (positron) beta particles from any source are emitted with a range of energies from zero to the characteristic (maximum) energy for the transition. They are absorbed in matter by two processes. Most of the beta energy is lost in collisions with atomic electrons proportionally to the atomic number of the intervening matter. The path is tortuous: only a small part of the energy is lost at each collision, leaving ion pairs in its wake. A significant part of the beta emission is reflected back to the origin. The transmission of beta particles in passing through matter shows an exponential decline: N = Noe-~x

(1.19)

where N and No refer to the transmitted and original numbers of beta particles, ~t is a constant and x is the thickness of the material. Positrons, in addition, undergo the annihilation reaction near the end of their paths with the emission of two 0.51 MeV g a m m a rays. The annihilation of positrons is a major source of g a m m a radiation from positron emitters. The gammas, which are emitted 180 degrees apart, are also coincident in time. This property can be used either to differentiate such emitters from other gamma emitters or as a means of collimating unscattered radiation. A small fraction of the emitted beta energy loses energy by radiation. When a beta particle comes close to the nucleus of an atom, it is accelerated by the electric field and emits a type of X-radiation known as brehmsstralung. The ratio of energy loss by radiation (Lr) to energy loss by ionization (Li) is given by:

Lr ZE L i - 750

(1.20)

where Z is the atomic number of the intervening m a t t e r and E is the characteristic (maximum) beta energy. B r e h m s s t r a l u n g is a significant factor only for high energy betas in high atomic n u m b e r absorbers, but it is always present when betas are absorbed. It has been used as a means of monitoring the activity of very large sources of low energy beta emitters such as tritium and carbon-14. The energy of brehmsstralung from carbon-14 is sufficient to allow field monitoring for the large sources used for interwell tracers if the container walls are not too thick.

Gamma radiation (and x-rays) G a m m a and x-radiation are absorbed through a number of interactions with a b s o r b e r atoms, only three of which are normally i m p o r t a n t . These are photoelectric absorption, Compton scattering, and pair production. Photoelectric

20

Chapter 1

absorption is a reaction of the g a m m a ray with the atoms of the absorber; Compton scattering is a reaction with the individual electrons; and pair production is an interaction with the electric field of the nucleus. Most tracer work in the oil field can also neglect pair production. G a m m a ray interactions with the nucleus are also possible and have been used for m a k i n g n e u t r o n sources but are not important to this discussion The different kinds of interactions described below affect the way gamma radiation is used, monitored and shielded.

t'E~--I~- E'O~ Compton Scattering

1' ~---~ 0 E~

e"

Photoelectric Absorption

Figure 1.9. Gamma ray interactions PHOTOELECTRIC ABSORPTION (1;) Here all the captured g a m m a energy is transferred to an orbital electron of the absorber atom, which is then ejected with the characteristic energy of the g a m m a photon, less the electron binding energy, BE, as shown in Fig. 1.9. For most g a m m a radiation, the electron binding energy is negligible. Photoelectric absorption is most important for low gamma energies and in high atomic number absorbers. The probability, ~, of this interaction's occurring is roughly proportional to the fifth power of the atomic number and inversely proportional to 3.5 power of the energy, as shown in Eq. (1.21), where k is a constant, Z is the atomic number, and E is the energy. kZ5 I;= E3.5

(1.21)

This reaction leads to the complete absorption of the g a m m a ray and is used in g a m m a ray spectroscopy to identify its energy level. The sensitivity of the photoelectric effect to atomic number makes it a useful analytical tool for qualitative analysis in the field and in the laboratory. It is most effective at low g a m m a ray energies and is useful for monitoring fluid density in the borehole and in pipes. COMPTON SCATTERING (~) In this process (Fig. 1.9), the g a m m a photons interact with the individual electrons of the absorber. Here, part of the energy of the photon is transferred to an electron, and the photon is deflected from its original path minus the energy

Radioactivity Basics

21

lost to the electron. In this process, Eo is the energy of the incident g a m m a ray, E' the energy of the deflected gamma ray, and ~ the scattering angle. The energy lost per impact depends upon the angle of incidence and leads to a continuous energy spectrum. The direction and energy of the deflected gamma photon is given by the Klein-Nishima equation, which relates the energy of the incident g a m m a ray to the scattering angle and the energy of the scattered g a m m a ray. The m a x i m u m energy loss occurs in a 180-degree collision, whereas the m i n i m u m energy loss is at a grazing collision where ~ approaches zero. Fig. 1.10 shows a distribution of scattered electrons from the interaction with gamma rays of energy E ~ The sharp line at the beginning of the Compton distribution is known as the Compton edge. This distribution is important in monitoring g a m m a radiation and will be discussed further in chapter 2. The probability (g) of Compton scattering changes slowly with energy and is effective over most of the energies of interest for oilfield work. Absorption is the ultimate fate of Compton-scattered photons. The attenuation of gamma radiation by Compton scattering is proportional to the density of the intervening material, and Compton scattering is frequently used for measuring the density of materials. Compton backscatter is used to monitor formation density in downhole logging with gamma sources.

f

io

Photo peak

~

dN

!

Energy (MeV)

Figure 1.10. Distribution of Compton-scattered electrons PAIR PRODUCTION (~) This process is important only for high-energy g a m m a radiation. In oilfield tracer work, this occurs mostly with g a m m a radiation resulting from neutron interactions near the wellbore Here, a g a m m a photon is converted into an electron-positron pair in the electric field of the nucleus. This cannot occur unless the energy exceeds 1.02 MeV, the energy equivalent to the two masses of the

22

Chapter I

electron pair (0.51 MeV). It is accompanied by the annihilation of the positron. This interaction probability is given by K: Gamma ray attenuation

The overall probability of attenuation of gamma or x-radiation is equal to the total attenuation coefficient, ~, which is the sum of the three processes discussed under g a m m a radiation above. ~t = I: + (~ + K:

(1.22)

The attenuation coefficient, ~, of a molecule is the sum of its atomic absorption coefficients. A mixture of compounds has the attenuation coefficient of the sum of the fractions each contributes. The attenuation of radiation in m a t t e r is a function both of the material and of the energy of the incident radiation. This is illustrated in Fig. 1.11 (White, 1952), which shows the a t t e n u a t i o n of g a m m a radiation in lead. In particular, because of the high atomic n u m b e r of lead, the photoelectric effect is dominant over a wide range of energies. Since this leads to the complete absorption of the g a m m a ray, the importance of high atomic n u m b e r materials as a shield for low energy radiation becomes obvious from this figure. The sharp breaks in the photoelectric attenuation curve are due to energy resonances associated with the K and L electron orbits. The loss of radiation is expressed here in terms of the m a s s a t t e n u a t i o n coefficient, the usual way in which g a m m a ray absorption is tabulated and a subject for further discussion later in this chapter. The relative importance of the three coefficients as a function of energy and atomic n u m b e r is shown more broadly in Fig. 1.12 (Evans, 1986). The three regions are separated by lines of equal coefficients: on the left is the line of ~ = ~, where the photoelectric and Compton coefficients are equal, and on the right, the line of ~ = ~, where the probability of a Compton effect equals t h a t for pair production. The average atomic number of formation materials is about 20. From this figure it is obvious t h a t for borehole work, Compton scattering is the predominant interaction between energies lying between 100 keV and 10 MeV. Most g a m m a rays will therefore undergo many Compton interactions in passing through matter. The ratio of Compton to photoelectric interactions can be used as an indicator of the thickness of material intersected by the g a m m a ray. For borehole fluids where atomic numbers are below 20, the photoelectric effect becomes more important. The g a m m a energies of most tracers in oilfield use lie below 4.0 MeV, hence for tracer experiments where m e a s u r e m e n t s are made in a field environment, such as near the borehole or a separation facility, Compton scattering is a major mechanism of gamma-ray attenuation.

23

Radioactivity Basics

200 100

E

10

I[

"

I " I

i I rilll'

i

i

I'! i I if|

"l

~

i i 1 ~'i!

-

L

-

E L~ .m 0

1.0

:$::

o 0 C 0

0.1

E (D

-Compton ",____\ ~,~___Total Attenuation scattering . \\.,, coefficient

-

:

:

~" "~-'.-....... -.7.--'...... . photoelectric

{D

,..:'"'

.01 P

.001 .01

\\.\

-x,,..... .......

_

_ ~.-~

Pair produc I

! I ILIlI|

0.1

i

1 Illltll

1.0

[

I

l

I I|NI~II

10

1

L

I

lllLt

100

Energy (MeV)

Figure 1.11. Gamma ray absorption in lead COLLIMATED BEAMS AND SOURCE GEOMETRY If a narrow beam of g a m m a rays of intensity Io passes through an absorber, a g a m m a detector in the path will observe only those g a m m a photons that have not been absorbed or scattered from the path, much as in the optical equivalent in Beer's law. Since the probability of reacting with a g a m m a photon is given by p, the attenuation of the beam follows an exponential decline in intensity with distance through an absorber and is given by: I = Ioe-~x

(1.23)

24

Chapter I

where I and Io refer to the final and original gamma ray intensities, respectively, x is the absorber thickness, and ~ is the linear attenuation coefficient. The mean free path of a gamma ray in any absorbing medium is obtained by analogy with the mean residence time from the first moment and is given by: = 1

(1.24)

_

I

I I IIIIII

I

I

I Iii1|1

I

t

I IIIIII

I

I

t III1:1

120 L.

0

~ 0 N

11111

-

8o 6o 40

-

_

~ Pair ~ production

j /

-

_-

J

Photoelectric . effect / ('~) / 1,

.

~

6~ /

/ ~1 -I "

C~176 ~II~7, effect ~ k

-

20

o O.Ol

,,,,,,,,

0.05 0.1

0.5

1

Energy in MeV

5

10

50

100

Figure 1.12. Relative importance of the three different gamma ray interactions For most materials and gamma-ray energies of interest, the primary mechanism of g a m m a ray attenuation is Compton scattering. The Compton-scattering coefficient is a function only of the material density, p, for those elements whose ratio of atomic number to atomic weight is about 1/2, true for most elements, and is usually tabulated in terms of the mass attenuation coefficient, expressed as ~/p, in units of cm 2 per gram. This has the advantage that the coefficient becomes independent of the kind of material in the absorber and is dependent only upon material density. I = Ioe-(WP)(P)t

(1.25)

The relationship between the linear and mass coefficients, ~] and I&n, respectively, is given by: ~m (m2/kg) = ~l ( m ' l ) p (kg/m 3 )

(1.26)

25

Radioactivity Basics

It should be noted t h a t the attenuation described above is true only for the narrow beam case, where the path is linear and in which scattered radiation does not r e t u r n to the path. This is shown in Fig. 1.13, part A. In most of our dealings with g a m m a radiation, this is not the case. Radiation is not totally absorbed, but as shown in part B of Fig 1.13, much of it is scattered back into the path. An exception is the response of a detector that can differentiate scattered radiation by energy discrimination.

Broad Beam Geometry

Narrow Beam Geometry

Source

~I

1

II ~

I I~

Collimators

Detector

Source

Detector

"

Absorber A

Absorber B

Figure 1.13. Narrow and broad beam geometry A detector looking at an uncollimated point source of radiation will see more g a m m a radiation t h a n in the narrow beam case shown above due to scattering from the intervening matter, as shown in part B of Fig. 1.13. To correct for the additional radiation scattered back into the path, a correction factor called the dose build-up factor, B, is added. It is a function of incident energy, composition and thickness of absorber, and geometry, and is t a b u l a t e d in handbooks for simple geometries. The radiation from a point source is emitted isotropically and moves out in all directions in spherical geometry. As a result, it decreases in intensity by the inverse square of the distance, d, from source to detector. The radiation from a point source at a distance, d, from it is as given by Eq. (1.27)" I=

IoBe -~t d2

(1.27)

26

Chapter I

This is m o s t i m p o r t a n t for shielding calculations where it is necessary to reduce all t r a n s m i t t e d radiation. Since the scattered r a d i a t i o n m u s t be lower in energy t h a n the original beam, a detector t h a t can discriminate against the lower energy r a d i a t i o n has a build-up factor of one. For radiation sources t h a t are dist r i b u t e d over a volume of space and are not point sources, the situation is more complicated, since the r a d i a t i o n e m i t t e d at each point in the source volume is isotropic a n d acts independently. In general, the radiation received from such sources does not follow the inverse square law unless the distance from source to detector is large compared to the dimensions of the source. In most cases, the r a d i a t i o n will follow the exponential decline given by Eq. (1.19) if an experim e n t a l l y or numerically derived coefficient (Reis, 1992) is used to replace ~. DISTRIBUTED SOURCES AND DETECTORS In m a n y common situations we do not deal with point sources or narrow b e a m geometry. These are usually dealt with by complex tables of functions and buildup factors. The w i d e s p r e a d development of computers has, however, m a d e it possible to calculate the g a m m a - r a y response specific to the situation w i t h o u t the need for elaborate tables of build-up factors. The principal method used for doing this is the Monte Carlo procedure.

Monte Carlo procedure In this procedure, all of the interactions a specific g a m m a ray can undergo are calculated from the known probability coefficient for each interaction, the initial e n e r g y of the g a m m a ray, and the properties of the m e d i u m . E n o u g h r a y s are t r a c k e d until the geometry of the source is defined and the detector response is constant. This m a y t a k e several million rays, but for r e a s o n a b l y simple geometries, it can be accomplished on a modern personal computer (Reis and Idrees, 1992). A r a n d o m n u m b e r g e n e r a t o r is used to initiate a g a m m a r a y from a point inside the source in any direction. If the nuclide emits more t h a n one g a m m a photon, t h e n o r m a l i z e d probability for each emission is used to choose the g a m m a ray. Until it collides with an atom, the g a m m a ray continues along a p a t h whose l e n g t h is calculated from the g a m m a r a y energy, the k n o w n collision probability, the density, and the atomic n u m b e r of the medium. If the collision r e s u l t s in a photoelectric absorption, the r a y is t e r m i n a t e d a n d a new r a y is s t a r t e d . If it r e s u l t s in a Compton scatter, the energy a n d direction of the s c a t t e r e d g a m m a r a y is c a l c u l a t e d from t h e K l e i n - N i s h i m a e q u a t i o n . The s c a t t e r e d r a y is tracked until it reaches the detector or is absorbed a n d can no longer reach the detector. A d i s t r i b u t e d source in cylindrical g e o m e t r y is the rule in m a n y borehole applications. The m o s t common case is the m e a s u r e m e n t of n a t u r a l g a m m a r a d i a t i o n from the s u r r o u n d i n g formation by a detector suspended in the bore-

Radioactivity Basics

27

hole. Another occurs w h e n g a m m a radiation induced in the s u r r o u n d i n g formation by a downhole neutron source is monitored by a g a m m a detector in the s a m e tool. A similar situation also occurs in an observation well w h e n a g a m m a - t a g g e d w a t e r t r a c e r is logged by a tool suspended in the borehole as it passes the well. Cylindrical geometry also applies when the radioactive source is in the borehole and a detector on the s a m e tool monitors the effect of the s u r r o u n d i n g formation on the e m i t t e d radiation. The l a t t e r is used to m e a s u r e f o r m a t i o n properties, such as density by monitoring g a m m a - r a y backscatter. Here the source and detector are shielded from direct interaction, so t h a t the detector only sees r a d i a tion scattered into it from the formation.

1.0

•

~

v ....}

y .........,,oo,o,0oo keY

0.5

I/

Calculated for Unscattered 1.46 MeV gamma rays

]/ '

0--=

0

2'~

r(cm)

~'o

7's

Figure 1.14. Depth of g a m m a penetration in boreholes

External cylinder, distributed source by Monte Carlo calculations Monte Carlo calculations have been reported for the 1.46 MeV g a m m a r a y from 4~ for a detector in an 8-in. d i a m e t e r borehole s u r r o u n d e d by an infinite medium. This is illustrated in Fig. 1.14 (Wahl, 1983), which shows the i n t e g r a t e d signal (normalized) produced from coaxial cylinders of p o t a s s i u m - b e a r i n g rock around the borehole, plotted as a function of formation thickness in centimeters. For a bulk density of 2.5 gms/cc, 90 percent of the u n s c a t t e r e d g a m m a radiation comes from a 15-cm thick a n n u l u s around the wellbore. For m u l t i p l y s c a t t e r e d r a d i a t i o n , t h e t h i c k n e s s is i n c r e a s e d only a few c e n t i m e t e r s . The d e p t h of investigation of all neutron- and gamma-logging tools is limited by the m e a n free p a t h of the emitted radiation in the surrounding formation. Most of the response at the detector comes from a 20-cm, or smaller, radius about the wellbore.

28

Chapter I

External cylinder, distributed source, spherical approximation Cylindrical geometry is a common oilfield source distribution. Borehole geometry can be substituted adequately for m a n y approximations by spherical geometry. One such procedure is described here (Ellis, 1987). The equation for g a m m a ray attenuation is given as" N = No e-pc~

(1.28)

where co is the mass absorption coefficient, p is the bulk density, and x is thickness t r a v e r s e d by the g a m m a rays. The m e a n free path, ~, for the g a m m a radiation is given by Eq. (1.24) above. _

x-

1

cop

(1.29)

For the 1.46 MeV g a m m a ray of 4~ co = .05 cm2/gm. If the bulk density is t a k e n as 2.5 gms/cm 3, t h e n the m e a n free path, ~, is 8 cm. For u n s c a t t e r e d radiation, the total flux, ~, from a spherical shell to a point detector at radius R can be expressed in terms of: n

9 = ~ (1- e -1~)

(1.30)

For this equation, 90 percent of the total flux comes from a spherical shell surrounding the detector at a radius equal to 2.3 ~. For these conditions, this is about 18 centimeters, which is in reasonable agreement with the Monte Carlo calculation of 15 cm.

Internal cylinder, distributed source, external detector A common geometrical distribution of tracers in the field is for the tracers to be in an internal cylinder with the detector on the outside. This distribution occurs in monitoring tracer solutions in pipes and in the borehole and also in g a m m a density measurements In these m e a s u r e m e n t s , it is important to know how much of the emitted radiation is absorbed by the intervening liquid. This can be estimated from the simple exponential absorption equation adequately for most purposes. A common way to do this is by charts of the type shown in Fig. 1.15. Here, ~ is the linear absorption coefficient in cm -1, D is the diameter of the pipe in cm, and f is the fractional loss of radiation, i.e., t h a t fraction t h a t does not arrive at the inner wall of the pipe. If ~D < 0.14, there is no loss. If ~tD > 5, the source behaves like an infinitely thick slab, where f = 1/~D, as the response decreases linearly with distance. The region between these is important for estimating how much tracer is required to monitor g a m m a radiation when the source is uniformly distributed in pipes, gathering lines, and borehole fluid.

Radioactivity Basics

29

Infinite slab, f = 1/I~D

-\ 0.1

Q2

0.3

0.4 Q5 0 6

0.8 "

~D

2

3

4

5

Figure 1.15. Gamma radiation from pipes

Neutron reactions with matter

Neutrons carry no charge and therefore have no coulombic interactions with matter. They are subject to scattering but may travel a considerable distance through m a t t e r (centimeters) without collisions. Most neutron reactions are with the nucleus. The neutron may either be scattered from its p a t h or it m a y be absorbed by the target nucleus. Neutron reactions with m a t t e r can be energy dependent so t h a t neutrons are usually divided into fast and slow neutron reactions, depending upon how they are classified. A common division in well logging is to classify as fast neutrons those having energies from about 10 eV to 14 MeV; whereas those with energies between about 0.1 and 10 eV are classified as epithermal neutrons, and the distribution of neutrons about the mode (0.025 eV at room temperature) as thermal neutrons. All of these energy divisions are, however, arbitrary. Neutrons lose energy and are slowed, in passing through matter, by scattering collisions, both elastic and inelastic, and by reaction with a target nucleus. Elastic collisions involve only a transfer of kinetic energy between particles. Fast neutrons can also lose energy by inelastic collisions of the (n,n') type for incident n e u t r o n s above some threshold energy. Here, the n e u t r o n loses some of its energy by forming an excited state with the target nucleus, which immediately decays to a ground state(s) emitting lower-energy n e u t r o n s and g a m m a radiation. Both reactions result in neutrons of lower energy. Neutrons react with m a t t e r by forming an activated complex with the target nucleus. The most likely reaction is radiative capture (n,7), where the compound

30

Chapter 1

nucleus de-excites by e m i t t i n g g a m m a radiation. An alternative de-excitation is by emission of a charged particle such as a beta, alpha, proton, or other particle. The probability of a n y given interaction's t a k i n g place is expressed by its cross section (~) in units of barns. One b a r n is 10 -24 cm 2. Each kind of n e u t r o n interaction has a cross section t h a t m a y be a function of the n e u t r o n energy. The total cross section for energy loss is the sum of all the interaction cross sections. ELASTIC COLLISIONS (MODERATING) Most n e u t r o n s are first slowed by elastic collisions of the billiard ball type. The n e u t r o n s lose kinetic energy by transfer to a t a r g e t nucleus at each collision as t h e y slow down. The actual a m o u n t of energy lost per collision depends upon t h e m a s s of the t a r g e t nuclei and the angle of incidence of the neutron. The m a x i m u m energy t r a n s f e r for a direct hit (180 ~ collision) is given by:

E2:E1{1(I:A)4A}2

(1.31)

w h e r e Ei is the initial neutron energy, Ef is the final neutron energy and A is the m a s s of the t a r g e t nucleus. It can be seen t h a t the m a x i m u m energy t r a n s f e r occurs w i t h a proton (hydrogen) t a r g e t w h e r e A = 1. The energy t r a n s f e r per collision decreases with increasing atomic weight. As a consequence of the s c a t t e r i n g reactions, a collection of n e u t r o n s in m a t t e r h a s a distribution of velocities m u c h like t h a t of a gas w i t h a MaxwellB o l t z m a n distribution of energies. The n e u t r o n s diffuse in all directions, ultim a t e l y forming a cloud of t h e r m a l neutrons. In this case the n e u t r o n flux becomes a function of position and energy. The principles of n e u t r o n diffusion have been well worked out in reactor theory and are detailed in a n u m b e r of texts. NEUTRON ABSORPTION The u l t i m a t e fate of the slowed n e u t r o n is capture by a nucleus to form an activated compound nucleus t h a t usually deactivates by the emission of g a m m a rays by m e a n s of the (n,7) reaction. Other reactions can lead to charged particles which are accompanied by g a m m a emission.

Thermal capture The cross section for a nuclear reaction as a function of the energy of the incident r a d i a t i o n is known as its excitation function. The cross section for the (n,7) reaction with a t a r g e t nucleus is inversely proportional to the n e u t r o n energy, v. The increase in cross section, ~, with decreasing n e u t r o n energy, v, is roughly proportional to l/v, and is known as the one-over-v rule. This relationship holds for n e u t r o n energies from a few h u n d r e d to less t h a n 0.01 eV, and is i l l u s t r a t e d for a silver t a r g e t in Fig. 1.16 (Lieser, 1986). Eventually all t h e r m a l neutrons are

Radioactivity Basics

31

captured by t a r g e t nuclei; however, as shown in the figure, resonance peaks of high cross section are found at higher energies, especially in the region above one electron volt. These resonances correspond to energy states in the nucleus; they differ for different target isotopes and can be used for analytical purposes. Cross sections for t h e r m a l neutron capture can exceed t h a t predicted from the 1/v rule, and for some nuclides can exceed 104 barns.

4

10

lo3. c~

0

c3 ~o .01

0.1

1

10

100

Energy, eV

Figure 1.16. Neutron cross section vs. energy for silver The process of slowing down or moderating neutron energies continues until the n e u t r o n s are at t h e r m a l energies. At room t e m p e r a t u r e , the most probable value is 0.025 eV. The energy in electron volts can be expressed in t e r m s of a velocity using the equation for kinetic energy, and the n e u t r o n velocity, v, at a known energy. 1

E = ~ Mv2

(1.32)

The velocity of n e u t r o n s at t h e r m a l energy (E is 0.025 eV) is 2200 m/sec, hence for any neutron energy in eV, the neutron velocity is given by: v=

= 2200 0.025

(1.33)

32

Chapter 1

The lifetime of neutrons under borehole conditions is in the order of milliseconds. The usual product of the reaction is a compound nucleus, which de-excites immediately with the emission of characteristic g a m m a radiation. The g a m m a radiation emitted in the capture reaction is called capture g a m m a emission. Some of the compound nuclei de-excite by emission of a beta (or other) particle, leading to beta decay, which is often associated with delayed g a m m a emission. The reaction probabilities are governed by the surrounding isotopic species, their cross sections, and the neutron energy. The interaction of neutrons with m a t t e r by emitting "capture gammas" as well as by delayed g a m m a emission is at the h e a r t of m a n y of the downhole neutron logging techniques. One of the log-injectlog methods for residual oil uses neutrons in a tracer tagging technique in which activation is used to monitor the presence of an injected material downhole. Neutron absorption is the principal method used for production of radioactive tracers. It is also used for activation analysis in the neighborhood of the borehole and as a general analytical technique. The n a t u r e and intensity of the g a m m a emission can be used to identify and analyze the material exposed to the neutron flux. Most radioactive materials produced for sale by neutron b o m b a r d m e n t of stable isotopes undergo beta decay. Fast neutron capture F a s t (high-energy) neutrons also have a chance of capture in which an activated state is formed and then undergoes a variety of de-excitation reactions such as (n,p), (n,a), and (n,2n) reactions in which a new nuclide is formed. Many of the fast neutron reactions have a threshold of neutron energy below which they cannot take place. These cross sections are usually far smaller t h a n those for thermal neutrons. This has, however, become important for special analytical techniques for the light elements and is also being used in such downhole logging procedures as oxygen activation for water tracing. ATTENUATION OF NEUTRONS IN MATTER The entire set of interactions of neutrons with matter, including those of scattering and absorption, can be expressed as the sum of these cross sections. The t r a n s m i s s i o n of a narrow neutron beam through a thickness, x, of m a t t e r is expressed in the same m a n n e r as for gamma ray transmission, by: N = NOe-~x

(1.34)

In the usual interactions where an uncollimated, broad beam of neutrons passes through matter, either a build-up factor or a Monte Carlo type procedure is required to calculate the attenuation, as for g a m m a radiation. The m e a n free path of the neutron is equal to 1/~t, calculated in the same m a n n e r as for g a m m a radiation. Interactions of neutrons with bulk m a t t e r are expressed in terms of macroscopic cross sections, Z, rather t h a n microscopic cross sections, ~.

Radioactivity Basics

NAP $:i = Ni(~i = ~ ( ~ i

33

(1.35)

where Ni is the n u m b e r of atoms of isotope i per cm 3, p is the density of the medium, and N A is Avogadro's number. This value, calculated for ~ at thermal energies, is widely used in logging measurements and expressed as capture units (cu). One cu = 1000Z. Given a neutron beam with a density of n neutrons/cm 3 and a neutron velocity of v cndsec, we define the neutron flux ~ = nv neutrons/cm2/sec., and the rate of reaction, R, as: R = CZ

(1.36)

A major application of neutron reactions in the oil field is in nuclear logging. The high hydrogen content of oil and water makes moderation of neutrons an important tool for monitoring porosity by the slowing down of neutrons in the fluidfilled pore space. This has become a relatively sophisticated m e a s u r e m e n t with corrections for the effect of borehole fluids as well as other environmental interferences. The downhole pulsed neutron generator is used to measure water saturation, by monitoring the decay of gamma radiation from the (n,7) reaction, following the injection of a 14 MeV neutron pulse. This tool is also used for chemical analysis of formation materials by identification of g a m m a radiation from inelastic and radiative capture reactions, as well as those resulting in particle formation. In this procedure, gamma radiation from inelastic scattering can be separated from capture g a m m a radiation by timing the data collection. This tool can also used to generate gamma-emitting tracers down hole. The logging applications are thoroughly described in texts (Tittman, 1986; Ellis, 1987) and in the literature; therefore they will not be discussed here. Their use for tracer applications, however, will be covered in later chapters.

SOURCES OF RADIOACTIVE MATERIAL The three sources of radioactive materials are: 1) primordial sources and their decay products t h a t have been in the earth since its origin; 2) radioactive materials generated naturally by reactions with cosmic radiation; and 3) radioactive materials t h a t are man made. Together these sources account for all the radioactivity on earth. These include the source of radioactive tracers for oilfield use as well as the source of the background count rate in nuclear counters.

34

Chapter 1

Primordial

sources

Primordial sources include nuclides whose half-life is long enough to have survived since the formation of the earth. The principal primordial sources are the 238U series, the 232Th series, and 40K. Others in this group are shown in Table 1.4 (Friedlander et al., 1981). TABLE 1.4 Other radioactive materials with half-lives long enough to survive on earth Radionuclide

Half-life, years

Isotopic abundance (%)

19~ 186Os 187Re

6.1 x I0 II 2.0 x I01 5 x 109

0.0127 1.6 62.6

174Hf 176Lu 152Gd 147 Sm 148Sm 144Nd 138La 123Te ll5In

2 x 1015 3.6 x 1010 1.1 x 1014 1.05 x 1011 7 x 1015 2.1 x 1015 1.35 x 1011 1.24 x 1013 5.1 x 1015

0.18 2.6 0.20 15.0 11.2 23.9 0.09 0.87 95.7

ll3Cd 87Rb 4~

9 x 1015 4.7 x I0 I0 1.28 x 10 9

12.3 27.83 0.012

The u r a n i u m and thorium series are so called because they are composed of a series of radioactive descendants (daughters) in secular equilibrium with the (original) parent activity. The decay of each member of the series results in a new radioactive isotope, each series finally terminating in a different lead isotope. The decay path for the uranium-238 series is shown in Fig. 1.17 (Ehmann and Vance, 1991). This series undergoes a series of transformation by alpha decay, indicated by the downward diagonal lines, and beta decay, indicated by a vertical rise. It begins with uranium-238 of atomic n u m b e r 92 and ends at lead-206, atomic n u m b e r 82. The radioisotopes in between are identified by their atomic n u m b e r and mass. Many of these alpha and beta transformations are associated with the emission of g a m m a radiation. When undisturbed by chemical separations, this entire group is in secular equilibrium with the parent isotope, and the total activity is the sum of the activities of all the members.

Radioactivity Basics

N

92

~ 90

Alpha decay

: ", !.,,,,

i "\

"~ 88 0~=86

35

]

%\

I

\x

t

~x 9

I

i 238

230 222 214 Mass number, A

206

Beta decay Pb-206

Figure 1.17. Uranium-238 decay series Potassium, which makes up about 2.4 percent of the crust of the earth, has three naturally occurring isotopes. One of these, 4~ is radioactive with a halflife of 1.25 x 10 9 years and an abundance of 0.0117 percent. It decays principally (89 percent) by beta decay to 4~ but about 11 percent of the decay is by positron emission to an activated state of 4~ associated with a 1.46 MeV g a m m a ray. The decay scheme is shown in Fig. 1.5. Manmade materials Nuclear reactors are the principal source of radioactive tracers. Some are separated from fission products formed in the reactors. Most are made by (n,y) reaction with thermal neutrons in a nuclear reactor and undergo beta decay; however (n,a), (n,p) and other neutron reactions are also used. Cobalt-60 is produced by activation of normal cobalt by 59Co(n,y)60Co. Carbon-14, on the other hand, is produced by the 14N(n,p)14C reaction, and tritium (3H) by means of the 6Li(n,a)3H reaction. The probability of a neutron reaction is given by the absorption cross section ~. These values are well known for most isotopes and for the neutron energy distribution found in the reactor. In order to prepare a radioactive nuclide by the (n,T) reaction, a suitable nuclide is exposed to a known neutron flux such as may exist in a nuclear reactor or defined neutron source. The reaction can be quantified. If r is the slow neutron flux in a given reactor position, h is the abundance of the isotope being irradiated, ~ is the absorption cross section for the nuclear reaction, and t is the time of irradiation, then R, the number of atoms of the isotope produced by neutron irradiation, is given by:

36

R = Oa ht

Chapter I

(1.37)

The rate of production of the radioactive product is controlled by its decay constant, k2. This situation is identical to that described in Eq. (1.2) for secular equilibrium except that R replaces N l k 1 as the source of radioisotope N 2. Hence the net production of N 2 is given by: N2 = R (l-e- L2t) ~2

(1.38)

If N 2 also has a significant cross section for neutron reaction, this m u s t be taken a step further to account for the additional loss of N2 by neutron reaction. In quantitative work, additional factors such as the geometry of the neutron flux and the self-absorption of the source m u s t also be considered. In all of these reactions the rate of growth of the nuclide is governed by the saturation factor, 1 - e -~2t. For material of long half-life, such as 14C, very long irradiation times are needed to obtain significant amounts of material. The a m o u n t of material produced is calculated in accordance with Eq. (1.38) above. The same kind of analysis and the same equation is used for materials produced by charged particle accelerators such as cyclotrons. These reactions generally lead to products that decay by positron emission or electron capture. Such isotopes as 57Co and 22Na are made by this method. Because of the limited path length of charged particles in matter, thin targets are used. Since the product nuclide will have a different atomic number from that of the target, it is usually available carrier-free. As a rule, neutron irradiation is far cheaper than charged particle irradiation. The proliferation of m a n m a d e isotopes and the increase in separated natural radioactivity have resulted in an increase in the background for nuclear counters. The release of fission-produced isotopes into the atmosphere from nuclear reactors and from nuclear bomb tests has also added a widespread background level of radioactive nuclides. On the average, however, naturally occurring radiation accounts for most background radiation. Cosmic radiation

The third source of radioactive materials is that arising from the reactions of cosmic rays with atmospheric and terrestrial components. This results in an increased counter background, both because of the radiation entering the counter space and because of the formation of radioactive nuclides. Spallation reactions are those in which the target nucleus is fragmented by reaction with the incoming high-energy particle to yield a number of nuclear products. Nuclear charts such as the one shown in Fig. 1.8 can be used to help anticipate the products of spallation.

Radioactivity Basics

37

Such isotopes as 14C and 3H are formed continuously in the atmosphere by direct interaction with high-energy particles in spallation reactions, as well as interaction with secondary radiation of lower energy. Tritium is formed at a rate of about 0.4 atom/cm2/sec, and carbon-14 at a rate of about 2.4 atoms/cm2/sec. Other nuclides formed in this manner include: 7Be 10Be 36C1 81Kr

half-life half-life half-life half-life

= 53.6 days = 2.5 x 106 years = 2.9 x 105 years = 2.1 x 105 years

Many of the cosmic ray-produced isotopes, particularly carbon-14, are used for age dating. They also provide a "natural" background limit of sensitivity for many tracer isotopes such as tritium and carbon-14.

REFERENCES

Bateman, H., "The Solution of a System of Differential Equations Occurring in the Theory of Radioactive Transformations," Proc. Cambridge Phil. Soc. (1910) 15,423. Browne, E., and Firestone, R.B., Tables of Radioactive Isotopes, Shirley, V.S., ed., John Wiley, New York (1986). Ehmann, W.D., and Vance, D.E., Radiochemistry and Nuclear Methods of Analysis, John Wiley, New York (1991). Ellis, D.W., Well Logging for Earth Scientists, Elsevier Sci. Pub., London (1987). Evans, R.D., The Atomic Nucleus, Krieger, New York (1982). Friedlander, G., Kenedy, J.W., Macias, E.S., and Miller, J.M., Nuclear and Radiochemistry, 3d ed., John Wiley, New York (1981). GE Nuclear Energy, Nuclides and Isotopes, 14th ed. (Chart of the nuclides prepared by Walker, F.W., Parrington, J.R., and Feiner, F.), General Electric Co. (Nuclear Energy Operations), San Jose, CA (1989). Heath, R.L., Scintillation Spectrometry Gamma Ray Spectrum Catalogue, (2 vols.) IDO-16880 (1964). Heath, R.L., Tables of Isotopes: CRC Handbook of Chemistry and Physics, 69th ed., CRC Press (1989). Kocher, D.C., Radioactive Decay Tables, DOEfrIC-11206 (1981).

38

Chapter 1

Lieser, K.H., "Fundamentals of Nuclear Activation and Radioisotopic Methods of Analysis," in Treatise on Analytical Chemistry, Elving and Kolthoff (eds.), Part 1, 14, 1, John Wiley, New York (1986). Radiological Health Handbook, Bureau of Radiological Health, U.S. Dept. of HE&W, Superintendent of Documents, Washington, DC (1970). Tittman, J., Geophysical Well Logging, Academic Press, Orlando, FL (1986). Tuli, J.K., Nuclear Wallet Cards (available on-line through Telnet), National Nuclear Data Center, Brookhaven National Laboratory, Upton, NY (1990). Wahl, J.S., "Gamma Ray Logging," Geophysics (1983) 48, No. 11, 1536. White, G.E., National Bureau of Standards Report 1003 (1952).

CHAPTER 2

MEASUREMENTS AND APPLICATIONS

INTRODUCTION In the previous chapter we laid the groundwork of nomenclature and principles required for the application of radioactivity to tracer problems. This chapter is concerned with the application of these principles to the measurement of radioactivity in the laboratory and in the field. Some of the counting procedures often used in tracer analysis are presented here in some detail for those who may be unfamiliar with them. The decrease in companies offering tracer services has left a void in the availability of much of this technology. The details offered here may help fill in the gap, and provide background for the specific applications to be discussed in the remaining chapters. Several texts on the detection and measurement of radiation are included in the list of references at the end of this chapter. Topics covered include 1) the major classes of detectors used for measuring radiation and the support systems required by these detectors to obtain count rate and energy data; 2) counting procedures used to monitor beta- and gammaemitting tracers in the field and in the laboratory; 3) radiotracer application to field problems using isotope generators, isotope dilution, and activation analysis; and 4) radiation dosimetry, licensing, and the control of radioactive materials.

RADIATION D E T E C T I O N AND MEASUREMENT

I n t e r a c t i o n o f r a d i a t i o n with m a t t e r Radioactive material can only be measured and identified by the radiation it emits. The detection of radiation is closely tied to its interaction with matter. If the radiation does not react in a recognizable way, it cannot be detected. The medium for this reaction is the detector. For radiation to be measurable, its energy must be transferred to the detector and the transferred energy must be measured. At the current state of the art, two major detection methods are recognized: one based on ionization and the other on conversion to light. Ionization is a primary method of interaction between radiation and matter for all charged particles and for gamma and x-radiation. Charge collection is therefore one of the principal methods used for detection of ionizing radiation. A second important detection method is conversion of radiation to light by scintillation counting. Alternative methods of monitoring radiation include conversion to light by photographic methods and conversion to heat (calorimetry). Neutrons are not charged and do not form ions directly. They are detected by nuclear reactions with materials that lead to ionizing reactions or light emission, which are then detected.

40

Chapter 2

Efficiency and geometry of detection In order to determine the quantity of radioactivity present in a given source, we must detect the radiation emitted and relate it quantitatively to the amount of radioactivity in the source. This requires a knowledge of the fraction of emitted radiation intercepted by the detector, and of how much of the incident radiation is converted to a measurable signal by the detector. The effectiveness of the transfer and its measurement is called the efficiency, E, of the detector and is expressed as the percent of incident radiation detected. Radiation is emitted isotropically from all points in a radioactive source. The fraction of radiation emitted by the source, which is intercepted by the detector, is called the geometry, G, of the detector with respect to the source. It is also expressed in percent. Because of these effects we normally measure a count rate, C, which is lower than the true disintegration rate, N, of the source. The measured activity of a source in counts, C, per unit time is related to the true activity in disintegrations, N, per unit time by the efficiency of counting, E, and the geometry of capture, G: C =NxExG

(2.1)

Here, E and G are expressed as fractions, and both factors are functions of the counting system used.

Signal-to-noise ratio In Eq. (1.10) of the previous chapter, we showed that at a 95 percent confidence level, the lowest detection limit for radioactivity is limited by background radiation (noise) to: 2 ~R(0) = 2~/2RB

(2.2)

t

Here, RB is the counter background and t is the time of counting. Radioactivity measured by the counter is also affected by the efficiency of counting and by the source-detector geometry, hence the detection limit must also be corrected to include both of these effects: 2(~R(0) =E2G~ 2RBt

(2.3)

Most laboratory counting systems for monitoring tracer concentration operate at 100 percent geometry. The factor ~ B / E is a figure of merit for comparing counting systems in terms of the signal-to-noise ratio. Sometimes presented in the inverse form, E2/RB, it is a common standard for judging counters and for altering counter operations to improve sensitivity. The sensitivity of the counter

Measurements and Applications

41

as defined here is the m i n i m u m signal-to-noise ratio at a confidence level of 95 percent.

Gas Counting Tube.

Voltage Source

Ionization path

-r-

Meter

Figure 2.1. Generalized gas counter C H A R G E C O L L E C T I O N I N GAS C O U N T E R S Ion collection in gas counters is a widely used m e t h o d for m o n i t o r i n g radiation. Fig. 2.1. shows a generalized gas counter consisting of a gas chamber with a central anode (positive electrode) and a negatively charged wall. The cylindrical geometry shown here is not required, although it is the most common. P l a n a r and spherical geometries m a y also be used. A source of voltage is i m p r e s s e d across the electrodes and a m e t e r is used to m e a s u r e the collected charge. D e p e n d i n g upon the gas and counter properties, a c o u n t e r can be operated within three different voltage regions. The counter can behave as an ion chamber, a proportional counter, or a Geiger counter, depending on the voltage region chosen. The three conditions are shown schematically in Fig 2.2 and described below.

The effect of an impressed voltage W h e n a radioactive event such as a particle or photon of g a m m a radiation passes through the gas in a counter, it loses energy in a m a t t e r of nanoseconds by collision with the molecules in the gas until all its energy is absorbed. Each of these collisions results in the formation of an ion pair. Depending upon the gas composition, it takes about 30 eV to form one ion pair in a gas (including air). A 300 keV ~ particle will thus form about 104 ion pairs if its entire p a t h lies within the gas. These ion pairs, composed of an electron and a positive ion, will normally recombine. If, however, an electric field is impressed upon the gas, there will be a m i n i m u m voltage at which some of the ions s e p a r a t e and move t o w a r d s the

42

Chapter 2

oppositely charged electrode. This results in the collection of a charge pulse with a height proportional to the number of ions collected. This is the region of recombination. As the voltage increases, the pulse height will increase until all the ions formed by collision of the passing particle or photon are collected. F u r t h e r increases in voltage cause no increase in current until secondary reactions of the ions in the field cause additional ions to be formed. This is called the saturation current. The voltage region in which it occurs is marked as region I in Fig. 2.2. Detectors operating in this region of voltage are called ion chambers. The size of the pulse collected is independent of the applied voltage and is a function only of the energy of the event. For each radioactive event occurring in the counter, a current will be generated that is proportional to the energy of the individual event.

/

f

01

J

III

Voltage

Figure 2.2. Voltage operation regions in gas-filled counters As the voltage is increased beyond the saturation value, the charge collected for each particle or radiation quantum begins to increase because the original ions are accelerated in the electric field until their velocity is so high that they initiate secondary ions, generating avalanches of new ions. This results in pulses containing a much greater charge than the original pulses. The size of each pulse is still proportional to the energy of the initial ionizing event but is simply amplified in the counter by ion multiplication. As the voltage is raised, amplification continues until the multiplication loses its proportionality. This voltage region is identified as region II in Fig. 2.2, and detectors operating within this region are known as proportional counters. If the impressed voltage is increased beyond the proportional region, the induced ion avalanches increase until the pulses are no longer proportional to the

Measurements and Applications

43

particle energy. This continues until a single event triggers n u m e r o u s avalanches, producing a large, single pulse of charge across the system regardless of its original source or energy. This voltage region is known as the Geiger region and is m a r k e d as region III in Fig. 2.2. Detectors operating here are known as Geiger-Mueller or GM counters. If the voltage is increased beyond this region, the counter goes into continuous discharge. In these discussions we have assumed that all of the radiation is absorbed by the counting gas in the detector, but the efficiency of detection is frequently much lower t h a n 100 percent. Gases have good stopping power for beta particles, alpha particles, and soft X-radiation; however they have very poor stopping power for g a m m a radiation. Here, most of the reaction of gamma radiation is with the walls of the counter, and only the inner layer of wall releases secondary electrons into the sensitive volume of the counter for counting.

Pulse counting and current counting These counters can be used either in pulse form, where each event is individually counted, or in current form, where the total charge is integrated and presented as a charge rate or activity. The pulse method is a much more sensitive counter for the number of events (count rate) t h a n the current method. In practice, however, the pulses generated in the ion chamber are very small, and the ion chamber is almost always used in the current form. The proportional and the GM counters are almost always used as pulse counters. In an energy sensitive counter such as the proportional type, it is possible both to count the separate pulses and to measure their energy. In this procedure, the number of events captured per unit time is the count rate, C. Their energies can be obtained by measuring pulse heights. The alternative method is to measure the average current generated by these events - - a function of the n u m b e r of events per unit time and the total energy absorbed. If the radiation event has an average energy, E (eV), the energy required to form an ion pair (eV) is W; J = 1.602 x 10 -19 ampere-seconds is the number of coulombs per esu of charge; and N events per second enter the chamber per unit time; the current, I, generated is given by: I =

JNE W

(2.4)

Most detectors in the ion chamber region measure current response. For such counters the average current collected in the saturation region is proportional to the energy absorbed by the counter, i.e., to the number of events collected in the counter and to the energy of each event. Thus, if the 1 MBq of a beta emitter with an average energy of 300 keV were counted in an ion chamber where W is

44

Chapter 2

30 eV per ion pair, 1.6 nanoamperes of current would be generated according to Eq. (2.4).

Outer electrode Guard ring Center electrode

> r-~ , r~.

Outer insulator ~ inner

I

,I,I ]

|

Figure 2.3. Cross section showing guard-ring construction Ion c h a m b e r

This is a simple and very stable counter with a long voltage plateau; however an electrometer or equivalent is required to monitor the very small currents it generates. The major problem in constructing an ion chamber is the current loss due to leakage paths along the insulator separating the electrodes. To reduce this loss, particularly at low current levels, a guard ring is installed, illustrated in Fig. 2.3 (Knoll, 1989). The ion chamber is relatively insensitive to t e m p e r a t u r e , and can be operated at several hundred degrees if the materials of construction can w i t h s t a n d the temperature. It can also be operated at high gas pressures to increase the g a m m a ray stopping power in the gas. The counter is easily constructed in the laboratory in virtually any configuration with commonly available materials. I n s u l a t i n g m a t e r i a l s should be as smooth as possible. Teflon is a useful insulating material for most normal uses. Synthetic sapphire is an excellent insulating material for high temperatures. The ion chamber is widely used for personnel dosimetry since it m e a s u r e s absorbed energy directly. A hand-held survey meter is calibrated to monitor the charge collected in air in coulombs/kg (roentgens) and can be set up as a "tissue equivalent" chamber for monitoring radiation exposure. A special form of the ion chamber about the size and shape of a pen is also used for personnel monitoring. It uses the discharge of a quartz fiber electrometer to monitor total radiation. The quartz fiber is attached to a pointer t h a t moves across a scale visible through a magnifying glass. Since the ion chamber is very tolerant of the composition of the counting gas, it can function using air as a counting gas. As a result, the chamber

Measurements and Applications

45

can be used to monitor ambient air for the presence of soft beta emitters such as t r i t i u m and carbon-14. It can also be used as a r a d i a t i o n detector for gas c h r o m a t o g r a p h y of C-14 and tritium tagged gases at the millicurie level, an important application in gas-tracer preparation. Because of its great stability, the ion chamber is still used in m a n y industries, including the oil industry, for level gauging. It is the method of choice for calibrating radioactive sources by comparison with primary standards because of its long-time stability. Calibration standards of better t h a n 0.1 percent accuracy can be maintained for years.

Proportional counter This counter differs from the ion chamber in t h a t a very high electric field is m a i n t a i n e d in the neighborhood of the anode. The only way to do this at a reasonable voltage is to use an anode made of small-diameter wire. For cylindrical geometry, the strength of the electric field, E, at a radius, r, from the anode is given by: V E(r) = r In(b/a)

(2.5)

where b is the radius of the cathode (the inner diameter of the counter), a is the radius of the anode wire, and V is the applied voltage. Smooth tungsten wires are available with radii in the order of 1 mil (.001 in., .025mm). End effects from the electric field can be avoided by the use of field t u b e s - - larger d i a m e t e r tubes (hypodermic syringe tubing) t h a t fit over the anode near the ends of the counter. The larger diameter reduces the electric field so t h a t no gas multiplication takes place at the ends. The active counter volume is the region between field tubes. An example of a flow-through counter is shown in Fig. 2.4 (Bennett and Yule, 1973). Most of the gases produced from an oil field can be used as proportional counter gases. This includes the usual hydrocarbons, carbon dioxide, and nitrogen. As a consequence, such counters can be used to monitor produced gas at the wellhead or separator, as well as to count collected field samples in the laboratory, providing w a t e r vapor and other condensables are first removed. In either case, the counter can be used for single samples by evacuation before filing. This and m a n y other geometries (Emery, 1966) have been used with success for both flowing and nonflowing counters. Electrons, attracted to the anode, are accelerated by this electric field until they gain enough energy to form new ion pairs in collision with gas molecules. These, in turn, strike molecules enroute, forming new ion pairs and ultimately creating an electron avalanche of far higher charge t h a n t h a t of the original pulse. Pulse amplification in this region can easily reach 104 times the original value. Pulse collection is more rapid t h a n in the ion chamber mode, and the counter is much more sensitive to gas composition t h a n the ion chamber. It requires special

46

Chapter 2

counting gases that do not form electronegative ions, thus oxygen must be excluded. Since the number of pulses collected is not changed by the multiplication, it has a good working plateau of count rate versus voltage, though it is not as stable as the ionization chamber. The proportional counter is used in the oil industry for neutron logging with a neutron-reactive fill gas. It is also used in the laboratory for monitoring tracer gases containing beta emitters such as tritium, carbon-14, sulfur-35, and krypton-85. In this procedure, the tracer is introduced into the counter with the counting gas, resulting in 100 percent geometry and efficiencies varying from 70 to 100 percent, depending on the beta energy and the counter size. Because the amplitude (height) of each pulse is directly proportional to its energy, pulse-height analysis can be used to identify a beta emitter by its energy. It can be used to analyze mixtures of isotopes having different energies without having to separate them. A plot of pulse height versus energy is linear and easily calibrated using sources of known energy and activity.

Gas inlet

insulator

field tube catlode

I Gas out

Figure 2.4. Proportional counter schematic

Geiger-Mueller counter Probably the most widely used of the gas counters, the GM counter produces very large pulses and can be operated with relatively unsophisticated components, although a special gas mixture is required for operation. Although it is used for personnel monitoring as well as for field and laboratory measurements, there is no obvious correlation with absorbed dose rate as there is for the ion chamber or proportional counter. A major problem with the use of this counter is the long dead time of the counter (ca. 0.1 seconds) due to slow anion collection. During this collection time, the counter is unable to respond to radiation. This is adequate for count rates below 104/minute, but not for high count rates where count losses can become excessive. The GM counter is frequently used as a sealed de-

Measurements and Applications

47

tector for monitoring external radiation. Gases have very little stopping power for g a m m a radiation, since most of the gamma interactions are with the walls of the counter. To increase the sensitivity for monitoring g a m m a radiation, the inner side of the counter wall is lined with a high z material such as bismuth. The lining is just thick enough to allow secondary radiation from any g a m m a interaction in it to escape into the sensitive volume. Because of the limited absorption of gamma radiation by the wall and in the counter gas, g a m m a counting efficiencies are low.

rr 0

f

j Voltage

Figure 2.5. Counter plateau as function of voltage A counting system is much simpler to construct for the Geiger counter t h a n for the proportional counter. Pulses are large enough to be counted with little if any amplification. The only additional equipment needed is the power supply and a counter or meter to display the collected counts. Geiger counters are also used as radiation survey meters, but their response is a function of the energy of the radiation. Such meters usually come supplied with calibration graphs correcting the recorded readings for the incident gamma energy.

Counter plateau vs. pulse-height plateau When a counter is used in any of the voltage modes described above, it should be operated in a stable voltage region. The stability of the region is described by the counting plateau. With increase in voltage, the variation of count rate should show a long region with little change in count rate. Unlike the data shown in Fig. 2.2, this is a plot of count rate, not of pulse height vs. impressed voltage, which describes the desired operating condition for any of these counting modes

48

Chapter 2

(Fig. 2.5). The plateau for all operating counters should be monitored periodically using a s t a n d a r d radiation source. The counter is usually operated at the voltage of the center of the plateau. The ion chamber usually shows the flattest and longest plateau of the three counters, and the GM tube the steepest.

Highvoltage i? supply i I Amplifier I Detector I" - - t - -

I I

ITimerll A

t I i I_ . . IScalerl . .

I I

I I

-- --I

i IRatemeterlBi

Figure 2.6. Simple counter system

C O U N T I N G SYSTEMS In most applications, radiation is monitored by counting individual electrical pulses initiated in some m a n n e r by the detector. This is true for the scintillation and semiconductor detectors to be discussed later as well as for the gas detectors described above. The systems used to support and collect the produced pulses are called counters or counting systems. With minor variations, depending upon the detectors used, these counting systems share the same kind of components. Those needed for counter systems are available as standard modules. An extraordinary range of pulse handling and logic circuits is commercially available. These modules are made to fit in the Nuclear I n s t r u m e n t S t a n d a r d (NIM) bin, where a single power supply provides power for all modules. These are the components referred to in the following discussion of counting systems.

Simple counters The output from a detector of radiation is a collection of events called counts, which are collected by tabulating devices called scalers. The n u m b e r of counts tabulated by a scaler has no intrinsic correlation with either time or energy. To m e a s u r e radioactivity, we need a count rate, hence we must also know the time interval during which the counts were collected. If the counter also produces

Measurements and Applications

49

pulses whose height is proportional to the energy of the event, the pulses may be analyzed further and sorted by pulse height to obtain the energy information. The simplest system only counts pulses. Geiger counter survey meters use such a system, often without an external amplifier. It is composed of the detector; a high-voltage bias supply, which all detectors require; an amplifier, if needed to increase the pulse size; and a readout giving a count rate. In most cases where radioactive tracers are counted in the field, only the counting rate is required, and a simple system will suffice. The count rate is obtained from the number of pulses collected during a fixed time interval. An automatic timer can record the n u m b e r of counts for a preset interval of time, automatically r e s e t t i n g the counter at the end of each interval, as shown in A, Fig. 2.6. This has obvious limitations for following radiation t h a t changes rapidly in intensity, as in following a moving pulse of tracer in a pipe or rapid decay in a short-lived isotope. A solution for this kind of monitoring is to use a count-rate meter t h a t directly converts the collected pulses to a pulse rate, marked as B in the figure. Count rate meters are commonly used in hand-held radiation monitors. Such monitors go directly from the amplifier (if any) to the rate meter with no other electronics. Both analog meters and digital methods are available and will be discussed later in this chapter.

Counters measuring energy When multiple tracers of different energy are used, it is often necessary to monitor the radiation energy in addition to the number of radioactive events. In t h a t event, assuming t h a t pulse heights are proportional to energy, the pulseheight distribution is also measured. If the detector produces pulses containing energy information, a preamplifier is usually required to transfer the signal to the amplifier without loss, and to reduce noise. The amplifier used m u s t be linear; i.e., it must amplify pulses of all amplitudes equally to avoid loss of energy information. The simplest way to sort the pulses by energy is through a singlechannel analyzer (SCA) composed of two discriminators. A lower level pulse discriminator (LLD) is used to eliminate all pulses below a preset level and to reduce noise by eliminating spurious low-level signals. An upper level discriminator (ULD) is used to discriminate against all pulses above a preset level. The two discriminators can be coupled together to define a region of pulse heights or energies, AP for any given pulse height. The count rate measured in t h a t region is AC. To obtain the spectrum, AC/AP is measured as a function of P. Since the pulse h e i g h t s are usually linear in energy, the pulse-height s p e c t r u m is equivalent to the energy spectrum of AC/AE versus E. A typical system used for all energy-sensitive counting systems is shown schematically in Fig. 2.7. These components are available commercially as modules or as an integrated system.

50

Chapter 2

BACKGROUND REDUCTION In operation, most detectors are surrounded by shielding, usually lead, to reduce background from external sources of radiation. F u r t h e r reduction is possible if counter m a t e r i a l s are carefully chosen to be free of m a n m a d e or n a t u r a l l y occurring radioactivity. Very low-level counting is often required, or at least desirable, in monitoring interwell tracers. This can be achieved by surrounding the counting detector with an external detector and using anticoincidence to cancel events t h a t occur simultaneously in both detectors. The outer detector is often referred to as a guard counter, with the assumption t h a t events external to the counting system represent background radiation and will be removed relative to those being counted. In this procedure, the signal from the outer detector activates a gate in an anticoincidence circuit. This module allows signals from the inner detector to be counted only if they are not coincident with signals from the outer detector. An example of this is low-level counting of radioactive gas tracers by proportional counting. In this system, the gases are counted in a proportional counter, mixed with the counting gas. This counter is surrounded by a GM counter, as shown in Fig. 2.8. Radioactive events such as cosmic rays originating outside the counters have enough energy to pass through both counters. The radioactive tracers in the proportional counter are beta emitters, entirely absorbed within the detector volume. If the two detectors are connected in anticoincidence, only the i n t e r n a l l y g e n e r a t e d signals will be counted. A l-liter proportional counter inside a 3-inch lead shield with an anticoincident guard counter can reduce the background to less t h a n 6 counts per minute. There may be some loss of counts due to accidental coincidences; however at the low counting levels normally found in gas tracer counting, this is negligible.

Proportional Counter

I

Preamp.

i rT-l

Linear Amplifier ~ !~ Timer

I I Upper& Lower High Voltage Discriminators Power Supply

Figure 2.7. Energy-sensitive counting system

Scaler

Measurements and Applications

51

Anticoincidence

/ Lead shield

fl

L i

/

':':-:-:-::':':':':':'::-'.-';

,':':':-:': ........... :':':'::': ............... :':':': ........... :':':'::':i-;-; ...... "

Inner counter iiiii::iiiiiiii:iiii:

I

guard amplifier

"t

/"

I "..

Inner amplifier

--'I !

!

Guard counter I

Figure 2.8. Background reduction by anticoincidence with guard counter

SCINTILLATION DETECTORS Ionizing r a d i a t i o n can interact with a n u m b e r of phosphors to produce scintillations of light. This includes some of our oldest known m e a s u r i n g techniques. Organic m a t e r i a l s such as anthracene, as well as solutions of some organic phosphors in suitable solvents and in plastics, are used for beta-particle and a variety of low-energy radiation detection. The interaction of organic materials with radiation is a property of the molecule. Most organic phosphors are composed of planar aromatic rings having a ~ electronic structure (Birks, 1964). Absorption of radiation raises the molecule to an excited state t h a t can de-excite by emission of light. Since this is a molecular property, the phosphor can fluoresce in vapor form, as a crystal, or in solution. It is also available dissolved in plastics obtainable in virtually any shape or size. Several inorganic materials are also capable of converting radiation to light. These include crystals such as NaI, CsI, LiI, Bi4Ge3012, (bismuth germinate, BGO), BaF2, CsF, ZnS, etc. The interaction of these materials with radiation is a p r o p e r t y of the crystal structure. Electrons in nonconducting crystals are restricted to discrete energy bands. In the pure crystal, electrons normally occupy the valence band t h a t is the level where they are bound to the lattice sites. To leave this level they must be excited to the conduction band, leaving a hole in the valence band. De-excitation from this level by production of a photon is an inefficient process, often occurring at too high an energy level to produce visible light. The region between these bands is forbidden. If a small amount of a suitable impurity is added as an activator, an intermediate energy band between these

52

Chapter 2

two bands becomes available. Electrons can de-excite back from these states to the valence band with the emission of a photon of visible light, as illustrated in Fig. 2.9. The sodium iodide NaI(T1) (thallium activated crystals) is the inorganic material most widely used for gamma counting because its high density gives it good stopping power, the high atomic number of iodine has a good photoelectric cross section, and it is transparent to the light it generates. These detectors require the use of a photomultiplier tube to amplify the scintillation pulses produced and convert them to an electrical pulse. Requirements for a useful scintillation detector are discussed in monographs (Birks, 1964) and texts (Tsoulfanidis, 1983; Knoll, 1989). In this section we will cover only the detectors most commonly used for monitoring gamma and beta radiation.

I Conduction Band I

I

Forbidde

I Valence Band

levels I

Figure 2.9. Mechanism of crystal scintillation

The p h o t o m u l t i p l i e r tube The photomultiplier tube (PMT) is basic to the use of all scintillation detectors. A diagram of a photomultiplier is shown in Fig. 2.10 (RCA, 1970). The PMT consists of an evacuated glass or quartz tube with a flat end for optical coupling to a crystal. The inside of the flat end contains the photocathode, which converts the light pulse to an electron pulse. Between the photocathode and the collection anode is a string of dynodes. Electrons from the photocathode strike the first dynode, where each is multiplied in number. Each succeeding dynode multiplies the electrons arriving from the preceding dynode. The final pulse produced can have a multiplication factor of about 1010 to 1012, depending on the number of dynodes. An electric field is used to focus and direct the electron pulses from the photo cathode and intervening dynodes to the anode. The amplified pulse will be proportional in height to the original light pulse and will have similar timing characteristics. A stable high-voltage source is required to bias the PMT electrodes, using a resistor string to provide the focusing and amplifying voltages

Measurements and Applications

53

needed at each dynode. These resistors are usually mounted inside the base of the PMT. Photomultiplier tubes are available commercially with a large range of photocathode diameters. Output from the PMT is usually fed to a preamplifier and then to a linear amplifier as illustrated in Fig. 2.7.

The Nal(T1) d e t e c t o r OPERATION OF DETECTOR The t h a l l i u m - a c t i v a t e d sodium iodide detector is the most common solid scintillator in use. It is composed of a single crystal, which is hygroscopic and must be hermetically sealed in aluminum to protect it from water vapor. One face is left covered with glass or quartz for optical coupling to the face of a photomultiplier tube (PMT). The coupling medium is a transparent, viscous fluid with a suitable refractive index, usually one of the silicones. The NaI(T1)-PMT combination is wrapped with black plastic tape to make it opaque, and the entire assembly shielded to reduce background. The crystal and PMT are available commercially as separate units or as a sealed package. The electronics needed for counting and measuring the pulses from the detector can be provided by a handheld survey meter, by laboratory survey meters, or by the electronic modules packaged in an NIM bin. In dealing with g a m m a radiation of different energies, it is convenient to be able to deal with a large n u m b e r of channels. For this purpose the single-channel analyzer described earlier is often too time-consuming and is replaced by the multichannel analyzer (MCA). The MCA is an electronic device t h a t can be used to sort rapidly all incoming pulses by amplitude into separate energy channels. For the NaI(T1) crystal, a 250-channel analyzer is commonly used. The use of the MCA is discussed in a later section. The light pulse generated in the crystal is transformed to a charge pulse by the PMT. The height of each pulse produced is proportional to the energy of the radiation q u a n t u m absorbed in the detector. The NaI(T1) is one of the most efficient detectors for g a m m a radiation up to several MeV in energy. Efficiency increases with detector volume, and crystals are available in large sizes up to several feet in diameter. For commonly available sizes, such as 2- to 3-in. diameter, it approaches an efficiency of 100 percent for energies below 0.5 MeV and about 50 percent for 1.7 MeV gammas. The radiation background also rises with increased crystal size. The tradeoff between efficiency and background is best evaluated in terms of the figure of merit discussed earlier, E2/B, and the permissible limitations on background. For most purposes, crystal sizes below 5-in. by 5-in. are the most useful. A variety of NaI crystal-PMT combinations are available commercially, including well crystals, which are commonly used in laboratory work for counting gamma-emitting tracers from interwell waterfloods. Such a detector is illustrated in Fig. 2.11. It allows a sample vial to be placed inside the crystal so t h a t it may be counted with virtually 100 percent geometry.

54

Chapter 2

Photons Photocathode \\ Focusing section

I i

i

/

\,1II

:j 7,,;

~--m

Photoelectron trajectories

Electron multiplier section

1 to 12 = Dynodes 13 = Anode

Figure 2.10. Photomultiplier tube

Aluminum enca ~sulation

We,, fk~, ) /-- '0~~ Figure 2.11. Crystal well counter

~,noo.

Measurements and Applications

55

ENERGY SPECTRUM FROM NaI(T1) CRYSTAL The pulses produced by the PMT are amplified and sorted according to pulse height to display a spectrum of energy versus intensity. The absorption of g a m m a radiation in a crystal follows the same processes as those described earlier for all matter. The three major processes are Compton scattering, photoelectric absorption, and pair production. In all of these, the gamma ray reacts with the material to produce energetic electrons, which will react in the crystal to produce excited states, resulting in the emission of photons. If the g a m m a radiation were released inside a crystal large enough to absorb all the emitted radiation, the energy spectrum would display a single peak for each g a m m a ray emitted. This total energy peak has a G a u s s i a n distribution instead of a single line, because the energy transfer from incident g a m m a ray to the produced light pulse is composed of several inefficient processes. The energy required to produce one information carrier (a photoelectron) is about 100 eV or more. The statistical fluctuations in the relatively small n u m b e r of carriers formed limit the resolution of the detector (Knoll, 1989). In real scintillation crystals, all the energy of the g a m m a ray is not captured. The radiation all comes from outside the crystal: some of the radiation m a y graze the crystal; some will scatter off the surroundings before entering the crystal; depending upon the crystal size, some of the incident radiation may pass through the crystal and not be captured at all; and all the processes by which g a m m a rays lose energy will be displayed. As a result, the spectrum will be far more complicated t h a n indicated above. Such a spectrum is illustrated in Fig. 2.12 for an isotope emitting two g a m m a rays. The photopeaks representing the characteristic energy of the two g a m m a rays are m a r k e d as ~1 and ~2. A backscatter peak due to escape of scattered radiation from the shielding usually shows up at about 0.25 MeV. Each g a m m a ray has a Compton continuum associated with it, with the Compton edge displaced about 0.2 MeV from the g a m m a ray photopeak. This was discussed earlier in chapter 1 and the process illustrated in Fig. 1.4. Resolution loss and other effects in the real crystal t u r n the sharp Compton edge shown in Fig. 1.4 to a bump in the curve. Pair production occurs at g a m m a energies above 1.02 MeV, resulting in the formation of two 0.51 MeV annihilation photons. One or both of these m a y escape the crystal, resulting in a single escape peak (esc 1) and a double escape peak (esc 2). Sum peaks can occur whenever two events take place within the resolving time of the detector and associated circuitry, shown in Fig. 2.12 as sum. (Cascaded g a m m a rays such as the 1.17 and 1.31 MeV gammas emitted by cobalt-60 usually result in an additional peak at the sum of these energies.) The response curve can be further degraded by secondary radiation, such as X-radiation and b r e m s s t r a h l u n g generated in or n e a r the crystal. The result of all this is a complex continuum of radiation with several peaks or humps. Each g a m m a energy is still identified by its photopeak; but with m a n y g a m m a

56

Chapter 2

rays and the associated Compton scatter arising either from one or from multiple sources, the spectrum can become difficult to resolve. The ability of the NaI(T1) detector to resolve a single emitted gamma energy is the figure of merit of the detector, R. This is quoted as "full width at half maximum" (FWHM) at the energy of the photo peak, usually expressed in percent:

FVCrIM

R=~

x 100

(2.6)

-ray ~2

Comp.~ edge

8

sum

i sca'er esc2 esc 1

____A.

Energy, MeV

Figure 2.12. Complex gamma spectrum The photoelectric peak produced by the 0.66 MeV gamma ray from 137Cs is a common resolution monitor, shown in Fig. 2.13 (Friedlander et al., 1981). A good sodium iodide crystal will have a resolution of about 7.0 percent. Also illustrated in the figure are additional peaks generated by the single gamma ray from 137 Cs. SPECTRUM ANALYSIS Simple spectra that contain only a few g a m m a sources yielding a few welldefined photopeaks are easy to resolve into the isotopic components. The peak energies associated with each known isotope are available from libraries (Heath, 1964) of data collected by NaI detectors under a variety of conditions. Such spectra can, however, become difficult to analyze with increasing n u m b e r of radioactive sources. This is due to the statistical noise associated with radioactivity,

Measurements and Applications

57

the relatively poor resolution of each photopeak, the Compton continuum associated with each g a m m a energy, and the secondary reactions t h a t can take place in the crystal. As a result the spectrum often shows relatively little character, particularly at low counting rates. These spectra are usually stored in computer memories. Modern advances in computational speed have made it possible to resolve m a n y such spectra using a variety of search and evaluation programs. The methods developed for analyzing such spectra are briefly described below.

'

I

'

1

'

I

~

I

FWHM Resolution- - - ~ XlO0 t-

Compton ~ edge [ J/! k ~ ~ " / R . e.~.~e..ff~,r ~ ,i

...... [

'

FWHM. l j l

x-ray

0

9

fl~ Photopeak /i/~/ -

I

i

I

i

I

Energy

! I ! Midp~ I ~ energy /i/ E 9

I

,,I

\

I

,

_

E

Figure 2.13. NaI(T1) detector resolution Two things are required from a g a m m a ray spectrum: identification of the component g a m m a sources and a measure of the activity of each source. The first of these requires peak energy identification (Carpenter et al., 1979). Search programs look for an increase in count rate associated with a m a x i m u m and compare this with a library of g a m m a ray energies. Poorly resolved peaks can sometimes be separated from the noise by programs t h a t differentiate the peak data and look for roots in the first and higher order differentials, or programs t h a t look for Gaussian or other specific shapes to fit the peak. In the use of multiple tracers in oilfield work, it is sometimes sufficient to identify the presence of a specific tracer, as described above. The amount of each component present is obtained from the areas under the peaks assigned to t h a t component. This can be done by graphical integration with suitable corrections for interference. It can also be done by curve fitting to preassigned shapes. For evaluation of complex spectra, two additional procedures

58

Chapter 2

have been used. The most common is spectrum stripping. In this procedure one isotope w i t h p r o m i n e n t photopeaks is identified. A spectrum of the pure component is made under the same conditions and used to fit the photopeaks in complex spectrum. This is then subtracted from the entire spectrum. The process continues, using the next prominent peak until all are analyzed. This procedure suffers from the propagation of errors, the last components having the greatest errors. The best programs for resolving and analyzing small peaks in a composite spectrum with little character are the least squares procedures (Schonfeld 1967; Yule, 1973). A set of spectra for each of the radiotracers present is divided into a set of energy channels. Intensities are calculated so that their sums best fit the composite spectrum, and the sum of the squares of the residuals in all the channels is a minimum. This is superior to the spectrum stripping method, since all components receive equal weight. It is the method commonly used in the oilfield for deconvolving g a m m a ray spectra emitted by n a t u r a l and m a n m a d e sources downhole.

L i q u i d scintillation counters AQUEOUS SOLUTIONS OF BETA EMITTERS The liquid scintillation counter (LSC) is the only method t h a t can be used for directly counting aqueous solutions of beta emitting tracers such as tritium and carbon-14 with 100 percent geometry and high efficiency. Until the development of this method, such materials could not be counted directly but first had to be separated from solution and then converted to a (tritium and carbon-14) form suitable for counting in a gas counter. The LSC is the most widely used detector for monitoring tracer solutions that emit radiation of low penetrating power, including solutions or suspensions of tracers that decay by alpha emission, beta emission, electron capture, or internal transition. It is the principal method used for counting the tritiated and carbon-14 tagged tracers used in waterflood tracing (Horrocks, 1974). A variety of solids can also be counted in the LSC by suspending them as a fine powder in a suitable "cocktail." In this counter, the solution is incorporated into a liquid scintillation "cocktail" within the sensitive volume of the detector. This avoids the need to penetrate the walls of an external detector and provides essentially 100 percent geometry. The principal problem in counting low-energy beta particles in the LSC is the reduction of light output due to the presence of interfering impurities, particularly the presence of water. Commercial cocktails capable of counting tritium efficiently in mixtures containing up to 50 percent water are now available. In such cocktails the water is usually in a colloidal suspension r a t h e r t h a n in solution.

Measurements and Applications

59

Beta particles are produced in a continuous energy spectrum, as shown in Fig. 1.4, r a t h e r t h a n as a single discrete energy. Spreading the energy spectrum out in this m a n n e r reduces the sensitivity of detection for an event. It is further reduced by inefficient conversion, since only about 10 percent of the beta energy is converted to light photons. There is also a lower limit of sensitivity imposed by noise discrimination and by the need for coincidence monitoring. As a consequence, particles below about 1 keV cannot be monitored. This is very important for tritium, less so for carbon-14 - - the two isotopes most widely used in the oil industry. The average energy of a tritium beta is only about 6 keV; t h a t of a C-14 beta is about 50 keV. COUNTER OPERATION The liquid scintillation cocktail consists of a solvent, a primary scintillator, an emulsifier and the radioactive sample. The solvent has the dual function of keeping this mixture in solution and of energy transfer. Most of the energy of the beta particle is dissipated in the solvent, which must provide a radiationless transfer of this energy to the primary scintillator. The scintillator then converts the radiation to a light pulse of which the height is proportional to the energy of the emitted radiation. The emulsifier serves to keep materials t h a t are not soluble, or would separate by gravity, suspended in the cocktail. Sample preparation consists of mixing a suitable scintillation cocktail with a known volume of sample in a scintillation vial. Aqueous solutions are commonly counted for most applications such as interwell tracing by incorporation into the cocktail as a colloidal suspension. It is important to m a i n t a i n a single colloidal phase in these cocktails since multiple phases can cause unreliable count rates. The formation of multiple phases depends on the fraction of w a t e r present, the ionic strength of the solution, and the temperature. To keep background levels down, the vials are made of low-potassium glass or plastic. The continuous energy spectrum produced by beta particles combined with the low energy of tritium and carbon-14 betas makes noise reduction vital in these m e a s u r e m e n t s . All i n s t r u m e n t s produced commercially reduce random noise by using two photomultipliers (PMT's) in coincidence to view the sample vial. This separates the random t h e r m a l effects, which are not coincident, from the true counts in the scintillation vial, which are coincident. The output of the two tubes is then summed to average out readings at different positions and to increase the sensitivity of measurement. This output goes into a multichannel analyzer, or a set of single-channel analyzers. At least three channels of data are needed if multiple tracers, e.g., C-14 and tritium, are to be counted. A schematic diagram of such a liquid scintillation counter is shown in Fig. 2.14 (Packard Inst., 1982). Most commercial instruments are automatic in operation. The samples are placed in a motor driven belt, which lowers each sample in t u r n to a shielded counting chamber for a preset period of time. Driven by microprocessors, these instruments can count up to several hundred samples sequentially for variable counting times.

60

Chapter 2

P"TI I 1 vial 0 PMT2!~

oo,nFI,o,_ dence

sum

ADCII !I~

Figure 2.14. Liquid scintillation counter Generally, provisions are made for one or more sets of calibration standards, for background counting and subtraction, and for efficiency corrections. Multiple tracers are identified, and the data are presented in terms of ~Ci/ml (MBq/cm 3) or equivalent units.

Quenching and efficiency measurements The addition of aqueous materials to the scintillation cocktail has two effects. It reduces the number of photons produced from each event, and it shifts the curves of energy distribution to lower energies. These combined effects are known as quenching (Fig. 2.15; Packard, 1982) and are important in m e a s u r i n g the efficiency of counting and in deconvolving mixed spectra. Quenching is a function of a great m a n y variables, including the amount of water, the n a t u r e of the solute, its concentration in solution, and the temperature. It may be different in each sample but must be corrected for in order to calculate counting efficiency. The two principal ways to obtain counting efficiencies from quenched samples are the channels ratio method and the external standard method. Both methods require a set of standards containing the same amount of activity, but different amounts of quenching. In the first method, the standards are counted in both a quenched region and in an unquenched region and the ratio of counts in the two regions plotted against the calculated efficiency, usually resulting in a smooth monotonic curve (Fig. 2.16; Packard, 1982). The efficiency of an unknown sample is obtained from its measured channels ratio using the s t a n d a r d curve. The external standard method uses a gamma source such as radium or cesium-137 to generate Compton-scattered electrons in the scintillator. These behave as beta particles and can be used to obtain a s t a n d a r d quench curve. The external standard method is the most widely used and can also be corrected for quench by applying various correction algorithms, including channels ratio. It usually has a very high activity and is dropped into position next to the unknown samples for only a few seconds after the sample has been counted for the required time.

61

Measurements and Applications

dN

pulse height

Figure 2.15. Effect of quenching

BO

o>,

60

40 ,-- - I

20

.00

.20

.40

.60

.80

1.00

Channel ratio

Figure 2.16. Channel ratio method for efficiency monitoring

Chapter 2

62

I

I

I

ched

I

I I I I I

8 ,

200

41)0

6~'5

I Channels I

I I

I I

I

I Unquenched I

I

1C.14

I

8

I

200

40O

III

675

Channels

Figure 2.17. Tritium and carbon-14 spectra in LSC A consequence of the spread in the beta spectrum and the effect of quenching is that only a limited amount of energy deconvolution is possible. If their energies are far enough apart, up to three different beta-emitting isotopes can be analyzed simultaneously. In most cases isotope separation must deal with overlapping spectra for each isotope. Energy (pulse-height) channels are chosen to minimize the overlap, and the isotopes are separated by solving simultaneous equations for the fractional concentration in each of the spectral regions. Two of the most frequently used isotopes are tritium and 14C. The beta spectrum for each of these, quenched and unquenched, is shown in Fig. 2.17 (Beckman, 1985). The effect of the spectral shift is made clearer here by showing the two spectra on the same

Measurements and Applications

63

energy (pulse-height channel) scale. The counting data are deconvolved with the help of data from a set of quench standards counted for each isotope. The presence of quenching agents such as water, salt, oxygen, or colored m a t t e r reduces the total light output from each isotope and changes the shape of each spectrum. Many modern i n s t r u m e n t s are equipped with microprocessors t h a t use the data from a set of quench standards counted for each isotope to calculate the amount of each isotope and the efficiency of measurement.

SOLID STATE IONIZATION DETECTORS Many semiconductor crystals have the ability to interact with radiation by producing ions. Such counters behave as parallel plate ionization chambers if an electric field is applied across the parallel faces. The radiation is absorbed in the crystal by forming electron-hole pairs equivalent to the ion pairs in a gas. Elecrons are raised into the conduction band of the crystal and migrate to the positive electrode. Positive charges (holes) are collected at the other electrode. The most successful semiconductors for monitoring radiation have been elemental germanium and silicon. The high density of these materials, particularly germanium, makes them very efficient g a m m a absorbers compared to gas. In addition, since only 3 or 4 eV is required to form an electron-hole pair, their energy resolution is much better t h a n that of any other detector. Diode detectors These materials lie within group IV of the periodic table and are quadrivalent. They can be made conducting by doping them with small amounts of group III or group V elements. If a group III material (e.g., boron) is used, it will be p type material m electron deficient, generating positive holes in the crystal. If a group V m a t e r i a l (e.g., phosphorus) is used as a dopant, it will be known as n type material and will have an excess of electrons. These holes and electrons formed in the p and n types, respectively, are charge carriers that are free to move under an electrical field. If n and p type materials are joined together to form a diode, and an electrical potential is applied, current will flow in only one direction. If the potential is reversed, the charge carriers will each flow away from the diode junction, leaving this region depleted. No current will flow except for t h a t generated thermally. If, however, an ionizing particle or q u a n t u m of energy passes through this depleted region, electron-hole pairs are formed and a current pulse will flow. The diode will thus act as a counter for ionizing radiation, yielding pulses whose height is proportional to the energy of the ionizing event. For penetrating radiation such as g a m m a and x-radiation, the depleted region near the diode junction is too thin to allow for efficient interaction with radiation.

64

Chapter 2

For both silicon and germanium diodes, lithium can be used to compensate for extra charge carriers as well as to greatly expand the depleted layer. The lithium "drifted" silicon detector is used as a detector for x-ray fluorescence analyses. Both must be kept at liquid nitrogen temperature to maintain the lithium-drifted layer. G e r m a n i u m detectors Because of germanium's high atomic number and density, germanium diodes are used for gamma counting. Lithium-drifted germanium diodes (Ge(Li)) are being phased out by ultrapure (intrinsic) germanium. The ultrapure germanium detector compares favorably with the Ge(Li) detector in that, although it has an equally thick depletion layer, it need not be stored at liquid nitrogen temperature when not in use. When in use, however, the germanium diode detectors must be operated at liquid nitrogen temperature to keep thermally induced noise from overwhelming the detector. Germanium detectors are less efficient than NaI(T1) detectors because of the much smaller useful volume. The efficiency of a Ge detector is usually quoted in terms of percent of NaI efficiency at a specific energy. Large Ge crystals can approach NaI efficiency but are quite expensive. The great advantage to using the Ge detector is the tremendous increase in spectral resolution; energy resolution obtained from a Ge detector is about 100x higher than that from NaI. Since the height and location of the photopeaks are used to quantify the gamma response, the narrowly defined photopeaks stand out from the Compton scatter far better in the Ge detector than in broad peaks generated in NaI. This also improves gamma analysis from the Ge detector. The background radiation level can be reduced by shielding and by use of a guard counter in anticoincidence with a detector, as described earlier and shown in Fig. 2.8. In this case, the result is a significant reduction in the Compton scattering relative to the photopeaks. This is because the Compton component of the spectrum includes many photons that were partially scattered and then escaped; whereas the photopeaks used to monitor the full energy have no escape. A NaI(T1) crystal is the usual guard counter. The shielded and cooled Ge detector produces small pulses of charge that are amplified in the manner illustrated in Fig. 2.6. Because of the high resolution of the energy pulses, a larger number of channels is useful for spectral display. Most energy resolution is done using 4000 channels. T h e r m o l u m i n e s c e n t dosimeters (TLD's) TLD's are semiconductors that respond to radiation by raising electrons to excited levels where they are trapped without the immediate emission of light. These excited electrons can be stored for long periods of time without loss of energy, so that the TLD acts as an integrating dosimeter. When the TLD is

Measurements and Applications

65

h e a t e d u n d e r controlled conditions, it emits light proportional to the energy originally absorbed, which can be monitored by a photomultiplier tube. The curve of light intensity as a function of temperature is called a glow curve. TLD's have in m a n y cases replaced the film badge in personnel monitoring for g a m m a and x-ray exposure. A n u m b e r of materials have been developed for this purpose including LiF, CaF2(Mn), CaSO 4, and others.

NEUTRON DETECTORS

Neutrons do not cause ionization in reacting with matter. They are detected only by means of secondary reactions t h a t produce a measurable signal. This is a two-step process: the neutron must react with the nucleus of a material having a high reaction cross section and this reaction must result in the emission of a particle of high ionization ability. The three most common neutron counters for oilfield work use the (n,p) and the (n,a) reactions. The boron trifluoride (BF3) detector uses boron trifluoride (BF3), enriched in 10B, as both the neutron target and the proportional counting gas. The lOB(n,a) reaction produces energetic alpha particles with high ionizing power and easy detectability. The high specific energy of the alpha particle makes it easy to detect even in the presence of high gamma radiation levels. The same holds true for the lithium iodide scintillation detector using the 6Li(n,(~) reaction. The energy of the emitted alpha particle is so much greater t h a n t h a t of the g a m m a radiation normally encountered t h a t it can be separated from interfering g a m m a background by energy discrimination. The most common detector used in the oil field is the helium-3 detector, which undergoes the 3He(n,p) reaction with neutrons. Helium-3 acts as the neutron target as well as the proportional counting gas. The neutron capture cross section here is considerably higher t h a n for the other two counters; in addition, the gas density can be increased by high-pressure operation without h a r m i n g the counter operation. All three of these counters are sensitive to t h e r m a l n e u t r o n s and give a response t h a t is independent of the neutron energy. To monitor higher energy neutrons by these detectors, the neutrons must be slowed down in a known way by interaction with an intervening moderator.

C O U N T R A T E M E T E R S , M U L T I C H A N N E L ANALYZERS, AND M U L T I C H A N N E L S C A L E R S Analog count rate meters

The analog count r a t e m e t e r (CRM) is the only m e t h o d for obtaining a continuous reading of the average activity in counts per unit time. It is also one

66

Chapter 2

of the oldest, cheapest, and most widely used methods for presenting counting data. The circuit for a typical meter is shown in Fig. 2.18. Here, the entering pulses from the counter deposit their charge in the capacitor, C, which is discharged through the resistor, R. This combination of resistor and capacitor is called a tank circuit. Equilibrium is reached after a few values of the time constant, RC, and the rate of discharge will equal the rate of charge. If N is the count rate in counts per second and q is the charge deposited by each pulse, then the average voltage produced is directly proportional to the count rate and is given

by: V = NqR

(2.7)

The produced voltage fluctuates about the average count rate as it charges (and discharges) with the random count rate. If necessary, the input pulses are shaped to remove any difference in count caused by pulse shape. If there is a change in count rate, the CRM will respond by approaching the new equilibrium value at a rate given by (1-e-t/RC), where t is the time and RC is the time constant.

I Tank circuit i "

_J-L Input pulses

I

I I

>

(r ~

I I

I

I

C

I

FI

Output voltage

I -

I I

-

Figure 2.18. Typical count rate meter circuit Short time constants provide more rapid equilibrium but larger deviations from the average. Long time constants show less deviation but a much slower response to changing signals. The counting error for the meter is usually expressed as the percent standard deviation. If ~ is the standard deviation and v is the average voltage, this is given by: ~_ = 1 v ~]2NRC

(2.8)

This kind of circuitry is normally found in pulse-counting survey meters, generally those using a GM tube or a NaI scintillator as a detector. Such meters

67

Measurements and Applications

usually have a choice of scales for counting ranges t h a t are adjusted by changing the value of the resistor, R, with a switch on the front panel. They also have adjustments for changing "percent standard deviation" by a switch on the panel t h a t alters the capacitance, C. Survey meters t h a t measure pulses r a t h e r t h a n current may be calibrated in terms of counts per unit time or as a "dose rate" in mR/hour or ~Sv/hr. These terms will be discussed in a later section of this chapter. The output is a measure of the average count rate and is displayed on a panel-mounted ammeter. The output can also be made to bypass the ammeter by means of a suitable set of pin jacks displaying the results on a strip chart recorder.

Tracer pulse -~

-__-_-_-_----------:_-_-.==_~ . . . . . . . . . . . . . . . . .

Flow

..._ v

Hv

(Survey meter)

Figure 2.19. Analog count rate meter and recorder The ability to record the activity as a function of time with a strip chart recorder provides a cheap and useful method for monitoring the m o v e m e n t of tracers through pipelines and other media in facilities, as illustrated in Fig. 2.19. Portable NaI survey meters draw relatively little current and can operate on dry cells for extended periods of time, as can some battery-operated strip chart recorders, allowing complete independence from other power sources. If the count rate varies significantly with time in the passage of a pulse of activity, the ratemeter will lag the data because of its response time. For precise work, the ratemeter output can be corrected for the lag (Pilgrim, 1965) with simple computational methods.

Multichannel analyzers Energy information is obtained from the amplitude (height) of the pulse. To extract this information in a useful way, the pulses must first be sorted according to pulse heights. This can be done in simple systems using a pair of pulse-height

68

Chapter 2

discriminators in a single-channel analyzer. For complex spectra, a multichannel analyzer t h a t displays the entire energy spectrum is a better solution. The multichannel analyzer (MCA) is the i n s t r u m e n t of choice for complex energy spectra. The price and size of MCA's has decreased significantly in the past few years, and such i n s t r u m e n t s are now available in portable units weighing only a few pounds, able to display at least a thousand channels, and not significantly more expensive t h a n a s t a n d a r d counting unit. Many MCA's can also support a sodium iodide/photomultiplier detector providing both signal amplification and high-voltage bias. In addition, MCA cards are available for insertion into personal computers t h a t allow all the functions of a stand-alone MCA. Most MCA's are capable of operating as a pulse-height analyzer (PHA) or a multichannel scaler (MCS). The pulse-height analyzing function of the MCA is its most widely recognized application; however the multichannel scaling function is also useful in a great m a n y field applications. The two modes of operation are illustrated in Fig. 2.20 (Tsoulfanidas, 1983) and discussed below. PULSE-HEIGHT ANALYZER MODE In the pulse-height analyzer mode (PHA), the MCA acts as though the incoming signal were received by a large n u m b e r of single-channel analyzers, each accepting a pulse of a different (energy) height Ei -+ AE. It achieves this by digitizing the incoming pulse height in an analog-to-digital converter (ADC). It t h e n stores a n u m b e r proportional to each pulse height, El, in a channel containing all pulses whose height is Ei -+ AE. Channels are sorted according to height, and each channel is given a separate address in the memory. The resolution of the system is AE, and the m a x i m u m content of a memory channel is about 16 million counts. The number of channels available is expressed in powers of 2 and varies from 28 (256 channels) to 213 (8192 channels) and above. (These are normally referred to as 250 channels and 8000 channels). The n u m b e r of channels, N, required to cover the signal from a given detector efficiently depends upon the resolution of the detector, G, and the range of g a m m a energies to be covered. A commonly used rule of thumb is given by: N =5

range (keV) G (keV)

(2.9)

Thus, a sodium iodide crystal with resolution of 50 keV and a range of 2000 keV would require 10,000/50, or about 200 channels. A germanium detector with a resolution of about 2 keV would require about 5000 channels. Hence, for work with the sodium iodide crystal, a 250-channel ADC would be adequate; whereas at least 4000 channels would be needed for the germanium detector. Modern MCA's are equipped with a cathode ray tube display t h a t shows the energy spectrum as it is collected. It can also display multiple (energy) regions of interest (ROI's) and the total count collected in each energy range. These can also be printed out on an X Y recorder.

69

Measurements and Applications MULTICHANNEL SCALER MODE

In the m u l t i c h a n n e l scaler (MCS) mode, the m u l t i c h a n n e l a n a l y z e r records each count as a function of a preset counting interval, At. Each channel is assigned a time interval during which it collects counts. At the end of each time interval, the signal is automatically transferred to a second channel where counts are collected for the same time interval. This continues until all the channels are full. The result is a continuous sequence of counts per unit time (At) as a function of time. This allows the collection and display of data from changing radiation intensity due to changes in tracer activity with changes in position or time. About 6 preset intervals are usually available from the front panel of the i n s t r u m e n t , r a n g i n g from 1 ~tsecond to 1 second, from 1 second to 106 seconds, or from any other desirable base. Since there are usually at least 1000 channels to fill, the actual time interval spent in monitoring can cover virtually any counting situation.

/"~_PHA

-"

ADC

-"-

address register

I

I memory I I cRT I t

~~,

MCS -"

data reg.

___J

Output

Figure 2.20. Multichannel analyzer diagram

The purpose of this mode is to monitor radioactive signals, which change with time. The MSC mode acts in m a n y ways as a count-rate meter, except t h a t the signal is digital, there is no lag, and the counting intervals are preset. Unlike the case of an analog meter, there is no need to pick a counting range, since each channel in the MCA will hold several million counts if need be. It also has the a d v a n t a g e t h a t the d a t a are visible on the cathode r a y display as t h e y are collected and can usually be stored in a battery-supported memory and off-loaded into a computer for further analysis or printed out on a strip recorder.

70

Chapter 2

Marinelli beakers

These are re-entrant beakers in which a gamma detector is surrounded by the sample in cylindrical geometry, as shown in Fig. 2.21. They are widely used for directly counting high-volume, low-level environmental samples. For multiple gamma energies, high resolution of the germanium diode is needed; for widely separated energies, however, the NaI detector can be used. Several computational methods have been described to calculate multiple tracer activities corrected for geometry, efficiency, and position (Verheijke, 1970; Suzuki et al., 1987; Dryak et al., 1989). Their principal application in the oil industry is for counting samples directly without the use of any intervening chemical or physical separation. In the event that a single gamma-emitting isotope is used, e.g., cobalt-60 from an interwell tracer experiment, a large sample could be counted directly in a well-shielded container by dipping a sodium iodide detector into the container. Simple calibration with a known amount of cobalt-60 activity is sufficient for conversion of counts to activity. Such counters are also useful for counting samples of sediment or water in the event of a spill. The more complex gamma-ray analyses required for the tracers used in following downhole acidization and fracturing are better analyzed using a Ge detector and a suitable computational technique.

[3

Marinellibeaker

i I NaI(TI)detector LFI~I~PMT > signal out

Figure 2.21. Marinelli beaker COUNTING RADIOACTIVE ATOMS In recent years, two new methods have been developed to measure the number of radioactive atoms present before they decay. This is a much more sensitive procedure than counting their rate of decay. These methods have a sensitivity about three orders of magnitude below counting methods with greatest sensitivity for long-lived nuclides. Available at several university and National Laboratory locations, these methods are important as a means of

Measurements and Applications

71

extending the dynamic range of interwell tracers. They are not cheap, but for some applications there is no reasonable substitute. These and newer methods may hold the future for tracer applications in environmentally sensitive areas.

A c c e l e r a t o r mass spectrometry This method (Bennet et al., 1978; Muller et al., 1979) accelerates negative ions using two 10 MeV Van de Graaff accelerators in tandem. Atoms are stripped of electrons and focused by electric and magnetic fields on the detector. Capable of rare to stable isotope ratios down to 1:1016, the method has been used for counting chlorine-36. This is a long-lived (T 1/2 = 3 x 106 yrs isotope generated by cosmic rays and available commercially. It has also been reported for counting other long-lived nuclides such as carbon-14 and beryllium-10.

Resonance ion spectrometry This method (Hurst et al., 1980) is based upon the use of lasers of appropriate frequencies to selectively bring the desired species to an excited state and then raise it into the ionization band. From that point, the ions are accelerated to a detector by electrostatic forces. The method has been used to measure krypton-81 trapped in glaciers with a sensitivity of 1000 atoms (Thonnard et al., 1988) and krypton-85 with a sensitivity of 3000 atoms. It has also been used for separating uranium-235.

USEFUL NUCLEAR PROCEDURES There are several nuclear procedures t h a t have reached a high stage of development in other fields but have been largely ignored by the oil industry. Many have applications that could be useful in a number of oilfield tracer problems. A few of these are introduced below and described in somewhat greater detail for suitable applications as they arise in later sections.

Isotope g e n e r a t o r s ADVANTAGES An isotope generator consists of a pair of isotopes in radioactive equilibrium, arranged so t h a t the short-lived daughter can be selectively removed from the generator as needed. It addresses a major problem in the use of radioactive tracers in boreholes, facilities and gathering lines: the danger of contamination of produced fluids and surface materials. It does this by providing a tracer, at the m e a s u r e m e n t site, of such short half-life that the radioactivity disappears by

72

Chapter 2

decay before contamination becomes a problem. This still provides sufficient activity at the test site to permit good measurements, normally a difficult thing to do. The time t h a t would be required to transport a tracer to the test site and place it down hole or in a gathering line would consume most short-lived tracers before they could be used. The isotope generator takes advantage of the long halflife of the parent isotope to transport the short-lived daughter tracer to the site as needed. Most downhole and facility m e a s u r e m e n t s are completed in a relatively short time. A very short-lived tracer could easily do most jobs if it were available at the downhole location in the test site on demand. PROCEDURES

In an earlier section we described secular and transient equilibrium of two radioactive species t h a t are related by the sequential decay of one radioactive species to form the other. This kind of equilibrium is used in isotope generators, sometimes called radioactive "cows," which are used to make short-lived isotopes available for experiments and tests by generating them in situ as needed from a longer-lived parent, as shown in Fig. 2.22 (Ehmann and Vance, 1991).

~).0 "',~

Mo-99 decay

regrowth 1.0

0

!

!

Decay time, days

Figure 2.22. Isotope generator In these systems, a long-lived parent is fixed upon a substrate in such a m a n n e r that the daughter activity can be "milked" off without removing the parent from the substrate. The d a u g h t e r activity is usually eluted from the generator by passing a small volume of solution through it, making a short-lived

Measurements and Applications

73

activity available where it never could have been transported otherwise. Other procedures are also used, but a simple method of stripping the daughter activity is required for use down hole. The short-lived daughter activity can be regenerated m a n y times by simply "milking" the generator in place. Although these cows are widely used in medicine, for some reason they have attracted little attention in the oil field. A partial list of commercially available cows is given in Table 2.1. (The Cs-137/Ba-137m generator is included because it has been available in the past and is particularly useful for oilfield applications.) Cows have great oilfield potential for tracer work in the borehole, in facilities, and in gathering lines. Such generators remove the hazard of surface contamination from produced tracers while permitting the use of high levels of downhole activity. BIOMEDICAL BASE Most of the current work in generator development is driven by the medical goals of reducing patient exposure and increasing the activity available for measurement. In addition to a vast collection of biochemical procedures, isotope generators are also used with such applications as gamma-ray cameras and positron imaging. Although many medical uses are not applicable to the oil field, several commercially available isotope generators can be adapted to satisfy oilfield needs. Table 2.1 lists some of these. For downhole use, they would have to be adapted to high pressure and remote operations, but for gathering lines and facility work they can be used virtually as purchased. Many isotope generators proposed and developed during the past 30 years have been described in reviews (Spytsin and Mikheev, 1971; Henry, 1971).

The technetium generator The most commonly used generator in medicine is the 99mTc generator. In this generator, the p a r e n t isotope, 99Mo (half-life = 66 hr) is prepared by the 98Mo(n,~) reaction. The parent isotope is fixed upon an ion-exchange material so that only technetium is eluted. As the parent decays, the technetium-99m (halflife = 6 hr) grows into transient equilibrium with it. It can be milked off (eluted) periodically, allowing new 99mTc to grow in, as shown in Fig. 2.22. The rate of growth of the Tc is given by the saturation factor 1 - e -~t. The amount of daughter available at any time can be calculated from the equations for transient equilibrium. Thus, four hours after a 10 mCi generator is milked, another 6.3 mCi of Tc becomes available. This generator is used in millions of medical and biochemical procedures worldwide. As a result, it is relatively cheap, available on short notice virtually anywhere in the world, with the generator activity g u a r a n t e e d for delivery date on site. The 99mTc isotope produces a 140 keV x-ray, which would require a detector capable of passing this energy through the pressure housing for downhole use or inserted through the wall for pipeline use.

74

Chapter 2

TABLE 2.1 Commercially available isotope generators

Daughter

Daughter half-life

Daughter gamma energy (MeV)

118 days

ll3mIn

103 min

0.39

132Te

77.7 hr

132I

2.3 hr

99 Mo

66 hr

99mWc

6 hr

0.14

137 Cs

27 yr

137mBa

2.6 min

0.67

280 days

68Ga

1.13 hr

0.511

Parent

Parent half-life

ll3Sn

68Ge

<0.77

Cs-137 has a 27-yr half-life and decays by ~ decay to the 2.6-min d a u g h t e r 137tuBa. Barium-137 is in secular equilibrium with the parent, hence it can be milked as frequently as desired. Cesium-137 is a commonly used downhole isotope but is always in equilibrium with its barium-137m daughter. When cesium-137 is used as a barium-137m generator, it can be milked to provide a continuous source of the 2.6-min activity for flow m e a s u r e m e n t s inside the borehole. The Ba-137m activity is reduced by a thousand in 26 min and by a million in 52 min; hence, no contamination occurs at the surface while more t h a n enough activity remains available for m e a s u r i n g flows in the borehole. The 137Cs: 137mBa generator has been reported several times (Newacheck et al., 1957; Gwyn, 1961; Turtiainen, 1986), for measuring flow rates in pipes, avoiding contamination problems downstream. These are discussed in greater detail in chapter 8 on tracer use in facilities. Measuring flow rates in the borehole should require only a pressure-shielded, remotely operated generator. Applications of isotope generators to specific oilfield problems will be pointed out in other sections as they become relevant.

Isotope dilution procedures Isotope dilution originated as a chemical technique for analyzing a specific m a t e r i a l in a mixture without having to isolate it quantitatively from the mixture. It is still used for t h a t purpose; however it is a powerful technique t h a t has m a n y other applications. It can be used to measure volumes and flow rates in both open and closed systems. It has been used to determine flow rates in pipes, streams, and estuaries, and for measuring the volume of cavities and storage vessels of unknown dimensions. The basic assumptions in isotope dilution are that the tracer is 1) conserved, 2) well mixed with the medium before measurement, and 3) ideal. Conservation

Measurements and Applications

75

of tracer is the basis for all isotope dilution methods. It can be used with either continuous or pulse injection of tracer to monitor mass, volume, or flow rate in a variety of situations, but its most important application to the oil industry is in measuring flow rates. MASS MEASUREMENTS In its original form for measuring the amount (mass) of a given material in a mixture, a radioactive isotope of known specific activity is added as a tracer for the desired component, x. The added tracer is well mixed with the material, a small amount of the mixture containing the added isotope is separated out, and its specific activity remeasured. The specific activity, am, of the tracer by itself is given by am = A/m, where A is the amount of activity in any consistent units and m is the weight in mg. The mixed material will have a specific activity of a'= A/(m + mx), where mx is the weight of x separated out with m after the tracer was added. Since the total amount of tracer, A, is unchanged, amx = a' (m + mx); hence: mx=m

(am -amx) amx

(2.10)

As an example, suppose we wish to analyze a hydrocarbon mixture for the amount of a specific hydrocarbon, HX. We can add a tritium tagged analog HX* having a specific activity, a, to the mixture. The tracer is first placed on a gas chromatographic column, the peak area noted using a suitable detector, and material from t h a t peak counted. The same thing is done with the mixed tracer material at the same position. If the initial activity, a, equals 104 cpm/mg, and if after mixing the new activity is 300 cpm in the same counting system, and the peak area represents 0.04 mg, then from Eq. (2.10), the amount of material in the gas is 0.3 rag. If the original volume of gas analyzed were 10 liters, the concentration of HX in the gas would be 0.3 ppm. This procedure is also used for monitoring trace amounts, where separation losses can be large. Although this procedure was first proposed and developed for use with radioactive isotopes, it is not restricted to radioactivity. It is a common analytical tool in mass spectroscopy using stable isotopes for isotope dilution. A n u m b e r of v a r i a n t s of this procedure have been described (Stary, 1986) for special situations. VOLUME MEASUREMENTS The specific activity of the tracer in terms of volume is given by a = A/v. If this is added to an u n k n o w n volume, after mixing the new material will have a specific activity, a ' = A/(v + v'), where v' is the amount of additional material in the mixture. Since the total amount of activity, A, does not change, the added volume, v', can be calculated in the same m a n n e r as above by:

76

v'= v

Chapter 2

(a-a') a'

(2.11)

In the case of large storage vessels a' is very much less t h a n a, therefore Eq. (2.11) reduces to v/v'= eda', so that the volume can be obtained from the ratio of specific activity before and after mixing. This method does not require a radioactive tracer but will work as well with any chemical tracer. FLOW-RATE MEASUREMENTS Flow r a t e s can be m e a s u r e d by isotope dilution using two different procedures: 1) injection of a solution containing a known concentration of tracer at a constant rate or 2) injection of a pulse containing a known total amount of tracer. The principles of the methods are given here, and details of m e a s u r e m e n t are described in chapter 8 on facilities. Its application to similar m e a s u r e m e n t s in the borehole is discussed in the section on borehole measurements in chapter 7. The volume measurements described above can be used to measure flow rates by the first method. Since tracer is conserved, then by analogy with Eq. (2.11) above, if a tracer with a known specific activity, a (in activity/unit volume), is injected into a pipeline at a constant flow rate, Q, the unknown (constant) flow rate of the pipeline, Q', is then given by Eq. (2.12), where a' is the specific activity after mixing and transport by the moving fluid, as: O ' = O (a-a') a'

(2.12)

This principle has been described (Clayton, 1966; Ljunggren, 1966) and used in a n u m b e r of procedures for accurately measuring flow rate in pipelines, rivers, and other regions of moving fluids. Flow-rate m e a s u r e m e n t s can be made using the second method by injecting a pulse of tracer containing a known amount of activity, A, and m e a s u r i n g the tracer concentration downstream after it is mixed with the flowing stream. Here, the conservation of activity is expressed as: A = J c(v) dv

(2.13)

w h e r e c(v) is the m e a s u r e d tracer concentration d o w n s t r e a m as a function of volume. The volume integral can be transformed to a time integral using J c(v) dv = Q ~ c(t)dt, where Q is the flow rate to be m e a s u r e d and c(t) is the measured concentration as a function of time. Hence: A Q = Jc(t) dt The response is measured at a point downstream where mixing is sufficient.

(2.14)

Measurements and Applications

77

Activation analysis A second nuclear technique used for analysis is activation analysis. This a method for determining the elemental composition of an unknown mixture by measuring the gamma rays emitted in response to an activation procedure, usually neutron activation. It is a rapid, nondestructive analytical procedure. The development of high-resolution gamma-ray spectroscopy has given the method an additional boost and has made multi-element analysis possible At this time, neutron activation analysis (NAA) is available to the public from a number of research reactors operated by universities, and by public and private research groups. Associated with these reactors is availability of hot laboratories, many equipped with remote handling and counting equipment. This analytical technique has not played a major role in the downstream part of the oil industry; however it has provided the base for the use of neutrons in downhole logging and for the analysis of complex gamma spectra. Most of the applications of neutrons in downhole logging are described elsewhere in the logging literature. This material is presented here as an overview of the basic process; greater detail on the use of neutrons for tracer applications will be provided in other sections. First demonstrated by Hevesy and co-workers in the late 1930's, activation analysis did not become important until large neutron fluxes became available from nuclear reactors. The procedure used is to expose the materials to a thermal neutron flux, with the concentration of each constituent obtained from the analysis of the emitted gamma radiation following the irradiation. The principles of NAA are the same as those used for producing radioactive tracers by neutron activation as given in Eq. (1.38); however the major difference lies in the need for reproducibility of conditions in order to assess accuracy of measurement. A great deal of work has gone into clarifying and eliminating sources of error (Erdtmann and Petri, 1986; Alfassi, 1990), and the method is capable of a high degree of precision and accuracy, with sensitivity in the micrograms-per-gram region. NAA is a nondestructive method widely used for multi-element trace analysis in biological and geological samples. Much of the analysis of extraterrestrial mineral specimens was done by NAA. It has been proposed for detecting nonradioactive tracers from interwell tracer tests, but it does not have the sensitivity required to be competitive with radioactive tracers. NAA is also being done by prompt gamma emission, combined chemical separation, delayed gamma emission, epithermal neutron analysis, cyclic activation analysis, pulsed neutron reactor analysis, and a host of other variants (Alfassi, 1990). In addition to NAA, many other nuclear reactions have been developed and have become routine analytical methods. Light elements such as 02, N2, F, Si, A1, etc., are quickly analyzed using 14 MeV neutrons from small generators. The availability of high-energy accelerators has added a large number of special

78

Chapter 2

analytical procedures, particularly useful in analyzing light elements such as nitrogen, oxygen, and fluorine, which are difficult to analyze by other means. The high-energy accelerators are also used to produce isotopes for special purposes, such as isotope generators.

DOSIMETRY Until now the m e a s u r e m e n t of radiation has been discussed only as a m e a n s of m e a s u r i n g the amount of radioactive material present in a source. The topic of dosimetry is concerned with the properties of the radiation field generated by the source and, in this context, with the effect of this radiation on humans. The units used to describe the radiation field and its effects are discussed below.

Dosimetry units Radioactive nuclides generate a radiation field. For g a m m a and X radiation the unit of field intensity used historically is the roentgen (R), the a m o u n t of radiation required to induce 1 electrostatic unit (esu) of charge in 1 cm 3 (.001293 grams) of dry air at s t a n d a r d t e m p e r a t u r e and pressure. The SI unit for this is the a m o u n t of radiation required to induce 1 coulomb in 1 kg. It has no name, hence by default the roentgen is still used, but it is equivalent to 2.58 x 10 -4 coulombs per kilogram (C/kg). Since m a n y old meters for monitoring exposure rate, calibrated in R/hr, are still in service, this unit may be expected to remain in use for a long time. The old unit for the a m o u n t of radiation or dose (H) absorbed by an object exposed to a radiation field is the rad, defined as the absorption of 100 ergs/gm or 0.01 joules per kilogram (J/kg) in the given material. The new SI unit is the gray (Gy), which is the absorption of 1J/kg. One Gy = 100 rad. Since 1.602 x 10 -13 J = 1 MeV, then one Gy = 6.24 x 1012 MeV/kg. The relationship between these units is given in Table 2.2. Since safety is an important consideration in the use of radiation, the effect of different kinds of radiation upon tissue must also be considered in the absorbed dose. The SI unit for the dose equivalent to correct the gray for the quality (Q), of absorbed radiation in tissue is called the sievert (Sv). It replaces the historic unit called the rem (roentgen equivalent man) (R). Because of the large i n s t r u m e n t and literature base using the old unit, both units will probably coexist for some time. New meters are also calibrated in ~tSv/hr. The units are defined as follows: Sv= GyxQ rem (R) = rad (R) x Q For X-ray, beta, and g a m m a radiation, Q is equal to 1, but for neutrons, alpha particles and other positive ions, Q>I and is a significant correction for the specific effects of radiation of different energy on tissue.

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79

TABLE 2.2 U n i t s of absorbed dose joules/kg

Gy R

1 .01

MeV/kg

ergs/gm

6.24 x 1012

104

6.24 x 1010

100

Gy 1

R 100

.01

1

Dose calculations ESTIMATED EXTERNAL DOSE FROM A POINT GAMMASOURCE The e s t i m a t i o n of dose r a t e from a source of radiation can be a complex m a t ter; however some simple procedures have evolved for e s t i m a t i n g dose in common situations. G a m m a dose r a t e s from a point source can be e s t i m a t e d from semiempirical equations and from tabulations. An isotopic point source of r a d i a t i o n in curies is r e l a t e d to the exposure rate in R/hr at 1 meter, by: CF R / h r = d2

(2.15)

w h e r e d is t h e distance from the point source in m e t e r s , a nd F is t h e exposure r a t e constant, t a b u l a t e d in Table 2.3 for some common g a m m a e m i t t e r s w h e r e C is in curies. For an exposure rate in mR]hr, C can be expressed in mCi's. As a rule of t h u m b , the exposure rate at one m e t e r can also be e s t i m a t e d from the equation: Exposure r a t e ( m R / h r ) =

6CEn d2

(2.16)

where: E = the g a m m a energy of the g a m m a ray in MeV; n = the n u m b e r of g a m m a q u a n t a per disintegration; C = the activity in mCi; d = distance from source in feet. The value for the constant changes to fit the units used for the p a r a m e t e r s of the equation. ESTIMATED INTERNAL DOSE FROM INGESTED BETA SOURCE It is commonly said t h a t pure beta e m i t t e r s such as t r i t i u m a n d carbon-14 p r e s e n t no r a d i a t i o n h a z a r d and are "safe" to use. This is not t r u e for m a t e r i a l t h a t h a s been ingested, in which case all of the beta energy is absorbed into the body. The dose received from an i n t e r n a l source of beta r a d i a t i o n such as t r i t i u m should be a n o t h e r source of concern.

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The l a r g e s t use of t r i t i u m in the oil field is in the form of t r i t i a t e d water. It would be instructive to calculate the dose r a t e in m R / h r (~Sv/hr) and the total dose received from the ingestion of 10 mCi (37 MBq) of t r i t i a t e d water. This is an i m p o r t a n t n u m b e r since 50 percent of the w a t e r enters the body t h r o u g h t h e skin. The following base is used for the calculation:

TABLE 2.3 Specific g a m m a ray constants

Nuclide Ba-133 Cs-137 / Ba-137 Cr-51 Co-57 Co-60 Ga-67 Au-192 1-131 1-132 Ir-192 Ra-226 Sc-46 Sn-ll3 Xe-133 Sb-124

F, g a m m a ray constants 2.4 3.3 0.16 0.9 13.2 1.1 2.3 2.2 11.8 4.8 8.25 10.9 1.7 0.1 9.8

1. The biological half-life of w a t e r in the body is about seven days. 2. The " s t a n d a r d " m a n weighs 75 kg (165 lb) and contains 43,000 gm of water. 3. The average energy of a t r i t i u m beta is 0.006 MeV. 4. One rad = 62.4 x 106 MeV/gm. 5. All the beta radiation is absorbed in the water. As a first step: 10 mCi 3.7 x 107dps 0.006 MeV 43000 gm x mCi x dis. = 51.6 MeV/gm sec hence: 3600 103mR 51.6 x 6 2 . 4 x 106 x rad = 3.0 mR/hr (30 ~tSv/hr)

(2.17)

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81

The retention of tritiated water in the body is controlled by its biological halflife. Compared to the short retention half-life of 7 days, the physical half-life of tritium (12.6 yr) is not significant. The average life, x, of tritium in the body is derived from the biological half-life by: 1 n ~ =~

tl/2 .693 - 10 days

The total dose within the range sources per year. The procedure say. A 2-ml urine of: 2x

(2.18)

received = 0.3 mR]hr x 24 hr/day x 10 days = 720 mR. This is of the average a m o u n t of radiation received from n a t u r a l used to monitor for ingestion of tritiated water is urine bioassample within 24 hours of ingestion should have a count rate

3.7 x 108 43000 = 1.7 x 104 counts per minute

(2.19)

Service companies are required by law to provide urine bioassays for oil company employees who may be exposed to large sources of tritiated water. The estimate of dose rate as calculated above can be generalized for any beta emitter assuming the conditions above for a standard man: Beta dose rate (mR/hr) = 50. C. E. n

(2.20)

where C is the radioactivity in mCi, E is the average beta energy in MeV, and n is the fraction of decays having that energy.

L I C E N S I N G AND C O N T R O L OF R A D I O A C T I V E M A T E R I A L The limits authorized by regulatory agencies for the safe handling of radioactive materials are based upon recommendations from two organizations: the National Council on Radiation Protection and Measurements (NCRP) in the U.S., and the International Commission on Radiological Protection (ICRP). The NCRP is an independent organization chartered by Congress, whereas the ICRP was set up by a technical society, the International Congress of Radiology. The two organizations are composed of representatives of m a n y technical societies and work closely together. Regulations setting the standards for control of exposure from the use of radioactive materials are governed by an appropriate national regulatory agency in each country. In the U.S. the situation is rather complicated. The Nuclear Regulatory Agency (NRC) and the Environmental Protection Agency (EPA) formulate the regulations. The NRC enforces the regulations together with agreement states states t h a t have taken over the regulatory function of the NRC by setting up

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an equivalent regulatory agency within their borders. Regulations covering naturally occurring radioactive material (NORM) and other nonbyproduct materials are controlled by the states, and these are quite variable. The regulations are given in Title 10 of the Code of Federal Regulations (10 CFR). Strictly speaking, these pertain only to reactor-produced isotopes. Naturally occurring isotopes and those produced by particle accelerators are controlled by the states. In practice, the NRC is concerned with any use of refined nuclides. Except for certain exemptions, all users of radioactive material must be licensed by the NRC or by an agreement state. A general license is given for the use of exempt quantities and concentrations of certain isotopes (10 CFR 30.18, 30.71 Schedule B) that excuses the user from applying for a specific license for these materials, but not from the regulations for safe use of radioactivity. The standards for safe use of radioactive materials are given in Title 10, Part 20 of the Code of Federal Regulations (10 CFR 20), and in the separate regulations derived from this code by agreement states. The pertinent regulations covering the licensing of radioactive materials for various uses are given in 10 CFR, parts 30 - 40. A license to use radionuclides is obtained from the appropriate state or federal agency upon request. It is initiated by filling out a special material license form in which the requester names the nuclides requested, their intended use, and the maximum quantities in possession at any time. The requester answers a number of questions on the ability of the users and the safe handling of the materials, including equipment handling, emergency procedures, and waste disposal. Requesters must show that they are equipped with the proper instruments for monitoring radiation dose and that they can maintain the required records. The records are important and subject to periodic review by inspectors. Recordkeeping by the users is at the heart of the radiation control system set up by the regulating authorities. This includes personnel exposure, radiation surveys, bioassay records, tracer receipts, waste disposal, history of all radioactive materials possessed by the user, and any other records required to show compliance with the regulations according to 10 CFR 20 or equivalent state regulations. Noncompliance with these requirements can result in fines and loss of license privileges. A complicated set of rules and regulations governs the transportation of radioactive materials. The transport of most of these materials falls under the Department of Transportation (DOT). The body of regulations is given under 49 CFR, parts 172 and 173. Shipment by air is covered in 49 CFR, 176 parts A-D and M, shipment by rail in 49 CFR 174, parts A-D and K. Shipment by public highway is covered in 49 CFR 177; and the pertinent DOT regulations to cover packaging, marking and labeling, placarding, monitoring, and shipping papers are found in 10 CFR 71.5. Materials classified as "limited quantities" have much simpler regulations. The amount and concentration allowed for each isotope is given in

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83

the above references. They require special marking and m u s t contain the statement "This package conforms to the conditions and limitations of 49 CFR 173.421 for excepted radioactive materials, limited quantities, N.O.S., UN4910." A level above "limited quantities" is t h a t of "low specific activity," which still is exempt from some of the packaging and shipping paper regulations.

R a d i a t i o n protection: ALARA a n d MPC At the time of writing, the U.S. is revising m a n y of its regulations for the control of radiation. The principles and the background behind the proposed regulations for radiation protection are given in the revised S t a n d a r d s for Protection Against Radiation, 10 CFR, part 20, published in the federal register for May 21, 1991. The old units for radiation and radioactivity are still used in these proposals, but the equivalent SI units are also shown in parentheses. They are worth reading for insight into the regulatory process in radiation control. These standards are essentially the same worldwide. The s t a n d a r d for radiation exposure places a limit on the m a x i m u m a n n u a l radiation dose t h a t an individual may receive. For occupationally exposed peronnel, this limit is 5 rem (50 mSv) per year. For the general public, it is reduced to 100 mR (1 mSv) per year. It is to be understood, however, t h a t the dose will be kept "as low as reasonably achievable," expressed by the acronym ALARA. The old m a x i m u m permissible concentrations (MPC) are to be replaced with a new set of numbers given in appendix B of the proposed regulations as Table 1 for occupationally exposed workers, Table 2 for unrestricted areas, and Table 3 for disposal into the sewer. The values for occupational exposure to some common waterflood tracers were abstracted from Table 1 above and appear in Table 2.4 in this chapter. For the first time, these regulations also go into detail on how the numbers were derived. The maximum permissible concentration (MPC) for unrestricted areas is widely used in calculating the a m o u n t of radioactivity to be injected in oilfield tracer tests. It is useful to u n d e r s t a n d how these n u m b e r s were arrived at and what they mean. The effluent concentrations listed in Table 2 of the appendix in the proposed regulations are equivalent to the radionuclide concentrations that, if ingested or inhaled continuously over the course of a year, would produce a total effective dose equivalent of 50 m r e m (0.5 mSv). The effluent concentration is divided into two parts, one for the limit in water and one for the limit in air. The "Annual Limit of Intake" (ALI) chosen is a factor of the chemical composition. The water limit is calculated from the ALI required to arrive at this dose. This is done by dividing the volume of water consumed in one year by the s t a n d a r d m a n by a factor of 50 to reduce the dose to 100 mR, and by an additional factor of 2 to remove age considerations.

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TABLE 2.4 M a x i m u m occupational concentrations (10 CFR 20, Appendix B, Table 1) Isotope

Class

H-3 C-14 C-14 C-14 Co-57 Co-57 Co-60 Co-60

water* CO CO2 compounds **W **Y **W **Y

Oral ingestion ALI, ~tCi 8 x 104

2 8 4 5 2

x x x x x

103 103 103 102 102

Inhalation ALI, ~tCi/ml DAC, ~Ci/ml 8 2 2 2 2 7 2 3

x x x x x x x x

104 106 105 103 103 102 102 10

2x 7x 9x 1x 4x 3x 7x I x

10 -5 10-4 10 -5 10 -6 10 -9 10 -7 10 -8 10 -8

* DAC includes skin absorption. ** ALI's a n d DAC's for aerosol with average d i a m e t e r of l~m. W = r a n g e of clearance half-times between 10 and 100 days. Y = g r e a t e r t h a n 100 days.

Table 3 of the above appendix gives the m a x i m u m permissible concentrations for disposal in sewers. It is derived from the ALI by dividing it by the a n n u a l w a t e r i n t a k e and reducing the concentration by a factor of 10. If sewage were the only source of w a t e r for th e reference m a n over one year, he would receive a c o m m i t t e d dose of 500 mR. U n d e r these conditions, presumably, ra dia tion would be a m o n g the least of his problems. T a b l e s 2 a n d 3 in th e proposed federal r e g u l a t i o n s d i s c u s s e d above a re a b s t r a c t e d in Table 2.5 using some of the t r a c e r elements t h a t are i m p o r t a n t for waterflood tracing as examples. TABLE 2.5 M a x i m u m concentrations, unrestricted areas

Isotope

Class

Table 2 Effluent concentrations Air, ~Ci/ml Water, ~Ci/ml

H-3 water* I x 10 -7 C-14 CO 2 x 10 -6 C-14 CO2 3 x 10 -7 C-14 Compounds 3 x 10 -9 Co-57 **W 4 x 10 -9 Co-57 **Y 9 x 10 -9 Co-60 **W 2 x 10 -10 Co-60 **Y 5 x i0 -11 # = average mo n th ly concentration

Table 3 Sewer release #, ~tCi/ml

I x 10 -3

1 x 10 -2

3 x 10 -5 6 x 10 -5

3 x 10 -4 6 x 104

3 x 10 -6

3 x 10 -5

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REFERENCES

Alfassi, Z.B. (ed.), Activation Analysis (2 vols.), CRC Press, Boca Raton, FL (1989). Beckman Instruments Nuclear Systems, "LS 6800, 7800, 9800 Series Liquid Scintillation Systems," Operating Manual (1985). Bennet, C.L., Beukins, R.P., Clover, M.R., Elsmore, H.E., Gove, H.E., Kilius, L., Litherland, A.E., and Purser, K.H., "Radiocarbon Dating with Electrostatic Accelerators: Dating of Milligram Samples," Science (1978) 201, 346. Bennett, E.F., and Yule, T.J., Argonne Natl. Lab. Rept. ANL7763 (1973). Birks, J.B., The Theory and Practice of Scintillation Counting, Pergamon Press, Oxford (1964). Carpenter, B.S., D'Agostino, M.D., and Yule, H.D. (eds.), "Computers in Activation Analysis and Gamma Ray Spectroscopy," Proc. Amer. Nuc. Soc. Conf., Mayaguez, PR, April 30 - May 4, 1978, DOE (1979). Clayton, C.G., and Smith, D.R., "A Comparison of Radioisotope Methods for River Flow Measurement," Proc., Symp. Radioisotopes in Hydrology, IAEA, Vienna (1963) 563. Dryak, P., Kover, P., Plechova, L., and Suran, J., "Correction for the Marinelli Geometry," J. Radioanal. Chem. (1989) 135, 4, 281. Ehmann, W.D., and Vance, D.E., Radiochemistry and Nuclear Methods of Analysis, John Wiley, New York (1991). Emery E.W., "Geiger-Mueller and Proportional Counters," in Radiation Dosimetry, Vol. II, Attix, F.E., and Roesch, W.C. (eds.), Academic Press, New York (1966). Erdtmann, G., and Petri, H., "Nuclear Activation Analysis: Fundamentals and Techniques," in Treatise on Analytical Chemistry, Elving and Kolthoff (eds.), Part 1, 14, 419, John Wiley, New York (1986). Evans, R.D., The Atomic Nucleus, Krieger, New York (1982). Friedlander, G., Kenedy, J.W., Macias, E.S., and Miller, J.M., Nuclear and Radiochemistry, 3d ed., John Wiley, New York (1981). Gwyn, J.E., "Fast Response Pulse Tests Use of Gamma Milking," Ind. Eng. Chem. (1961) 53, 908. Heath, R.L., Scintillation Spectrometry Gamma Ray Spectrum Catalogue, (2 vols.) IDO-16880 (1964). Henry, R., "Isotope Generators, Present and Future," J. Nucl. Bio. Med. (1971) 15, 105. Horrocks, D.L., Applications of Liquid Scintillation Counting, Academic Press, New York (1974).

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Hurst, G.S., Payne, M.G., Kramer, S.C., and Young, J.P., "Resonance Ion Spectroscopy and One Atom Detection," Rev. Mod. Phys. (1979) 51, 767. Knoll, G.F., Radiation Detection and Measurement, John Wiley, New York (1989). Korff, S.A., Electron and Nuclear Counters, D. Van Nostrand, New York (1955). Ljunggren, K., "Review of the Use of Radioactive Tracers for Evaluating Parameters Pertaining to the Flow of Material in Plant and Natural Systems," Proc., Symp. Radioisotopes in Hydrology, IAEA, Vienna (1963) 303. Muller, R.A., "Radioisotope Dating with Accelerators," Physics Today (1979) 32, No. 2, 23. Newacheck, R.L., Beaufait, L.J. Jr., and Anderson, E.E., "Isotope Milker Supplies 137Ba from Parent 137Cs," Nucleonics (May 1957) 15, No. 5, 122. Packard Instrument Co., "How to get the Best Results from Your Scintillation Counter," LSC Workshop Manual, 3d ed. (1982). Pilgrim, D.H., "Correction of Ratemeter Readings with Varying Count Rates for Response Time Lag," Int. J. Appl. Radiation and Isotopes (1965) 16, 461. Radiological Health Handbook, Bureau of Radiological Health, U.S. Dept. of HE&W, Superintendent of Documents, Washington, DC (1970).

RCA Photomultiplier Manual, Tech. Series PT-61, RCA Solid State Division, Electro-Optics and Devices, Lancaster, PA (1970). Schonfeld, E., Nucl. Instrum. Methods (1967) 52, 177. Spytsin, V.I., and Mikheev, N.B., "Generators for the Production of Short-lived Radioisotopes," At. Energy Rev. (1971) 9, No. 4, 787. Stary, J., "Determination Techniques Based on Radiotracers," in Treatise on Analytical Chemistry, Elving and Kolthoff (eds.), Part 1, 14, 241, John Wiley, New York (1986). Suzuki, T., Inokoshi, Y., Chisaka, H., Nakamura, T., "Optimum Geometry of Large Marinelli-type Vessels for In-situ Environmental Sample Measurements with Germanium (Lithium) Detectors," Appl. Radiat. Isot. (1987) 39, No. 3, 253-56' Thonnard, N., Willis R.D., Wright, M.C., and Davis, W.A., "Resonance Ion Spectroscopy and the Detection of 81Kr," Nuc. Instruments and Methods in Phys. Res. B (1987) 29,398. Tsoulfanidis, N., Measurement and Detection of Radiation, Hemisphere Publishing Corp., Washington, DC (1983). Turtiainen, H., "Flow Measurements with Radioactive Tracers Using the Transit Time Method," Valt. Tek. Tutkimuskeskus Tutimuksia (Aug. 1986) 421.

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Verheijke, M.L., "Calculated Efficiencies of Na(T1) Scintillation Crystals for Marinelli Beakers with Aqueous Sources," Int. J. Appl. Radiat. Isotop. (1970) 21, No. 3, 119. Wahl, J.S., "Gamma Ray Logging," Geophysics (1983) 48, No. 11, 1536. Wilkinson, D.H., Ionization Chambers and Counters, Cambridge University Press, London (1950). Yule, H.P., J. Radioanal. Chem. (1973) 15, 695.

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CHAPTER 3

INTERWELL

WATER TRACERS

INTRODUCTION The usefulness of waterflood tracers is based upon the assumption t h a t the movement of the tracer reflects the movement of the injected water. How closely this holds true depends upon how closely the tracer follows the injected water through a formation without significant loss or delay. This in turn depends upon how well the chemical composition of the tracer meets the constraints set by the properties of the formation. Radioactive isotopes are used to tag chemical tracers to provide analytical tools of high selectivity and sensitivity. The tracer properties, however, are defined only by their chemical composition. This chapter is concerned with designing and carrying out a waterflood tracer test using both radioactive and nonradioactive tracers. Information is presented on the choice and preparation of tracer materials, field injection procedures, and methods for collecting and analyzing samples of produced water for tracers. Ionexchange procedures are emphasized because of their importance in both chemical and radioactive tracers.

FUNCTIONS OF A WATERFLOODING TRACER Waterflooding and water-based floods are the most widely used secondary and tertiary oil recovery methods. The principles of waterflooding are described in most standard reservoir engineering texts and in special waterflood monographs (Craig, 1971; Wilhite, 1986). Application of the theory to field operations is hampered by a lack of detailed knowledge about the reservoir and how the fluids move through it. In cases where the water entering the field comes from m a n y different sources, managing the waterflood operation can become difficult. The addition of a tracer to the injected water is the only means of distinguishing between injection water and formation water, or between waters from different injection wells in the same field. Tracers are added to waterfloods for many reasons and in a variety of circumstances. They can be a powerful tool for describing the reservoir, investigating unexpected anomalies in flow, or verifying suspected geological barriers or flow channels. They can also be used in a test section of the field before expanding the flood. Flow in most reservoirs is anisotropic. The reservoir structures are usually layered and frequently contain significant heterogeneities leading to directional variations in the extent of flow. As a result, the m a n n e r in which water moves in the reservoir can be difficult to predict. Tracers are used in enhanced oil recovery pilot tests to monitor the actual water-flow pattern during the test.

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The ability to identify the water source is basic to the use of tracers for all the purposes described above. The tracer response as a function of position and time provides a qualitative description of fluid movement that can play a useful part in managing the flood; however it is also possible to obtain quantitative measure of water movement in the reservoir from the tracer data.

History and development An ideal water tracer must meet two requirements: it must faithfully follow the path and velocity of the water with which it is injected, and it must be easy to identify and measure quantitatively. Differences in test and operating conditions can lead to large differences in apparent tracer suitability. These differences have led to contradictory conclusions about tracer use. Tracers have a long history of use for tagging water. Suitable materials for this purpose have included everything from sticks, dyes, and mushroom spores to chemical and radioactive tracers. Early work on tracers for use in following water in streams, underground caverns, sanitary systems, ground water, and oil fields reported tests on the use of a variety of materials as water tracers. (Slichter, 1905; Fox, 1952; Kaufman and Orlob, 1956; Halevy et al., 1958; Barker et al., 1959; Skibitzke et al., 1961; Halevy et al., 1962; Weibenga et al., 1967). Tracer suitability has varied with the constraints and conditions of the tests. Tracers for streams, both open and underground, have few constraints except for environmental conditions. Tracers for following water through aquifers and for following groundwater flow are much more constrained. Various organic materials, including such compounds as dextrose, picric acid, glycine, salicylic acid, fluorescene, and a variety of alcohols, have been tested with generally poor results; tracers either did not survive or showed long delays in appearance (Greenkorn, 1961; Lansdown, 1961). Inorganic compounds such as tritiated w a t e r and simple anions such as nitrate, halides, and thiocyanate fared much better. Highly oxidized anions such as dichromate, permanganate, and borate did poorly, as did a number of cations, including radioactive isotopes. The search for water tracers for use in waterflooding oil fields followed the same p a t t e r n as the tests above. Many organic and inorganic compounds were tested (Watkins, 1957; Heemstra et al., 1961; Greenkorn, 1961). Because of differences in conditions, some of the data are contradictory, but over the years a small group of tracers has come to be regarded as generally useful for oilfield waterfloods.

Reservoir constraints The survival of tracers depends upon the nature of the oilfield reservoirs in which they are used. These reservoirs (and the materials used for standard test

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91

cores) have certain properties t h a t act as constraints on the permissible properties of the tracers. These materials generally have negatively charged surfaces and contain varying amounts of clays with high cation-exchange capacities. The reservoir environment is a reducing one and the surface-to-volume ratio of the porous medium is large. Oil, water, and gas can coexist in the reservoir, and there can be a significant population of bacteria. Successful tracers are those that are not delayed or lost by interacting with these reservoir properties. By definition, these are ideal tracers (Lake, 1990) and should be carried at the velocity of the injected water. The reservoir constraints can show up in different ways TRACER EXCHANGE Ions adsorbed on the reservoir surfaces are free to exchange with ions in solution and tend to be in equilibrium with them. This is a reversible process known as ion exchange. The negatively charged surfaces of the reservoir absorb positively charged ions by electrostatic forces. If the tracer ions are positively charged, they can exchange with the cations adsorbed on the reservoir surfaces. The small diameters of pores in the reservoir and the low velocity of most waterfloods ensure t h a t there will be a local equilibrium between the ions on the surfaces and those in the water. Tracer ions are immobile when on the surface and only move at water velocity when in the water. Depending upon the nature of the cation, there is a fixed probability that it will spend a certain fraction of time on the surface; hence, the tracer ions will be delayed relative to w a t e r passage by the fraction of time they spend on the immobile surface. The velocity of the tracer pulse containing positively charged ions will thus be lower t h a n the w a t e r velocity. If the cation is very strongly absorbed by the surface, it may become essentially immobile and entirely lose its ability to trace the water. A similar effect can occur if some of the tracer is soluble in the oil phase. The fraction of tracer in the oil will move at the velocity of the oil phase; if the oil is immobile, the tracer will be delayed relative to the water phase by the fraction of time it spends in the oil, as in the case above. If the oil phase is mobile, the situation is more complicated; however the tracer velocity will not truly reflect the velocity of the water. In either event the tracer is no longer an ideal tracer, even though ultimately it may all be produced. TRACER REACTION In the case of tracer delay, as described above for reversible ion exchange, the tracer will arrive later t h a n the water; but all of it will ultimately arrive since the tracer is conserved. In cases where exchange is irreversible, or where there is a change in chemical form as by bacterial attack or chemical reaction, some or all of the tracer may never be produced with the water. In this case, the tracer is not conserved and is no longer ideal, even though a reduced tracer pulse may arrive without apparent delay.

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Tracer materials t h a t lose solubility or react chemically with the ions in solution are also undesirable for the above reasons. Thus, carbonate and sulfate ions, which can react to form insoluble precipitates with m a n y common reservoir ions, are undesirable tracers unless the latter are absent from the reservoir. The use of radioactive cobalt and cesium as cations for w a t e r tracing was recently reported (Wood, 1989). Cesium-134 and -137 and cobalt-57 and -60 used as cations, with and without ethylenediamine tetraacetic acid (EDTA) as a complexing agent, were injected into a small waterflood pilot in a carbonate reservoir. In the case of carbonate reservoirs, however, the charge on the surfaces depends upon the pH of the formation water. If the surfaces were negatively charged they would become anion exchangers, and cations r a t h e r t h a n anionic tracers would be required. If the clay content is low, such cationic tracers would be suitable. The only other report of injections of cationic tracers in the literature (Asga~pour, 1987, 1988) showed no tracer response (except for tritiated water) aider two years. TRACER MATERIALSFOR INTERWELLUSE While ideal tracers are desirable, there are many situations in which nonideal tracers are adequate for flow description. In the case of fracture paths, where surface-to-volume ratios are relatively low and velocities are r a t h e r large, dyes may be satisfactory indicators even if some of the dye is lost by absorption on the reservoir. If the only purpose of the tracer is to indicate the source and direction of flow through the reservoir, as to identify sealing or conducting faults, a small delay in tracer arrival may not be important and can be ignored. A long delay, however, may result in undue dilution of tracer, making detection difficult. The delay may also imply a nonexistent flow behavior and should be avoided. In general, tracers for waterfloods should be ideal. They should be anionic or neutral materials t h a t are totally water soluble and do not react chemically or physically with other materials in the reservoir. This precludes the use of cations, large, polarizable molecules such as dyes, or easily reduced or reactive materials. Materials that are extractable into the oil, have a high vapor pressure, or are subject to bacterial attack should also be avoided.

R a d i o a c t i v e a n d u n t a g g e d c h e m i c a l tracers There is a widespread misconception that "chemical" and radioactive tracers are different kinds of tracers. In fact, all waterflood tracers are compounds having specific chemical properties. Radioactive isotopes can be used to tag some of the compounds that have proven to be suitable for this purpose. This provides these compounds with a highly selective and sensitive analytical method. While we refer to them as radioactive tracers, it is important to remember t h a t they are radioactively tagged chemical tracers. The same materials without a radioactive tag are also useful tracers.

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93

Except for the nitrate and bromide ions all waterflood tracers in current use can be tagged with radioactive isotopes. There is no radioactive isotope of suitable half-life for either the nitrate or bromide tracers. The use of radioactivity provides a very sensitive analytical method for detecting and m e a s u r i n g waterflood tracers. In addition, it almost doubles the tracers available for use, because the detection limit for radioactive tracers is sufficiently lower t h a n t h a t for the chemical itself that tracers rarely interfere with chemical analysis. The discussion of waterflood tracers in this section will begin with radioactively tagged tracers, taking into consideration their chemical nature. It will be followed by a discussion of the analytical problems and procedures specific to nonradioactive tracers.

RADIOACTIVELY TAGGED TRACERS FOR WATERFLOODS R a d i o a c t i v e t r a c e r s a v a i l a b l e for field use

The n u m b e r of radioactive tracers suitable for use as waterflood tracers is severely limited by two factors: the tracer must have the chemical properties required to survive the environment, and it m u s t have nuclear properties t h a t m a k e it suitable for monitoring. As a result, only a m a x i m u m of four nuclides combined in only three different chemical forms are currently used for waterflood tracing. In m a n y cases the number of tracers listed below is adequate; however m u l t i p l e - p a t t e r n floods can place a severe strain on the n u m b e r of applicable tracers. The current list of radioactive waterflood tracers with a good history of success in the field is limited to the materials in Table 3.1. Comments appear in the literature from time to time suggesting t h a t various tracers are not "ideal" because of properties that alter their path from t h a t of the injected water. Such comments argue t h a t tritiated water, for example, can lose tritium to the reservoir by exchange with hydrogen ions in connate w a t e r or with other fixed sources of hydrogen ions. Similar arguments are made t h a t anionic tracers move "faster" t h a n neutral tracers because they are excluded from the connate w a t e r layer by their negative charge. Many other such comments are passed on by word of mouth. At present there is no quantitative evidence of any significant differences in field behavior among the common tracers. Virtually all easily available radioactive nuclides of practical half-life are either cationic or otherwise unsuitable for tracing water. Many field and lab tests have, however, established such ions as thiocyanate and hexacyanocobaltate as stable anionic carriers for the normally cationic cobalt isotopes and for 14C. Many tests using these tracers have been carried out in oilfield waterfloods throughout the world.

94

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TABLE 3.1 Radioactive interwell water tracers Compound (ion)

Formula

Radioactive Isotope

Hexacyanocobaltate

Co(CN) 6-

60Co, 58Co, 57Co, 14C

Tritiated Water

HTO

3H

Thiocyanate

SCN-

14C, 35S

Halides

Cl-, I-

36C1' 125I

Alcohols

CnH2nOH

3H, 14C

HEXACYANOCOBALTATEIONS The hexacyanocobaltate ion is a very stable ion with a formation constant of about 1038. It was first introduced as a groundwater tracer (Halevy et al., 1958) and is now widely used as a cobalt isotope carrier throughout the world. It is, however, currently prohibited in the British sector of the North Sea because of some accidents in which the tracer (Co-60) remained in the well tubing following injection in a well on a North Sea platform. Although the reasons for this are not known, errors in the preparation of the compound are suspected. This author has been involved in more than thirty waterfloods in the continental United States and Alaska in which Co-60 was injected as the hexacyano complex. In all of these, the surface tubing was monitored until the count rate returned to background, and no evidence of tubing contamination was found. Similar results were noted in a recent paper, where no cobalt-60 contamination was reported after logging the wells (Lichtenberger, 1989). This material should, however, always be tested before injection to ensure that it is an anionic complex. Hexacyanocobaltate can be used as a carrier for the two cobalt nuclides as well as for carbon-14. Cobalt-60 undergoes beta decay with a 5.3-yr half-life and the emission of two high-energy gamma rays (1.17, 1.13 MeV) per beta. It can be monitored in a 3-in. diameter Nal well counter with an efficiency of about 60 percent. Cobalt-57 decays by electron capture with a 9-mo half-life, and can be counted with good efficiency (>90 percent) in a Nal well counter. Both nuclides undergo beta decay and can also be counted in a liquid scintillation counter with more than 90 percent efficiency. TRITIATED WATER Tritiated water has the longest history of use as an oilfield tracer. It differs from conventional water in that it contains hydrogen of mass 3 instead of mass 1. Its chemical properties are otherwise identical; however a kinetic effect is noted due to the relatively large mass difference between the two hydrogen isotopes.

Interwell Water Tracers

95

Although this is not sufficient to affect the use of tritiated w a t e r as a w a t e r tracer, the difference in rate constants is sufficient to allow enrichment of tritium in w a t e r by electrolysis. Tritium undergoes beta decay with a half-life of about 12.7 years. It emits beta particles of very low energy and no g a m m a radiation, hence it presents virtually no external radiation hazard. Tritiated w a t e r has a biological half-life of about a week in the body. The low energy of the beta requires internal counting by liquid scintillation. It can be counted directly in a 50 percent mixture of produced brines with about 25 percent efficiency. The figure of m e r i t can be significantly increased by distilling off the w a t e r sample before counting it. OTHER ANIONIC COMPLEXES Despite the success of the complex cobalt cyanide as a waterflood tracer, the only other complex anions proposed in the literature are the chelating complexes of e t h y l e n e d i a m i n e tetraacetic acid (EDTA) and its analogs (Watkins et al., 1962), using radioactive cations. They have not had a high success rate in oilfield practice because of exchange with other cations in solutions t h a t form stronger complexes and/or are far more numerous. The areas of use would depend on the presence and concentration of competing divalent ions such as Ca++ t h a t form strong complexes in solution. Iridium-192 has been proposed as the (IrC16) -3 ion, a complex t h a t has not been successful with use in normal brine solution. A n u m b e r of complex cyanides are potential candidates for tracing waterfloods: the dicyanoaurate (Au(CN)2)-2, the dicyanomercuric, and the t e t r a c y a n o n i c k e l a t e complexes have formation constants on the order of 10 40 and merit investigation. The dicyanoaurate has been tested successfully (Thatcher and Ramsey, 1977) as a g r o u n d w a t e r tracer; however no reports on the use of these or other complex cyanides for waterflood tracing have been found in the literature. The 186-day half-life gold-195 and 100-yr half-life nickel-63 isotopes would be suitable for tagging these complexes. The hexacyanocobaltates seem to have been successful cobalt tracers; however in view of the aforementioned problems reported in the North Sea, an effort should be made to find additional gamma-emitting tracers. SPECIALTY TRACERS A n u m b e r of specialty radioactive tracers have been reported and used for waterfloods, including short-lived anions such as the 8-day half-life 1-131. Shortlived isotopes are useful where injection response is relatively fast, as in a suspected fracture or thief zone. As a rough rule of thumb, they can be used for periods up to six times the half-life before handling and analytical problems become too great. Chlorine-36 is a m a n m a d e isotope having a half-life of 3.5x105 years. It is quite expensive to make because of its long half-life; however it can be detected in very small quantities by atom counting as described in chapter 2, using accelerator mass spectrometry.

96

Chapter 3

Several reports have been published on the use of tagged alcohols as water tracers. All the simple alcohols partition into oil and are subject to bacterial attack, the partition coefficients increasing with carbon number. For methanol the effect is negligible (Wood et al., 1990), and for ethanol the partition is quite small; however for propyl alcohol and the higher-carbon n u m b e r alcohols the effect of partition is quite noticeable. For tracer tests in which identification of the source of the water is the only objective, this may not be significant; otherwise alcohol will lag the waterfront. In general the odd carbon number alcohols are more resistant to bacterial attack than the even-numbered ones. Some of the alcohols, such as isopropyl and tertiary butyl, are particularly resistant and can serve as biocides. If there is a high concentration of a naturally occurring isotope in the formation water, it can serve as a carrier, allowing otherwise unusable ions to serve as tracer, e.g., naturally occurring strontium ions in solution for 90Sr. The tracer will be carried by the mass effect of the naturally occurring strontium isotopes in solution, reducing the lag. In the case of strontium, the exchange of 90Sr with the natural strontium isotopes on the reservoir surface in the formation still causes a significant lag. Tests performed in the North Slope of Alaska showed a significant delay in the arrival of Sr-90 over that of tritiated water, despite the presence of strontium ion in the produced water (Loder, 1992). The use of 22Na has been proposed (Bjornsted et al., 1990) on a similar basis using a sensitive analytical method for 22Na. In very saline brines it may, however, be possible to eliminate much of the lag by a sufficiently high concentration of the naturally occurring sodium isotope. The water volumes involved in most waterfloods are large, so that dilution of the injected tracers is extensive and sensitive methods of analysis are required. The high cost of labor precludes the use of m a n y chemical manipulations for analyzing samples. Therefore, the tracers chosen should be easily analyzed using automatic or semiautomatic methods of high sensitivity and selectivity. Radioactive materials are uniquely suited to this purpose, since the combination of suitable chemical form and specific radiation properties provides both high sensitivity and selectivity. In addition, radiation monitoring lends itself to automatic counting operations. Generally, analysis of these compounds should use a separation scheme t h a t accomplishes as much of the analysis as possible by direct counting. Many p a t t e r n floods can be followed using only four different tracers, although occasionally more are needed to avoid ambiguity. In some patterns, two or three tracers may be sufficient to provide unambiguous answers.

Tracer quality control Remarkably little quality control is exerted in the sale of waterflood tracers. The stated quality and quantity of the tracers provided are usually accepted at

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97

face value. Few people seek evidence of either radiochemical purity or amount. There have been many cases of error in these factors, and failed tracer projects have been attributed to such errors (Omoregie et al., 1987). At the current state of waterflood tracing, two kinds of companies are usually involved in a field tracer injection, each licensed separately: the supplier who provides the material in the correct chemical form and activity to the service company; and the service company that injects the material in the field and deals with the client. Quality control is minimal; often the service company supplies the tracer design, injects the tracers, and provides the tracer response data to the client. In other cases, the client may design the test and analyze the water for produced tracer, while the service company acquires the tracer and does the field injection. Testing to verify how much of each tracer was injected or whether the right tracer was supplied is rarely done. In the preparation of specialty organic compounds labeled with radioactivity, it is conventional for the supplier to provide data such as radiochromatograms showing that the compound is properly labeled and contains the correct amount of radioactivity. Such evidence should also be requested for waterflood tracers The best way to verify the actual quality and q u a n t i t y of a tracer is by analysis of an aliquot of the batch of tracer material to be injected. In this context, an aliquot is a small, measured volume of the actual tracer solution shipped for field injection. This aliquot can be analyzed by the supplier, the service company, the user, or an independent laboratory. The principal source for an independent laboratory is either a university with a nuclear engineering d e p a r t m e n t or a government laboratory. In the United States, a n u m b e r of universities with nuclear engineering d e p a r t m e n t s (Shirley, 1988) m a i n t a i n research reactors and laboratories t h a t are available for such purposes. The National Laboratories, most of which were originally nuclear laboratories, may also be suitable sources for tracer analyses. Proper verification should establish the isotopic purity and a m o u n t of activity provided, and t h a t the isotope is attached to the desired chemical form. This is particularly i m p o r t a n t for the hexacyanocobaltates. It is quite possible, for example, to have cobalt-60 in a solution of the hexacyanocobaltate w i t h o u t the hexacyano complex being radioactive or the cobalt-60 being in the desired complex form. The chemical form of the cobalt can only be monitored in the laboratory. A simple test for the radioactive hexacyanocobaltate is to pass a small a m o u n t t h r o u g h a cation exchanger in series with an anion exchanger. The material should pass through the cation exchanger but be counted on the anion exchanger, and the g a m m a spectrum should show only Co-60 present. Even if nothing is done to verify the isotopic composition in advance of the injection, it is still possible to verify it after the fact on samples of wash water t a k e n from the injector. Very little tracer is required to make such a test; the service company doing the injection can easily save a few milliliters of the

98

Chapter 3

washings for this purpose. In view of the North Sea problems with Co-60 tagged hexacyanocobaltate, it would be a wise thing to do for this tracer. Any laboratory capable of handling even small amounts of radioactivity can do the ion exchange test indicated in the previous paragraph.

Tracer preparation The p r e p a r a t i o n of field quantities of tracer for waterflood tracing is a specialized area. Most service companies or users of these tracers will never be involved in the preparation. It is nevertheless of some importance to be aware of the preparation procedures in current use. Preparation of any of the tracers used for waterflood tracing must be done in a suitably licensed laboratory by personnel trained in the safe use of radiochemical procedures. Both the preparation and the transport of these materials require governmental approval. In the United States this may involve several agencies. TRITIATED WATER Tritiated water is available as a byproduct of nuclear reactor operation from m a n y sources in the USA and abroad. It can also be made from the oxidation of t r i t i u m gas (HT) over certain hot metal oxides, supported platinum, or other catalysts. Copper oxide pellets at about 850~ are commonly used. Hightemperature alloys are required for containing the hot copper oxide pellets. HEXACYANOCOBALTATES The hexacyanocobaltates are prepared by oxidation of the cobaltous ion to the cobaltic form in the presence of excess cyanide solution (Fernelius, 1946). Some heat is required; the synthesis can start with metallic (elemental) cobalt wires or pellets. The isotope is normally produced by irradiation of cobalt-59 in a nuclear reactor by the (n,T) reaction. The elemental cobalt is first dissolved in aqua regia to form cobaltous chloride and the excess acid removed. The Co-60 tagged cobaltous chloride is also available commercially. Cobalt-57 is made in an accelerator by the (p,a) reaction on nickel-60, as discussed in chapter 2. It is generally more costly than neutron-produced isotopes because of the high cost of accelerator operation. The reaction of cobalt-60 or cobalt-57 (*Co) tagged cobaltous chloride with cyanide to form the complex ion is a two-step process. In the first step, the cobalt reacts with the cyanide to form insoluble cobaltous cyanide: *Co ++ + 2 C N ' = *Co(CN)2

(3.1)

In the second step, the precipitated cobaltous cyanide is further treated with an excess of cyanide and the solution is then heated to form the complex cyanide. In this process, the cobalt is oxidized to the plus three state (cobaltic), with the

Interwell Water Tracers

99

appearance of a yellow color typical of the complex, and water is reduced with the elimination of hydrogen as a gas. The complete reaction is given by: 2*Co(CN)2 + 2 H 2 0 + 8KCN = 2K3*Co(CN)6 + H2 + 2KOH

(3.2)

The reaction can be performed in a single step combining steps one and two, usually in the presence of ammonia. THIOCYANATE ION The thiocyanate ion is formed by the direct reaction of elemental sulfur with a cyanide salt in the presence of heat. The reaction is given as: KCN + S = KSCN

(3.3)

The carbon-14 tagged thiocyanate is prepared with carbon-14 tagged cyanide. The sulfur-35 tagged compound is prepared using tagged sulfur. Both tagged cyanide and tagged elemental sulfur are commonly available. FIELD TRACER VERIFICATION Some verification procedures can be performed in the field or at the service company laboratory. Tritium or carbon-14 sources, for example, should never be associated with penetrating g a m m a radiation, however some x-radiation may be present from large sources in thin-walled vessels. For multi-curie tritiated water sources, the b r e m s s t r a h l u n g g e n e r a t e d by the t r i t i u m betas is sufficient to permit m e a s u r e m e n t of the x-rays through a glass or a l u m i n u m ampoule. This can be m e a s u r e d by the vendor or service company through a glass ampoule or before it is transferred to a steel transport vessel for shipment and injection at the field. Carbon-14 tagged compounds of field strength can usually be monitored in the field by m e a n s of the b r e m s s t r a h l u n g generated through the steel tubing. A detector calibrated for the tubing used is needed for quantitative measurements. The supplier should provide radiochemical evidence t h a t the tagged compound has the correct chemical and radioactive composition. The hexacyanocobaltate ion can be purchased from several suppliers and the a m o u n t of tracer present can be monitored externally, depending on the cobalt isotope used. Cobalt-57 is a low energy e m i t t e r and can only be monitored t h r o u g h t h i n shielding. Cobalt-60 emits high-energy r a d i a t i o n b u t can be monitored through relatively thick shielding using a survey m e t e r calibrated in suitable units. A reasonable estimate of any g a m m a - e m i t t e r activity can be obtained from the equation for a point source of activity using the g a m m a factor to estimate the amount of radioactivity required to emit m e a s u r e d radiation for the thickness of lead shielding and distance of m e a s u r e m e n t . This is shown in Eq. (3.4) for a survey meter calibrated in mR/hr. In this equation, F is the g a m m a factor, h is the thickness of lead shielding expressed in the n u m b e r of half-value thicknesses, and d is the distance in meters from the survey m e t e r to the source.

100

Chapter 3

Values for F and h for some common tracers were given in Table 2.3; more extensive tables are available from s t a n d a r d handbooks (CRC). For Co-60 the half value thickness (h) is 0.5 in. and the g a m m a factor, F, is 1.32 mR/hr per meter per millicurie. F(2) h R (mR]hr) = d2 (3.4) Unshielded cobalt-60 sources can emit dangerous levels of radioactivity and should only be handled in a properly equipped laboratory t h a t meets government regulations. The chemical form of the cobalt can only be monitored in the laboratory from an aliquot as discussed earlier. TRACER INJECTION PROCEDURES Radioactive tracers generally come in small packages. Even for giant fields, the required tracer volume rarely exceeds a few milliliters. This makes shielding and shipping easier for g a m m a emitters; it also makes pulse injection of tracers easy to accomplish. Mixing with injection w a t e r in the borehole and in the formation near the wellbore ensures that the tracer is mixed in much more t h a n a small pulse. When a continuous tracer injection is desired, the mechanics of injection and of travel through the formation smoothes the pulses out enough t h a t periodic small pulses cannot be distinguished from a single continuous pulse at the production wells. The output from a pulse injection of tracer gives the same information as t h a t from the tracer front produced by a continuous injection of tracer, since the former is the differential of the latter. The pulse injection is, however, much easier and cheaper to perform, and the data are easier to analyze. Because of the very high specific activity of tracers used for waterfloods, it is important to avoid spills of concentrated tracer. Except for emergencies, concent r a t e d radioactive tracers in open containers should be handled only in laboratories designed for this purpose under controlled conditions. The i m p o r t a n t safety and handling procedures for field injection have been covered in chapter 2, including some factors specific to tritiated water tracing. In the early days of waterflood tracing, it was common to transfer the concentrated tracer from a container to the injection well by hand. Hypodermic syringes were a common means of transfer, but direct pouring or pumping of the tracer from an open container was also used. As the activity of the injected tracer quantities increased, these procedures were largely replaced by methods t h a t eliminated the handling of open sources at the field. These can be divided into two types. In one, the tracer is transported to the field in a suitably shielded, sealed glass vial. The glass vial is then transferred by hand to a breaking tool at the injection well. The tool assembly is pressure tested at the desired pressure, the vial is broken, and the contents are flushed into the injection stream. The advantage of this method is t h a t the small size of the vial allows reduced shielding volumes

Interwell Water Tracers

101

to be used. The disadvantage lies in the exposure of personnel to radiation during the transfer of the vial from the shielded container to the breaker tool, as well as the danger of breakage by dropping the vial during transfer, thus releasing concentrated tracer solutions at the field site. The second method used to transfer water tracers into an injection well uses the shipping container as a transfer cylinder, which avoids tracer handling by personnel at the field. The shipping container is designed and tested as a transfer cylinder under oilfield pressure and temperature conditions. It is fitted with inlet and outlet valves, and usually with suitable check valves to prevent backflow. A typical setup is shown schematically in Fig. 3.1. The container (shielded as necessary) is connected to the injection stream at its downstream end, while the u p s t r e a m end is connected to a pressurized water source. The water source may be obtained from the injection stream by suitable valving (as shown here) or from an external source such as a clean water supply or a pump truck. The system is tested under pressure for leaks and the tracer injected by opening proper valves. Many combinations of valves and gauges are possible. Simple strain gauges are often used for pressure measuring since they are easy to decontaminate. The advantage to this method is t h a t it avoids h a n d l i n g concentrated tracer solutions in the field, reducing the possibility of radiation exposure and the chance of releasing dangerous quantities of radioactivity in the field. This is probably the safer method and for beta emitters and low-energy g a m m a emitters such as 57Co or 125I, it is often the method of choice. The disadvantage is t h a t the larger size container requires much more shielding when used with high-energy gamma emitters such as 60Co.

{~

ressuretes

Pressuregauge

0o

s

~Tracer InjectionValve or Orifice 'rl' out ~ 0 Injectionline ~'~X

Figure 3.1. Waterflood tracer injector

~ water ~ ,n Water flow 0

102

Chapter 3

Sinker bar

Shear pin

Crushing rod Tracer vial Temporary seal Flow ports

S

~-'~, I

Collar stop

Figure 3.2. Wireline tracer injector Service companies vary in their systems for delivering and injecting tracers. One fixes the tracers in a gel and uses a piston drive to inject the gelled tracer through high-pressure grease fittings. One oil company (Wood et al., 1989) t r a n s fers the tracer vial to a piston-driven breaker on a wireline. The vial and the piston assembly are placed down hole, flow is started, and the vial mechanically s m a s h e d opposite a desired interval. Packers are used to divert flow from unwanted zones. This process is illustrated in Fig. 3.2. O t h e r special procedures have been devised for special circumstances. A special procedure was devised for injecting a curie (37 GBq) of 24Na (half-life = 15 hours) in a special steam pilot test. In this case 24Na was produced in a swimming pool reactor at a university by an (n,~) reaction on 23NaOH. The irradiated vial, which was fitted with a septum, was transferred to a shielded container at the reactor and t r a n s p o r t e d to the field location by truck. A hydraulic piston containing two hypodermic needles was driven through the septum at the well location and the tracer injected into the well by passing injection w a t e r through the vial by way of the needles. The injection was performed at slightly higher t h a n atmospheric pressure. Tritiated w a t e r is considered to be one of the safest tracers to handle because of its very low radiation energy and its short residence time in the body. While t h e r e is no radiation danger associated with tritium, open sources pose an

Interwell Water Tracers

103

ingestion hazard, particularly in enclosed areas, t h a t is not shared with nonvolatile water tracers. Tritiated water vapor enters the body through the skin as well as by mouth and nose, and large amounts of tritiated water in the body can provide an instant internal dose of radiation that can do damage. Such undiluted sources should never be opened in an enclosed space except in a properly designed laboratory.

Field t r a c e r design The design of a field tracer test has two components: a tracer part and an analytical part. The tracer component includes choosing the tracers for each well, 'estimating the required amount of each activity, dealing with the regulations and the plan for acquisition and injection of the tracers into the ground. The analytical part includes selecting an analytical strategy, setting up a sampling schedule, and determining the detection limits of the tracer materials. The amount of radioactive tracer required for a field test is governed by two limits: 1) sensitivity of detection at the lower limit and 2) m a x i m u m permissible concentration (MPC: defined in chapter 2) at the upper limit. In order to exceed the lower limit but not the upper, one must therefore estimate by how much the injected tracer will be diluted when it is produced. In fields with large reservoir volumes the cost of tracer materials can impose an upper limit well below the MPC. There are two methods in current use for determining how much tracer m u s t be added to meet these limits. The most widely used method is the total dilution model, which is discussed below. An alternate method is based upon a model originally proposed by Brigham and Smith (1964) and since modified by Abbaszadeh and Brigham (Abbaszadeh-Dehgani, 1982). A detailed discussion of this method, written by Dr. Abbaszadeh, is given in the appendix of this volume. TOTAL DILUTION FIELD TRACER This method estimates an average concentration of produced tracer on the a s s u m p t i o n t h a t the injected tracer is uniformly diluted by the entire swept water volume when it is produced. This is the most widely used method and is discussed below. The rule of t h u m b most commonly used in the field is to assume t h a t the injected tracer will be diluted by the total volume of water displaced in the flow pattern. Sufficient tracer is added to ensure detection at this concentration. The peak tracer concentration is presumed to lie well above the average. The first part of the calculation is to estimate an anticipated dilution volume. This volume is obtained by calculating the water-filled pore volume between the injector and the s u r r o u n d i n g producing wells. Radial geometry is generally assumed for regular patterns, but it is usually modified by any known reservoir

104

Chapter 3

conditions, such as large permeability differences between strata, known flow channels or barriers, odd pattern geometry, etc. This dilution volume is an estimate that, when used intelligently, has given consistent results in a wide variety of field situations. The smallest injection pulse required is usually the amount of tracer needed to produce an average concentration of 10 times the minimum detection limit in this dilution volume. Since in most cases produced water is reinjected into brine- and oil-filled formations in the ground, no legal problem arises with exceeding the m a x i m u m permissible concentration (MPC); however the convenience of being able to handle freely and ship the produced water samples makes this a practical requirement. Therefore, the maximum concentration in the produced water should be less than the MPC. To ensure that the produced tracer concentration will not exceed this number, the smallest dilution volume required to meet the MPC is calculated. This is considered a worst-case scenario and should not exceed a few percent of the estimated dilution volume for the entire pattern. The anticipated dilution volume, Vd, can be calculated from pertinent reservoir data as above, using a radial approximation to the pattern geometry. Line floods and odd p a t t e r n floods may require different geometries, as do special geologic features. If r is the distance from injector to producers, ~ is the porosity of the formation, h is its thickness, and Sw is the water saturation, then the swept volume for a radial approximation to the area is given by: Vd = nr2hSw@

(3.5)

The sensitivity of detection for a radioactive isotope is calculated from the instrumental background with no tracer present, as given by Eq. (2.3), for a geometry factor of one. It is a measure of the signal-to-noise ratio arrived at from purely statistical considerations. The m i n i m u m detection l i m i t (MDL) is the calculated value at two s t a n d a r d deviations and is usually quoted as the 95 percent confidence level (see chapter 2). The m i n i m u m tracer activity, A, required to exceed 10 x the MDL is given by: A > 10 x M D L x V d = 2 0 ~ EtV s

xV d

(3.6)

where Cb is the background count for counting time, t, E is the counting efficiency of the detector for this isotope, Vs is the sample volume, and Vd is the dilution volume of the reservoir. The proposed MPC for some of the common waterflood tracers is discussed in chapter 2 and given in tables 2.4 and 2.5. There is usually at least an additional order of magnitude between the m a x i m u m produced tracer concentration and the MPC.

Interwell Water Tracers

105

ABBASZADEH-BRIGHAM MODEL This model, which is discussed in the appendix, is introduced here only for purposes of comparison. It assumes a mechanism of tracer transport in which the injected tracer pulse moves through the formation by convective and dispersive forces, arriving at the s u r r o u n d i n g producers according to the s t r e a m l i n e s generated by the geometry of the flow pattern. The tracer arriving at the producers is diluted by untagged water arriving under other streamlines. This model treats heterogeneity by dividing the reservoir into a set of homogeneous layers. The injected tracer is distributed among these layers according to their respective conductivities (kh). These tracer pulses, moving independently through each of these layers, mix at the borehole to generate the tracer-response curve. A computer program uses the thickness and permeability of each layer and the pattern geometry to estimate the amount of injected tracer required to produce a desired maximum tracer concentration. Equivalently, a heterogeneity index such as the Dykstra-Parsons coefficient can be used to generate pseudolayers for design of a tracer test. TRACER ANALYSES:SENSITIVITY, DYNAMICRANGE, AND SELECTIVITY

Sensitivity The m i n i m u m detection limit (MDL) is a measure of the sensitivity of the counting system. It is a m e a s u r e of the signal-to-noise (s/n) ratio, fixed by constraints in the counter and by the background radiation level (noise). As shown in Eq. (3.6), the factors controlling the MDL are ~]Cb / (EtVs). The background count, C b, the counting efficiency, E, and the counting time, t, are generally fixed to minimize the MDL at normal operating conditions. The easiest constraint to change is the volume of sample counted, V s . This volume cannot exceed the sensitive volume of the counter, but the tracer it contains can be increased by concentrating the tracer. Enriching the tracer in the counting sample has the same effect as increasing the sample volume, Vs. If the tracer in a liter of collected sample can be concentrated into a one-ml counting volume, this is an enhancement factor of 1000 in the term Vs, since it is equivalent to counting a sample 1000 times its size. As environmental concerns have increased and costs of m a n y tracer materials have risen in recent years, pressure has mounted to decrease the a m o u n t of radioactivity used. Tracer enrichment, which reduces the a m o u n t of tracer prepared, is the most influential factor in this decrease, but decreasing the noise level in the counter (low level counting), and increasing the counting efficiency can also help. The sensitive volume of the liquid scintillation counters used for counting most waterflood tracers is determined by the volume of the counting vial used. Most common is the 20-ml scintillation vial. Commercial scintillation cocktails will accept up to 50 percent produced brine, depending upon salinity; however,

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the counting efficiency, E, decreases (particularly for tritium) as the percentage of water in the vial increases. The volume of water accepted is the sample volume, Vs. If smaller vials are used, the detection limit is lowered because a lower counting volume results in a lower background. If larger vials are used, the counting efficiency can be increased by lowering the percentage of water in the cocktail while increasing the sample volume. A number of choices are involved in maximizing the sensitivity for any given set of tracers. No strong advantage is gained by reducing the sample volumes below the minimum counting volume of the instrument. The sensitive volumes of gamma counters are limited by the size of the well in the NaI scintillation well crystals used in automatic gamma counters. This limits the size of the ion exchange column used for retaining gamma-emitting tracers. As above, increasing the enrichment factor is the best way of lowering the detection limit.

Dynamic range One of the important characteristics of a tracer is its dynamic range. This is the ratio of m a x i m u m acceptable tracer concentration to m i n i m u m detection limit (MDL). The greater the dynamic range, the greater the reservoir distance over which the tracer can be monitored. High initial tracer amounts are normally needed in order to detect tracers in wells very far from the injector. Unfortunately, the dynamic range of most tracers is quite low, and the injection of high initial amounts would cause unacceptably high levels of tracer activity at the close wells. This is true for chemical as well as radioactive tracers. Because of the upper limit for an acceptable tracer concentration at the closest wells, the only way to increase the dynamic range is to decrease the minimum detection limit. The importance of dynamic range is hidden by the often erroneous belief t h a t the individual patterns in a waterflood are all balanced. Normally, only enough tracer is injected for comfortable detection of the tracer at the closest producers. In practice the actual flow often goes outside the marked pattern. In large, multipattern fields, tracer is often detected beyond the pattern boundary; however, the concentrations are usually so low and sporadic that results cannot be quantified. This is a major cause of a low apparent material balance for the tracer. Material balance is i m p o r t a n t if the tracer response is to be used for q u a n t i t a t i v e measure ments. Lack of a material balance also prevents a true picture of how the injected water in the pattern is being distributed. The m a x i m u m produced tracer concentration is limited by external factors such as cost, as well as the MPC in unrestricted areas. The lower limit is set by the statistics of counting; however there is no arbitrary limit to the enrichment permitted in the effective volume Vs. Since the maximum concentration is fixed by outside constraints, sample enrichment is the most effective way to increase the dynamic range of a tracer. Contamination with naturally occurring tritium

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and carbon-14 in surface water may place an ultimate limit to useful enrichment of these isotopes. Many methods are available for enriching the produced w a t e r in the common waterflood tracers listed above. Tritiated w a t e r is not commonly enriched because of its relatively low cost and its high MPC in unrestricted areas (electrolytic enrichment of tritiated water is available). The major problem with tracer enrichment is the difficulty of doing it in a cost-effective manner. E n r i c h m e n t is commonly used for all the tracers discussed here with the exception of tritiated water.

Selectivity A second factor in the analysis of field water samples for tracer is selectivity. A gamma- or beta-sensitive counter can resolve the respective tracers according to their energy; however the two kinds of activity must be counted separately to avoid counting g a m m a emission associated with beta rays. A good analytical scheme will separate beta- from gamma-emitting tracers. The separated activities are then placed in suitable counters t h a t can take advantage of the energy discrimination in each section. Carbon-14 and tritium are low-energy beta emitters. They can be counted simultaneously in a liquid scintillation counter (LSC) using beta energy discrimination to separate their activities. Likewise, Cobalt-57 and cobalt-60 can be counted simultaneously in a NaI well counter by g a m m a energy discrimination. Since a waterflood sample may have all four tracers, a scheme for separating gamma- and beta-sensitive components from each other will provide good selectivity since the characteristic energies are suitably separated and are characterized in each group. Ideally, separation and enhancement would be carried out in the same step.

Analytical strategies In tracer tests involving several tracers and multiwell patterns, analytical costs can equal or exceed the cost of acquiring and injecting the tracers. As a result, the analytical strategy chosen will affect the cost as well as the design of the field test. A poorly chosen analytical strategy can result in the p r e m a t u r e termination of the test. There are m a n y ways of separating and enriching different ionic species, including precipitation, volatilization, distillation, extraction, and a host of other methods. Enrichment, group separations, and energy discrimination can, however, become quite labor intensive. If a significant amount of bench work m u s t be done to achieve these ends, the cost for analysis of a large a r r a y of field samples can become prohibitive. The availability of automatic liquid scintillation counters and g a m m a counters makes the counting and energy discrimination much less labor intensive.

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Continuous separation schemes such as liquid chromatography with ion exchange resins are usually less labor intensive t h a n batch methods. They are also good methods for combining group separation with isotope enrichment. This procedure has wide application to the separations of chemical as well as radioactively tagged tracers. The concept of ion exchange is also important in the interaction of aqueous solutions with the reservoir. ION EXCHANGE CHROMATOGRAPHY Almost all w a t e r solutes used as water tracers are anions and undergo ionic reactions. Ion exchange is the reversible exchange of ions (of the same sign) between a mobile solution and a stationary (solid) phase. The ions m u s t be able to transfer freely between phases. Ion exchange is a property of m a n y earth materials, including soil; and as a consequence it causes problems in finding tracer for following ground w a t e r movement. The significance of ion exchange for w a t e r tracers was discussed earlier in this chapter. It accounts for the loss of tracer and the delay in arrival due to interactions of nonideal tracers with the reservoir surfaces. In addition, there are m a n m a d e ion exchange materials that are used to separate and isolate ions for analytical purposes. The word chromatography comes from its early association with the separation of solutes t h a t moved through a stationary column in colored bands. Chrom a t o g r a p h y is named according to the mobile phase used: if the mobile phase is liquid it is called liquid chromatography (LC); if the mobile phase is a gas, the term gas chromatography (GC) is used. In this chapter we will be concerned only with liquid chromatography. Ion-exchange chromatography refers here to a procedure for analyzing a mixture of ions in solution. The chromatographic system is composed of a column containing a stationary ion-exchange phase, a mobile phase with a system for delivering it, and a detector with a recorder. The chromatographic process consists of passing the solution (mobile phase) through the column, allowing the solutes to distribute themselves between the stationary and mobile phases, according to how strongly molecular forces bind the solute in each phase. A suitable mobile phase is used to move the solutes through the column. Since solutes move only w h e n t h e y are in the mobile phase, each solute will move at a r a t e depending on the fraction of time it spends in the mobile phase. If no other forces were involved, solutes having different residence times on the column would move through the system in discrete bands. In practice, the bands spread out as they move because of the finite time required for the solute to transfer between phases. The solutes, separated according to their affinity for the column, are t r a n s p o r t e d by the mobile phase to the detector, which is sensitive to the ion concentration.

Applications to tracers Although the basic principles are the same, there is a significant difference between ion-exchange chromatography used for the separation and analysis of

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u n t a g g e d ions and its use for separation and e n r i c h m e n t of radiotracers. Analytical s t r a t e g y in the use of liquid c h r o m a t o g r a p h y for nonradioactive tracers is geared to the analysis of very small-volume (microliter) water samples using high-performance liquid chromatography (HPLC). The procedure used for analysis of ions in aqueous solution is known as ion chromatography (IC). Detection methods for individual tracer ions are specific rather t h a n universal and, while tracer enrichment can be done, it is not a normal r e q u i r e m e n t of the methods. Application of ion exchange to the analysis of nonradioactive tracers will be discussed in a later section of this chapter. Analytical strategy in the use of chromatography for radioactive waterflood tracers is designed to separate a very dilute solution of radioactive ions from large-volume (liter) water samples of relatively high ionic strength. The method of detection is a general procedure of high selectivity and sensitivity. The operational strategy here is how best to combine the enrichment and separation procedures with the counting procedures for maximum sensitivity and to do so in a cost-effective manner. This application of ion-exchange chromatography can be identified as "classical" chromatography, compared to "ion" chromatography as practiced in the analysis of nonradioactive ions. CLASSICAL LIQUID CHROMATOGRAPHY

Background ClaSsical chromatography reached its peak during the period of the Manh a t t a n Project, leading to and following the development of the atomic bomb and the nuclear power reactors. An enormous amount of work was done on the ion exchange separation of inorganic ions in aqueous solution by liquid chromatography. Much of the chemistry of the transuranic elements was elucidated using these techniques. Separations of materials such as the rare earths, which had taken years of fractional crystallization to accomplish, were now performed in hours. Virtually all the possible inorganic ions were examined in this manner, m a n y in the form of anionic complexes (Krause and Nelson, 1956; Nelson et al., 1960). Radioactive counting was used as a universal monitor for the species under study. Ion separations were performed by passing an aqueous solution of ions through a glass column packed with ion-exchange beads. Columns were typically about a centimeter in diameter. A typical column and response curve is shown in Fig. 3.3. The column shown in part A is a glass tube 1 to 2 centimeters in diameter, with a frit at the bottom to hold the ion-exchange beads. A solution of ions flows through the column by gravity under atmospheric pressure. The ions are separated as shown by the response curve in part B of the figure. Fluid volumes are usually in the order of hundreds of milliliters. The ion-exchange beads used for this purpose are porous, spherical particles composed of organic polymers with various degrees of cross linking. The polymers contain covalently bonded acidic or basic functional groups t h a t serve as

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exchange sites. Acid groups such as the (SO3H) sulphonic acid group result in strong-acid cation-exchangers. Alkaline groups such as the quaternary ammonium group form strong base anion-exchange sites. These beads have high ion-exchange capacities, in the order of milli-equivalent/gram. Other groups, some with lower acidity or alkalinity, are used for intermediate strength exchangers. Beads are hydrophilic and readily take up water with considerable swelling. The higher the cross linking of the polymer, the lower the swelling, the higher the selectivity for different ions, and the slower the rate of diffusion in the bead.

A. Ion exchange column

B. Ion exchange response

Solution

8 9~ 2 4OO Volume ml.

Figure 3.3. Separation of ions by an ion-exchange column.

Distribution coefficients and ion selectivities Tracer ions in solution will freely exchange with the ions on the exchanger. The strength with which a given ion is bound to the ion-exchange resin in equilibrium with the solution is given by its distribution coefficient, Kd. This is the ratio of the equilibrium concentration of the ion on the exchanger to that in the solution. If a solution of tracer ions is passed through the column of ion-exchange beads, the tracer ions will move down the column at a rate depending, among other things, on the Kd for the tracer ion. The tracer ions will move at a lower rate than that of the flowing solution, since the ions are mobile only when they are not on the ion exchanger. The produced tracer pulse will also be broader than

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the injected pulse because of dispersion and the delay in transfer of ions between mobile and immobile sites. If the Kd is very high, the tracer ions can effectively become immobile, as they will spend virtually all of their time on the exchanger. Different distribution coefficients for each of the species result in an order of selectivity for separation of the ions. In addition, the higher the charge on the ion, the more tightly it is bound to the ion exchanger, and the longer its residence time on the column. This procedure can be used to collect and concentrate ions from solution. For ions that have a high degree of selectivity for the resin, high enrichments can be achieved by passing large volumes of dilute ion solutions through small-volume ion-exchange columns. This is the procedure described earlier for collecting hexacyanocobaltates from produced w a t e r in waterflood tracing. These trivalent ions are very firmly bound by the resin and thus easily concentrated on a small column. The strong base anion-exchange resins are good concentrators for such anions as SCN', as well as Co(CN6) ~3. The collected cobalt activity is counted by inserting the entire column in a NaI(T1) well counter. Typically, such wells will accept a column 1/2 in. in diameter by 2 in. long. Automatic gamma counters can accept large numbers of tubes for computer-controlled analysis. These tubes fit into special racks, which are passed into the counter. Such counters have, in effect, 100 percent geometry and can simultaneously count multiple isotopes such as 57Co and 60Co with high efficiency by using energy discrimination to separate them.

Ion separation Ideally, the ion exchangers used for this purpose should be highly selective for a single tracer ion and effectively t r a n s p a r e n t to all other tracers, which would allow a high degree of enrichment for each tracer with no interference from other tracers. Unfortunately, this is not common. At the very least, it is necessary to s e p a r a t e the g a m m a - e m i t t i n g tracers from the beta emitters. If beta- and g a m m a - e m i t t i n g tracers are absorbed on the same column, they m u s t be separated to allow the beta emitters to be counted without interference from beta radiation also emitted by the gamma-emitting isotopes. Soft beta-emitting carriers such as carbon-14 tagged thiocyanate ion should be removed from the column and collected in a volume of solution small enough to fit the sensitive volume of the liquid scintillation counter. A liter sample of produced water can easily be separated into a small volume of resin containing the cobalt isotopes for gamma counting and a volume of solution containing the thiocyanate. The process of removing an ion from the resin column by passing an ionic solution t h r o u g h it is called elution and the solution used referred to as the eluent. The process consists of replacing the tracer anion, A, on the column by exchanging it with a replacing anion, B, from solution. If the subscript r refers to ions on the resin, s refers to ions in solution, m is the charge carried by B, and n is the charge carried by A; then the exchange reaction can be written as:

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mA r + nB s = mA s + nB r

(3.7)

If [A] and [B] are the molar concentrations of the respective species, the equilibrium constant for the reaction can be written as: KB A

=

[A]rm[B]n [A ]sTM [B]n

= s

(3.8)

This is a measure of the selectivity of the resin for one ion over another, known as the selectivity coefficient, S. The number depends on a multitude of experimental conditions and is usually supplied by the manufacturer for many of the common ions. Generally, selectivity increases with cross-linking of the resin. Perchloric acid is the customary eluent for the thiocyanate and hexacyanocobaltate ions. The problem with eluting strongly adsorbed tracers from such columns is that the eluted volumes tend to be large in classical ion-exchange chromatography. The band of tracer ions spreads as it moves down the column, producing a diluted solution of tracer. If the produced tracer volume is larger than the sensitive volume of the LSC's, there will be a loss of enrichment. The increased solution volume arises from dispersion induced by delay in the exchange of the tracer ions in the stationary phase with those in the mobile phase. It can be reduced by reducing the flow rate of the eluent through the column, by increasing the ionic strength of the eluting solution, or by using displacing ions of higher selectivity. When two strongly absorbed anions need to be separated, specific chemical reactions must be used to differentiate them. Some of the procedures developed for high-performance liquid chromatography (HPLC) and discussed in the section on chemical tracers can be useful here. In addition to the ion-exchange resins and procedures discussed above, there are special-function organic resins such as chelating resins that preferentially sequester divalent cations. Some inorganic ion exchangers (Qureshi and Varney, 1991) composed of hydrous oxides and phosphates of some of the group 3, 4, and 5 elements are highly selective for some aqueous ions. These can be anionic or cationic, depending upon the pH of the solution. In the years since the Manhattan Project, a number of new ion-exchange procedures and types of ionexchange materials have been developed (Walton and Rocklin, 1989). New ionexchange materials with highly specific ion characteristics were found, and new developments continue to be announced annually. An annual review volume of Analytical Chemistry devoted to new developments in analytical methods includes a section on ion-exchange chromatography (Analytical Chemistry, July 1992). New ion-exchange procedures have been developed for anion separation and concentration. Many have great potential in radioactive tracer applications, including such methods as ligand exchange, ion pair chromatography, ion exclusion

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c h r o m a t o g r a p h y and the combinations of column c h r o m a t o g r a p h y with liquid extraction. The original work done on the nuclear projects monitored radioactivity as a universal detector. This is still the most sensitive of all universal methods. For nonradioactive materials, they were reduced to using time-consuming wet chemical methods for detection and analysis. New universal detection methods t h a t do not require radioactivity have since come into being and will be discussed under nonradioactive tracers in this chapter.

Other procedures Beta emitting tracers t h a t are absorbed on an ion-exchange column can also be counted by placing the resin in a liquid scintillation counter (LSC) with some loss of sensitivity, depending on the beta energy. In addition to the chromatographic methods described above, much work was also done on other separation processes such as liquid-liquid extraction. The Carbon-14 tagged SCN" ion can be separated by extraction as a complex thiocyanate using tributyl phosphate and a cation such as Zn +2, which forms suitable thiocyanate complexes. The complex is extracted into a small volume of toluene, which is counted at high efficiency in a liquid scintillation counter. Tritiated w a t e r is the cheapest and safest of the tracers to work with and normally does not require enrichment. The m i n i m u m detection limit (MDL) for tritiated w a t e r in a modern liquid scintillation counter is about 20 Bq/liter. The only s e p a r a t i o n procedure commonly used for t r i t i a t e d w a t e r is distillation, usually performed in a simple side-arm flask with air cooling. It can increase counting efficiency and reduce interference from naturally occurring radioactive material. The low concentration at which the other isotopes are used keeps them from interfering with the direct counting of tritium. Sensitivities (MDL) in the order of 0.1 Bq/liter are easily achieved for the other nuclides using the enrichments described above. Other strategies are available for both the chemistry and the counting procedures, depending upon the particular isotopes used and equipment available. Cobalt-60 or other g a m m a emitters can be counted directly in a Marinelli beaker or similar arrangement. The high resolution of germanium diode counters allows energy discrimination between many different g a m m a emitters in the same sample without separation. This is not as sensitive as the enrichment procedures. Other continuous separation methods are not dependent on ion-exchange resins. Even such simple methods as batch distillation and extraction can be made to work in these schemes without becoming too labor intensive. The design of a tracer test for a waterflood depends on two laboratory functions: the analytical method used and the MDL achieved in the laboratory. Tracer costs depend heavily on the analytical strategy t h a t is chosen.

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NONRADIOACTIVELY TAGGED TRACERS FOR WATERFLOODS The n u m b e r of field-tested tracers with a successful track record for use in waterfloods is limited to those listed in Table 3.1. These are the halide ions, n i t r a t e ion, thiocyanate ion, hexacyanocobaltate ions, and isotopically tagged water. Other tracers could be used in this application, but a literature search has revealed no reports of successful use. Unlike radioactive tracers, the detection methods and analytical procedures used for chemical analysis are quite variable. It is not possible in a book of this size to adequately cover all of these procedures; however the major procedures will be described, and suitable references provided. Waterflood tracing is one of the areas in which untagged chemical tracers are competitive with radioactively tagged tracers. The difference is t h a t the need to find a suitable radioactive nuclide is now replaced by the need for a suitable analytical method. In the following discussion, the term chemical tracer will be used for nonradioactive tracer, while recognizing that radioactive tracers are also chemical in nature. Most of the tracer tests reported in the literature use at least some chemical tracers, generally in small pilot floods. The greatest problem with the use of chemical tracers in large waterfloods lies in the very large amounts of materials required. The only way to reduce this is by lowering the detection limit. New analytical methods are constantly lowering the minimum detection limit (MDL) for potential tracer materials. The problem is still one of finding materials with a low MDL t h a t can survive the reservoir and follow the velocity path of the w a t e r front. Most of the principles for design of a chemical tracer test are not different from those for a radioactive tracer test, except t h a t our u n d e r s t a n d i n g of the MDL is somewhat different; however one factor in chemical tracer use t h a t is not usually important in radioactive tracers is the natural occurrence of some tracer materials in the environment. If it exceeds the MDL for the tracer, the natural concentration in the produced water must replace the MDL in the tracer design equation. Radioactive tracers are monitored by counting the radiation emitted, and the error in counting is obtained from purely statistical considerations, based upon a binomial distribution. For these tracers the net count rate m e a s u r e d is also a m e a s u r e of the variance (Chapter 2) of the count rate. The error in the determination of zero count rate is the estimate of minimum detection limit (MDL); errors involved in handling and analyzing the samples are not included. In the instrum e n t a l methods used to measure chemical tracers, the estimate of error is not obtained from the m e a s u r e m e n t itself but must be determined independently. This is important, since most of the analytical procedures required are performed by laboratories outside the control of the people designing the tracer test. In any tracer design we should know the MDL and how it is derived. In addition, we m u s t know the fraction of active (measurable) material in the tracer, the actual

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volume m e a s u r e d by the instrument, the kind of s t a n d a r d s used, and how they relate to the tracers dissolved in produced water. One advantage to dealing with radioactive tracers is t h a t the analytical procedures and detection methods are very similar. In dealing with nonradioactive tracers, the situation is much more complex. The past two decades have seen a tremendous expansion in analytical methods. Many new analytical tools have become available whose impact is just beginning to be felt. Much of this work is reported in special interest and analytical journals. Some reviews are available and will be referenced here, but the scope of analytical methods is too great for an adequate review in the present work. Analytical methods are greatly affected by other materials in solution. Successful analysis of a tracer in a specific produced water sample does not ensure equal success in a produced water sample of a different composition. Given good analytical data, the required amount of tracer material needed, Ws, can be calculated by following the procedure of Eq. (3.2) but changing the p a r a m e t e r s as needed. If Ms is the molecular weight of the tracer compound, Ma is the molecular weight of the active tracer material, n is the number of moles of active material per mole of m a t e r i a l used, and MDL is the m i n i m u m detectable limit, expressed as a weight of active tracer per unit volume of produced water, then: MS

Ws = n x Maa x (MDL) x V d

(3.9)

It is interesting to see how this calculation compares with the results from the Brigham Smith model. In the pilot flood discussed by Brigham and Smith (1964), the tracer was injected in a bounded 2lie-acre five-spot. The pore volume within this inverted five-spot is given by the product of area x thickness x porosity x w a t e r saturation. Since this is a bounded five-spot, the area is t h a t of the square bounded by the producers, which are 331 ft apart. Using the given porosity of 0.26, the water saturation of 0.55, and a thickness of 12 ft, the dilution volume is calculated from Eq. (3.3) as 5.33 x 106 liters. Assuming a density of one for the water, the addition of 91 moles (200 lb) of ammonium thiocyanate results in a concentration of 19 ppm. This is a reasonable estimate of the average concentration in the produced response curve. In another paper, Wagner (1974) reports 240,000 lb of a m m o n i u m nitrate inected into a p a t t e r n flood in Canada. The p a t t e r n pore volume is given as 50 million bbl. Converting these numbers to an average concentration in ppm results in a value of 75 ppm, in agreement with the author's comment t h a t this was far more t h a n needed. Even at a cost of $2.00/lb, and neglecting freight and handling costs, this was an expensive tracer test. Chemical tracers available

As indicated earlier, nitrate, thiocyanate, bromide, and iodide ions have been the most successful of the inorganic tracers. The best analytical method for these

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anions at this time is ion chromatography, which is capable, with suitable detectors, of monitoring most common anions at a minimum detection limit (MDL) of about 25 ppb (parts per billion) in the presence of a 5 percent brine solution. This can, however, vary with the ions in solution and must be tested for the brine in actual use. Nitrate is the cheapest of the tracers; ammonium nitrate contains the highest fraction of tracer per unit weight of material and is the most efficient form for any of these tracers. Widely used as a fertilizer, ammonium nitrate can also be a powerful explosive when mixed with m a n y organic compounds and m u s t be t r e a t e d with care. It seems to be quite safe in aqueous solution. There m a y also be a problem due to a relatively high nitrate background frequently found in produced water. If the n a t u r a l nitrate concentration in the produced w a t e r is 500 ppb, this concentration replaces the MDL, and the weight of tracer material required (10 x MDL) is 1026 kg or 2250 pounds per million barrels. For a p a t t e r n exceeding 10 million barrels in volume, this can become a logistics problem. Iodide and, to a lesser extent, bromide have been successfully used as w a t e r tracers, even though both are considerably more expensive t h a n nitrate or thio cyanate. The radioactive tracers described previously use the hexacyanocobaltate complex ion to carry the cobalt isotopes as well as carbon-14. The cobalt isotopes are used only in sub-micro quantities. Newer methods now enable us to m e a s u r e nonradioactive cobalt in the nanogram region leading to concentrations in the ppb (parts per billion) range. The analytical combination of ICP/MS (inductively coupled plasma/mass spectroscopy) can detect m a n y of the transition elements (including cobalt) at the ppb level, in the absence of interferences. Most of these interferences are cationic and can be removed by taking advantage of the fact t h a t the cobalt tracer is anionic. Absorbing the tracer on an anion-exchange resin allows the tracer to be separated from the cations and enriched; alternatively the cations can all be removed by a cation exchanger, leaving the anionic complex in solution. Chemical tracers appear to offer a cheap alternative to radioactive tracers. In small pilot operations, this is probably true, since the small reservoir volumes require relatively small amounts of tracer and allow the use of simple, inexpensive analytical procedures. For large, multiwell pattern fields, however, the large amounts of tracer required with even highly sensitive analytical methods are expensive, and sensitive analytical methods are at least as costly as radiochemical methods.

Potential tracers

The point has been made previously in these pages t h a t most of the organic tracers tested for waterflood tracing have not survived the reservoir environment. There exist, however, organic materials t h a t do look promising for use as

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water tracers. These are strongly acid perfluorinated compounds (organic compounds in which all the hydrogens have been replaced by fluorine), including such species as trifluoracetic acid (TFA). This strong acid exists in solution as the trifluoracetate ion. It is a bactericide that does not appear to extract into oil, is stable under reservoir conditions, and can be monitored by IC with the usual sensitivity for anions. Unlike many fluorinated compounds, it has no special sensitivity for electron capture detection. Many of the perfluoro compounds are currently drawing interest as groundwater tracers. These compounds can be separated and detected with high sensitivity (ppb) by ion chromatography, as shown in the next section. It is difficult to predict the success of such tracers for oilfield use. These are large molecules with significant aromatic character whose behavior as waterflood tracers will depend on how much they partition (if at all) into the oil phase, their absorption on the reservoir surfaces, and how well they can be measured in produced brine of high ionic strength. They should be tested for oilfield use. The complex cyanides of several of the transition metals are unusually stable and should be investigated for use as tracers. The dicyanoaurate complex ion, (Au(CN)2) , and the tetracyanonickelate complex ion, (Ni(CN) -24), both have stability constants in excess of 10 40 and should be suitable for this purpose. The gold complex has been tested successfully as a groundwater tracer (Thatcher and Ramsey, 1977). It should also be detectable at the parts-per-trillion level by ICP or by the combination with mass spectrometry. All the alcohols except methanol partition into oil; these should not be used except where residence time is not important. While isopropyl alcohol is relatively resistant to bacterial attack, many of the alcohols are not and m a y be degraded during use. They should not be considered ideal tracers. The importance of knowing the minimum detection limit (MDL) for the tracer in the actual produced water used cannot be overemphasized. The MDL for a chemical tracer is site-specific and dependent upon the ionic s t r e n g t h of the produced water, as well as on other interferences in the water. It is also strongly dependent on the analytical laboratory, the analytical procedure used, and probably the analyst as well. This is particularly important when using new or relatively untested tracers.

Analytical methods In dealing with radioactive tracers, the primary analytical need was to separate and concentrate low levels of tracer ions in the presence of high concentrations of other ions. Sample size was usually measured in liters, and radiation counting was the universal detection method. In dealing with nonradioactive tracers, the analytical needs are for high-resolution separation and detection sensitivity. Sample size is measured in microliters (~tL), typically about 50~L.

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The high sensitivity arises from narrow, sharply resolved separations and lowvolume detectors, which results in high peak concentrations at very low noise levels. A preconcentration step is sometimes required to keep tracer quantities at manageable levels; however sample volumes for this are in the milliliter rather than the liter range. Procedures for enrichments beyond the normal range are discussed later in this chapter. Analytical methods are constantly changing, driven by changes in other technologies. Currently the method of choice for the anions used in waterflood tracing, such as nitrate, thiocyanate, and the halides, is ion chromatography (IC). This is a liquid chromatographic method using ion-exchange resins. Until the development of IC, there were no sensitive general methods for anion analysis. This development has opened the doors to the use of chemical tracers in waterfloods. The equipment and time required for making measurements at the ppb level indicated above are comparable in cost to those used for monitoring radioactive tracers. The classical colorimetric methods are cheaper but at a cost of two orders of magnitude in sensitivity. It is important for any designer of tracer tests using chemical tracers to understand the limitations in the methods m in particular, to know the detection limits for the procedures used. A brief description of ion chromatography is given below. ION CHROMATOGRAPHY Ion chromatography is the application of high-performance liquid chromatography (HPLC) to the separation and analysis of inorganic ions in aqueous solution. In an earlier section we described the application of liquid chromatography (LC) with ion-exchange resins to the separation of ions in aqueous solution. These separations required low flow rates, and the ions were eluted in broad, dilute bands. Since all the early work was done with radioactive species, radioactive counters served as universal monitors. In working with nonradioactive ions, separate chemical methods were required for each ion. In the period following these developments, operating procedures changed to meet the burgeoning needs of the biomedical profession. This led to the development of HPLC, which resulted in much higher resolution in the separation of materials by liquid chromatography. The analytical application of high-performance liquid chromatography is based upon the same considerations as classical chromatography. It requires a column containing a stationary phase, an automatic detection system, and a system for delivering the mobile phase. The operational characteristics of the two are, however, very different. For HPLC, the stationary phase is optimized to reduce band spreading as much as possible, and the column carefully packed with very small, micrometer-sized particles of low solute exchange capacities, to improve the mass-transfer rate. Column diameters are kept small (millimeters) for the same reason. High pressure operation is generally required in order to have reasonable flow through the system.

Interwell Water Tracers

119

The mobile phase, which transports the solute through the column, is chosen to enhance the separation of solutes by the stationary phase and to be compatible with the detector. The flow rate of the mobile phase is usually computer controlled and can be programmed for a variety of operations including variable flow rates and variable composition. Many detectors of different sensitivities and selectivity are available that can generate a chromatogram showing a peak for each solute according to its arrival time. The solutes are identified by the arrival time of the peaks and the concentrations obtained from the peak areas. Both of these require calibration of the chromatogram with known standards. By going to such narrow, closely packed columns with very small-diameter beads of uniform size and low exchange capacity, it was possible to obtain sharp separations in a relatively short time. New ion-exchange materials were developed for this purpose: in particular, ion-exchange beads with capacity limited to a small, porous layer at the surface. Such columns, well packed to prevent voids, required pressure differences of several thousand pounds per square inch to maintain the desired flow rates. The development of a universal, sensitive ion detector coupled with the optimized system described above resulted in the first general, sensitive, analytical method for nonradioactive aqueous ions. Such a procedure was first reported by Small et al. (1975), using new ion-exchange materials of low capacity. In this work, conductivity served as a universal monitor; the conductivity of the ions eluted from the column was monitored while the conductivity of all other ions was suppressed by adding a second column that reacted with the ions from the eluting agent to form nonconducting compounds. This resulted in high sensitivity because of the high concentration of ions in very narrow bands and the low level of background interference. A schematic of the equipment is discussed below and shown in Fig. 3.4. The chromatographs used for analytical separations are far more complex than the simple schematic shown. These very sophisticated, relatively expensive instruments are usually based on computers that permit very precise control of both the eluting fluids and the fluid movement in the column. Despite, or perhaps because of, the complexity of the controls, the sensitivity and precision of the results are very dependent upon the ability of the analyst. Fig. 3.4 demonstrates the principle of ion chromatography and the resultant analysis of a mixture of anions in a dilute aqueous solution. In this case, the sample is placed on the anion-exchange column and eluted with a strong solution of NaOH. The samples are small, usually in the 50 to 100~tL range. The anionexchange column separates the anions according to their distribution coefficients, resulting in the formation of the sodium salts of these ions, e.g., NaC1, NaBr, NaNO3, etc., in the presence of large amounts of NaOH. The solution is then passed through a suppresser column containing a cation-exchanger in the hydrogen form. This converts the sodium salts to the acids HC1, HBr, and HNO3,

120

Chapter 3

but converts the excess NaOH eluent to water. Thus, the conductivities of the anions are enhanced by the exchange of hydrogen for sodium ions. The background conductivity is reduced to a very low number by converting the hydroxide ion to water. This detection method is restricted to salts of relatively strong acids whose ionization constant is less than 10 -7 (pK less than 7). For weak acids such as HSCN, where pK > 7, other systems or detectors are used. An example of typical anionic analysis by IC is shown in Fig. 3.5 (Small, 1981).

Sample

in~

/Pump ~ Eluent (NaOH) J "<--Anion exchangecolumn ~--Cation exchangecolumn

Conductivitcell y Sau~ple

Figure 3.4. Ion chromatograph schematic The minimum detection limit (MDL) for the ions measured by this procedure is often undefined. Since it is a measure of the ability of the detector to distinguish between signal and system noise, it can be defined in terms of a signal-tonoise (s/n) ratio. This is an important parameter in determining the "zero" level of tracer in the field, and a suitable s/n ratio should be demonstrated by the analyst. The minimal s/n limit should be at least three times the average amplitudes of signal to noise. A number of variations and addenda have accrued since the method was first proposed by Small; however the principles have not changed significantly. Hollow fiber suppressers and membrane suppressers that can be continuously regenerated have replaced the suppresser column. Nonsuppresser methods (singlecolumn) using high pK eluent solutions to replace anions (Gjerde et al., 1979) have been developed and are now widely used, particularly for low pK materials.

Interwell Water Tracers

121

New ion-exchange resins and packings are replacing older ones and new, highersensitivity detection methods have been developed. The limit of detection for most common anions in most oilfield brines is now in the 25 to 50 ppb (part per billion) range. For produced waters of high ionic strengths, this limit may be an order of magnitude higher; however a precolumn t r e a t m e n t can often reduce such interferences.

F 0.-

Cl

HPO~."

SO -

minutes

Figure 3.5. Anion separation and analysis by IC Current detection methods for ion chromatography can be divided into three classes: 1) electrochemical methods, including amperometric, potentiometric, and conductimetric procedures; 2) spectroscopy, which includes ultraviolet/visible absorbance, refractive index, fluorescence, and atomic absorption/emission; and 3) postcolumn reactions, which use a secondary reaction to monitor tracer response. Miniaturization of detection volume, driven by other analytical needs, has resulted in sensitive volumes in the microliter region. Ultraviolet spectra are used for detecting many common tracer ions such as iodide, bromide, and nitrate ions with high sensitivity. Specific ion electrodes and potentiometric detectors are used for single-ion detection, with sensitivities in the ppb region. Postcolumn reactions usually involve addition of color-forming agents, but other procedures are possible. Many books and review articles have been written on detectors for liquid chromatography (Scott, 1986; Vickrey, 1983). Detector development is a

122

Chapter 3

very active field, and current reviews are found in the analytical chemistry literature. A number of specialized methods have been used successfully to separate anions with a very high affinity for anion-exchange resins. These include some anions with water-tracing potential, such as iodide, thiocyanate, and metal cyanide complexes. In gradient elution, the concentration of the eluting solution increases with time as it passes through the column. The ion makeup of the solution may be altered as well. Most modern chromatographs can be programmed to do this in a reproducible manner. In mobile phase ion chromatography (MPIC), a quaternary ammonium hydroxide such as tetrabutyl-ammonium hydroxide (TBAOH) is added to the eluent to provide a cation, which interacts with the anions to be measured, forming ion pairs that are eluted from the column. The column used for this kind of separation need not have ion-exchange properties. The eluent usually contains dielectric modifiers such as acetonitrile. The separation and elution of several complex cyanides in the presence of 40 percent acetonitrile (Hilton and Haddad, 1986) is demonstrated in Fig. 3.6. The composition of those complex cyanides that may be of interest as tracers is indicated on the figure. A different approach for eluting iodide and thiocyanate from an ion-exchange column uses eluents of high ionic strength, measuring the concentrations using both ultraviolet absorption and amperometric detection (Ito and Sunahara, 1990). The authors reported a detection limit of 5 ppb for both ions with amperometric detection based on a 100~tL sample and at a s/n of 2. Similar results were reported for the UV detection. A number of polyfluorinated aromatic compounds have been tested for use as groundwater tracers (Bowman, 1984; Bowman & Rice, 1986; Hydro Geo Chem, 1986) but have not been reported as waterflood tracers. These are all strong acids and should be completely anionic at reservoir temperatures. In particular, the" pentafluorobenzoate (PFBA), meta-trifluoromethylbenzoate (m-TFMBA), and the tetrafluorophthalate (TFPA) have shown good resistance to adsorption and to biological degradation in underground tests for periods of up to two years. They can be analyzed with good selectivity and sensitivity by ion chromatography. An example of such analysis using ultraviolet absorption at 205 nm for detection is shown in Fig. 3.7 (Bowman, 1984). This analysis includes several other ions, such as iodide, thiocyanate, and bromide, which are useful for waterflood tracing. Ion chromatography is an active field that is changing and growing to fit the needs of a number of widely different technologies. It is not possible in this text to adequately cover all the ways in which ion chromatography can be used, but a large body of literature details new methods of analysis. References giving extensive reviews are Smith, 1988; Shpigum and Zolotov, 1988; Small, 1989; Gjerde and Fritz, 1986; Walton and Rocklin, 1989; Haddad and Jackson, 1990).

123

Interwell Water Tracers

Ag(CN)2

~[li]

Co(CN)"3 [6

Au(CN)~ / .p~[ll]

i

ll]

|

,

20

lO

o

q

30

i

40

Time, min.

Figure 3.6. Separation of complex cyanides

.< fn II

~"0" 3.~ E:

rn

LI- LI_ i < o ~

mc~

2-

~1o !

Time, minutes

2's

Figure 3.7. Separation of perfluoro and other anions by IC

124

Chapter 3

The aforementioned annual review issue of Analytical Chemistry also covers new developments in IC. MINIMUM DETECTION LIMITS The dynamic range of a tracer was defined earlier as the ratio of the minim u m detection limit (MDL) to the maximum permissible concentration (MPC). For chemical tracers the MPC is fixed by two factors: cost and interference. The injection of even relatively cheap chemicals becomes costly if large quantities m u s t be dealt with, and very high injected concentrations may have a deleterious effect in the reservoir. The best way to increase the distance over which a tracer can be tracked is to lower its detection limit. A way to visualize this is to consider a hypothetical, multi-pattern five-spot waterflood in which the distance between injector and detector is 1000 ft; the average formation thickness is 50 ft; the porosity, ~, is 0.25; and the w a t e r saturation, Sw, is 50 percent. The tracer quantities required to produce 10 times the detection limit (MDL) at the closest wells were calculated using Eq. (3.6). Tracer for detection at wells outside the pattern at twice the distance from the producer will also be diluted by the additional volume of water due to the added distance, plus water from other injection wells; hence an additional factor of 10 is needed to detect the tracer at these wells. The results are shown in Table 3.2. Detection limits were chosen to correspond to values expected from different laboratory situations for a one molar saline oilfield brine. A commercial laboratory using s t a n d a r d methods should achieve a sensitivity of about 1 ppm. Such a laboratory using some special methods can reduce this to between 20 and 50 ppb. To achieve a sensitivity of 1 ppb or below requires additional method development. The sensitivity of m e a s u r e m e n t by ion chromatography (IC) is limited by a n u m b e r of factors. For general methods and universal detectors, a rough rule of t h u m b places a limit of about 1 ppm as indicated above. To go beyond this, special procedures are required. These can be divided into three classes: 1) using large injection volumes; 2) preconcentration of the sample; and 3) special analytical methods. Sample enrichment can be obtained because it is possible to inject relatively large volumes into an ion chromatograph without loss of chromatographic efficiency. A 2-ml sample injected in place of a standard 100-~tl sample can result in an enrichment factor of about 20, all other things being equal. This can be increased by a factor of 10 or more by using columns of high ion-exchange capacity. Results are frequently reported at the ppb level using this method, but mostly for solutions of very low ionic strength. Interferences from other ions in solution limit its use in more concentrated solutions. The most widely used method for increasing the sensitivity of m e a s u r e m e n t is by using a precolumn to selectively trap the tracer, which is then eluted onto the

125

Interwell Water Tracers

ion chromatograph for measurement. Both the trapping and release of the tracer must be quantitative; this is normally done for the enrichment of the radiotracers described earlier. It should work well for such tracers as thiocyanate and the hexacyanocobaltates, which are selectively trapped on strong base ion exchangers. Some method development will probably be required. In addition, special detection methods such as ICP, mentioned earlier for transition elements such as cobalt, can add both sensitivity and selectivity. Sensitivities of 1 ppb and less should be possible using such procedures. Many special analytical techniques have been developed for enhancing the separation and selectivity of ion chromatographic techniques. These include ion-interaction chromatography as described earlier and illustrated in Fig. 3.6 for separation of several metalocyanide complexes; and the use of chelating phases, micelle exclusion, and a large variety of other named and unnamed procedures. The literature on ion chromatography in all of its manifestations is large and has become very specialized. Method development has become the province of specialized chromatographic laboratories. TABLE 3.2 Effect of MDL on detection in far wells (MDL) (mass/vol)

Tracer required, near wells @ 10 x MDL (1000 ft)

Tracer required, far wells @ 100 x MDL (2000 fL)

i ppm (m/v)

12,250 lb

122,500 lb

10 ppb

1225 lb

12,250 lb

1 ppb

122.5 lb

1225 lb

T R A C E R SAMPLING AND ANALYSIS IN THE F I E L D

Conventional field sampling Most waterflood tracer programs fail because of poor sampling. Sampling is usually the cheapest part of a tracer program; it is far better to take too many samples than not to take enough. To ensure adequate field sampling, a sample frequency schedule is required. The correlation between breakthrough time and the shape of the tracer response curve is discussed in chapter 4. It is shown that the shorter the breakthrough time, the narrower the response curve (Wagner et al., 1974). As a consequence, sample frequency should be highest at the start of the flood to avoid missing early breakthrough. It can be decreased over time until a minimum monthly or other "caretaker" sampling time is reached. Initially, only some of the collected samples need be analyzed, and the intermediate samples discarded if no

126

Chapter 3

t r a c e r is found. Once tracer is found, all samples are counted until the tracer production curve is defined. Samples can be collected at the wells or from a test separator shared by a number of wells, provided the stream is sampled only near the end of the test when the w a t e r is representative of the currently sampled well. Samples can also be collected at the separators. Well sampling usually involves a w a t e r separation problem t h a t can be avoided by sampling at the separators, but samples may be contaminated with water from a previous well. In some cases, a small separator can be installed at the wellhead. This is the best of both worlds, particularly at low water cuts. A separator for sample separation and collection at high wellhead pressure is shown in Fig. 3.8. Such separators can be easily assembled from commercially available high-pressure bombs and fittings.

Leaving gas, oil, and brine

Entering oil, gas, and brine

!

q

@

!

D

Brine collected

Figure 3.8. Wellhead oil-water separation

Continuous t r a c e r analysis in the field Since concentration is an intensive property, the results obtained from a slipstream of the produced w a t e r are equivalent to those obtained by sampling the full-produced stream. This provides an alternative to collecting individual w a t e r samples, which can be a useful procedure for pilot tests. The two basic methods for doing this are the differential method, which monitors produced t r a c e r concentration as a function of time, and the additive method, which monitors total collected tracer as a function of time. The choice depends upon the analytical method available for the specific tracer being used. The additive method is described here.

Interwell Water Tracers

127

ADDITIVE PROCEDURE In the additive procedure, tracer is continuously stripped from a small s l i p s t r e a m t a k e n from the wellhead in the field. This is limited to t r a c e r s for which such a collection method is available. In this example, tagged hexacyanocobaltate ion is firmly retained on a strong base anion-exchange resin at low ionic-strength produced brine. The slipstream of produced w a t e r is passed t h r o u g h an ion-exchange column wrapped around a NaI g a m m a counter. As tracer arrives at the well, the cobalt activity t h a t builds up in the exchanger can be monitored by the increase in the g a m m a radiation emitted. This has been done as a m e a n s of collecting data from a producing well (Zemel, 1984). The t r a c e r was injected as a pulse using 57Co tagged hexacyanocobaltate, which emits low-energy radiation (<100 keV) and is counted with high efficiency by the scintillation detector. A schematic of the system is shown in Fig. 3.9 (Shell, 1984). The slipstream of produced water from the well is passed through a simple oil-water separator and, if necessary, a filter, then through a column filled with the ion-exchange resin. The tube is wrapped around a NaI(T1) scintillation detector, the output of which is fed into a digital rate meter (a portable pulse-height analyzer in the multiscaler mode). Background is minimized by discriminating against radiation greater t h a n the cobalt-57 photopeak and by lead shielding. A constant - - or at least a known m flow rate through the column is required. A typical t r a c e r response is shown in Fig. 3.10 (Shell, 1984). The counter records the passage of a tracer pulse as the total g a m m a count rate, R(t), from the ion-exchange column at t h a t time. This is an integral curve, giving the number of counts collected as a function of time. It approaches the total count rate asymptotically as the pulse is produced from the well. The form of the response curve is the same as t h a t from a step function, i.e., a continuous injection of tracer, due to continuously summing the response from a pulse injection of tracer. Because this is a summing method, it improves the likelihood of tracer detection for methods of relatively low sensitivity but lowers sensitivity to an individual m e a s u r e m e n t . This procedure smoothes the response curve so t h a t the effects of individual excursions are not visible, which m a y not be desirable if individual data points are important.

Conversion of radiation to concentration data for additive method To be useful, the radiation data collected in the additive m e t h o d m u s t be converted to concentrations and the time base converted to cumulative volume. This requires two calibrations: one to convert the radiation m e a s u r e d in counts per unit time to activity in becquerels or curies and the second to relate the radiation response to a fixed volume of sample. The conversion of radiation to activity is obtained by counting a known activity of the tracer injected into the system or into a surrogate system. The ratio of the known activity, A, to the counts per

128

Chapter 3

Signal "-I~l

Water & oil out Fluids Separator

from well head

L

Photomultiplier

T

u.....-...-....~" o~:,..'--'--'u ~-.~:~::-~<-~

A

J Filter

tube

..... J/NaI(TI) crystal

~:.'.".'.'.:.--'t3

Water in

I Digital rate meter

i

> Water out

Coil of ion exchange resin

Constant rate pump (low flow rate)

Figure 3.9. Continuous tracer monitoring equipment

0

i01

g, O

0~-

Time

Figure 3.10. Field response from continuous tracer collection

Interwell Water Tracers

129

unit time, Ro, measured in the system, is the radiation correction factor K = AfRo, which corrects for efficiency and geometry of counting. In order to correlate a volume element with the radiation measurement, R(t), the flow rate, Qs, of the stream entering the ion-exchange column m u s t be known. Ideally, to simplify the conversion, this flow rate should be constant. The sample volume, Av, for any counting time, t, is QsAts, where Ats is an arbitrary time interval at the counting time, t. Hence, the integral of count rate as a function of time can be converted to a function of concentration in t e r m s of activity per unit volume by: K C(t) = QsAts R(t)

(3.10)

Unlike normal sample-based response curves, this is a continuous function. The time element, Ats, can be unity or any other fixed value and the curve can be transformed directly from the radiation measured to the desired concentration form. Time interval Ats sets the volume over which the produced activity is averaged. Its choice will depend upon the nature of the response curve, and the "smoothness" of the data. Production data are used to convert the time base to cumulative volume. Graphical differentiation of the curve of C(t) vs. time yields the normal response curve for a pulse injection, and the cumulative time scale is converted to cumulative volume by means of the production or injection data. Three typical curves derived from such data are shown in Fig. 3.11. These are: 1) a cumulative curve generated from the continuously collected radiation data; 2) a differential curve, dC/dt vs. v, derived from the cumulative curve (this would be the response expected from an injected pulse of tracer); and 3) the same derivative curve, normalized to the peak concentration. Such a procedure would be particularly useful in tracer tests where the time of arrival of the tracer can vary widely depending upon information not known in advance. This can involve the possibility of thief zones, the effect of well treatments, and m a n y other variables. The t a s k of guessing how m a n y samples to take, when to start, how frequently to sample, and how often to analyze the samples can be difficult. It can also lead to excessive expenses if too m a n y samples are used, or to missed data if guesses are too far off. This procedure has the advantage of providing immediate tracer information, without supervision, on a continuous basis. As in all experimental methods, there are m a n y sources of error. Counting errors can be usually be guarded against by s t a n d a r d feedback procedures. Probably the greatest source of distortion of the tracer response curve is poor flow control of the sidestream entering the counter system, which can be caused by two-phase flow, solids clogging the system, or pump problems.

Chapter 3

130

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. I....! .........................i........................-~....................... 0.8 .......................~-:.-...................=.................

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Contiriuous

.

.

ii'ze

l'"

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150

colliection .

're'nii'ai

.... i ......................

200

250

300

volume

Figure 3.11. Continuous and derivative tracer response curves DIFFERENTIAL PROCEDURES Where a detailed response curve is required in a tracer test, a differential method is preferred. This method requires a sensitive analytical procedure and in some ways is better fitted to chemical tracer detection t h a n to the additive method. In this procedure a slipstream of produced water is passed through a small s e p a r a t o r to remove oil and any other interferences. The "clean" w a t e r can be passed t h r o u g h a detection cell for direct analysis if a suitable procedure is available. In principle, there are m a n y analytical techniques and a n u m b e r of electrochemical and spectrometric detectors available (Scott, 1986). Automatic sampling using ion chromatography, as shown in figs. 3.5 and 3.7, can provide on-line analysis in minutes, allowing virtually continuous analysis. Since continuity of analysis does not require continuous analysis, samples analyzed at longer intervals can provide all the data required for a tracer response curve. The analysis of thiocyanate by IC using K2HPO4 as an eluent and spectrophotometric detection at 190 nm has been reported at a detection limit of a few ppb (Meek and Pietrzyk, 1988). If radioactive tracers are to be used, the sampled tracer concentration should not exceed the MPC for unrestricted areas. This limits the radioactive w a t e r tracers t h a t can be directly analyzed to tritiated water. Other radioactive w a t e r tracers require enrichment before counting, if they are to be below the MPC in the sampled w a t e r stream. Automatic sampling can, however, be combined with

Interwell Water Tracers

131

an enrichment procedure to allow counting of periodic samples. An example of such a procedure is to divert, periodically, a fixed volume of water from the slipstream through a small-anion exchange cartridge. If Co-57, Co-58, or Co-60 is used as a tracer, the ion-exchange cartridges can be counted by an automatic scintillation counter. It is not necessary to sample continuously to construct a good tracer response curve. Differential methods place less strain on the system since they do not require continuous storage of tracer and yield concentration as a function of time without further calculations. The only additional requirements are a calibrated detector and a means of automation. No such methods have been reported in the oilfield literature, but automated differential methods are commonly used for routine analysis in commercial laboratories and in many chemical plants. Suitably sensitive potentiometric, amperometric, or spectrometric detectors, for example, can be used to monitor specific ions such as the perfluoro acids, nitrate, iodide, and thiocyanate. This can be done either by continuous ion detection on a slipstream or by sequential analyses of samples using ion chromatography.

REFERENCES

Abbaszadeh-Dehghani, M., "Analysis of Unit Mobility Ratio Well-To-Well Tracer Flow to Determine Reservoir Heterogeneity," Ph.D. dissertation, Stanford University, Stanford, CA (Aug. 1982). A1-Dolaimi, A.M., Berta, D., Dempsey, M.J., Smith, P.J., "Evaluating Tracer Response of Waterflood Five-Spot Pilot: Dukan Field, Qatar," paper SPE 17989 presented at SPE Middle East Oil Tech. Conf., Manama, Bahrain, March 11-14, 1989. Asgarpour, S., Crawley, A.L., and Springer, S.J., "Performance Evaluation and Reservoir Management of a Tertiary Miscible Flood in the Fenn-Big Valley South Lake D-2A Pool," paper no. 87-38-07 presented at 37th Ann. CIM Petrol. Soc. Tech. Mtg., Calgary, Alberta, Canada, June 7-10, 1987. Baldwin, D.E. Jr., "Prediction of Tracer Performance in a Five-Spot Pattern," J. Pet. Eng. (April 1966) 513-17; Trans. AIME, 237. Bjornstad, T., and Rogde, R.A., "An Improved Gammaspectrometric Method for Trace Analysis of 22Na," Nuc. Instruments and Methods in Phys. Res. (Oct. 1990). Bowman, R.S., "Analysis of Soil Extracts for Inorganic and Organic Tracer Anions via High-Performance Liquid Chromatography," J. Chromatog. (1984) 285, 467. Bowman, R.S., and Rice, R.C., "Transport of Conservative Tracers in the Field under Intermittent Flood Irrigation," Water Res. (1986) 18, 1531-1536.

132

Chapter 3

Brigham, W.E., and Smith, D.H., "Prediction of Tracer Behavior in Five-Spot Flow," paper SPE 1145 presented at the SPE Conference on Production Research, May 3-4, 1965. Burwell, F., "Multiple Tracers Establish Waterflood Flow Behavior," Oil & Gas J. (Nov. 28, 1966) 76-79. Champion, C.A., Schaller, H.E., and Jackson, B.R., "Some Recent Applications of Radioactive Tracers on Determining Subsurface Flow Behavior," paper SPE 1246 presented at 40th Annual Fall Meeting, Denver, CO, October 3-6, 1965. Craig, F.F., The Reservoir Engineering Aspects of Waterflooding, Vol. 3, Doherty Monograph Series, SPE, Richardson, TX (1971). Fernelius, W.C. (ed.), Inorganic Synthesis, Vol. II, McGraw-Hill, New York (1946) 225. Fox, C.S., "Using Radioactive Isotopes to Trace the Movement of Underground Isotopes," Municipal Utilities (April 1952) 90. Gjerde, T.G., and Fritz, J.S., Ion Chromatography, 2d ed., Huethig, New York (1987). Gore, G.L., and Terry, L.L., "Radioactive Tracer Techniques," JPT (1956) 8, 12. Greenkorn, R.A., "Experimental Study of Waterflood Tracers," J P T (1962) 14, 87-89. Haddad, P.R., and Jackson, P.E., Ion Chromatography, Principles and Practice, Elsevier Sci. Pubs., Amsterdam (1990). Halevy, E., and Nir, A., "The Determination of Aquifer Parameters with the Aid of Radioactive Tracers," J. Geophys. Res. (1962) 67, 2403-2409. Halevy, E., Nir, A., Harpaz, Y., and Mandel, S., "Use of Radioisotopes in the Studies of Groundwater Flow: Part I. Laboratory Experiments on the Suitability of Various Tracers," in Second U.N. Internatl. Conf. on the Peaceful Uses of Atomic Energy, United Nations, Geneva (1958), 158-161. Heck, E.T., "Tracing Fluids Between Wells," Producers Monthly (July 1954) 18, 7, 31-33. Heemstra, R.J., Watkins, J.W., and Armstrong, F.E, "Laboratory Evaluations of Nine Water Tracers," Nucleonics (Jan. 1961) 19, No. 1, 92, 94-96. Hilton, D.F., and Haddad, P.R., "Determination of Metalo-Cyano Complexes by Reversed Phase Ion Interaction High-Performance Liquid Chromatography," J. Chromatography (1986) 361, 141. Holm, L.W., "Design, Performance, and Evaluation of the Uniflood Micellar Polymer Process - - Bell Creek Field," paper SPE 11196 presented at Ann. Fall Tech. Conference, AIME, New Orleans, LA, September 26-29, 1982.

Interwell Water Tracers

133

Hydro Geo Chem, Inc., "Two Well Recirculation Tracer Tests at the H-2 Hydropad, WIPP, Southeastern New Mexico," SAND86-7092, Sandia National Labs., Albuquerque, NM (1986). Jenkins, R.E., and Koepf, E.H., "New Tools and Methods Improve Fluid Tracing," Oil & Gas J. (Apr. 1, 1963)61, No. 13, 102-104. Johnson, E.L., and Haak, K.K., "Anion Analysis by Liquid Chromatography," in Liquid Chromatography in Environmental Analysis, Laurence, J.F., (ed.),

Humana, Clifton, NJ (1983). Jones, T.L., Kelley, V.A., Pickens, J.F., and Upton, D.T., "Integration of Interpretation Results of Tracer Tests Performed in the Culebra Dolomite at the Waste Isolation Pilot Plant (PIPP) Site," SAND92-1579, Sandia National Laboratories, Albuquerque, NM (1992). Josendal, V.A., Sandiford, B.B., and Wilson, J.W., "Improved Multiphase Flow Studies Employing Radioactive Tracers," AIME Trans. (1952) 195, 65. Kaufman, W.J., and Orlob, G.T., "An Evaluation of Groundwater Tracers," Trans. Am. Geophys. Union (1956), 37 297-306. Lake, L.W., Enhanced Oil Recovery, Prentice-Hall, Englewood Cliffs, NJ (1989). Lansdown, A.R., "Application of Tracers in the Steelman Pilot Waterflood," Can. Min. and Metal. Bull. (1961) 54,593, 695.

Lichtenberger, G.J., "Field Applications of Interwell Tracers for Reservoir Characterization of Enhanced Oil Recovery," paper SPE 21652 presented at the Production Operation Symposium, Oklahoma City, OK, April 7-9, 1991. Meek, S.E., and Pietrzyk, D.J., "Liquid Chromatographic Separation of Phosphorus Oxo Acids and Other Anions by Post Column Indirect Fluorescence Detection," Anal. Chem. (1988) 60, 1397. Omoregie, Z.S., Jackson, G.R., Martinson, L.A., and Vasicek, S.L., "Monitoring the Mitsue Hydrocarbon Miscible F l o o d - Program Design, Implementation and Preliminary Results," 38th Ann. CIM Petrol. Soc. Tech. Mtg., Calgary, Canada, June 7-10, 1987. Preprints V1 (1987) 97-121 (Paper No. 87-38-06). Qureshi, M., and Varshney, K.G., Inorganic Ion Exchangers in Chemical Analysis, CRC Press (1991).

Scott, R.P.W., Liquid Chromatography Detectors, Elsevier Sci. Pubs., Amsterdam (1986). Shirley, D.A., Committee Chairman, University Research Reactors in the United States m Their Role and Value, National Academy Press, Washington, DC (1988). Shpigum, O.A., and Zolotov, Y.A., Ion Chromatography in Water Analysis, Halstead, Div. of John Wiley, New York (1988).

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Skibitzke, H.E., Chapman, H.T., Robinson, G.M., and McCullough, R.A., "Radiotracer Techniques for the Study of Flow in Saturated Porous Materials," Intl. J. Appl. Radiation and Isotopes (1961) 10, 38-46. Skilbrei, O.B., Hallenbeck, L.D., and Sylte, J.E., "Comparison and Analysis of Radioactive Tracer Injection Response with Chemical Water Analysis into Ekofisk Formation Pilot Waterflood," paper SPE 20776 presented at the Ann. Tech. Conf., New Orleans, LA, Sept. 23-26, 1990. Slichter, C.S., "Field Measurements of the Rate of Movement of Underground Waters," USGS Water Supply Papers, No. 140 (1905). Small, H., Ion Chromatography, Plenum Press, New York (1981). Smith, R.E., Ion Chromatography Applications, Chemical Rubber Co. Press (1987). Tarter J.G., Ion Chromatography, Vol. 37 of Chromatographic Science Series, Cazes, J. (ed.), Marcel Decker, New York (1987). Terry, R.E., et al., "Manual for Tracer Test Design and Evaluation," Tertiary Oil Recovery Project, Institute of Mineral Resources Research, University of Kansas (May 1981). Thatcher, L.L., and Ramsey, D.A., "Anion Complexes of Gold as Ground-Water Tracers Determined by Neutron Activation Analysis," 3d Intl. Nuc. Methods in Environ. & Energy Res. Conf. Int. Atomic Energy Agency Rept. (Oct. 10, 1977) 265-275. Trocchio, J.T., "Investigation and Effect of Fluid Conductive Faults in the Fateh Mishrif Reservoir, Arabian Gulf," paper SPE 17992 presented at SPE Middle East Oil Tech. Conf., Manama, Bahrain, March 11-14, 1989. Wagner, O.R., Baker, L.E. and Scott, G.R., "The Design and Implementation of Multiple Tracer Programs for Multifluid, Multiwell Injection Projects," paper SPE 5125 presented at 49th Ann. SPE Tech. Conf. and Exhibition, Houston, Texas, October 6-9, 1974. Watkins, J.W., Armstrong, F.E., and Howell, W.D. "Interwell Uses of Radioactive Isotopes in Oil Field Exploration," in Contributions to ECAFE, Development of the Petroleum Resources of Asia and the Far East, Bureau of Mines/Geological Survey (1962), 238-270. Watkins, J.W., and Mardock, E.S., "Use of Radioactive Iodine as a Tracer in Water-Flooding Operations," Petroleum Trans. AIME (1954)201,209-216. Watkins, J.W., Mardock, E.S., Armstrong, F.E., and Heemstra, R.J., "Waterfloods Benefit by Radioactive Tracer Techniques," Petrol. Eng. (Sept. 1957) 29, 10, B53B63; Mines Mag. (Oct. 1957) 87-91. Wheeler, V.J., Parsons, T.V., and Conchie, S.J., "The Application of Radioactive Tracers to Oil Reservoir Waterflood Studies," paper SPE 13985/1 presented at the SPE/AIME Offshore Eur. '85 Conf. at Aberdeen, Scotland, Mar. 10-13, 1985.

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135

Wiebenga, W.A., Ellis, W.R., Seatonberry, B.W., and Andrew, J.T.W., "Radioisotopes as Groundwater Tracers," J. Geophysical Res. (1967) 17, No. 16, 4081. Wilhite, G.P., Waterflooding, SPE Textbook Series, Vol. 3, SPE, Richardson, TX (1986). Wood, K.N., Lai, F.S., and Heacock, D.W., "Water Tracing Enhances Miscible Pilot," paper SPE 19642 presented at the Annual Technical Conference, San Antonio, TX, October 8-11, 1989. Zemel, B. (1984) Internal rept., Shell Development Co.

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CHAPTER 4

FIELD

EXAMPLES

AND DATA ANALYSIS

INTRODUCTION In the previous chapter we introduced the use of tracers for conventional waterfloods in the oil field, including the choice and preparation of tracer materials, design of tests, and the laboratory and field procedures required for a successful test. In this chapter, we will discuss some of the published literature on waterflood field tracer applications and describe some of these applications to specific field problems. The chapter will also deal with the use of tracer response data to estimate the distribution of injected water in a p a t t e r n and the pore volume swept by the injected water.

WATERFLOOD LITERATURE Much of the work done on tracers in waterfloods is not reported in the literature. The information these tests yield is often only of local interest, the test may not have been successful, or it may be tied to an otherwise proprietary process. Those t h a t are reported are usually presented as part of a much larger project wherein the tracer aspects are of minor importance to the author. As a result, a good deal of the detailed information about tracers in the oil field travels only by word of mouth. Few of the papers reporting the use of tracers in waterfloods give any details on the choice of tracers, design of the tracer test, analyses of the tracers in the produced water, or analysis of the tracer data. The reported tracer data are usually concerned with reservoir description and its effect on the waterflood. Tracer data are otherwise of qualitative interest, and in some cases the tracers used are not even identified. The papers referenced in chapter three discussed the application of new tracers, determined their utility, and provided general information on their behavior. Only a handful of papers in the literature discuss the actual tracer procedures in the field. Most papers describing the use of radioactive isotopes for oilfield waterfloods do not identify their chemical form. They are merely identified as Co-60, Co-57, tritium, and C-14; however, as indicated earlier, the chemical forms required are quite specific. This is not obvious to those who are unfamiliar with oilfield tracer usage and this lack of information can lead to an unsuccessful test. It should be noted t h a t a large fraction of oilfield tracer work is reported by such societies as the Society of Petroleum Engineers (SPE) or the Petroleum Society of the Canadian Institute of Mining (CIM). Two kinds of publications are associated with these societies. Most reports appear first as preprints of oral presentations given at a society meeting. These are chosen by abstract and are

138

Chapter 4

not subject to peer review. Reports t h a t are printed in the Society journals are subject to peer review and thus have been much more closely s c r e e n e d . FIELD TRACER REPORTS A bibliography of waterflood tracer reports is given at the end of this chapter. Most of the papers in the literature use tracers for qualitative reservoir description. They indicate the utility of the method but rarely provide quantitative information or details on the tracer design, analyses, or procedures. A few papers have gone beyond this to provide additional insight into waterflood behavior in the reservoir. Some of these are discussed below. The papers described here were chosen because they illustrated tracer applications beyond t h e conventional reservoir descriptions. These include: 1) the use of tracer data in combination with other m e a s u r e m e n t s to arrive at information not available from either m e a s u r e m e n t alone; 2) the use of conceptual models of tracer response to account for areal dilution and reservoir heterogeneity; 3) the use of computer-based simulators for matching tracer data to reservoir models; and 4) the use of tracer response curves for calculating w a t e r distribution and swept volume. Included in this group are also some papers t h a t offer details on tracer procedures. The qualitative n a t u r e of much of the reported tracer data has led some engineers to devalue the use of tracers for waterfloods. This is unfortunate, since there is no other way to follow w a t e r movement through the reservoir. Some of t h e procedures discussed in the following sections provide a more q u a n t i t a t i v e picture of w a t e r movement in the reservoir. In addition, the revolution in compUter development and the ever-increasing speed of computation have provided powerful new tools for reservoir simulation of tracer and other data.

C o r r e l a t i o n o f t r a c e r d a t a w i t h field m e a s u r e m e n t s Reservoir descriptions obtained by the use of tracers are based on horizontal, two-dimensional flow information. We generally think of flow p a t t e r n s in t e r m s of the directional effect of heterogeneities on horizontal flow in the patterns. The North West Fault Block (NWFB) tracer study is no exception to this. The strong n o r t h w e s t e r l y flow trend t h a t was found was associated with nonsealing fractures oriented in the same direction. The effect of vertically distributed heterogeneities is less obvious. In order to examine the vertical effects, the tracer test d a t a m u s t be combined with other techniques, in the NWFB study, tracer response data were combined with downhole productivity profiles to correlate tracer appearance and position down hole - - an effective way to enhance the utility of tracer data.

Field Examples and Data Analysis

139

Vertical structure in the reservoir is obtained from well logs and core data. In heterogeneous reservoirs, large-scale correlations can result in structures t h a t are not visible on the wellbore scale. Such correlations can strongly affect flow but are difficult to identify without the help of tracers. An example is given in a tracer study from the North West Fault Block described below. NORTH WEST FAULT BLOCK

The waterflood consists of 18 inverted nine-spot patterns on about 80-acre spacing plus four line-drive injectors in a large pattern flood in the Prudhoe Bay, North West Fault Block, Alaska. Each of the injectors was tagged with one of four tracers: Co-57 and Co-60 tagged hexacyanocobaltate ion, C-14 tagged thiocyanate ion, and tritiated water. This study examined the data from one of these nine-spot patterns using tritiated water as a tracer. A detailed analysis (Nitzberg and Broman, 1990) of the movement of water in one of the injection patterns showed that it did not move as anticipated. Early b r e a k t h r o u g h of the tracer in the surrounding wells showed t h a t much of the injected water moved out through a "thief zone." The flow was found to be highly stratified over large reservoir distances, as shown in Fig. 4.1.

NW

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SE

140

Chapter 4

The w a t e r entered a thief zone 10 ft thick at the injector (well R-7) and appeared at the surrounding wells at virtually the same (subsea) depth. A schematic of the tracer movement along a cross section that extends from R-11 on one side, intersects the injection well, and continues on through R-12 to N-6 on the other side, a distance of a mile, is shown in Fig. 4.1. Tracer (tritiated water) data, production logs, and well-response data were used to identify the depth of w a t e r production at the surrounding wells. These data clearly show the high degree of vertical segregation in the reservoir.

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Figure 4.2. Map showing line of cross section for Fig. 4.1 The initial simulation, based upon a large n u m b e r of core m e a s u r e m e n t s , assumed a much higher vertical to horizontal permeability (kv/kh) ratio t h a n appears to exist in the field. It predicted t h a t gravity would cause the injected w a t e r to move downward, or "slump," leading to an efficient sweep of the reservoir. The tracer studies show that, on a field scale, this did not happen. The effective kv/kh ratio appears to be much smaller than that given by core measurements, and as a result, the field is much more stratified t h a n predicted. The heterogeneities in a two-inch core plug were not representative of those t h a t exist across several thousand feet of interwell distance in this reservoir. A reduction of about two orders of magnitude in the kv/kh ratio initially obtained from the core

Field Examples and Data Analysis

141

data was required to account for this kind of segregation. These results showed t h a t the waterflood was not sweeping the reservoir efficiently, and t h a t profile modifications would have to be undertaken to improve the flood. None of the details of the tracer program are given. The responding producers varied from 2400 ft to 6000 ft in radial distance from the injector. Although numerous faults cross the area of flow, they appear to have no effect on the water crossing the fault. There is, however, significant flow along the fault. The map in Fig. 4.2 shows the wells responding to injector R-7 and the orientation of the cross section described in Fig. 4.1. From this, it is also clear t h a t the designation of "nine-spot" is a convenient r a t h e r t h a n a realistic designation of the pore volume responding to the injector.

Flow m e c h a n i s m s The travel time of a water tracer from injector to producer is normally related to the interwell distance and to the conductivity of the reservoir in the direction of response. This is a function of such reservoir properties as directional variations in permeability and/or thickness, the presence of flow barriers or paths due to fractures and faults, etc. It can also be a function of other factors, such as different mechanisms of flow. Two different tracer studies were used to identify capillary imbibition as a flow mechanism in two North Sea fields. In both cases, tracers injected at the very s t a r t of the waterflood were delayed relative to the response from a later tracer injection. Only a small fraction of the water and tracer initially injected was produced. The initial water (and tracer) injected presumably reacted with a water-wet reservoir, u n d e r s a t u r a t e d with respect to water, and was therefore imbibed into the reservoir, displacing oil in the process. Production of water and associated tracer at the nearest producer was delayed until the imbibition was satisfied. EKOFISK FIELD This study confined itself to accounting both for the delay in arrival time and for the small a m o u n t of w a t e r and tracer produced from an initial w a t e r injection. No attempt was made to explain the difference in response at each of the three production wells in the pilot. It was, however, noted t h a t there were m a n y well production problems, and many workovers were required. Two tracers were used in this test in an unconfined four-spot pilot waterflood in the Ekofisk field in the North Sea (Sylte et al., 1988; Skilbrei et al., 1990). The configuration of the pilot area is t h a t of a central injector (B-16) surrounded by three producers, B-19, B-22, and B-24, in an approximately equilateral configuration about 1250 ft from the injector at a depth of about 10,000 ft. Tritiated water was injected continuously, as a step function, from the s t a r t of

142

Chapter 4

the waterflood. A total of 12.8 MM bbl of tritium tagged water were injected at an average concentration of 2235 Bq/L (9.6~Ci/BB1) over a period of 34 months, while only 530,000 bbl of water were produced. Both tracer and w a t e r response were unexpectedly late and different at each of the three producers. The greatest and earliest response occurred at well B-22, the least and latest at well B-24. The differences were attributed to well problems. Tritiated water was injected as a step function, presumably to use the injected tracer concentration as a measure of the amount of injected water produced. The same information is available from a pulse injection of tracer, which is, however, much easier to perform and can be measured with higher sensitivity. This is one of the few papers in which the authors recognized the correspondence between the fraction of injected tracer produced and t h a t of the injected water: i.e., ~hat production of 2 percent of the injected tracer is equivalent to production of 2 percent of the injected water. An iodide tracer (I-125) t h a t was injected as a pulse 13 months after the tritium injection was started broke through in a much shorter time interval t h a n the tritium and at a much higher apparent dilution. The short (60-day) half-life of 1-125 limited the duration of iodide tracer data to about a year. Injection was stopped between July and December 1987 and was restarted along with recompletion, restimulating the three production wells, and opening up new production zones. Both the tracer and the watercut data showed the effect of these changes. Tracer-response data for the two tracers and for the watercut are presented in years in Fig. 4.3. The results of the tracer test data were explained on the basis t h a t w a t e r injected initially (tritium tagged) was imbibed into the formation at the low initial w a t e r saturation, thus accounting for the delay in arrival time and the small fraction of w a t e r produced in the pilot, but t h a t w a t e r injected l a t e r (iodide tagged) moved through the reservoir by normal convective and dispersive processes. The authors noted t h a t the concentrations of some of the common ions in the produced w a t e r followed the changes in watercut and tritium concentration and t h a t the difference in concentrations could serve as a tracer for injected water. This is oRen true when there is a difference in ion concentration between injected and produced water. The sensitivity for a method such as this, which depends upon the difference between two relatively high concentrations, is, however, much lower t h a n t h a t for an added tracer because of the propagation of errors of measurement. The difference method often fails because these errors of measurement are not considered. GULFAKS FIELD Tritiated w a t e r was injected as a tracer in a waterflood in F a u l t Block 3G in the Gulfaks field in the North Sea (Rogde, 1990). The fault block contains two

Field Examples and Data Analysis

143

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90

144

Chapter 4

9

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Figure 4.4. Map of fault block 3G producers, A-1H and A-2H, and an injector, A-5H, as shown on the map in Fig. 4.4. As in the Ekofisk case described earlier, two tracer pulses were injected into A-5H. The first pulse (400 curies of tritiated water) was injected ten days after the s t a r t of the waterflood. Sixteen months after injection, with neither a watercut or tracer response at well A-1H and only limited response at well A-2H, a second pulse of 135 curies of tritiated water was injected into well A-5H. Shortly after this injection there was a large increase in tracer response resulting in a second peak at well A-2H and a second rise in watercut. There was also a tracer and a watercut response leading to a sharply rising tracer peak at well A-1H, shown in Fig. 4.5. The tracer responses are indicated by the black circles and the solid lines. The water breakthrough at each producer is shown by the empty circles. The times at which each tracer pulse was injected are indicated by the arrows. History m a t c h i n g of the tracer response showed t h a t differences in t h e response of the second tracer at each of the two wells, A-1H and A-2H, could be explained by the normal transport of water by convective and diffusive forces, as expected for an ideal water tracer. As in the Ekofisk case, the small and delayed tracer (and watercut) response to the initial injection was accounted for by imbibition. The authors concluded t h a t the low-permeability sands also act as vertical permeability barriers, since capillary forces reduce the efficiency of the gravity forces.

145

Field Examples and Data Analysis

A finite difference simulator was used to evaluate several different flow models. The simulated response is shown by the dashed lines in Fig. 4.5. The best fit was obtained for a three-layer model, which gave the best history match for the watercut while still accounting for the difference in arrival time at the two producers. It contained a low-permeability layer to account for the delay due to imbibition, and a layer having a reduced vertical to horizontal permeability ratio (kv/kh).

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P h y s i c a l model o f t r a c e r movement Brigham and Smith (1964) described a semianalytic model for predicting tracer breakthrough times and peak concentration in a five-spot waterflood pattern.

146

Chapter 4

In their concept, the tracer pulse moves radially from the injector to the producers through homogeneous, noncommunicating layers, with longitudinal dispersion in the direction of flow. The number of layers, their thickness, and their permeability are used to represent the reservoir heterogeneity. The tracer pulse moving through each layer is diluted at the producers by untagged water from other streamlines in the same layer. This dilution effect is a consequence of p a t t e r n geometry. Production of the combined tracer responses from all these layers makes up the response curve of tracer concentration as a function of the cumulative volume of water injected. Tracer responses determine the shape of the curve and the maximum concentration of tracer produced. The authors used this model to predict peak height, breakthrough time, and shape of the produced tracer response curve from the amount of tracer injected and the p a t t e r n geometry. Subsequent papers by Brigham and his co-workers refined the model (Brigham and Abbaszadeh, 1984) and provided an analytical solution (Abbaszadeh, 1982) to the equations of flow in a stream tube with longitudinal dispersion. These are the only publications of any method for relating peak tracer response to the amount of tracer material injected. Deconvolution of the tracer pulse in terms of layers also allows an estimate of reservoir heterogeneities. The method is described in detail in the appendix of this work; however, an interesting application to tracer tests in general is discussed below. APPLICATIONS OF THE BRIGHAM MODEL Following the publication of the Brigham-Smith paper (1964) and subsequent papers by Abbaszadeh and Brigham (1984), a number of tracer tests based on this model were reported. Several papers originating from Canada reported the use of the Brigham-Smith model to determine the amount of tracer to add in miscible drives and in waterflood tracer tests (Wagner et al., 1974; Davis et al., 1976). Wagner et al. reported the results of several waterflood tracer tests, discussed some of the uses of tracers, and gave a list of preferred tracers for waterfloods. These included tritiated water, thiocyanate, nitrate, the halide ions, fluorescent dyes (for fracture paths) and the lower alcohols (methyl, ethyl, and isopropyl). They show the results obtained from several tagged waterfloods, including some that involved the simultaneous injection of a gas (solvent) and water in a water-alternating-gas (WAG) process. The Brigham model's calculation for peak-produced tracer concentration was modified to take into account the coproduction of oil and gas with the water. Wagner et al. used a two-layer model to arrive at some sensitivity predictions for peak produced tracer concentrations in the South Swan Hills (Canada) tracer program. They varied the permeability and porosity of the top layer to determine b r e a k t h r o u g h time. The permeability of the bottom layer was varied to keep injectivity and reservoir volume constant. Tracer data obtained seemed to fit the predicted design calculations. Although no other quantitative use was made of the tracer data, the results of these calculations illuminate a number of factors

Field Examples and Data Analysis

147

involved in designing a tracer test. A gas tracer was used for these simulations, but the kind of results obtained are valid for any test in which the tracer is ideal, such as water tracers. The calculated tracer response curves for b r e a k t h r o u g h at 15, 24 and 36 months are shown in Fig. 4.6a. Early tracer breakthrough times are associated with high-concentration maxima and narrow produced pulses, as demonstrated by the three pulses shown. The area under the peak m u s t remain constant as long as the a m o u n t of tracer is conserved. Hence, as b r e a k t h r o u g h times increase, produced pulse heights decrease and pulse widths m u s t increase. At

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Figure 4.6. Produced concentration vs. breakthrough time

148

Chapter 4

very early breakthrough times, the pulses are very narrow and the peak heights high. As the time required for breakthrough becomes longer, the difference in peak heights for successive breakthrough curves becomes smaller. Consequently, the frequency of sampling should be high at the beginning of the flood to guard against missing early breakthrough associated with narrow produced peaks. As the flood progresses, and as the pulses get broader and less likely to be missed, the sampling frequency is decreased. It has long been recognized that no matter how short the duration of the injection interval, the tracer response curves are quite broad. Reservoir parameters seem to be more important than injected pulse width in determining the shape of the tracer response curve. This is demonstrated in Fig. 4.6b, which shows the predicted peak tracer concentrations as a function of the breakthrough time for different tracer injection times. For the same amount of activity, injection time is proportional to pulse width: the shorter the duration of the pulse, the narrower and more concentrated it becomes. The figure shows that the peak-produced concentrations of tracer are relatively independent of the injected pulse width over a wide range of pulse widths. Only for early breakthrough times is there a significant difference in the height of the produced pulse. As breakthrough times increase, the effect of the width (duration) of the injected pulse becomes less and less important. For the case simulated here, it becomes negligible for breakthrough times exceeding three months. This simulation also implies that a series of small pulse injections having equal concentrations will produce virtually the same output as a continuous injection. The significance of the detection limit for monitoring an interwell tracer test, which may not be obvious to many engineers, is demonstrated more clearly in Fig. 4.7a and b. These figures show the time interval during which detectable levels of tracer are produced for different predicted breakthrough times. The effect of detection limits in these measurements is illustrated by comparing the result at a detection limit of 1 pCi/L in Fig. 4.7a with that of 10 pCi/L, as shown in Fig. 4.7b. At the predicted breakthrough time of 24 months, shown in Fig. 4.6a, most of the produced tracer would be invisible at the detection sensitivity of 10 pCi/L. The detector would see little more than the peak concentrations. The interrelationship between these factors is also important in setting up a sampling program. As was shown earlier in Fig. 4.6a, the peak concentrations change as a function of predicted breakthrough time. The sensitivity required for detection is lower for early breakthrough and increases with delay in breakthrough. Factor a in Fig. 4.7a and b is a measure of longitudinal dispersion, which has no major effect on these sensitivities. S i m u l a t i o n of a tracer pulse

Operation of an oil field in a large waterflood is complicated by the mass of collected data that must be analyzed and used to optimize field operations. This is

149

Field Examples and Data Analysis

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, I

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J

33 36 39 42 4.5 48

B r e a k t h r o u g h Time, M o n t h s

10-

ca

9

A ~ = 0.00385 b

E

7

E

6

r" O :,~ o

5 -

4.~ (9

3

d ~ ,4,,,i

- cx = 0.385

4-

210

0

!

,

,

3

6

9

,

12

,

15

18

21

24

27

30

33

36

39

42

45

B r e a k t h r o u g h time, m o n t h s

Figure 4.7. Detection time vs. breakthrough time and sensitivity particularly true in heterogeneous reservoirs with odd pattern geometry. In order to handle the data load, oil companies usually resort to large computer-based simulators. Such simulators are governed by a set of transport equations that describe the movement of the reservoir fluids: oil, gas, and water. The equations are solved numerically by a finite difference method. The known geology, well

150

Chapter 4

logs, core and laboratory data, together with flow of production data, are input into the simulator to provide the necessary reservoir description. The fluid flows predicted by the simulator are history-matched with those observed in the field by modifying the reservoir description and the relative permeabilities to fit the observed flows. This is apt to be a lengthy process. Tracer response data are a function of the actual flow between injectors and the responding producers. In a multipattern waterflood, these data provide the only means of identifying the distribution of injected water. Simulation of the tracer pulses is the best way to integrate real flow data into the system since it forces the simulator to address the actual flow distribution and the response curve shapes, in addition to total fluid flow. Simulators for large fields use a finite difference grid for the numerical solution of the flow equations. These simulators use large grid blocks to cover all the pattern areas but are not suitable for simulating the movement of the smallvolume tracer pulse, due to numerical dispersion. Methods that have been developed for reducing and perhaps eliminating this effect offer the most likely path for the future. New algorithms and analytical procedures will also presumably evolve. The tremendous increase in computational speed generated by the computer revolution is making simulation of tracer data a far easier and simpler procedure. Analysis of tracer response data is the only way to obtain quantitative information about the flow of injected water in the formation. This is a difficult analysis and requires the use of computer-aided simulators in order to integrate all the pertinent reservoir data. Only in the past few years has there been much work published on the analysis of field tracer data. Some of these papers are discussed in the following sections. An alternative method used for simulating fluid displacement in a reservoir is the streamtube method, in which the streamlines connecting flow between injectors and producers are used to define a fixed number of stream tubes. All flow is divided between these streamtubes with no flow across them. Fluid displacements are treated as single-phase displacements. Methods for calculating streamtube displacements are relatively simple and allow approximate fluid displacement to be calculated. Examples showing the use of the streamtube method are included below. BIG MUDDYFIELD TESTS Four tracers were used in Big Muddy field in a preflush for a low-tension polymer pilot flood in Wyoming (Gilliland and Conley, 1976). The one-acre pilot five-spot was placed within an existing five-acre, five-spot pattern, as shown in part a of Fig. 4.8, in order to confine the flow to the pilot area. Thirty-three curies of tritiated water were injected into well I-1. Well I-2 received 10,500 pounds of thiocyanate ion. Well I-3 received 2650 gallons of ethyl alcohol, and well I-4 had 2400 gallons of methyl alcohol. The best data came from tritiated water and

Field Examples and Data Analysis

151

thiocyanate. None of the ethyl alcohol was produced. The straight-chain aliphatic alcohols with even carbon numbers are much more subject to bacterial a t t a c k t h a n those with odd ones and make poor tracers for this and other reasons. Methanol is also a difficult tracer to use since 1) it must be collected with care to avoid loss of tracer and 2) it is also subject to bacterial attack. The Big Muddy pilot was simulated as a three-layer model based upon available field and lab data and reported flow rates in the pilot area. The first simulations of the tracer response curves gave a poor fit to the tracer data. To improve the fit, a streamline model of the pilot, including the offset producers, was generated, as shown in part b of Fig. 4.8. Based on the results of this model, the pilot section was enlarged to include the area shown in the figure.

P-1

P-2

I-1

9

P-5 I-4 P-4

I-2

I-3 P-3

,9 Injection well 9Production well

b

Figure 4.8. Map and streamline plot of Big Muddy field A 3D compositional simulator (UTCOMP) was used to fit the tritiated w a t e r and thiocyanate tracer response data to a model of the reservoir (Agca et al., 1987). Set up in the petroleum engineering d e p a r t m e n t at The University of Texas at Austin, this finite-difference compositional simulator handles multiple tracers, variable flow rates, longitudinal and t r a n s v e r s e dispersion, compositional changes, and most other reservoir parameters. It contains a numerical control method for reducing truncation error. To test the simulator, it was first tried on an analytical model of a homogeneous five-spot reported by Abbaszadeh and Brigham (1983). The result for a Peclet n u m b e r (L/a) of 500 is compared with the analytic result in Fig. 4.9. The injection rates to the central producer were changed to reflect the streamlines going to the central injector from each of the producers. Adjustments in both

152

Chapter 4

longitudinal and transverse dispersivity also improved the fit, and the addition of a reversible adsorption for each of the tracers gave an excellent fit for the tracer response from tritiated water and a good fit for the thiocyanate data. There is no

UTCHEM Results Analytcal Results

0.16

tO

o m

col

,L__

~9

0.12

o cO (~

0.08

j

L_

(1) 0

J

L_

!-- 0.04.

0.00

ooo

9

,

030

060

.,

,12o

o:9o

P. V. I n j e c t e d

Figure 4.9. Simulated response to five-spot at a/a = 500

tO

.m

a

~

v m

Simulation Field data

+

~"

§

~9 (1) 9

t--

i

._o r I-. .

0.oo

.

.

0.56

.

1.11

.

1.67

P.V. Injected

2.22

2.78

§

0.00

0.56

1.11

1.67

P.V. Injected

Figure 4.10. Simulated tracer response, Big Muddy field

2.22

2.78

Field Examples and Data Analysis

153

experimental evidence t h a t either of these tracers adsorbs on the formation surface, but the m a t h e m a t i c a l relationship used here may well relate to a different mechanism. The simulation (Agca et al., 1987) of the response curve for tritiated w a t e r is shown in Fig. 4.10a and that for thiocyanate in Fig. 4.10b. The longitudinal and transverse dispersivity and other p a r a m e t e r s t h a t were generated to fit the tracer data were also used to simulate the low-tension polymer flood t h a t followed the preflush (Saad et al., 1989). These p a r a m e t e r s would not have been available otherwise. RANGER FIELD TRACER TESTS Most field-tracer data are reported in the form of a case s t u d y with some qualitative reservoir i n t e r p r e t a t i o n added. In this case study, the t r a c e r d a t a were t r e a t e d f u r t h e r by two different procedures to obtain a more q u a n t i t a t i v e reservoir description. In one procedure, the tracer data were fitted to a s t r e a m tube model to arrive at a reservoir description in terms of layer thickness and permeability. In the second, the data were used in a compositional simulator, together with other field data, to arrive at a more detailed reservoir description containing fluid saturations as well as permeability and layer distributions. A n u m b e r of tracer tests in various fields were reported in water- and steamflood projects (Lichtenberger, 1990). Multiple tracers were used for monitoring waterflood m o v e m e n t and residual oil in a surfactant polymer pilot field in the McCleskey s a n d s t o n e in the Ranger field in Texas. Only the d a t a from this waterflood will be discussed here. Although partitioning tracers were used in the pilot to m e a s u r e residual oil, a discussion of the residual oil m e a s u r e m e n t s is deferred to chapter 5. A tracer test was also reported for a s t e a m drive in the Potter sand of the Midway Sunset field in California. Steam tracers are discussed in chapter 6.

Field data The Ranger field test discussed here concerns a waterflood in the McCleskey s a n d s t o n e shown as area 1 on the map in Fig. 4.11 (Lichtenberger, 1990). The sandstone occurs at a depth of about 3400 ft, with a net pay v a r y i n g from 7 to 25 ft. The average porosity is about 14.7 percent and (air) permeability ranges from 200 to 1500 millidarcies. Well spacing is nominally 40 acres. Five different tracers were used in this five-spot pilot. Two tracers, thiocyanate ion and tritiated water, were injected together into well 3-38 to evaluate their use as w a t e r tracers. A different cobalt isotope was injected as the hexacyanocobaltate into each of the other three wells. Cobalt-57, -60 and -58 were injected into wells 3-41, 3-42, and 3-45, respectively. In addition to the w a t e r tracers, isopropyl alcohol (IPA) and t e r t i a r y butyl alcohol (TBA) were also injected into well 3-38 as p a r t i t i o n i n g tracers for monitoring residual oil. These will be discussed separately in chapter 5 on unconventional waterflood tracing.

154

Chapter 4

Distance, feet x 1000

O O

o I"

5

40"

X

,I-I

g4

q,-

r O

=

,I-I

u)

3

mu

Q

2 1

2

3 4 Field map

5

6

Figure 4.11. Field map of McCleskey pilot area

Ten curies of tritiated water and 5655 pounds of thiocyanate were injected into well 3-38 and monitored at the responding production wells, 3-37, 3-39, and 3-40. The a u t h o r "normalized" their response by dividing the produced tracer concentrations by the total amount of tracer in pounds or activity originally injected. These results are shown in Fig. 4.12. The response data have the dimensions of reciprocal liters and are expressed as micropercent per liter (!1%/L) versus cumulative water injected. There does not seem to be any physical meaning to these units. The response curves from one of the wells were the same for HTO and SCN. For the other two wells, the SCN peak was about twice as high as t h a t for HTO. The author interpreted these data to show t h a t the thiocyanate was a better tracer. Normalization is done to compare the response from tracers t h a t were injected at different initial concentrations. It should be done by using injected tracer concentration as the normalizing factor, not the total weight or activity injected. Unfortunately, as the author probably recognized, the average injected concentrations of the two tracers are unknown and probably differ. The 10 curies of tritiated water, in a volume of 20 ml or less, was washed out of its container by an unknown amount of water that probably differed for each injection. This is not easily compared with the mean injected concentration of the 5600 pounds of thiocyanate injected from a vacuum truck by a different dilution factor.

155

Field Examples and Data Analysis

f~

..I

Well 3-37

Well 3-39

12.

1.0.

0.8.

F TO 0.6:

IF

0.4'

81

0.2'

A

100

?

!

200 300 Time, days

J-

-

'

o.el

'

100

400

200

300 400 Time, days

500

10

-

.j

8

f ~

-

Well 3-40

SCN

8' 0

100

200

300

400

500

Time, days

Figure 4.12. Tracer response, Ranger field A b e t t e r w a y to compare the tracers would be by the m a s s fraction or activity of each recovered and by their m e a n residence times, or m e a n volume swept. The m e a n r e s i d e n c e t i m e w a s not m e a s u r e d ; however, t h e a u t h o r showed t h a t essentially the s a m e fraction of each tracer was recovered from the responding

156

Chapter 4

wells, which implies that they are equivalent. There is also a problem with the assumption that the amount of activity initially injected is accurately known. In the absence of quality control by the service companies, reported activity of injected tracers is always suspect. It is unfortunate that we do not have more published data comparing multiple tracers under controlled field-test conditions. All the tracer recoveries reported were rather poor; however the cobalt returns were considerably lower than the others. This may be due to the fact t h a t the produced activities were not corrected for radioactive decay, which causes underestimation of all the radioactive tracers relative to stable tracers. The very short half-life of Cobalt-58 easily accounts for its nonappearance at the surrounding wells and the very low return of Co-57. It was, however, noted t h a t examination of well tubing after the injection showed no residual cobalt contamination from the longer-lived cobalt-60. This is an interesting observation, in view of the problems with cobalt isotopes in the North Sea. The response data from these tests were analyzed in two different ways and are separately reported. The streamline model shown in Fig. 4.13 was used by Lichtenberger (1990) to analyze flow in the immediate pilot area based upon tritiated w a t e r response. Flow for the entire flooded area (pilot included) was analyzed using a computer-based simulation (Allison, 1988), shown in Fig. 4.14.

Streamtube model A streamtube model of the pilot area was generated, based upon average production and injection rates and the known reservoir parameters. The heterogeneity of the reservoir was simulated using layers of different permeability and thickness, superimposing tracer flow, and mixing using the analytical solution of flow in a streamtube with longitudinal dispersion (Abbaszadeh-Dehghani, 1984). The model was then matched to fit the tritium response data from the field. Enough layers were chosen to fit the field data to the desired precision. The model may not be real in terms of the reservoir, but the results are fair approximations to field behavior. The resultant streamline distribution, as illustrated in Fig. 4.13, shows t h a t a sizable fraction of the injected water flows outside the pattern and is not captured by the wells sampled, thus explaining the low tracer recoveries. A number of problems are associated with such a simplified model. The model assumes constant flow at the wells and constant fluid saturations, neither of which is true. Such models can, however, be set up and run in a fraction of the time required for a full field simulator, and yield useful data for reservoir management. Compositional simulator Data obtained from the Ranger Field test, reported by Lichtenberger (1990), were used in the compositional simulator described earlier for the Big Muddy field test (Allison, 1988; Allison et al., 1991). Here, the log, core, and production d a t a were entered in the simulator and the necessary reservoir p a r a m e t e r s changed to simulate the tracer response data from the field.

Field Examples and Data Analysis

li

',,

,.

\

157

t~ll/

Figure 4.13. Streamtube model, McCleskey sandstone

The initial area of interest is also shown on the map in Fig. 4.14. It includes 4 injectors and 13 producers in an area of 150 acres. Seven different tracers were injected. The final simulation covered the entire 17-well p a t t e r n over a total of 320 acres. In order to keep run times economical, large grid blocks were used (100 ft at each dimension). Sensitivity tests showed t h a t special procedures instituted to minimize numerical dispersion were successful. In m a n y respects this procedure is very different from the s t r e a m t u b e model used in the earlier t r e a t m e n t of the Ranger field in McCleskey sandstone, described above. The effect of variables t h a t cannot be treated by the s t r e a m t u b e model can be considered here in some detail. This includes transverse dispersion, variable well rates, variable mobile oil, and variations in areal and vertical permeabilities. The simulated tritiated water responses for wells 3-37, 3-39, and 3-40 are compared to the field data in Fig. 4.14. In this case, the reservoir model chosen m u s t fit field constraints known from core data, well logs and production data. It must also find the reservoir conditions that fit the produced tracer data. In order to fit the tracer response at the different wells, it was necessary to account for significant variations in areal and vertical permeability. The field was treated as a three-layer problem with permeabilities adjusted in each layer to fit the field data. Areal heterogeneities were required in each layer to account for different arrival times at the wells. The simulated tracer response was very sensitive to small variations in transverse dispersion. No significant difference was found between the behavior of the tritiated water and t h a t of the thiocyanate in the modeling, in contrast to the normalized response reported in the case study.

Chapter 4

158

~.

o=

8

Well 37

=o

100'

8 0.

200

400 600 Time, days

6o 3o 0

800

0

200

9

simulated

16 i g

600

3

-.

400

o

4~.C~

0

200

I

9

400

600

Time, days

'

~. 44

Cobalt-58

800

45 0

o

9

"

Cobalt 60

43

".l~__._well shut in "

9

37

1

O'

I

I "4o

"

s

9

8

-

~Tritiated

4 -

Well 40

-

800

Pattern map

9 Field data m

400 600 Time, days

I

1

3~ e

57 60

_ I

2

I, e

3

feet x 1000

Figure 4.14. Simulated vs. field tritium tracer response, McCleskey sandstone Many wells were producing oil as well as water. Mobile oil was also treated in the model in association with measurements of residual oil, but the discussion of these results will be deferred until chapter 5, where the use of tracers for measuring oil in place is considered.

Field Examples and Data Analysis

159

NIITSU OILFIELD TRACERS The use of large simulators for tracer studies is time-consuming and therefore expensive in computer time. The analytic model of Abbaszadeh (1982) for flow in s t r e a m t u b e s is much cheaper and faster to use, but not as accurate. By combining these two, useful tracer results can be obtained t h a t are not available from either method alone. In a tracer study of a pilot test in the Niitsu oil field in J a p a n (Ohno et al., 1987), a streamtube model was used to do a preliminary analysis of the tracer response. A modified three-dimensional black-oil simulator was then used to analyze the data in greater detail. From these data, the authors derived a reservoir model of the area and a vertical distribution of heterogeneities in the pilot area. The model was also used to calculate three-dimensional sweep efficiency as a function of time.

Tracer behavior This paper was concerned primarily with the use of tracer data to analyze flow in the reservoir but largely ignored the source of the tracer data. This is a common situation where the people who do the reservoir analysis are not known by those who analyze the samples and who may be doing it long before the reservoir analysis. In this case, there are problems associated with the tracer data. Four tracers n iodide, nitrate, chloride, and thiocyanate n were tested for loss by static adsorption on reservoir sand using water of three different compositions: distilled water, a synthetic formation water, and two real formation brines. This was not a severe test, and all of the tracers passed it except for thiocyanate ion in the two formation brines. There was no loss of thiocyanate for the first 30 days but a continuous loss in activity from 30 days onward, an unexpected behavior for this ion. The same kind of problem turned up later in the field test, where only the data collected within the first 45 days after injection could be used because of decreasing thiocyanate concentration after t h a t time. The analytical procedure used is not given, and whereas analytical interferences could be the source of the problem, the incubation period followed by a continuous loss of thiocyanate makes bacteria a more likely cause. Bacterial decomposition of thiocyanate is not common but is known (Hydro Geo Chem, 1986; Jones et al., 1992). The problem is often an aerobic one t h a t can be eliminated by the addition of biocides to the collected samples. Tracer loss in the formation is commonly ascribed to adsorption, but there is no evidence to show that thiocyanate ion is adsorbed in the kind of formation materials described here. It is not a likely mechanism for simple anions in a negatively charged formation. The use of a polymer option in a black-oil simulator for following tracers is probably adequate for that purpose, but these tracers do not show the kind of surface coating ability that polymers do. Tracers can be lost in m a n y ways, and it m a y be t h a t some of these can be s i m u l a t e d by such adsorption behavior; but loss by surface coating adsorption is not likely.

160

Chapter 4

Thiocyanate ion was chosen as tracer and injected continuously (a step input) at a concentration of 1000 ppm. The injection water consisted of a brine solution injected at a rate of about 176 B/d (28m3/d). The formation w a t e r contained a somewhat lower chloride concentration t h a n the injection water. Tracer breakthrough occurred at C-39 18 days after injection and at C-85 after 20 days. No tracer was detected at C-49 during the test period. The tracer response data are shown in Fig. 4.15. The difference between the produced and injected brine concentration was examined for its possible use as a tracer for injected water, but the difference between the two was insufficient for this purpose. The produced chloride concentrations at each well are shown by the relatively horizontal curves intersecting the left axis of Fig. 4.15. The produced thiocyanate concentrations at wells C-39 and C-85 are marked on the figure and read on the right axis.

Pi l o t a r e a

Tracer response

i.

//

9

:

8

i

,...~

..................

[

~ ..... .

/.

. . . . , .... ..

z/~ 20

Mar

10

I,o 20

April 10

"

Figure 4.15. Niitsu pilot pattern and tracer response

Test analysis The tracer test was part of a larger study done in anticipation of an enhanced oil recovery test. The pilot was composed of a new injector, R-2, and t h r e e existing producing wells, C-39, C-40, and C-85, each about 30 meters from the injector, as shown on the map in Fig. 4.15. The t r a c e r d a t a were first analyzed using the analytic model described in Abbaszadeh (1982) and Abbaszadeh and Brigham (1984) for the injection of a tracer pulse. Tracer response data from the step injection had to be converted to its pulse equivalent by differentiating the data from the response curve with

Field Examples and Data Analysis

161

respect to injected volume. The thiocyanate response was matched (Abbaszadeh and Brigham, 1989) by choosing layers of thickness, h, and permeability, k. The fit obtained with four layers is shown in Fig. 4.16 for wells C-39 and C-85. Because of the errors introduced in differentiating the data, problems in fitting the unbalanced pilot, and the lack of dispersion data, absolute numbers for permeability and thickness could not be obtained but could only be estimated relative to each other. The calculated data from Fig. 4.16 were integrated to yield volumetric data and, as shown in Fig. 4.17, part a, matched the field tracer production on a volumetric basis. This was good enough for ordering the vertical permeability distribution; however it did not account for the early water breakthrough observed in wells C-49 and C-85.

Well C-39

O.Ol

Well C-85 0.001

~~ o

o

dC Oo

0

i

o

.

.

.

.

.

.

.

.

O

dC o ~

.

o

~-:~-i

2 4 6 8 Injected volume, bbls x 1000

:------~

2

, '

'

i

4

:

6

:

?

s

Injected volume, bbls x 1000

Figure 4.16. Four-layer fit to tracer data: C-39, C-85 The field data were analyzed further using a black-oil simulator with a polymer option that was used to simulate the tracer. Several flow models were tested using, in addition, the core data from the four research wells. The best fit was obtained using a model combining a vertical thief zone in layer 2 with a radial permeability distribution for the other three layers. The effect of the n a t u r a l water drive on the production times was also put into the model, resulting in a good match of tracer simulation with field data as a function of time for both wells, as shown in Fig. 4.17, part b. One of the major objectives of this kind of test is to estimate the sweep efficiency of the flood. This study allowed the estimate of both vertical and

162

Chapter 4

b C-39

0.1

400-

E D.

C

"

.o .= u

0

o

1

2

,

,

'

4

'

o

|

6

V o l u m e Injected, bbls x 1000

20

30

40

50

Time, days

Figure 4.17. Tracer concentration vs. injected volume and time data

~c~

I

lh'~2.'.o~-. ! i h-< I dz~, f/Wt/~-<,,l~\~ \ik\i 'f f( ~. {l~i ' )/lJll J!HI \Kx'x.~, lllf/Xl I'~~x,-'b.<~/lll..Z I \\~L~

!

I

I

I

i

,i!,

, ,

eli c4oi ! , I

I I

i

Figure 4.18. Estimated sweep efficiency

60

70

Field Examples and Data Analysis

163

horizontal sweep as a function of time. The areal sweep of layer 2 at the tracer b r e a k t h r o u g h time at well C-39 is shown in Fig. 4.18.

M a l j a m a r u n i t tracers ~ r e e tracers were used in a tracer survey to identify flow channels in the Maljamar Cooperative Unit in the San Andreas formation (Pittaway et al., 1986; Beier and Sheely, 1988) in preparation for a CO2-enhanced oil recovery project. The tracers used were tritiated water, 1-125 as iodide ion, and C-14 in an unidentified form, presumably as thiocyanate. Tritiated w a t e r alone had been used in a n e a r l i e r s u r v e y to identify flow channels between 62 injectors and the surrounding 177 producers. Twenty-five producers responded during the 12-week sampling period. The second survey was made to identify injection sources for the 19 tracer producers showing the greatest response to the earlier test. There was a significant difference in tracer response between the two surveys, probably due to changes in production operations between tests and to the difference in the way the tracers were injected. In the first test, a total of 124 curies of tritiated w a t e r was injected into five headers supplying the 62 injection wells. The a m o u n t of tritium going to each well was estimated from the flow distribution from the headers. The amounts of tracer for the second test were based upon the results from the first, but the three tracers were injected individually into each well. The two methods of tracer injection are not equivalent and can result in different amounts of tracer being injected into each well. The a m o u n t of t r a c e r recovered at each well was calculated from t r a c e r response curves using produced volumes; however m a n y of the response curves were incomplete, leading to artificially low recoveries. The authors refer to a paper by Deans (1978) to calculate the swept volume from the first moment of the produced tracer curve. They estimate the swept volume, Vs, from the product of the m e a n produced volume and the ratio of the m e a n w a t e r rate between the injector and producer, Qip, and the m e a n w a t e r production rate, Qp, as shown in Eq. (4.1): Vs =

Vp

(4.1)

where Vp, the m e a n produced volume, is calculated from the first moment of the produced tracer concentration, C, as a function of the produced volume, Vp, as discussed later in this chapter and shown in Eq. (4.2) below: oo

_ Vp =

JCVdV oo

J

CdV

(4.2/

164

Chapter 4

Qip, the flow rate between injector and producer, is estimated from the fraction of injected tracer produced at the well at the m e a n injection rate, Vi: m

Qip = ~ Qi

(4.3)

Here, m is the a m o u n t of tracer produced at a given well, M is the a m o u n t of tracer originally injected, and Qi is the m e a n injection rate; hence, the swept volume can be expressed in terms of the injected and produced flow rates and the fraction, m/M, of water going from the injector to the producer: mQiVs = ~ ~ppVp

(4.4)

M e a s u r e m e n t in terms of flow rates can be a problem in oil fields where the flow rates are variable and m e a n flow rates are difficult to assess. Another way of calculating the swept volume is shown later in this chapter. Cationic reservoir The only paper in this group in which the tracer procedures are given in detail is one in which cationic tracers are used. It has interest for this reason as well as for the u n u s u a l choice of cationic tracers for a waterflood. The latter m a y be due in p a r t to the l i t e r a t u r e practice of using only the isotope to describe waterflood tracers. In a recent paper by Wood et al. (1990), as mentioned earlier, the authors reported success in using radioactive cations as w a t e r tracers in a small flood in a carbonate reservoir. The tracers were tested by means of a single-well test in which they were injected into the reservoir together with a known a m o u n t of tritiated water. After a delay of three days, the tracers were back-produced. When all the tracers were recovered, the interwell test proceeded using cesium-134 and -137 and the two cobalt isotopes Co-57 and -60 as water tracers. The authors give details of the procedure used to design and carry out the test and of the tracer analysis. They describe a procedure for inserting tracers at a given depth down hole by breaking a vial of tracer solution in the borehole at the formation depth. Packers were used to isolate the zone. The operation was carried out with a remotely operated vial breaker. It seems a safe operation. The procedures used are excellent and the descriptions easy to follow. Cobalt-60 was injected in two different forms: as an EDTA complex and as the cobaltous ion. Co-57 was injected only as an EDTA complex. The cesium isotopes were injected as the Cs + ion. The authors claimed t h a t all except the Co-57 were produced; however this contradicts experience in sandstone cores and reservoirs. Cs + and divalent ions such as Co +2 are strongly absorbed by clays and anionic surfaces. Without carrier, they are normally absorbed by formation materials.

Field Examples and Data Analysis

165

This implies t h a t the reservoir in question is not anionic and contains little clay. Since carbonate reservoirs can be cationic at lower pH's and may not have much clay available, they seem to meet these criteria. The only other literature reports (Asgarpour, 1987, 1988) on cationic tracers in carbonate reservoirs reported the use of tritiated water, Cs-134, Cs-137, Co-60, and Eu-152/154 as tracers for following a waterflood in a dolomite reservoir in the Fenn-Big Valley field in Alberta, Canada. Neither the tracer details nor the chemical form of the tracers is given. Results are reported only for tritiated water. No response had been reported from the cationic tracers in over two years.

V O L U M E T R I C ANALYSIS OF F I E L D T R A C E R DATA Tracers are added to waterfloods for a variety of reasons, all of which stem from the singular property of an ideal tracer m that it acts as an analog of the element of water with which it is injected. This permits the use of tracer data for reservoir description, both for qualitative and quantitative observations in the field, and for use in simulators to quantify the water's movement through the reservoir. One aspect of this property seems to be largely overlooked. If the injected tracer acts as an analog of the injected water, analysis of the tracer movement should be equivalent to analysis of the water movement. This aspect has two consequences: one concerning the distribution of the injected w a t e r and the other concerning the mean pore volume swept by it. The water analog means that the distribution of injected tracer in responding wells is equivalent to the distribution of the injected water. If 100 curies of tritiated water were injected into the formation and 19 curies of tritiated water were produced at a responding well, 19 percent of the water from this injector should also have been produced at this well. The fraction of injected tracer from a given source t h a t is produced at a responding well is the same as the fraction of injected water produced there. A second consequence of the tracer-to-water analog is the ability to estimate swept pore volume. If an ideal tracer pulse is injected into the formation under water drive, the cumulative volume injected when tracer appears at a responding well is a measure of the pore volume swept by the injected water to t h a t point. The tracer response to the pulse injection, expressed as a tracer concentration per unit of injected volume, C(V)i, is distributed over a wide range of volumes. The m e a n of this distribution represents the mean volume injected. It seems reasonable to equate this with the mean pore volume swept; however the injected water arriving at a well m u s t compete with other responding producers for the same water. This is expressed, as above, by the fraction of injected water arriving at the well. Therefore, that part of the mean pore volume swept only between the

166

Chapter 4

corresponding well pair is given by the fraction of injected water produced at the responding well times the overall mean volume swept. This calculation makes it possible to use field tracer data directly for waterflood m a n a g e m e n t without waiting for modeling, simulation, or a n y t h i n g more complex t h a n a hand calculator, although a spreadsheet on a personal computer can be handy. These are not the only kinds of quantitative information available from t r a c e r response curves. Analysis of tracer response curves can also yield useful data about reservoir heterogeneities and layering. This aspect is discussed separately in the appendix. Basic assumptions

We define an ideal w a t e r tracer as one t h a t is miscible with water, following identically the movement of the water and undergoing no loss or separation from the injected w a t e r during its movement through the reservoir, but one t h a t can be identified and measured independently of the water. The w a t e r from any given injection well can be treated as an incompressible, continuous stream made up of macroscopic elements, large compared to the reservoir pores but small compared to the reservoir volume. Injection of a tracer pulse identifies an element of volume. The tracer response observed at a producing well is identical to t h a t of the water in the volume element being traced. The tracer response monitored at the field is a direct measure of the movement of the w a t e r injected from t h a t source. Hence, analysis of the tracer response is equivalent to analysis of the w a t e r response, and the mass balance of the tracer reflects t h a t of the injected water. Tracer response curves

When a pulse of injected tracer is produced at the surrounding wells, it generates a distributed tracer response curve at each well. This is due to the distribution of flow paths, and of flow rates within each path, by which w a t e r moves through the reservoir. The n a t u r e of the response curve depends on the p a r a m eters used to categorize the concentration data. Tracer concentration can be expressed in terms of time, t, of injected volume, Vi, or of produced volume, vp. Most t r a c e r concentration data are expressed in terms of elapsed time, C(t), because in most cases the people providing the tracer concentration data do not have the volumetric data available. A disadvantage to time as a base is t h a t v a r i a t i o n s in injection r a t e result in a biased response curve. If the t r a c e r concentration is expressed as a function of cumulative volume injected, C(Vi), it is r a t e - i n d e p e n d e n t , a l t h o u g h the n a t u r e of the r e s p o n s e curve is not independent of changes in rate. The concentration can also be expressed in terms of cumulative produced volume, C(Vp). A typical response curve is shown in Fig. 4.19.

Field Examples and Data Analysis

mode

167

mean

r ~

0 r 0 tO 0

cumulative volume

Figure 4.19. Tracer response curve showing landmarks LANDMARKS

At least three landmarks are recognized in a tracer distribution curve. These are shown in Fig. 4.19. The first indication of tracer response in the field is commonly known as the breakthrough (BT) response. It is common to describe sweep efficiency in terms of this landmark, expressed in terms of cumulative volume injected. Unfortunately, this is not a well-defined m e a s u r e m e n t in the field. It is very dependent on the sensitivity of the m e a s u r e m e n t device and the sample frequency. The maximum of the tracer response curve is the mode of distribution. It represents the most probable response; while multiple peaks in the distribution do occur, there is usually a "highest" peak present. The m e a n of the distribution relative to the injected volume represents the mean volume injected. In a homogeneous, one-dimensional system, neglecting dispersion, the breakthrough, BT, is a measure of the pore volume swept by the water. In a two- or three-dimensional heterogeneous reservoir, the BT response is a function of the p a t t e r n geometry and the heterogeneities. It is only an indicator of the volume swept by the fastest paths between injector and producer, not a m e a s u r e of the total pore volume swept between injector and producer. The total pore volume swept by the injected water is the sum of all the paths by which the water moves between the two wells and is better measured by the mean of distribution. The response curves can also be normalized with reference to one of the landm a r k s as a means of emphasizing certain aspects of the curve. This is sometimes useful in comparing data from different parts of the field. CURVE NOISE

One normally expects tracer response curves to be reasonably smooth and continuous. In m a n y cases, this is so; however many exceptions are found, particularly in large m u l t i p a t t e r n waterfloods. It is not unusual to have a continuous

168

Chapter 4

response curve interrupted by one or more samples having either no tracer or a very low tracer concentration. Alternately, sometimes a sample of high tracer concentration will occur while adjacent samples are reading zero. Other variations are possible. Many of these effects can be traced to the production well. They can be caused by m a n y uncontrolled factors, such as pressure variations in the well resulting in cross flow, deposition of scale, gas breakthrough, etc. They can also be due to changes in well operation, workovers and a variety of h u m a n factors. It is unfortunate t h a t the people who analyze the response curve m a n y months or even years after the event have no way of knowing what caused the odd effects.

Tracer response analyses using moments MOMENT ANALYSES Tracers are widely used in the chemical process industry for analyzing nonideal flow in chemical reactors. There is a well-developed base of theory and practice in the chemical engineering literature relating tracer response to nonideal flow through chemical reactors (Levenspiel, 1962). In this application, a stimulus is applied by injecting a tracer at the inlet of the system either in the form of a narrow pulse (delta function) or as a continuous injection (step function), and the tracer response as a function of cumulative time is monitored at the output. The tracer distribution curve generated at the outlet is used to analyze flow through the reactor. The two kinds of input yield the same kind of information, but for simplicity the discussion here will be restricted to the use of a tracer pulse input. Analysis of the tracer distribution curve is done by relating the moments of the distribution curve to possible flow models in the reactor. Any distribution curve can be analyzed in terms of its moments using conventional statistical analysis. The first moment of a distribution is the mean of the distribution, the second m o m e n t represents the variance, the third moment the skewness, etc. In chemical reactor analyses, only the first two moments are usually analyzed. The first moment of the tracer distribution curve is the mean residence time. The second m o m e n t (the variance) can be related to the Peclet number, a dimensionless n u m b e r giving the ratio of convective to dispersive forces. From these moments alone, flow conditions varying from plug flow to fully mixed flow can be described in a reactor. Even more complex flow behavior with different interconnected flow regions has been treated in this fashion (Himmelblau and Bischoff, 1968). The problems of nonideal flow in a reservoir differ from those in a chemical reactor in m a n y ways. In each case, however, nonideal refers to u n k n o w n flow description r a t h e r t h a n to flow t h a t cannot be described by known hydrodynamics. There is no background of theory and practice for tracer response from reservoir data comparable to t h a t used in the chemical process industry, but

Field Examples and Data Analysis

169

some of the methods should still be applicable. If the injected w a t e r in a waterflood traverses a volume only once in passing through the reservoir, then m o m e n t analysis can be used to define t h a t volume. A major difference in this analysis from t h a t used for chemical reactors is t h a t we are not interested in the m e a n residence time but are interested instead in the m e a n pore volumes. The two are obviously related. FIRST MOMENT The m e a n of any distribution is given by its first moment. For the produced t r a c e r d i s t r i b u t i o n (produced tracer concentration vs. c u m u l a t i v e volume injected) at each well, the first moment of the distribution, C = f(V), is given by the integral expression below: _ V=

JCVdV (4.5)

oo

J

CdV

Since the tracer production curve is actually composed of a discontinuous set of points, the integral can be approximated by the s u m m a t i o n as shown below, where V is the m e a n volume, and ~(1) = ~ is the first moment of the distribution. oo

~CVAV

g=V= 0

(4.6)

~CAV 0 Subsequent moments about the m e a n are defined by the general expression: oo

J

C(V-V)ndV

~(n) =

oo

(4.7)

J

CdV

where ~t is the first m o m e n t and n represents the n u m b e r of the m o m e n t about the mean. For n - 2, this is the second moment about the mean. EXTRAPOLATION OF INCOMPLETE DATA The problem with calculating the m e a n from the first m o m e n t is t h a t tracer response curves from field wells are quite spread out and often incomplete. This is one of the major problems in analyzing field data. In order to m e a s u r e the first

170

Chapter 4

moment, we must complete the distribution curves by extrapolation of the collected data. To extrapolate data from a distribution curve, it is necessary to predict the path of the curve and be able to calculate the expected values to the end of the curve. This has two requirements: first to find a function that can reasonably be expected to describe the data path; second, that the function be bounded, i.e., that its value to infinity be fixed and calculable. There are at least two functions that are bounded and that might reasonably be used for extrapolating such data: the error function and the exponential function. In this author's experience, only the exponential function has been successful for this purpose. Most field data, given enough time, will ultimately show an exponential decline. If the tail of the tracer response curve can be fitted to an exponential decline, its value to infinity can be calculated. The moments of the response curve can then be obtained by dividing the data into two parts, one representing the data from zero to point Ve, where it can be treated as exponential, and the second covering the extrapolation of the exponential part from Ve to infinity. The best fit of the tail of the tracer curve to an exponential decline is first found numerically or graphically. It can then be expressed in the form (Deans, 1964): -/VaVe/ C = Ce e

(4.8)

where 1/a is the slope of the line and Ce is the measured tracer concentration at the value of Ve for which the exponential fit starts. If Eq. (4.8) is substituted for C in Eq. (4.5), it can be shown by simple integration that the denominator of Eq. (4.5), integrated from Ve to oo, is given by Eq. (4.9): oo

xJCee-(V~e / dV = aCe

(4.9)

Ve Substitution of Eq. (4.8) for C in the numerator of Eq. (4.5) gives an integral that can be integrated by parts. Its value from Ve to r162 is bounded and given by Eq. (4.10): oo

Ce~ e v e- ( V ~ e ) dV = aC e(a + Ve)

(4.10)

Hence, the expression for the first moment given by Eq. (4.3) can be replaced by the expression:

Field Examples and Data Analysis

_

171

Ve JCVdV + aCe (a+Ve)

V=

Ve

(4.11)

J

CdV + aC e

SECOND MOMENT

The analysis above is concerned only with the first m o m e n t of the distribution. In a completed response curve, the second moment is a measure of the width of the distribution. This can be related to the number and size of reservoir paths, to the dispersion along these paths, to the extent of layering, to reservoir heterogeneities, and to a variety of wellbore effects. At this point there does not seem to be an obvious interpretation. While it is unlikely t h a t any single technique is capable of resolving all these factors, it might be valuable to combine these kinds of data with logging, geologic, and production data in a simulator to improve our u n d e r s t a n d i n g of flow in the reservoir. There is no known background of data correlating any of the moments of the tracer response curves with field conditions or operation. A considerable amount of information is available directly from tracer response curves without the need for other techniques. This includes 1) an estimate of the pore volume swept by the injector to each of the responding producers; 2) an estimate of material balance of produced and injected waters for each responding well; and 3) estimate of reservoir heterogeneity by deconvolution of the tracer response for the Abbaszadeh-Brigham method (1982).

Distribution of injected water between producers The amount of injected tracer produced at each well can be estimated from the production data at t h a t well and the produced tracer concentrations. The total amount of tracer, mip, produced at any given well, p, from injector i is given by the integral of the produced tracer concentration as a function of the produced water, ~C(V)ip dV. For the discrete data from the tracer response, this is better expressed as the summation ~C(V)ipAV, taken over the entire curve. Incomplete data can be extrapolated by the procedure described earlier, where the data are s u m m e d graphically to the point where the response curve has an exponential decline, and the extrapolated decline from Eq. (4.9), aCe, is added: Ve mip = ~ C A V + aCe o

(4.12)

172

Chapter 4

Following the same kind of a r g u m e n t as before, the distribution of tracer is equivalent to the distribution of the injected water. If M is the amount of tracer originally injected, the fraction of injected water, f, produced at a well is given by: f= mip M

(4.13)

If 10 percent of the injected tracer is produced at a given well, it m u s t follow t h a t 10 percent of the injected water was also produced there. The procedure is presented here as a means of extrapolating incomplete data. It can be used any time after the curve has peaked for making estimates of water distributions early in the life of the flood, subject to later correction. There is no obvious correlation between the volume of injected water produced at a well and the reservoir pore volume swept out by this water. A large fraction of injected water can move easily to a producer via a high-permeability p a t h w i t h o u t sweeping a large reservoir volume in its path. These d a t a can be normalized to give the distribution of injected water for the entire pattern and for the entire field. MASS B ~ C E IN WATERFLOODTRACERS One of the problems in dealing with waterflood tracers is t h a t the mass balance is frequently less than 100 percent, as was discussed previously in chapter 3. This is particularly true of the distribution of tracer and hence of w a t e r in large p a t t e r n floods. A major reason for this is the limited dynamic range of currently available tracers. We design tracer tests assuming t h a t the tracer responds only at the wells immediately surrounding the injector in each pattern. If the tracer is spread over a larger swept volume or subjected to a higher dilution t h a n expected, the produced concentration may be too low to measure. P a t t e r n maps are not inviolate, and there may be a different distribution of sinks and sources in the reservoir t h a n indicated by the pattern map. Other factors, such as a high degree of imbalance, can also can cause high dilutions and distort the results. If the concentrations are below the minimum detection limits, they will not be recorded. The dynamic range of a tracer is the range of concentrations that can be measured. The maximum amount of tracer injected is usually limited by a number of external factors over which we have little control, such as costs, safety factors, and logistics. The only way to significantly increase the dynamic range of the tracing process is to find new tracers having lower detection limits, or to lower the detection limit on the tracers now in use, as discussed in earlier chapters. SWEPT PORE VOLUME FROM FIRST MOMENT If the injected water is tagged with a pulse of tracer, the cumulative volume of w a t e r injected into the formation when the tracer arrives at a producer is the pore volume swept by the injected water. The identification of this volume is

Field Examples and Data Analysis

173

complicated by the fact that the produced tracer concentration, C(V)i, is distributed over a wide range of injected volumes, r a t h e r t h a n produced as a sharp pulse. The tracer b r e a k t h r o u g h volume is sometimes used as a locator of the swept pore volume. This number is a function of the sensitivity of m e a s u r e m e n t and is really only a measure of the fastest paths. A better locator for the swept volume is the mean of the distribution, the average (pore) volume swept by the injected water, V, as shown in Eq. (4.5). This is the first moment of the distribution. It represents the mean of the swept volume, averaging the shortest with the longest flow paths swept by the injected water in arriving at this well. A second complication arises because the tracer data are often incomplete. For this case, the curve m u s t be extrapolated using the procedure derived in Eq. (4.11). For the i n t e r m i t t e n t field data, the integral is better replaced by a summation as shown in Eq. (4.14). Ve ~_CVdV +aCe (a+Ve) --

0

V =

Ve

(4.14)

~ C d V + aCe O

The error in the mean volume calculated in this m a n n e r can be estimated numerically by assuming different values for the slope of the curve. Tracer response curves are incomplete only because the program was not carried on long enough, although in large pattern floods this may take m a n y years. It is, however, a useful method for estimating the swept volumes early in the life of any flood. Water moves in the reservoir in accordance with the gradients arising from the producing wells (pressure sinks) and injection wells (pressure sources) distributed through the reservoir. The volume swept by the injected water is a response to these forces. The fraction of this swept volume accruing to a given production well is reduced by the fraction of the total injected water t h a t arrives there. This can be calculated from Eq. (4.13). The net volume swept for well i is therefore: - -

- -

m i

Vsi = f V s = ~iiVs

(4.15)

The above discussion assumes that the pattern obtained by connecting the n e a r e s t producers s u r r o u n d i n g each injector with lines will define the flow between injectors and producers. In fact, it often does not; the actual flow may bypass some wells in the pattern, or behave "badly" in other ways. It is one of the functions of a tracer to detect this kind of behavior, for there is no other way that such imbalance can be detected in a multipattern field. Swept volume measured

174

Chapter 4

is still a valid estimate of sweep even if the pattern turns out to be different from expectations.

Comparison with other calculations In discussing the Maljamar pilot study (Beier and Sheely, 1988) earlier in this chapter, we referred to an equation (Deans, 1971) giving an estimate of the swept volume, Vs, between a corresponding well pair from the product of the m e a n produced volume, Vp, and the ratio of the mean water injection rate, Qi, to the m e a n w a t e r production rate, Qp, as shown: mQi Vs = ~ ~

Vp

(4.16)

In the development we used here, the swept volume, V si, was calculated as: m

Vsi = ~ V j

(4.17')

where Vj is the mean injected volume from the corresponding injector. If these values for swept volume are to be the same, then Vsi = Vs, and: Vj _ Qi

vp Qp

(4.18)

but the m e a n flow rates, Q, are the mean volumes injected or produced per unit time averaged over the entire time interval; hence the ratio of the m e a n injection rates m u s t be equal to the ratio of injected mean volumes. This is clearly true under reasonably steady-state flow conditions, or under randomly distributed variations about the mean flow rate; however the concept of m e a n flow rate is probably not applicable to cases where there are major flow stoppages or unpredictable, nonrandom changes in flow rates. Unfortunately, these conditions are not uncommon in large waterfloods.

Comparison with simulated results The analysis of water distribution and of swept pore volumes in a multiwell p a t t e r n is difficult to do analytically; however it can be simulated with somewhat greater ease. Use of the first moment method to calculate the swept volume between wells was simulated (Maroongroge, 1993) using a three-dimensional compositional simulator, UTCOMP. The simulated reservoir consisted of a square block 165 ft on edge and 20 ft thick. Four wells - - two injectors and two producers m were located in the block in a pattern shown in Fig. 4.20. A 10-percent pore-volume slug of tracer was injected into injection well no. 1. No t r a c e r was injected into well no. 2. Both injection wells were operated at a constant injection rate. The swept volume to each producing well was obtained using two different methods: in the first it was obtained from the s u m m e d concentration contours, and in the second it was calculated using the first moment

175

Field Examples and Data Analysis

from the simulated response and the fraction of total injected tracer produced at each responding well. The results for the two producing wells in Fig. 4.21 show the fraction of pore volume swept vs. the (normalized) remaining concentration. It is seen that the two methods become equivalent as the longer streamlines are produced. To reduce numerical dispersion, the swept volumes were extrapolated to zero grid block size.

82.5

~producer

49.5

'

r

~ ...... ~,,~..~,.,~...-.~

F -

.

:

,

~~

!

~-...%:'-'i

16.5

co o (1) L_

,'

t

.,.!-.;..:~ ............... ".-".~

...........

.m

"i

,m

13 -

No 1

16.5

I

~ ....................

Inject tracer No2

(No tracer added)

-!""i !~i~ . . . . . . . . . . .

r .........................

i [

~#.i

i

|

- 49.5

.....................

I ..........................

producer ~io 2

J? - 82.5 ~ ' " ' . . . , : - 82.5 - 49.5

-

16.5

16.5

x-direction

Figure 4.20. Pattern for simulated tracer injections

! 49.5

82.5

176

Chapter 4

=0

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

0.8

.

.....................................................

g.

~ 0.6 =

r

i V_ 1 F r o m concentration cont urs 0.4 .............................................!...... ~ .............................. !............................................7

0.2

_.-...2..2........................... i............................................ !

V

f

sl

'

i .......................................

First moment calculation i

L. . . . . . . .

0.0

........ 10 -3

1.0

.......

0.8

i ............................................................... .~ .................................................................................................................................

10"4

10 -5

1 -6

i. . . . . . . . . . . . . . i

,.

I

o i i l i ~o 0.6 ........................................................... t................................................................ ~............................................................... . ~ V S2 F r o m concentrption contours

=e 0.4 .....:--.-:--:---_-.-=--:.-=......_.=-_---_--~-.--.-~-~,.-=-------=-~--= ..............,,.................,=.............

=o 0.2

~

m

VS~

.................................................................

From first moment calculation

~. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

O.

0.0 . . . . . . . 10 -3

i...... 10-4

~ 10-5

.

, 10 -6

Normalized cutoff concentration

F i g u r e 4.21. C o m p a r i s o n wells 1 a n d 2

F i e l d results, N o r t h West F a u l t B l o c k FIELD DESCRIPTION T h e p r o c e d u r e s d i s c u s s e d in t h e p r e v i o u s section w e r e u s e d to m a k e e s t i m a t e s of s w e p t p o r e v o l u m e s a n d i n j e c t e d w a t e r d i s t r i b u t i o n s in t h e N o r t h W e s t F a u l t B l o c k w a t e r f l o o d a t t h e P r u d h o e B a y field in A l a s k a , o n e of t h e l a r g e s t w a t e r f l o o d s in N o r t h A m e r i c a . I n i t i a t e d in 1984, t h i s l a r g e p a t t e r n flood c o n s i s t s of 18 i n v e r t e d n i n e - s p o t p a t t e r n s on a b o u t 8 0 - a c r e s p a c i n g p l u s four l i n e - d r i v e i n j e c t o r s . E a c h of t h e i n j e c t o r s w a s t a g g e d w i t h one of f o u r t r a c e r s " Co-57 a n d Co-60 t a g g e d h e x a c y a n o c o b a l t a t e , C-14 t a g g e d t h i o c y a n a t e ion, a n d t r i t i a t e d

Field Examples and Data Analysis

177

water. The p a t t e r n map showing the two injection patterns under discussion in this chapter is given in Fig. 4.22 (BP Alaska, 1989).

II Injectors 9Producers

"

\

1011

9

II

0

l N

0

Figure 4.22. Two tracer injection patterns in the North West F a u l t Block Reservoir volumes in the waterflood patterns are large, and most of the tracer response data from the field are incomplete. Early tracer results showed a strong northwesterly flow trend in the field. As shown in Fig. 4.1, there was also a very low ratio of vertical to horizontal permeabilities leading to highly stratified flow. To alter this, major changes were made in flow distribution and considerable well work was performed to cut off thief zones. Many of the wells were also involved in miscible injection procedures. As a result, the tracer data are often quite irregular as well as incomplete. This is a common situation in m a n y oilfield waterfloods. Tracer data from two of the injection patterns in M pad, M-03 and M-14, are presented here to illustrate the method of calculating swept pore volumes and w a t e r distributions between well pairs. One h u n d r e d curies of t r i t i a t e d w a t e r had been injected as a tracer pulse into each of the two injection wells in J a n u a r y 1985. W a t e r samples, collected from all the s u r r o u n d i n g wells on a preset schedule, had been analyzed for all four tracers and corrected for decay.

178

Chapter 4

As is often the case, these data were recorded by sample date for each well. Daily injection and production data for the two injection wells and for the surrounding producers were obtained at a later time from an on-line computer data base at another location.

Calculation methods The first step in this procedure is to convert the tracer data from a function of time (date) to one of cumulative volume. The daily injected and produced water volumes are first summed to give cumulative volumes, and these are tabulated as a function of date. The t r a c e r concentrations are t h e n i n s e r t e d for the appropriate dates. S t a n d a r d spreadsheet functions are used to accumulate the volumes automatically as a function of time, eliminate data t h a t have no tracer analysis, and construct a table containing only those dates and cumulative volumes for which a tracer concentration is recorded. Despite the large amount of data collected for the six-year interval covered by the tables discussed here, the table can be assembled by means of a spreadsheet on a personal computer in an hour or two if a data base is available. Most of the effort required is to obtain and assemble the original data; if this procedure is used from the start of a waterflood tracer test, it can be m a i n t a i n e d with little effort. This basic table is used to obtain all the functions required for plotting the data, estimating the swept volume, and calculating the distribution of injected water. The basic functions for these calculations m AV, CAV, and CVAV m are also obtained by s t a n d a r d spreadsheet calculations t h a t automatically propagate sequential numbers in a column and multiply numbers in different columns row by row. They also provide the sums ZCAV and ZCVAV to fit in the appropriate equations. It should be noted t h a t the same functions are also available from built-in statistical programs in h a n d calculators. These are not automated but are adequate for calculations using small amounts of data. Once a sufficient number of data points have been collected, the best smooth curve can be drawn through the points. Such a curve can be analyzed using a fraction of the data points used to derive the curve. This can be done easily on a hand calculator. Two kinds of tables are used for the water calculations. The amount of tracer (water) produced at a well is the sum of CAV for the entire producing interval, derived from the table of concentration versus produced volumes, Vp. The fraction of injected tracer (water) produced at a given well is simply the a m o u n t calculated above divided by the original amount injected. This is illustrated by the calculation of water distribution between M-03 and M-10 given below. The pore volume swept between wells is calculated from the table using cumulative injected volumes, Vi. These calculations are illustrated in the analysis of tracer response for the well pair M-03/M-23 given below.

179

Field Examples and Data Analysis

,=,42c,

m =_ m m

Well M-10

m

,,

I

~ 1

2

I , 3

I , 4,

I l 5

I | 6

CUMULATIVE PRODUCED VOLUME, MMBLS

Figure 4.23. Tracer production at M-10 from M-03

WATER PRODUCTIONAT WELL M- 10 FROM M-03 For well M-10, responding to the injection of water from well M-03, the prouced tracer is calculated as shown in Table 4.1. The basic table of data is given in the left three columns relating time, cumulative (produced) volume, Vp, and tracer concentration, Cp. The data in the next two columns are derived automatically from these by s t a n d a r d spreadsheet manipulations - - AV and CAV. The sum of all the values in the last column, ZC AV, is the required value. The tables used here are abbreviated to save space. Only a representative part of the data is needed for these calculations. The data can be completed by using the graphical extrapolation discussed earlier to calculate the constant a and value aCe. Fig. 4.23 shows the tracer response at well M-10 from injection into well M-03. The g r a p h of concentration, C, versus cumulative produced volume, Vp, is plotted on semilog paper. The exponential extrapolation can be done in this m a n n e r or it can be done numerically. For these cases, the best fit is shown graphically. The value of the constant, a, was obtained from two points on the extrapolated line, C 1,V1 and C2,V2, as shown below. The results of the calculations are given at the bottom of Table 4.1. The extrapolation added an additional 32 percent of tracer, and hence of water, to t h a t accounted for by the data if the zone had not been shut in.

180

Chapter 4

TABLE 4.1 Calculation table for tracer produced at M-10 from M-03 Date sample collected 10 Sept. 86 14 Oct. 86 4 Nov. 86 3 Dec. 87 1 Jan. 87 1 Feb. 87 2 Mar. 87 29 Apr. 87 17 Jun. 87 16 Jul. 87 12 Aug. 87 10 Oct. 87 3 Dec. 87 9 Feb. 88 6 Apr. 88 25 Oct. 88 12 Nov. 88 26 Jan. 89 11 Mar. 89 9 May 89 18 Jul. 89 3 Sept. 89 3 Oct. 89

Cumulative volume produced

Tritium concentration ~tCi/bbl

Volume difference AV

581264 685692 748109 820782 900363 1008745 1107647 1310703 1471977 1580180 1674265 1883129 2095121 2356681 2549282 2831008 2932037 3307456 3532805 3821343 4213944 4545824 4740709

0.24 0.91 1.3 1.9 2.5 2.52 2.57 2.98 3.18 2.47 3.49 3.67 3.14 3.55 2.67 1.27 2.34 2.54 1.87 1.97 1.72 1.44 1.32

581264 104428 62417 72673 79581 108382 98902 203056 161274 108203 94085 208864 211992 261560 192601 281726 101029 375419 225349 288538 392601 331880 194885

Product C*AV 139,503 95,029 81,142 138,079 198,953 273,123 254,178 605,107 512,851 267,261 328,357 766,531 665,655 928,538 514,245 357,792 236,408 953,564 421,403 568,420

675,274 477,907 257,248

~CDV = 9,716,567 a = 3.36, Ce = 1.32 m = ~:CAV + aCe - 14.2 x 106 ~tCi = 14.2 Ci Ln C--!I- V2-V______I C2a

(4.19)

In this well, water production dropped from several thousand barrels per day (BPD) to about 100 BPD following well repairs to shut off a thief zone at points shown by the arrows on the curve. These were made after about 5.3 million barrels of water had been produced, resulting in very erratic changes in tracer concentration with little additional water production, as shown on the graph. The response, extrapolated to infinity at this point, shows t h a t m = 14.2 curies of

Field Examples and Data Analysis

181

t r i t i a t e d w a t e r would have been produced. Since M = 100 curies were injected into well M-03, m/M = 14.2 percent of the w a t e r injected at M-03 would have been produced at this well if the thief zone had not been shut in. This represents the w a t e r distribution history in the formation up to this point. WATER PRODUCTION FROM M-03 TO M-23 The production data for M-23, the other well responding to M-03, are shown in Fig. 4.24a. The data are plotted on semilog paper to show the extrapolation. A d a t a table similar to Table 4.1 was used to calculate the tracer sum, ZCAV. The r e m a i n d e r of the tracer produced was estimated from the extrapolation. There have been several workovers at M-23 and a reduction in watercut. Normally the extrapolation would have been made by drawing a line averaging the highs and the lows. In this case, two extrapolations were made as shown: one for the highest and one for the lowest slope from the curve. The q u a n t i t y of additional tracer collected was so low t h a t neither extrapolation generated significantly different figures. Between 11 and 12 percent of the w a t e r injected into M-03 was produced at M-23. SWEPT PORE VOLUME CALCULATIONS FROM M-03 TO M-23 D a t a collected for the injection of w a t e r from M-03 to M-23 are given in Table 4.2. These are similar to the data table from production well M-10 except t h a t injected volumes, Vi, are used instead of produced volumes, Vp. In order to

TABLE 4.2 Swept volume calculations for M-03 to M-23 Cumulative volume 3803000 4320000 5600000 6292000 6592000 6915000 7278000 7634000 8020000 8462000 9063000 9832000 10192000 Table sums

Concentration ~CI~bl (C) 0.28 1.31 1.57 1.83 2.05 1.99 2.48 3.34 2.76 2.97 2.36 2.49

Volume difference, Av 0 517000 1280000 692000 300000 323000 363000 356000 386000 442000 601000 495000 360000 12757170

B*C CAV 0 144760 1676800 1086440 549000 662150 722370 882880 1289240 1219920 1784970 1168200 896400

A*D CVAV 6.2536E+11 9.3901E+12 6.8359E+12 3.619E+12 4.5788E+12 5.2574E+12 6.7399E+12 1.034E+13 1.0323E+13 1.6177E+13 1.1486E+13 9.1361E+12 1.008E+14

Chapter 4

182

99

~

~

r

M =12 Ci

9e ~

1.0

~

M=

"

Well M-23

I,

0.~

1

1

I

2

3

I

I

4

1

5

6

[

7

CUMULATIVE PRODUCED VOLUME, MM B B L a.

~ ~

V = 9.2 MM BBL

111

~ i z O

1.0

9

8

_~

4

8

~

Well M-23 ~

0.1

I 3

~ 4

I 5

I 6

~ 7

f i r ~ I 8 9 10 11 12 13 14 15 16

CUMULATIVE (MM) B A R R E L S OF WATER INJECTED AT M-03

bl

Figure 4.24. Tracer production and volume swept at M-23 from M-03.

Field Examples and Data Analysis

183

calculate the first m o m e n t , the functions AV, CAV, and CVAV are derived autom a t i c a l l y from c u m u l a t i v e volumes and concentrations using s p r e a d s h e e t functions. The m e a n volume was calculated according to Eq. (4.14). The results of the calculations are shown below: a = 2 . 1 6 x 106 Ce - 2.49 pCI/bbl V e - 1.02 x 10 7 bbl m

Vs =

CVAV + aC e(a + Ve) ~CAV + aCe

aCe (a+Ve)

= 5 . 3 8 x 106 =12.35x106

= 9.2 MM bbl swept

The d a t a were extrapolated graphically using the plot of concentration versus injected volume on semilog paper, as shown in Fig. 4.24b. The v a l u e s for the extrapolation constant, a, for the point C e,Ve, and for the m e a n volume, V, injected are given above. The total m e a n pore volume swept (Vs) was calculated as 9.2 MM bbl, as shown. The arrows on the injection curve show points of disruption w h e r e w a t e r injection was i n t e r r u p t e d for periods of more t h a n a month. Injection r a t e s varied by a factor of more t h a n five for significant periods of t i m e d u r i n g the course of t h e flood. F r o m t h e s e d a t a , the total pore volume s w e p t in the p a t t e r n w a s calculated as shown above. The swept volume assigned to the well pair M-03 and M-23 alone is less t h a n that. It is decreased by the fraction, f = m/M, of injected t r a c e r (water) produced at M-23. An average of 11.5 curies of t h e 100 curies injected were produced at M-23; hence the volume swept b e t w e e n M-03 a n d M-10 is" mvr 11.5 V3,1o = ~ =~ 9.2 MM bbl = 1.1 MM bbl

SWEPT PORE VOLUME CALCULATIONS FROM M-03 TO M-10 Using a d a t a table similar to Table 4.3, the swept pore volume from M-10 responding to injection at M-03 was calculated to be 9.7 MM bbl. The r e s u l t s are shown in Fig. 4.25. The arrows on the curve show flow i n t e r r u p t i o n s of g r e a t e r t h a n one m o n t h . C o m b i n i n g these d a t a w i t h those from Table 4.3, t h e pore volume swept between M-03 and M-10 is given by: 14.2 V(M-3/M-10) = 1--0-0-(9.7) = 1.4 MM bbl, not very different from the volume swept between the well pair M-03 and M-23.

184

Chapter 4

~

4 w

3-21B

V = 9.7 MMBbls

oeO"~176~

1.0I---

~ o

g-_ 8t---o

gl-

Well M-IO

|

.e \

5i-4~

2--0.1

3

4

5

6

7

8

9

10 11 12 13 14 15 16

C U M U L A T I V E W A T E R I N J E C T E D A T M-3, M M B B L S

Figure 4.25. Total swept pore volume from M-03 to M-10

PRODUCTION RESPONSE AND SWEPT VOLUMES F R O M M- 14 TO M - 0 4 AND M - 2 0

The responses at wells M-04 and M-20 from water injection into well M-14 are shown in Fig. 4.26. The data are all plotted on a semilogarithmic base to show the extrapolations. The swept volumes from M-14 to M-04 and to M-20 are shown in Fig. 4.27. There is a significant difference in the pore volume swept between the injector to each of the two responding wells. Most of it comes from the higher concentration of tracer produced at M-20. The tracer response at well M-04 is shown in Fig. 4.26. The extrapolation is quite straightforward: 16 curies of tritiated water were produced. One hundred curies of tritiated water were injected into M-14; hence only 16 percent of the injected water was produced there. The swept volume for the p a t t e r n is given in Fig. 4.27 as 20 MM bbl. The swept volume for the well pair is thus calculated to be 0.16 x 20 = 3.2 MM bbl. For M-20, the tracer response is also shown in Fig. 4.26. The response at well M-20 was strongly affected by workovers lowering the watercut. The p a t t e r n volume swept is shown in Fig. 4.27 to be 33 MM bbl. A high and a low extrapolation were used, as shown, giving an average of 29_+4 percent for the water produced at this well; hence, the swept volume for the well pair is the product of these two, or about 11 MM bbl. This is more than three times the volume swept to M-04.

Field Examples and Data Analysis

185

~m

E)--Q i m 3-r-~u

M = 3 3 Ci

/

~m |

m (

]1

Well M20 2--

1

M = 2 5 Ci

1,

0

!

1

2

I

3

, I

,L

4

5

!

6

m = 16.1 Ci

m m m

n

Well

I

1

,, !

2

CUMULATIVE

!

3

M4

I,,

4

I

5

,

I

6

PRODUCED VOLUME, MM BBLS

Figure 4.26. Tracer production at M-04 and M-20

186

Chapter 4

9 Produced @ M-04

m

--

9Produced @ M-20

,,.,..

~," O 9

iii1_

9

MM Bbls ~o ~

=

,

9 9

9

HI

-I~ 2

4

I I I I,,! 6

8

I ! ! ! I I I I I I I I ! I I I I I.I 10

12

14

16

18

20

22

24

26

I I

28

C U M U L A T I V E W A T E R INJECTED @ M-14, M M B B L S

Figure 4.27. Total swept volume from M-14 to M-04 and to M-20

REFERENCES

Abbaszadeh-Dehghani, M., "Analysis of Unit Mobility Ratio Well-to-Well Tracer Flow to Determine Reservoir Heterogeneity," Ph.D. dissertation, Stanford University, Stanford, CA (Aug. 1982). Abbaszadeh-Dehghani, M., and Brigham, W.E., "Analysis of Unit Mobility Ratio Well-to-Well Tracer Flow to Determine Reservoir Heterogeneity," report, Contract No. DE-AC03-81Sll164, U. S. DOE, San Francisco (Dec. 1982). Abbaszadeh-Dehghani, M., and Brigham, W.E., "Analysis of Well-to-Well Tracer Flow to Determine Reservoir Layering," JPT (Oct. 1984) 1753-62. Agca, C., Pope, G.A., and Sepehrnoori, K., "Modeling and Analysis of Tracer Flow in Oil Reservoirs," J. Pet. Sci. Eng. (1990) 4, 3-19. Allison, S.B., "Analysis and Design of Field Tracers for Reservoir Description," M.S. thesis, The University of Texas at Austin, Austin, Texas (1988). Allison, S.B., Pope, G.A., and Sepehrnoori, K., "Analysis of Field Tracer Response for Reservoir Description," J. Pet. Sci. Eng. (1991) 5, 173-186.

Field Examples and Data Analysis

187

Asgarpour, S., Crawley, A.L., and Springer, S.J., "Performance Evaluation and Reservoir Management of a Tertiary Miscible Flood in the Fenn-Big Valley South Lake D-2A Pool," paper no. 87-38-07 presented at 37th Ann. CIM Petrol. Soc. Tech. Mtg., Calgary, ,alberta, Canada, June 7-10, 1987. Asgarpour, S., Todd, M.R., "Evaluation of Volumetric Conformance for Fenn-Big Valley Horizontal Hydrocarbon Miscible Flood," paper SPE 18079 presented at 63rd Ann. SPE Tech. Conf., Houston, Oct. 2-5, 1988; Proc. EOR/General Petroleum Engineering (1988), 231-244. Beier, R.A., and Sheely, C.Q., "Tracer Surveys to Identify Channels for Remedial Work Prior to CO2 Injection at MCA Unit, New Mexico," presented at SPE/DOE Enhanced Oil Recovery Symp., Tulsa, OK, April 17-20, 1988. Bragg, J.R., Gale, W.W., Mcelhannon, W.A. Jr., Davenport, O.W., and Petrichuk, M.D., "Loudon Surfactant Flood Pilot Test," Proc., 3d Joint SPE/DOE Enhanced Oil Recovery Symp., Tulsa, OK, April 4-7, 1982 (1982) 933-952 (SPE/DOE10862). Brigham, W.E., and Abbaszadeh-Dehghani, M., "Tracer Testing for Reservoir Description," J P T (May 1987) 519. Clifford, P.J., and Duthie, A., "Analysis of a Polymer Well Treatment in the Beatrice Field," paper SPE 16550 presented at the SPE Offshore Conf., Aberdeen, Scotland, Sept. 8-11, 1987. D'Hooge, J.A., Sheely, C.Q., and Williams, B.J., "Interwell Radioactive Tracers An Effective Reservoir Evaluation Tool: West Sumatra Field Results," SPE paper 8434 presented at the Ann. Fall Tech. Conference, Las Vegas, Nevada, Sept. 2326, 1979. Deans, H.A., "Using Chemical Tracers to Measure Fractional Flow and Saturation In-Situ," paper SPE 7076 presented at 5th Symp. of Improved Methods of Oil Recovery, Tulsa, OK, April 16-19, 1978. Emory, L.W., Mungen, N., and Nicholson, R.W., "Caustic Slug Injection in the Singleton Field," J P T (Dec. 1970) 1569-1576. Felsenthal, M., "How to Diagnose a Thief Zone," JPT (July 1973) 839-840. Gilliland, H.E., and Conley, F.R., "Pilot Flood Mobilizes Residual Oil," Oil & Gas J. (Jan. 1976)43-48. Hagoort, J., "The Response of Interwell Tracer Tests in a Watered-Out Reservoir," paper SPE 11131 presented at SPE Ann. Tech. Conf. and Exhibition, New Orleans, Sept. 26-29, 1982. Heck, E.T., "Tracing Fluids Between Wells," Producers Monthly (July 1954) 18, 7, 31-33. Hoiland, R.C., Joyner, H.D., and Stalder, J.L., "Case History of a Successful Rocky Mountain Pilot C02 Flood," paper SPE/DOE 14939 presented at SPE/DOE Fifth Symp. on Enhanced Oil Recovery, Tulsa, OK, April 20-23, 1986.

188

Chapter 4

Holm, L.W., "Design, Performance, and Evaluation of the Uniflood Micellar Polymer Process - - Bell Creek Field," paper SPE 11196 presented at the Ann. Fall Tech. Conference, AIME, New Orleans, LA, Sept. 26-29, 1982. Hydro Geo Chem, Inc., "Two Well Recirculation Tracer Tests at the H-2 Hydropad, WIPP, Southeastern New Mexico," SAND86-7092, Sandia National Laboratories, Albuquerque, NM (1986). Jenkins, R.E., and Koepf, E.H., "New Tools and Methods Improve Fluid Tracing," Oil & Gas J. (Apr. 1, 1963)61, No. 13, 102-104. Jones, T.L., Kelley, V.A., Pickens, J.F., and Upton, D.T., "Integration of Interpretation Results of Tracer Tests Performed in the Culebra Dolomite at the Waste Isolation Pilot Plant (PIPP) Site," SAND92-1579, Sandia National Laboratories, Albuquerque, NM (1992). Lansdown, A.R., "Application of Tracers in the Steelman Pilot Waterflood," Can. Min. and Metal. Bull. (1961) 54,593, 695. Levenspiel, O., Chemical Reaction Engineering, John Wiley, New York (1972). Lichtenberger, G.J., "Field Applications of Interwell Tracers for Reservoir Characterization of Enhanced Oil Recovery," paper SPE 21652 presented at the Production Operation Symposium, Oklahoma City, OK, April 7-9, 1991. Maroongroge, V., Ph.D. dissertation [as yet untitled], The University of Texas at Austin, Austin, TX (1994). Nitzberg, K.E., and Broman, W.H., "Reinterpretation of the Northwest Fault Block, Prudhoe Bay, Alaska, Reservoir Description Based on Waterflood Performance," paper SPE 20548 presented at Ann. Tech. Conf., New Orleans, LA, Sept. 23-26,1990. Ohno, K., Nanba, T., and Horne, R.N., "Analysis of an Interwell Tracer Test in a Depleted Heavy-Oil Reservoir," paper SPE 13672 presented at California Regional Mtg., Bakersfield, CA, March 27-29, 1985. Pitttaway, K.R., Albright, J.C., Hoover, J.W., "The Maljamar Carbon Dioxide Pilot: Review and Results," paper SPE 14940 presented at the SPE/DOE 5th Symp. on EOR, Tulsa, OK, April 20-23, 1986. Rogde, S.A., "Interpretation of Radioactive Tracer Observations in the Gulfaks Field," presented at Intl. Energy Agency Symp. on Res. Eng., Paris, France, Oct. 8, 1990. Saad, N., Pope, G.A., and Sepehrnoori, K., "Simulation of Big Muddy Surfactant Pilot," SPE Res. Eng. (Feb. 1989) 4, 1, 24. Skilbrei, O.B., Hallenbeck, L.D., and Sylte, J.E., "Comparison and Analysis of Radioactive Tracer Injection Response with Chemical Water Analysis into Ekofisk Formation Pilot Waterflood," SPE paper 20776 presented at the Ann. Tech. Conf., New Orleans, LA, Sept. 23-26, 1990.

Field Examples and Data Analysis

189

Sylte, J.E., Hallenbeck, L.D., and Thomas, L.K., "Ekofisk Formation Pilot Waterflood," paper SPE 18276 presented at Ann. Tech. Conf., Houston, TX, Oct. 2-5, 1988. Terry, R. E., et al., Manual for Tracer Test Design and Evaluation, Tertiary Oil Recovery Project, Institute of Mineral Resources Research, University of Kansas (May 1981). Tinker, G.E., "Design and Operating Factors that Affect Waterflood Performance in Michigan," paper SPE 18276 presented at the Ann. Tech. Conf., New Orleans, LA, Sept. 20-29, 1988. Trocchio, J.T., "Investigation and Effect of Fluid Conductive Faults in the Fateh Mishrif Reservoir, Arabian Gulf," paper SPE 17992 presented at SPE Middle East Oil Technical Conference, Manama, Bahrain, Mar. 11-14, 1989. Wagner, O.R., Baker, L.E. and Scott, G.R., "The Design and Implementation of Multiple Tracer Programs for Multifluid, Multiwell Injection Projects," paper SPE 5125 presented at 49th Ann. SPE Tech. Conf. and Exhibition, Houston, Texas, Oct. 6-9, 1974. Wagner, O.R., "The Use of Tracers in Diagnosing Interwell Reservoir Heterogeneities m Field Studies," JPT (Nov. 1977) 1410-1416. Weller, W.T., and Lechtenberg, H.J., "Coalinga Field, California Polymer Flood," paper U.S. DOE Report SAN/1556-2 (July 1977). Wheeler, V.J., Parsons, T.V., and Conchie, S.J., "The Application of Radioactive Tracers to Oil Reservoir Waterflood Studies," paper SPE 13985/1 presented at the SPE/Offshore Eur. '85 Conf. at Aberdeen, Scotland, Sept. 10-13, 1985. Wood, K.N., Lai, F.S., and Heacock, D.W., "Water Tracing Enhances Miscible Pilot," paper SPE 19642 presented at the Annual Technical Conference, San Antonio, TX, Oct. 8-11, 1989.

This Page Intentionally Left Blank

CHAPTER 5

UNCONVENTIONAL

WATERFLOOD

TRACING

INTRODUCTION In the previous discussions on waterflood tracing we considered only the use of nonreactive, ideal tracers for following the path of injected water. In all cases, the tracer was injected with water at the wellhead and the water produced from well sampled at the surface for tracer analysis. There are alternatives both to the use of ideal tracers and to the normal injection/production procedures. When properly used, these alternatives can yield useful information in conjunction with conventional waterflood tests. Alternative tracer tests used in waterfloods are of two kinds: 1. Those in which reactive, nonideal tracers are used. These allow us to monitor a variety of conditions, processes, and reactions in the reservoir. Some examples are tracer m e a s u r e m e n t s of residual oil in the reservoir and of the chemical conversion of sulfate ion in injected water to hydrogen sulfide. 2. Those t h a t use alternate methods of injecting or analyzing produced tracers. These include logging and sampling observation wells for monitoring movement of fluids and solutes in vertically separated layers, single-well tracer tests to monitor the flow velocity field, and the downhole tracer sampling or analysis in production wells. Some of these related tracer procedures will be discussed in this chapter.

R E S I D U A L OIL M E A S U R E M E N T S BY T R A C E R S R e s i d u a l oil is a poorly defined term in oilfield practice. For a homogeneous, water-wet laboratory core t h a t has been saturated with oil and then waterflooded until no further oil is produced, the residual oil left in place is a well-defined number. It represents a relatively sharp endpoint of essentially immobile oil, for reasonable capillary numbers. Neglecting end effects, the residual oil left is the same throughout the core. For a nonhomogeneous water-wet core, there is a distribution of permeabilities in the core. The residual oil left after waterflooding can be distributed over a range of values (Deans, 1978). In this case there is a well-defined number for the average or mean residual oil in left in place, but it is not uniformly distributed. In the three-dimensional reservoir of the oil field there are likely to be both areal and vertical permeability variations, noncommunicating layers, and physical heterogeneities such as fractures and faults. Any water drive for producing oil will follow the paths of highest conductivity in the reservoir. The least permeable areas m a y never be swept by the water; the most permeable will be swept m a n y times over; and much of the reservoir will lie in between. As a result the residual oil in the reservoir when w a t e r breaks through

192

Chapter 5

will vary according to position in the reservoir. There will be an average residual oil in place but it is not likely to be uniformly distributed. It is this average residual oil that is the target for potential enhanced recovery methods. M e t h o d s in use

There are several methods now in use for measuring residual oil in the field. These include a n u m b e r of log-inject-log (LIL) methods, the single-well tracer test (SWTT), and the two-well tracer test (TWTT). Other methods of m e a s u r i n g resid ual oil include core measurements and logging, although most logging methods use the LIL method to obtain quantitative results. The SWTT covers the largest near-wellbore region; it can extend up to 15 or 20 ft from the wellbore. With the exception of the two-well tracer test, all of the methods m e a s u r e residual oil in the well-swept region around the wellbore. This m e a s u r e s the ultimate residual oil for a region that can be swept in its entirety. It is not likely to be the same as the oil in place either before or after an EOR process. Two of the tracer methods, the SWTT and the TWTT, will be discussed here in greater detail. The log-inject-log (LIL) method is a borehole logging method t h a t often involves the use of tracers. This aspect will be covered separately in the chapter on borehole tracers. Both the SWTT and the TWTT depend upon the arrival of times of two tracers t h a t have different partition (distribution) coefficients between oil and water. In both methods, the tracer is injected at the surface with injection water, and samples of water are collected from the production stream for analysis. This use of tracers for monitoring residual oil was demonstrated in the laboratory (Raimondi and Torcaso, 1965). Its use for monitoring residual oil in an oil field was first proposed in a patent in 1971 (Cooke). This is a chromatographic procedure in which the difference in the residence times between partitioning tracers is used for measuring the residual oil in place. Partitioning tracers

An ideal water tracer follows only the water path and moves with the velocity of the water. The presence of an oil phase in the reservoir has no direct effect upon the tracer path or its velocity. This is desirable for tracing water. If we wish to probe the oil phase we need a tracer that can interact with it in some manner. One way to do this is to introduce a nonideal water tracer t h a t can partition between the oil and water phases.

Tracer method In the tracer method, a set of partitioning tracers is injected into the reservoir and monitored at a producer. The difference in residence times between tracers

Unconventional Waterflood Tracing

193

of different partition coefficients is used to determine the residual oil of the pore volume swept by the tracers. The principles, equations, and conditions required to apply the method in the field are discussed below. PRINCIPLES In this method, water containing a pulse of tracer is injected into a reservoir containing oil and water. If the tracer is in local equilibrium with both phases, its molecules will move freely back and forth between them with normal waterflood velocities. When the tracer molecules are in the water phase they will move with the velocity of the water and when they are in the oil phase they will move with the velocity of the oil. If the oil is at residual saturation it will be essentially immobile. In t h a t case the tracer molecules will only move when they are in the water phase. The net result is that the partitioning tracer pulse will lag behind the waterfront. The extent of lag will depend on the fraction of time the tracer spends in the oil phase compared to that in the water phase. If we can measure how much the pulse is delayed, and we know the equilibrium distribution of tracer molecules between the two phases, we can calculate the residual oil saturation, Sor, in the region contacted by the water. This is an essential number for evaluating secondary or tertiary recovery schemes. EQUATIONS Let us suppose that two tracers are injected simultaneously into the reservoir, containing oil and water, and using water as an injection medium. Let tracer 1 be a partitioning tracer and let tracer 2 be an ideal, nonpartitioning tracer. The n u m b e r of tracer 1 molecules in the oil phase at any given time, Nlo, is equal to the concentration, C lo, of tracer 1 in the oil, times the volume of the oil phase Vo. Likewise, the number of tracer 1 molecules in the water at any given time, N lw, will be its concentration, C lw, in the water, times the volume of the water phase, Vw. The ratio of the number of molecules in each phase, Nlo:Nlw, is the same as the ratio of m e a n residence times, t lo:tlw, t h a t the average tracer molecule spends in the immobile relative to the mobile phase. This is the delay factor, ~, which can be expressed as shown below: N lo C lo Vo t lo Nlw - Clw Vw - tlw - ~

(5.1)

The ratio C l o / C l w = Kd is the distribution or partition coefficient of the tracer. This is a thermodynamic function that depends upon temperature, salinity, concentration, etc., but can be measured in the laboratory. The coefficient becomes i n d e p e n d e n t of t r a c e r concentration as the t r a c e r c o n c e n t r a t i o n approaches infinite dilution, the region where most radioactive tracers are used. For two phases, the phase volumes can be expressed in terms of their fractional volumes or saturations. Here, the oil saturation, So = Vo/(Vo+Vw); the water

194

Chapter 5

saturation, Sw = Vw/(Vo+Vw); and So + Sw= 1. Hence, delay factor ~ can be expressed as: Sor = Kd l~Sor

(5.2)

If the residence time of the partitioning tracer is t i and the residence time of the water tracer is tw, then tl will be delayed relative to tw by the delay factor as given by: Sor t 1 = tw(1 + ~) = tw{ 1 +Kd(l_Sor) }

(5.3)

Thus, if Kd is known from laboratory m e a s u r e m e n t s , and ti and tw are measured in the field, the last expression can be solved to give Sor as a function of the arrival times and the Kd directly: tl-tw _ At Sor = [ t l - t w + t w K d ] - [At+ twKd]

(5.4)

For this development we used one partitioning tracer and one nonpartitioning tracer. This was done for convenience and is, in fact, the most obvious way to do such a test in the field; however it is not necessary to use a nonpartitioning tracer. The only test requirement is that there be as many tracers as there are phases, and t h a t their partitioning coefficients be known and be sufficiently far apart to give a significant At. Thus, tw can be replaced in the equations above by any of the arrival times for partitioning tracer whose Kd is known. It can easily be shown that if two partitioning tracers are used, the residual oil is given by: tl -t2 Sor = tl - t2 - t 1K2 + t2K1

(5.5)

where the partition coefficients of the two tracers are K1 and K2, and the respective arrival times of the two tracers are t 1 and t2. This development is based upon the oil's immobility in accordance with the definition of residual oil. The equations shown above can, however, also be modified to include a mobile oil phase.

Residence times and volumes In the discussions above, residence time was used as an indicator of the time required by each tracer to traverse the volume swept between the injector and the producer. As we noted in chapter 4, the production response from a tracer pulse injection is a broadly distributed function. For the produced tracer concentration as a function of time, the mean of the distribution is t a k e n as the mean residence time. This is the first moment of the distribution. In the discussion of swept volume in chapter 4 we used cumulative volume rather t h a n elapsed time. Elapsed time and cumulative volume injected are directly proportional to each

Unconventional Waterflood Tracing

195

other at constant flow rates. If ti is the elapsed time and Vi is the cumulative volume injected during t h a t time interval, assuming t h a t both tracers follow the same path, t h e n ti = aVi, and the residence times in Eq. (5.4) are directly convertible to mean retention volumes as shown: a(V1-Vw) AV So = [ a ( V 1 - V w ) + a V w K d ] = [AV + VwKd]

(5.6)

Residual oil and flow path It is generally assumed, for ease in calculations, t h a t flow rates in the field are constant, t h a t patterns are balanced, and t h a t there is a steady state in the flow distribution. In practice this is probably not true. Flows tend to be erratic as wells are treated, stimulated, and shut in for various lengths of time. In m a n y cases major changes in the flow distribution develops as the field ages. The m e a s u r e of residual oil obtained by tracers in the two-well tracer test is an estimate of residual oil as a function of the history of the field to t h a t time. Residual oil measured is the average for the volume swept up to t h a t time. The basic assumption in the two-well tracer test is t h a t both tracers follow the same path through the reservoir. In general, this should be true since they both move only with the moving water; however in a field case where pressure distributions can vary widely with time, it may be possible for tracers with very different residence times to develop different paths. DISTRIBUTION COEFFICIENTS The distribution coefficient for most partitioning tracers between oil and w a t e r is a function of the composition of the oil, the water, and of the reaction temperature. For low tracer concentrations such as those used for radioactive tracers, the distribution coefficient is independent of concentration. At higher concentrations required for some chemical tracers, the distribution coefficient m u s t be also be known as a function of the tracer concentration. The distribution coefficient, Kd, m u s t be determined under reservoir conditions of composition and temperature if it is to be used for monitoring residual oil in the reservoir. These conditions are best known near the beginning of a waterflood or after a field has been watered out.

Standard laboratory measurement of distribution coefficients The tracer methods described above require laboratory m e a s u r e m e n t s of the distribution coefficients made with fluids of field composition, and over the pressure and temperature range of the reservoir. The methods used for this are standard physico-chemical measurements. In all of them it is important to establish an equilibrated system. This generally takes time, and most such m e a s u r e m e n t s are time consuming. For complex, multiphase systems, this is still the procedure used. A classical method used for m e a s u r e m e n t s under reservoir conditions is illustrated in Fig. 5.1. This consists of a high-pressure window cell in which a

196

Chapter 5

tracer is equilibrated between two immiscible phases by agitation or by countercurrent flow. In the case illustrated here, oil and water form a visible twolayer system in the cell, while oil percolates up through the water and water drops down through the oil. Countercurrent circulation is continued until the tracer concentration is in equilibrium with both phases. Measurements are made as a function of temperature and pressure and, if necessary, as a function of tracer concentration. Sensing devices (not illustrated) are usually fitted to the equipment for monitoring physical properties of each phase such as temperature, pressure, density, viscosity, etc. The usual condition for equilibrium is that the same tracer concentrations are achieved if the test point is approached from both sides of the equilibrium, e.g., initial equilibration with the tracer in one phase followed by a second equilibration with the tracer in the other phase, or by approaching an equilibrium temperature from higher and lower temperatures. Concentrations are monitored by taking samples from each phase for analysis.

High pressure Two-phase counter-current contactor

[~

Magnetic oil pump

mple loop Water

Oil m phase

Water _ phase

I~ I---1

Sample loop Oil

Figure 5.1. Classical system for measuring Kd

Magnetic water pump

Unconventional Waterflood Tracing

j

Valve

197

Oil

Tee Oil

Phase separator

phase Brine

phase

Capillary coil Brine

Figure 5.2. FIA method for measuring Kd

There are many variations on this theme, and there are simplifications. An excellent method devised for measuring Kd's for single-well tracer tests in a twophase system is described in detail in a paper by Carlisle and Kapoor (1982). More recently, a new, much faster procedure using Flow Injection Analysis (FIA) for measuring the distribution coefficient of tracers was described in a paper by Knaepen et al. (1988). FIA has become a major analytical method in the past two decades (Karlberg and Pacey, 1989), as well as one of the faster methods for measuring distribution coefficients between oil and water (Carlisle, 1991).

FIA method for measuring distribution coefficients The FIA method for measuring Kd is a rapid procedure capable of measuring distribution coefficients with live crudes under reservoir conditions of pressure and temperature. In this procedure, the oil and brine are passed through a tee that serves as a segmenter, producing a regular flow pattern of alternating segments of the two fluids. The fluids then enter a capillary tube where equilibration takes place because of the strong internal circulation set up between the two phases. When a partitioning tracer is present in the water phase, it is rapidly equilibrated between the two phases. After equilibration, the two phases are separated by a gravity separator and analyzed separately for tracer concentration. A schematic of the method is shown in Fig. 5.2. The alternation of phases in the capillary is shown in the figure. In each phase, circulation is visible to the eye in a t r a n s p a r e n t capillary (not illustrated in the figure). The tracers are usually analyzed by a chromatographic procedure.

198

Chapter 5

Tracer detect~ ~ ~, L.J-~

Non-partitioning tracer pulse >,~ J./ t Partitioning ~1 ~,~ 1[,/tracer pulse ~J . ~ek Time t ' -

Tracer injection point I

I

,L

Brine injection

F!

I I

Brine collection vessel

Figure 5.3. Chromatographic method for measuring Kd

Chromatographic method The distribution coefficient can also be measured in the laboratory by a chromatographic method, in which a pulse containing both a nonpartitioning and a partitioning tracer is passed through a chromatographic column such as a laboratory core, packed column, slim tube, or other linear flow system containing oil at residual saturation and water. The tracers are injected in the water phase, which also acts as the driving fluid. If the oil is fixed at residual oil saturation, Sor, the distribution coefficient can be obtained from the measured retention time of each tracer in the injected pulse, from Eq. (5.6) as shown below: Kd = (ti- tw) (1-Sor) tw Sor

(5.6)

This is the inverse of the method used to measure residual oil in the field. Since the residual oil saturation is known for the laboratory core, the distribution coefficient must be found. The usual equilibrium conditions of temperature and composition must be known, and the flow rate must be low enough for local equilibrium to prevail. As a practical matter, the difference in retention times should be great enough to allow good statistics of measurement. This method, illustrated in Fig. 5.3, is the simplest of the three and places the least burden on the analytical procedure. The tracers are injected as a pair at position 0 in the figure and are transported through the medium by the injected brine. The response of the water tracer and the partitioning tracer at the detector, as a function of time, is shown in the plot above the slim tube. Here, t and refer to the two mean residence times. Only the shape of the curve is important in calculating the time of arrival. A common procedure for radioactively tagged

199

Unconventional Waterflood Tracing tracers tracer, tracers or two tectors

is to use a C-14 tagged partitioning tracer and a tritiated w a t e r as w a t e r and an on-line beta scintillation detector for both tracers. Chemical can be monitored equally well using a common detector for both tracers, single, spatially equivalent detectors. A n u m b e r of chromatographic deare suitable for use in aqueous solution.

TABLE 5.1 T e m p e r a t u r e coefficients Kd Tracer

Kd @194~

A

B

Isopropyl Alcohol

0.26

2.15

-992.6

n-Propyl Alcohol

0.28

1.72

-883.1

n-Butyl Alcohol

1.23

2.52

-882.2

Acetone

0.47

1.02

-498.8

Phenol

1.07

-1.17

+435.5

EQUILIBRIUM CONDITIONS

Temperature effects Over a limited range, the effect of temperatures on the distribution coefficient can be represented by a semi-empirical equation of the form: B Log K = A + ~

(5.7)

where T is the t e m p e r a t u r e in degrees Kelvin, A is a constant related to the e n t h a l p y (AH), and B a constant related to the entropy change, AS. By solving this equation together with Eq. (5.4), and using two different partitioning tracers in addition to the w a t e r tracer, the effect of t e m p e r a t u r e can be eliminated if Ai and Bi are known for the two partitioning tracers, to give the following expression for residual oil, Sor: (02-1)B2/w Sor = eT_/w(OI_I)B1AV + (02 - 1)B2/w

(5.8)

ti where: Z = A1B2-A2B1, W = B2 - B1, and 0= tw For most reservoirs, the temperature lies within a range of values for which a plot of log Kd versus l f r , as shown in Eq. (5.7), is linear. Table 5.1 gives values of A and B for some common partitioning tracers, which were m e a s u r e d using a dead (degassed) North Slope oil from Alaska (Zemel, 1989). These numbers are

200

Chapter 5

dependent upon the composition of the oil and water, and should be determined for each field oil and brine. A plot of log K vs. l i t for the range of temperatures in a North Slope reservoir at t h a t time is shown in Fig 5.4. The slope of the line is a function of the polarity of the tracer among other things. In principle, it is possible to find tracers with a zero or very small t e m p e r a t u r e coefficient for any given system.

,,_--------- Phenol N-butanol

o,

Acetone N-propanol I-propanol !

t

1/T ( degrees Kelvin)

Figure 5.4. Log Kd vs. temperature

Effects of composition In the course of m e a s u r i n g distribution coefficients by the FIA method described above, Knaepen et al. made a series of measurements using pentanol and ethyl acetate as partitioning tracers. Measurements were made using North Sea crude and isooctane as the hydrocarbon phase versus brines of different composition. This was done with and without gas, and at different t e m p e r a t u r e s and pressures. The Kd value of the tracers was found to be a function of temperature, as expected. The Kd's increased with brine salinity and with oil d e n s i t y (composition). The effect of dissolved gas on Kd was small at room t e m p e r a t u r e but became quite large at elevated t e m p e r a t u r e s . The expected error of the m e a s u r e m e n t was calculated and compared with the experimental value. For a [~ range between 0.2 and 0.6 and for Kd values ranging from 3 to 8, the authors showed t h a t the error in measuring Kd by this method led to an absolute error in the calculated residual oil (Sor) of less t h a n 1 percent of pore volume.

Unconventional Waterflood Tracing

201

Composition changes due to waterflood When w a t e r is injected into the reservoir, the composition of both the oil and the w a t e r changes. The oil composition changes because the water dissolves some of the hydrocarbons, particularly the gases, as it advances. The water at the front is soon s a t u r a t e d with hydrocarbons and moves on at a fixed composition in equilibrium with the oil in place. The composition of the w a t e r changes as it mixes with formation w a t e r of a different composition. The w a t e r behind it that has been in equilibrium with residual oil now moves into equilibrium with the original oil, resulting in an increasing band of equilibrated w a t e r behind the displacement front. Behind this equilibrated zone is a region of residual oil t h a t has been extracted by variable amounts of injected water. This is the region where the oil composition, and hence the Kd for the tracer, will v a r y with position. This highly qualitative picture is complicated by a lack of knowledge of how compositional changes are induced by waterflooding and how they affect tracer distribution coefficients. One way to find this out would be by laboratory experiments in which a field oil is continuously swept by brine, while the compositions and the Kd of a tracer are determined at equilibrium conditions. No such data have been reported in the literature. Attempts to calculate Kd's for these tracers on theoretical grounds have not been very successful. Very little work has been reported on how composition affects the distribution coefficients of the tracers. Those m e a s u r e m e n t s t h a t have been reported (Knaepen et al., 1988) show t h a t "degassing" has a major effect on the Kd of several common tracers. It would be useful to know how the composition changes as the waterflood goes on, and how it affects the Kd. Most of the changes in water composition occur because of mixing with formation w a t e r of different composition, although solution (and precipitation) of reservoir m a t e r i a l s can also cause compositional changes. W h e r e a s the ionic strength of the brine is known to be important, the effects of other components are not well understood.

S i n g l e - w e l l t r a c e r test for r e s i d u a l oil SYMMETRY PROBLEM The tracer method for residual oil described above requires two spatially separated wells: one as an input, the other as an output. If a single well is used, the s y m m e t r y between input and output response nullifies the chromatographic effect. If several tracers are injected simultaneously into a formation, the tracer with the highest partition coefficient travels the shortest distance from the well while the one with the smallest coefficient travels farthest. When the flow is reversed, the tracer movement is also reversed, each tracer moving back the same distance it moved out. This is shown schematically in Fig. 5.5. The center of the frame represents the wellbore; the formation is at residual oil; and the tracer

202

Chapter 5

pulse is injected by a water drive. The block in the upper section of the figure represents a tracer pulse in the wellbore containing a homogeneous mixture of two tracers with different partition coefficients. The middle section shows the separation of the two tracers along a radius from the well after the pulse has been injected into the formation. Each tracer moves a different distance from the wellbore, depending upon their respective Kd's. When the well is r e t u r n e d to production, each tracer moves back in the same m a n n e r it moved out, resulting in a reconstituted pulse as shown in the bottom section. The relative movement of the two tracers is independent of either the injection rate or the production rate. The block in the lower section of the figure shows the reconstituted pulse. As shown in the figure, dispersion does take place, but the reconstituted pulse differs from the original pulse only in t h a t it is more dispersed. This is because dispersion takes place during each stage and its effect is additive on both injection and production. This dispersion effect is not sufficient to be useful for residual oil determination (Chase, 1971).

Tracer mixture in original pulse Tracer position in formation after injection

A

racer m in 'oduced

Figure 5.5. Effect of symmetry in single-well test

ASYMMETRY SOLUTION In order to use a single well as both input and output, one m u s t introduce an element of asymmetry. Deans (1971) proposed a m e a n s whereby a t r a c e r injected into the reservoir could react in place to create that asymmetry. In this

Unconventional Waterflood Tracing

203

procedure, a tracer is injected into the formation until it is at a distance, r, from the injector. Flow is stopped to allow the tracer to react with the formation water and be partially hydrolyzed at this position. This results in the formation of a new tracer material there. The "new" tracer and the remaining unhydrolyzed tracer make up a new tracer pair, located at a distance, r, from the injection well. When the well is produced, both tracers travel back to the wellbore from distance r, at which they were formed. Since they have different Kd's, they will arrive at different times. The fact that one tracer originated at the wellbore is no longer significant. The residual oil can now be calculated from the two residence times of the returning tracer pair. The residual oil measurement is independent of the amounts of tracers present, as long as their concentrations are high enough to be measured with precision in the produced water. This is shown in Fig. 5.6. In part A, the tracer material is shown as an annular ring injected into the formation. In part B, new tracer is being formed by hydrolysis of the material in the ring. In part C, the two tracers are returning to the wellbore.

A. Injection

B.Reaction

C. Production

Figure 5.6. Asymmetric response from SWTT In the single-well tracer test (SWTT) first proposed by Deans and since amplified and described in a number of publications (Deans, 1978; Deans and Majoros, 1980; Deans and Carlisle, 1986), the materials used are the alkyl esters of the lower fatty acids and alcohols. The choice of ester is dictated by the temperature of the formation and is pH dependent. The most widely used ester is acetyl acetate, which hydrolyzes to form ethyl alcohol (the "new" tracer) and acetic acid. The effect of the acid formed in the reaction is probably small because of the natural buffering of the formation. C2H5COOC2H 5 + H20 = C2H5COOH + C2H5OH

(5.9)

204

Ethyl acetate + water = Acetic acid + ethyl alcohol

Chapter 5

(5.10)

FIELD PROCEDURES The procedure used in the field is to allow the injected ester to r e m a i n in position over sufficient time to form enough alcohol to be easily measured. The hydrolysis time required is estimated from laboratory tests over a range of temperatures. In field operations, a minitest is usually performed first to verify the hydrolysis time required, as well as other parameters. A material balance tracer such as methyl alcohol is usually added to monitor the mass balance for each injection to ensure t h a t there are no errors in the returns. The tracer response data are profiles of tracer concentration vs. produced volume. These are corrected as needed, and a simulator program is used to choose the best fit in terms of residual oil. An example of the procedure (Deans, 1978) is shown below in figs. 5.7 and 5.8. The tracers used here have relatively high vapor pressures and m u s t first be corrected for tracer loss by vaporization. A tracer response curve, corrected only for tracer loss, is shown in the upper graph in Fig. 5.7a. These data are t h e n input into a simulator program containing the distribution coefficient (Kd) data, and the injection-production history of the test. This program matches profile shapes by varying dispersion and produces the corrected tracer response curve, shown in the lower graph of Fig. 5.7b. The produced tracer profiles are t h e n simulated using various values of Sor to find a best fit, as shown in Fig. 5.8. In this case, the best match is for an S or of 26 percent. The computer model used here is based upon flow through a m a t r i x of pores in the medium, as is found in sandstone formations. There were problems associated with the use of the method in some limestone formations, where dead-end pore effects can become important (Deans and Carlisle, 1986), t h a t required a more complex computer model. Because the tracers are formed as a radially distributed source in the formation, the SWTT may be subject to error if there is a linear velocity field present. This can occur if a well-developed water drive is present in the field, but this drift can be accounted for by a two-dimensional simulator program. The SWTT procedure has been widely used as a means of measuring residual oil saturation. It has been applied to more than 300 oilfield reservoirs worldwide and is accepted as a m a t u r e procedure (Chang and Maerefat, 1986) whose results compare favorably with those obtained by other near-wellbore methods. The presence of a linear velocity field is, however, another way of introducing a s y m m e t r y for a single-well test (Deans and Tomich, 1975). In this procedure, hydrolysis is not needed. It requires only t h a t there be an independent linear velocity field in the formation. Two tracers injected radially into a reservoir layer will s e p a r a t e into two distinct annuli surrounding the injector because of the their different Kd's. When the injection stops, the tracers will only be transported by the linear velocity field. This will place them in different positions relative to

Unconventional Waterflood Tracing

205

the injector. When the well is produced radially, they will now arrive back at the well at different times. Both the residual oil and the drift velocity can be derived from the measured residence times of two tracers with different Kd's. No field applications have been reported.

a. Tracer response

t~

1

0.12

0.24

0.10

0.20

+"~%Iv:Ethyl.

0.6

t ~ ~ Acetate

0.4

if4' ~r ~ethanol #,o "~ T'I -

8

~ 0.08 Lg

,00 o

E

~

"~ 0.2

e 0

% k.... + o

%

,

oo

Eth~O~

o

,9 ',I~,..

0.16

tLU

0.12

~

0.08

--= o >

0 o

0.04

o~176 c .... o i,.. 0.02. ~e~lDOo I ,,.,,+o 1 . o..-..,,j,. -

0.0 0

~0.06

I '#..

-

2000

t~

E

0.04

0.0 4000

b. Corrected tracer response F 0

~o

0.6 9L L

9

~;

D

0.4

d)

E

o >

0.2

o.o --'~~ 0

D.24

P

i e-e i ~

/

-

(

(1) ,,i-i

(I) o

<

t--

0.16

"-' LU

0.08

-0

E

2000

Bbls of Brine Produced

Figure 5.7. Tracer response in SW2~

0.0 4000

Chapter 5

206

0.12, m

0 r

.~ 0.08 ,,I,,,,I

i.l.I

m

'35~

4

%%

% OC'~

2 )%

O >

0.00 0

400

800

1200

1600

2000

Bbls of Brine P r o d u c e d

Figure 5.8. Fit to residual oil

Dual-completion, single-well test for residual oil An alternative to the TWTT that also uses a single well is dual completion in a single well. Here a well packer acts to separate input from output and allow the use of a single well for measuring residual oil in a defined region of the reservoir. A schematic of such a test well is shown in Fig. 5.9. Such a test for measuring residual oil does not appear to be reported in the literature, but in principle it should work. The tracer is injected at a different depth t h a n the production interval. As shown in the sketch, a packer is used to separate the injection from the production interval. In this case, the tracer is injected into an upper interval through the annulus and produced from the lower interval by way of the tubing. The reservoir volume swept by the test would depend to great extent upon the ratio of horizontal to vertical permeability in the regions u n d e r test, and on the vertical distance between the input and output layers. Such a test should be relatively easy to model. This is, in effect, a two-well t r a c e r test using a vertical r a t h e r t h a n a horizontal separation between the wells. Its a d v a n t a g e over the single-well t r a c e r test is t h a t any pair of partitioning tracers can be used without the need for hydrolysis. As in the TWTT, the swept volume and material balance can be determined from the response of the nonpartitioning tracer. Such a test can be done in any existing well without a great deal of additional cost. It is a relatively cheap method for testing an EOR procedure since the residual oil in place can be measured before and after the EOR test without the need of special measures to fix test conditions. In a complex reservoir, tests can even be done in different parts of the reservoir using different

Unconventional Waterflood Tracing

207

wells for testing. A disadvantage may be the importance of gravity effects in such a vertically oriented test. The major difficulty in carrying out the test lies in ensuring a good separation between tracer injection and production in the wellbore. This requires good cement bonding with no leakage between wellbore and formation, which is sometimes a problem in older wells.

Production Injection

Formation

II

I

Formation

Packer

Figure 5.9. Dual-completion single-well test

Two.well tracer test (TWTT) for residual oil Despite the origins of the residual oil tracer test as a two-well test, there have been no reports of an interwell test until recently. There is, however, a significant difference between the TWTT and other near-well methods such as the SWTT.

208

Chapter 5

This lies in the reservoir volume encompassed by an interwell test compared to t h a t in the neighborhood of the wellbore. RESERVOIR CONDITIONS FOR TWO-WELLTRACER TEST The only way to m e a s u r e the average residual oil in the entire swept region between wells is by an interwell method such as the two-well tracer method. Two of the major objections to the TWTT for residual oil are 1) the fluid compositions between wells are not known so t h a t partition coefficients cannot be properly d e t e r m i n e d in the laboratory, and 2) it takes too long to get results in fields of any size. These a r g u m e n t s m a y not be valid on two occasions: at the s t a r t of a waterflood and when a field has been long flooded out.

Tracer injection in watered out fields Most of the waterflood tracer data reported in the literature fit this case. They are largely concerned with a section of field at or near residual oil, and with some kind of tertiary recovery process. Water (brine) is usually the only flowing phase. As in the previous case for a field at connate water, the tracer response curves can be used to determine sweep efficiency and directional permeability. They can also provide qualitative data on reservoir flow barriers and channels. As will be shown, they can also be combined with data from partitioning tracers to provide information on the residual oil in the swept areas. Tracing water-swept regions of an oil field allows us to take a d v a n t a g e of the known injection history to chose a suitable test site and to design a suitable test. Since the purpose of such waterflood tests is usually as a pre-flood in preparation for testing an EOR method, the test should be designed for this purpose. Such a test should provide a m e a s u r e of how much pore volume is swept by the injected w a t e r and how the injected water is distributed among the producers. In the case of a well-swept field following a waterflood, such as a new waterflood, the reservoir conditions are known. The composition of the formation brine and of the residual oil in place are available. This allows distribution coefficients to be m e a s u r e d in the laboratory using real or synthetic m a t e r i a l s of reservoir composition under reservoir conditions of t e m p e r a t u r e and pressure. The pilot site should be reasonably representative of the field, if possible; however the reservoir test volume should be kept as small as possible while remaining representative. Smaller test volumes make it easier to obtain complete tracer response in a reasonable period of time. There is, unfortunately, no way to overcome the time required for a water pulse to travel from an injector to a producer. Ideally, both partitioning and nonpartioning tracers should have been added to a new waterflood at the start, avoiding the need for m e a s u r e m e n t s long after the flood has ended. Tracer injection at start of a pattern water flood Injected w a t e r moves out slowly through the formation. Normal frontal velocities in waterfloods are in the neighborhood of a foot per day. As a result, it m a y

Unconventional Waterflood Tracing

209

take m a n y months or even years for injected water to reach the surrounding producing wells in fields of any size. This kind of time scale imposes certain logical restrictions upon waterflood tracing. There is little gain in doing a tracer program t h a t bears fruit long after anyone is interested in its results. Good waterflood m a n a g e m e n t requires some knowledge of sweep efficiency and direction as soon after water breakthrough as possible. For this reason, it is desirable to inject tracer as early as possible in the life of a flood, preferably near the very beginning. If a partitioning tracer is also added at the same time this can add residual oil data at a time when an EOR process is to be considered. When water is injected into the formation in a waterflood, it will enter into equilibrium with its surroundings. This is true for both t e m p e r a t u r e and composition. The water front will quickly reach the initial temperature and composition of the reservoir. As a result the injected tracers will be in equilibrium with oil and water of the known composition and at a known t e m p e r a t u r e m t h a t of the reservoir before waterflooding started. These conditions can be reproduced in the laboratory to measure the partition coefficients of the tracers between the reservoir water and oil. While the complexities of flow in a reservoir do not lend themselves to easy analysis, analyses of tracer data should be a first step in such understanding. Analysis of the tracer response curve for a nonpartitioning tracer allows us to estimate the volume swept by the injected water and to determine the distribution of injected water among the responding wells. Addition of a partitioning tracer will also allow an estimate of the residual oil in the swept volume. The arguments against early tracer injection are mostly t h a t there is no need for a water tracer since water breakthrough is self tracing. This is not really true since not only is there the problem of distinguishing water from different sources among different producers, but of simply identifying a "pulse" of injected water. Without this ability to identify a pulse, we cannot directly monitor the reservoir volume swept by a given water source, and no simulation or other reservoir management tool can logically follow the details of a pattern water injection. TWO-WELL TRACER TESTS FOR RESIDUAL OIL: FIELD RESULTS During the past few years several two-well tracer tests for residual oil have been reported in the literature. These include several tests in small sections of dolomite reservoirs in Canada (Tang et al., 1991; Wood et al., 1990), several tests in both sandstone and limestone reservoirs (Lichtenberger, 1991), and a comp u t e r simulation of the residual oil saturation in one of the fields reported by Lichtenberger (Allison et al., 1991). A test reported from France (Rochon and Causin, 1989) gave conflicting results because of poor data.

Landmark method In his paper, Tang (1991) proposed that since the co-injected partitioning and nonpartitioning tracers follow the same path, except for the delay in arrival and

210

Chapter 5

more spread-out response of the partitioning tracer, the two tracers should have similar response curves. Hence, the two tracer residence times could be obtained by relating them to an equivalent landmark in each curve. This can be easier to do th an locating each mean residence time and should give the same results. Tang and Harker (1990) first tried this by using gas tracers for residual oil in a gas cap and showed in their examples that the landmark method gave consistent results. This is discussed further in the chapter on interwell gas tracing. For the two-well tracer test for residual oil in a water-saturated zone, they related the times of arrival of a partitioning and a nonpartitioning tracer to that of the times of the peak (mode) for each of the response curves. The arrival time was then applied to any identifiable landmark, such as the time at half-peak height. In this method, Cp(~) is the concentration of the partitioning tracer and Cn(t) is that of the nonpartitioning tracer at their respective landmark times, ~ and t. If each value is normalized by dividing it by the concentration at the peak value of the respective response curve, the two values become equivalent: ep(~) Cn(t) C p(max) = C n(max)

(5.11)

The ratio of the production times for the partitioning and the nonpartitioning tracers are equal to ~/t. Since, following Eq. (5.3), = (1+[3)=

1+ Kd 1-SorJJ

(5.12)

the ratio of arrival times will directly yield ~; hence S or can be calculated if the partition coefficient Kd is known. Experiments were performed in the R-5 zone of the Judy Creek Beaverhill Lake "A" pool shown using tritiated normal butanol (TNB) and carbon-14 tagged isoamyl alcohol (CIA) as partitioning tracers, and tritiated water (HTO) as the nonpartitioning tracer. In order to smooth out the response curve, Tang used the ratios of cumulative tracer responses, R, rather than of the instant values, C, and showed that the following identity could be substituted for the previous one of Eq. (5.9): Rp(~) Rp(t) Rp (max) -- Rp (max)

(5.13)

It should, however, be noted that each of these of individual readings represents real data, and such smoothing of data loses sensitivity to the individual response. Using these values and comparing results for R/R(max) at breakthrough, at peaks, and at intermediate points, the author showed consistent

Unconventional Waterflood Tracing

211

results for residual oil saturations. Thus, at t r a c e r b r e a k t h r o u g h , the ratio R:Rmax = 0. The ratio of the b r e a k t h r o u g h time for tritiated w a t e r to t h a t for t e r t i a r y butyl alcohol from Fig. 5.10 is 1.8, equal to the ratio of t/x, and equal to the value of (1 + [~). The Kd at this t e m p e r a t u r e for tritiated normal butanol (TNB) is given as 1.95, and the residual oil is calculated to be 27 percent using Eq. (5.12). The same procedure can be used for any other times to arrive at similar values. The response data used are t a k e n from Fig. 5.10, and values derived from them are given in Table 5.2.

TABLE 5.2 L a n d m a r k production times and Sor R Rmax

HTO t, days

TNB x, days

Sor

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1.8

3.1

27

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2.88

5.03

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Leduc test The same method was used in a pair of tests in the Leduc field (Woodbend D2A pool; Wood et al., 1990). The distance between wells is quite small, as shown in Fig. 5.11. Tritiated methanol was used as a nonpartitioning tracer here instead of tritiated water, because of a background of tritiated w a t e r left from previous tests run in this field. A separate test was made to verify t h a t the methanol did not partition into oil. In these tests, a comparison was made between residual oil s a t u r a t i o n s obtained by the two-well test, the single-well test, and sponge coring. The methods were compared by cost, results, and radius of investigation, shown in Table 5.3. Since the radius of investigation for the two-well test was so small, the single-well test and the two-well tests were reasonably comparable.

Chapter 5

212

TABLE 5.3 Comparison of residual oil methods, Leduc field Method used

Investigation radius (meters)

Results in %

Interwell test

35 -+ 1

64

Single-well test a. Single porosity

40 -+ 3

b. Dual porosity

35 -+ 3

Sponge Core

Cost ($Canadian)

33

25

4.6

80

0.1

125

Two computer models were used to match the single-well test results in the dolomitized limestone of the formation, the dual-porosity model yielding the better results.

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Unconventional Waterflood Tracing

213

Leduc Observation

j e

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Figure 5.11. Well pattern for Leduc test

Ranger field test Two-well tracer tests were reported for measuring residual oil in a sandstone formation in the Ranger field in Texas (Lichtenberger, 1991). A map of the test area is shown in Fig 4.13. The results from this test were discussed in chapter 4 in connection with water tracers. The tracer response data used for m e a s u r i n g residual oil were illustrated in Fig. 4.14 but were not discussed. Both tritiated w a t e r and thiocyanate ion were used as n o n p a r t i t i o n i n g tracers. Isopropyl alcohol (IPA) and tertiary butyl alcohol (TBA) were the partitioning tracers. The data in these figures were smoothed using a three-point moving average. Breakt h r o u g h times were obtained by fitting a parabola to the first few unsmoothed points and extrapolating to zero concentration. The residual oil was estimated by comparing the b r e a k t h r o u g h times of the partitioning and the nonpartitioning tracers using eqs. (5.3) and (5.4). Data from the two partitioning tracers, TBA and IPA (isopropyl alcohol), were also used to calculate residual oil. Residual oil calculated from the response to injector 3-38 is shown in Table 5.4. The measured distribution coefficients for the tracers used are: Kd (TBA) = 0.20 and Kd (IPA) = 0.4. The average Sor was 0.38. TABLE 5.4 Residual oil measurements, M cCleskey sandstone Tracer pair

Well 3-37

Well 3-39

Well 3-40

TBA/HTO

0.44

0,44

0.42

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0.33

---

0.39

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0.35

---

0.32

214

Chapter 5

This use of breakthrough time for time of arrival is not the same as that proposed in the landmark method of Tang. It really allows only the shortest and most direct flow lines to respond. Such a procedure will probably result in lower than expected oil saturations. Field breakthrough times are also very dependent upon detection sensitivity, sampling frequency, and other factors; thus, they should not be relied on too heavily.

Compositional simulator, Ranger field The data from the Ranger field were also studied in a three-dimensional compositional simulator at the University of Texas. The results of the waterflood

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Ranger field simulations UTCHEM ~

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Figure 5.12. Simulated oil saturations, Ranger field

Unconventional Waterflood Tracing

215

tracer were also discussed in chapter 4. Figure 4.16 showed the field and simulated response of the three wells in Table 5.3 to tritiated water. Residual oil m e a s u r e m e n t s were not discussed at that time. An analysis by Allison (1988) of the r e t a r d a t i o n of TBA relative to tritiated water between wells 3-38 and 3-40 yielded an average oil saturation of 0.38 + 0.05. In the waterflood simulation, the reservoir was divided into three layers of different permeabilities. The simulator was used to estimate the oil s a t u r a t i o n for each of the three layers at the end of the tracer sampling period (Allison et al., 1991). The contour maps are shown in Fig. 5.12. Mobile oil also occurred in the field. M a n y of the wells produced oil during the tracer test. This is not uncommon in m a n y tracer tests. In order to properly simulate fluid movement in the reservoir, this also had to be simulated. These contour maps are therefore an estimate of the distribution of all the remaining oil saturations in the reservoir.

O B S E R V A T I O N WELLS The primary purpose of an observation well is to obtain information about (fluid) tracer movement in the formation, between injector and producer, as a function of depth. By placing an observation well between the injector and producers, it is possible to monitor the passage of a tracer pulse in the formation at t h a t point. Two kinds of observation wells are used: logging wells and sampling wells. Unlike normal production wells, both are t r a n s p a r e n t to the flow and do not impart any dilution or mixing factors to it. This is a substantial improvement over samples obtained at a producing well. The logging well follows the passage of a tracer pulse by monitoring the radiation emitted by the tracer as it passes a detector in the well. No direct contact occurs between the injected tracer and the detector. A sampling observation well makes contact with the injected tracer but takes very small samples t h a t do not significantly distort the flow lines. A recent review (Widmyer, 1986) lists 44 references to both sampling and logging observation wells for use in oil recovery processes; however most of these refer to temperature observation wells for use in thermal pilots r a t h e r t h a n the tracer observation wells considered here. Pilot tests have been designed in which only an injector and a set of surrounding observation wells were used (Stiles et al., 1983).

Advantages and disadvantages An observation well provides several advantages over a conventional production well, the greatest of which is that it allows us to observe flow in a linear portion of the reservoir over the full depth of the formation. This is equivalent to being able to do a core experiment in an unaltered slice of the reservoir. Unlike laboratory core experiments, it is done in situ, unobtrusively, and without end

216

Chapter 5

effects. Enhanced oil recovery (EOR) floods pass laboratory core tests with flying colors before they go to the field. The reasons for failure in the field are the unexpected reservoir properties t h a t cannot be simulated by a laboratory core. An observation well provides the only way to observe the movement of a w a t e r front, an oil bank, or a chemical front, in a vertical slice of the reservoir. Since it can be closer to the injection well than the production wells, an observation well yields data much earlier. It can monitor the vertical distribution of injected water over the entire depth of the formation and the flow rate of injected w a t e r at each depth, by repeating m e a s u r e m e n t s at different time intervals. It can provide undiluted samples for compositional analyses of EOR flood fronts. It is very difficult to obtain such samples, undiluted by mixing and dilution effects, at a production well. The principal disadvantage of an observation well is the loss of production capability and cost of drilling a nonproducing well. In m a n y cases, however, existing wells can be converted to observation wells at a relatively low cost. Infill wells can also serve as observation wells before being converted to production. In principle, any well can be converted to an observation well by stopping flow into the well for a logging well, or reducing it to a small fraction of the ambient flow for a sampling well. A second disadvantage is t h a t it is restricted to a single location, hence it can only observe flow along a single radius from the injector. In an older field where the flow patterns are better known, a suitable radius for test can be chosen by field experience. It should also be noted t h a t logging and sampling wells need not be mutually exclusive.

Logging observation wells In this context, logging observation well refers to a well t h a t does not communicate directly with the reservoir fluids. It uses a g a m m a detector on a wireline to monitor the radiation emitted by injected tracers passing the well. REQUIREMENTS AND LIMITATIONS A logging observation well for tracers can still function as a conventional logging well in all other respects. It requires only a suitable g a m m a - e m i t t i n g tracer from the injection well. Any existing well can also be used for this purpose with minor modifications, providing it can be logged and there is no injection or production of fluid at the well. The most important factor in converting a field well to a logging observation well is to avoid distorting the flow p a t t e r n in the field. G a m m a - e m i t t i n g tracers are required because of the need for penetrating radiation to reach the detector. In principle, g a m m a radiation can be generated from nonradioactive tracers by n e u t r o n capture reactions; however, due to competition from naturally radioactive materials, the low neutron flux available

Unconventional Waterflood Tracing

217

down hole, the high dilution factors of injected tracers, and the lack of suitable materials of sufficient cross section, this has not been practical to date. COMPARISON WITH WATERFLOODTRACING The requirements of a tracer test for a logging observation well differ in m a n y ways from those for a conventional waterflood tracer test. The applicable tracers here are limited to gamma-emitting isotopes t h a t can survive the reservoir constraints. The detection system is limited to conventional g a m m a logging tools. The m i n i m u m detection limit (MDL) is set by the statistics of the background g a m m a count rate at each depth in the borehole and the sensitivity of the tool. The m a x i m u m amount of tracer injected is, however, still limited by the maxim u m permissible concentration (MPC) for unrestricted areas in the produced water from the surrounding wells. SUITABLE TRACERS The only commonly available gamma tracers for following a waterflood front are the Co-60 and Co-58 tagged hexacyanocobaltates. The dicyclopentadien complex of Fe-59 can be used for following an oil bank. There are few suitable g a m m a - e m i t t i n g tracers for following the movement of the chemical front, as distinct from the water front, in the enhanced oil recovery processes in common use. The materials used in chemical floods are generally organic compounds and the usable radioactive isotopes of carbon, nitrogen, and hydrogen are not g a m m a emitters. Tracers such as iodine can be inserted by addition to double bonds in m a n y of these materials. Unfortunately, the only available g a m m a - e m i t t i n g isotope of iodine having sufficient energy for this purpose is 1-131. Its eight-day half-life is too short for m a n y interwell distances, although it can be used in most small pilot areas. Other g a m m a tracers are possible; however, as indicated earlier, none has been tested as a waterflood tracer in the oil field. For short enough residence times, one can even consider tracers with half-lives of a day or less. Some of the polymers used for enhanced oil recovery processes can form complexes with the transition metals, many of which have gamma-emitting isotopes. These could serve as tracers for the polymer in question, but to date no developm e n t work of this kind has been reported. The possibility also exists of using other logging tools for observing the passage of a pulse of tracer. At this writing, the low relative sensitivity of any of the possible logging tools to potential chemical tracers is more limiting than detection of gamma emission. TRACER DETECTION Tracers for logging wells are monitored in the borehole by s t a n d a r d g a m m a logging tools. These are NaI(T1) crystal detectors, which can include energy discrimination. This reduces efficiency of detection but allows background discrimination. Energy discrimination can also be useful for m a k i n g observations on sequential tracer injections using different tracers. The overall efficiency of

218

Chapter 5

detection depends upon the size of the detection crystal, on the diameter of the well, on the amount of shielding imposed by well casing, cement, well fluids, and t h a t built into the tool. The detection limits and the depth resolution also depend upon the speed of logging. By convention, the g a m m a response obtained from all g a m m a logging tools downhole is expressed in API units. This holds for these m e a s u r e m e n t s as well as for the g a m m a ray background log required for determining detection sensitivity. Laboratory tests may also be used to calibrate detectors for this kind of geometry and to obtain efficiency and geometry corrections. In addition, proprie t a r y tools can be operated in any m a n n e r desired so long as all m e a u r e m e n t s are normalized to the same standard. Most g a m m a logging is done by service companies; however such wireline tools are not expensive and can be operated by company personnel.

API units of measurement All g a m m a logging m e a s u r e m e n t s in the borehole are reported in t e r m s of API (American Petroleum Institute) units r a t h e r t h a n by count rate. The API unit refers to a s t a n d a r d calibration facility set up by the American Petroleum I n s t i t u t e at the University of Houston, in Texas. It contains a p p r o x i m a t e l y 4 percent potassium, 24 ppm of thorium, and 12 ppm of uranium. Total activity is chosen to be twice the average from a mid-continent shale. The quantity of radiation measured by the counter inside this calibration facility is defined as 200 API units. Logging tools are calibrated at this facility, or in secondary facilities derived from this one, f o r a reading of 200 API units. WELL FIELD EXPERIENCE Although a number of tracer logging tests have been performed in the industry, few have been reported in the literature. Of three such tests t h a t have been described, only one gives any details about the t r a c e r procedures or d a t a analysis. All of the tests described report the count rate in API units, the conventional radioactivity m e a s u r e m e n t used in logging reports. A common feature of all the tests described in the literature, and of unreported data observed by the author, is the unexpectedly thin layers through which the tracers seem to flow. In all cases, flow seems to occur in layers in the order of a foot in thickness. This m e a s u r e m e n t can be considerably less, since it is doubtful t h a t the logs could resolve g a m m a response from layers less than a foot thick. Generally the formation is divided into vertical zones or layers t h a t are in the order of tens to h u n d r e d s of feet thick. These are based upon geologic and petrophysical data. The g a m m a response reported from most logging observation wells shows responding layers t h a t are far thinner t h a n expected from logs and cores. A typical section of a g a m m a log from an observation well is shown in Fig 5.13. In this figure, each small division represents two feet. This is a composite log showing the background g a m m a log, overlain with three tracer logs

219

Unconventional Waterflood Tracing

taken about a week apart. The log shows three clearly defined regions where tracer is moving past the observation well; however the thickness of reservoir for each these regions is only in the order of a foot. The principles for designing a tracer test for a logging observation well are reasonably straightforward and will be discussed later in this chapter. Only one of the papers on logging observation wells (Gesink et al., 1985) discusses the design of the tracer test. The example presented there is illustrative and will be discussed below.

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Chapter 5

Brunei observation well This test (Gesink et al., 1985), performed in the Seria field in the Sultanate of Brunei in Borneo, used Co-60 as the hexacyanocobaltate for a tracer. The tracer was injected in well 663 and monitored in the observation well, 671. The well locations are shown on the schematic in Fig. 5.14. A schematic of the vertical distribution in the formation at the pilot area is shown in Fig. 5.15, which shows the boreholes of both wells in relation to the m a r k e d formation layers and the perforated intervals. Only the K and L sands are perforated, as shown in the figure. The authors describe the design and analysis of the test in detail. They first determined how much Co-60 was required in order to produce a response of 50 API units at the detector and then estimated how much Co-60 would have to be injected to produce the required activity at the neighborhood of the wellbore. The required tracer concentration was estimated by the total dilution method described in chapter 3. This assumes t h a t the injected tracer pulse is diluted by the entire displaceable pore volume between the injector and the observation well as it moves out. They calculated the anticipated response for Co-60 in API units by analogy with known logging data on formations containing various amounts of K-40 as minerals, and correlation of the g a m m a radiation emitted by Co-60 with t h a t from K-40. The correlation used is shown in Fig. 5.16. It is assumed t h a t the

Log deflections, API units

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Figure 5.16. Response of detector to 4~ and 60Co radiation

Unconventional Waterflood Tracing

100ft

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well

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Figure 5.14. Map of well locations, Brunei pilot test

,oo. s-66~ its-o7, Injection well - ~ t Observation well ,,

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Figure 5.15. Vertical cut through Brunei pilot area

221

222

Chapter 5

materials are uniformly distributed about the borehole, and t h a t the detection sensitivity for Co-60 is not significantly different from that for K-40. The logging data in the borehole (in API units) plotted against the activity of K-40 in Bq/kg of formation gave a straight line plot, which extrapolated to zero. These units were converted to Bq/m 3 of formation, a s s u m i n g a density of 2000 kg/m 3 for formation material, and it was found t h a t a concentration of 2.1 MBq/m 3 of 40K results in a response of 50 API units on the log. By comparing the emission probability of a g a m m a ray from 40K with t h a t from 60Co, the authors concluded t h a t only 0.11 MBq/m 3 of 60Co would be required to produce the same signal. The tracer occupies only the water-filled fraction of the rock, given by the porosity, @, times the w a t e r saturation, Sw. Hence, the required tracer concentration, corrected for the water-filled pore space by dividing it by r is given by 0.11/r = 0.4 MBq/m 3. The total a m o u n t of tracer required was calculated using the total dilution model discussed in chapter 4, and multiplying the estimated dilution volume by the a m o u n t of tracer concentration required to give a signal of 50 API units. About 90 mCi of 60Co were injected as the hexacyanocobaltate ion with the injection water. The tracer was divided between the K and L sands in proportion to the rates at which water was injected into each of these sands. The observation well was initially logged twice a week to catch early response. Well log data are shown in Fig. 5.17. The sequential logs in the figure were t a k e n about 5 days apart. These are net logs after subtracting the averaged background count rate at each depth. Vertical dotted lines in the figure represent 100 API units. This should be compared with the average base log scale on the left, which is also 100 API units. The authors were able to identify tracer movement in a n u m b e r of s t r a t a and to show t h a t the tracer data were self-consistent and accounted for all the w a t e r movement. In common with all tests reported in the literature, the log showed t h a t the w a t e r moved through the reservoir in thinner and more numerous layers t h a n were expected from either core or log data. The responding layers are approximately a foot thick. In preparation for the test, a permeability profile derived from core and log data was set up to predict the expected tracer response. Fig. 5.18 shows the comparison of this profile with logging results. Generally the tracer response at the observation well occurred much earlier t h a n expected and through much thinner and fewer intervals.

D e s i g n o f a logging observation well t r a c e r test The requirements for a tracer test using a logging well are not different in kind from those for a tracer test in a conventional waterflood. Each requires a method for e s t i m a t i n g the dilution of the injected tracer pulse in the neighborhood of the test well and a method for estimating the tracer response at the

223

Unconventional Waterflood Tracing

d e t e c t o r . B o t h t h e a n t i c i p a t e d t r a c e r d i l u t i o n a n d t h e d e t e c t o r r e s p o n s e a t t h e obs e r v a t i o n well, h o w e v e r , a r e v e r y d i f f e r e n t f r o m t h a t of t h e c o n v e n t i o n a l w a t e r flood t r a c e r . T h e w a t e r a t t h e o b s e r v a t i o n well is n o t c o m m i n g l e d w i t h w a t e r f r o m o t h e r s o u r c e s , a n d t h e c o u n t i n g e n v i r o n m e n t of t h e d o w n h o l e d e t e c t o r for t h e p a s s i n g t r a c e r p u l s e is q u i t e d i f f e r e n t f r o m t h e l a b o r a t o r y s a m p l e c o u n t i n g environment.

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Figure 5.18. Comparison of log results with core predictions TEST DESIGN FACTORS The design of a logging tracer test has two parts: 1) to estimate the tracer concentration when the pulse reaches the observation well and 2) to estimate the response of the detector in the borehole to the diluted pulse in the surrounding formation. The first p a r t requires a physical model of how the t r a c e r pulse is diluted as it moves through the formation. The second part requires an estimate of the effective source-detector geometry and of the efficiency of the service company detector. These are not clearly defined quantities. The amount of tracer required must exceed the g a m m a ray background in the borehole, since the statistics of counting background in the wellbore determine the m i n i m u m detectable count rate to be exceeded at a 95 percent confidence level. The g a m m a - r a y background in the borehole must be m e a s u r e d as a function of depth before any tracer is produced at the observation well. Since the q u a n t i t y of 60Co cannot be increased forever without exceeding limits for the MPC of the water produced from the field, an upper limit is placed on the amount of tracer t h a t can be injected.

Unconventional Waterflood Tracing

225

DILUTION OF TRACER PULSE The first factor in the design of a tracer test is to estimate the expected tracer concentration in the neighborhood of an observation well. To do this requires a model of how the injected tracer moves through the formation. One model (Brigham and Smith, 1964) seems very attractive for this purpose. It treats the t r a c e r as an a n n u l a r ring moving radially from the injector with Gaussian dispersion in the direction of flow. Unlike a conventional waterflood tracer test, the tracer pulse is not mixed and diluted with other w a t e r at the production well; dilution occurs only in the injection well and during transit in the formation. A pulse of tracer injected at the surface will also be diluted to some extent by mixing with untagged injection w a t e r during its passage through the tubing. F u r t h e r reduction of this pulse will occur in several ways. It will be divided v e r t i c a l l y at the wellbore into s m a l l e r pulses according to the r e l a t i v e conductivity of the horizontal s t r a t a intersecting the wellbore. The tracer pulses in each of the horizontal, conducting s t r a t a are separately diluted f u r t h e r by dispersive forces as they move out radially from the injection well. The n u m b e r of strata, their thickness, and their permeability are, in principle, a measure of the heterogeneity of the system. A second model is empirical; it assumes t h a t the injected tracer is continuously diluted by the formation water displaced in its path, ignoring the effect of layers and yielding an average concentration, without regard to peaks and valeys, at the position of measurement. This is the most common method in use. The dilution of the tracer as estimated in the Seria field discussed above was done this way. It is a conservative estimate that assumes no flow mechanism but has a history of success for use in waterfloods, and its prediction is not expected to be better t h a n a factor of two. Often the background counting rate is m e a s u r e d and enough tracer injected to exceed this by a fixed amount. This is generally done by guess and usually involves an excessive amount to be certain of good response at the g a m m a detector.

Brigham dilution model for Brunei test The dilution of the t r a c e r as estimated in the Seria field d i s c u s s e d a b o v e guesses at the average concentration r a t h e r t h a n the peak concentration. The model of Brigham and Smith (1964) treats the tracer as a band moving radially from the injector with Gaussian dispersion in the direction of flow as discussed above. The original method assumes t h a t flow from the injector is radial and hence divergent, and neglects the convergent flow at the producer. This leads to error in calculating tracer response at the producing wells, which is discussed in the appendix together with the modified model for correcting the error. Flow in the neighborhood of the observation well, which is usually much closer to the injector t h a n to any of the producers, is, however, only divergent and the original model of Brigham and Smith is correct for this purpose. In this case, an a r b i t r a r y n u m b e r of layers can be chosen as a base. It is of interest to compare the results

226

Chapter 5

obtained by using the Brigham and Smith model (1964) to those from the Brunei test. Brigham and Smith proposed that the midpoint concentration (Cmp) of a band of tracer moving through the formation be defined by the following equation: 35 A Cmp = 12.8 hr

1.5 ~0"5

(5.13)

where: A = total amount of activity injected, h = thickness of formation, r = the porosity, Sw = w a t e r saturation, L = distance from injector to producer, and a = the dispersivity. All distances are in feet, and 35 is a conversion to cubic meters. A dispersion constant of 0.05 ft was arbitrarily chosen for lack of any experimental data. We substituted the data provided in the paper (Gesink et al., 1985) for the formation r = 0.33, Sw = 0.8 (although the numbers in the paper are somewhat loose). Assuming a dispersion constant of 0.05 ft, we obtained for the t r a c e r moving through the k layer (22.7 mCi injected, 110 ft from the injector, and 26 ft thick) Cmp = 3 5 ~ C i / m 3 and for the L layer (68 mCi injected, 140 ft from the injector, and 133 ft thick), Cmp = 14. The amount of tracer required to produce a signal of 50 API units in the neighborhood of the wellbore was estimated in the paper as 0.4 Bq/m 3, equivalent to l l ~ t C i / m 3. The results of these calculations are close enough to this value to serve as estimates for test design. TRACER RESPONSE AT OBSERVATIONWELL The tracer response at the borehole can be estimated in three ways: the semiempirical method used for the Brunei test discussed above; Monte Carlo calculations using one of the m a n y popular codes such as Briesmeister (1986); and laboratory measurements, which can also be used to calibrate detectors for this kind of geometry and to obtain efficiency and geometry corrections. Only the first of these methods is normally used.

Potassium-40 comparison The 4~ correlation, as used in the Brunei test, empirically correlates literature values for a known, uniform tracer concentration of 4~ in the formation with the tracer response in the borehole in API units. The method has the advantage of dealing directly in API units. The depth of penetration of g a m m a rays from a uniformly distributed source of 40K in the formation (Wahl, 1983) is discussed in chapter 1 and provides a good basis for this use. The energy of the 60Co g a m m a rays is not too different from that of the g a m m a ray emitted by 40K, and for this purpose the responses should be similar. Monte Carlo calculations The response at the detector for any source and borehole configuration can be calculated with high accuracy by the use of Monte Carlo calculations. This presents the advantage of fitting the geometry of the well and detector in use.

Unconventional Waterflood Tracing

231

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Figure 5.21. Maljamar gamma response vs. depth and time distort the flow lines. The only way for this to happen is to sample at such a low rate and/or frequency that the flow lines between the injector and the surrounding producers are not significantly perturbed by the sampling. The radial movement and dispersion of a tracer pulse from the injector is the same for any observation well. A sampling well differs from a logging well in that detection is at the surface. The concern here is how to get the sample to the

232

Chapter 5

surface without loss or contamination, rather t h a n of detection problems in the borehole. In principle, it would seem that samples could be analyzed downhole instead of being taken to the surface; but in practice, the borehole is a hostile environment for most analytical procedures and downhole analysis is not feasible at the current state of the art. With a major development program, current analytical techniques could be made to work downhole. The residence time distribution of the tracer response at the borehole is broad enough t h a t a high analysis frequency is not usually needed. A sampling well has one significant advantage over a logging well in t h a t it is not restricted to gamma-emitting tracers or to radioactivity. Hence, C-14 and tritium tagged tracers or a variety of nonradioactive chemical tracers can be used. This can be of great importance in monitoring the chemical front in an enhanced oil recovery method, as distinct from the water front. Since sample volume, as well as the counting efficiency and geometry at the surface, can all be far greater t h a n is possible with downhole logging, the dynamic range of the tracers used can also be very much higher. Also, any field production or injection well can be converted to a sampling observation well at a relatively low cost. The only requirements are 1) that the sampling volumes be low enough t h a t the flow lines near the wellbore are essentially undisturbed and 2) t h a t all of the desired flow zones be open. The disadvantage of a sampling observation well is t h a t it m u s t access the flow without significant disturbance, and that it is much more difficult to collect a vertical suite of samples t h a n to log a well over the same interval. There are, however, mechanical solutions to the sampling problem that can simplify vertical sample control. In the case of a chemical flood or some other EOR procedures, a sampling well may be the only way to monitor the actual movement of the chemical front. The best solution in that case is to combine the logging and the sampling functions. In this way a well can be logged separately for g a m m a radiation for the w a t e r front and sampled only when and where a g a m m a response is found. An observation well can be drilled for the express purpose of collecting downhole samples. The borehole can be small in diameter and only needs protection for sampling. Some of the new coiled tubing procedures advocated as a substitute for logging may be used for this. Completion can include a screen, if needed, and a packer t h r o u g h which samples may be withdrawn. In cases where the observation well is fairly shallow, this may be an attractive way to do a pilot flood in the field.

Monitoring tracers injected at an observation well An observation well need not be restricted to monitoring flow from a known injection source. Such wells have a history of use for monitoring g r o u n d w a t e r movement and for monitoring linear drift in the single-well tracer test. These

Unconventional Waterflood Tracing

229

induction log. This is shown in Fig. 5.19b. The first response shown in the figure followed the injection of 700 bbl of brine; the second was obtained after 1600 bbl had been injected. The response shows one streak at 4550 ft and one at 4553 ft. This is far more resolution t h a n was available from the induction log. No other details are given.

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Maljamar pilot observation well Co-58 and Co-60 were used by Conoco (Albright, 1984) to trace a post CO2 brine flush in a five-acre (2 x 104 m 2) inverted five-spot pilot in the Maljamar field in New Mexico. A map of the pilot is shown in Fig. 5.20. The area is dolomitic with two geologically separate zones. Tracers were injected with the brine phase for sampling at the producers. Cobalt-60 was injected into the sixth zone, a dolomitic sand, and cobalt-58 was injected into the ninth zone, a dolomite, to determine w h e t h e r the zones communicated by monitoring t h e m at the observation wells. Two logging wells, placed between the injector and one of the producers (#359), were used to monitor the flow. It is unfortunate t h a t the paper

230

Chapter 5

gives n e i t h e r the tracer form nor the a m o u n t injected, nor does it give the procedure used for selectively injecting tracers into each zone. Each of the tracers was injected as a seven-day pulse. In this pilot the tracer logging was done by company personnel using a small logging tool acquired for this purpose. The tracer logs showed independent flow through the two strata. The log response at well 363, 100 ft from the injector, to Co-60 in the sixth zone is shown in part a of Fig. 5.21. Each of the strata showed independent flow through m a n y t h i n n e r layers. Similar data were obtained from Co-58 in the other zone. The change in tracer response as a function of time for flow through the layers at 3701 and at 3704 ft in the sixth zone is shown in part b of Fig. 5.21. These turned out to have non-Gaussian distributions with slowly decreasing tails, a common response in such observations. R e s i d u a l oil at an observation well

A logging observation well can provide a shorter path for monitoring residual oil by means of the two-well test procedure discussed earlier in this chapter. This carries two advantages: 1) it extends the list of usable g a m m a tracers by permitting much shorter half-lived material to be used; and 2) it allows residual oil to be measured before and after an EOR test, along the same path. The use of 1131 tagged iodoethanol has been proposed (Cassad and Gant, 1982) as a partitioning tracer for this method, using another g a m m a emitter such as Co-60 tagged hexacyanocobaltate as a water tracer. The difference in g a m m a ray energies would be used to separate the activity from the two tracers by energy discrimination. Short-lived gamma-emitting tracers such as the eight-day half-life 131iodine are not normally used for logging observation wells; however if the residence time of the tracer is short enough, within about six half-lives, :this can be a useful tracer for this purpose. One advantage to the use of 1-131 is t h a t it is a cheap, universally available tracer widely used in the biomedical field. This is important because iodine tagged organic compounds are also widely available and can be tailored to fit water-soluble organic compounds with suitable partition coefficients into oil. By using either two iodine-tagged partitioning compounds or one partitioning compound and a Co-60 or Co-58 tagged nonpartitioning compound, the residual oil in each layer can be tracked by the residence times of each pair. This is an in-situ method for monitoring residual oil in each separate layer in the formation without outside interference. It can be a useful and relatively inexpensive pilot EOR testing method, since by using packers to isolate a zone for injection, the test can also be confined to a small horizontal segment.

S a m p l i n g observation wells Like a logging observation well, a sampling observation well differs from a producing well in t h a t it is t r a n s p a r e n t to flow in the reservoir: i.e., it does not

Unconventional Waterflood Tracing

227

The ever-increasing speed of small computers has even made this method available to home computers. Since 90 percent of the tracer response comes from the 18-cm-thick annulus around the wellbore, the tracer pulse can be treated as if it were in an infinite medium. In general, Idrees and Reis (1992) showed t h a t the a t t e n u a t i o n of g a m m a radiation in formation material is exponential and follows the form: Ti = ~io e'{~(r-rw)}

(5.14)

where 7io is the attenuated g a m m a flux, 7i is the flux at the edge of the borehole, ~, is the linear attenuation factor, r is the distance from the center to the outer limit of the detection volume, and rw is the wellbore radius. The cumulative fraction, G, of g a m m a rays reaching the detector from a radial source extending 20 cm into the formation is obtained by i n t e g r a t i n g the equation for g a m m a flux over the source position: G=

e-~'rw(1 + krw) - e'er(1 + ~x) e-krw(1 + krw)

(5.15)

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(5.16)

OTHER FIELD TRACER TESTS The other two tracer tests reported for observation wells were quite different in concept and are discussed below. While they give no details of design, they illustrate some of the properties of such tests.

Means San Andreas observation well A tracer test was performed by Exxon (Stiles et al., 1983) in the Means San Andreas unit in Texas. This was an interesting pilot in t h a t it was an entirely nonproducing pilot flood using observation wells both for logging and for sampling. This method was chosen because a dearth of time and available CO2 limited the CO2 pilot to a very small test. Observation wells were fiberglass encased to permit induction logging. The 11a-acre pilot is shown in Fig. 5.19a. All the wells were (pressure) cored using tritiated w a t e r to monitor m u d w a t e r invasion. The formation is a very heterogeneous dolomite. The effective permeability by well test was an order of magnitude higher t h a n indicated by cores, implying significant nonmatrix flow such as that through fractures. A preliminary brine injection was made to provide constant salinity for the induction logging. Production logs (radioactive and t e m p e r a t u r e ) made during the brine injection showed t h a t 80 percent of the w a t e r was entering a 20-ft interval between 4550 and 4570 ft. The induction log showed response to the

Chapter 5

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Figure 5.19. San Andreas pilot map and gamma log from well 9271 brine injection at well 9271, 58 ft from the injector, in 13 days, a limited response at well 9272, and virtually no response at well 9273. In order to verify the nonradial character of flow in this small pilot, a radioactive tracer was injected with the brine. A very large slug (100 mCi, 3.7 GBq) of Co-58 was injected into the l l/2-acre pilot, presumably as the hexacyanocobaltate. Cobalt-58 has a half-life of 71 days and emits gamma radiation at 0.51 MeV and at 0.81 MeV. G a m m a response was seen on the log at well 9271 in less t h a n a day but showed two responding layers where only one had been seen in the

Unconventional Waterflood Tracing

233

procedures can be used equally well for monitoring the local velocity of formation water in the neighborhood of any well. This does not require a well dedicated to observation but can be done at any well where a significant velocity field is expected: a newly drilled infill well, an injection well, or an operating well taken offstream. Neglecting wellbore effects, the "drift" rate arrived at by this procedure is not different from that observed in the normal use of an observation well where the pulse originates at a known injection well. A loss in vertical resolution often results with this method, since the tracer is usually added at the surface and the borehole is open for its entire depth. The major difference here is that unlike the case for a conventional observation well, the source of the drift is not identified, although in many cases the source may not be i m p o r t a n t or can be inferred. In this procedure a pulse of tracer is placed downhole by injection into the wellbore, or into a zone of the wellbore isolated by means of packers. The well is shut in and the tracer pulse allowed to "drift" out of the borehole under the local velocity gradient in the formation. The drift is allowed to continue for a time, td, long enough for the tracer to move a distance, r, from the neighborhood of the wellbore. This distance depends upon the local velocity field and the time, td, that the pulse was allowed to drift. At the end of this time, the well is produced back. The tracer moves out linearly in the velocity field but is produced back radially by pumping the well at a known rate, Q. The radius of drift, r, is calculated from the pump rate, Q, and the arrival time, t a , of the produced tracer pulse. The drift velocity is obtained by dividing the drift radius, r, by the drift time, td. A schematic of the procedure is shown in Fig. 5.22. Here, the tracer in the figure on the left moves from A to B, a distance, r, in the linear velocity field shown. Since the well is produced radially, the volume, Q, defined by the distance, r, is produced when the well is turned back on. The produced tracer response curve is shown at right. In general, the returning pulse will be distributed over time. The locator for the travel time of the pulse is the mean of this distribution, the first moment, ta. As discussed in chapter 4, this is given by: ]~ t C(t) At t a = ]~C(t) At

(5.17)

hence, a volume, V = Qta, with a drift radius, r, is produced according to the following expression, where ~ is the porosity, Sw is the water saturation, and h is the formation thickness: V= Qta = ~ r2hOSw

(5.18)

and the drift rate, Vd, is given by: r 1 ~ Vd = td = td

Qta ~h(~Sw

(5.19)

234

Chapter 5

This procedure can be coupled with a directional g a m m a detector to assign a direction as well as a velocity to the point of investigation. Conceptually, a logging well surrounded by an annulus containing a fixed concentration of tracer could be logged by a directional g a m m a detector. Assuming t h a t the annulus is open to flow from the formation, and that the logging region is entirely separate from the annulus, the well could be logged without mixing the fluid in the annulus. The direction and velocity of flow at any depth in the neighborhood of the well could be obtained from the rate of change in counting data with time and direction. Determination of the velocity of a g a m m a source moving away from a detector in a porous medium has been reported in the literature (Jassti and Fogler, 1990). This kind of analysis could at least provide qualitative velocity vectors at the well.

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Figure 5.22. Drift test at an observation well INTERWELL REACTIONS When materials are injected into the formation, there is always a chance t h a t unexpected reactions can take place between injected materials and reservoir components. When the reaction involves a change in the chemical form of the injected material, an isotopic tracer can oi~en shed light on the mechanism.

Conversion of injected sulfate ion to hydrogen sulfide When seawater was injected into a California waterflood in 1962, an increase in the H2S content of the gas was noted. Since the sulfate concentration of the injected water was about 1400 ppm, compared to 100 ppm in the produced water, it was thought t h a t this increase could be due to the reduction of the injected sulfate ion by bacteria. There had, however, been no published evidence to this

Unconventional Waterflood Tracing

235

effect. It was therefore of some interest to establish a relationship between the injected sulfate ions and the produced H2S. This could best be done by injecting 358 (half-life = 87 days) tagged sulfate ions with the injected sea water. Tritiated w a t e r was added as a co-tracer to obtain information about the flow path and the volumetrics of the water injection (Zemel, 1964). A small tracer slug composed of 5 Ci of tritiated water and 500 mCi of sulfur35 tagged sulfate ion was injected with the sea w a t e r by m e a n s of an injection well. T r a c e r b r e a k t h r o u g h was noted within about two days at a well 300 ft away. The sulfur-35 was found in the produced water as sulfate ion and in the produced gas as H2S. T r i t i a t e d w a t e r was detected s i m u l t a n e o u s l y in the produced water. The t r i t i a t e d w a t e r was counted directly in a liquid scintillation counter (LSC). The sulfate was concentrated from 24 ml of produced w a t e r by precipitation as benzidene sulfate (benzidene is a known carcinogen and should be handled with care) and the precipitate dissolved in an alcohol solution of Hyamine 10X (a commercial cocktail) for counting in the LSC. The detection limit for tritium in the Packard Model 3365 Tri-Carb LSC was 0.3 ~Ci/bbl at a 95 percent confidence level. The sulfate ion could be measured with a higher sensitivity due to the concentration step. Its detection limit was 0.01 ~tCi~bl (42 gallons). Sulfur-35 as H2S in the produced gas was counted in an ion chamber at the Shell production lab in California. Their results were corrected for efficiency using a B u r e a u of S t a n d a r d s S-35 s t a n d a r d source. All three tracer results are plotted as concentration vs. time (in days), as shown in Fig. 5.23. The ratio of activities of produced 358 as H 28 in the gas to t h a t of sulfate in the brine is about 10 percent when all results are averaged. No effort was made to analyze the oil for dissolved H2S. These curves have the same shape and, hence, the same flow paths. It is known (Voge, 1939; Sakai, 1983) t h a t 358= and ( 3 5 8 0 4 ) = ions do not undergo significant sulfur exchange at reservoir t e m p e r a t u r e . The source of the S-35 tagged H2S must therefore be reduction of the injected S-35 tagged sulfate ion. The production data for the breakthrough well for the two weeks after injection averaged 50 MCF/day of gas and 460 bbl of water. Although the daily analysis varied widely, the produced gas contained a daily average of about 2500 ppm of H2S, and the produced water an average of 1400 ppm of sulfate ion. The amount of sulfate required to produce a given concentration of H2S is given by: [804] G p(gas) W(SO 4) = W(H2S) x [I-I2S] x ~ x p(brine--------) where: W(SO 4) = concentration of sulfate in brine in ppm W(H2S) = concentration of H2S in the gas in ppm [X] = molecular weight of species X

(5.20)

Chapter 5

236

G = MCF gas produced/day B = barrels of water produced/day p(gas) = gas density in pounds/MCF p(brine) = brine density (pounds/bbl) Assuming a density of 44 lb/MCF for the gas, and of 355 pounds/bbl for brine, this calculation accounts for the conversion of about 100 ppm of sulfate ion, which corresponds to about 7 percent of the sulfate present in solution. In view of the scatter in the data, this is in reasonable agreement with the value of about 10 percent from the radioactivity measurements. We therefore conclude t h a t all of the produced hydrogen sulfide was formed in transit by reduction of part of the injected sulfate ion.

A S-35 tagged sulfate

60

6

O Tritium tagged water S-35 tagged H2S in gas

50 -

m

o

o "o

::L

t~

4-

40--

2~

,m

i,m Im

30

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e~

~m m

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(.

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I

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4

6 8 10 12 Days after injection

14

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Figure 5.23. Conversion of sulfur-35 tagged sulfate to H2S It is of i n t e r e s t to compare the results from this experiment with the hydrogen sulfide concentration found in parts of the field that are still producing n a t u r a l formation water of relatively low sulfate concentration (ca. 100 ppm). If one uses the radioactivity derived number of 10 percent of the sulfate converted to H2S, for the produced gas:water ratio of 9 SCF/bbl, an H2S concentration of

Unconventional Waterflood Tracing

237

9 ppm is predicted. This agrees well enough with the magnitude of concentration of 2 to 6 ppm found in this part of the field. This test confirms that the production of hydrogen sulfide can be entirely explained by the reduction of sulfate ion in the formation. It does not say anything about the mechanism of reduction. The current mechanism accepted by the industry is bacterial reduction. While this appears likely, it has not been demonstrated here. Reduction of sulfate to sulfide by reaction with hydrocarbons has been demonstrated in the literature (Toland, 1960); however the kinetics of reaction are far too slow for any appreciable reduction to have occurred at the temperature of the formation in this experiment. The assumption t h a t the reaction takes place inside the reservoir does not preclude the possibility that the entire reaction can take place at the inlet or outlet to the reservoir. Nothing done here excludes either the neighborhood of the wellbores or the inlet and outlet tubing from accounting for all of the reaction taking place.

FLOW THROUGH FRACTURES The discussion up to this point has been concerned with flow through porous media, which is quite different from flow in fractured systems. Much of the published work in geothermal and other fracture-dominated systems is devoted to the m a t h e m a t i c a l analysis of tracer response data. Only some of the nonmathematical material on experimental work is reviewed here. Over the past two decades, m a n y papers have been presented on tracer studies of flow t h r o u g h fractured reservoirs, and on their interpretation. Tritiated water, 1-131, Br-82, nonradioactive halide ions, and dyes such as fluorescene have been the most widely used water tracers in the field. Iodide ion was widely used in lab tests. In addition, there has been some use of organic esters as a means for estimating t e m p e r a t u r e and cooling times from the kinetics of hydrolysis (Robinson et al., 1984; Robinson, 1984). The driving force in these studies has been to arrive at a suitable flow model. The model used for flow in porous media is not really suitable to describe flow through fractures. A series of experiments on flow through hydraulically fractured hot dry rock (HDR) was reported by the Los Alamos National Laboratory. 1-131, Br-82 (35-hr half-life), and fluorescene were used as tracers, and injection and production logs were used to determine where the radioactive tracer entered and left the formation. The Br-82 was injected by means of a downhole tool designed to smash a tracer vial by remote control. The data interpretation was assisted by borehole televiewers, caliper logs, t e m p e r a t u r e surveys, and spinner surveys (Dennis et al., 1981; Tester et al., 1982; Robinson et al., 1984). The residence time distribution (RTD) of the system was monitored by fluorescene and Br-82.

238

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The d a t a were used to determine the flow fraction into different fracture zones and to estimate fracture volumes. It also was used to note borehole pathology such as bad cement and flow behind casing. Flow models for analyzing the data were based upon dispersion through a collection of fractures. The first moment of the tracer response curve (TRC) as a function of injected volume was taken as the mean volume of the fracture system. The modal volume (cumulative volume injected to peak of TRC) was taken as the volume of the most conductive direct paths. Work was also reported on the use of hydrolysis reactions (of amides and esters) to map the temperature field. A tracer study of the Weirakei geothermal field in New Zealand (McCabe et al., 1980) used 1-131 and Br-82 for tracing injected water. Analysis of the tracer residence time distribution (Fossum et al., 1982) led to estimates of the Peclet numbers and of the peak (mode) arrival times. Fair matches were found between the flow model and the field data, except t h a t late tracer response of field data was not fitted. F u r t h e r work at the Stanford Geothermal Program (Stanford University) led to more complex models (Walkup & H o r n e , 1985) using diffusion in the rock matrix to account for the tailing of the data. This gave a better value for fracture aperture by decoupling it from other reservoir parameters. As part of a cooperative program on geothermal fields (Horne et al., 1987) at the University of U t a h Research Institute (UURI), several soluble, substituted aromatic hydrocarbons were tested for use as water tracers at high t e m p e r a t u r e s (200~ and 250~ In the presence of oxygen, none of the compounds survived. Under anaerobic conditions, fluorescene, the benzenesulfonic acids, and the substituted benzoic acids survived through 250~ None of the perfluorinated acids survived 200~ Perfluorinated alkanes were proposed for gas tracing. F r a c t u r e d crystalline rock reservoirs are also found in conventional hydrology, and tests have been reported in such media. Tritiated w a t e r was used to monitor flow between two wells in a buried, crystalline basement rock under the S a v a n n a h River Nuclear plant (Webster et al., 1970). The data fit assumptions t h a t flow was through a homogenous region of intersecting fractures. Tracer data were used in conjunction with tiltmeter data to arrive at fracture geometry estimates in a steam pilot in the Athabaska tar sands in Canada (Palmer et al., 1990). Many papers on mathematical models and simulators for analysis of tracer response d a t a from fractured reservoirs are found in the literature. For the purposes of the present work, we have restricted ourselves to those t h a t are directly involved in dealing with experimental field data.

D O W N H O L E I N J E C T I O N AND S A M P L I N G The average waterflood tracer is injected and sampled at the surface; however t h e r e are other ways of carrying out either or both of these procedures. It is

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239

possible, for example, to sample or inject at points downhole, with the advantage that one can monitor the flow in isolated zones of interest. Downhole injection at a selected interval has been mentioned in earlier parts of this chapter. Although it can be done by a variety of methods, it is not very common because of the additional cost. The usual procedure involves the use of packers to isolate a section of formation. Tracers can be introduced at a downhole zone by remotely breaking a vial of tracer at the zone (Wood et al., 1989) or by a tracer injection tool at the location. Downhole sampling at the production well is rarely done and has not been reported. It can be done by a variety of mechanical methods such as lowering a sample bomb on a wireline to sample fluids at the region of interest down hole, or continuous sampling could be done by means of coiled tubing using a lift method such as gas lift or a downhole pump. The advantage to collecting samples down hole is that the tracer response (if any) for each flowing zone can be determined as a function of depth, allowing us to determine a production profile for the water tagged by each responding tracer.

REFERENCES

Albright, J.C., "Use of Well Logs to Characterize Fluid Flow in the Maljamar CO 2 Pilot," paper SPE 13142 (1984); JPT (Aug. 1986) 883-890. Allison, S.B., Pope, G.A., and Sepehrnoori, K., "Analysis of Field Tracer Response for Reservoir Description," J. Petrol. Sci. Eng. (1991) 5,173-86. Briesmeister, J.F., "MNCPmA General Monte Carlo Code for Neutron and Photon Transport," Manual LA-7396-0M, Rev. 2, Los Alamos Natl. Lab. (1986). Brigham, W.E., and Smith, D.H., "Prediction of Tracer Behavior in Five-Spot Flow," paper SPE 1145 presented at SPE Conf. on Production Research, May 3 4, 1965. Carlisle, C.T., and Kapoor, S., "Development of a Rapid and Accurate Method for Determining Partition Coefficients of Chemical Tracers Between Oil and Brines (for Single-Well Tracer Tests)," U.S. DOE Rept. DE-AC19-79BC10100, Washington, DC (1982). Carlisle, C.T., personal communication (1991). Casad, B.M., and Gant, P.L., "Reservoir Evaluation Using Partitioning Tracers," U.S. Patent 4,876, 449 (1989). Chang, M.M., and Maerefat, N.L., "State of-the-Art Report Summarizing Techniques for Determining Residual Oil Saturations and Recommendations for Research and Development," Natl. Inst. Petrol. and Energy Res. Topical Rept. NIPER-64 (Dec. 1986).

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Chase, C.E., "Finite Element Analysis of Single Well Backflow Tracer Test in a Homogeneous Medium," paper SPE 3485 presented at 46th Ann. Fall Mtg., New Orleans, LA, Oct. 3-6, 1971. Cooke, C.E. Jr., "Method of Determining Residual Oil Saturation in Reservoirs," U.S. Patent No. 3,590,923 (1971). Deans, H.A., "Using Chemical Tracers to Measure Fractional Flow and Saturation In-situ," paper SPE 7076 presented at 5th Symp. of Improved Methods of Oil Recovery, Tulsa, OK, April 16-19, 1978. Deans, H.A., "Method of Determining Residual Oil Saturations in Reservoirs," U.S. Patent No. 3,623,842 (1971). Deans, H.A., and Majoros, S., "The Single-Well Chemical Tracer Method for Measuring Residual Oil Saturation: Final Rept.," DOE/BC/20006-18 (Oct. 1980). Deans, H.A., and Tomich, J.F., "Method to Measure Fluid Drift and Immobile Phase Saturation," U.S. Patent No. 3,902,362 (1975). Dennis, B.E., Potter, R., and Lolar, J., "Radioactive Tracers Used to Characterize Geothermal Reservoirs," Trans., Ann. Geothermal Council Resources Mtg., Davis, CA, V, 324-332 (1981). Fossum, M.P., "Tracer Analysis in a Fractured Geothermal Reservoir: Field Results from Weirakei, New Zealand," Stanford Geothermal Program, SPGTR-56, Stanford, CA (1982). Gesink, J.C.J., van den Bergen, E.A., de Monchy, A.R., Rijinders, J.P., and Soet, J., "Use of Gamma Ray-Emitting Tracers and Subsequent Gamma Ray Logging in an Observation Well to Determine the Preferential Flow Zones in a Reservoir," JPT (April 1985) 711-719. Horne, R.N., Johns, R.A., Adams, M.C., Moore, J.N., and Stiger, J.N., "The Use of Tracers to Analyze the Effects of Reinjection into Fractured Geothermal Reservoirs," Rept. No. EGG-M-11887, E. G. and G. Inc., Idaho Natl. Eng. Lab. (1987). Idrees, M., and Reis, J.C., "Attenuation of Gamma Rays from Radioactive Tracers in Geologic Formations," Nucl. Geophys. (1992) 6, 4, 499. Jassti, J.K., and Fogler, H.S., "Determination of Flow Profiles in Porous Media Using Shifts in Gamma Spectra," AIChE J. (1990) 36,827. Karlberg, B., and Pacey, G.E., Flow Injection Analysis: A Practical Guide, Elsevier Sci. Pub., New York (1989). Knaepen, W.A.I., Tijssen, R., and Van den Bergen, E.A., "Experimental Aspects of the Partitioning Tracer Test for Residual Oil Saturation Determination Using FIA-Based Laboratory Equipment," paper SPE 18387 presented at SPE Eur. Petrol. Conf., London, Oct. 16-18, 1988.

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Lichtenberger, G.J., "Field Applications of Interwell Tracers for Reservoir Characterization of Enhanced Oil Recovery," paper SPE 21652 presented at Production Operation Symp., Oklahoma City, OK, April 7-9, 1991. McCabe, W.J., Manning, M.R., and Barry, B.J., "Tracer Tests -- Weirakei," Inst. Nuc. Sci. Rept INS-R-275, Dept. Sci. and Ind. Research, Lower Hutt, New Zealand (1980). Palmer, I.D., and Moschovidis, Z.A., "Fracture Geometries Consistent with Tiltmeter Data and Pressure and Tracer Communication in the GLISP (Gregoire Lake In-Situ Steam Pilot) I-1 Stimulation," paper 88-39-70 presented at 39th Ann. CIM Petrol. Soc. Tech. Mtg. & Can. Gas Processors Assoc. 2nd Quart. Mtg., Calgary, Alberta, Canada, June 12-16, 1988 (preprints 2). Raimondi, P., and Torcaso, M.A., "Mass Transfer Between Phases in a Porous Medium," SPEJ (Mar. 1965) 51. Robinson, B.A., and Tester, J.W., "Dispersed Fluid Flow in Fractured Reservoirs: An Analysis of Tracer-Determined Residence Time Distributions," J. Geophys. Res. (1984) 89, No. B12, 10374-10384. Robinson, B.A., Tester, J.W., and Brown, L.F., "Reservoir Sizing Using Inert and Chemically Reacting Tracers," preprint SPE 13147 presented at 59th Ann. SPE of AIME Tech. Conf., Houston, TX, Sept. 16-19, 1984. Robinson, B.A., "Nonreactive and Chemically Reactive Tracers: Theory and Applications," Ph.D. dissertation, MIT (1984). Rochon, J., and Causin, E., "Comparison of In-situ Measurements of Residual Oil Saturation," Proc., Fifth Hung. Hydrocarbon Inst. Impr. Oil Recovery Eur. Symp., Budapest, April 25-27, 1989, 769-778. Sakai, H., "Sulfur Isotope Exchange Rate Between Sulfate and Sulfide and Its Application," Geothermics (1983) 12, No. 2/3, 111. Stiles, L.H., Chiquito, R.M., George, C.J., and Long, L.D., "Design and Operation of a Tertiary Pilot: Means San Andreas Unit," paper SPE 11987 presented at 58th Ann. Tech. Mtg., San Francisco, CA, Oct. 5-8, 1983. Tang, J.S., and Harker, B.C., "Interwell Tracer Test to Determine Residual Oil Saturation in a Gas-Saturated Reservoir. Pt. 1: Theory and Design and Pt. 2: Field Application," paper CIM/SPE 90-130 presented at CIM Petrol. Soc./SPE Intl. Tech. Mtg., Calgary, Alberta, Canada, June 10-13, 1990. Tang, J. S., "Interwell Tracer Tests to Determine Residual Oil Saturation to Waterflood at Judy Creek BHL 'A' Pool," paper SPE 20543 presented at Tech. Conf. of Petrol. Soc. of CIM and AOSTRA, Banff, Alberta, Canada, April 21-24, 1991. Tester, J.W., Bivins, R.L., and Potter, R.M., "Interwell Tracer Analysis of a Hydraulically Fractured Granitic Geothermal Reservoir," SPEJ (Aug. 1982) 537.

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Toland, W.G., "Oxidation of Organic Compounds with Aqueous Sulfate," J. Amer. Chem. Soc. (1911, 1960) 82. Tomich, J.F., Dalton, R.L. Jr., Deans, H., and Shallenberger, L.K., "Single Well Tracer Method to Measure Residual Oil Saturation," J P T (Feb. 1973) 211. Voge, H.H., "Exchange Reactions with Radiosulfur," J. Amer. Chem. Soc. (1939) 61, 1039. Wahl, J.S., "Gamma Ray Logging," Geophys. (1983) 48, No. 11, 1536. Walkup, G.W. Jr., and Horne, R.E., "Characterization of Tracer Retention Processes and their Effect on Tracer Transport in Fractured Geothermal Reservoirs," paper SPE 13610 presented at the SPE California Regional Mtg., Bakersfield, CA, Mar. 27-29, 1985. Webster, D.S., Proctor, J.F., and Marine, I.W., "Two-Well Tracer Test in Fractured Crystalline Rock," General Ground Water Techniques, USGS Water Supply Paper 1544-I, U.S. Govt. Printing Office, Washington, DC (1970). Widmyer, R.H., "Use of Monitor Observation Wells in the Monitoring and Evaluation of Oil Recovery Projects," Proc., 5th SPE/DOE Enhanced Oil Recovery Symp., Tulsa, OK, April 20-23, 1986, 2,425-436 (paper SPE/DOE 14956). Wood, K.N., Tang, J.S., and Luckasavich, R.L., "Interwell Residual Oil Saturation at Leduc Miscible Pilot," paper SPE 20543 presented at 65th SPE Tech. Conf., New Orleans, LA, Sept. 23-26, 1990. Zemel, B., by permission BP, Alaska, 1989. Zemel, B., internal report, Shell Development Company, 1984.

CHAPTER 6

INTERWELL GAS TRACING INTRODUCTION Gas injection is used in a variety of secondary and tertiary floods. In each of these, the gas injection may have an entirely different function and, hence, a different behavior in the reservoir. The function of the tracer used m u s t be related to the operation being carried out and to the behavior of the injected gas. Such operations frequently involve phase changes, and the role of the tracer in the operation should be understood in order to u n d e r s t a n d the tracer response. Use of tracers for solvent flooding, as in miscible injection, for example, m u s t be understood in terms of the behavior of the miscible slug. Early b r e a k t h r o u g h of t r a c e r gas raises questions about the integrity of the miscible slug. Use of gaseous tracers for following steam floods is based on the premise t h a t the tracer chosen will follow only the vapor phase. Such materials as alcohols, which form azeotropes, might not be suitable tracers for either phase. In all cases, the tracer should identify the source of injected gas and be able to monitor its appearance in the field. From these data, one can obtain directional flow trends, discern the presence or absence of flow barriers or conductive channels, and note unexpected response times. Unlike ideal w a t e r tracers, gas tracer injection usually involves reaction with other materials in the reservoir. All gases partition into both oil and w a t e r according to their distribution coefficients; therefore a t r a c e r gas usually moves at a different velocity t h a n t h a t of the carrier gas. As a result, the concept of an ideal tracer m u s t be modified to suit the process being traced. In particular, the identity of the tracer pulse with an element of the co-injected gas may be lost.

GAS T R A C E R S F O R O I L F I E L D U S E

C h e m i c a l a n d p h y s i c a l restraints As discussed in earlier chapters, the oil field is a complex environment with a n u m b e r of chemical and physical restrictions. Most of the reservoir properties pertinent to tracer use are the same as for water tracers and can be described by a relatively small set of chemical and physical restrictions. The only additional constraints lie in the different effects of t e m p e r a t u r e and pressure on the tracer itself. This can be important where phase changes are involved. The reservoir is a porous medium with a high surface-to-volume ratio. Reservoir surfaces are usually negatively charged and contain clay with high cation exchange capacity. It is a reducing environment in which oil, water, and gas are in contact. A significant bacterial population is often present, particularly at injection and production

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ports. An ideal gas tracer is one t h a t survives these constraints while following the path of the carrier gas for the specific operation defined.

History and development The development of gas tracers in the oil industry is quite different from t h a t of w a t e r tracers. For various reasons, including lack of simple, sensitive analytical methods for gaseous tracers, the variety of gas tracers reported has been relatively limited. GAS TRACERS USED FOR INTERWELLTESTS Helium was identified early in the century (Satterly and McLennan, 1918) as the result of a emission and its presence was related to the presence of radon in oilfield gas. It was tested as an oilfield tracer (Frost, 1946, 1950; Wallick, 1953) but never found favor because of the high natural helium content (ca. 160 ppm) of reservoir gas. It is still a useful tracer where reservoir dilution volumes are not too high. The availability of radioactive tracers following World War II made gas analysis simple and immediately added several gas tracers t h a t survived the reservoir environment. Tritium, krypton-85, tritiated m e t h a n e (Welge, 1955), xenon-133 with a five-day half-life (Armstrong et al., 1960, 1961), and tritiated ethane, propane, and butane (Godouin et al., 1967) were quickly added to the list of gas tracers. The use of carbon-14 tagged hydrocarbons has not become as popular due to its higher cost. Tritiated hydrocarbons, which can often be made by catalytic exchange with tritium, are considerably cheaper, both because of the cheaper synthetic route and the lower cost of tritium. Iodine-131 as methyl iodide (Armstrong, 1960) has been used as a wellbore tracer but is not suitable for reservoir gas tracing. No other radioactive tracers have been identified for gas tracing. The use of higher carbon number alkanes as separate tracers raises a question about tracer velocity. Godouin et al. (1967) established t h a t no isotopic exchange occurs between tritiated and nontritiated hydrocarbons. Unfortunately, hydrocarbons can partition into both oil and water, and as a result, hydrocarbons of different molecular weights and structures will have different retention times in the reservoir, leading to different apparent velocities for each of these tracers. The development of the electron capture detector (ECD), with its high sensitivity to sulfur hexafluoride (SF 6) and to certain halofluorinated compounds, made it a valuable tracer for atmospheric research (Collins et al., 1965). Sensitivities in the order of 10 -14 (v/v) have been reported (Dietz and Cote, 1971) for SF6 using a t r e a t e d molecular sieve for separating it from air. Sensitivities of 10-11 are easily obtained for SF 6 in hydrocarbon gas without any special t r e a t ment. The use of SF 6 as a gas tracer is now widespread in the oil field. It has been reported for use in interwell gas tracing for miscible injection of nitrogen

Interwell Gas Tracing

245

(Langston et al., 1983) and of CO2 (Craig, 1985). It has also been reported for use as a leak detector in facilities and pipelines. Halofluoro compounds such as the freons have been used as tracers (Dietz and Dabbert, 1983) but are coming under increasing regulatory pressure and have an uncertain future. Other gas tracers t h a t have been reported for atmospheric monitoring include helium-3 (Halverson et al., 1979) and perdeuterated m e t h a n e (CD4) (Alei et al., 1987; Cowan et al., 1975). Helium-3 is the nonradioactive d a u g h t e r of tritium decay. The authors claim a sensitivity of 5x104 atoms/cc (8 x 10 "14 moles/m 3) using a gas-spectrometric technique. Although this is an expensive tracer, the extraordinarily high sensitivity of detection and ease of separation from field gas may m a k e it of value in gas tracer work. CD 4 is relatively stable to exchange and does not exist naturally. It is easily made in the laboratory and is detected by mass spectrometry. The authors claim a sensitivity of about 7x10 -15 moles per cubic meter, which includes an enrichment of CD4 by separation of methane from air. It could not, therefore, be used to enrich a field gas composed largely of methane, which seems to limit its use as a field gas tracer. The radioactive tracers reported for use in following gas injection into oilfield reservoirs generally include the following materials: tritium as tritiated hydrocarbons and as t r i t i u m gas, carbon-14 tagged hydrocarbons, and k r y p t o n - 8 5 (xenon-133 has limited use due to its short half-life). The only nonradioactive t r a c e r in common use is SF6. Helium has a limited use in situations where reservoir dilution volumes are not high. Any tracer t h a t 1) is a gas under reservoir conditions, 2) has a low detection limit, and 3) can survive the reservoir environment is eligible for use as a tracing gas. The tracer should be affordable and, if it occurs naturally in the reservoir, its concentration should be low enough t h a t it can be overcome at a reasonable cost. To be a gas at reservoir pressures, the tracer's critical t e m p e r a t u r e m u s t lie below the reservoir t e m p e r a t u r e . Nitrogen has been used (Cooke et al., 1982) with success for gas tracing. In some fields the natural concentration of argon in the reservoir is low enough t h a t it can be used as a tracer. Argon is a relatively low-cost tracer. Compounds such as carbon monoxide (CO) and nitrous oxide (N20) , which are stable and unreactive under reservoir conditions, are good candidates for gas tracers. The n u m b e r of potential tracer materials is high, the problem generally one of analytical sensitivity. CO can be m e a s u r e d by infrared spectra to the 0.1 ppm range and can be tagged with C-14 to provide higher sensitivity. Nitrous oxide can be m e a s u r e d chromatographically using an electron capture detector to a sensitivity of about 10 ppb. Perfluoro methane (CF4) and ethane (C2F6), also with current limits of detection of about 0.1 ppm, would be good choices except t h a t no ultrasensitive methods have been developed for analyzing them, as has been done with other perfluoro compounds. The Brookhaven National Laboratory has tested cyclic perfluoro compounds as gas tracers (Dietz and Dabberdt, 1983)

246

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because of the very low level at which they can be detected by electron capture detection (ca. 10 -12 g/cc). These compounds are, however, relatively large molecules with substantial partition into the oil phase, resulting in a significant lag of t r a c e r relative to the gas front if an oil layer is present (Dugstad et al., 1992). This is an interesting procedure because of the sampling method (Senum et al., 1992), in which the produced gas is passed through a solid absorbent t h a t collects the tracer for later analysis.

N O N I D E A L B E H A V I O R OF GAS T R A C E R S

Gases and gas tracers differ in m a n y respects from water and w a t e r tracers. The differences involve more t h a n the obvious distinctions of physical properties and require somewhat different approaches. In waterflood tracing we have the option of dealing with tracers t h a t do not interact with other reservoir materials. They are restricted to the water path, are immiscible with oil, do not interact with the formation materials, and are representative of an element of water. In gas tracing this is not so. All the materials t h a t are suitable for gas tracing partition into both oil and water. As a result, when a gas is injected into a reservoir, the tracers used to define its path undergo chromatographic separation. The reservoir acts as a chromatograph in the field, very much as an analytical chromatograph does in the laboratory. The injected gas serves as the carrier gas, and the residence time of the tracer in the reservoir will depend only on the properties of the tracer, not those of the carrier gas. This aspect of gas tracers is often overlooked in designing a t r a c e r program. The superficial velocity of the carrier (injected) gas and the velocity of the gas tracer are not usually the same.

P a r t i t i o n o f g a s tracers a n d injected g a s velocities All gas tracers known to survive the reservoir and remain gaseous under reservoir conditions will partition into oil and water. This is true for the so-called noble gases such as helium, xenon, and krypton, as well as for SF6, CO2, and the tritiated hydrocarbons. All gas tracers are transported through the reservoir at the superficial velocity of the gas they are tracing. This is true w h e t h e r the carrier gas s t r e a m is composed of a single substance or a mixture of hydrocarbons. They are, however, carried by the gas only when they are in the gas stream. During the time they spend in the oil phase, they move at the velocity of the oil phase. Because of its low viscosity, the velocity of gas is enough greater t h a n t h a t of either of the liquid phases t h a t the latter can be regarded as immobile with respect to the gas. In m a n y cases, the liquid phases are at residual s a t u r a t i o n and hence are truly immobile.

Interwell Gas Tracing

247

The fraction of time a tracer spends in the liquid phase compared with that in the gas phase is proportional to the number of tracer molecules found in each of these phases at a given time. Assuming that the tracer molecules are sufficiently mobile, local equilibrium will prevail. The equilibrium distribution of tracer molecules between phases is governed by the thermodynamic distribution coefficient Kd. Given three phases in the r e s e r v o i r - oil, water, and g a s - and three gas tracers that can partition into the oil and the water, and using the same nomenclature and development as for nonideal tracers in chapter 5, where Cip is the concentration of tracer, i, in one of the liquid phases, p, and Cig is the concentration of ith tracer in the gas phase: Cip

IQ= cig

(6.1)

The number of moles in each phase is obtained by multiplying the tracer concentration in each phase by the phase volume. If the phase volumes are normalized as phase saturations, the delay factor, ~, of tracer relative to the carrier gas is given by the product of the distribution coefficient by the ratio of saturations, as shown below: Sip = Kd Sig

(6.2)

As a consequence of this delay in each liquid phase, the tracer velocity must lag the superficial velocity of the (injected) carrier gas. Since there are normally three phases in the reservoir, three tracers are required to account for the delay. For each tracer, i, the apparent residence time, ti, is given by: So Sw} ti = tg{1 + Kio-~-g + Kiw Sg

(6.3)

where the saturation condition is" So+ Sw + S g = 1

(6.4)

If three gas tracers are injected into the reservoir, the transit time, ti, for each tracer is measured, and the distribution coefficients, Kij, for oil and water are known for each tracer, then the transit time of the injected gas, tg, and the oil, water, and gas saturations in the path of the gas can be found by solving Eq. (6.3) above for each of the three tracers, plus Eq. (6.4), the saturation condition. If the partitioning coefficient into water, Kiw, is small compared to the one for oil, Kio, this system could be reduced to three equations; however it would then require additional knowledge about the saturation condition, such as total porosity or the water saturation, Sw. Otherwise, the four equations above must be solved simultaneously.

248

Chapter 6

An alternative method of expressing the distribution coefficient is by using Henry's law, an ideal gas law that relates the concentration of tracer in the liquid to its partial pressure in the gas. These constants were used to determine the residual oil saturation in a field pilot described in the section of this chapter on field procedures.

Distribution coefficient measurements Distribution coefficients for gas tracers between gas, oil, and w a t e r are measured by the methods described for water tracers in chapter 5. The distribution coefficients, Kd, of several common gas tracers for a North Slope reservoir oil u n d e r several reservoir conditions were measured in the laboratory using the procedure illustrated in Fig. 5.1, and the results are given here in Table 6.1. For all the gas tracers tested here, the Kd values were independent of pressure and t e m p e r a t u r e within the ranges shown. This is a high-pressure region, and these are relatively low Kd's. For higher values of Kd, the pressure dependence would be more significant. The actual Kd used should be measured using oil of the composition found in the reservoir to be tested. The Kd values for gases in this system appear to be less sensitive to composition, pressure and t e m p e r a t u r e t h a n the Kd's for tracers used between oil and water, although there are also oil-water tracers of such polarity t h a t the Kd's are independent of t e m p e r a t u r e and pressure over a reasonable range of values. The data in Table 6.1 are given to one standard deviation, g. TABLE 6.1 Partition coefficients (Kd) for gas tracers in a synthetic North Slope crude Tracer

CH3T

CO

Kr

N20

KD

0.24 + .02

0.22 _+.01

0.39 _+0.01

0.66 _+0.01

Temperatures range from 82~ to 105~ Pressures range from 2000 PSI to 3000 PSI.

The tendency of gas tracers to partition into reservoir liquids places some limitations on the use of tracers for following gases injected into the formation; however it also presents an opportunity, since this nonideal behavior can be used to monitor fluid saturations in the path of an injected gas. This assumes t h a t the tracers are in local equilibrium with each phase. Although this is probably the case at normal gas injection velocities, it may not hold true at the very high gas velocities that can occur in gas fingers or through thin stringers.

Interwell Gas Tracing

249

Traced gas procedures Gas is injected into reservoirs for a number of reasons, which will be divided into three categories for this discussion. The first of these, pressure maintenance, includes gas flooding and related operations. It is a common reason for injecting gas in the reservoir as it is depleted and also provides useful storage for produced gas t h a t cannot be shipped or flared. Also in the first category is the use of gas tracers for reservoir description and for following the s t e a m phase in steam injection. The second category for gas injection, often referred to as solvent flooding or miscible flooding, is used to increase the a m o u n t of oil produced by one of a n u m b e r of enhanced oil recovery processes. The third category includes the use of gas tracers to measure residual oil in the formation. PRESSURE MAINTENANCE A considerable a m o u n t of gas is reinjected into the ground to m a i n t a i n reservoir pressure in a process much like waterflooding. Because of density differences it is often operated in a vertical (gravity stable) manner, or it may be used as a horizontal drive. Such injections can be tagged to look for suspected leakage and control the distribution of the injected gas. A similar situation holds for gas storage in the reservoir by reinjection if the produced gas cannot be shipped under current conditions. The gas tracer concepts differ from those for w a t e r tracers principally in t h a t the tracer used can be delayed by partition into the oil so t h a t its velocity will be less t h a n that of the injected gas. For some uses, such as identification of source of leaks, this delay in arrival time m a y not be crucial. SOLVENT FLOODING This refers to those enhanced oil recovery methods whose main oil recovery function works by "extraction, dissolution, vaporization, solubilization, condensation or some other phase behavior change involving the crude" (Lake, 1989). Other processes, such as viscosity reduction, solution gas drive, and oil swelling may also be important, but the primary process must be one of the above. RESIDUAL OIL The only realistic method for monitoring residual oil in a gas-enhanced oil recovery method is by an interwell tracer test. There are no single-well gas tracer methods for residual oil. An example of such use would follow the injection of lean gas, stripped of the higher hydrocarbons, into a reservoir to remove oil from the reservoir by an evaporative mechanism. The injected gas becomes enriched in the higher hydrocarbons as it moves through the reservoir, ultimately leaving a residual oil in place t h a t can be monitored by the two-well procedure described earlier for waterfloods. Since all gas tracers partition, three partitioning tracers are required if three phase saturations are to be measured. In this procedure, the

250

Chapter 6

t r a c e r response curves are m e a s u r e d at the responding wells and the m e a n residence times calculated. Both the residual oil and the frontal velocity of the injected gas can then be derived by solving the three equations for each tracer as given by eqs. (6.3) and (6.4). If the residual water saturation, Sw, is small, and its value is known, only two tracers are required to obtain the residual oil satuation.

FIELD P R O C E D U R E S As in the case of the water tracers described in earlier chapters, there are two parts to any field tracer test: the tracer part, which is concerned with the choice of tracers and design of the tracer test, and the analytical part, which is concerned with sampling and analysis of samples.

Tracer procedures and design The r e q u i r e m e n t s for design of a gas tracer test differ from those for a waterflood tracer test in m a n y properties other t h a n miscibility, including the compressibility of the gas and its solubility in oil. Both have a significant effect upon the calculated dilution of the tracer. Where gas lift is used for oil production, tracer dilution will also be caused by gas-lift gas. Phase transitions are important in m a n y processes such as steam injection, and the low viscosity of the gas phase can lead to early breakthrough. Another i m p o r t a n t factor for gas tracers, but usually not for water tracers, is density. Tracer gases are often significantly lighter or heavier t h a n the injected gas, e.g., helium or sulfur hexafluoride. Such tracers should be blended with other gas to neutral buoyancy before injecting a pulse of tracer, to avoid separation of tracer and carrier gas. DILUTION VOLUMES The quantity of gas tracer required for a successful interwell test is calculated in the same m a n n e r as for any other interwell tracer test. The quantity injected is chosen to ensure t h a t the produced tracer concentrations exceed a m i n i m u m detection limit but do not exceed a predetermined upper limit. This requires a way of estimating the volume in which the tracer will be diluted, Vd. The same two procedures are used to estimate the dilution volume, Vd, for a gas tracer as were used in the waterflood design discussed in chapter 4. These are: 1) the total dilution model, in which the volume, Vd, is estimated using the gas-filled pore space at a radius, r, to the average distance from the closest producers, and the thickness, h, of the formation; and 2) the model of Brigham and his coworkers (Brigham and Smith, 1964; Abbaszadeh and Brigham, 1984), which estimates the amount of tracer required to achieve a given peak concen-

Interwell Gas Tracing

251

tration using the dilution given by the p a t t e r n geometry, the n u m b e r of layers and their permeability, and the dispersivity of the tracer. The amount of tracer required based upon reservoir pore volume does not take into account the reservoir pressure and m u s t be increased because tracers are commonly analyzed in terms of volume per unit volume (v/v) at surface conditions. Design of a gas tracer test takes into consideration the total gas volume at surface conditions when calculating dilution volumes. Some exceptions to this occur if samples are t a k e n at the wellhead under pressure, or if a slipstream is used for on-line analysis at wellhead pressure. The increase in dilution volume is due to several factors: 1. There is an increase in dilution volume because gas is used under reservoir conditions. Since gas is compressible and reservoir pressures can be m a n y hundreds of atmospheres, reservoir gas dilution volumes expanded to surface conditions can be quite large. 2. There is a second increase due to the large volume of solution gas dissolved in the reservoir oil, which is released by the reservoir oil at surface (separator) conditions. 3. If lift gas is used to produce the wells, dilution from this source m u s t also be included. Since the gas-lift gas is recirculated, it also has the potential for contaminating other wells with produced tracer. This raises the dilemma of using enough tracer to overcome the dilution but not so much t h a t it will be a source of contamination for other wells.

Sampling and analysis TRACER SAMPLING Velocities of gases can be considerably higher t h a n those of liquids because of their higher mobility. As a result, tracer b r e a k t h r o u g h can occur quite early if there is a continuous gas path from injector to producer. Such paths can form by gravity override, through permeable channels or fractures, by viscous fingering, and/or a number of other mechanisms. Sampling programs for gas tracers need to be prepared for this. It is more important in gas tracing t h a n in w a t e r tracing to collect early samples on a frequent schedule. All of the collected samples do not need to be analyzed; selected samples may be analyzed on a regular basis until tracer is found. If no tracer is found, the samples lying between those analyzed can be discarded. Most gas samples are collected at a gas-liquid separator. This has the advantage of providing a gas sample from which the condensable liquids have been separated. Separator pressures are usually only a few atmospheres, and samples are easy to collect. The principal problems with sampling using a facility or test sepa r a t o r are dilution of tracer by the separator gas volume and contamination by tracer from other wells. A small test separator similar to the one in Fig. 3.8 can

252

Chapter 6

be mounted on individual wells. In all cases, it is necessary to flush the sample cylinder with sample gas before collecting a sample for analysis. The phase behavior of the tracer and its partition into the liquid phases in the separator should always be kept in mind when choosing sampling conditions. It is also possible to collect samples by passing the produced gas through a suitable absorber. Inorganic and carbon molecular sieves for this purpose are sold by chromatography supply houses. This provides the advantages of avoiding shipment of high-pressure gas samples and keeping the samples in a small volume. This kind of procedure may require one or more "guard" absorbers to remove water, CO2, or other deleterious materials from the collecting absorber. Many of these collectors are quite reusable and very cost-effective compared with the cost of owning and shipping high-pressure sample cylinders. Such a procedure is described by Senum et al. (1992) for collecting halofluoro compounds from a gas stream using a commercially available carbon absorber. NONRADIOACTIVE TRACER ANALYSIS Most analysis for nonradioactive tracer gases is done by gas chromatography (GC). In GC, gas is the mobile phase while the stationary phase is either a solid phase in gas-solid chromatography (GSC) or an adsorbed liquid phase gas in gas-liquid chromatography (GLC). Most of the tracers used here are analyzed by GSC using such solid phases as molecular sieves, carbon molecular sieves, and porous polymers. GSC separates the simple gases into sharply resolved narrow bands t h a t can be detected with a high signal-to-noise ratio. New column procedures coupled with a variety of old and new detection methods are constantly improving the selectivity and sensitivity of available materials. The most common detectors used for gas tracers are the electron capture detector and the thermal conductivity detector. High sensitivity and selectivity are also obtained by coupling the column to optical and mass spectrometers. The electron capture detector (ECD) is the most sensitive of the conventional gas detectors t h a t can be used with gas tracers. It is very sensitive to the presence of certain sulfur compounds such as SF6 and CS2, as well as to a number of halofluoro and cyclic perfluoro compounds. Detection limits are in the parts-pertrillion (ppt) region. It also has good sensitivity to some other gases, such as nitrous oxide (N20) in the parts-per-billion (ppb) region. This detector operates as an ion chamber in reverse. It contains a source of beta radiation (usually tritium or nickel-63) and operates in the ion recombination region, as shown in Fig. 2.1. In this region the ion current is very sensitive to gases t h a t form negative ions. Reported sensitivities to SF6 are as high as 10 "15 v/v (volumes per unit volume). It is, however, linear over a limited range of concentrations (1:100). The "reversed" ionization chamber is sensitized to a variety of simple gases when operated in the proportional region (Fig. 2.2) in the presence of a noble gas such as helium or argon and a constant source of beta radiation. This is called the

Interwell Gas Tracing

253

in the ppb region, although there seems to be a lot of "art" involved in its use. Carbon monoxide can also be detected and analyzed by infrared detection in the u n s e p a r a t e d gas, although the sensitivity of m e a s u r e m e n t in a chromatographic peak is greater. The t h e r m a l conductivity detector is a stable detector of moderate sensitivity, linear over five orders of magnitude. It is a nondestructive method, frequently used where highest sensitivity is not required. These detectors do not usually identify a specific compound; rather, the compounds are identified by the order in which they are eluted from a gas chromatographic (GC) column. It is important to r e m e m b e r t h a t except for the radioactive tracers, few analytical methods are specific for the tracer material. There are, however, analytical tools for direct analysis of tracer without separation, including optical techniques, using tuned lasers and solid state diode detectors, t h a t can both identify and m e a s u r e some compounds in the ppb level in the presence of a large matrix of other compounds. Many tracers are usable only under certain circumstances. If the argon concentration in the reservoir gas is low enough to allow its use as a tracer, a t h e r m a l conductivity detector is sufficient. Argon is a relatively cheap tracer gas, and high detection sensitivity is not needed. Helium can often be used in small reservoirs, despite its high concentration in the subsurface, because of its low price. ANALYSIS OF RADIOACTIVETRACERS All beta-emitting tracers, as well as those emitting low-energy g a m m a radiation, can be counted directly in one of the gas counters. This includes krypton-85, xenon-133, and tritium gas. Tritiated and C-14 tagged hydrocarbons, as well as C-14 tagged carbon monoxide, can also be counted in a gas counter. E n e r g y discrimination can be used to count both tritium and either C-14 or Kr-85 tagged tracers s i m u l t a n e o u s l y in the same sample. All the t r i t i a t e d compounds can either be counted in a gas counter or converted to water using a n u m b e r of oxidation schemes, and the water counted in a liquid scintillation counter (LSC). Procedures for counting the radioactive tracers have been discussed in chapter 2. For high tracer sensitivity by gas counting it is important to keep the background low. This is best done by combining passive shielding by means of a dense metal such as lead, with active shielding using anticoincidence techniques. A properly shielded proportional counter can count one-liter gas samples with a background of less t h a n 3 pCi per liter. The gas samples are usually collected in the field and sent to an outside laboratory for analysis; however they can also be counted in field laboratories or on line. A problem sometimes arises with proportional counting in the presence of such gases as SF6, which form negative ions t h a t interfere with the counting by reducing its efficiency. Unless it is stripped from the gas before counting, SF6 can interfere with the counting of tritium tagged gases. If nitrous oxide, N 2 0 , is

254

Chapter 6

substituted for SF6, there is a reduction in sensitivity but not as much interference with the counting. Although most available gas tracers are counted internally in gas counters, both Kr-85 and Xe-133 can also be counted externally by g a m m a counters, but with much poorer efficiency and geometry. The geometry can be improved by using a Marinelli type of counter in which a central detector is surrounded by a large volume of gas in a closed vessel. Krypton-85 is a very poor g a m m a emitter, producing only 0.025 gammas per beta. Xe-133 emits very low-energy radiation so t h a t its detection efficiency by an external detector is quite low. Their major use in the g a m m a mode has been for detecting tracer from steam floods at a field location. ON-LINE TRACER ANALYSIS Procedures are available for directly analyzing produced gases for tracer on line at the field location. Most of the me~thods for doing this require t h a t water, CO2, and/or other interferences be removed from the sample s t r e a m before analysis. This can usually be done by inserting a guard column in front of the analyzer. Carbon monoxide can be both identified and measured by infrared absorption with remarkably little interference from other compounds in the h y d r o carbon stream, except t h a t water must be removed. The sensitivity of an electron capture detector (ECD) for SF6 is so much greater than for any other component normally in the hydrocarbon stream that, except for stripping out water, SF6 can be monitored continuously on line with little interference. The hydrocarbon mixture serves as the carrier gas without interfering with the SF6 measurement. The response from the ECD is linear with the concentration of SF6 for about two orders of magnitude and, as in all work of this kind, frequent and accurate calibrations are needed for good results. Commercial equipment used for continuous monitoring of SF6 in the atmosphere will also work using hydrocarbon s t r e a m s as a carrier gas. Helium can also be monitored on line continuously (Ahner and Genser, 1979) by means of a helium leak detector. The response is linear over about six decades. Radioactive gases can be counted on line in a flow-through gas proportional counter using the dry hydrocarbon stream as the counting gas. Two tracers, such as tritium and carbon-14 or krypton, can be counted simultaneously in this environment using energy discrimination. The sensitivity of the counting procedure can be significantly enhanced by operation at high pressure; unfortunately, this also raises the background, as shown in Eq. (2.3). For such cases, the ratio of ~/B/E (where B is the background count rate and E is the counting efficiency) can be minimized to choose the optimal pressure. As in any other counting procedure, a counting p l a t e a u m u s t be established. The principal interference in the counting procedure is the presence of naturally occurring radon, levels of which can be quite high in some cases. Radon can be removed by a p p r o p r i a t e

Interwell Gas Tracing

255

(cryogenic) absorption columns; however the easiest solution may be simply to collect samples and delay counting for about a month to reduce the activity of the 3.7-day half-life radon to negligible levels. In addition to analytical problems, gas tracer may face unexpected dilution problems due to the presence of lift gas injected into the well and solution gas released in the separator. Procedures currently used to correct for these conditions are described in the section on field tracer tests. VERIFICATION OF TRACERS Today, virtually all tracer users buy rather than make their own tracers. All gas tracers, both radioactive and nonradioactive, bought for interwell tests need to be verified as to quality and quantity before use by requiring the supplier to provide an analysis. For elemental radioactive tracers like tritium, krypton-85, and xenon-133, evidence of radioactive and chemical purity and amount, including an estimate of error, should accompany the material. Questions about such problems should be answered by calling on the supplier before the test is started. Most suppliers of tritiated or C-14 tagged compounds will supply radio chromatograms and other data showing that the correct compound is properly tagged with the desired isotope. Many tritiated compounds are made by catalytic exchange with tritium gas, producing a variety of tritiated compounds in addition to the one desired. It is important to have some assurance of purity of the tagged tracer, particularly with regard to separation from labile tritium. The user should also determine the kind and degree of purity required for the test. For all radioactive tracers, an aliquot of material should be obtained, if possible, and given to the laboratory that will be analyzing the samples as a check on the quality of the material and as an aid in sample analysis. Nonradioactive tracers, being more conventional tracer materials, are often not scrutinized as carefully as radioactive tracers. Tracer costs usually require that the lowest acceptable grade of material be used as a tracer. It is still important to know that this is the material ordered and that the quantity is correct. A gas cylinder of known pressure and volume can easily be obtained to help the analyzing laboratory verify quality and quantity of tracer material as well as freedom from analytical interferences.

FIELD TRACER TESTS

Gas tracing and reservoir description A major application of gas tracers is following the path of gas injected into the reservoir to identify gas breakthrough by well and by geological feature. Problems in the well are easily distinguished from geological problems, The

256

Chapter 6

presence of fractures, thief zones, conductive or sealing faults, and other geologic anomalies is usually identified by tracer response. In this case, if partitioning causes a lag in tracer response relative to that of the gas, it may not be important within reasonable limits. There are, however, gas tracer responses t h a t can indicate other problems. Early tracer breakthrough in a miscible drive m a y also be an indicator of failure in the drive, which can occur by a variety of mechanisms such as gravity override, viscous fingering, or breakdown of miscibility. A few gases have been reported in the literature for use in tracing injected hydrocarbon gas, mostly tritium gas, tritiated hydrocarbons, Kr-85, and SF6. All have been successful as tracers, except t h a t there have been some u n r e p o r t e d cases of nonappearance of tritium gas. All of these tracers partition into oil (and water) to a greater or lesser extent and will lag the front. This becomes important for the higher-carbon number tracers, and for long tracer residence times. Tritiated alkanes of different chain length are commonly used as equivalent tracers, even though their partition coefficients are different. This should not be done if their t r a n s i t times are important; however all the materials mentioned in the previous section, including CO, N 2 0 , helium-3, nitrogen, etc., can be used as tracers u n d e r the right circumstances. The important factors in the choice are t h a t there be no n a t u r a l interferences and t h a t the tracer follow the intended operation, in this case the gas movement. COALINGA FIELD Three gas tracers were used to map the continuity of sand layers in a complex channel sand reservoir in California (Tinker et al., 1973). Geologic studies suggested t h a t channel boundaries would limit the reservoir continuity to a width of 300 to 500 ft, which would severely limit a proposed waterflood for this field. Tracers were injected to map the continuity of the sands in this field. An injection well was cased and perforated through each of the sands, allowing tracers to be injected separately into each sand. Different layers were injected with t r i t i u m gas, tritiated methane, or Kr-85, and the gas was sampled at surrounding wells. Tracers were collected at the wellheads and analyzed on site. The gas samples were collected in beach balls and the gas analyzed for each of the tracers in a t e m p o r a r y laboratory set up in the field. The tracers were s e p a r a t e d by both chemical and physical methods. Tritium gas was stripped from the other tracers by cryogenic trapping. It was either counted in an ion chamber or oxidized to w a t e r over hot copper oxide and counted in a liquid scintillation counter (LSC). Tritiated m e t h a n e was burned to water and counted in an LSC. Krypton-85 was s e p a r a t e d from the other components by burning them to water, which was absorbed in a trap. The krypton-85 was counted in an ion chamber. The beach balls used, while thick walled, were permeable to gas. The half-life for tritium loss by diffusion through the walls was about 15 days; for m e t h a n e it was about 2 months. The samples were analyzed within a few hours, well within this time frame. When they can be used within the time constraints, beach balls are cheap,

257

Interwell Gas Tracing

disposable sample vessels. The response 'pattern of the wells to the t r i t i u m injection is shown in Fig. 6.1. The tracer test in these oil-desaturated intervals was an important Yeservoir characterization test for a proposed waterflood. The tracer work served as a calibration for the indirect evaluations, showing better continuity t h a n could be inferred from an outcrop study. The same three tracers were reported for following gas in several field tests. In one test (Welge, 1955), the preferential flow direction was determined, and a good correlation was claimed between the tracer response and the fraction of gas produced. Tritium gas and Kr-85 were used to spot sources of p r e m a t u r e gas b r e a k t h r o u g h in a small field in Louisiana (Calhoun 1968), and for following the flow of gas in the F a i r w a y field (Calhoun 1970). Four t r i t i u m - t a g g e d hydrocarbons were used in a field in North Africa for following injected gas flow (Comier et al., 1967).

/,, ,-, "-'<

71~

rg" V

o ~ o ]oi

z-T~176 ~~o/

_

" /~i'~,,

" ~

f

~ e/17!,ooo i)i '~ //`l/Ifeet ~njectionwell

","'~ _~176176176

Figure 6.1. Tritium response, HX sand, East Coalinga field

DUAL COMPLETION WELL An interesting v a r i a n t on the tests described above is a nitrogen-foam field test (Kuehne et al., 1988) performed in a dual completion well in the P a i n t e r Reservoir in Wyoming. The tracer test was not particularly successful. It is reported here because it represents a way of doing an interwell test using a single dual completed well. This may be usable for testing EOR methods in the field much more cheaply t h a n by a standard interwell test. In this test, SF6 was used as a prefoam tracer and freon-ll3 as a postfoam tracer for a nitrogen foam

258

Chapter 6

test in the field. Tracers were injected into the injection string. The SF6 did not respond in the production string until three months later, at very low SF6 concentrations. The freon, on the other hand, responded at high concentrations in three days. The reason for this is not known; one possible explanation is the opening of a t e m p o r a r y channel at the wellbore connecting the injection and production intervals from the foam test. R e s i d u a l oil in the g a s c a p

The injection of gas to produce oil from the gas cap by vaporization of the residual oil in place was mentioned earlier. Here, produced gas is treated to remove all liquefiable components and the "dry" gas reinjected into the gas cap. In principle, multiple tracers can be used to measure the residual oil left in place as discussed earlier. In practice, no measurements of residual oil in a gas cap have been reported, with one exception, which is reported below. LANDMARK METHOD FOR RESIDUAL OIL Little has been reported in the literature on the m e a s u r e m e n t of residual oil s a t u r a t i o n in gas-saturated reservoirs, and until recently nothing has appeared on the use of interwell tracers for this purpose. The only reported use of interwell tracers for this purpose appeared in two recent papers (Tang and Harkins, pts. 1 and 2, 1990).

Laboratory experiments In the first paper, the authors demonstrated that the chromatographic separation of two tracers could be used to measure residual oil saturation to gas using both static and dynamic tests in the laboratory. A number of tracers were tested for use in the field. Three tracers were chosen, based upon their partition coefficients and their sensitivity to an electron capture detector. These were SF6 and two freons: F12 (dichlorodifluoromethane) and F13B1 (bromotrifluoromethane). The tracers were measured by gas chromatography using an electron capture detector. The equipment used for dynamic tests in slim tubes is shown in Fig. 6.2. The slim tube is a long, narrow-bore tube commonly used for miscibility m e a s u r e ments in the industry. It serves the same purpose as a laboratory core. Here, an 18-m by 8-mm o.d. tube was packed with 80-100 mesh glass beads, for a pore volume of 164 ml. The slim tube was first s a t u r a t e d with a synthetic reservoir oil and then flooded to residual oil with reservoir gas. The tracers, contained in the tube shown in the figure, were injected as a pulse with the carrier gas by opening the two valves while the gas was injected at a constant rate. The effluent gas was sampled and analyzed by the attached gas chromatograph (GC) in the figure. The equipment was maintained at constant pressure and temperature.

Interwell Gas Tracing

259

It should be noted that the kind of equipment illustrated here can be used for measuring partition coefficients in any multiphase system, including water as well as oil. The equipment described earlier in chapter 5 for measuring partition coefficients between oil and water can be used equally well for this purpose. The Henry's law constant, H, for each of the tracers was determined for the equilibrium partition coefficients between field oil and gas under reservoir conditions (4.14 MPa and 68~ Henry's law is an ideal gas law relating the concentration of gas in a solution, Ni, with its partial pressure, Pi, in the ambient gas in contact with it, as given by Eq. (6.5). Gas solubility is often expressed in tables of Henry's law constants as Hi: Ni = HiPi

(6.5)

9 ,: 9

:

..,_ '

Oven

Gas : meter ..........................

Slim tube

-

oo,O i l ~ r

'fL~il

Baoores

control

.,

P u m p ....

S a m p l e loop m ~ m

a~

I j'

~

I

~ =

1~1

LI.H

Figure 6.2. Slim tube measurements of partition coefficients

Analysis of the data was based upon the plate concept of chromatic separation (Martin and Synge, 1941). Tang and Harkins (1990) expressed the peak retention volume, Qr, in pore volumes as: Qr = Qg(1 + 13)

(6.6)

260

Chapter 6

where Qg is the peak retention volume for a nonpartitioning tracer and ~ is the chromatographic retention factor. This is the same ~ factor presented in another m a n n e r in Eq. (6.2). Here, the ~ factor can be expressed as: zRTSro 1 = HVS-----~= *HSg where: z = R = T = V = H = Sg =

(6.7)

the gas compressibility factor, the gas constant, temperature, ~ oil volume, liters/mole, Henry'slawconstant, gas saturation.

The method was tested using slim tubes in the two-phase gas-oil system illustrated in Fig. 6.2. The plot of peak retention volume, Qr, versus 1/*H gave the expected straight line whose slope is the residual oil saturation in the system, Sor, and whose intercept on the volume (Qr) axis is the retention volume for a nonpartitioning tracer. If H is known, the residual oil saturation could be calculated to an accuracy of one percent pore volume, or vice versa. An example of this from one of the reported slim-tube experiments is shown in Fig. 6.3.

"1-

5

t~ co E 0 0 c~

4

Actual Sor = 0.32 Calc. Sor = 0.32

3

F13B1//" E

2

-1~

0

1

L_

0

rr

0

'

,

I

I

,.

1

Peak retention volume, Qr

Figure 6.3. Residual oil by Henry's law plot

2

Interwell Gas Tracing

261

Field test The laboratory method described above was tested in the Golden Spike D3 "A" pool, a carbonate reservoir in Alberta, Canada. The same tracers, SF6 and two freons, F12 (dichlorodifluoromethane) and F13B1 (bromotrifluoromethane), were used to m e a s u r e the residual oil saturation in the gas-saturated reservoir. Two existing wells 150 m a p a r t were selected as injector and producer. They were recompleted and perforated in a 5-m zone in the gas cap, 60 m above the production zone and 3 m below the main reef barrier. A minitest using tritiated m e t h a n e and tritium gas was done first to delineate interwell communication. The methane responded as expected with response observed in 5 days. There was no response from the tritium injection. Occasional nonresponding tritium injections have been reported over the years by word of mouth, but this is the first written commentary. The amount of each tracer required was calculated from the minitest, p a t t e r n volume, and tracer detection limits. The tracers were premixed and added to the dry injection gas as a liquid under pressure. The pilot test was operated under steady state conditions, at a constant injection and production rate and at unit mobility ratio. The production well operated at a constant rate of 72,000 std m 3 per day. A solenoid-operated automatic sampler u p s t r e a m of the test separator collected four samples of produced gas per day. Operating conditions were chosen to fit the streamline model of Brigham and his coworkers (Brigham and Smith, 1964; Abbaszadeh and Brigham, 1984). As a first step in this test, the model was used to identify contributing layers by matching a nonpartitioning tracer profile. A residual oil saturation was assigned to these layers and the values adjusted to fit the chromatographic data. Field test results SF6, the most volatile of the tracers, broke through in 4.4 days. Examination of the profile suggested three contributing layers, as shown in Fig. 6.4a. The response from F13B1 and F12 is similar to t h a t from the SF6, except t h a t the arrival time for each is later, 5.1 and 6.1 days, respectively. The responses of the three are shown in a cross-plot in Fig. 6.4b. The concentration in the response curves shown here was quite noisy. This is an unfortunate consequence of the individual character of t r a c e r response. This noise was reduced by using the cumulative recovery instead of the individual responses, shown in the figure, where cumulative recovery is plotted on the same time scale as concentration. The cumulative data are much smoother but give up sensitivity to individual response. Fig. 6.5a shows how well the tracer responses for the three tracers imitate one another. Each of the three tracers showed the same recoveries of 9 percent and 18 percent for peaks 2 and 3, respectively. The use of equal recovery times shows an equivalent correlation. The cross-correlated d a t a are connected in equal recovery lines at 2 percent, 9 percent, 18 percent, and 22.5 percent, as shown in

262

Chapter 6

the figure. The correlation with such obvious landmarks as peaks is quite good, and the data from each of these equal recovery tielines gave a straight line when plotted against 1/*H. Residual oil saturation is obtained from the slope of the line. The intercept on the volume axis is the response from a nonpartitioning tracer. Fig. 6.5b illustrates a typical plot. A plot could also be made connecting the breakthrough times; however breakthrough times are too dependent on other considerations to be accurate landmarks.

b 3oo-

100

8 0 O_

"

0

o

.'" :"'\ F12 [-' I ",--"--"-,

l

1'

0

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I

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i

ii

g " peak3 i i! 8~ ~ 50 Production time, days

100

0.0

0

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3F

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I i

50 100 Production time, days

,

Figure 6.4. Formation layers and tracer response to field test

Analysis of data The authors used a transformation technique, based on the correlations described above, to analyze the field tracer response data. Residual oil is determined only by the relative separation between the partitioning and nonpartitioning tracers. In this procedure, equal cumulative recovery times for partitioning and nonpartitioning tracer responses were used to measure the separation between them. The correlation is demonstrated in figs. 6.4 and 6.5. The relationship, at a given recovery, between the partitioning tracer, ~r, and the nonpartitioning tracer, tr, at equal recovery times is given by: Sor

-

l:r = tr{ 1 + .TZSg},,= tr{ 1 + ~}

(6.8)

where *H is the effective Henry's law constant, defined in Eq. (6.6), Sor is the residual oil saturation to gas, and Sg is the gas saturation. This equation is equivalent to the two-phase version of Eq. (6.3), where 1/*H = Kd. Since a third phase is also present, the residual water saturation, Swr, this expression provides

Interwell Gas Tracing

263

only the ratio of Sor:Sg. Hence, an additional saturation condition is needed. This could have been provided by using three tracers with known distribution coefficients in water and oil and applying the procedures given by eqs. (6.3) and (6.4) in this chapter. Other alternatives include a knowledge of the porosity and swept volume, a knowledge of the average water saturation, or similar data. In this example, the authors used the knowledge that the water saturation in the field was 8 percent.

a

300

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/

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,"

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"~ 50

Production time, days

F1381

sF~ 100

0t 4O

R= 18% peak 3 Sor = 19%

50

60

70

80

90

Production time, days

Figure 6.5. Cross correlated tracer response and residual oil plot The authors then suggested a general landmark method to determine residual oil from the chromatographic separation of the partitioning and nonpartitioning tracer response curves. This method was used later for monitoring residual oil in a waterflood and described in greater detail in a later paper (Tang and Harkins, 1991), which is reviewed briefly below. The standard correlation between arrival times of partitioning and nonpartitioning tracers is expressed by: = t(1 + ~)

(6.9)

which states that if a gas tracer partitions into the oil, it will be delayed relative to a nonpartitioning tracer by the factor (1 + ~), and its peak concentration will be lowered by the same factor because of conservation of mass. Hence, if Cp(max) and Cn(max) are the peak (landmark) tracer concentrations for the partitioning and nonpartitioning tracers, respectively, then:

264

Cn(max) = Cp(max)(1 + ~)

Chapter 6

(6.10)

Normalizing any concentration point on the curve by its peak concentration allows the transformation: Cp(~) Cn(t) = C p(max) C n(max)

(6.11)

With Eq. (6.9), this provides the l a n d m a r k base for calculating ~ from the chromatographic response curves and the residual oil ratio from the slope of the line from Eq. (6.8).

Solvent injection (MI) tracing PHASE BEHAVIOR In this enhanced oil recovery (EOR) method, a mixture of gases called solvents is injected into the reservoir to interact with the oil in place to form a single, stable, combined phase. The gases injected for this purpose are usually cheap, nonreactive, easily available gases such as hydrocarbons, carbon dioxide, and nitrogen, which can form a miscible bank with the oil. The miscible bank may form on first contact or may develop through multiple contacts. The hydrocarbons used may vary from methane to natural gas liquids (NGL). Miscible injection (MI) has proven to be an effective enhanced oil recovery (EOR) procedure leaving a low residual oil in place. The miscible process results in the formation of a b a n k of oil t h a t can be propagated through the field. Because of the high mobility of the injected gas, there is always a danger t h a t if it loses its miscibility it will move on independently, bypassing the bank. This can occur by a n u m b e r of mechanisms, such as fingering processes and the force of gravity. Because of the density difference between the gas and the oil, there is also a possibility t h a t the gas can sepa r a t e vertically from the oil, unless the gas is injected from the top down in a gravity stable injection. In either case, the gas could bypass the bank and destroy or limit the effectiveness of the EOR process. To decrease the relative permeability of the reservoir to gas, it is common to alternate injection of w a t e r with injection of gas in a process known as water-alternating-gas (WAG). This process unfortunately carries with it the possibility of water's blocking some of the oil. In stratified formations of differing properties, it is also possible for solvent, oil, and water to enter different parts of the reservoir.

Phase transport The basic assumption in tracing gas through the formation is t h a t both the injected gas and the tracer remain gaseous during their passage through the formation. If one or the other fails in this regard, the tracer is no longer a valid indicator of the movement of the injected gas. Tracers for following gaseous behavior are chosen because they are gaseous under reservoir conditions. Many uses of

Interwell Gas Tracing

265

t r a c e r gases fulfill this condition; however injected gases t h a t are intended to form a miscible liquid phase with the oil in place put a different r e q u i r e m e n t on the function of an added tracer. They also place a burden on the designer of det e r m i n i n g w h a t the tracer is or should be tracing and how best to i n t e r p r e t the tracer-response curve. The success of the miscible injection (MI) is a function of a n u m b e r of variables. The chemistry and physics of the process are reasonably well known and have been discussed in monographs (Stalkup, 1983), texts (Lake 1990), and the open literature. All MI processes are successfully tested in laboratory cores and slim tubes before undergoing a field test in a reservoir. Most projects fail in the field because of an unexpected reaction to reservoir properties. Details of how these materials move and interact in a complex reservoir, however, are known only by inference. In complex patterns it becomes difficult even to infer how the materials move and interact without the use of tracers. In most MI processes, a solvent m a t e r i a l t h a t is miscible with the oil is injected into the reservoir as a slug. Generally the slug of solvent is followed by a cheaper chase fluid (gas) t h a t is compatible with the solvent to reduce the cost of the operation. Many such processes have now been reported in the literature, and in a number of these, both the injected gas and the injected w a t e r were tagged with tracers. Some of these reports, a few of which are described below, discuss tracer design and analysis in reasonable detail. The projects reported below share several important aspects. All present the details of the tracer design as part of the overall MI design and use injection and production logs and observation wells to define fluid movement into and out of the reservoir at the wellbore. The tracer programs are carried out over a long enough time span to be important to m a n a g e m e n t of the field. At present, analysis of the tracer response curve from the gas injection is still largely qualitative in nature, due to m a n y theoretical and practical complications. It is not clear from any reported work what the significance of early breakthrough of a gas tracer is, or how to distinguish an early gas tracer response due to a bypassed bank from early breakthrough of the solvent from a miscible bank. Nothing was reported on quantifying the distribution of tagged solvent among the producers or on estimating swept volumes. While much computer simulation was reported, none involved the gas tracer response. Field test results

RAINBOW KEG RIVER B POOL A miscible injection (MI) was performed in the Rainbow Keg River B pool in Alberta, Canada. Initiated in 1984 (McIntire et al., 1985; Mazzocchi et al., 1988), it employed n a t u r a l gas liquids (NGL) as a miscible solvent. Tritiated methane, tritiated ethane, and tritiated butane were injected into each of six injection wells

266

Chapter 6

as tracers. The tracer design, injection, and analytical procedures are described in the paper, as are the results of the operation. This was a gravity stable injection in an atoll-type reef t h a t had been waterflooded before the miscible injection. Tracers were added to determine when the solvent was completely spread across the top of the atoll before starting the drive and to detect early breakthrough. Tracer amounts were chosen to be ten times the minimum detectable concentration. The tracer was injected as a pulse of high concentration subject to dilution from two sources: 1) dilution and dispersion occurring in the reservoir, Vd; and 2) dilution due to expansion to surface conditions and to tracer partitioning to nonanalyzed fluid at the surface, Vs. The reservoir dilution volume, Vd, per well was determined from the type curves given by Abbaszadeh-Dehghani and Brigham (1987) for a staggered line drive using a modified dispersivity (a) measured in laboratory cores. The condition shown in Fig. 6.6 for a / a = 5000 was used. This is a plot of C p/Co as a function of injected volume. The initial concentration, Co, was obtained by assuming t h a t the injected tracer was diluted in the borehole by the injection volume, Vo, which was t a k e n as one wellbore volume or 14 m 3 (88 bbl). The value of Cp, the peak tracer concentration at the producer is used to arrive at a reservoir dilution factor, Vd, of about 7 x 10 ~5, the factor by which tracer concentration is reduced in the formation. Only one layer was assumed here. The minimum detectable limit for unrestricted areas (MDL) is given as 370 Bq/m 3 (10 pCi]l). The gases were collected at the field from test separators and counted in a liquid scintillation counter after burning to water. The combustion procedure was not given, but the most common procedure used is to pass the gas over a column of hot (800~ copper oxide pellets. This converts the tritiated hydrocarbons to tritiated w a t e r and carbon dioxide. The natural CO2 and H2S components were removed before burning the samples. A dilution volume, Vs, for each tracer gas in the separator was calculated from the distribution of the untagged material between gas and oil in the separator, and from the tracer concentration in the w a t e r of combustion. For any hydrocarbon, the combustion reaction can be written as: CnHm + (n + m]4) 0 2 = nCO2 + (1/2)m H 2 0

(6.12)

From this equation, the relationship between C g, the tracer concentration in the s e p a r a t o r gas at s t a n d a r d conditions, after nonhydrocarbons are removed, and Cw, the tracer concentration in the combustion w a t e r collected, can be calculated as: Cg = .00038 m Cw

(6.13)

where m is the average number of hydrogen atoms per molecules in the separator hydrocarbon gas. This is further corrected by the mole fraction of the t r a c e r hydrocarbon found in the gas at separator conditions, the gas-oil ratio, and the

Interwell Gas Tracing

267

expansion to surface conditions to yield the additional factor by which the tracer concentration in the collected sample is reduced. The m a x i m u m dilution in the separator occurs for butane, which has the highest partition into oil. The sum of these effects is the surface dilution factor, Vs, = 2.3 x 10-3.

4 o

3

x o

_.o2 0 1

0

I

0.6

0.8

I

I

1.0

I

1.2

Pore volumes injected

Figure 6.6. Reduced tracer concentration as a function of injected volume

Two 500-ml samples (at 10 atmospheres) were required for each analysis, one for total tritium content and one for the specific tracer analysis. To determine if more t h a n one t r i t i a t e d hydrocarbon is present, p a r t i c u l a r fractions were s e p a r a t e d by cryogenic methods before burning. In general, if (n) tracers are present in the sample, (n) combustions are required. Since duplicate samples are surely needed, this represents a very sizable sample load. The total a m o u n t of tracer, A, required per well was calculated by: A=

(MDL)xVo _ 370 Bq/m3 x 14m3 VdxV s - (7x10-5)(2,3x10-3) = 3"2x101~ Bq = 0.86 Ci

(6.14)

This calculated amount was arbitrarily multiplied by a factor of about 12 to ensure detection at the wells. Ten curies of each tracer were placed in 50-ml glass implosion ampoules in the depressured wellhead. The ampoules were shattered by repressuring the wellhead, and the tracer flushed into the formation by the injected gas. A map of the traced area showing which tracers are injected into each well and their early response in the neighboring wells is shown in Fig. 6.7.

Chapter 6

268

Tracer injectors | ethane methane A butane

9-10

13-2

tOO0 fizz

Meters

Figure 6.7. Tracer m a p of Rainbow Keg field In the second paper (Mazzocchi et al., 1988), the tracer results were b r o u g h t up to date. Stated objectives of the tracer program were to monitor solvent movem e n t to e n s u r e good areal coverage of the flood, which was essential to e n s u r e a uniform drive w i t h o u t bypassing. These objectives were met. Solvent (gas) channeling was observed in some of the early wells and injection and/or production volumes reallocated to achieve good solvent spreading. Tracer h a s been identified at each producing well. Tritiated b u t a n e was the last tracer to respond, p r e s u m ably due to its chromatographic retention on s t a t i o n a r y oil on the reservoir. A s i m u l a t o r model was developed to follow the flood; however it does not seem to have been used to t r a c k the t r a c e r movement. No t r a c e r response d a t a were reported. SOUTH SWAN HILLS MI FLOOD T r a c e r s were used to follow the flow of gas and w a t e r in a miscible WAG ( w a t e r - a l t e r n a t i n g - g a s ) injection i n i t i a t e d in t h e S o u t h S w a n Hills field in Alberta, C a n a d a , in 1973 (Wagner et al., 1974; Davis et al., 1976). This w a s a

Interwell Gas Tracing

269

horizontal flood in a limestone reservoir involving 27 five-spot patterns. Tritiated water, (ammonium) nitrate, and isopropyl alcohol served as w a t e r tracers. Tritium gas, tritiated ethane, and Kr-85 were used to tag the injected gas. Injection of all the radioactive tracers was performed by a contractor. The gas tracers were shipped to the field in the amounts allocated for each well, and the contents displaced from the t r a n s p o r t cylinders into an "isotope" chamber using methane. Each isotope chamber was equipped with a floating piston to separate the tracer from pump fluid (oil or alcohol). Tracers were pumped from the isotope chamber into the wellhead at normal wellhead pressure, to mix with injected gas. The gas tracers were counted at the field by a gas proportional counter, using energy discrimination to distinguish between Kr-85 and tritium. Possible interference from n a t u r a l radon is not mentioned. When tritium was detected in the counter, an additional sample would be taken and sent to a suitable laboratory for f u r t h e r analysis. (This requires separation of tritium (hydrogen) gas from tritiated ethane before counting. Cryogenic separation over a suitable chromatographic column is a common method). The sensitivity of detection for the gas tracers used here was given as 1 pCi/L m quite a high sensitivity for a field counter. From Eq. (2.3) for counter sensitivity, a one-liter counter at 100 percent counting efficiency and a 30-min counting time should have a s t a n d a r d background level of about 6 cpm. This requires a very well-designed counter system and careful operation. The a m o u n t of tracer required in these tests was calculated by the BrighamS m i t h model for a layered five-spot p a t t e r n (Brigham and Smith, 1964), using the tracer sensitivity for the counter as given above. The model was modified to compensate for tracer dilution at the surface due to expansion from reservoir pressure and by solution gas (Wagner et al., 1974). The expected peak tracer concentration was calculated using known reservoir p a r a m e t e r s in the modified B r i g h a m - S m i t h model. The authors found reasonable correlation between produced and calculated peak tracer concentrations. A discussion of tracers for this and other miscible floods is also given. Downhole injection and production logging is the only way to know where injected and produced fluids enter or leave the reservoir. In the tracer test performed here, both injection and production logging were used to monitor the specific depths at which fluids were injected and produced at the surrounding wells. Injection profiles were obtained using both radioactive and spinner surveys on all the injection wells in the pilot at least once a year. A typical injection profile obtained from a South Swan Lake production unit is shown in Fig. 6.8. In this figure, the perforated intervals in the well are shown in black. On the left side of the well is the anticipated profile based upon best prior knowledge. On the right of the well is the actual injectivity profile found for w a t e r injection, which is significantly different from t h a t anticipated. On the far right is the profile of injected solvent a year later in the same well.

Chapter 6

270

Theoretical profile ,0,

Zone I

I0

ZO

_0

30

Perforated interval

40

D

8400

Actual profile 1973 (water)

0

10

o 58'/o

20

30

58%

40

$0

Actual profile 1974 (solvent) 60

0

5

I0

20

$0

40

$0

55% jl... -.--., 1%

Z~

/ ~6%

~/.'_____.;

23% Zone 3

i

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3:".

31% .-~

- ~,.

~ 8 Yo 3%

3%

11%

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Figure 6.8. Injection profile, South Swan Lake production unit The depths at which the injected and produced phases enter and leave the reservoir can determine the success or failure of any enhanced oil recovery test. Profiles were also run on selected producing wells where b r e a k t h r o u g h occurred to correlate this with an appropriate injectivity profile. The unit production and injection profiles were then integrated to give an overall injection-production profile for the reservoir, showing t h a t the vertical injection and production profiles were not balanced. The original injection program had matched injection rates with porosity r a t h e r t h a n permeability in an effort to ensure uniform sweep in each zone. The wells were extensively worked over to reduce injectivity in the more permeable upper zones and enhance injection in the lower zones. Wherever cross-flow was observed, the thief zones were plugged back. The tracers were used together with well profiles and other field data to correct for channeling and to try to m a i n t a i n desired pattern flow by altering well production and injection rates. MITSUE MI FLOOD This was a large MI flood using 56 injectors and 140 producers in a sandstone reservoir in n o r t h e r n Alberta, C a n a d a (Omoregie et al., 1987). This is a first

Interwell Gas Tracing

271

report giving the tracer program design and preliminary results. A total of 43 injectors were tagged with one of six gas tracers in two stages. All patterns were five-spot. Six gas tracers were used to distinguish breakthrough from the different injectors at each producer. These were tritiated methane, tritiated ethane, tritiated butane, freon-ll, krypton-85, and SF6. The latter two are excellent gas tracers; however the reasons given for their choice are based on assumptions of tracer behavior t h a t are not necessarily valid. Krypton and SF6 are both gases under reservoir conditions since they are above their critical temperatures at the reservoir temperature of 63 ~ Both, however, also partition into the oil. Krypton is an inert gas for most chemical reactions but not for partitioning between gas and oil or dissolving in a miscible oil bank. Tritiated water was the sole water tracer used. The required tracer quantity per well was chosen to give produced concentrations below the m a x i m u m permissible concentration in unrestricted areas (MPC), and above the minimum detection limit (MDL). The tritiated water tracer was assumed to be diluted by the total pore volume of the pattern and multiplied by a factor of four. Gas tracer quantities were calculated in the same manner, except t h a t produced concentrations were also corrected for gas volumes at reservoir conditions. No corrections were indicated for the presence of water or oleic phases in this pore volume but probably were made. To ensure success in monitoring the produced tracer, the calculated activities were further increased by another factor of 3 for tritiated water and by a factor of 10 for the gas tracers. A sketch of the tracer injection system (using t r a n s f e r cylinders) is shown in Fig. 6.9. A detailed safety procedure for injecting the tracer is included in the paper. This is a good injection procedure and well worth following. The tritiated hydrocarbon samples were analyzed by combustion to water and the tritiated water counted in a liquid scintillation counter. The analytical procedure used here is the same as that used for the Rainbow Keg miscible injection test described earlier. The Rainbow Keg analytical procedure is referenced here, but no other details are given. Some of the tracers used were also analyzed for total activity before injection. Results of the analysis of Kr-85 agreed with the nominal value; however the analytical results for tritiated methane activity were a factor of ten lower t h a n the nominal value. This should severely limit the interwell distance over which this tracer could be monitored in the field. Few tracers are actually verified for type and amount delivered to the field. This is one of very few papers reporting such m e a s u r e m e n t . Errors in tracer amount or tracer type are more common t h a n most people realize and should be monitored far more frequently. Many of the injectors were monitored on a regular basis for injection profiles. A sampling observation well was also in use. Reservoir fluids were also monitored t h r o u g h the sampling observation well for compositional and t r a c e r analyses. Kr-85 was counted directly in separator gas by a proportional counter.

272

Chapter 6

There is no indication as to whether the samples were counted in the field or at a laboratory. The sulfur hexafluoride and freon were measured by gas chromatography using an electron capture detector. Minimum detection limits reported for the radioactive tracers are given in Table 6.2. The MDL's for SF6 and f r e o n - l l are both given at 0.1 parts per billion (ppb).

Injection system

Transfer system

0

...-

,

,,

N2 supply Transfer manifold

Injection vessel

Injection manifold

Figure 6.9. Gas tracer injector, Mitsue field

TABLE 6.2 MDL for tracers used in Mitsue field Tracer Tritiated hydrocarbons Krypton-85 Tritiated water

Becquerels per cubic meter

Curies per liter

185 Bq/m 3

5 pCi/L

37 Bq/m 3

1 pCi/L

0.185 MBq/m 3

5 nCi/L

Tracer breakthrough occurred earliest (about 70 days) at the observation well, 264 meters from the injector. It showed tritiated methane and f r e o n - l l breaking through together with tritiated water, as shown in Fig. 6.10. This is a sampling observation well, which limits its production to less than 20 m3/day to minimize the distortion of flow lines. Its relationship to the injection well and to the rest of

Interwell Gas Tracing

273

the p a t t e r n was not stated clearly in the paper. The b r e a k t h r o u g h velocity of about 3.8 m/day is very high and raises the question of w h e t h e r the gas tracers r e p r e s e n t the solvent bank. Times of arrival of the tracers suggest multiple s t r a t a with different reservoir paths for the gases and for water. The only other b r e a k t h r o u g h occurred about a year after injection at another well where the same three tracers appeared together, although no experimental tracer data are shown on the response curves. Data were insufficient for further analysis. The significance of breakthrough of tracer was not discussed.

240C I

_I

~g

I I I

, / ,

f:l.

._

20 C"

| I !

! I

tO (D

I t i

i

N,..-

I I

I

i il 0

30

;P

i

0-

V ,,

v

I

~1200

,.~^\ I v \j

.....

r

II, I-~

5

I

40

!

~ i: __J l_, 100

__I

101

,

I

l

2OO

300

Time since injection, days

400

o 500

I i

Figure 6.10. Tracer response Mitsue field JUDY

CREEK

MI FLOOD

This is an MI water-alternating-gas (WAG) flood performed in a limestone formation in Alberta, Canada (Jonasson, 1986). Each of sixteen solvent injectors was tagged with a tritiated hydrocarbon (normal alkanes) from C5 to C8. These were analyzed in the produced oil samples using fractional distillation combined with gas chromatography to relate the components to the tracer activities. In addition, two w a t e r injectors on the field perimeter were tagged with tritiated water. Both injection and production logs were used to identify the flowing layers in the reservoir. The injection log data were used to alter injection rates and WAG cycles to prevent w a t e r and solvent from entering different zones due to gravity segregation.

274

Chapter 6

In a later review of the results of the tracer program (Wood et al., 1990), the tracer injection and analysis programs were described in some detail. These high-molecular weight tracers were chosen intentionally to keep the tracers in the oil or solvent mixture, a choice driven by the extensive use of lift gas in the field and the likelihood of contamination by recycling produced gas tracers by means of the lift gas. Most of the traced solvent floods reported in the literature had tagged the solvent gases r a t h e r t h a n the oil bank. Tritiated toluene was added later as an additional tracer. The hydrocarbon tracers were injected by a standardized procedure. In the first step, the necessary equipment was connected at the wellhead and tested for leaks under operating conditions. A pressure intensifier pump was used to flush the tracer from a transfer cylinder using a miscible solvent under pressure. This was followed by two cell volumes of solvent, a cell volume of a water-methanol mixture, and finally by a nitrogen flush. A portable tritium air monitor was used at the injection site to monitor the air for tritium leaks. Oil samples were collected from each well at the wellhead for tracer analysis. Samples were analyzed by first distilling off 100 ml of a clear fluid at 180~ and counting it in a liquid scintillation counter. If tritium activity was present, the sample was then further fractionated by distillation and the tritium activity in the separate fractions counted. Each fraction was also analyzed by chromatography for composition. The limitation in the method was the low concentration of tritium and the poor separation efficiency for closely spaced fractions. The error was minimized using a linear regression method. Tracer results were used to confirm each pattern's contribution to tertiary oil response at specific producers. Tracer results were also used to change field operations when response did not follow expected patterns. A typical response pattern is shown in Fig. 6.11. FENN-BIG VALLEYMI FLOOD This flood consists of seven seven-spot patterns operated as a miscible injection with a WAG ratio of 1.0 (Asgarpour et al., 1987; Asgarpour et al., 1988). While no tracer design, analysis, or injection data are given, all the water injections and the gas injections were traced. The water was tagged with tritiated water and with a collection of cationic tracers: Co-60, Eu-152 and 154, Cs-134, and Cs-137. Tritiated water was the only water tracer responding after more t h a n four years of flooding. It is very unlikely t h a t there will be a measurable response from the cationic water tracers. Tritiated methane, ethane, propane, and butane were used as gas tracers, and all apparently responded, however no tracer response data are given. The only gas tracer data given are in a table of tracer velocities based upon the b r e a k t h r o u g h times at the producers. The authors made no attempt to model the gas tracer data because of complications due to solution gas dilution and phase separation; instead they matched the

Interwell Gas Tracing

275

tritiated water response using the model of Abbaszadeh and Brigham (1984) and a computer model based upon the work of Yuen et al. (1979). Based upon breakthrough times, there was a strong directional flow for the field. Insufficient tracer data were given to allow any other conclusions.

/

./

!

T-3 Toluene 4-9

.~<-----+ = > p -

.o:~

2-9

§

,o /

~,::-§ cs I

Tracers injected

C5 C6 o4 C7 C8

= = = =

T-3 T-3 T-3 T-3

N-pentane N-hexane N-heptane N octane

. . . . . . . .

Scale .

=,3-9

.

.

_

.

.

.

.

800 meters

I

I r~

x.,'~l

I

I ,~ 23'~'J l

Figure 6.11. Response pattern, Judy Creek field STEAM TRACING Steam flooding is a secondary recovery method in which steam is injected into the formation in order to mobilize oil by using heat to decrease the oil viscosity. The injected steam also acts as a drive for the mobilized oil. It is generally used for (but not restricted to) heavy, viscous oils. A number of oddly assorted materials have been used and proposed as "steam tracers" without acknowledgment t h a t steam undergoes a phase change in giving up its heat. The only true steam tracer is water: in this case, tritiated (or deuterated) water. This is not necessarily the most desirable tracer for tracing separately the velocity of either the gas (steam) phase or the condensate (water) phase. On the other hand, a watersoluble salt t h a t follows the movement of condensate is not the same as a steam tracer and does not follow the path of the steam.

276

Chapter 6

The use of tracers in steam drives seems to have caused more confusion t h a n most oilfield tracer applications. A report on the use of 1-131 tagged NaI tracers for s t e a m injection profiling claimed t h a t a methyl alcohol solution of Na1131 followed both steam and water. From the description, this p r e s u m a b l y m e a n t 1-131 tagged methyl iodide. Another report on the use of tracers for following a steam flood chose tritiated water because of its "thermal stability." A report t h a t advocated the use of dissolved salts (rather t h a n radioactive m a t e r i a l s ) for following the areal sweep of "steam" also defined tritium as a "water soluble radioactive material." There seems to be a reluctance to recognize any difference between the behavior of water as a liquid and as a vapor. Steam behavior A steam drive in an oil field is associated with the transport of two separate phases: a lighter, gaseous steam (water) phase t h a t tends to move through the top of the formation, and the denser liquid w a t e r phase m the condensate which tends to move along the bottom. Condensate is continuously formed from the cooling steam as it moves through the formation. At some point in time the steam front m a y break through to a producer forming a continuous steam zone. Once b r e a k t h r o u g h occurs, steam can move through this zone at a high rate in accordance with its low viscosity. Because of the difference in densities, condensate will move preferentially down dip, and the steam up dip, in the formation. In a two-dimensional reservoir layer, the steam originates at the wellbore and expands radially along a front that is constantly converted to w a t e r as it gives up heat. The condensate formed from the steam is composed of w a t e r condensed from the steam at the reservoir surface. Because of the density difference between steam and condensate, there is a vertical profile of increasing steam zone with height. The distribution of steam and water in the borehole is usually not uniform. M e a s u r e m e n t of its distribution in the borehole is a specialized form of injectivity logging that was separately discussed in chapter 5. GAS TRACERS FOR STEAM (VAPOR) The choice of tracer depends upon the part of the steam process under study. The inert gases, particularly Kr-85 and Xe-133, have been used for m a n y years for following the steam vapor front. Xenon-133 has a five-day half-life and emits soft g a m m a rays. Krypton-85, which undergoes beta decay, emits a g a m m a ray with only about 0.4 percent of the beta radiation. Methyl iodide and ethyl iodide tagged with iodine-131 have a long history of use as gas tracers in boreholes by service companies. Unfortunately, these materials undergo hydrolysis to the alcohol and 1-131 tagged iodide ion and are not suitable vapor phase tracers. Methyl, ethyl and the higher alcohols have also been used for steam tracing, but the problem with using them is t h a t they form azeotropes. These m a y proportion themselves differently from the way the water vapor and condensate do. Without laboratory work in determining their path, alcohols can give confusing results.

Interwell Gas Tracing

277

Very little has been reported about this early history of steam tracers in the industry. Only within the past few years have any comments been made upon tracer suitability for borehole steam (Nguyen et al., 1988; Crowe, 1990). In principle, any gas t h a t 1) does not react with steam, 2) is stable at these t e m p e r a tures, 3) does not partition into the water, 4) is not present in the steam n a t u r ally, and 5) is separately measurable can serve as a gas phase tracer. This could include such gases as SF6 and tritium or C-14 tagged methane, and perhaps CO and N20, in addition to helium, Kr-85, and Xe-133. The lower perfluorinated alkanes such as CF4, C2F6 and C3F8 are good candidates for small volume steam gas tracing even though they are not sensitive to electron capture detection. Neon and argon as nonradioactive tracers are also quite useful for tracing the relatively small steam volumes in the usual steam reservoir. WATER TRACERS FOR CONDENSATE Condensate tracers, which were described in chapter 5 on waterflood tracers, m u s t meet the same requirements as water tracers in order to survive the environment. A n u m b e r of salts have been used and proposed as steam tracers without the user's having recognized t h a t they only follow condensate. Condensate tracers respond differently from water tracers in one important respect: as long as they are under the influence of the steam zone they are subject to dilution by untagged condensate. Several inorganic anions are suitable for use as condensate tracers, including nitrate, iodide, chloride, bromide, thiocyanate, and hexacyanocobaltate ions, as well as the radioactive analogs used in w a t e r tracing. In recent years questions have been raised about the long-term stability of the hexacyanocobaltates at steam temperatures; however these tracers have been used successfully, as described below, in the Peace River steam flood. STEAM TRACER INJECTION Injection of tracers in a steam well requires access to hot lines t h a t m a y be u n d e r pressure and difficult to work with. A major difficulty in working with steam lines is finding and eliminating leaks before tracer is injected. Leaks discovered after tracer injection has started are difficult to handle on these hot lines. Gas tracers are best injected from a pressured source, or using a mechanically driven pump. Condensate tracers are injected as a w a t e r solution. Once a leak-tight connection has been made between the steam line and tracer vessel, the injection process is identical to that used with a pressurized water line.

Tracer field results TIA JUANA & JOBO STEAM DRIVES The literature reports of tracers used in steam drives give few, if any, details of tracer design, injection, or analytical procedures. Tracer tests were described in the Tia J u a n a steam drive (Van Der Knapp, 1980) and in the JOBO steam

278

Chapter 6

drive (McGee, 1986; Yibirin and McGee, 1988), both in Venezuela. In the Tia J u a n a drive, Kr-85 was added under gas drive before steam was started to see where vapor would go, Unsurprisingly, the gas traveled up dip. The carrier gas used had a high radon content that agreed in arrival time (about 2 days) with t h a t of Kr-85; thus it served as an internal tracer. Tritiated water was injected with steam in a few wells. The only reported use of the data was to note the longer b r e a k t h r o u g h time and the flow direction of condensate and oil. Three tracers, 14CH4, Kr-85, and CH3T, were used to follow the steam (vapor) front from three different steam injectors in the JOBO steam drive. High total tracer recovery (72 percent) was correlated with poor sweep efficiency and presumed due to steam channeling. Results reported in a variety of other steam floods are not significantly different from the ones mentioned above. A report of tracer use in a C a n a d i a n s t e a m flood (Miller 1989) and one from the Kern River Field in California (Billingsley et al., 1975) are typical of tracer usage in steam floods. MIDWAY SUNSET STEAM PILOT Tracers were used to follow the movement of both steam and condensate in a steam drive in the Midway-Sunset field in California (Lichtenberger, 1991). The steam drive consisted of six seven-spots in a strongly dipping reservoir. Ethyl, methyl, isopropyl, and tertiary butyl alcohols were used as steam (vapor) tracers. Nitrate, iodide, and thiocyanate ions were used as condensate (water) tracers. The alcohol vapor tracers were analyzed by gas chromatography; however there were apparently many problems associated with the analysis. No lab work seems to have been reported to justify these materials as steam tracers. A possible source of problems t h a t is not mentioned is the effect of bacteria on alcohol samples saved for later analyses. Attempts to measure the inorganic ions in solution by ion electrodes were defeated by interference due to sulfide (HS') ions in the condensate. KERN RIVER STEAM FLOOD A large-pattern steam flood in the Kern River field in California (Blevins and Billingsley, 1975) was analyzed in great detail for distribution of heat and steam. The authors reported the use of tritiated water for the steam, and of nitrate, bromide, and chloride ions as water tracers. The tracers were injected continuously at a constant concentration. The tracer data and the heat b r e a k t h r o u g h were used to account for production allocations for individual p a t t e r n s . Unfortunately, no tracer data are made available, and no explanation is given for how these results were obtained. PEACE RIVER STEAM PILOT Strictly speaking, this steam tracer study (Heisler, 1986) is not a gas tracer test. It differs from the others reported here in that it treats the movement of both steam and condensate. It is an interesting test that, unlike the other steam

Interwell Gas Tracing

279

tracer tests reported, provides all the details of the tracer design and analysis. J u d g i n g from the sampling schedule reported, many hundreds of samples were analyzed for tracer, over a significant part of the test life. The Peace River in-situ project is a complex steam pilot to recover bitumen from the Bullhead sand in northern Alberta. The sand is underlain by a permeable water zone that provides fluid communication, and thus heat, between wells. The producers were all steam soaked in several cycles before starting the steam drive. The thermal process involved alternating between periods of high injection rates with low production and periods of high production with low injection rates. The tracers were injected into the pilot about 80 days after hot water injection had begun and four days before the start of a new cycle of steam injection into the wells. The pilot consisted of seven seven-spots, as shown in Fig. 6.12.

Design The tracer test was designed to minimize the amount of bench work required for sample analysis. The three condensate tracers t h a t were chosen emitted g a m m a radiation of different energies and could all be extracted by passing a liter of sample through a small anion-exchange column. These were the 5.6-yr half-life Co-60, the 270-day half-life Co-57, and the 60-day half-life 1-125. The anion-exchange columns containing all three tracers were counted in an automatic g a m m a counter, and all three tracers were analyzed simultaneously using energy discrimination. The tracer quantities required for the test were estimated using a dilution volume calculated from the water-filled pore volume for the expected reservoir path at ten times the m i n i m u m detection limit. In order to extend the useful tracer life for one-liter samples to about eighteen months, tracer quantities were increased to compensate for the decay of the 60-day halflife of the 1-125 and of the 270-day Co-57. Each pattern received 5 Ci of tritiated water plus one of the three tracers (60Co(CN)6 -3, 57Co(CN)6 -3, or 1251 as the iodide ion), as shown in Fig. 6.12. The quantities of tracer injected into each well were as follows: 25 mCi of 57Co injected into wells 13, 15, and 17; 500 mCi of 131I injected into wells 12, 14, and 16; and 30 mCi of 60Co injected into the central injector, well 11. The tracers were brought to the well sites in transfer cylinders suitable for injection. They were connected to the hot water injection line using a side arm and injected by pressurized hot water controlled by a set of valves. An extensive sampling program began with daily samples for the first two weeks and then tapered off to thrice weekly for a month, twice weekly for another month, and, finally, once weekly. Samples were collected at the production lines, and coolers were used to prevent flashing. Sample analysis for these tracers consisted of passing the collected sample through a small anion-exchange column and transferring the column to an automatic g a m m a counter. Each sample was automatically counted using a NaI well crystal. The count rate in each of three energy regions of interest was recorded

280

Chapter 6

and converted to activities using counting standards of known activity for each tracer. Corrections were made for overlapping counts from tracers in other energy channels and for background. Automatic half-life corrections were made on all samples. The tritiated water was counted directly in a liquid scintillation counter.

20

12 1-125

27 70

17

0 I

30

27

"[

13

_

Co-57

11

Co-60

Co-57

16

1-125 6"0

1

I

Scale

200m I

9Injector 0 Producer

34

_

e14

,40

1-125

15

Co-57 50

Figure 6.12. Tracer pattern, Peace River steam pilot Tracer result

About 50 percent of the tritiated water and 30 percent of each of the g a m m a emitters were produced within the first 160 days after injection. Breakthrough of injected tracers occurred very early in this small pilot. Tracer response curves from three of the producers are shown in the paper. Two of the curves, from wells 34 and 145, are reproduced here in Fig. 6.13. In each of these figures, the tracer concentration in Bq/ml is plotted on semilog paper as a function of time (days) since injection. All of the response curves showed an exponential decline with time, with a very similar slope for the tracers injected in pairs. This is indicated for well 34 by the line drawn through the response curves for both the tritium and the iodide tracers. The exponential decline seen here is expected from tracer response curves, as discussed in chapter 4. The data in these figures exhibited this decline throughout almost five decades of concentration.

Interwell Gas Tracing

281

In Fig. 6.13, the response for well 34 shows only tritiated w a t e r and 1-131 from well 14. There is no Co-57, and hence no water from the neighboring injector, well 13. The data from well 145 shows response from all three surrounding injectors; however the four tracers are produced in different proportions, indicating anisotropic flow. The Co-60 is recorded from only two separated samples. The flow does not appear to be radially distributed, even for the inner patterns.

Well 34

102

_

t,.
E

~

Well 145

10a~

o L_

c::: 1.0, ro 0 0

0.1

-5

15

35

75

Time since injection, days

-5

15

35

75

Time since injection, days

Figure 6.13. Tracer response from two wells The author also compared the tracer response of the condensate tracers with t h a t of tritiated water from the tracer pairs at three wells. The daily sample concentrations show the usual individual character. To smooth the data, the author plotted instead the ratios of cumulative produced tritium concentration to t h a t of cumulative produced condensate tracer. These ratios were normalized by the ratio of injected activities. If more t h a n one tracer pair responded at a well, all gamma-emitting tracers produced were taken to represent condensate.

Analyses of results A considerable amount tracer data was apparently recovered from this test, but most of it is not available from the paper. Answers to questions about flow rates, volume calculations, sample handling, etc., are not in the paper but are presumably available from the collected data. The author recognized t h a t two tracers injected in the same well should be correlated, in the same producer, by time of arrival and by the fraction of injected activity produced; however the procedures he used do not seem w a r r a n t e d by the data. He proposes, without proof, that the ratio, C1:C2, of the produced tritiated w a t e r tracer to t h a t of the condensate tracer should be the same as the ratio of

282

Chapter 6

the two injected activities if normalized for the ratio at which they were injected. He found, as shown in Fig. 6.14, t h a t the ratio of the activities became relatively constant shortly after the individual activities peaked, but at ratios of about 1.7 instead of 1.0 as he had expected. The constant ratio simply verifies the visual observation t h a t both tracer concentrations are decreasing at the same rate. As discussed in chapter 4, the ratio of total activity produced from two coinjected tracers, m l :m2, should be proportional to the ratio of amounts injected, M2" M1, if they behave in the same manner: m 1 ~C 1 AV1 Q1]~C1At M2 m2 = ]~C2AV2 = Q2ZC2At = M1

(6.15)

where Qi is the production rate of tracer, i, as function of time, and Ci is its concentration, summed over the entire production interval. There is, however, no obvious relationship between the ratio C1:C2 of produced activity at any given time and t h a t of the two coinjected tracers, although such a correlation may still be valid. Since the collected data show t h a t the decline of the tracer response curve is exponential for at least five cycles, these curves could be extrapolated with a good deal of confidence. This should allow a very good estimate of the total a m o u n t of each injected t r a c e r produced at the responding well, using the procedures described in chapter 4. The a u t h o r also attempts to calculate the size of the "steam chest" between wells by relating the accumulated tracer produced at breakthrough time (BT) to the ratio of the amounts of tracers injected. Accumulated tracer produced at BT is essentially zero. Tracer response at breakthrough is a steeply rising curve. The ratio of responses from two such rapidly changing curves is a virtually meaningless number. In wells producing a mixture of gas, steam, hot water, and oil, the w a t e r production rate is usually quite erratic, so that the time scale is not an accurate reflection of the volumes produced. A better correlation of arrival times is the m e a n residence time of the tracers, which could be calculated from the data by the procedures given in chapter 4. If both tracers share the same m e a n residence time (or mean volume swept), it is likely t h a t they follow the same path. SAMPLE COLLECTIONAND ANALYSIS Gas tracers are used to follow steam (vapor) movement in the reservoir. Samples are usually collected or monitored at each well site. Gas should first be separated from the condensate and other liquids by means of a small separator, a procedure frequently performed to determine the source of'steam b r e a k t h r o u g h at a field well. The produced steam can be monitored continuously for gas tracers at the well, or samples may be collected for analysis. This is usually done for chemical tracers by a gas chromatographic method or by g a m m a counting for radioactive tracers. Several procedures are available for doing this.

Interwell Gas Tracing

IE3 E

283

Well 35

E2

Well 145 ,i

f - ,,,

0

1

0

-5

45

95 Time, days

145

O,

-5

i

95 Time, days

Figure 6.14. Ratios of tracer response for wells 35 and 145 If a g a m m a - e m i t t i n g tracer is used for gas tracing, a simple m e t h o d for monitoring the t r a c e r response at the wellhead is to pass a s i d e s t r e a m of the produced s t e a m (gas) t h r o u g h a c o n t a i n e r t h a t acts as a Marinelli beaker, in which a s u i t a b l e g a m m a detector is suspended. This can be a n y t h i n g from a 55-gallon d r u m to a 5-gallon pail. A heat-protected scintillation detector is excellent for use w i t h e i t h e r Kr-85 or Xe-133. If the s t e a m is g e n e r a t i n g too m u c h h e a t for use w i t h a crystal counter, passing the s t e a m t h r o u g h a water- or air-cooled copper coil will reduce the t e m p e r a t u r e sufficiently. This method is p a r t i c u l a r l y useful for detecting the source of s t e a m b r e a k t h r o u g h at a well. The use of a d r u m for collecting tracer in the neighborhood of a detector allows easy detection, while activity levels r e m a i n low enough t h a t there is no h a z a r d to personnel. N e i t h e r of t h e s e two t r a c e r s is r e t a i n e d by the body. The short (5-day) half-life of Xe-133 m a k e s it more desirable for this purpose. On-line m e t h o d s for continuous t r a c e r analysis are not r e s t r i c t e d to radioactive tracers. Helium can be monitored on line by m e a n s of a H e - t u n e d leak detector (Ahner, 1979). SF6 can be monitored continuously by an electron-capture detector, and tracers such as CO can be followed by infrared absorption. All these t e c h n i q u e s require the removal of w a t e r vapor from the s e p a r a t e d gas by such d e h y d r a t i n g agents as molecular sieves, by use of m e m b r a n e s permeable to w a t e r vapor, or by a suitable cold trap. W a t e r (condensate) s a m p l e s collected from a s e p a r a t o r probably r e p r e s e n t m o s t l y produced steam. A wellhead s e p a r a t o r for hot w a t e r collection is easily constructed of a piece of pipe or tubing and a cooling coil. At these t e m p e r a t u r e s , the w a t e r usually s e p a r a t e s quickly from oil and a sample is easily obtained. As in the case of steam, w a t e r tracers can be collected for l a t e r analysis or m a y be

284

Chapter 6

analyzed on site by means of a suitable counter a r r a n g e m e n t or by some specific analytical method.

GAS T R A C I N G IN U N C O N V E N T I O N A L R E S E R V O I R S The oil industry has participated in a number of variants from conventional oilfield practice, and tracers have played an important role in some of these. This has been particularly true in geothermal production, underground coal conversion, in-situ oil shale conversion, and m e t h a n e production from u n d e r g r o u n d coal. Some of the methods and procedures developed here are also applicable to conventional oilfield practice and are of interest in their own right. A study of the use of tracers in tests of underground coal gasification and oil shale retorting (Lyczkowski et al., 1976) discusses various mathematical models for flow t h r o u g h a distribution of fractures. These models were used for discussion of tracer tests in oil-shale laboratory experiments using Kr-85 (Lorenze 1973), and in an underground rubblized shale oil retort using helium (Loucks, 1977). An experimental tracer system to monitor flow in underground coal gasification was described and the tracer response data were analyzed. In this experiment, helium was injected as a tracer pulse during each of a series of forward and reverse burns. The helium response was analyzed on line by means of a mass spectrometer (not described). Tracer response data were used to calculate void volumes and the Peclet numbers for several "burns" and were related to the amount of coal consumed. In an underground coal gasification (UCG) environment, helium was used in conjunction with a portable "leak detector" as a tracer for following gas flow (Ahner, 1979). The leak detector is a commercially available mass spectrometer tuned to He-4. It serves as a stable, continuous, on-line tracer detection system with a dynamic range in excess of six decades. Although it is used in the oil ind u s t r y for this purpose, it is r a r e l y described in the l i t e r a t u r e . In this i n s t r u m e n t , a tunable leak is used to control the sampling rate into the highvacuum spectrometer. Since the leak rate m u s t be small to m a i n t a i n the high vacuum, a low-volume "probe" is required to provide quick response. It is also necessary to remove any w a t e r or hydrocarbon from the stream. This is a very useful system for small reservoir volumes as are found in m a n y steam drives and geothermal reservoirs. In large reservoirs, the high n a t u r a l concentration of helium in the ground would require too large a helium tracer pulse to overcome the natural background. The equipment described above was used to characterize the flow paths in different phases of UCG by monitoring the tracer response from a pulse tracer (He) injection. The tracer-response curves were used to determine the m e a n residence times for each experimental phase and, from this, to estimate the active void volume. The presence of multiple peaks or humps was taken to be an

Interwell Gas Tracing

285

indicator of multiple paths. Changes in m e a n residence time as the experiments went on were associated with changes in the fracture paths. Krypton-85 was used as a tracer to follow the flow of air into a subbituminous coal seam in the San J u a n basin in New Mexico (Nuttal et al., 1980). The purpose of the test was to characterize the flow u n d e r p r e b u r n conditions. A simulation using pressure-dependent permeability was found to fit the system, giving a qualitative fit for the produced tracer data. This work was p a r t of a study of UCG t h a t is still continuing (Klett et al., 1978; Williams et al., 1980). A t t e m p t s to produce tight gas-bearing sands and oil shales yielded some interesting tracer studies following the use of underground nuclear explosions for this purpose. Some of these tracer studies have a potential for use in the more conventional oilfield applications. Considerable effort was expended in the use of tracers to determine flow patterns in explosively fractured oil-shale rubble beds (Turner et al., 1978). Several continuous instrumental methods were devised for monitoring helium, SF6, or Kr-85 as gas tracers. The He-4 tuned "leak detector" was used for helium, an electron capture (EC) detector for SF6 detection, and a gas counter for detecting Kr-85. A portable tracer gas analyzer was devised using mass spectrometry as a detector for nonradioactive gas tracers. The tracers used were SF6, Kr, Ne, He, and four freons (F12, 13, 14, and 22; Uhl 1982). The unit has a 20-channel sample port (multiplexed) and was used to analyze flow though a rubble bed using m a n y tracers. Some of this is applicable to other gas experiments in oil fields.

REFERENCES Abbaszadeh-Dehghani, M., and Brigham, W.E., "Analysis of Well-to-Well Tracer Flow to Determine Reservoir Layering," J P T (Oct. 1984) 1753-1762. Ahner, P.F., and Genser, R.W., "Helium Tracer Studies to Characterize Underground Flow Paths," Proc., 5th U.S. DOE Underground Coal Conversion Syrup., J u n e 18-21, 1979, 199-211. A]ei, M., et al., "Determination of Deuterated Methanes for Use as Atmospheric Tracers," Los Alamos Natl. Lab. Rept. LA-10909-MS (1987). Armstrong, F.E., Fletcher, G.E., and Howell, W.D., "Radioactive Tracers in Miscible Phase Petroleum Production Operations," TID-21 199 (1963). Armstrong, F.E., "Field Use of Radioactive Gas Tracers," Petrol. Engineer 32 (13) (1960) B34-B36.

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Armstrong, F.E., Howell, W.D., and Watkins, J.W., "Radioactive Inert Gases as Tracers for Petroleum Reservoir Studies," Bureau of Mines Rept. BM-RI 5733 (1960). Arnold, F.C., "Incorporation of Wellbore Steam Segregation in Steam Stimulation," paper CIM/SPE-90-87 presented at the Joint SPE/CIM Mtg., Calgary, Alberta, Can., June 10-13, 1990 (preprints 2, 1990). Asgarpour, S., and Todd, M.R., "Evaluation of Volumetric Conformance for FennBig Valley Horizontal Hydrocarbon Miscible Flood," EOR ! General Petroleum Engineering, Proc. 63rd Ann. SPE Tech. Conf., Houston, Oct. 2-5, 1988 (1988) 231-244 (SPE 18079). Asgarpour, S., Crawley, A.L., and Springer, S.J., "Performance Evaluation and Reservoir Management of a Tertiary Miscible Flood in the Fenn-Big Valley South Lake D-2A Pool," paper 87-38-07 presented at 37th Ann. CIM Petrol. Soc. Tech. Mtg., Calgary, Alberta, Can., June 7-10, 1987. Bennett, R., Schettler, P.D., and Gustafson, T.D., "Measuring Low Flows in Devonian Shale Gas Wells with a Tracer Gas Flowmeter," Energy for the Future: Proc. Eastern Regional SPE Conf., Charleston, WV, Nov. 1-4, 1988 (1988) 369372 (paper SPE 18556); SPE Formation Evaluation (June 1991) 2{}9. Billingsley, R.H., and Blevins, T.R., "The Ten Pattern Steam Flood," preprint SPE 4756 presented at 45th Ann. SPE of AIME Calif. Regional Mtg., April 2-4, 1975. Blevins, T.R., and Billingsley, R.H., "The Ten-Pattern Steamflood, Kern River Field, California," J P T (Dec. 1975) 1505. Brigham, W.E., and Smith, D.H., "Prediction of Tracer Behavior in Five-Spot Flow," paper SPE 1145 presented at SPE Conf. on Production Research, May 3 4, 1965. Brigham, W.E., and Abbaszadeh-Dehghani, M., "Tracer Testing for Reservoir Characterization," J P T (May 1987) 519-527. Burwell, E.L., and Howell, W.D., "Krypton-85 Tracer Aids Evaluation of Underground Combustion Oil Recovery Tests," Prod. Mon. (Jan. 1965) 29, No. 1, 21-23. Calhoun, T.G., and Tittle, R.M., "Use of Radioactive Isotopes in Gas Injection," preprint. SPE 2277, 43rd Ann. SPE of AIME Fall Mtg., Sept. 1968. Calhoun, T.G., and Hurford, G.T., "Case History of Radioactive Tracers and Techniques in Fairway Field," preprint SPE 2853 presented at the SPE of AIME Mtg. on Practical Aspects of Improved Recovery, Ft. Worth, TX, Mar. 6-10, 1970.

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287

Collins, G.F., Bartlett, F.E., Turk, A., Edmonds, S.M., and Mark, H.L., "A Preliminary Evaluation of Gas Air Tracers," J. Air Poll. Contr. Assoc. (1965) 15, No. 3, 109. Cornier, J.J., Godouin, M., and Thibierge, P., "Study of an Oil Field (Hassi Messaoud) by Injection of Tritiated Methane, Ethane, Propane, and Butane," Proc. IAEA Symp. Radioisotope Tracers in Ind. and Geophys., Nov. 21-25, 1966, 161-175, (1967). Cooke, R.W., "Areal Sweep Efficiency Determination in Steam-Drive Projects Utilizing Chemical Tracers," preprint SPE 11805 presented at the SPE of AIME Intl. Oilfield & Geotherm. Chem. Symp., Denver, CO, June 1-3, 1983, 281-288. Cooke, T.L., Brown, L.F., and Meadows, W.R., "Tracer Experiments in Eastern Devonian Shale," paper SPE 10797 presented at the SPE/DOE Unconventional Gas Recovery Conf., Pittsburgh, PA, May 16-18, 1982. Cowan, G.A., Ott, D.G., Turkevich, A., Machta, L., Ferber, G.J., and Daly, N.R., "Heavy Methanes as Atmospheric Tracers," Los Alamos Rept. LA-UR-75-88 (1988). Craig, F.F. III, "Field Use of Halogen Compounds to Trace Injected CO2," preprint SPE 14309 presented at the 60th Ann. SPE of AIME Tech. Conf., Las Vegas, NV, Sept. 22-25, 1985. Crowe, T.L.A., "Radioactive Steam Tracer Comparison between Krypton-85, Xenon-133, NaI-131 (Methyl Alcohol Base), and NaI-131 (Water Base)," Proc., 60th Ann. SPE Calif. Regional Mtg., Ventura, CA, April 4-6, 1990, 205-214. Davis, J.A., Blair, R.K., and Wagner, O.R., "Monitoring and Control Program for a Large Scale Miscible Flood," preprint SPE 6097 presented at 51st Ann. SPE of AIME Fall Mtg., Las Vegas, NV, Oct. 3-6, 1976. Dietz, R.N., and Cote, E.A., "Tracing Air Pollutants by Gas Chromatographic Determination of Sulfur Hexafluoride," Envir. Sci. Tech. (1973) 7, No. 4, 338. Dietz, R.N., and Dabberdt, W.F., "Gaseous Tracer Technology and Applications," BNL33585, Brookhaven National Laboratories (July 1983). Dugstad, D., Bjornstad, T., and Hundere, I., "Measurements and Applications of Partition Coefficients of Compounds Suitable for Tracing Gas Injected into Oil Reservoirs," Revue de l'institut fran~ais du pdtrole (Mar.-April 1992) 47, No. 2. Frey, R.P., "Operating Practices in the North Cross CO2 Flood," Proc., 22nd Ann. Southwest. Petrol. Short Course Assoc. Mtg., 165-168 (1975). Frost, E.M., "Helium Tracer Studies in the Elk Hills, California, Field," Bureau of Mines Rept. BM-RI 3897 (1946).

288

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Godouin, M., Comier, J.J., and Thibierge, P., "Study of an Oil Field (Hassi Messaoud) by Injection of Tritiated Methane, Ethane, Propane, and Butane," Proc. IAEA Symp. Radioisotope Tracers in Ind. and Geophys., 161-167, IAEA, Vienna (1967). Halverson, J.E., Pendergast, M.M., and Boni, A.L., "The Use of Helium-3 as a Gas Tracer for Mesozoic Meteorological Studies," Rept. DP-MS-79-51 presented at Atmospheric Tracer Workshop, Los Alamos, NM, May 23-24, 1979, 2-7. Heisler, R.P., "Interpretation of Radioactive Tracer Results in a Steamdrive Project," preprint SPE 15092 presented at the 56th Ann. SPE of AIME Calif. Regional Mtg., Oakland, CA, April 2-4, 1986. Hoiland, R.C., Joyner, H.D., and Stalder, J.L., "Case History of a Successful Rocky Mountain Pilot CO2 Flood," Proc., 5th SPE/DOE Enhanced Oil Recovery Symp., Tulsa, OK, April 20-23, 1986, 2,199-208 (paper SPE/DOE 14939). Howell, W.D., Armstrong, F.E., and Watkins, J.W., "Radioactive Gas Tracer Survey Aids in Waterflood Planning," World Oil (1961) 152, No. 2, 41. Jonasson, H.P., "Reservoir Surveillance Program: Judy Creek Beaverhill Lake "A" Pool Hydrocarbon Miscible Flood," paper 86-37-34 presented at 37th Ann. CIM Petrol. Soc. Tech. Mtg., Calgary, Alberta, Can., June 8-11, 1986 (preprint 1, 467-479). Klett, R.D., Tyner, C.E., and Hertel, E.S., "Geologic Flow Characterization Using Tracer Techniques," Sandia Nail. Labs. Rept. SAND80-0454 (1980). Kuehne, D.L., Ehman, D.I., and Emanuel, C.F., "Design and Evaluation of a Nitrogen-Foam Test," preprint SPE 17381 presented at SPE/DOE Enhanced Oil Recovery Symp., Tulsa, OK, April 17-20, 1988. Lake, L.W., Enhanced Oil Recovery, Prentice-Hall, Englewood Cliffs, NJ (1989). Langston, E.P., and Shirer, J.A., "Performance of Jay/LEC Fields Unit Under Mature Waterflood and Early Tertiary Operations," presented at the 58th Ann. SPE of AIME Tech. Conf., San Francisco, CA, Oct. 5-8, 1983. Lichtenberger, G.J., "Field Applications of Interwell Tracers for Reservoir Characterization of Enhanced Oil Recovery," paper SPE 21652 presented at Production Operation Symp., Oklahoma City, OK, April 7-9, 1991. Lorenze, P.B., "Radioactive Tracer Pulse Method of Evaluating Fracturing of Underground Oil Shale Formations," U.S. Bureau of Mines Rept. 7791 (1973). Loucks, R.A., "Occidental Vertical Modified In-Situ Process for the Recovery of Oil from Shale," U.S. DOE Rept. TID-28053 (Nov. 1977).

Interwell Gas Tracing

289

Lyczkowski, R.W., Thorsness, C.B., and Cena, R.J., "Use of Tracers in Laboratory and Field Tests of Underground Coal Gasification and Oil Shale Retorting," Calif. Univ., Livermore, Rept. UCRL 81252 (June 16, 1976). Martin, A.J.P., and Synge, R.L.M., "A New Form of Chromatography Employing Two Liquid Phases," Biochem. J. (1941) 35, 1358. Mazzocchi, E., Nagel, R.G., Hunter, B.E., Peggs, J.K., and Fong, D.K., "Tertiary Application of a Hydrocarbon Miscible Flood: Rainbow Keg River 'B' Pool," Proc., 6th SPE/DOE Enhanced Oil Recovery Symp., Tulsa, OK, April 17-20, 1988, 355379 (paper SPE/DOE 17355). McGee, J.H., "The Jobo Steamflood Project: Evaluation of Results," preprint SPE 15649 presented at the 61st Ann. SPE Tech. Conf., New Orleans, LA, Oct. 5-8, 1986. Mcintyre, F.J., Polkowski., G., and Bron, J., "Radioactive Tracer Application to Monitoring Solvent Spreading in the Rainbow Keg River B Pool Vertical Hydrocarbon Miscible Flood," preprint SPE 14440 presented at the 60th Ann. SPE of AIME Tech. Conf., Las Vegas, NV, Sept. 22-25, 1985. Miller, K.A., Stevens, L.G., and Watt, B.J., "Successful Conversion of the Pikes Peak Viscous Oil Cyclic Steam Project to Steamdrive," Proc., 59th Ann. SPE Calif. Regional Mtg., Bakersfield, CA, April 5-7, 1989 (preprint SPE 18774, 285303). Nguyen, T.V., and Stevens, C.E., "The Use of Inert Gas Radioactive Tracers for Steam Injection Profiling," preprint SPE 17419 presented at the SPE Calif. Regional Mtg., Long Beach, CA, March 23-25, 1988. Nuttal, N.E., and Travis, B.J., "Modeling and Interpretation of Two-Phase Flow and Tracer Studies from a Subbituminous Coal Seam in the San Juan Basin of New Mexico," Proc., 6th DOE Underground Coal Conversion Symp., July 13-17, 1980 (Ii-40-Ii-48). Omoregie, Z.S,, Jackson, G.R., Martinson, L.A., and Vasicek, S.L., "Monitoring the Mitsue Hydrocarbon Miscible Flood: Program Design, Implementation, and Preliminary Results," paper 87-38-06 presented at 38th Ann. CIM Petrol. Soc. Tech. Mtg., Calgary, Alberta, Can., June 7-10, 1987 (preprints 1, 97-121). Pittaway, K.R., Albright, J.C., and Hoover, J.W., "The Maljamar Carbon Dioxide Pilot: Review and Results," Proc., SPE Permian Basin Oil & Gas Recovery Conf., Midland, TX, March 13-14, 1986 (SPE/DOE 14940, 137-143). Rebgetz, M.D., Watt, J.S., and Zastawny, H.W., "Determination of the Volume Fraction of Oil, Water, and Gas by Dual Energy Gamma-Ray Transmission," Nucl. Geophys. (1991) 5, No. 4, 479.

290

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Rupp, K.A., Styler, J.W., Nelson, W.C., Christian, L.D., and Zimmerman, K.A., "Design and Implementation of a Miscible Water-Alternating-Gas Flood at Prudhoe Bay," preprint SPE 3272 presented at the 59th Ann. SPE of AIME Tech. Conf., Houston, TX, Sept. 16-19, 1984, 1. Satterly, J., and McLennan, J.C., "The Radioactivity of Natural Gases of Can.," Trans. Royal Soc. Can. (1918) 12, 153. Senum, G.I., Fajer, R.W, Harris, B.R. Jr., DeRose, W.E., and Ottaviani, W.L., "Petroleum Characterization by Perfluorocarbon Tracers," paper BNL 46883 presented at 8th SPE/DOE Enhanced Oil Recovery Symp., Tulsa, OK, April 2124, 1992. Stalkup, F.I., Miscible Flooding Fundamentals, SPE Monograph Series (1983). Tang, J.S., and Harker, B.C., "Interwell Tracer Test to Determine Residual Oil Saturation in a Gas-Saturated Reservoir. Pt. 1: Theory and Design and Pt. 2: Field Application," paper CIM/SPE 90-130 presented at CIM Petrol. Soc./SPE Intl. Tech. Mtg., Calgary, Alberta, Can., June 10-13, 1990. Tang, J. S., "Interwell Tracer Tests to Determine Residual Oil Saturation to Waterflood at Judy Creek BHL 'A' Pool," paper SPE 20543 presented at Tech. Conf. of Petrol. Soc. of CIM and AOSTRA, Banff, Alberta, Can., April 21-24, 1991. Tinker, G.E., "Gas Injection with Radioactive Tracer to Determine Reservoir Continuity, East Coalinga Field, California," preprint SPE 4184 presented at the 43rd Ann. SPE of AIME Calif. Regional Mtg., 1972. Turner, T.F., and Moore, D.F., "Final Report on the Use of Gaseous Tracers in the Western Research Institute 10-Ton Nonuniform Oil Shale Retort Tests," DOE/FE/60177-1979 (Dec. 1985). Uhl, J.E., "Multiple Tracer Gas Analyzer," paper SAND-82-0214C presented at Symp. Argonne Natl. Lab. Instrum. and Contr. for Fossil Energy, Houston, TX, June 7-9, 1982. Van Der Knapp, W., "M-6 Steam Drive Project. Preliminary Results of a Large Scale Field Test," preprint SPE 9452 presented at the 55th Ann. SPE of AIME Fall Tech. Conf., Dallas, TX, Sept. 21-24, 1980. Wagner, O.R., Baker, L.E., and Scott, G.R., "The Design and Implementation of a Multiple Tracer Program for Multifluid, Multiwell Injection Projects," preprint SPE 5125 presented at the 49th Ann. SPE Fall Mtg., 1974. Wallick, G.C., and Jenkins, R., "Analysis of Short Time Tracer Injection in Underground Formations," J. Appl. Phys. (Dec. 1953) 25, No. 12.

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291

Welge, H.E., "Super Sleuths Trace Flow of Injected Gas," Oil & Gas J. (Aug. 29, 1955) 77-79. Williams, F.L., Nuttall, H.E., Tyner, C.E., and Jacobson, R.D., "Tracer and Air Acceptance Characterization of a San Juan Basin Coal," Proc., 6th DOE Underground Coal Conversion Symp., July 13-17, 1980 (Ii-34-Ii-37). Wood, K.N., Cornish, R.G., Lal, F.S., Taylor, H.G., and Woodford, R.B., "Solvent Tracers and the Judy Creek Hydrocarbon Miscible Flood," paper CIM/SPE 90-79 presented at CIM Petrol Soc./SPE Intl. Tech. Mtg., Calgary, Alberta, Can., June, 10-13, 1990 (preprints 2). Yibirin, J.G., and McGee, J.H., "The JOBO Steamflood Project: A Preliminary Evaluation of Results," preprint SPE 17388 presented at the SPE/DOE Enhanced Oil Recovery Symp., Tulsa, OK, April 17-20, 1988. Yuen, D.L., Brigham, W.E., and Cinco-Ley, H., "Analysis of Five-Spot Tracer Tests to Determine Reservoir Layering," U.S. DOE Rept. SAN 1265-8, Washington, DC (Feb. 1979).

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CHAPTER 7

DOWNHOLE TRACERS

INTRODUCTION Downhole tracers are used to investigate the region in and around the oil well, the link connecting the oil-bearing reservoir with the surface facilities. It is the only path of communication with the reservoir; the conduit for production of oil, gas, and water from the reservoir; and for secondary and tertiary injections into the reservoir. Because of its importance, a large number of tracer procedures have been developed to study the integrity of the wellbore, how fluids enter and leave it, and conditions affecting well operation down hole. This section is concerned with the use of tracers for following wellbore operations and for investigations in the neighborhood of the borehole. T r a c e r d e t e c t i o n in t h e b o r e h o l e

The borehole of an oil well is a difficult environment to work in. Temperatures, pressures, and flow forces can be high, and space is very limited. The small diameter and relatively great depth of the wellbore limit the size of the equipment and the kinds of operations that can be carried out. Virtually all monitoring operations in the wellbore are carried out by special tools that are moved up and down the wellbore on a wireline. Most such operations are contracted by independent logging companies t h a t provide both wireline and tools. These companies usually perform the logging operation and, depending upon the type of operation, often provide an interpretation of the logging results. This is not a requirement, and simple gamma-detection wireline tools are often operated by oil c o m p a n y personnel. While there are m a n y kinds of logging operations, the nuclear logs are the principal ones of interest in tracer studies. These allow the use and detection of g a m m a - e m i t t i n g radioactive tracers for following the movement of fluids and solids in the neighborhood of the borehole. Very few other detection methods have been used for following downhole tracers. Magnetic resonance logs have been used with responding ions as tracers in log-inject-log studies. In principle, electrochemical detectors can also be used to follow water tracers in this environment; but in practice very little has been done with them. These detectors require direct contact with the tracer in aqueous solution and, usually, a relatively "clean" environment. Electrochemical detectors have been used for gas tracers, and for monitoring the hydrogen ion concentration in water down hole. Three kinds of tracer operations involving radioactivity are used to tag gases, liquids, or solids moving in or about the wellbore:

294

Chapter 7

1. In the conventional procedure, radioactively tagged material is injected into the well and a radiation monitor on a wireline used to follow its movement or location down hole for well treatments and production logging. 2. In a second method, a nonradioactive tracer is activated down hole by neutron radiation, forming a new gamma-emitting tracer, monitored by a downhole detector. This may be a n a t u r a l l y occurring material, such as the fast neutron activation of oxygen in water used to trace leaks behind casing, or an added material, activated for this purpose as in the fast neutron activation of barium. 3. In the third method, capture gamma radiation, induced by neutron irradiation of a nonradioactive material, is related to the macroscopic thermal neutron cross section, and hence to a measure of the amount of absorbing material present. This is illustrated by the log-inject-log tracer procedure for residual water. Currently, only radioactive tracers that emit penetrating (gamma) radiation are used for downhole measurement; however it is also possible to use beta emitting tracers for gas tracing down hole. An ion chamber can be used as a beta detector, so long as the gas that enters the chamber is free of condensed liquid phases such as water or oil. Ion chambers can be designed to operate under borehole temperatures and pressures, and most produced gas can be used as the counter gas. The principal detector used for monitoring gamma radiation down hole is the sodium iodide scintillation detector. Described in chapter 2, this detector has high sensitivity for gamma radiation and can operate under borehole conditions (although temperature and pressure protection are usually required); however, it suffers from relatively poor energy resolution. The detector of choice for resolving g a m m a spectra is the intrinsic germanium detector, used for virtually all laboratory spectral analysis. Unfortunately it requires liquid-nitrogen cooling to operate, is much more expensive, and is considerably less sensitive t h a n the NaI detector. As a result, with some exceptions, it is not used for oilfield logging. It should, however, make a significant improvement in spectral deconvolution if the cost of operations could be reduced. The Geiger-Mueller or GM tube has largely been replaced by the scintillation detector but is still in use in wells where high temperatures and other conditions make the use of scintillation detectors chancy. The principal downhole neutron detector is the He-3 filled proportional counter. There is an odd division in the oil industry whereby tracers monitored in the wellbore are categorized as logging procedures, whereas those monitored at the surface are regarded as tracer procedures. We will ignore this distinction here. The use of logging procedures for characterizing fluids and formation properties has been well described in the logging literature and we do not feel it needs further exposition in these pages; however, logging procedures that involve the traditional use of tracers as described above will be discussed.

Downhole Tracers

295

FAST NEUTRON ACTIVATION OF TRACERS For most materials, fast neutrons are the most penetrating kind of radiation generated down hole. They are particularly useful for dealing with problems outside of the wellbore in cased and cemented wells. The most useful source of fast neutrons in the wellbore is the downhole accelerator, in which deuterons are accelerated against a tritium target to undergo the d(T,n)a reaction described in chapter 1. The reaction can take place at relatively low accelerating voltage and yields mostly 14 MeV neutrons. Most fast neutrons lose energy by elastic collisions. A small n u m b e r of them enter into inelastic collisions with target nuclei, characterized by a minimum energy threshold t h a t must be exceeded for the reaction to take place. The cross section for the reaction is usually quite small, in the millibarn region. Exceptions include the 138Ba(n,2n)137Ba reaction, which has a cross section of 1 barn. One of the more widely used fast-neutron reactions downhole is t h a t with oxygen, used for detecting water behind casing.

Leaks behind casing Wells are cased and cemented to the formation in order to contain the movem e n t of fluids between the formation and the surface within the wellbore. Paths of communication outside the casing can cause serious difficulties by allowing flow between formations at different pressures. This can lead to contamination of shallow potable aquifers by oil and brine from deeper layers, and to undesirable flow between oil- and water-bearing formations. Channeling of w a t e r within the cement annulus provides the principal paths for such movement. Such external paths are difficult to detect. Radioactive tracer logs, as well as noise and temp e r a t u r e logs, have been used for this purpose, although some of these methods require access to the channel from the wellbore. Logging by fast neutron activation can detect channels t h a t leak between sands in unperforated parts of the reservoir without accessing the wellbore.

Oxygen activation log The oxygen activation log is based ( W h i c h m a n et al., 1967) upon the activation of oxygen in w a t e r by high-energy (14 MeV) neutrons. The threshold energy for reaction is 10 MeV. When water is irradiated by these neutrons, some of its oxygen is converted to 16N by the 160(n,p)16N reaction. The reaction cross section is 40 millibarns. The nitrogen-16 produced by the r e a c t i o n t h e n undergoes beta decay with a half-life of 7.1 sec, with 69 percent of the beta decay path accompanied by a 6.13-MeV gamma ray.

16N --)~+ 160 + T (6.13 MeV)

296

Chapter 7

The high-energy gamma ray easily penetrates the casing, cement, tubing, and fluids in the well and is measured by the detector in the borehole. This is a relatively inefficient procedure, because of the poor (NaI) detector efficiency for this high g a m m a energy and poor source geometry from the narrow cement channels. As a result, counting statistics will be poor. A logging tool suitable for this kind of operation, together with a generalized schematic of the neutron generator and the g a m m a ray detectors in the borehole is shown in Fig. 7.1. The detectors are located at different distances from the neutron source. A third detector, much farther away, called a GR (Gamma Ray) detector is often used with other logging tools as an add-on to monitoring natural gamma radiation. This is also shown in the diagram, as it is used in some of the oxygen activation procedures discussed later in this chapter.

,/

Channel cross section

Downhole tool

!eutron ge Water channel (moving down) Detector 1 Detector 2

GR detector

Figure 7.1. Oxygen activation tool showing downflow measurements

Downhole Tracers

297

In this figure the tool is shown in the wellbore with w a t e r moving down a channel in the cement between two sands, The channel is also shown in cross section on the upper right side of the figure. The sands are normally perforated for access, although this is not shown here. In this method, the 16N generated from oxygen in the water serves as a water tracer. The velocity of the water moving in a channel is obtained by timing the change in g a m m a radiation between two detectors a known distance apart. For downward flow in the channel, as shown here, they are positioned below the neutron generator and for upward flow above the generator. CONTINUOUS NEUTRON ACTIVATION A procedure for monitoring water flow behind casing by oxygen activation was first described by Arnold and Paap (1979). They used a pulsed neutron source with two g a m m a detectors mounted above it and timed the resulting change in g a m m a radiation at two detectors a known distance apart. Arnold and Paap derived an equation to account for the count rate, C, observed from the g a m m a radiation emitted by the 16N induced in the water. The equation was solved numerically for the count rate to be expected for various w a t e r velocities, v, flow channel cross-sectional areas, A, radial distances from the flow channel, r, and volumetric flow rates, q. From this, they arrived at a relationship between C/q and velocity, v. If distance r is known, the flow rate can then be calculated from the velocity and the count rate at the detector without knowing the cross-sectional area of the flow channel. The velocity, v, is obtained from the measured activity at each detector as shown below. The induced 16N activity decays exponentially according to its decay constant, ~. As the w a t e r travels past each detector, the activity decreases by ~t, the decay constant times the travel time. The travel time, t, can therefore be expressed as the distance between detectors, d, divided by the w a t e r velocity, v. Hence, the count rate, C i, at each detector can be presented as: C 2 = C 1 e -(~v/d)

(7.1)

The velocity, v, of the water moving in the channel is therefore given directly by: ~d v = ln(C 1/C2)

(7.2)

The distance, r, from the sonde to the flow channel was estimated from an empirical relationship between the ratio, Caleb of the count rate at two different energies and the intervening mass. The count rate at the high energy, Ca, was t a k e n from the region between 4.92 and 7.2 MeV, and Cb, the low-energy, countrate, from the region between 3.25 and 4.0 MeV. A plot of C a]Cb as a function of

298

Chapter 7

the intervening mass (gm/cm 2) for different casing diameters and thicknesses gave a linear fit. Although presented as an empirical relationship, the procedure described above is based upon the way g a m m a radiation interacts with m a t t e r by Compton scattering and by photoelectric absorption. The upper channel used here represents mostly unscattered primary radiation, whereas the lower energy channel is mostly Compton scattered radiation. For known densities, the ratio of unscattered to scattering radiation is a function of the thickness of the intervening material; it can therefore be used to estimate the distance from source to detector.

Background problem The activity due to the flowing w a t e r m u s t be corrected for the s t a t i o n a r y signal g e n e r a t e d by activation of oxygen bearing materials in the well w h e n there is no flow, as well as for the normal instrumental g a m m a background in the borehole. This is done by calibrating the sonde for the stationary signal and, for the i n s t r u m e n t a l background, in a part of the well where there is no flow. Unfortunately, the chemical composition of materials in the neighborhood of the well bore can be variable, and flow can occur in unexpected regions. As a result, background m e a s u r e m e n t s made at different locations and different times m a y not always be directly comparable with the m e a s u r e m e n t s made under flowing conditions, which can lead to large errors in evaluating flow. SHORT PULSE NEUTRON ACTIVATION The short pulse activation was proposed (McKeon et al., 1991) as a means of avoiding the problem of background calibration. Instead of using a continuous (pulsed) n e u t r o n signal with a short b r e a k for g a m m a acquisition, a short neutron activation period of 1 to 15 sec is used, followed by a longer period of 20 to 60 seconds for gamma-ray acquisition. This allows time for a distinct nitrogen16 t r a c e r pulse to be generated in the water. The emitted g a m m a radiation, monitored by the detectors, marks the arrival of the pulse at each detector. The w a t e r velocity is obtained by measuring the time required for the pulse to travel the fixed distance from the source to the detector. Since the 16N pulse has a halflife of 7.1 sec, the time of detection is limited, which places a lower limit on the w a t e r velocity t h a t can be measured. There are usually three g a m m a detectors, as shown in Fig. 7.1, each at a different distance from the source to allow for different response times. Fig. 7.2 (McKeon et al., 1991) shows a simulated 16N pulse tracing flow in a channel. As shown, the signal at the detector is a function of time. It is composed of three parts: a constant instrumental background, an exponentially decreasing signal from the decay of stationary activated material, and the peak from the moving w a t e r signal. The total count is the sum of all three signals. The neutron activation time, tA, is also shown in the figure in black. While no counts are

299

Downhole Tracers

acquired during activation, the water (tracer) pulse is still moving during this time and it must be accounted for. If d is the distance between detectors, and v is the water velocity, the arrival time of the pulse peak, tp, is given by half of the activation time plus the measured travel time, d/v: tA d tp = ~ + v

(7.3)

:i

i ~

6-

r--

m Neutrons on ~ Background ~ Stationary

2-

0

0.0

2.5

5.0

7.5

10.0

12..5 15.0

17.5

20.1

Time (sec)

Figure 7.2. Simulated 16N pulse in flowing water The best locator for the the response curve, rather other distribution is given the count rate, C = fit), is a

travel time of the tracer pulse is the first moment of than the peak position. The mean, t,, of this or any by its first moment, as discussed in chapter 4. Here, function of t, and the moment can be expressed as:

oo

~tC(t)dt =

+

oo

(7.4)

~C(t)dt 0

The magnitude of the gamma signal increases with the time of activation, tA, however, if tA is long compared to the transit time, part of the water signal is lost. Also, if the water velocity, v, is too low, errors in locating the peak occur because the curve shape is altered with time due to the exponential decay of the

300

Chapter 7

signal at the half-life of 7.1 sec, shown in Fig. 7.3. The authors simulated the pulse shapes to be expected from the 16N gamma rays using a Monte Carlo Neutron and Proton (MCNP) transport code (Briesmeister et al., 1986). The (simulated) total count as a function of flow velocity (for a given activation time and radial distance) is shown in Fig. 7.3a. As seen in the figure, the pulses become increasingly asymmetrical as the flow rate decreases due to the exponential decay of the stationary signal. At high-water velocities, the pulse can be detected by the GR detector (#3) with very little shape change, since by the time the pulse reaches this position the activated stationary component is gone, as shown in Fig. 7.3b. The activity also falls off exponentially with the distance from the tool to the water channel as expected, but because of the high energy of the emitted gamma ray, it is not significantly affected by casing thickness.

Neutrons on

16o

50

,,,!

/,

120-

/

..,'o

0.0 ft/min \

30'

; /

0

40

.0 ft/min

e-

o

,

~ f t / m i n

lO'

400

0

10

9

~ 20

~ 30

40

20'

i 50

0

Time, ser

5

10

15

20

Time, sec. b

Figure 7.3. Simulated response for different flow rates The activation times used depend upon the water-flow rate and the positions of the detectors. For any given situation in the well, there is a tradeoff between signal strength and the sensitivity with which velocity can be measured. A long activation provides high signal strength at the price of losing part or all of the signal, particularly at high-water velocities. The low oxygen activation cross section together with the relatively lowneutron flux down hole generate a low-activity pulse. Counting statistics can be improved by summing the data acquired in multiple activation cycles. Numerical

Downhole Tracers

301

techniques are used to estimate the flowing profile and to separate the total count into the three components. Field data from several examples (McKeon et al., 1991), not reproduced here, d e m o n s t r a t e the presence of water channels behind casing. Several measurements were also reported from the EPA leak test well in Ada, Oklahoma. This included a set of leak rate m e a s u r e m e n t s set by EPA observers u n d e r blind conditions, in good agreement with actual flow velocities. These log data give only flow velocity. In order to obtain the flow rate, the radial distance to the leak channel must first be estimated. The flow rate, Q, can then be estimated from the total flowing count rate, C3, by: Q = C3

b [v2e (xd/v)] GS

(7.5)

where b is a proportionality constant, v = flow velocity, d = travel distance, G = geometry factor, and S = neutron output. All except the geometry factor are measurable. Since the actual dimensions and position of the channel are not likely to be known, the geometry factor would be very difficult to estimate. Pulse evaluation The major advantage to the pulse method over the continuous proCedure is the formation of a discrete pulse as an entity clearly separable from background. This is i m p o r t a n t since it avoids all questions as to w h e t h e r channel flow is occurring, particularly at low flows. Both methods suffer from very low count rates because of poor counting efficiency, limited neutron flux, and the lowreaction cross section. The statistics of counting are significantly improved by s u m m i n g the results from a number of repetitive pulse cycles at a given duty station. A theoretical study of the oxygen activation technique by Ostermeir (1991) compared the pulse technique with the continuous method. A pulsed neutron generator is used in both techniques. The big difference is the time interval between repetitive pulses. In the continuous technique, the repetition rate of the tool is so much faster t h a n the acquisition rate that it is essentially a continuous pulse. In the pulse technique, the author suggests, the optimal period between pulses is twice the source-detector spacing divided by the flow velocity. For a 60-cm spacing and a 10-cm/sec flow rate, this requires a period of 12 sec between pulses (the pulse rate of the tool is in millihertz.) The author calculates the effect of changing many of the parameters and estimates the uncertainties associated with the measurement. He also examines the continuous method and shows that for nonoptimal flow velocities at larger (radial) distances from the flow channel, the background count rate can entirely obscure the flow response. This effect is shown in Fig. 7.4 for a channel-flow velocity of 10 cm/sec and channels offset a radial distance of 7, 11, and 15 cm from the detector. The three response curves

302

Chapter 7

for channel flow are indicated by arrows as oxygen response, compared with the horizontal lines showing the background associated with each offset.

lOO 9o 80

0 v

Oxygen . ~ , response ~ \

&,,/ \~/

60

....

t_ ~

40

Q)

zo

.....

~ ;

7cm \

.....

~

Background @

7cm

crn

lo

o

Channelvelocity(cm/sec)

Figure 7.4. Background effect in continuous oxygen activation

Injectivity profiles by oxygen activation A recent report (Scott et al., 1991) describes the use of oxygen activation to measure injectivity profiles in the Keparuk River field in Alaska. Wells in this field are completed in a manner that makes conventional production logging difficult, as shown in the well configurations of figs. 7.5, 7.6, and 7.7. The tubing section across the perforations through the C sand intervals has a much thicker wall, due to the addition of hardened blast joints and blast rings. The thicker walls absorb more radiation and require higher levels of g a m m a activity for penetration. This and the mixing induced by the injection m a n d r e l s have resulted in poor production logs using 1-131 tagged radioactive tracers. Oxygen activation was used here as an alternate method for measuring an injectivity profile, since the much higher energy g a m m a and the high, well-defined flow rates should give good results here.

Injected water velocity measurements An injectivity profile was measured for well 2W-14 using the method described above and illustrated in Fig. 7.5, showing the well configuration and the resultant velocity measurements. The measurements described here were made with a 11y16-in. diameter tool fitted with a neutron generator and three g a m m a ray detectors, spaced at 1, 2, and 15 ft from the neutron source and identified as

303

Downhole Tracers

the near, far, and GR detectors. The pulse technique was used with an activation period of 2 or 10 sec to generate the tracer pulse, followed by a longer (60-sec) data acquisition period for following its movement. To obtain adequate counting statistics, the procedure was repeated for 3 to 6 cycles (about 4 to 7 minutes of data), depending on the activation time. This method was first tested in well 2W14 at a water injection rate of 2500 bbl/day (75 fdmin.). For this flow rate, most measurements were made with the gamma ray (GR) detector 15 ft from the neutron source. Staggered measurements were made across each interval to improve the resolution.

Gamma log -

-.,~-"--I

D 790

";t '960 7

Well schematic I

I

=

Downhole water velocity ft./min. , ~, , ~, ' ~ ' ~, ' ,| Measurement stations 7900

1 B

20 e--

C~

i~ l

0i 7980

Figure 7.5. Injected water velocity profile on well 2W-14 Measurements were made in the C sands, starting in the B sand below the perforated interval (7960 ft), and from stations chosen at staggered locations moving up the well. Since the steel tubing is also activated by the generated neutrons, this is used to confirm the station position. The left side of the figure shows the background gamma log for the well and the depth in feet. The middle

304

Chapter 7

section shows the well configuration with the perforated section marked in black on the right and the measuring stations m a r k e d as teeth on the left. These station positions were verified by monitoring the neutron-activated sites in the steel tubing. The well configuration shows blast rings, indicated by hatch marks, over most of the perforated section. The section on the right shows the results of velocity m e a s u r e m e n t s for the depth interval as a function of depth. The water velocities are derived from the time required for the induced pulse to travel the distance to a detector. The travel time is taken to be one-half the activation time plus the first moment of the response time, in accordance with Eq. (7.3).

Gamma Well log schematic

Cumulative injection rate BWPD i'

9

9

1

w

Injection loss BWPD/FT i ......

|

1

|

B

l

Figure 7.6. Injected water flow rate profile in well 2W-14

Injected water flow rate Since the geometry of the flow relative to the detector is clearly known here, the velocity profile shown in Fig. 7.5 could be expressed in terms of injected flow rate as barrels of water per day (BWPD), corrected for variations in flow tubing

305

Downhole Tracers

diameter. This is shown in Fig. 7.6, as is the fluid loss into each of the responding sand intervals, in BWPD/ft. Produced water flow rate In principle, measurement of water production profiles does not differ from that of water injection profiles, except that only the water part of the production is monitored by this method. A production profile taken from well 2W-12 was made with the same procedure used for measuring the injection profiles in well 2W-14. The results, illustrated in Fig. 7.7, show that most water production in this interval occurs in the C1 sand from 7622 to 7627 ft.

Gamma ray log

Water production Water production rate (BWPD) per foot (BWPD/ft)

,~ 121

Figure 7.7. Injected water flow-rate profile in well 2W-12 This is a useful indicator for sections where water production is high. For wells where both oil and water are produced, this tracer response log is not sufficient for good water-flow rates, although high water-cut zones can be identified. The authors report that at a combined oil- and water-flow rate of about 4000 bbl/day, and a water-cut of less than 60 percent, laboratory experiments show

306

Chapter 7

t h a t the oxygen activation technique (OAT) gives numbers in agreement with the in situ water velocity. When the oil phase is dominant, the OAT velocity is higher t h a n the average water velocity because it is carried by the faster moving oil phase. This is enhanced in deviated wells because some water travels up on the high side of the well with the oil, while the remaining water travels at a lower speed either upward or downward on the low side of the pipe. Interaction of the flows in the wellbore makes it difficult for any single-phase tracer procedure to monitor two-phase flow without additional knowledge about the flow regime. A separate tracer for each phase might avoid some of these complications.

O t h e r f a s t neutron a c t i v a t i o n s There are several isotopes with a natural abundance of 60 to 70 percent and a high activation cross section that could provide gamma emitting tracers by fast neutron activation down hole. These include: 69Ga(n,2n)68Ga, 121Sb(n,2n)120Sb, and the 138Ba(n,2,)137mBa with an activation cross section of about 1 b a r n (1000mb), and 63Cu(n,2n)62Cu with a cross section of 500 mb (25 percent abundance). The only one of these currently used in the oil field is barium; its applications are discussed below. FAST NEUTRON ACTIVATIONOF BARIUM The fast neutron reaction t h a t produces radioactive barium in place is the 138Ba(n,2n)137mBa reaction. This reaction has a threshold energy of 10 MeV and a cross section of 1.05 barns for 14 MeV neutrons, or about 50 times the 160 cross section. The produced barium-137m decays to stable 137Ba with a half-life of 2.6 minutes, emitting a gamma ray with an energy of 0.66 MeV. The high cross section and the short half-life of the product nucleus make this a relatively effective process. Several situations in which the presence of barium can be of importance in production operations are discussed in the following section.

DRILLING MUD

BEHIND CASING

A recent patent (Jordan et al., 1988) discusses the use of fast neutron activation for locating barite-weighted drilling fluid remaining in the annulus after a cementing operation. The authors use a standard pulsed neutron capture tool ("cyclic activation tool," Dresser Industries) consisting of a 14-MeV neutron generator with two spaced gamma detectors below. The generator was pulsed on for 4 milliseconds and off for 6 milliseconds. Data are collected only during the last part of the off cycle to allow decay of gammas from prompt neutron reactions. The barium data were corrected for changes in activating conditions by comparing them with the results of the competing 56Fe(n,p)56Mn reaction, generated by activation of the casing. This reaction can act as an activation monitor since the iron content of the casing is constant except at the joints. The casing has a

Downhole Tracers

307

cross section of about 100 millibarns. Mn-56 decays by beta decay with a half-life of 2.6 hr, emitting several g a m m a rays. The authors used the net activity of the 0.847 MeV g a m m a photo peak as an activity monitor. Tests were done inside a test casing fitted with concentric canisters of different weights of barite. B a r i u m scales downhole The procedure described above can be applied to other production operations involving barium. The major problem in its use is the possibility of b a r i u m cont a m i n a t i o n because of barite from mud remaining in the neighborhood of the wellbore. Another possible application for this reaction is the identification of b a r i u m scale down hole. B a r i u m sulfate causes severe problems in m a n y oil fields. It is a difficult scale to remove chemically unless identified early. This procedure m a y provide a useful method for locating scale buildup and monitoring the effectiveness of scale treatments down hole. Nonradioactive barium has some potential as a location tracer used with this procedure, particularly where it may be necessary to repeat a m e a s u r e m e n t at intervals. It requires a way of putting sufficient barium solution at the desired position. Barium is easily placed in cement or in a steel pin in the casing. It can be used in solution even in normally precipitating conditions by the formation of complex ions of sufficient strength. Some of the barium crown ether complexes are w a t e r soluble and should be stable enough for this purpose.

LOG-INJECT-LOG TRACER PROCEDURES

M a n y common logging tools can be used to make estimates of the oil saturations in the neighborhood of the wellbore. These estimates are not usually accurate enough to be used for determining residual oil. In order to increase the accuracy of the methods, a procedure known descriptively as log-inject-log (LIL) has come into use. In this procedure, the formation water in the neighborhood of the wellbore is monitored (logged) with a suitable detector for background. Tagged w a t e r is injected to displace the formation water, and the well is logged again using a detector sensitive to the injected water. Assuming t h a t residual oil is immobile, t h a t the formation water is displaced by the injected water, and t h a t the formation porosity is known, this procedure can be used to m e a s u r e the w a t e r s a t u r a t i o n directly. Residual oil s a t u r a t i o n is derived from the w a t e r saturation by the saturation condition: Sor = 1- Sw

(7.6)

A variety of logging procedures and detectors have been used with this technique. The downhole log m e a s u r e m e n t s must be accurately related to the w a t e r s a t u r a t i o n in the formation, and borehole effects must be kept from interfering

308

Chapter 7

with the formation measurement. A tool frequently used for this purpose is the pulsed neutron capture (PNC) tool.

R e s i d u a l oil by n e u t r o n - a c t i v a t e d brine tracer The PNC tool is the s t a n d a r d 14 MeV downhole neutron g e n e r a t o r with g a m m a detectors spaced at various distances from the generator, and associated timing and monitoring circuitry. The neutron generator is t u r n e d on for a fixed period of time to produce a burst of neutrons. The neutrons are thermalized in the formation and captured by formation materials in an (n,y) reaction with prompt emission of g a m m a radiation, monitored by the g a m m a detectors on the PNC. The capture g a m m a radiation is a direct measure of the neutron capture reactions t a k i n g place. Following the neutron burst, the decay of the capture g a m m a radiation is monitored for a fixed period of time using a sequence of timed gates. These neutron emission gamma counting cycles are averaged over a n u m b e r of cycles to reach satisfactory statistics. The decay in g a m m a count rate is directly proportional to the rate of neutron decay. The neutron population as a function of time is given by the following expression: N = Noe "Zvt

(7.7)

where Z is the macroscopic absorption cross section, v is the velocity of the neutrons, t is the time, and No is the neutron population at zero time. The cross section data are obtained from the decay constant, k, of the g a m m a decay curve. The neutron velocity, v, at formation temperature is known, hence the decay cons t a n t for the g a m m a decay curve, ~., is equal to Zv, and the neutron lifetime is inversely proportional to Zv. The exponential neutron decay curve can be sepa r a t e d into two components by a set of timed gates for a given set of conditions" a borehole component t h a t decays with a relatively short half-life and a formation component with a relatively long half-life, shown schematically in Fig. 7.8. This is i m p o r t a n t because it provides a m e a n s of s e p a r a t i n g out the borehole component and allows a m e a s u r e m e n t of the fluid saturations in the formation without interference from fluid in the borehole. The simple correlation between g a m m a decay r a t e and cross section used above assumes t h a t the cloud of neutrons is uniform. In fact, it is not; and some additional corrections m u s t also be made for neutron diffusion. Any water-soluble material t h a t 1) does not react with the formation m a t e r ials, 2) follows the water path, and 3) has a high capture cross section can serve as a water tracer for this log-inject-log procedure. Most formation waters contain chloride ions. Chlorine has a much higher cross section for neutron capture t h a n other formation materials normally present. For this reason, the chloride present in formation brine is frequently used as a water tracer. Displacing the formation

309

Downhole Tracers

w a t e r with a brine of a very different salinity makes it possible to distinguish between the two waters. This technique is widely used for s a t u r a t i o n m e a s u r e m e n t s in the log-inject-log method. The brine s a t u r a t i o n is obtained from the difference in the capture cross sections before and after displacing the formation w a t e r and the known porosity of the formation, ~: Sw =

Zl-Zf

(7.8)

~(Z2-Zd) Here, E 1 and Z2 are the capture cross sections of the formation w a t e r and of the injected brine, respectively, as measured on samples in the laboratory, Zf and Y-d are capture cross sections measured by the PNC tool down hole in the presence of oil and formation water and of oil and displacing water, respectively, and ~ is the porosity of the formation. The residual oil is derived from this by the saturation condition; Sor = 1 - Sw. The difference in salinities m u s t be quite large or the propagation of errors of m e a s u r e m e n t can nullify it.

\ 10G

.>__
,--..Far \

\ Near \ \

Neutron Pulse on

\

'

'

"

5 o o

Gamma decay, lasec.

Figure 7.8. Decay of g a m m a activity following a neutron pulse

310

Chapter 7

W a t e r s a t u r a t i o n by n e u t r o n - a c t i v a t e d boron t r a c e r This is a v a r i a n t of the log-inject-log procedure t h a t can be used for m e a s u r ing w a t e r s a t u r a t i o n as described above and can also be used to follow w a t e r movement behind casing. The latter application is described here using boron as a tracer. In this procedure (Blount, 1990), a boron solution is injected into the wellbore. If channels are present and accessible through the wellbore, the boron solution will move through them and show up in the formation above or below the perforations. A pulsed neutron capture (PNC) tool is used to log the wellbore. Neutrons are thermalized in the formation and react with the boron in solution to emit the capture g a m m a s recorded by the tool. The neutron source activates a boron solution t h a t has been pumped into the channel. It does not differ in function from pumping in a radioactive tracer and monitoring the movement of the radioactivity. It differs in kind because it monitors an induced g a m m a signal r a t h e r t h a n a direct boron signal. The boron log suffers from the same problem associated with the radioactive tracer injection: it can only access channels t h a t communicate with the wellbore through perforations. Channels t h a t are not accessed by perforations are not visible to this procedure. The PNC log is a relatively expensive log to run and, except for special situations, m a y not offer any advantages over downhole production logs using radioactive tracers. The boron tracer technique uses the PNC tool to monitor change in g a m m a radiation due to the presence of boron, and the change in capture cross section is determined from this. The well is first logged with the PNC tool and both the wellbore Z and the formation Z determined. With the PNC tool above the perforations, a boron solution is then pumped into the perforations at pressures below fracture gradient. As soon as the boron solution fills the wellbore, the well is again monitored for the wellbore Z. The boron solution is displaced from the wellbore and the well is logged again. Logs of two wells showing large channels above and below the perforations are shown in Fig. 7.9. The formation Z shows an increase by a factor of two, clearly indicating the presence of boron in channels behind the casing. Interference due to boron in the wellbore is eliminated by delayed counting as shown in Fig 7.8. An important property of the PNC tool is the ability to measure the amount of material in the formation in the presence of a significant amount in the borehole. RADIOACTIVE TRACERS In principle, a solution tagged with a known concentration radioactivity can be injected into the formation and counted to give a direct m e a s u r e m e n t of residual w a t e r and, hence, of residual oil. We could not find such m e a s u r e m e n t s reported in the literature. The major difficulty in this type of measuring m a y be in getting rid of the effect of the radioactivity in the borehole. At this writing, we

Downhole Tracers

311

are u n a w a r e of any procedure currently in use for doing this without affecting the radioactivity in the formation.

0 GR 50 0 b

,

I

Formation sigma

.

40 I

0 GR 50 0

Formation s!gma

4O

Figure 7.9. Channel flow by LIL with boron as a tracer

RADIOACTIVE TRACERS FOR WELL TREATMENT DOWNHOLE Downhole t r e a t m e n t in oil wells refers here to the kinds of t r e a t m e n t s (excluding mechanical treatments) initiated at the surface but applied to a limited section of the borehole, often many thousands of feet below the surface. They can be divided into two classes: 1) well stimulation t r e a t m e n t s and 2) well control treatments.

312

Chapter 7

In some cases the t r e a t m e n t s are simple and the results well known from experience in the field; in others they are used as a form of shock therapy, often with little concern about how the procedure is applied. The procedure is important, however, and is expected to produce certain results. The treatments may be complex and must be applied to very specific locations in the wellbore for success. In such cases, tracers can be a powerful tool for verifying t h a t the t r e a t m e n t is successful and is applied to the specific area(s) required. The primary advantage of using (gamma-emitting) radioactive tracers for these applications lies in the ability to monitor them at the downhole location by means of a g a m m a detector on a wireline. A second advantage, one of increasing importance, is the ability to monitor both sequential and simultaneous operations by using tracers of different gamma energies. STIMULATION TREATMENT The production of hydrocarbons from an oil-bearing formation is limited by the permeability of the formation in the neighborhood of the wellbore. Production can often be increased by acidizing or adding solvents, surfactants, or a variety of other treatments that remove obstructing materials from the neighborhood of the wellbore. In low-permeability formations, hydrocarbon production can also be increased by inducing fractures at the wellbore. These kinds of well t r e a t m e n t are defined as well stimulation, and all share the characteristic t h a t they are expected to increase fluid entry into the borehole. The t r e a t m e n t may be different, but a similar situation holds in reverse for injection wells. CONTROL TREATMENT Not all production from the wellbore is desirable. Hydrocarbon production is often accompanied by undesirable amounts of other materials. There are m a n y examples of this. In unconsolidated formations, sand production can cause severe erosion problems and can lead to plugging of the well. Formations t h a t produce much brine and little or no oil place a strain upon disposal facilities and should be plugged. Formations t h a t produce water incompatible with other w a t e r produced in the wellbore can result in scale deposition and should be plugged back if possible. The control of undesirable production down hole is defined here as control treatment. All procedures for controlling this kind of production, including sand control, gel treatments, cement squeezes, flow diversion, etc., fall into this class. Similar control t r e a t m e n t s can be used for wells t h a t act as injectors for secondary recovery processes such as water flooding and various enhanced recovery procedures. TRACERS USED FOR WELL TREATING Gamma-emitting tracers have long been used in wellbore treating and stimulation operations (Flag et al., 1954; Gore et al., 1956). Early t r e a t m e n t s were limited to a single gamma-emitting tracer; energy discrimination down hole was not initially available. Tracer tagged stimulation t r e a t m e n t s were monitored

Downhole Tracers

313

down hole by a gamma counter on a wireline by Geiger counters. Introduction of the energy-sensitive scintillation (NaI) counters enabled the counter to follow, simultaneously, the fate of two or more tagged t r e a t m e n t s downhole using tracers having different energies. Procedures for tagging sand particles with a n u m b e r of radioactive isotopes, e.g., 51Cr, 192Ir, 198Au, 468c, 1248b, and llOAg, were well known. Baking sand coated with a suitable tracer solution at high temperature is a common procedure for tagging sand. A variety of tracer solutions for following liquid injections were also available. A number of radioactive isotopes have been identified (Pemper et al., 1988; Taylor et al., 1989; Gadeken et al., 1987) for use as downhole tracers, but the isotopes listed above plus 131I account for most of the downhole tracer work. These gamma-emitting tracers were used to verify the path of injected acids, and to observe the effect of flow diverters on the acid path. They were used to look at induced fractures and to estimate the position and extent of traced sand injected into the fracture at the wellbore face. The radioactive tracer log and the temperature log are the common ways of monitoring the extent of injected sand. A difficulty with monitoring the extent of traced sand from the wellbore is that if the wellbore and the fracture entry are not parallel, they may intersect at an angle and suggest a foreshortened extent of sand. Some early a t t e m p t s were made to look at two simultaneous downhole operations by using two tracers that differed widely in half-life (Pearce, 1979; Lindley and McGhee, 1983); however this is expensive and of limited effectiveness. Recent improvements in techniques for analyzing g a m m a ray spectra now permit the use of multiple tracers down hole. This allowsthe simultaneous monitoring of related downhole operations and has resulted in an expanded capability for analyzing and following downhole stimulation. The procedures used and the kind of results obtained are discussed below.

Spectral gamma ray analyses The rapid development of computer aided methods for analyzing g a m m a spectra in the past decade has had a significant effect on the logging industry. The effect on the petroleum industry lies principally in the ability to do g a m m a ray spectroscopy down hole. These techniques were developed originally to separate the uranium, thorium, and potassium components of n a t u r a l g a m m a ray logs, and have had a revolutionary effect upon the use of tracers for following downhole stimulations. NaI SCINTILLATION DETECTORS NaI(T1) detectors used for gamma ray detection are energy sensitive and can be used to obtain a spectrum, generated by the g a m m a radiation from the natural components in the borehole (U, Th, K), plus any gamma-emitting tracers added. The photoelectric peaks are used to identify each g a m m a ray energy

314

Chapter 7

associated with a radioisotope and to eliminate radiation from other sources. The gamma ray spectrum is complex, as discussed in chapter 2, because of the relatively poor resolution of the photo peaks and the competing reactions of gamma radiation in matter. This often results in a poorly resolved spectrum with little character, which limits the number of nuclides that can be used simultaneously but is adequate for most downhole processes. Such tracers make it possible to follow the results of sequential processes down hole and to distinguish between the fate of a proppant and that of the fluid transporting it. Photoelectric peaks are used to identify the separate gamma emitters by energy, and a variety of methods are used to deconvolve the gamma spectrum into its isotopic components, as discussed in chapter 2. Some of these procedures are used with modifications by the service companies and are discussed below. At this writing, the higher resolution germanium detector has not been reported for use by service companies, although it has been reported in this kind of downhole operation (Anderson et al., 1986). The high cost of germanium detectors and the requirement of liquid nitrogen temperatures make this too costly for most downhole work. A natural gamma-ray spectrum taken with a germanium detector downhole is shown in Fig 7.11. It is interesting to compare this spectrum with the (solid) curve from a NaI(T1) detector shown in Fig. 7.10. DECONVOLUTION OF GAMMASPECTRA There is a significant difference between spectral deconvolution as normally practiced in the laboratory and that which is required down hole. In the laboratory, the source detector geometry is fixed and chosen to optimize the analytical procedure. The laboratory spectrum can be deconvolved in terms of a collection of Gaussian photo peaks and an associated Compton continuum. Simple spectrum stripping is adequate for many laboratory applications. The purpose of the analysis in the laboratory is to determine quantitatively the amount of each isotope present in the sample. In the spectra collected down hole, the source-to-detector geometry is not fixed and, in general, is not precisely known, although it is usually assumed to be radially distributed about the borehole. The source-todetector distance will also vary depending upon where the tracer is distributed in and around the borehole. As a result, the shape of the spectrum will depend upon how much of the gamma radiation is degraded by Compton interactions. Resolution of the spectrum into the respective photo peaks will also depend on the choice of geometric models. In general, numerical methods of deconvolution give better statistics than spectrum stripping for downhole use.

Natural radioactivity The earliest use of spectral deconvolution down hole was in the resolution of natural radioactivity into its three components. The numerical methods used are discussed here as an illustration of the general procedure applicable to all downhole tracers.

Downhole Tracers

315

K-40 Th+U+K I

,,

I i

dN

.-, "--

I, ~,.

!yf - \

t ~,,

x ,.

Energy (MeV) I W1

I

W9

I

W~I

I W4

I

WR

I SCNt.uMeE~oCR

Energy windows

Figure 7.10. N a t u r a l radiation g a m m a spectrum G a m m a r a d i a t i o n downhole arises mostly from the m e m b e r s of the U-238 series, the Th-232 series, and K-40. These were discussed earlier in chapter 2, and the U-238 series illustrated in Fig. 1.17. Each of the series contains a n u m ber of g a m m a emitters. A typical downhole spectrum is shown in the composite curve labeled (Th + U + K) in Fig. 7.10 (Schlumberger, 1986). This curve shows relatively little character, although it is composed of emissions from a large n u m ber of individual g a m m a emitters. Superimposed on the s p e c t r u m is a characteristic photopeak from each of the three sources, which also shows up as a bump on the composite curve. These are a thalium-208 peak from the thorium series, a bismuth-214 peak from the u r a n i u m series, and the potassium-40 component of n a t u r a l l y occurring potassium. The composite curve is, however, a linear combination of the g a m m a radiation from all three sources, regardless of character. Therefore, it can be resolved into its constituent sources by monitoring the count rate in each of three spectral regions or channels, and solving the three equations in three unknowns. The channels are usually chosen to include one p r o m i n e n t p h o t o p e a k for each of the three sources. The count rate for each channel, i, is given by the following expression: C i = Uij + Thij + Kij

(7.9)

where C is the m e a s u r e d count rate, i is the channel n u m b e r or window, and j represents the source of radiation: e.g., j = 1 for K, j = 2 for U, j = 3 for Th. Thus, if i=l is the potassium channel, Kij = C l l K is the contribution due to potassium

316

Chapter 7

in t h a t channel, Uij = C 12U is the uranium series contribution to the count rate in t h a t channel, and Thij = C13Th is the thorium series contribution. The total count in this channel, C1, is given by the sum of these contributions: C 1 = C l l K + C12 U + C 1 3 T h Similar equations are written for the other two counting channels, C2 and C 3. In matrix notation, the three simultaneous equations can be written as:

E]

(7.10)

[C]= C2 = [A][W] = [A] C3

Here [A] is the square matrix of the coefficients Cij, and [C] and [W] are column vectors as sbown. Solution of the three equations in three u n k n o w n s gives the contribution from each of the separate sources. To convert the counts to concentrations, a standard containing a known amount of the three components at radioactive equilibrium is counted in the same counter. As in all counting systems, there is an independent counting error, equal to the square root of the count rate, associated with each of the measurements in all of the channels. This error is propagated throughout the system since the solutions are a function of all the count rates. In general these errors will not be equal; hence simple averaging will not equitably distribute the error. A weighted average is therefore used to distribute the most probable error. In order to minimize the errors, a larger number of channels is chosen than is needed to solve for the three components. In the case illustrated in Fig. 7.10, five window channels are used. The equations can be written in a similar m a n n e r in matrix form. In this case, [C] is composed of the count rate in each of the five channels, [W] is composed of the elemental concentrations of potassium, uranium, and thorium in ppm or weight percent, and [S] is a 3 X 5 sensitivity matrix for channel i and source j, expressed in counts/second/ppm. Coefficients of this matrix are calculated by a weighted least squares method to minimize the error (Beers, 1959; Serra et al., 1980; Smith et al., 1983). The solution for each of the elemental concentrations can be expressed in the following form, where S contains the new coefficients: g

[W] = S [C]

(7.11)

In addition to the independent errors noted above, other sources of error present are a function of the conditions of m e a s u r e m e n t down hole (Smith et al., 1983). In all of these systems, variations in downhole conditions m u s t also be t a k e n into account. Calibrations must account for casing diameter, thickness, and density, the properties of the cement annulus, and any other variations t h a t

Downhole Tracers

317

are known to affect calibration conditions. Spectral analysis of naturally occurring radioactivity is widely used in the oil industry because of the added geochemical information. Germanium detector comparison As a standard for comparison with the scintillation detector, a natural gamma ray spectrum taken with a high resolution germanium detector downhole is shown in Fig 7.11 (Zhao et al., 1993). It is important to recognize the relative ease of deconvolving this spectrum into its component sources, compared with that from the NaI detector. The detector used here was mounted in a vacuuminsulated cryostat using solid propane as a coolant (-170~ The resolution was 5 keV for the 1.33 MeV gamma of Co-60, measured at the end of 3500 meters of cable.

0_

v

>

N

8

~>

rn

Energy, MeV

Figure 7.11. Natural gamma spectrum with Ge detector

The authors point out t ha t the 1.76-MeV gamma ray of Bi-214, used for identification of uranium by the NaI detector (Fig 7.10), is a ninth generation decay product of U-238. If the U-Ra equilibrium is destroyed by solution or reaction, the apparent uranium concentration can be off by a very large factor. The high resolution of the Ge detector will allow even third generation decay products, always in equilibrium with U-235, to be correctly detected.

318

Chapter 7

Radioactive tracers downhole

Analysis of g a m m a emission from downhole tracers is done in the same m a n ner as for naturally occurring radioactivity. The procedures have been described thoroughly in the literature (Gadeken and Smith, 1986; P e m p e r et al., 1988; Gadeken et al., 1988). The resolution of the NaI detectors limits the useful n u m ber of windows (channels) to 256. These channels can be grouped into a smaller n u m b e r of windows, as desired, for data analysis. One service company uses 13 windows to collect the data; another uses 25. In general, when downhole tracers are used, the added activity will be much larger t h a n background, but some of the background can be subtracted by energy discrimination if need be; otherwise the use of downhole tracers involves the same kind of spectral analysis as described for n a t u r a l radioactivity. Typical spectra of tracers frequently used in downhole surveys are shown in Fig. 7.12 (Schlumberger, 1986). The counting errors associated with deconvolving a complex spectrum limit the n u m b e r of tracers t h a t can be used simultaneously to a m a x i m u m of three

~

6

0.88

1,38

041

Agl 1o

0.38

Au198 1131

Sc 46 .......

1.69

2.10

---ir192

0.91 " ~ :

Sb124

~'-~

2.62 _ a __Th232

I 46

K4O ~.~_~

0

i

0:5

1.12

1:0

1.76

1.'5

2.18

2:0

U238

2:5

3:0

Gamma ray energy, MeV

Figure 7.12. Typical downhole gamma spectra of common tracers

Downhole Tracers

319

isotopes (Gadeken and Smith, 1989). Better results are obtained with a lower number. Most of the downhole work to be discussed here is concerned with tracers used to differentiate between the placements down hole of two or more simultaneous or sequential operations. The g a m m a tool identifies the location of each tagged t r e a t m e n t in the borehole by its deconvolved energy signature. The depth of p e n e t r a t i o n is e s t i m a t e d from the ratio of the Compton to photoelectric response in the detector. The source geometry in the borehole is usually not known. Most service companies a s s u m e a radially distributed source as a first approximation, even though some of the downhole fracture t r e a t m e n t s are not intended to be radially distributed. This is probably adequate for the limited qualitative interpretations required. E a r l y use of these multiple tracer techniques pointed out m a n y problems in the application. A set of tests reported by Williams et al. (1986) showed the utility of the method but also m a n y of the unexpected difficulties. Early problems in s e p a r a t i n g the components of the g a m m a spectrum resulted in large errors in isotope assignment. The authors reported difficulties due to degradation of the radioactivity of the tagged sand under storage, requiring frequent monitoring and calibration. There were also problems with movement of tagged sand in the formation following the fracture t r e a t m e n t , most of which have since been resolved. The use of tracers to follow well stimulation is now conventional oilfield practice. Tracers are injected with the hydraulic fluid used to fracture the formation, with any acid or other intermediate t r e a t m e n t to clean the fracture up, and with the materials used to prop the fracture open. They are particularly important in a staged sequence of treatments. At least ten different g a m m a - e m i t t i n g tracers have been identified for this purpose. By proper choice of tracer energy, it is possible to follow the results of three or four sequential operations, or to follow sepa r a t e parts of the same operations, distinguishing the hydraulic fluid from the proppant carried by the fluid.

Depth of treatment penetration from tracer data PRINCIPLES OF MEASUREMENT The depth of penetration of g a m m a radiation into the formation is relatively small. The m a x i m u m distance from the wellbore to the full penetration through casing, cement, and formation, for a 1.5 MeV gamma, is less t h a n 8 in. (20 cm); however this is i m p o r t a n t in differentiating between m a t e r i a l left inside the borehole and the m a t e r i a l injected into the formation. A major difficulty in monitoring radioactive materials down hole has been to distinguish between

320

Chapter 7

source distance and source strength, i.e., between a small source n e a r the detector and a large source far away. A photoelectric peak at the detector down hole records the arrival of unscattered radiation from the neighborhood of the borehole. Most of the radiation arriving at the detector is scattered by the intervening m a t t e r due to Compton interactions, the most likely reaction for g a m m a energies between 100 keV and 3 MeV in formation materials. The linear absorption coefficient for Compton scattering (except for the lightest elements) is proportional to the bulk density in the intervening path. For material of equal density, the ratio of u n s c a t t e r e d (photoelectric) to Compton scattered radiation should be inversely related to the distance from the source. A Monte Carlo simulation was used by Jassti and Fogler (1990) to derive the ratio of scattered (Compton) to the unscattered (photoelectric) radiation arriving at a detector from a point g a m m a source (0.365 MeV) in a sandstone medium. The ratio was found to increase monotonically with distance from source to detector and was a good measure of location in the near region of the wellbore. They made laboratory m e a s u r e m e n t s of the velocity of an injected tracer pulse moving away from the detector in a sandstone core and concluded t h a t the velocity of the pulse could be determined accurately from the a t t e n u a t i o n r a t e of either scattered or unscattered radiation, and t h a t it was independent of pulse spreading. Application of the ratio of scattered to unscattered radiation for monitoring distance of penetration can, in principle, be extended to distributed sources, given the geometry of the source. DOWNHOLE MEASUREMENTS WITH LOGGINGTOOLS Measurements of this ratio in a downhole detector were used by Anderson et al. (1986) as an indicator of source distance. They proposed t h a t the ratio, RC, of counts in the photo peak (unscattered) region, P, to that in a Compton (scattered) region, C, was related to the distance between source and detector. P RC = ~

(7.12)

They tested the concept using a Cs-137 (E = .667 MeV) as a point source and applied it to a field fracture test using sand tagged with Ir-192 as a proppant. A germanium detector was used to collect the data. The region from 220 to 250 keV was chosen for the scattered radiation, and from 295 to 612 keV for the relatively unscattered radiation. The ratio of counts in the two regions was used to distinguish the tracer response due to nearby material in the wellbore from the distant material in the fracture. This procedure was used earlier in the application of 160 activation by Arnold and Papp (1979), who empirically correlated the ratio, P, of count rates at high

Downhole Tracers

321

versus low energies, with the distance from source to counter. The data were calibrated for the density of casing in the well and used to estimate the distance to a cement channel. In a recent patent, Smith and Gadeken (1989) describe a NaI logging counter with one high-energy and two low-energy windows. Two count-rate ratios were derived from these windows. One, Re, the ratio of counts from the high-energy window (photoelectric effect) to those from one of the low-energy windows (Compton scatter) was related to distance from the source. A second ratio, Rp, was t a k e n between the two "low" energy windows, where the low energy window was sensitive to the iron (casing) because of its high photoelectric absorption, whereas the higher energy window responded to Compton scattering as well. Most downhole g a m m a tools are encased in steel and are usually insensitive to low-energy radiation. There are, however, several processes within the wellbore where useful m e a s u r e m e n t s can only be made at these low energies. In succeeding papers (Gadeken et al., 1988; Gadeken et al., 1989; Gadeken and Smith, 1989; and Smith and Gadeken, 1990), the authors expanded the concepts of using energy ratios for estimating relative distance, discussed in the para g r a p h above. They proposed a model in which the tracer is distributed cylindrically about the detector at two locations: one inside the borehole and the other in the formation outside the casing. For a given casing diameter, they treated each t r a c e r as having two spectra, one for each location. The spectra are deconvolved by treating the tracer at each location as a separate component. The authors demonstrated the technique using simulated spectra for 46Sc and 192Ir, showing t h a t the four-component t r e a t m e n t gave superior results to the two-component t r e a t m e n t and t h a t the propagation of errors severely limited the n u m b e r of tracers t h a t can be analyzed simultaneously. In the studies above, the authors also related the counting ratio, Re, of high-energy (unscattered) to low-energy (Compton scattered) counts to D, the distance between source and detector: B

RC = A + D--~

(7.13)

They showed t h a t a plot of RC versus 1/D2fits a fairly straight line where A and B are constants dependent on the tracer type and the casing diameter. For a single tracer, this was proposed as a means of locating the m e a n distance (radial) of cement or gravel packs. They claim good results using this method on data from a published cement study (Kline et al., 1986). In real cases in the field, the tagged materials are distributed over large intervals. The radial distances obtained from logs are only approximate but can provide an indicator of relative position. The authors gave a number of field examples. In a n o t h e r paper on the use of multiple tracers for monitoring downhole t r e a t m e n t s , P e m p e r et al. (1988) pointed out t h a t the choice of low-energy window width should be the best compromise between sensitivity and statistical

322

Chapter 7

fluctuations. An increase of width from 30 to 40 keV gave a 23 percent increase in sensitivity, and from 30 to 80 keV gave a 60 percent increase. They also showed that when multiple tracers are used down hole, or natural background is high, the Compton ratio, RC, for measuring source-detector distance should be corrected for the extra background, B, in the Compton component due to tracers other than the present one for which RC is being calculated: P RC = C-B

(7.14)

A variety of simple functions have been proposed to relate this ratio, RC, with the (radical) distance from the source to the detector. They are all qualitative in nature and are used only as indicators of whether the source is inside or outside the casing.

Downhole tracer procedures There are now numerous papers reporting the use of tracers for following downhole operations. Such operations as acidizing, flow diversion, squeeze cementation, fracturing, and fracture propping are frequently tagged (Gadeken et al., 1988; Pemper et al., 1989; Taylor and Bandy, 1989; Gadeken and Smith, 1989; Kennedy et al., 1990; and Schwanke et al., 1990). The procedures used in designing such operations almost always involve several different service companies. These usually include a tracer company, a pumping company, a logging company and the oil company requesting the test. Radioactive tracers must properly follow the materials being traced. This requires that the tracer have the same transport properties as and be well mixed with the material being traced. In a rare procedural paper, Priest (1988) describes the handling problems and procedures used for injecting radioactively tagged sand. The author discusses the safety aspects of transporting and using radioactively tagged sand in the field. He also describes surface injection and mixing equipment, as well as procedures, and provides several case histories. The author makes the point that radioactive tracers for sand fractures should be injected as close to the well as possible to reduce the chance of radioactive contamination at the well site. DOWNHOLE TRACERTEST DESIGN In a series of papers referenced above, Gadeken discusses the design of such tests down hole. The design of a tracer project for downhole logging is based upon proper placement of the tagged material and the ability to monitor its placement downhole by the emitted radiation. Success in the test requires good coordination among all the companies taking part in the operation (Haliburton, 1990). The tracers must be properly chosen and placed down hole at the assigned depth, and

Downhole Tracers

323

good logging practice m u s t be followed. As much as possible should be known about all aspects of the test to maximize the information extracted from the log. Tracer concentrations should be high enough to allow for good statistics in the m e a s u r e m e n t s and to avoid large background corrections; however, excessive tracer concentrations should be avoided. The scintillation detectors used in these logs are designed to have a linear response for radiation levels up to about 6000 API units. Counting rates much higher t h a n this are counterproductive. They distort the response and obscure the differences in tracer location. The rule of t h u m b for tracer addition is to add a few tenths of a millicurie of tracer (depending on the tracer) per 1000 pounds of solids or gallons of fluid. This usually gives readings from several hundred to a few thousand API units; however many other factors can play a role in the tracer activity logged down hole. Experience in local operations of this type is a great help. A graph of recommended tracer concentrations in millicuries per 1000 for the common tracers used in downhole logging is shown in Fig. 7.13 (Haliburton, 1990). This figure includes correction for decay of the tracer during the time between tagging and logging. If logging speeds are kept low, in the order of 10 ft/min, even low radiation levels can be used successfully. As in all such treatments, the tracer response should be one to two orders of magnitude above background to minimize the counting error. Downhole test problems Tracers are used to track injected fracturing fluid, acidizing or other well treating solutions, flow diverters, cement squeezes, and a variety of other downhole treatments. In all of these, the tracer log must be indicative of the location of the injected t r e a t m e n t in the borehole. Many of these procedures are combined and performed simultaneously, while others may be done in a sequential order. In some of these procedures, e.g., fracturing, it is important to show t h a t the injected materials have moved beyond the wellbore casing. A major source of confusion in interpreting logs for depth of penetration is inadvertent deposition of tracer inside the wellbore. The common radioactive materials used for the downhole studies described here are cationic (except for 131I). The formation surfaces tend to be anionic and will attract and absorb cations. This can be advantageous if carefully thought out, since it might put more tracer near the well surface of the injection treatment region. It can, however, cause problems in log interpretation if it simply deposits on the well surfaces. Corrosion down hole often involves iron oxide surfaces, which can be anionic and thus adsorb cations. In acid solution there is little problem with cation absorption; however at intermediate to high pH, the addition of carrier and the use of a complexing agent is warranted.

Post-test evaluation of the downhole tracer log for t r e a t m e n t penetration can be so complicated by tagged materials left in the borehole that every effort should be made to avoid this problem by using clean operating procedures and paying

324

Chapter 7

careful attention to detail. In some cases it may be necessary to swab or even to produce the well in order to remove u n w a n t e d tracer m a t e r i a l s from the borehole. The deleterious effect of such r e m n a n t s upon the a p p a r e n t radial d i s t a n c e of t r a c e r s from the borehole was d e m o n s t r a t e d in l a b o r a t o r y m e a s u r e m e n t s using Sc-46 as a tracer (Gadeken et al., 1989) placed in an annulus around the wellbore. The data showed that the apparent Compton ratio increases almost linearly as the fraction of total tracer concentration, f, changes from being all in the formation (f = 1) to being all inside the borehole (f = 0). It is accompanied by an a p p a r e n t decrease in the diameter of the tagged a n n u l u s calculated from Eq. (7.12) as the fraction of tracer remaining in the borehole increases. This can be a significant source of error.

,O

Au198

10 ,

~=

O= ~~ t,._

*._.~

"Se

=7 O ~

1

=:'IT:

I

/,-

J

z ,,'" /

/

/,,

. .

.

--

. .

. .

. .

0

..

..

..

..

..

... Sb124

~'

__._.,. . ~ "

,1

..

/

Z

a"O_ ) - -~

go

/

/__/

~

1 131

r,

" - ~ - ~ _ _ _ ~ . ~ . ,__ w

'

'

'

10

20

30

~

"-'~ -

Ir192 Sc46 Ag110

40

50

60

70

80

90

10b

Estimated time between tagging and logging, days

Figure 7.13. Recommended tracer concentrations for downhole operations

In general, better quality results are obtained when the best counting statistics are available. Larger diameter detectors provide better data t h a n small ones because of higher counting efficiency. Averaging results from several passes of the log improves the counting statistics and the log interpretation from a test. As the number of tracers used increases, the counting error (signal-to-noise ratio) also increases and makes interpretation more difficult. The needs of the test m u s t be balanced against the desire for better data. A 31/2-in. diameter detector

Downhole Tracers

325

is more efficient t h a n a smaller one, but it may not pass through tubing. Similar compromises are required for other factors. Given a choice, it is preferable to have simple r a t h e r t h a n complex test conditions. The assumption t h a t all stages of a multistage test remain separate in the borehole is not always valid. Mixing effects in the borehole can cause staged treatments to mix in unexpected ways. In all cases, as much auxiliary log and other data as possible should be gathered to help analyze the results. Despite the problems t h a t can occur in such tests, the successes outweigh the failures. Tracers provide a unique ability to monitor specific downhole operations t h a t is not otherwise available. The downhole environment is not always well understood. Only by the use of such tracer tests can we learn to fit downhole procedures to the specific well environment under test.

Proppant tagging Tracers for fracture proppants come in two general types: sand coated with a tracer fixed on the surface by heat t r e a t m e n t or resin coating, and as porous nonsand particles. The direct coating of tracer on the sand particle is the oldest method in use, usually accomplished by coating the sand with a solution of the desired tracer salt and baking the sand in an oven. Iridium, gold, and silver salts are easily reduced to the metal, and scandium salts to the oxides. The procedure requires careful handling and a clean sand surface for adhesion, and there may be some difficulties with tracer loss by friction or by wash-off. There have been reports of tracer loss from some proppants. One method of improving adhesion to the sand has been to coat the baked-on tracer with an epoxy resin. Curable resincoated proppants have also been used to prevent loss from the fracture during cleanup and production (Norman et al., 1990). The second method, coming into general use, is to absorb the radioactive material onto a porous ion exchange particle that may also serve as the proppant or be mixed with the another proppant as a tracer. In this procedure, the radioactive cation is adsorbed on a carrier such as aluminum oxide (A1203), which has ion exchange capacity and can be loaded with suitable ions. This procedure has the additional advantage t h a t the tracer can be absorbed in the a l u m i n u m oxide as a nonradioactive isotope. It can be permanently fixed on the substrate at high t e m p e r a t u r e and then activated in a research reactor, which simplifies the handling, m e a s u r i n g , and packaging of the tracer. Most of the commonly used tracers, such as 192Ir, 195Au, 468c, and llOAg, can be produced by an (n,~ reaction on the naturally occurring element. Cross sections are high, and there is little interference. The only possible problem with this type of tracer tag is t h a t the t r a c e r dynamics during injection into the formation can be different from those of the proppant. Differences in size and density between tracer and proppant can lead to errors in interpretation if they cause separation of the tracer from the proppant.

326

Chapter 7

Tagging injected liquids Any of the radioactive tracers discussed here can be used to trace injected fluids as long as they are completely soluble and do not react with materials in the wellbore. As indicated earlier, exceptions to ideal behavior can be designed into the fluid to ensure reaction with a desired component down hole. A variety of traced fluids have been used down hole. Virtually any downhole liquid t r e a t m e n t can be tagged, including acids, solvents, detergent solutions, scale and corrosion t r e a t m e n t s , and m a n y m o n o m e r and polymer solutions. M a n y liquids are injected in conjunction with other m a t e r i a l s , such as flow d i v e r t e r s a n d proppants, which may or may not be tagged. An alternative to the use of tagged fluids is the use of radioactively tagged particles of neutral density in the fluid. Tagged ion-exchange beads can be used for this purpose. Their density can be adjusted to fit the density of the brine, and multivalent ions are strongly absorbed by these beads. The beads will not travel far into the fracture but are permeable to water, which lets them act as m a r k e r s for w a t e r entry positions into the formation. They can be used to locate naturally occurring fractures at the borehole since the beads will collect at the perforations and can be logged after the injection.

Field examples HYDRAULIC FRACTURE TRACING Fractures are induced downhole by injecting a fluid into the well at sufficient pressure. A proppant is injected with the fluid to keep the fracture open when the pressure is released. One of the problems in this practice is to establish t h a t the fracturing fluid and the proppant carried by the fluid enter the same interval, and t h a t the proppant is deposited at the proper location in the formation. Fig. 7.14 shows a log of a fracture study in which 46Sc was used to tag the fluid and 192Ir was used to tag the proppant (Gadeken and Smith, 1989). The log shown is an average composed of three logging passes to improve the counting statistics. The n a t u r a l g a m m a - r a y log on a scale of 0 to 150 API units is shown on the left side of the wellbore schematic. Horizontal lines indicate 100-ft intervals. The "fit error" curve is an indicator of statistical error. The wellbore schematic shows the perforated interval. The two channels on the right of the wellbore show the tracer response curves on a scale to 1500 API units and the relative distance from the borehole, from n e a r to far. In the region from X220 to X360 there is a significant increase in the distance of penetration, which indicates good fracture propping. The relative distance plot shows a small increase to about X360, which suggests limited success in this region. The presence of both 46Sc and 192Ir throughout the logged interval suggests sand deposition inside the wellbore. The operating company had indicated t h a t the pumping rates were higher t h a n desirable, which could account for

327

Downhole Tracers

sand deposition. Overall results show that the fracture extended beyond the perforated interval but was not propped as effectively as expected.

Tracer log Relative Gamma log i 0 API 150! o API 1000 distance near far fit error I .....

1

_

,

_

~" rfit error .,,.~lamma

l~

7 ,i ,ix3oo! "

i

0_

1 ~,,j

!

Ir-192 - Sc-,

c-

i,

!

",..L . . . . .

Figure 7.14. Tagged fracture study showing fracture fluid and proppant TAGGED GRAVEL PACK TRACING An alternative use for tagged particles is in sand control for wells drilled t h r o u g h unconsolidated formations. Gravel packs are used to prevent sand incursions in the well, to maintain high permeability, and to prevent sand fines from plugging the perforations. The use of tracers for monitoring sand control is widespread in the oil field (Bruist et al., 1983; Jefferis et al., 1983; Gadeken et al., 1991). In recent years, this has been combined with an acid wash followed by prepacks set behind the perforations as auxiliary sand control. In all cases, placement of the gravel packs and/or prepacks downhole is an important concern.

328

Chapter 7

Tracer tagging for particles used for gravel packing is the same as that described above for fracture proppants. A tagged gravel pack study was used to confirm the completion procedures in an offshore California field (Bruist et al., 1983). Two tracer applications were used here: one for the tagged gravel pack and one for a radioactive m a r k e r for depth control in perforating. In this case, the collar locator did not accurately pick up the collars. In order to place the perforations accurately, a short joint of drill pipe with a p e r m a n e n t radioactive m a r k e r was positioned about 100 ft above the firing head. This was then correlated with the gamma ray log and with radioactive markers in the casing to position the guns for firing. A small amount of 10- to 20-mesh gravel was tagged with llOAg by a hightemperature baking procedure, uniformly mixed with the rest of the gravel in the slurry, and pumped down hole. The gravel was logged after placement by a g a m m a ray tool, and a neutron log run concurrently to compare "near" (borehole saturation) with "far" (formation saturation) to determine whether the annulus contained water. The results are shown in Fig. 7.15. Agreement between the two logs was expected for a good gravel pack. TAGGED DIVERTERS AND MULTISTAGEACID TREATMENT The effect of diverting agents on the injection of acid is a common concern in such treatments. Diverters are injected before injecting acid to divert the acid from entering intervals t h a t are highly water s a t u r a t e d in favor of less permeable formations producing oil. The results of a m u l t i s t a g e tagged acid t r e a t m e n t were reported by Kennedy et al. (1990). The t r e a t m e n t consisted of: 1) injecting a water zone diverter tagged with 2.7-day half-life 198Au and logging the well; 2) acidizing the well with 124Sb as a tracer (in the ammonium chloride post flush) and relogging the well; 3 ) a d d i n g nitrogen foam as a diverter and acidizing with 468c as a tracer in the post flush; and 4)injecting additional nitrogen foam and reacidizing, using 192Ir as an acid tracer. Fig. 7.16. shows results of the test logs. The well schematic shows perforations in two zones, A and B. The n a t u r a l gamma-ray spectrum is shown on the left of the well schematic, an induction log on the right side, and five channels showing the results of each t r e a t m e n t on the far right. The first log (Au) shows the invasion of the diverter into zones A and B, with most going into zone B. The first acid treatment (Sb) and the first foam plus acid t r e a t m e n t (Sc) showed little change in the distribution. Only the second foam plus acid t r e a t m e n t (Ir) showed a significant effect in zone A. This treatment was followed by an increase in oil production from the well. D i r e c t i o n a l o r i e n t a t i o n a t the borehole

Some of the procedures that take place in and around the borehole are associated with a preferred direction. The most prominent of these is fracturing.

329

Downhole Tracers

Much theoretical work has been done on predictions of fracture properties. The position of entry of fracture proppants and of fracturing fluids at the borehole is not generally known. The height of the fracture proppant is the only property conventionally measured at the borehole; very little work has been done on orientation of the proppant at the wellbore. The only additional equipment needed to measure the orientation at the borehole is a directional gamma detector.

Gamma ray logs CNL log 12/29 12/30 12/31

Tracers AuAu SbSc Ir ~GR

r

top gravel

A

c J.

u w

top gravel J

j.

j,

_ _

B

|

~xxl

L~

_

top gravel

Figure 7.15. Silver-110 tagged gravel pack logs

>

L

Before After Acid treatment

Figure 7.16. Tagged diverter and multistage acid treatments

A detector can be made directional by surrounding it with a shield of dense, high-atomic-number material with an opening in one direction. A sodium iodide scintillation detector within such a shield is a simple, relatively efficient arrangement. The shield material, thickness, and the shape of the slit will limit the directional resolution of the detector. More complicated arrangements, such as

330

Chapter 7

coincident crystal pairs, are also possible. The shield must be capable of rotation and also be coupled to a direction-sensing device such as a gyroscopic compass. A recent paper described the testing and use of a prototype directional g a m m a tool (Gadeken et al., 1991). In this tool (Fig. 7.17a), tungsten was used to shield a 1/2-in. diameter by 8-in. long NaI crystal. The included angle of the slit was about 40 degrees. The rotating shield was coupled to a 3-axis accelerometer to determine the gravity vector relative to the tool axis, for directional orientation. The tool was tested in a t a n k using 192Ir in four simulated fracture planes. Fig. 7.17b shows the response of the tool to each of these fracture planes. F r a c t u r e planes p e n e t r a t i n g the wellbore show the expected dual response lobes in direction of the plane; however, those that are offset or tangential to the borehole show single lobes t h a t point in the direction of the offset fracture plane. Two tests were also reported on field fracture logs. In the fracture orientation measurements described above, the fracture is presumed to be conventionally tagged with a radioactive isotope. Orientation is determined by monitoring the residual tag with the directional tool. An alternative way to do this would be to inject a tracer from a downhole tool and monitor where it goes, using the directional monitor during the process. To m a k e this effective, the two tools need to be combined.

r~,~,.~..,.~r

SI Tungsten Shield Rotoscan tool

Simulated fracture planes

Figure 7.17. Directional tool showing response to simulated fractures

331

Downhole Tracers

An interesting application of a directional monitor would be to observe the direction and velocity of flow at an observation well, presuming that flow at the wellbore is indicative of flow direction from the well. In this procedure, a tracer pulse would be placed in the borehole and its rate of disappearance and direction of flow monitored at each depth. Procedures such as this are used for monitoring groundwater flow in hydrology; they could also be useful in oilfield work. Jassti and Fogler (1990) proposed a method for monitoring the velocity of a tracer pulse in the near-wellbore region, as referred to earlier in the chapter. This could be combined with a directional monitor to provide both direction and velocity of flow in the neighborhood of the wellbore.

Diameter of exposed crystal '

.E_

Lv//

Total no.

//

/

/

/

/

of holes, N

~ _

focal

~

plane

R

\

\

\\

Depth of focus, X \

Figure 7.18. Focusing collimator

FOCUSING COLLIMATOR An alternative directional method used in medicine is to combine relatively low-energy radiation with a focusing collimator. For low-energy radiation, the high atomic number shield becomes essentially opaque because of the predominance of the photoelectric effect. As a result, a cone-shaped array of holes in a

332

Chapter 7

lead or tungsten shield acts as a lens, focusing the radiation from a small area on the detector. An extensive literature can be found on the design and application of such collimators. A schematic of such a detector is shown in Fig. 7.18 (Hine and Sorenson, 1970). Collimators are used at g a m m a energies up to about 500 keV, with some loss of resolution; the resolution at lower energies is much higher. The choice of focal plane and depth of field depends upon the n u m b e r of holes, their shape and size, the dimensions of the collimator, and other factors. As in optical lenses, the depth of field decreases as the focal length increases; however the shape of the focus at the surface does not have to be circular but can be a vertical or horizontal slit if desired. Relatively low-energy g a m m a radiation limits this i n s t r u m e n t to studies inside the wellbore; however it would be able to monitor flow direction and tracers at the perforations. It could also be useful for examining the wellbore down hole and for following the effects of radioactively tagged wellbore treatments, such as corrosion and scale inhibitors on the casing. Technetium-99 would be a useful tag for such work, since it is readily available, easily inserted into corrosion and scale inhibitors, and has a suitable energy and half-life. Nondirectional tools capable of monitoring such low-energy radiation downhole are commercially available (Gadeken et al., 1989), and it should not be difficult to fit a collimator to such tools.

Anomalous background interference: Radioactive scale Background count rates in the borehole are normally due to the presence of n a t u r a l radioactivity on the ground. Another source of natural radioactivity t h a t has become increasingly important with the use of sea water for w a t e r flooding, is scale deposition in the borehole. The scaling is caused by the reaction of sulfate and carbonate ions with alkaline earth cations (Ca++, Sr ++, Ba ++, and Ra ++) to form insoluble scales. These cations are denoted as the group II cations in the periodic table. Radioactive scale can form wherever the concentration of these ions is high enough to meet precipitation conditions and wherever r a d i u m ions are mobile with oilfield brines. The secular equilibrium between the members of the natural radioactive series was discussed in chapter 1. Radium is a component of both the 238U and the 232Th series. Chemically, it is a member of the alkaline e a r t h group. When a solution carrying radium ions is present and scaling conditions exist for the other members of the alkaline earths, it will co-precipitate with them. The r a d i u m in the scale will s t a r t a new radioactive series. Depending upon the local concentration of radium in solution, and time for the new radioactive equilibrium, the scale can easily reach radioactivity levels of hundreds of API units (Smith, 1987). Scaling conditions usually occur at the wellbore when two incompatible waters meet, or when a change in pressure or t e m p e r a t u r e lowers the solubility

Downhole Tracers

333

of the precipitating species. Not all scales of this type are radioactive, nor is all anomalous radioactivity in the borehole due to scale. When radioactive scale is diagnosed, it can be removed by acidization, if it is predominantly a carbonate scale. Some of the sulfate scales are, however, difficult to remove by chemical t r e a t m e n t and m u s t be removed mechanically. Legal problems are associated with removal of the scale if it is brought to the surface. N a t u r a l l y occurring radioactive materials (NORM) in the North Sea, Western Europe, the United States and Canada, and m a n y other parts of the world are controlled by essentially similar regulations, which are discussed further in chapter 8. The presence of scale is not necessarily bad, since scale formation can also serve to seal off a water producing formation to increase the productivity of the well by decreasing the water cut. The presence of barium scales down hole can also be detected by the fast neutron reaction 138Ba(n,2n)137mBa, described earlier in the discussion of a proposal (Jordan et al., 1988) for locating mud behind casing.

O T H E R GAMMA-RAY T R A C E R M E T H O D S Several downhole processes are important to the operation of a well, including the placement of cement, mud, and completion fluids, and the displacement of some of these by other materials. The displacement process is assumed to be piston-like, although leaks behind casing show that this is not always true. Very few tests have been reported on how these materials are displaced downhole. An exception to this is the cement study reported below.

Cement behind casing Cementing is one of the important downhole procedures. Tracer methods for monitoring cement, usually restricted to marking a cement position, are rarely applied to the entire process down hole. An example of a continuous method for following cement placement down hole was given in a recent paper by Kline (1986). This paper also describes the method used for tagging the cement with tracer and the procedures used to monitor it down hole. This tracer method was used to measure cement coverage behind casing. Assuming a piston-like displacement of mud by cement, it is also a monitor of mud displacement. Short-lived tracers were used to tag the cement as it was pumped down hole. To ensure uniform tracer injection under variable cement flow rates, the cement flow rate was monitored by an accurate magnetic flow meter. The meter output was fed to a proportioning controller t h a t drove a laboratory chrom a t o g r a p h y pump to inject the required amount of tracer solution into the cement stream. To avoid contamination with radioactivity, the pump handled only oil. A floating piston was used to separate the pumped oil from the aqueous

334

Chapter 7

tracer solution. The tracer solution was forced out of the shielded container by the oil and mixed with the cement at the T-section. A schematic of the procedure is shown in Fig. 7.19. The cement was tagged with one of three gamma-emitting tracers: the 8.1-day half-life 1-131, the 2.7-day Au-198, or the 1.5-day Br-82, and was monitored with an energy sensitive gamma-ray tool immediately after cementing. Injected tracer levels of about 0.1 mCi/bbl gave enough signal down hole to be easily monitored by the tool by means of energy discrimination.

From pump truck

Magnetic flowmeter

Cementing line injection joint

~ ~

s

I I

,

Pump

, I ,

circuit

I

control

To cementing head

Wa~rC~Shielded 'dL~ tracervessel

Injection pump

Oil reservoir

Figure 7.19. Schematic of constant tracer injection system for tagging cement The physical model used for these tests assumes a radial, horizontal cross section of the dimensions shown in Fig. 7.20b. The bypassed mud is assumed to be in the outer layer in this model. The gamma signal, I, from the tagged cement is given by: r(1)

I=

K/

Jr(2)

e'~rdr r

(7.15)

where r(1) is the outer radius of the cement and r(2) is the outer radius of the casing. The gamma-ray absorption as a function of radial distance was measured experimentally using tagged cement poured around sections of casing into molds of different diameters. The absorption due to the casing and the fluid inside the casing are constant and are lumped into the constant, K, in the equation. The

335

Downhole Tracers

results of these measurements are shown in Fig. 7.20a. The method was applied in an experimental program of ten wells. Fig. 7.21 is a schematic of the cemented annulus in one of these wells. In this figure, the superficial cement radius calculated from the tracer log is plotted along the profile obtained from the 4-arm caliper prior to r u n n i n g casing. The same profiles are run on both sides of the center line. Arrows are used to indicate where the cement radius is smaller than the caliper radius and the cement does not completely fill the annulus, leaving a void. For most of the wellbore, the cement annulus is greater t h a n the caliper radius, indicating t h a t the borehole was washed out from post-drilling operations. From SP logs, the greatest enl a r g e m e n t occurs, as expected, in shales or shaley sands and the least in permeable sands; hence it is probably not an artifact due to radioactive filtrate. Various procedural variations were tested during the program, but no superior methods were found, given good cementing conditions. The author concludes t h a t poor cement zones are not directly related to mud displacement at normal levels. A paper by Smith and Gadeken (1990) used the change in the photoelectric to Compton ratio with distance to analyze the data reported above and verified the results reported by Kline. Both of these methods assume t h a t the tracers are radially uniform, since the detectors are nondirectional. Recent development of a directional detector, reported earlier in this chapter, would provide a useful way of determining how radially the cement is distributed.

1.0

>..

.0=

0.5

0.0 2.75

3.50

5.00

'

. . . .

6.50

by-passed mud

Radius, inches a. G a m m a response

b. Model

Figure 7.20. Cylindrical model showing gamma absorption curve

Chapter 7

336

Cement radius sCaliper

radius

TOP-s~f4cement

SP log

Float collar 4628

Figure 7.21. Calculated cement radius in typical well Well tracer method

Channels behind the casing that are accessible to the wellbore are often detected by the response of the tracer-loss log (Schlumberger, 1973) used in injectivity logging. This is described in greater detail in the section below on production logging. Channels behind casing can always be monitored by injection of water containing a tracer whenever channeling from some zone is suspected.

PRODUCTION LOGGING Production logging uses gamma-emitting tracers and a wireline g a m m a tool to monitor the depths at which fluids are injected or produced in the borehole. Most of the work reported is concerned with fluids injected downhole for secondary or tertiary recovery methods. The purpose of logging is to provide a flow profile t h a t characterizes the flow distribution of these fluids at the borehole face and, presumably, indicates how they move through the formation. These are single-phase injections except for steam, which for tracing purposes can often be treated as two independent single phases.

Downhole Tracers

337

Production logging should cover fluid production downhole as well as injection. Downhole production logging is often more complicated for two reasons: 1) it usually involves at least two and often three phases, which can be difficult to decipher; and 2) disposal of the radioactive tracer produced at the surface can be a safety and regulation problem. As a result, relatively few produced fluids are monitored. Most production logging monitors only the injection of fluids into the formation. At this writing, very little logging of produced fluid has been reported; however there are some interesting exceptions. In at least three cases, production wells were monitored through the annulus of rod-pumped wells (Simon and Keely, 1969; Petovello, 1975; Hammack et al., 1976) using radioactive tracers. All reported simultaneous use of multiple logging m e a s u r e m e n t s , including fluid density and temperature, as well as other logs. The two-phase flow regime was decoded by combining the tracer survey with the densitometer evaluation. The data were used to determine fluid production as a function of phase and position. The densitometers described were based on g a m m a absorption using a single g a m m a source. In principle, separate tracers can be used to monitor each produced phase, providing the phases flow separately and can be accessed by the tracer. No work of this nature has been reported.

Water injection logging The use of tracers for following the injection and production of fluids in and out of the formation has been critically reviewed in a recent SPE monograph on production logging (Hill, 1990). The author describes the tools; discusses the operational details, procedures, and log interpretations; and compares the use of tracer techniques with other competitive and supportive logging techniques. The following will briefly summarize sections in the monograph that refer to the use of tracers for this purpose. Twenty-five references are given. One of the principal uses of tracers in the wellbore is in the area of production logging. The widest application has been for monitoring the downhole injection profile of water injection wells. In this application, a pulse of radioactive tracers is added to the injected water stream from a tool on a wireline down hole. As the w a t e r moves down hole, the movement of the tracer pulse in the borehole is monitored by r a d i a t i o n detectors on the tool. Two kinds of tracer-logging procedures are commonly used to monitor the injectivity profile: the tracer-loss log and the velocity shot log. In both of these procedures, 1-131 tagged iodide solution is the commonly used tracer material. It emits easily measured g a m m a radiation; because of its widespread use in medicine, it is cheap and readily available; and the short (8-day) half-life reduces the possibility of contamination problems. A schematic of a generic wireline tool used for production logging is shown in Fig. 7.22. It contains a tracer injector that can be controlled from the surface and

Chapter 7

338

either one or two gamma detectors that are normally NaI(T1) scintillation detectors. There may also be a collar locator. Other logging tools such as temperature monitors are frequently added. The length of the tool and the arrangement of parts are variable.

1 3/8" O.[

J, rracer ~jector

41/2'

Motor Detector No. 1

{I

E

N,

, - Casing Collar Locator

,---Detector No 2

Figure 7.22. Wireline tool for production logging TRACER-LOSS LOG In this procedure, the tool is lowered down hole, a single pulse of tracer is injected into the water stream, and the fate of the pulse is monitored as it moves down hole. The tool used is similar to the one shown in Fig. 7.22 except that only one detector is required for the tracer-loss log. The tracer pulse is injected 20 to 30 ft below the tubing tail but well above the perforations. The pulse is mixed into the injection water by passing the tool through it several times. The tool is then dropped below the pulse and the gamma intensity measured as it is logged up through the tracer pulse. At the

Downhole Tracers

339

start, the tracer pulse is logged several times while the pulse is still above the perforations to establish a base for 100 percent flow. This procedure is repeated as the pulse moves down hole. A gamma-intensity peak is recorded for each downhole location. A maximum of about 15 passes can be made before the tracer slug dissipates or becomes stationary. Injection of tracer is preceded by a g a m m a log of the well for background subtraction and for identifying flow behind casing. A typical tracer-loss log is shown in Fig. 7.23 (Hill, 1990). In this figure, the well schematic is in the center, the logs of the tracer pulse at different depths are on the left of the well, and the time each log was taken is shown on the right. A total of thirteen logs were taken over a depth of 100 feet. The log is analyzed by assuming that the total flow rate into the well is constant, and t h a t the tracer loss is directly proportional to the water loss. The amount of radioactivity, A, in the measured pulse is given by: A = ~Cdv

(7.16)

where C is the tracer concentration in activity per unit volume, and v is the volume. The log, however, monitors the radiation, R, emitted by the pulse as a function of depth, 1, rather t h a n its concentration, C, as a function of volume, v. Since counting conditions and dimensions are the same throughout the borehole, the radiation emitted should be proportional to the concentration: A = ~Cdv = k~Rdl

(7.17)

where k is a proportionality constant. The area under the log curve is simply the integral ~Rdl. The area, A100, under the tracer peaks logged above the perforations, therefore, represents the amount of tracer injected at zero tracer loss. It is equivalent to 100 percent flow, Q100. When the tracer pulse moves past a permeable zone, it loses tracer to that zone in proportion to the loss of water. The area, A1, under the curve in the downstream log is a m e a s u r e of the activity remaining in the pulse at that depth. Each log area, AI, reflects the remaining water distribution as it moves down the wellbore past succeeding zones, so t h a t in principle, AlOO = ~ i - 1 - Ai. The ratio of Ai to AlOO, the area at 100 percent, is taken to be the fraction, F, of flow remaining at that position:

F

-

Qi Ai QlOO - A 10o

(7.18)

The distance between tracer-peak locations in the tracer-loss method tends to be large, so that the depth resolution of the log is relatively poor. Resolution also suffers when the tracer slugs measured are opposite fluid entry zones, since this skews the assignment of depth to a flow rate. This method also depends upon complete mixing of the tracer pulse with the fluid in the wellbore, which may be r a t h e r poor at the beginning. Other problems arise because of 1) distortion of the tracer pulse by tool passage and 2) incomplete mixing of the slug with injection

340

Chapter 7

water. As a result, it is considered to be primarily a qualitative method. Resolution can be improved somewhat by timing each tracer pass and using the velocity calculated to improve the resolution. Further details are given in the monograph.

.:,,,

~~__

|

5200

time

run #

0:00

1

0:29

_.....--

1

i

,..

2

1:06

3

1:38

4 5 II

2:54

6

7 5300~

4:28 11:32

!

I

i

19n_ 13

I

I

Figure 7.23. Tracer-loss log A possible variant of the tracer-loss procedure would be to use a tagged, water-permeable particle of neutral buoyancy as a tracer. The tracer pulse would be composed of a mixture of tagged particles instead of a tagged solute. The log areas discussed above would still measure the remaining water flow; however the flow entering each porous zone should be marked by the deposition of the tagged particles, assuming that the particles are larger than the pores. Since they are permeable to water, they should not cause a significant resistance to flow. A gamma log of the wellbore after the test, under these flow conditions, should be a direct monitor of the distribution of particles and, hence, of the flow entering

341

Downhole Tracers

each zone. In principle, ion-exchange beads of suitable density would be ideal for this purpose; however, there is always the danger that such particles might stick on other wellbore surfaces and give false information. A major application of the tracer-loss method is identification of flow behind casing. This is evidenced by a secondary peak that moves independently up or down the well as shown in Fig. 7.24 (Schlumberger Ltd., 1973). Here, a channel between sands 3 and 4 results in an upward flow of a pulse monitored by the six sequential logs, t l through t6, shown on the figure. A channel is also evident between sands 2 and 1, resulting in a downward movement of the pulse.

Timed gamma ray surveys

Well sketch

tl

12

t3

t4

~

ffi

I

Sand -3

Sand "2 Channel Sand

Figure 7.24. Channel flow identification by tracer-loss log

342

Chapter 7

=.! t

tc'

.-

2 seconds

Figure 7.25. Velocity shot log detection interval VELOCITY SHOT LOGS In the velocity shot procedure, a tracer pulse is injected into the flowing stream from the logging tool positioned down hole, illustrated in Fig. 7.22. The tool requires both detectors shown here. The velocity of the moving w a t e r is obtained from the transit time of the tracer pulse between the two detectors mounted a fixed distance apart. A typical response at the two detectors is shown in Fig. 7.25 (Hill, 1990). Here, Atpp is the transit time for the pulse m e a s u r e d from the two response peaks, and Atle is time between leading edges. This log assumes a constant wellbore diameter, true for cased holes, and a constant flow rate between detectors, generally true if there is no fluid loss between the detectors. If a fluid exit occurs between the detectors during the tracer passage, the depth resolution of the log is limited to twice the detector distance. Corrections for variations in wellbore diameter and for fluid exit between detectors are discussed in the monograph. Analysis of the data is based upon the inverse relationship between flow rate, Qi, and transit time, ati. If the total flow rate (above the perforations) is QlOO and the equivalent transit time is At 100, then: Qi QlOO

-

Atloo Ati

(7.19)

The time interval between peaks can be obtained using several different landmarks, as shown in Fig. 7.25. The choice of landmarks depends more upon ease of characterization t h a n differences in operation. The usual choice is the peak m a x i m u m . Most choices are equivalent with known corrections. Depth resolution can be improved by decreasing the distance between detectors. One way to do this is to use overlapping intervals where the tool is moved a distance

343

Downhole Tracers

less t h a n the detector spacing. This improves the resolution to twice the interval for which t r a n s i t times are determined. A comparison of the results obtained using the interval method vs. the standard method is shown in Fig. 7.26 (Hill, 1990). Solid lines in the figure show the result obtained using the standard method. Dotted lines show those from the interval method. In the case illustrated here, the resolution improved from 12 ft for the standard method to 4 ft for the interval method.

% Flow Entering Interval 100 f

50

Depth (ft.)

% Total Flow 50

0 5020 Q

26

5030

I

r'"

IO0

OOO~~ .........................

15

5040

Figure 7.26. Comparison of interval with velocity logs A major problem in log interpretation arises when the flow changes from turbulent to laminar. In turbulent flow the pulses are sharply defined and the peaks easily characterized. When the flow becomes laminar, the pulses become very dispersed, and landmarks suitable for timing pulse arrivals are difficult to define. An example is shown in Fig. 7.27 (Hill, 1990), where the second detector shows no peak. In such cases, tangency to the baseline can serve as a timing landmark. Other procedures are discussed in the monograph. The m a n n e r in which the tracer was injected can also have a significant effect on tracer dispersion in laminar flow. The velocity shot log is the preferred procedure for injectivity profiles because of its superior depth resolution. In laminar flow, this is probably the only current way to measure low flow rates in a well. It is sensitive only to flow in the borehole and cannot detect flow through channels outside the casing. The tracer-loss log,

344

Chapter 7

on the other hand, has poor depth resolution but is sensitive to flow in channels outside the borehole. Other logs, such as temperature and flow meter, are capable of making similar measurements and can be run simultaneously, mounted on the same tool. Running a combined log in such m e a s u r e m e n t s serves to increase not only the confidence level in the measurements but also the breadth of the well response.

Lower detector response

Upper detector response T

i?j

T

/

.._l,

Figure 7.27. Velocity-shot in laminar flow

Tracer dilution logging The tracer dilution method for measuring flow is described in chapter 2, and its application to monitoring flow in pipelines, rivers, and other bodies of water is discussed in chapter 8. The tracer-dilution method depends upon the conservation of tracer and requires adequate mixing of injected tracer with the flowing fluid. In pipelines and bodies of water, good mixing depends to a large extent upon the vagaries of flow. To ensure that the injected tracer is sufficiently mixed with ambient fluid, the tracer injection and the detector are usually spaced a relatively large distance apart. This is not required if good methods are available for mixing the tracer into the moving fluid. The tracer dilution method for monitoring fluid flow in the borehole differs from its other applications in that a wireline tool contains both the injection and the measuring device, unlike monitors for pipeline flow where the detector and the injector are both outside the pipe. Proper mixing can be ensured by using a turbine or fan on the tool to mix the injected tracer with the ambient fluid in the

Downhole Tracers

345

wellbore. Both chemical and radioactive tracers can be used with this method, given a suitable detector for the chemical tracer used. For radioactive tracers, the large a n n u l a r volume scanned by the detector for the mixed tracer reduces the requirements for total mixing of the injected tracer. In effect, the detector m e a s u r e s the radiation from the flow-weighted average tracer concentration. Incomplete mixing can be used to determine flow by isotope dilution, providing a proper concentration m e a n can be found. This has been d e m o n s t r a t e d analytically (Barry, 1978) and experimentally (Hull, 1957) under certain circumstances. Incomplete mixing allows the close spacing between detector and injector, required for m e a s u r i n g flow in the borehole with high depth resolution. T r a c e r dilution logging can be done using either a pulse injection or a continuous (constant rate) injection of tracer. The two methods are discussed below. PULSE METHOD Although the tracer loss log discussed earlier is a pulse method, it is not a tracer dilution log, which is based upon the conservation of tracer, since tracer is not conserved in the tracer loss log, where loss of tracer is proportional to the loss of injected water. In the pulse dilution method, a pulse containing a known a m o u n t of tracer, A, is injected into the borehole from a downhole tool, where it is mixed with the injection (or production) fluid. The concentration, Co, of the diluted tracer pulse transported in the borehole by the injected or produced fluid, is monitored as it passes a detector mounted on the tool. The area, ~C(t)dt, under the concentration vs. time curve, and the total amount of tracer injected are used to calculate the flow rate, Q, in the borehole at t h a t depth. As shown in chapter 2, this is given by: A Q = j C ( t ) dt

(7.20)

The simplest configuration for such a wireline tool is shown in Fig. 7.28. It contains a pump capable of injecting a fixed volume, Vo, of tracer on demand, a t r a c e r solution of known concentration, Co, and a detector d o w n s t r e a m t h a t monitors the diluted t r a c e r concentration as a function of time. Auxiliary mechanical and electronic control and monitoring equipment are also needed. The tracer solution is dispensed through the counting chamber as a pulse of fixed size by an intermittent, single-stroke pump, e.g., a syringe pump, which empties the counting chamber at a stroke. The mixing device needs only to provide lateral mixing of tracer with the injection fluid in the annulus between the tool and the casing. For this purpose, a wide variety of pumps for mixing and circulating fluids can be used. The tool operates on a wireline and should be able to m e a s u r e flow rate directly at any point in the borehole, regardless of its inclination, flow regime, or flow rate, except, as for any t r a c e r method (Hill, 1989), at exit or entrance flow locations. A second detector can be added to the

346

Chapter 7

tool to serve as an indicator of equilibrium or to allow the velocity shot method to be used. This is a discrete method t h a t m u s t be pulsed at intervals, as the tool is moved up or down the wellbore, to log the flow profile in the well. It would be particularly useful for monitoring very low flow rates as well as for monitoring the effectiveness of such wellbore t r e a t m e n t s as temporary or p e r m a n e n t flow diversion. The resolution of the log with respect to depth is limited by the distance between source and detector required for radial mixing. In common with all the methods for monitoring flow down hole, it may not give accurate readings when fluid exit or entrance points lie between the detector and the injector.

Wire

line-~~ I

,/

| II

N

Tracer detector

Tracer I1------- solution

Tracer ~ , l l ) I injectioni "1 I~1 pump

Tracer circulating pump

Figure 7.28. Wireline tool for tracer dilution pulse logging Addition of a second detector at a fixed distance from the first lets the tool function both in the pulse dilution and in the pulse velocity mode. This has several advantages: it permits a cross check of flow rates for a known flow diameter; a measure of diameter when it is unknown; and, for the pulse dilution method, a check on mixing equilibrium by comparing results at two positions.

Downhole Tracers

347

Chemical tracers

M a n y i n s t r u m e n t a l methods are suitable for monitoring the concentration of the diluted chemical tracer as it passes by, including a wide range of optical and electroanalytical methods. The mass of injected tracer, A = C o x V, is known and fixed in the tool. The flow rate, Q, is obtained from Eq. (7.20). Most chemical detectors measure tracer concentration, so t h a t the area under the concentration versus time curve at the detector, ~C(t)dt), is readily obtained by a s t a n d a r d integrator to yield the flow rate at that depth: CoVo Q = ~C(t)dt

(7.21)

This is a good method for monitoring single phase injection of production profile with chemical tracers and detectors if the fluids are reasonably clean, the usual case for injected fluids. Additional mixing may be required for m a n y chemical detectors t h a t sample only small w a t e r volumes. The larger the volume sampled by the detector, the less critical additional mixing becomes. Radioactive tracers

The procedure above differs for radioactive tracers, only because the radiation detector does not measure concentration directly but monitors the radiation, R(t), emitted by the tracer in the neighborhood of the detector. All s t a n d a r d counting systems contain a "scaler" t h a t integrates the radiation versus time curve to give a total n u m b e r of counts for the time interval. R(t)dt = N is the net n u m b e r of counts collected from the pulse after it has passed the detector and the background has been subtracted. The integral, ~R(t)dt, of the radiation pulse can be converted to t h a t of the concentration integral, ~C(t)dt, if both the counting geometry and efficiency are known for the a n n u l a r distribution of tracer about the detector. For a centralized tool in a cased hole, these are essentially independent of position. Hence, the detector can be calibrated by measuring the count rate when the tool is placed in a section of borehole containing a known concentration (activity per unit volume) of the tracer. This can also be done in the laboratory, calculated numerically, or some combination of these methods m a y be used. Eq. (7.20) can now be rewritten as: AK Q = ~R(t)dt-

AK N

(7.22)

where A is the amount of injected activity, K is the calibration factor in counts per unit time per microcurie (or other activity unit) per unit volume, and R(t)dt = N is the area under the flow curve. Once a tool has been calibrated, it will give the local flow rate directly from the net counts m e a s u r e d down hole. Conversion of the calibration constant to tracer pulses of different energy and a n n u l a r spacing should be a straightforward calculation.

348

Chapter 7

The total (net) count, N, from the passage of the diluted pulse is monitored by a scintillation detector mounted on the tool at a distance from the injector and s u m m e d by the counter. Since it monitors the entire volume of the annulus, small heterogeneities in mixing will have little effect. Normally the concentration of the tracer solution and the volume of the tracer slug injected are fixed and the size (mass) of the injected pulse is known in advance, so these need not be measured down hole. For chemical tracers, the pulse size is difficult to measure directly down hole; however, for radioactive tracers the total activity, A, is easily monitored downhole by a 4n counter. This activity will usually be in the millicurie region and can be monitored by an ion chamber, a very stable counter t h a t maintains its calibration over long periods of time (years). While such measurements are not necessary for the method, they can provide a simple check on the tool operation. CONTINUOUS METHOD The second method for measuring flow rate by isotope dilution is the continuous (constant rate) injection method. Here, a tracer solution of known concentration, Co, is injected downhole at a constant rate, Qo, into a m a i n s t r e a m of unknown flow rate, Q. The tracer will mix with the mainstream and at equilibrium will have a concentration, C, as monitored downstream at a point where the tracer is well mixed with the fluid. A single m e a s u r e m e n t of the final (equilibrated) concentration combined with the known initial tracer concentration and injection rate enables us to calculate the flow rate, Q, of the m a i n s t r e a m , as shown in chapter 2 by: Q = Qo

Co-C C

(7.23)

In conventional pipelines and in monitoring flow in bodies of water, the analyses are done on collected samples. For the downhole tool, the flowstream is monitored continuously without the need for samples. For most cases, the injected concentration, Co, will be so much greater than the diluted concentration, C, that Eq. (7.20) reduces to: Q=

Q~176 c

(7.24)

The tool shown in Fig. 7.28 can be used for the continuous method by changing the tracer injection from intermittent pumping at a known volume of stroke to pumping at a constant rate. A variety of flow controllers, capillary leaks, and rate controlled pumps are available commercially for constant rate injection of tracer solutions. C h e m i c a l tracers

Chemical tracers are well suited to this method since the detectors monitor the diluted tracer concentration directly. The product of the constant tracer

Downhole Tracers

349

injection rate, Qo, and the initial tracer concentration, Co, is the constant mass flow rate, so t h a t the flow rate, Q, of the stream is inversely proportional to the diluted tracer concentration, C, from Eq. (7.24) above. Hence, a log of reciprocal concentration versus depth is a relative flowrate profile of the well. In m a n y cases, this is all t h a t is required. This can also be used to check the system by comparing the sum of all individual flows to the total flow. The tracer capacity of a downhole tool is limited by the maximum tracer concentration and by the tool's limited volume, hence detectors of a wide dynamic range are needed. Radioactive tracers

For radioactive tracers, the same situation holds, except t h a t the detector monitors the radiation emitted by the tracer solution in its neighborhood r a t h e r t h a n the tracer concentration. As in all isotope dilution methods, the injected tracer m u s t be equilibrated by mixing with the flowing fluid before it is monitored by a detector, usually a scintillation device, mounted on the tool at a fixed distance from the injector. At equilibrium, this entire volume is filled with diluted tracer at a fixed concentration, C, while the detector measures only a fixed count rate, R. The calibration constant can be obtained experimentally by measuring the radiation level for a known concentration of tracer in the borehole or the laboratory, or by calculating it numerically from known nuclear and material data, so that Eq. (7.24) can be replaced by: Q-

QoCo L kR - R -

(7.25)

where k is a calibration constant expressed in activity per unit volume per count rate, ~Ci/IJcpm. Once derived, such constants are easily extended to other energies and well diameters. Since activity flow rate QoCo is constant, the log of reciprocal count rate versus depth is the injection (production) flow-rate profile of the well, as shown in Eq. (7.25) where L = QoC o/k is a constant. This may be all that is needed, since the flow profile can be calibrated for individual depths by matching the sum of all the individual flowrates to the known total injection or producion rate of the well. PRODUCTION LOGGING FOR GAS: FIELD STUDY The only application of tracer dilution logging as a means of monitoring a production profile was recently reported for gas production using a nonradioactive tracer (Bennett et al., 1991). The major difficulty with monitoring production profiles in producing oil wells is in analyzing multiphase flow. In the case of wells producing a single phase such as gas or oil, this problem disappears. In this procedure, the authors describe a tracer flow meter in which the gas production profile is determined by measuring the dilution of an injected tracer by wellbore gas. This is the only reported instance of the use of a nonradioactive tracer for production logging.

350

Chapter 7

This is a tracer dilution method rather than the usual tracer velocity method used for production logging in the wellbore. As a result, it measures flow rate r a t h e r t h a n linear velocity. This is a much more desirable m e a s u r e m e n t for managing a well and also has the advantage of reducing some of the variables in production logging. It is independent of changes in well diameter. The tool, shown in Fig. 7.29, has a 3-in. diameter and a length of 91/2 ft. It is made up of three components: a continuous tracer injector (using a controlled gas leak), a mixing section for mixing the tracer with the gas from the borehole, and a concentration-sensitive tracer detector containing its own mixer, downstream of the injection mixer. Mixing was induced by two pumps in the logging tool, one of which mixes the injected tracer thoroughly with the produced gas in the wellbore, while the second passes the mixed sample through the measuring chamber. It is interesting to note t h a t such a method could also be used to count betaemitting tracer gases in a gas counter downhole. The resolution of the tool is limited by the spacing between injector and detector: in this case, 45 in. The tool is operated by lowering (or raising) it at a constant logging rate. As the tool moves down the well, the flow remains constant due to the steady upward flow of gas, and so does the concentration, C. Depending upon the logging rate, and the rate at which tracer mixes within the new gas stream, there can be a sharp peak when it reaches a flowing zone, since additional gas suddenly flows

14I-"

14

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45"

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Flow controller

!-~-[~

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[~l:tIill T

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Figure 7.29. Gas tracer flowrate meter

Solenoid

Computer

q

.j .- =

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convertel

Downhole Tracers

....

351

oon

AJ

9149

/1

9

9

.,,o

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,

9

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.

.

.

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4000

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Figure 7.30. Gas production rate profile from tracer log between tracer source and detector. By differentiating both sides of Eq. (5.16), it can be seen t h a t the change in flow rate dQ,/dt, produces a proportional change in the concentration, dC/dt: de C dQ dt - (Q-QO) dt m

(7.26)

This is of limited quantitative use because of the incomplete equilibration of tracer with new gas in this short time interval. The tool was tested in a Devonian shale gas well in Kentucky and r u n in 41a-in. casing with 17 perforations shot in the test interval. The tool was lowered down hole on a wireline and the flow rate of the gas, Q, at a given depth was det e r m i n e d from the change in injected tracer concentration in accordance with Eq. (7.20). The logging rate was 6 ft/min. The flow rate in this well is low with individual flow zones varying from 1.0 to 9.2 MCFD. Passage of a 3-in. diameter tool through the 4 l~-in, casing required correction of the relative velocity of the gas both because of the tool's displacement and its logging speed. The results of the log are shown in Fig. 7.30. This figure shows both the tracer log and a t e m p e r a t u r e log t h a t was r u n concurrently. Spinner logs and sonic gas-detector logs were also reported. Only the tracer log detected all the flowing perforations and gave quantitative m e a s u r e m e n t s of mass flow from the responding zones. The sum of the flows from the tracer survey showed reasonable agreement with total flow from the well. The

352

Chapter 7

small circles above the graphs show the nominal perforation positions. The flow rates in this well are so low that the laminar flow would have made a conventional pulse velocity log difficult to interpret. The particular tracer used in this work was not named, but any gas tracers for which a suitable detector exists should be adequate. The detector used was described as electrolytic without giving details but apparently is sensitive to a sulfur-containing gas. An electron capture detector would be suitable for such gases as SF6.

Production logging with isotope generators The use of radioactive tracers for monitoring flow originating down hole carries with it the chance of contamination at the surface. In recent years, environmental awareness has limited such usage more than reason would normally dictate. The contamination problem can, however, be entirely avoided by using short-lived tracers that largely decay before reaching the surface. The only practical way that short-lived radioactive tracers can be available for measurements down hole is by an isotope generator. Most measurements of fluid movement down hole are done over short intervals of depth and do not require long-lived isotopes. These measurements can be done with relatively low-energy radiation, since the radius of measurement is only a few inches of formation fluid in the borehole. Any of the production logging procedures discussed earlier in this chapter, including the velocity shot and isotope dilution by either the pulse or continuous method, can be done using an isotope generator. Higher tracer concentrations can be generated down hole than can conveniently be placed there by conventional tracers, important for measuring very high flow rates. The highest resolution log, using isotope dilution, is obtained by the continuous tracerdilution method. An isotope generator can be stripped in a continuous mode producing tracer at a constant rate. This could be hazardous if conventional radioactive tracers were used for monitoring produced fluids, but the short halflife of the produced tracer eliminates the contamination problem. AVAILABLE ISOTOPE GENERATORS Isotope generators are available with daughter half-lives ranging from fractions of a minute through many hours or more. Currently, all commercially available generators are medical products not designed for downhole use. Table 2.1 gives a partial list of commercially available generators. A half-life of a few minutes would be sufficient for most fluid velocities measured down hole. The 137Cs/137mBa (Cs-Ba) generator, which yields the 2.6-min 137mBa daughter, would be ideal for most production logs. Cesium-137 is widely used as a gamma source for density logging down hole. The emitted gamma ray is, however, entirely due to the daughter activity in equilibrium with it. Cesium-137 decays to

Downhole Tracers

353

Ba-137m by beta decay with a 93 percent probability and a half-life of about 27 yr; no g a m m a s are emitted. Barium-137m decays to stable Ba-137 by the emission of a 0.66 MeV g a m m a with a half-life of 2.6 min. The decay schemes have been shown in Fig. 1.5 and are written below in the two stages: 1) 137Cs --> 137mBa § ~, T1/2 = 27 yr 2) 137mBa --~ 137Ba + 7 (0.66 MeV), T 1/2 = 2.6 min This generator and a number of other generators for short-lived isotopes have been described in the literature (Spytsin and Mikheev, 1968) and have been used (Turtiainen, 1986; Newacheck et al., 1957; Gwyn, 1961; Kugener et al., 1972; Arino et al., 1973) for monitoring flow in pipes. The technology for preparing isotope generators is well known. As discussed in chapter 2, most isotope generators are simply composed of a tubular column containing a parent isotope firmly fixed upon a substrate material. The daughter is eluted from the generator, as needed, by passing a small volume of solution through the column. It should be simple to adapt such a generator for use at reservoir pressure and temperature. A shortlived isotope such as Ba-137m in secular equilibrium with its p a r e n t can be eluted at a constant rate. The equations relating the buildup time and decay of any tracer pair were discussed in chapter 1. The large number of pulses available from such an isotope generator allow higher depth resolution from tracer pulses using either the velocity shot or the isotope dilution method. In the case of the isotope dilution log, resolution is limited only by the distance needed for radially mixing the tracer with local fluids at a given logging rate. Tracer can be eluted in either a water- or an oil-soluble form, depending upon the isotope, as complex ions of suitable solubility, allowing tracing of either produced oil or water down hole. In addition, cesium-137 is a relatively cheap and readily available isotope, so t h a t the cost of tracer used down hole is negligible. An isotope generator (ll3Sn/ll3mIn) for injectivity logging has been reported (Sun, 1991) but not as a downhole tool. The generator produces the 100-min halflife i n d i u m - l l 3 m daughter from l l 5 - d a y half-life Sn-113. This was milked at the surface to fill the tool with tracer as a substitute for 1-131. The 50 mCi (1,71 GBq) generator lasted about six months. A downhole generator could use a much shorter half-life daughter activity generated down hole. ISOTOPE GENERATORS FOR DOWNHOLE LOGGING The use of isotope generators for production logging has significant advantages in two areas: 1) safety in handling radioactive tracers in the field and in monitoring produced fluid without surface contamination; and 2) high-resolution injectivity and productivity profile logs over a wide range of downhole flow rates. A tool for doing production logging is shown schematically in Fig. 7.31. Such a

354

Chapter 7

tool can be operated in the tracer dilution mode, or as a velocity shot or tracer loss log, with few of the problems associated with handling radioactivity in the field.

i~---- Wireline 0 Eluent

NaI(TI) detector

,.q

_

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/, ll f

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Dilution tool Figure 7.31. Wireline tool for tracer dilution log using isotope generator The tool shown in Fig. 7.31 can perform the same function as those shown in figs. 7.22 and 7.28 for production logging by various procedures, although its internal construction is different. It is composed of four parts: 1) an isotope generator; 2) an elution pump operated either as an intermittent, pulsed, constantvolume injector or as a continuous, constant mass (activity) rate injector; 3) a mixing pump or fan to mix the tracer with the borehole fluid; and 4) a downstream detector. Addition of an optional second scintillation detector would also allow the velocity shot log to be run. The isotope generator is a shielded unit that can be mechanically set in place with conventional tools. Tracer is milked from the unit by passing a small volume of eluent through it by means of an elution pump. This pump has a dual function: 1) it transfers tracer from the generator, and 2) it injects the transferred tracer into the circulating pump for mixing with

Downhole Tracers

355

wellbore fluid. It can therefore serve as a fixed volume injector for the pulse dilution or velocity shot method, or as a constant-rate tracer injector for the continuous dilution method. The a m o u n t of tracer eluted for either a pulse or the constant-rate injection can be calculated from the radioactive decay laws discussed in chapter 1. An ion chamber is shown in the figure as an optional device for m e a s u r i n g the amount of tracer injected by the tool. It is not required but is relatively easy to do and provides a check on the operation of the tool. It also allows controlled variations in the size of tracer pulses to monitor unexpected flow situations. Tracer production logging is normally done with iodine-131 (half-life = 8 days) as a tracer. This isotope is widely and cheaply available because of its m a n y medical applications. It has, however, a very low maximum permissible concentration (MPC) for u n r e s t r i c t e d areas because it is preferentially accumulated in the thyroid. These production logs are usually handled by small, independent logging companies who provide a relatively cheap service. In normal field practice, the radioactive iodide solution is brought to the field in a vial and transferred into the injectivity tool at the site by hand, usually by means of a syringe. The isotope generator is a better way to handle the tracers because it avoids the problem of dealing with open radioactive solutions in the field. The generator can be installed in the tool as a safely shielded device t h a t has been preloaded in the laboratory. Until activated down hole, the tracers are immobile. Production logs can also be used to verify the success of downhole treatments, even those t h a t use tagged materials to monitor their placement. The tracer response from the production log can be separated from t h a t of the tagged treatment by energy discrimination, half-life, and radiation level. The short half-life of the tracers used in the production log prevent it from interfering with placement logs. The flow into or out of the treated zone is the only criterion for success of m a n y of these treatments. CONTINUOUS TRACER PRODUCTION FROM AN ISOTOPE GENERATOR For those generators operating in secular equilibrium, it is possible to strip tracer continuously from a generator at a constant rate. The m a x i m u m amount of activity obtainable by continuous elution can be calculated from Eq. (1.16) for secular equilibrium, which can be rewritten as: A2 = AI(1 - e x~-t )

(7.27)

Here, A2 = N2~2, is the radioactivity of the d a u g h t e r isotope, A1 t h a t of the parent, and ~2 the decay constant of the daughter expressed in consistent units. The m a x i m u m formation rate, R, for continuous stripping of tracer is obtained by setting the derivative of this equation with respect to time equal to zero. The result at t = 0 is given by the following expression, where ~.2 = In 2frl/2, as shown in Eq. (1.5):

356

Chapter 7

dA2 Alln2 R = dt = A1 ~2 = ~ TI/2

(7.28)

This is the m a x i m u m stripping rate of activity per unit time. The stripping rate depends on other factors as well, so that the true production rate is usually lower, but it is a reasonable guide. According to Eq. (7.28), the shorter the halflife, the higher the stripping rate; hence, for Ba-137m (tl/2 = 2.6 min), a 10 mCi source of 137 Cs would have a maximum stripping rate of 2.7 mCi per minute. For an activity having a half-life of one hour, the maximum stripping rate for a 10mCi source would be 120 ~Ci per minute. These are very high downhole activities. A barium-137m generator should be able to handle a very high range of flow rates. The continuous isotope dilution procedure described earlier becomes simple for isotope generators meeting these criteria, since the stripping rate fixes QoC o, the activity injected per unit time, once the system has been calibrated for activity injected per unit time as a function of the flow rate, Qo. This can be done in the laboratory and removes the need to monitor the injected tracer concentration down hole. The scintillation detector for monitoring the diluted tracer is already calibrated for the tracer used and the borehole size. Hence, the well can be logged continuously, since the tracer stripping rate, the net counting rate at the scintillation detector, and the calibration factors are all known. Eq. (7.21) for flow rate, Q, would now be expressed as: Q =

kl(Qo) L2 k2R = R

(7.29)

where k l is the calibration constant relating the tracer injection rate, Qo, to the activity injected per unit time, QoCo, and k2 is the calibration constant relating the measured count rate, R, from the diluted tracer to the tracer concentration per unit volume per count rate. Since Qo is preset and constant, the reciprocal of the count rate R is directly proportional to the flow rate by the constant L2, the log of 1/R vs. depth is a flow-rate profile of the well, and can be calibrated by matching L2 to make the sum of the partial flows equal the known total flow rate in the well, without knowing the other constants in the system. As discussed earlier, a second scintillation counter at a greater distance from the injector can be used to ensure that equilibrium mixing has occurred.

Gas production logging with an isotope generator The isotope generators heretofore discussed have been concerned with monitoring such liquids as water cr oil. Before leaving this subject, we shall also consider the use of gaseous isotopic tracers generated down hole. The only shortlived gas tracer available for logging gas wells is krypton-81m, which is produced by the decay of rubidium-81 by positron emission and electron capture. The p a r e n t isotope decays with a half-life of about 4.6 hr. This is a relatively short

Downhole Tracers

357

half-life for an isotope generator; however rubidium-81 is widely used in biomedical studies and as a result is available daily by air express at most locations (corrected for decay at time of delivery). It is also relatively cheap and very competitive in cost with such radioactive gas tracers as 85Kr and 133Xe. Krypton-81m decays with a half-life of 13 seconds, emitting a 190 keV g a m m a ray with an efficiency of 67 percent. It forms krypton-81, which has a half-life of 2.1 x 105 years. The generator is available at an activity of 10 mCi with the rubidium absorbed on a solid support. The Kr-81m is stripped by passing an inert gas t h r o u g h the generator. There are no other volatile products. Gas velocities are usually at least an order of magnitude higher t h a n water velocities, so the short half-life should be quite usable for logging gas injection profiles and for many gas producing formations. Operated as a continuous tracer dilution log, the m a x i m u m stripping rate of 0.5 mCi/sec should be more t h a n sufficient for most gas-logging needs. Generators currently available a r e designed for medical use r a t h e r t h a n downhole operation. A typical commercial generator is illustrated in Fig. 7.32; it consists of a tube containing the generator and a bypass. Humidified oxygen or air is passed through the generator to elute the generated 81mKr with an elution efficiency greater than 80 percent.

Injection logging of steam wells Steam injection is a very productive recovery method, and for extremely viscous oils it, may be the only recovery method. One of the purposes of injecting steam is to heat the formation and lower the viscosity of the oil in order to produce it by conventional means. The vapor phase (steam) contains most of the thermal energy. For this reason, it is important to know the quality of the steam actually injected into the formation and how this is distributed as a function of depth. Steam is composed of liquid water and steam vapor, which differ widely in density. It has long been known (Arnold, 1990) t h a t as steam flows t h r o u g h pipes, T's, and bends, its components segregate and the quality changes. We can measure steam quality at the surface, but we need to know its quality when it enters the formation down hole. Many years ago, when steam tracing was relatively new, service companies commonly used 1-131 tagged methyl and ethyl iodide, and even elemental iodine, for steam (vapor) tracing, and NaI solutions for water (condensate) tracing down hole. This practice continues to some extent, even though the unsuitability of the tracers used for steam (vapor) has long been known. This was discussed in chapter 6. It is only recently that the use of alkyl iodides as steam tracers has been questioned publicly (Nguyen et al., 1988; Griston, 1990). The best tracers currently available for following the injection of steam (vapor) down hole are the

358

Chapter 7

radioactive gases Kr-85 and Xe-131. The major problem with their use is the poor efficiency with which they are measured by downhole radiation detectors. Kr-85 decays by ~ decay with a half-life of about 10.6 yr, but only a small fraction of the decays (0.4 percent) are accompanied by gamma radiation (0.52 MeV). Xenon-131 decays by electron capture with a 5.3-day half-life, but it emits soft x-rays (81 keV) that are detected with poor efficiency because of absorption by the media, and shielding of the downhole detectors.

Air or _,, oxygenout ~

~.....~.,~

-" )~ Kr-81 gas generator

Air or oxygenin ,< "~, 3-way stopcock

Figure 7.32. Medical 81Rb-81mKr applicator

FIELD INJECTIVITYPROFILE MEASUREMENTS Injectivity profiles in steam injection wells require two-phase flow measurements. The procedures used are otherwise similar to those used for conventional injectivity profiles. The density difference between the steam vapor and the condensed water allow them to be treated independently. Some of the procedures currently in use in several thermal wells in California are described in a recent paper (Nguyen et al., 1988). Krypton-85 or 131Xe was used as a steam tracer and 1-131 tagged iodide ion ,:r used as a water tracer. The authors also showed that 1-131 tagged methyl iodide is not a suitable tracer for steam. The logging tool used in these procedures contains two gamma detectors a known distance apart, but no tracer injector. In a departure from conventional downhole production logging, the dual counter is first lowered to a desired depth in the well and the tracer pulse injected at the surface under nitrogen pressure. The transit time of the pulse between the two detectors a fixed distance apart is used to calculate the pulse velocity. This is repeated until the desired interval is covered. The fraction of total flow past the tool is given by the ratio of total transit time (for entire flowing zone) to transit time at that depth. The authors demonstrate the procedures required for three different locations of the tubing tail with respect to the perforations. Including a pressure gauge with the gamma

Downhole Tracers

359

tool m a k e s it possible to estimate downhole steam quality from the gas and liquid velocities, the steam flow rate and the downhole pressure. These d a t a together with downhole flow profiles were used to calculate a downhole h e a t profile. STEAM TRACER SURVEY EVALUATION A survey of procedures and results obtained from t r a c e r surveys of steam injectors (Griston, 1991) revealed t h a t the low radiation levels found in m a n y surveys led to inconsistent results. The two tracers used, 85Kr and 131Xe, produce g a m m a r a d i a t i o n with relatively little p e n e t r a t i n g radiation. The wellbore environment in a steam injector is severe, and logging tools are limited to a one- to two-hour exposure time to reduce the risk of failure. The NaI scintillation detectors are the most sensitive of the available detectors but are very limited in high-temperature operation. Geiger counters, depending upon the g a m m a - r a y energy, have only about 10 percent of the efficiency of scintillation detectors but are a p p a r e n t l y more stable under these conditions. The higher energy of the 85Kr g a m m a and the b e t t e r t e m p e r a t u r e stability of the GM counters have m a d e this combination the s t a n d a r d for most s t e a m t r a c e r surveys. The combination of low detected activity and high steam velocity results in low signals for tracer arrival at the dual detectors. In an example given by the author, a 50 mCi slug of 85Kr gave a barely detectable signal at the top detector, but was not detectable at the bottom detector, for a 0.1 sec sampling interval. Because of the low signal-to-noise ratio of these data, the conventional peak-topeak methods for determining transit time gave poor results. The a u t h o r proposes instead a procedure in which statistical errors for the background and tracer response are each minimized and the ratio of tracer to background radiation (signal-to-noise) is maximized. Using simulated data, an a u t o m a t e d tracer analysis method (ATAM) was set up for identification of t r a c e r arrival and t r a n s i t times. True tracer arrival time of the simulated pulse at each detector was found to be the time required to reach 50 percent of the m a x i m u m (average) radiation. The automatic feature was chosen to avoid subjective t r a c e r evaluation. D a t a were simulated using single phase conditions. Two-phase flow as experienced in the injection wells would add additional uncertainties to the calculated profile. The author discusses results of a tracer survey performed in several different steam injection wells. The results of a survey of a steam drive project near Coalinga, California, are shown in Fig. 7.33. The principal conclusion from these tests is t h a t the reliability of the tracer survey depends strongly on improving the poor signal-to-noise ratio. Repetition of the data t a k e n at each location is important to improve the statistics. The author proposes, as a standard procedure, that the transit time for three tracer pulses be logged at each location. A second source of unreliable tracer data is fluctuations in steam-injection conditions during the survey. He proposes t h a t a separator be

360

Chapter 7

placed downstream of the wellhead choke for monitoring injection steam rate, pressure, and quality. One of the reasons suggested for low tracer concentration is dilution by steam during the injection interval. If it required a second to inject the tracer pulse into steam traveling at a linear velocity of 100 ft/sec, the tracer pulse would be 100 ft long and of far lower concentration. A reduction in the required pulse injection time to 0.5 sec or less would increase its detectability.

10

00 ,

" '-

~1~0 lIB

II

84 0---

10

Top detector

A

Bottom detector

~1 i,~/i ~

'AAi

"~ 1so-I

I

11

1?

13

14

16

~

10

Top I detector I~ I~i

11

12

13

Bottom detector

l:t

15

Elapsed time, seconds

Elapsed time, seconds 10

Minimize

~m..===m

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At k

.1

.01

.001

Arrival time 8

9

10 11 12 13 Elapsed time, seconds

14

15

Figure 7.33. Steam injection survey

Krypton-81 steam injectivity profiles These are difficult field experiments, made more difficult by the poor signalto-noise ratio of the data. In reviewing the steam injectivity tests described

Downhole Tracers

361

above, it seems strange t h a t the downhole injection procedures of the velocityshot tests are not used for equivalent tests in steam injection. It is not clear why tracers for monitoring injectivity profiles for steam should be injected at the surface instead of at the tool down hole. There may be problems with injecting gas in a high-quality steam environment, although the physical problems, from this perspective, do not seem insurmountable. Presumably there is not enough dem a n d for this kind of work for the service companies to invest the time needed for development. A short tracer pulse from the injection tool should have a far better signal-to-noise level t h a n the stretched-out pulse originating at the wellhead. A tool designed around the 81Rb/SlmKr generator would be almost ideal for a tracer-dilution log for measuring steam injectivity profiles. The major problems are: 1) w h e t h e r a Kr-81 generator could operate at these temperatures, and 2) how to ensure adequate transverse mixing of the tracer across the annulus at these high linear flow rates. The NaI scintillation detector is a good detector for this 190 keV g a m m a radiation if protected from thermal damage, but the response could be improved by using walls both thinner and fabricated of material of lower atomic number. Steam wells are not very high-pressure wells, and the wall thickness of the tool could be reduced considerably without losing strength. The pulse-velocity method would only require fast pulse injection; transverse mixing would not be very important. INJECTED STEAM QUALITY High-quality steam for steam injection is produced in a generator and distributed to the field wells for injection. Depending on the properties of the distribution network, the quality and mass flow of steam delivered to the various wells vary widely, and the system can be sensitive to minor fluctuations in delivery. For this reason, as well as the needs indicated in the preceding paragraph on downhole steam surveys, it is desirable to monitor the steam quality delivered at the wellhead for each well. Methods have also been proposed for m e a s u r i n g steam quality at the formation face down hole (Zemel and Clossman, 1985) using radiation absorption. Injected steam quality can be measured at the wellhead by a number of methods. The low liquid (high void) fraction of high-quality steam makes it a difficult measurement. The high-attenuation cross section of water for thermal neutrons has attracted attention (Woiceshyn et al., 1986; Strom 1987) to the use of neutron t r a n s m i s s i o n as a sensitive quality monitor. There is also the added advantage t h a t steel pipe is relatively transparent to neutrons, so t h a t the measurement can be made at the wellhead from outside the pipe. A n e u t r o n densitometer was reported (Wan, 1991) for continuously monitoring steam quality through pipe. This is a portable meter t h a t has been certified for field use by the Atomic Energy Board of Canada and the Radiological H e a l t h section of the state of California. The densitometer consists of 1) a neutron source in a shielded moderator that produces a thermal neutron stream

362

Chapter 7

and 2) a thermal neutron detector that measures neutron transmission. The neutron source is located on one side of the pipe and the detector on the other side. The developers normalized the transmitted neutron fraction, N*, by relating it to the intensities when pure water and pure steam were present and t h e n correlating with steam quality for various conditions of pressure, mass flow rate, and pipe diameter. In order to use these correlations, the two-phase mass flow rate m u s t be known. By using a flow nozzle as a flow m e a s u r i n g device, the authors were able to determine both steam quality and mass flow rate.

BOREHOLE PROCESSES Procedures in which a tracer is injected at the surface and monitored as it returns to the surface to follow a procedure down hole are included in this group. This includes mostly drilling mud and completion fluids but is expanded here to include drill-bit monitoring. Mud water invasion

One of the few downhole processes monitored at the surface is the behavior of mud as it circulates through the borehole during drilling. The purpose of tracing the circulating mud here is to determine the mixing of mud water with formation water. This is important in two areas. In drilling cores, it is important to know how much of the cut core is flushed by mud water during the drilling operation in order to correct the fluid saturations measured from the core. During logging operations it may be difficult to know the salinity of the formation water because of mixing with mud water. This can be i m p o r t a n t for log interpretation. To monitor its presence, the drilling mud can be tagged with a suitable tracer t h a t identifies the drilling mud water. The majority of work in this area has been concerned with mud/water invasion in cores. The oldest of the tracers used for this purpose is tritiated water (Armstrong et al., 1961; Miller et al., 1975). It has been in use for more t h a n 30 years for this purpose. Tritiated water is advantageous for mud-water monitoring because the Dean S t a r k distillation used to separate the core fluids separates the tritiated water along with the core water. This can be analyzed by counting tritium in the water. A v a r i e t y of other tracers have also been used for tracing mud. These include deuterated water (D20), and the nitrate, iodide, thiocyanate, acetate and dichromate anions. Many cations and some anionic dyes have also been used. The problem with using tracers that are not distilled with the core water is t h a t a separate extraction step is required to separate the tracer from the core for analysis. Any tracer used for mud water should also be tested to ensure t h a t it is

Downhole Tracers

363

following the water. All the tracers discussed here require t h a t the water be separated from the mud before they can be analyzed. The mud system is small enough in volume t h a t a great m a n y materials are potentially useful as tracers. The best way to test a material for use in such a system is to inject a pulse containing a known amount of the material into the mud while it is being circulated down hole, assuming t h a t there is no lost circulation. The mud return is sampled at the surface, and the tracer concentration, c, as a function of time, t, is measured. If there is no loss of tracer, the response function, ]~cAt, should be equal to the amount of tracer originally added, divided by the flow rate. One of the easiest ways to do this for an ionic species is by m e a n s of an ion electrode. Ion meters have become almost as common as pH meters. A small hand or powered filter press combined with a microelectrode is sufficient for these measurements. It may be possible to find an electrode system t h a t can operate directly in the mud without the need for a separation step. Another possible procedure is to use a short-lived gamma-emitting tracer such as Tc-99m. This tracer (half-life = 6 hr) is available from an isotope generator. It emits a soft g a m m a ray (0.14 MeV), which is largely absorbed in the mud system and presents no radiation hazard; however a NaI or plastic scintillator probe in the mud r e t u r n should be able to monitor its presence without any trouble. The system can be calibrated with a known concentration of technetium to give true concentrations. In the usual procedure for mud-water invasion, a small volume of tritiated w a t e r (or other tracer) is thoroughly mixed with the mud. This may require at least one round trip in the hole and is done before the coring operation. The tracer concentration is calculated to allow a water dilution factor of at least 10 without loss of measuring range. The maximum concentration of tracer is limited by environmental concerns. In the case of tritiated water, the concentration and amount needed is usually well below the MPC for unrestricted areas, so t h a t no special disposal or cleanup procedure is normally required for the tagged mud. A sample of the mixed mud is taken for analysis at the s t a r t of the coring operation. Mud samples are also t a k e n t h r o u g h o u t the coring operation at intervals equivalent to set depths of coring or drilling. These samples are collected at the surface but corrected to the drilling depth by the trip time of the mud to the surface. Water is separated from all the mud samples and analyzed for tracer. Tritiated water may be filtered but the water is usually flash distilled in simple side-arm distilling flasks before counting. For other ions, centrifugation or high-pressure filtration is required. The measured tracer concentrations in the mud are plotted against depth to provide a corrected mud tracer concentration for the core being cut at each depth. The collected core sections are extracted by a Dean S t a r k distillation, and a sample of the water from each section is counted for tritium. The ratio of tritium

364

Chapter 7

in the core w a t e r to t r i t i u m in the m u d at t h a t depth is a m e a s u r e of the invasion of the core by m u d water. HYDRAULIC BEHAVIOR OF MUD An interesting application of tracers in m u d is to study the hydraulic behavior of m u d in the wellbore. A p a t e n t (Hall, 1989) proposed the use of an injected t r a c e r pulse for following the hydrodynamics of drilling mud, in the s a m e m a n n e r as is done in for chemical reactors (Levenspiel, 1962), and as discussed in chapter 4 of this work. The first and second m o m e n t s of the t r a c e r response curve are used to d e t e r m i n e the m e a n residence time and the variance of the distribution. The a u t h o r used lithium bromide as a tracer and ion c h r o m a t o g r a p h y as an a n a lytical m e t h o d for both ions. The Li + ion a p p a r e n t l y does not absorb on the walls. S a m p l e s were collected at the surface for analysis. There were no c o m m e n t s on how or if the samples were s e p a r a t e d from the m u d before analysis by ion chromatography. ZnBr2 was also suggested as a tracer, but the hydrolytic behavior of this m a t e r i a l m i g h t m a k e interpretation difficult. Drill-bit

wear

Drill bits w e a r out or become inoperative for a n u m b e r of reasons. Pulling a bit either too early or too late can be costly. There have been several p a t e n t s over the years on methods for identifying drill-bit problems before they become severe. To date, none of these methods has been widely received in the oil field. One of the earliest (Warren, 1949) proposed an u n n a m e d tracer placed behind a welded "spacer" at critical places on the drill bit. W h e n the spacer m a t e r i a l w e a r s through, the tracer is released as a wear indicator (compressed gas is included to disperse the tracer). A m e t h o d for identifying m i s a l i g n m e n t of a drill cone as soon as it h a p p e n s was proposed in a p a t e n t (Graham, 1961). In this method, a vial of radioactive t r a c e r is cut w h e n the axis of the cone moves off center, r e l e a s i n g t h e t r a c e r into t h e m u d column. Kr-85 was proposed as a w e a r indicator in several patents. In some, tracer was released into the m u d s y s t e m with the aid of various propellants and detected by m e a n s of a radiation probe. In one (Fries, 1974), the k r y p t o n is mixed with the bearing grease and released to the m u d w h e n the grease seal fails. In the l a t t e r case, a special s e p a r a t o r at the m u d - r e t u r n draws the gas into a counter. Most of these m e t h o d s depend on the use of a significant a m o u n t of radioactive m a t e r i a l and on difficult m a n u f a c t u r i n g or detection problems. There are now some very sensitive detectors for certain gas tracers, e.g., SF6, by electron capture. A large enough a m o u n t of SF6 can be dissolved and/or dispersed in the grease to be easily detected in the event of a grease seal rupture. A primitive gas s e p a r a t o r should be sufficient to allow SF6 to be m o n i t o r e d by m e a n s of an electron capture detector. The presence of SF6 would actuate an a l a r m indicating bit problems down hole.

Downhole Tracers

365

REFERENCES

Akers, T.J., and Hill, A.D., "Radioactive Tracer Logging in Laminar Flow," Proc., Cndn. Well Logging Soc. Formation Evaluation Symp., Calgary, Alberta, Can., Sept. 29-Oct. 2, 1985. Anderson, J.A., Pearson, C.M., Abou-Sayed, A.S., and Myers, G.D., "Determination of Fracture Height by Spectral Gamma Log Analysis," preprint SPE 15439 presented at the 61st Ann. SPE Tech. Conf., New Orleans, Oct. 5-8, 1986. Arino, H., and Kramer, H.H., "A New Cs-137/Ba-137m Radioisotope Generator," Intl. J. Appl. Radiation and Isotopes (1968) 19, 816. Arnold, D.M., and Paap, H.J., "Behind Casing Fluid Flow Detection in Producing Wells Using Gas Lift," U.S. Patent No. 4,057,720 (1975). Arnold, D.M., and Paap, H.J., "Quantitative Monitoring of Water Flow Behind and in Wellbore Casing," paper SPE 7107; JPT (Jan. 1979) 31, No. 1, 121-130. Arnold, F.C., "Incorporation of Wellbore Steam Segregation in Steam Stimulation," paper CIM/SPE-90-87 presented at the Joint SPE/CIM Mtg., Calgary, Alberta, Can., June 10-13, 1990 (preprints 2, 1990). Barry, B.J., "Flow Measurement by the Dilution Method with Incomplete Mixing," Intl. J. Appl. Radiation and Isotopes (1978) 29, 525. Bennett, R., Schettler, P.D., and Gustafson, T.D., "Measuring Low Flows in Devonian Shale Gas Wells with a Tracer Gas Flowmeter," Energy for the Future: Proc. Eastern Regional SPE Conf., Charleston, WV, Nov. 1-4, 1988, (1988) 369372 (paper SPE 18556); SPE Formation Evaluation (June 1991) 269. Bennett, R., Schettler, P.D., and Gustafson, T.D., "Measuring Low Flows in Devonian Shale Gas Wells with a Tracer Gas Flowmeter," Energy for the Future: Proc. Eastern Regional SPE Conf., Charleston, WV, Nov. 1-4, 1988, (1988) 369372 (paper SPE 18556); SPE Formation Evaluation (June 1991) 269. Bevington, P.R., Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill, New York (1969). Blount, C.G., and Copoulos, A.E., "A Cement Channel Detection Technique Using the Pulsed Neutron Log," SPE Formation Evaluation, 485 (Dec. 1991). Briesmeister, J.F., "MNCP--A General Monte Carlo Code for Neutron and Photon Transport," Manual LA-7396-0M, Rev. 2, Los Alamos Natl. Lab., 1986. Bruist, E.H., Jeffries, R.G., and Botts, T.M., "Well Completions in the Beta Field, Offshore California," preprint SPE 11696 presented at the SPE Calif. Regional Mtg., Ventura, CA, March 23-25, 1983.

366

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Flag, A.H., Meyers, J.P., Terry, J.P., and Mardock, E.S., "Radioactive Tracers in Oil Production Problems," paper 424G presented at the Fall Mtg. of Petrol. Branch AIME, San Antonio, TX, Oct. 17-20, 1954. Fries, B.A., "Surface Detection During Drilling of Oil-Well Drill-Bit Failures," Proc., IAEA Conf. on Indust. Applic. Radioisotopes and Radiation Tech., Grenoble, France, Sept. 28-Oct. 2, 1981 (IAEA-CN-40/75P). Gadeken, L.L., Gartner, M.L, and Sharbak, D.E., "Improved Evaluation Techniques For Multiple Radioactive Tracer Applications," Trans., 12th SPWLA French Sect. (SAID Intl. Formation Evaluation Symp.), Paris, France, Oct. 2427, 1989 (paper no. Kk, 1989). Gadeken, L.L., Ginzel, W.J., Sharbak, D.E., Shorck, K.A., Sitka, M.A., and Taylor, J.L., "The Determination of Fracture Orientation Using a Directional Gamma Ray Tool," 32nd SPWLA Logging Symp., Midland, TX, June 16-19, 1991. Gadeken, L.L., and Smith, H.D., "A Relative Distance Indicator from Gamma Ray Spectroscopy," paper SPE 17962 presented at the 6th SPE Middle East Oil Tech. Conf., Manama, Bahrain, March 11-14 1989. Gadeken, L.L., Smith, H.D. Jr., and Seifert, D.J., "Calibration and Analysis of Borehole and Formation Sensitivities for Gamma Ray Spectroscopy Measurements with Multiple Radioactive Tracers," Trans., 28th Ann. SPIWA Logging Symp., London, June 29-July 2, 1987, 1. Gore, G.L., and Terry, L.L. "Radioactive Tracer Techniques," JPT (1956) 8, 12. Graham, J.W., "Bearing Wear Indicator for a Roller Bit," U.S. Patent 3,011,566 (1961). Griston, S., "Evaluation of Radioactive Tracer Surveys for Steam Injection Wells," paper SPE 20031 presented at Calif. Regional Meeting of SPE, Ventura, CA, April 4-6, 1990. Gwyn, J.E., "Fast Response Pulse Tests Use Of Gamma Milking," Ind. Eng. Chem. (1961) 53, 908. Haliburton Logging Services, Inc., "Tracer Scan Services" (1990). Hammack, G.W., Myers, B.D., and Barcenas, G.H., "Production Logging through the Annulus of Rod-Pumped Wells to Obtain Flow Profiles," preprint SPE 6042 presented at 51st Ann. SPE Tech. Conf., New Orleans, Oct. 3-6, 1976. Hill, A.D., Production Logging: Theoretical and Interpretive Elements, SPE Monograph Series 14, SPE, Richardson, TX (1990). Hine, G.J., and Sorensen, J.A. (eds.), Instrumentation in Nuclear Medicine (2 vols.), Academic Press, New York (1974).

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Hull, D.E., "The Total-Count Technique: A New Principle in Flow Measurement," Intl. J. Appl. Radiation and Isotopes (1957) 4, 1. Jassti, J.K., and Fogler, H.S., "Determination of Flow Profiles in Porous Media Using Shifts in Gamma Spectra," AIChE J. (1990) 36,827. Jefferis, R.G., Bruist, E.H., and Botts, T.M., "A Field Proven System for Selective, Multizone, One-Trip Gravel Packing," paper SPE 11697, presented at the SPE Ann. Calif. Regional Mtg., Mar. 23-25, 1983, Ventura, CA. Kennedy, D.K., Kitziger, F.W., and Hall, B.E., "Case Study on the Effectiveness of Nitrogen Foams and Water Diverting Agents in Multistage Matrix Acid Treatments," preprint SPE 20621 presented at the 65th Ann. SPE Tech. Conf., New Orleans, Sept. 23-26, 1990. Kline, W.E., Kocian, E.M., and Smith, W.E., "Evaluation of Cementing Practice by Quantitative Radiotracer Measurements," paper SPE 14788 presented at IDAC/SPE Drilling Conf., Dallas, TX, Feb. 10-12, 1986. Knapp, F.F. Jr., and Butler, T.A., Radionuclide Generators, ACS Symposium Series 124, American Chem. Soc., Washington, DC (1984). Kugener, J., and Marsigne, C.H., "G~n~rateur-injecteur de radio~l~ment (c~siumbaryum). Caract~ristiques physicochimiques du traceur," Rept. HJ011/R184, Electricit~ de France (1972). Levenspiel, O., Chemical Reaction Engineering, John Wiley, New York (1972). Lindley, B.W., and McGhee, B.F., "An Investigation of a High-Strength Proppant Tail-in at McAllen Ranch Field," preprint SPE 11935 presented at the 58th Ann. SPE Tech. Conf., San Francisco, CA, Oct. 5-8, 1983. Lopus, T.A., Seifert, D.J., and Schein, G.W., "Production Improvement Through Identification of Conductive Natural Fractures Utilizing Multiple Radioactive Isotope Technology," paper SPE 16192 presented at the SPE Prod. Oper. Symp., Oklahoma City, March 8-10, 1987. Matherne, B.B., and Hall, B.E., "A Field Evaluation of a Gravel-Diverted Acid Stimulation Prior to Gravel Packing," preprint SPE 19741 presented at the 64th Ann. SPE Tech. Conf., San Antonio, TX, Oct. 6-11, 1989. McKeon, D.C., Scott, H.D., Olesen, J.R., Patton, G.L., and Mitchel, R.J., "Improved Method for Determining Water Flow Behind Casing Using Oxygen Activation," preprint SPE 22130 presented at the 65th Ann. SPE Tech. Conf., New Orleans, LA, Sept. 23-26, 1990. McKeon, D.C., Scott, H.D., and Patton, G.L., "Interpretation of Oxygen Activation Logs for Detecting Water Flow in Producing and Injection Wells," Soc. Petrol. Well Log Analysts 32 Ann. Logging Symposium, June 16-19, 1991.

368

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Newacheck, R.L., Beaufait, L.J. Jr., and Anderson, E.E., "Isotope Milker Supplies 137Ba from Parent 137Cs," Nucleonics (May 1957) 15, No. 5, 122. Nguyen, T.V., and Stevens, C.E., "The Use of Inert Gas Radioactive Tracers for Steam Injection Profiling," preprint SPE 17419 presented at the SPE Calif. Regional Mtg., Long Beach, CA, March 23-25, 1988. Norman, L.R., Terracina, J.M., McCabe, M.A., and Nguyen, P.D., "Application of Curable Resin-Coated Proppants," preprint SPE 20640 presented at the 65th Ann. SPE Tech. Conf., New Orleans, LA, Sept. 23-26, 1990. Ostermeir, R.M., "Pulsed Oxygen Activation Technique for Measuring Water Flow Behind Pipe," The Log Analyst (May-June 1991) 309. Pearce, R.M., "Evaluation of Fracture Treatments Using Tracer and Temperature Surveys," Proc., SPE of AIME Low Permeability Gas Reservoirs Symp., May 20-22, 1979 (SPE 7910, 7-14). Pemper, R.R., Flecker, M.J., McWhirter, V.C., and Oliver, D.W., "Hydraulic Fracture Evaluation with Multiple Radioactive Tracers," Geophysics (Oct. 1988) 53, 10. Petovello, B.G., "Well Evaluation by Production Logging," Petrol. Engineer (Aug. 1975) 48. Priest, M.A., "Injection of Radioisotopes at Wellhead Improves Fracturing Operation," preprint SPE 17464 presented at the SPE Calif. Regional Mtg., Ventura, CA, March 23-25, 1988. Schlumberger Interpretation Charts, Schlumberger Ltd., New York (1986). Schlumberger Production Log Interpretations, Schlumberger Ltd., Houston (1973). Schwanke, B.E., Hopkinson, E.C., and Taylor, J.L. III, "Gamma Ray Tracers Help Evaluate Acid Diversion," Petrol. Eng. Int. (Feb. 1990) 62, No. 2, 40-41. Scott, H.D., Pearson, C.M., Renke, S.M., McKeon, D.C., and Meisenhelder, J.P., "Applications of Oxygen Activation for Injection and Production Profiling in the Kuparuk River Field," paper SPE 22130 presented at the SPE Intl. Arctic Tech. Conf., Anchorage, AK, May 29-31, 1991. Senum, G.I., Fajer, R.W, Harris, B.R. Jr., DeRose, W.E., and Ottaviani, W.L., "Petroleum Characterization by Perfluorocarbon Tracers," paper BNL 46883 presented at 8th SPE/DOE Enhanced Oil Recovery Symp., Tulsa, OK, April 2124, 1992. Serra, O., Baldwin, J., and Quirien, J., "Theory and Practical Applications of Natural Gamma Ray Spectroscopy," Trans., Soc. Prof. Well Log Anal., 21st Ann. Mtg. (1980, paper Q). Smith, A.L., "Radioactive Scale Formation," JPT (June 1987) 697.

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369

Smith, H.D. Jr., Robbins, C.A., Arnold, D.M., Gadeken, L.L., and Deaton, J.G., "A Multifunction Compensated Spectral Natural Gamma Logging System," preprint SPE 12050 presented at the 58th Ann. SPE Tech. Conf., New Orleans, LA, Oct. 1983. Smith, H.D. Jr., and Gadeken, L.L., "Method for Determining Depth of Penetration of Radioactive Tracers in Formation Fractures," U.S. Patent 4,825,073 (1989). Spytsin, V.I., and Mikheev, N.B., "Generators for the Production of Short-lived Radioisotopes," Atom. Energy Rev. (1971)9, No. 4, 787. Taylor, J.L. III., and Bandy, T.R., "Tracer Technology Finds Expanding Applications," Petrol. Eng. Int. (June 1989) 61, No. 6, 31-34, 36. Taylor, J.L. III., and Chisholm, J.W., "Tracers Can Improve Hydraulic Fracturing," Petrol. Eng. Int. (July 1989) 61, No. 7, 22, 24-25. Turtiainen, H., "Flow Measurements with Radioactive Tracers Using the Transit Time Method," Valt. Tek. Tutkimuskeskus Tutimuksia (Aug. 1986) 421. Wan, P.T., "Measurement of Steam Quality Using a Neutron Densitometer," J. Can. Petrol. Tech. (1991) 6, No. 30, 29-33. Warren, J.B., "Means of Detecting Wear on Bits," U.S. Patent No. 2,468,905 (1949). Whichman, P.A., Hopkinson, E.C., and Youmans, A.H., "Advances in Nuclear Production Logging," Trans., 8th SPWLA Ann. Logging Symp., Denver, CO, June 11-14, 1967. Williams, R.L., and McCarthy, J.T., "Using Multiple Radioactive Tracers to Optimize Stimulation Designs," preprint SPE 16383 presented at SPE Calif. Regional Mtg., Ventura, CA, April 8-10, 1987. Woiceshyn, G.E., Yuen, P.S., John, H., and Manzano-Ruis, J.J., "Measurement of Steam Quality, Mass Flowrate, and Enthalpy Delivery Rate Using Combined Neutron Densitometer and Nozzle," paper SPE 14907 presented at SPE/DOE Mtg., April 1986. Zemel, B., and Clossman, P.J., "Steam Quality Measurement: Apparatus and Method," U.S. Patent No. 4,712,006 (1987). Zhao, J., Liu, J., Zhang, R., Ni, H., and Wu, S., "High Resolution Borehole Logging Techniques to Analyze Elements in Formations," Proc., Intl. Symp. Nuclear Tech. in Exploration of Energy and Nat. Resources, IAEA, Vienna (1990) (Paper IAEA-SM-308/53).

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CHAPTER 8

TRACERS

IN FACILITY

OPERATIONS

INTRODUCTION This section is concerned with the use of tracers in oilfield facility operations and will cover operations used to gather, separate, store, treat, and measure the fluids produced at an oil field before sending them on for sale or reinjecting them into the ground. In addition, use of tracers in environmental problems and the monitoring and t r e a t m e n t of corrosion, erosion, and scale throughout the oil field are covered here. Related to the use of radioactive tracers is the use of radiation for monitoring facility operations. The scattering and transmission of g a m m a and neutron radiation is a useful way of looking inside pipelines, storage vessels, and a variety of facility operations. Small radiation sources are used in m a n y industries for this purpose and are of value in the oil field as well. The following section t r e a t s the applications of tracers to m e a s u r i n g flow rates in pipes and for meter proving and the use of small neutron and g a m m a radiation sources for monitoring fluid saturations in multiphase flow in pipes.

FLOW-RATE MEASUREMENT Tracers have been used to measure the flow of liquids, gases, and solids in m a n y areas and situations. Flow rates measured by tracers have been reported in pipelines and tubulars, ducts and airways (Gilath, 1977), chemical reactors (Levenspiel, 1962), canals and streams (Clayton and Smith, 1963), estuaries (Timblin and Peterka, 1963), s a n i t a r y sewers (Kuoppamaki, 1977), and body fluids (Stewart, 1897). Measurements have been reported in multiphase flow, in both open and closed systems, and over a very wide range of flow rates. The meas u r e m e n t s are easy to make, and with a little care the results rival most other methods for accuracy. These methods have a history of use over more t h a n three decades; accuracy reported over this time period is better t h a n I percent. As discussed in chapter 2, the two methods most commonly used in measuring flow rate by tracers are isotope dilution and tracer-pulse velocity. The former was discussed in chapter 2, and the application of both methods to flow m e a s u r e m e n t s down hole was described in chapter 7. The p r e s e n t c h a p t e r discusses the use of these methods for measuring flow in and around facilities, including gathering lines, pipelines, and to a variety of surface flow situations. As indicated above, virtually all the reported flowrate m e a s u r e m e n t s using tracers involve surface flow conditions. These are the historical foundations upon which all tracer flow methods discussed in this chapter, as well as in other parts of this book, are based.

372

Chapter 8

Isotope dilution Two methods are used to monitor flow rates by isotope dilution: constant-rate or continuous tracer injection and pulse tracer injection. The pulse method is further subdivided into total count, total sample, and split stream methods, named for the procedural variations introduced by different investigators. The differences and applications of the methods are discussed below All of the variants of the isotope dilution method are based upon the concept that the tracer is conserved. The measured dilution of the tracer injected into the unknown flow is used to determine the unknown flow rate. The dilution measurement m u s t be made downstream from the injection, at a point where the injected tracer is well mixed with the flowing fluid. Good lateral mixing is generally required. CONTINUOUS INJECTION METHOD In the continuous injection method, a known concentration, Co, of tracer is injected at a known flow rate, Qo. A sample of the fluid is taken for analysis from the point downstream where the tracer is laterally mixed. The tracer injection is continued until the measured activity at the measuring point is constant. At this point, the flow rate in the system, Qx, is obtained from the relationship: - C o - Cx Qx = {4o Cx

(8.1)

In most cases, Cx is so small compared to Co that this reduces to: Qx = Qo~x

(8.2)

where C o is the initial concentration of the tracer being injected into the system downstream, and Cx is its concentration in the moving fluid at the sampling point. These measurements are independent of system size and shape, and no system calibration is needed. Fig. 8.1 shows tracer of initial concentration Co being injected at a flow rate, Qo, into a stream of unknown flow rate, Qx. A plot of the sample tracer response as a function of time, at the sampling point downstream, is shown below the flowline. At equilibrium, the concentration of tracer downstream reaches the constant value Cx. At this point, a single sample is sufficient to calculate the flow rate; only enough downstream samples are analyzed to ensure concentration equilibrium. Most of the work reported in the literature has used radioactive tracers, but it is not a requirement of the method. In single-phase flow, a number of instrumental methods can be used for nonradioactive tracers. A tracer sensor should be inserted in the line to announce when to sample. As long as a constant tracer concentration, Cx, is achieved, sampling time is not critical. The biggest source of

Tracers in Facility Operations

373

error is poor lateral mixing of tracer with the flowing fluid. The specific problems associated with measurements of flow velocities in rivers, streams (Clayton, 1963), and other hydrological flows were the subject of a symposium sponsored by the International Atomic Energy Agency (IAEA, 1963). Studies have been made to determine the distance from the injector required for good mixing to occur during turbulent flow in pipelines, and for methods of injecting tracer to improve mixing with the moving fluid. Reported accuracy of the continuous injection method (Clayton et al., 1967) is about 1 percent, with a somewhat greater accuracy obtained using special procedures.

Tracer. rl Q o ~n LIJCo

o '

Qx

Tracer Qx out C Flow

>

/4

Cx

Time

Figure 8.1. Flow by constant rate injection PULSE INJECTION METHODS The pulse injection method is the second variant of the isotope dilution method discussed in chapter 2. In this method, the known activity, A, is injected into the system in the form of a pulse. The concentration of tracer as a function of time, c(t), is measured at a point downstream from the injection point after lateral mixing has been achieved, and the flow rate, Q, calculated from the equation for conservation of tracer: A = Q~c(t)dt

(8.3)

374

Chapter 8

Since all the injected activity, A, m u s t ultimately pass the sampling point downstream, a tracer response curve will be generated from the analysis of samples taken as a function of time, as illustrated in Fig. 8.2. Here, a pulse of tracer containing an activity, A, is shown injected into the flowstream at the injection point. The tracer response curve generated at the sampling point is shown in the figure above the flow line.

Injected pulse, A

Tracer response at sampling point

Cx

Time

0

F,ow,Ox Inject'ion point

f

I

I Sampling or counting point

Figure 8.2. Pulse tracer injection The concentration function, c(t), can be obtained in several ways. The most straightforward method is simply to analyze samples taken as the pulse passes, by taking as m a n y samples as needed, over the time period required to define the curve. At low flow rates in rivers or streams, this can be a simple matter. At high flow rates, particularly in pipes, sampling can be a very difficult procedure. If, however, g a m m a - e m i t t i n g tracers are used, sampling can be avoided. In principle, a chemical tracer sensor could be inserted in the line to avoid the need for sampling; however no such procedure has been reported for chemical tracers. Total count method In the case of gamma-emitting tracers, the activity in the pipe can be monitored by a counter mounted on the outside of the pipe. The radiation counted will be proportional to the radioactivity passing the counter on the pipe. If c(t) is the concentration of activity per unit volume passing the counter as a function of time, and if r(t) is the radiation measured at the counter at the same time, the two can be related by a calibration constant, k:

c(t) = kr(t)

(8.4)

Tracers in Facility Operations

375

where k is a constant converting the measured count rate at the detector to the tracer activity in the pipe, thus correcting for the efficiency of counting, the effect of shielding, and the source-to-detector geometry of the external counter. The counter can be calibrated to convert the measured radiation to the concentration of activity in the pipe at any time, before or after the experiment, so long as the counter-source geometry and efficiency are reproduced. Radiation counters tabulate all the counts collected during a counting period in a tabulated output called a scaler. The total number of counts collected in the scaler, minus the background, is the integral value, ~r(t)dt, the net n u m b e r of counts, R, collected over the time period required for all of the injected activity to pass the external counter. From Eq. (8.4), since the tracer concentration is directly related to the radiation counted, this can be expressed as: ~c(t)dt = k ~ r ( t ) d t

(8.5)

As a result, we can now change Eq. (8.3) by: A = Q ~ c(t) dt = Q k j r(t)dt = QkR

(8.6)

In the total count method (Hull 1957), we can therefore rewrite Eq. (8.6) as: Q-

A kR

(8.7)

where R is the total number of counts collected, and k is a calibration factor. The calibration is specific, relating the activity (count per unit time) per unit volume for a given counting situation. For use in a pipeline, a counter should be calibrated by placing it on a section or equivalent of this diameter pipe filled with a tracer solution of known concentration of activity and measuring the count rate. This can also be done numerically from nuclear data by Monte Carlo calculations.

Split stream method A variation of the total count method proposed by Hull (1957) m e a s u r e s the tracer response of a small s t r e a m split from the main line. In this variation, a convenient sidestream of fluid is taken from the main flow and passed through a counting chamber. The counter is immersed in this chamber to measure the flow rate. Since the tracer pulse is fully mixed with the main flow, all sidestreams should give the same flow rate. The counter is calibrated in the new chamber to obtain the calibration factor, k. This method is not restricted to closed systems but can also be used to m e a s u r e the flow rate in ditches, open channels, and rivers, so long as the restrictions of isotope dilution are met. More importantly, it removes the restraint of measuring tracer in the pipe and allows m e a s u r e m e n t in a sidestream under much more convenient conditions. Fig. 8.3 shows a pulse of t r a c e r moving down the pipe with the tracer concentration, c, as a function of time, t, at the split point. At this point the tracer is uniformly mixed in the pipe so t h a t the tracer responses through the pipe and through the split s t r e a m are

376

Chapter 8

equivalent. Therefore, the equivalent analysis can be performed in the analyzing chamber. This is basic to the use of chemical tracers, since a variety of instrumental detection methods can now be used. Many methods have been developed for on-line analytical measurements in chemical plants; such instruments can be used in a portable device connected to the main flow for this purpose. Chemical tracers can be used if i n s t r u m e n t a l methods with a sufficiently rapid response time are available for on-line measurement of the chemical tracers. Pulse velocity in most pipeline situations is too uncertain and too fast to permit success with blind sampling methods.

Tracer injected

f

t

Split

stream I

Analyzer or counter

Figure 8.3. Bypass vs. line measurements Most open-channel and hydrologic work is now done with dyes and other nonradioactive tracers; however much of the early work used radioactive tracers. A split s t r e a m has the distinct advantage t h a t tracers can be m e a s u r e d in situ by radioactivity or other instrumental methods t h a t do not require sampling. Blind collection of samples for analysis at a later time is a tedious process, fraught with uncertainties regarding when to start, what sample frequency to use, and how long sampling should be continued. The size of the bypass is not important so long as all the requirements of the isotope dilution method are met. It is not even required t h a t the tracer move uniformly through the vessel in the sidestream. If flow moves through the side vessel in a nonuniform manner, as by channels, the total flow is unchanged. In this case, however, it is important that the tracer not bypass the detection device. Detection methods such as radiation counters are relatively insensitive to the problem of bypassing, since they are averaging devices t h a t measure all the material contained in the side vessel regardless of where it is positioned. Most chemical

Tracers in Facility Operations

377

detection devices, such as ion electrodes, are microdevices t h a t only detect tracer at their interface with the solution. An advantage of the tracer methods is the ease with which they can monitor the flow rates in a complex manifold of mixed flow sources. This can be a problem in manifold gathering lines (Hall, 1957), as is shown in Fig. 8.4, where flow from four sources is combined into a single outlet. The flow rate from A and B can be obtained by injecting tracer at source A and monitoring at positions 1 and 2. The other two flow rates can be separated out by adding tracers at source D and monitoring at positions 3 and 4. Thus, the flow rate from D is given by subtraction of the flow at position 4 from t h a t at position 3. Flow at C is obtained from position 3 minus 2, and flow at B from position 2 minus 1. In general, given any number, n, of independent sources of flow in this kind of configuration, the flow rates of the individual sources can be deconvoluted by a sequence of subtractions.

T•acer I A I I g in, A

N

Tracer in, D

I

I C I

Detectors

I~'g I

Ntr

Figure 8.4. Monitoring mixed flow

Total sample method A second way to evaluate the tracer-response function, c = f(t), is by w h a t is sometimes called the total sample method. Here, a very small s t r e a m is t a k e n continuously from the main flow by means of a pump. The sample is collected in a c o n t a i n e r and the contents mixed for analysis, yielding a mechanically integrated sample with an average (mean) concentration, ~. If T is the sampling period required to collect the entire sample interval, F is the counter correction, and the other values are as before, then: Q -

AF ~T

(8.8)

Chemical tracers are commonly used with this method, since there is no special advantage to measuring radiation over any other instrumental analytical

378

Chapter 8

methods. Continuous analytical methods allow the tracer concentration to be followed as total sample is collected.

Pulse velocity Use of the pulse velocity method for measuring flow rate m u s t go back into prehistory with the first m a n who timed a stick moving on a river to estimate the velocity of the water. It is most widely used with gamma-emitting tracers because it yields flow data without sampling, mixing, or calibration problems. As indicated by its name, this procedure measures the time required for the pulse to travel between two points a known distance apart. This procedure, used for production logging down hole, was covered in chapter 7. Its original use in pipeline measurements will be covered here.

Injected pulse here Flow

Detector 1

---(II Moving pulse

Detector 2

RA t

Detector response

Figure 8.5. Pulse velocity method The flow rate is calculated from the measured transit time, t, between the two detectors, the distance between them, and the cross-sectional area in the region between the two points. This is shown in Fig. 8.5 witti a tracer pulse moving down the pipe of diameter D a distance, L, between the two detectors. A typical tracer response, R, at the detectors, as a function of time is shown in the lower right corner of the figure. Q=

xD2L 4t

(8.9)

The procedure illustrated here uses gamma-emitting tracer. This is the preferred method, since the pulse can be monitored externally; however a variety of

Tracers in Facility Operations

379

chemical detection procedures, including conductimetric, electrochemical, or spectrometric detectors, can be used under the right circumstances, providing they can be inserted through the line. When cross-sectional areas show considerable variation in the region between the detectors, the pulse-velocity method may not be applicable unless these differences can be compensated for as described in chapter 7 in the section on production logging down hole (Hill, 1990). For regions of constant cross section, such as pipes, it is a very useful method. It has also been reported for m e t e r proving (Clayton et al., 1964). Mixing is not usually a problem in this procedure. The pulses tend to be reasonably symmetrical and the peak is the usual l a n d m a r k for timing the pulses. Problems may arise in using this method for l a m i n a r flow because of the parabolic velocity gradient, which distorts the peak shapes. If the m e a n diameter of the flow channel is not known, the pulse velocity and isotope dilution method can be combined. The isotope dilution measured at either detector gives the average flow rate to t h a t point. The calculated pulse velocity between the two detectors divided into the average flow rate is a measure of the average cross section of the interval. The methods described above usually require some additional knowledge. The pulse-velocity method requires a knowledge of the cross-sectional area of the pipe, and the pulse-dilution methods require calibration of the detector or other m e a s u r e m e n t s either on site or at some equivalent location. For work on pipelines, however, the cross-sectional area is usually known.

FLOW-RATE APPLICATIONS Many references are found on tracer methods for measuring flow rate, some of which are included in the bibliography at the end of this chapter. Only a small n u m b e r of references on tracer flow-rate m e a s u r e m e n t s actually refer to oilfield applications; however m a n y of them are applicable to similar problems in the oil field and can be a source of answers when such problems arise. Installed meters are widely used in the oil industry for metering flow at the surface with a variety of methods; however there are a great m a n y cases in which surface flow is unmetered. Many gathering lines and injection lines in the field are not metered, and m a n y t h a t are metered require calibration t h a t is often neglected. In addition, water in ditches and channels is difficult to meter; as a consequence, this is rarely done. Yet the fate of these produced and run-off waters often raises environmental concerns t h a t could be answered by monitoring the flow rates. For all these situations, tracer methods can provide a reasonable and relatively simple solution. SINGLE- AND MULTIPHASE FLOW Measuring multiphase flow is always a problem in the oil field. In a field experiment by McCloud et al. (1972) on two-phase flow, m e a s u r e m e n t s were made

380

Chapter 8

of both condensate and gas velocities by segregating the flow. The 1.83-hr halflife Ar-81 and 10.6-yr half-life Kr-85 were used as gas tracers, and 36-hr half-life Br-82 tagged bromobenzene as an oil tracer. The short-lived tracers were prepared by neutron irradiation at a local university reactor and flown to the site.

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Figure 8.6. Schematic diagram of multiphase tracer test Experiments were performed in small-diameter pipes in the laboratory and in five-mile long, 6-in. diameter condensate line from an offshore platform. The condensate line was located beneath 56 ft of water and required divers to attach the radiation detectors to the line. The tracer pulse velocity method was used for these measurements. A schematic diagram of the test line showing the tracer injection point and each of the numbered detector positions is shown in Fig. 8.6. Test pulse velocities were as high as 280 ft/sec in the gas phase. The tracers were injected as sharp pulses using high-pressure nitrogen as a drive. The tracer injection system is shown in Fig. 8.7. The gases were brought to the site in transfer cylinders (bombs) and injected by opening valves to the nitrogen source. The Br-83 tagged condensate tracer was provided in glass ampules, which were smashed by tightening down valve stems as shown in the detail in Fig. 8.7. Tracer pulse velocities were too high for the response time of the analog count rate meters; however digital rate meters (multiscalers) had no problems with the measurements. Both kinds of meters were used. Typical measurements of gas and liquid flow velocities in the condensate line are shown in Fig. 8.8. Four detectors

Tracers in Facility Operations

381

were placed at different distances apart, both in the water and on the platform. The detectors were numbered 1, 2a, 3, and 5. The distance from 1 to 2a was 14.2 ft, t h a t from 2a to 3 was 25 ft, and that from 3 to 5 was 120.8 ft. Fig. 8.8a shows

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382

Chapter 8

the results for gas velocity (Ar-81) as measured by a multichannel scaler. The results of the condensate velocity measurements (Br-82) using a rate meter and strip chart recorder are shown in Fig. 8.8b. The travel time between 2a and 3 is m a r k e d on both figures. Gamma-ray density measurements were used to distinguish between gas and liquid. This method measured phase velocity, not flow rate. To obtain the flow rates, the cross sectional area of the phases would also have to be known.

Sludge in pipes The pulse velocity method only measures a mean travel time between two points a known distance apart. The flow rate calculation is based on the assumption t h a t the cross-sectional area is known over the measured interval, as it is for most pipelines. The isotope dilution methods measure a flow rate at the measuring point, which is independent of the cross-sectional area. The simultaneous use of both methods over the same interval was proposed in the previous section as a general method for correcting pulse-velocity m e a s u r e m e n t s when the average cross-sectional area is different from its nominal value. The inverse of this can be used to correct the actual cross section of flow when the cross-sectional area is reduced because the line is partially obstructed by immobile material; hence, it can be used to detect the presence of, and measure the extent of, deposits such as sludge, scale, and other material in gathering lines. Two papers (Lee, 1960, and Fediw et al., 1981) have reported this kind of m e a s u r e m e n t to determine the amount of sludge in large, unmetered water and gas lines, respectively, although the methods were somewhat complicated. Fediw et al. reported on the use of SF6 as a tracer in a 54-in. diameter, 12-mile coke-oven gas line. Flow rates varied from 100 to 800 ft3/sec. Quick-action ball valves were used to collect a sample per second, and a freon "pre-tracer" was used to alert the system when to s t a r t collecting SF6 samples. The results reported showed a sludge content of 20 to 40 percent. This is a case in which radioactive tracers would have been preferable, since no pretracers are needed and sampling would be avoided.

Line metering by tracer A n u m b e r of flow-rate m e a s u r e m e n t s in pipes and tubulars have been reported in the literature. The accuracy obtained with the tracer methods has been well established (Clayton et al., 1967); thus, the use of tracers can be recommended for meter proving (Kurten, 1977) and monitoring flow rate in unmetered lines. Radioactive tracers are not required, and chemical tracers are commonly used. A commercial nitrous oxide (N20) tracer flowmeter for use in pipelines was described by Rau (1966). Tracer injection and sampling were automated, and an infrared detector was used to monitor the nitrous oxide. The pipeline operator

Tracers in Facility Operations

383

reports an overall error of about 1 percent compared to installed meters. A portable tracer injection-detection unit (Dorr, 1966) was designed for such chemical tracers as ammonia. Neon was used as a tracer for meter proving in small fields in Holland (Nederveen et al., 1989) to calibrate the accuracy of venturi meters for metering wet gas. The major problem reported with the use of neon was its high cost, which led to analytical problems in monitoring extremely low concentrations of neon. It is better to choose a tracer whose dynamic range is known to exceed requirements before starting such a test. The m a i n advantage to the use of g a m m a - e m i t t i n g tracers is the ability to monitor the tracer externally without having to sample the line or analyze samples. Most of the measurements reported used the pulse-velocity method. The procedure brings no loss in accuracy and, for field applications, a tremendous gain in convenience. The simplicity of data acquisition and interpretation makes this by far the easiest way to meter a line. If chemical tracers are used, the continuous injection method is probably the easiest, since it simplifies the sampling and requires no calibration. The automated pulse-injection sampling procedures using i n s t r u m e n t a l analyses described above can also be brought up to date with modern chromatographic detection for metering gas lines. Chemical tracers can also be measured in situ by inserting suitable detectors through the pipe walls. This would avoid the need to take samples. Electrochemical and optical (spectrometric) detectors have been developed for monitoring the concentration of m a n y chemical species. Many are used u n d e r flow conditions, particularly in chromatographic applications, and should be applicable to oilfield pipes used for single-phase flow. The problem is t h a t m a n y oilfield fluids are not "clean"; oilfield water is usually contaminated with oil, and the produced oil often contains water. This contaminates the m e a s u r i n g interface and results in poor measurements. The contaminant often makes the liquids opaque to optical detectors in the useful spectral regions and causes problems with electrochemical detectors because of surface alteration by the contaminants. Recent developments in electrochemical detectors have improved both their response time and their ruggedness. Some of these detectors may be presently applicable or may become so in the near future. All of these procedures require a way to inject the tracer into the system. This can be done through a valve present in the line or by hot-tapping one into the line at a suitable position. Injection procedures, whether radioactive or not, should include a means of first leak-testing the fittings and then doing the injection under line pressure. It should also include a means of decontaminating the injection port afterwards. In all m e a s u r e m e n t s of this type, good results require good housekeeping. For ease in entry, some sort of lubricator is desirable, as is a smalldiameter injector for use at high pressures. Tracer pulses should be injected in as short a time interval as possible, particularly when pipe flow rates are high, to avoid diluted pulses.

384

Chapter 8

LINE METERINGWITH ISOTOPE GENERATORS The disadvantage to using radioactivity lies in the dangers of contaminating the fluids and of exposure to radiation. These can be avoided by using an isotope generator to generate a short-lived activity in the pipe. A short list of isotope generators is given in Table 2.1. The 137Cs]137mBa generator for measuring flow rate in pipes and for meter proving has been reported in several publications (Newacheck et al., 1957; Gwyn, 1961; Kugener et al., 1972; Arino et al., 1973; and Turtiainen, 1986). The Ba-137m half-life of 2.7 min is long enough to allow flow measurement at most flow rates in the field and is too short to be a contamination hazard. The amount of Ba-137m milked for a pulse injection can be tested in situ and limited to avoid a radiation hazard, or the tracer can be milked continuously and injected at a constant rate. Other generators with longer-lived daughters and different energies are available. One of the earliest commercially available generators for this purpose was described by Newacheck et al. (1957), who proposed its use for flow measurements in pipes. The generator was composed of two vessels, one containing the flushing (eluting) solution, the other containing a water-filled ion-exchange cartridge on which the cesium-137 is fixed. Solution is transferred to and from each cylinder by gas-driven pistons controlled by a set of electrically operated valves. The generator and the sequence of steps required to milk it are described below and shown in Fig. 8.9. The generator is shown at rest in step 1. Barium-137 and the flushing solutions are being withdrawn into their respective pistons in step 2. In step 3, the generator piston is delivering the barium-137. Step 4 follows immediately after step 3 to flush out the remaining tracer. After this step, the system is ready for the next injection. The system was designed for a maximum injection pressure of 600 lb/sq in. The design of this generator was limited by the relatively poor selectivities of the ion exchange resins available forty years ago. The ion exchange cartridge used was capable of only 20 milkings before the cesium-137 parent began to break through. At the end of this time, a new cartridge would be required. Such generators are not commercially available today. Materials are now available that have selectivities many orders of magnitude higher for separating barium from cesium and should be usable for thousand of injections before any cesium would begin to leak. The generator described above was used to monitor flow through a process unit with residence times in the order of seconds. Detectors were placed on the 12-in. diameter, schedule-40 pipelines entering and leaving the unit as shown in Fig. 8.10 (Gwyn, 1961). The generator was used to inject a short pulse of barium137 upstream of the system. Flow rate was determined by the pulse velocity method. The single-channel analyzer (SCA) is used to choose the radiation energy detected. It can be used to reduce noise and permit multiple tracer use.

Tracers in Facility Operations

385

The count rate meter (CRM) serves here as a digital-to-analog converter. Many inexpensive radiation survey meters come equipped with CRM's and can be h a r n e s s e d to a chart drive as shown by the dashed line connecting detector 1 directly to the CRM. The fast response time in this experiment requires a low time constant for the CRM with poor counting statistics, some of which can be overcome by a high radiation level, and post t r e a t m e n t of the collected data. A modern multiscaler would have been be more suitable for this job. A variant of the procedure for monitoring flow rate in a pipe or gathering line proposes the placement of a gamma ray density device at a point between the two detectors, which would also allow flow rate to be obtained from the transit time of the pulse, and the density of the stream used to estimate the fluid saturations.

I=~~

flushing lution

9

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137 137 Cs- Ba tivity

-

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9~1;I Injection

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~-

Figure 8.9. Barium-137m generator for flow measurements

386

Chapter 8

Vessel or

Flow ~ Detecto~ 1 IBa-137m

injector I

pipe

Detectot 2

I s,,AH CRM I IcRM I--t scAI I I

I Scalerl

CRM = Count rate meter

I Scaler I

Stripchart recorder

SCA =Single channel analyzer

Figure 8.10. Pulse velocity monitor using a barium-137m generator

OTHER ISOTOPE GENERATORS FOR FLOW MONITORING In areas where the emission of radiation is undesirable or not permitted, it may be avoided by using low-energy gamma emitters that do not penetrate the pipe walls. A suitable source is the 99Mo]99mTc generator, producing the 6-hr Tc activity, which emits a 140 keV x-ray. This energy is too low to penetrate most oilfield flow lines; hence it presents no external radiation hazard. It can, however, be detected internally by inserting the detector through the pipe. A 1/2 in. diameter NaI crystal inside a high-strength aluminum alloy or carbon fiber sheath is easily installed through a lubricator mounted on a valve. For most facility operations, the pressures are low enough that little more is needed. For higher pressures, several methods are available for inserting detectors into pipelines. The 6-hr half-life of Tc-99m requires a longer period of time to be reduced to safe levels t h a n the 2.6-min Ba-137m, but the time is short enough to ensure safe operations. For the concentrations used in most pipelines, a reduction in activity by a factor of 1000 would be sufficient. Radioactive decay alone can accomplish this in 2.5 days. The additional dilution with pipeline fluids and dispersion in the line should reduce this time to a few hours. The Tc-99m generator has become so widely used in medicine throughout the world t h a t it is universally available on relatively short notice. In the U.S., it is available in two days at most, calibrated to contain the desired activity on either the evening or the morning of the day of arrival.

Tracers in Facility Operations

387

F L O W R E G I M E IN P I P E AND G A T H E R I N G L I N E S The previous section dealt only with single-flowing phases; however two- and three-phase flows are common in the oil field. How the phases move through the pipe depends on a number of variables, one of which is the fraction of space occupied by each phase. To the extent that each phase has a different absorption coefficient for g a m m a radiation, the phase saturations can be determined by monitoring their absorption of g a m m a radiation. The distribution of the flowing phases in the pipe is the flow regime. This may vary throughout the pipe and will determine to what extent tracers can be used to monitor flow rates of the flowing phases. To a large extent, this depends upon the connectivity of each phase. In a level, uniform section of pipe where the phase saturations are known, tracers can be used to monitor flow if certain conditions are met. One such condition is segregated flow. Here, the flow velocities can be m e a s u r e d by a pulse velocity method, the area of the flowing cross section determined from the phase fraction of the pipe cross section, and the flow rate calculated from the product of the two. Other conditions may provide other solutions. The discussion below is concerned with the m e a s u r e m e n t of phase saturations and flow rates in pipes.

Single-energy g a m m a - ray transmission For a pipeline handling gas and condensate, the flow regime and phase distribution m a y vary widely in different parts of the line, depending upon bends and dips, the presence of sludge, scale or corrosion, local t e m p e r a t u r e differences, and a variety of other factors. In that event, single-phase flow m e a s u r e m e n t s by themselves should be combined with an indicator of the flow regime. This can be done by g a m m a - r a y transmission through the pipe using an external g a m m a source on one side of the pipe across from an external detector on the other. The measurements do not interfere with the flow and are best done by transmission; but some m e a s u r e m e n t s can be performed by g a m m a - r a y backscatter. The differences in density between condensate and gas are great enough to make void (gas) space in the line easy to detect. If slug flow replaces stratified flow, slugs of gas moving down the pipe should be very easy to identify. The presence of condensate slugs in a gas line is typically identified by the sharp decrease in t r a n s m i t t e d g a m m a radiation, as shown in Fig. 8.11. The kind of data shown in Fig. 8.11 are commonly collected using a small 137Cs source and a NaI(T1) detector. Since the denser phases tend to go to the bottom of the pipe, it is usually b e t t e r to scan the pipe vertically with the detector at either the top or bottom of the line, and the source across from it. Lines of this type may vary from 2 or 3 in. to 60 or more in. in diameter, and the source s t r e n g t h needed will vary accordingly. Procedures for e s t i m a t i n g the required s t r e n g t h are discussed in chapter 1. Narrow beam geometry is not

388

Chapter 8

required unless density measurements are to be made; in that event, the gamma source should provide a well-collimated beam if the radiation is to follow the exponential decline given by I = I oe-~ d. The pipe wall density remains constant so that the only changes in density will be due to the movement of slugs of liquid and gas. The movement of gas and liquid is easily monitored by the abrupt differences in density. In oilfield work there are frequently two liquid phases, water and oil; and this method will not distinguish between them unless the density difference is greater than usual.

Flow direction v

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50

60

Figure 8.11. Condensate slug monitoring by gamma ray absorption SINGLE-ENERGY GAMMAFOR THREE-PHASE FLOW By itself, a single-energy gamma ray density meter can normally distinguish between gas and liquid, but not between two liquids of similar densities. To measure three-phase flow, oil and water must be monitored separately. The applicability of tracer methods to monitoring three-phase flow must depend strongly on four factors" the flow regime, the phase saturations, how well the injected tracer pulses mix with the intended phases, and physical conditions in the pipeline. For uniform sections of pipe, flow measurements should be possible under certain

Tracers in Facility Operations

389

conditions. If, for example, gas is the major part of the flow, with oil and w a t e r segregated at the bottom of the line, the liquid phase space is defined by the g a m m a density meter, and tracers may be able to monitor the oil and w a t e r velocities, providing the individual flows can be accessed independently. No isotope dilution m e a s u r e m e n t s in mixed phases have been reported, but this would seem to be a viable method, at least under some conditions. Short-lived isotopes from isotope generators should eliminate any hazard associated with radioactivity from such measurements.

Dual-energy gamma for three-phase flow THREE-PHASE SATURATIONS G a m m a transmission can be used to distinguish between oil and w a t e r if low energy (E) g a m m a rays can be used to take advantage of the high sensitivity of the photoelectric absorption coefficient, ~, to atomic number, z, since ~ is proportional to z 5, and z for oxygen is 8, compared to 6 for carbon. The photoelectric absorption coefficient, ~, is also proportional to E-3.5; hence, g a m m a rays of different energies will lose different amounts of radiation in water and oil. This has been demonstrated with g a m m a sources of two different energies (Rebgetz et al., 1991; Tomada et al., 1987; Watt, 1967). In this procedure, two low-energy g a m m a sources are combined in a small space on one side of the pipe. An energy-sensitive detector is mounted across from them on the other side of the pipe. Each source emits g a m m a radiation of a different energy, a r r a n g e d in narrow beam geometry. The lower energy beam of g a m m a radiation loses energy, mostly due to the photoelectric effect, which is sensitive to the atomic n u m b e r of the intervening material The higher energy beam is more sensitive to the density of the intervening material because of Compton scatter. If the pipe contains a mixture of oil, gas, and water, each beam will t r a n s m i t a different a m o u n t of radiation in accordance with how it reacts with these materials. The amount of radiation lost in passing through them is a function of their mass absorption coefficients, ~lij, which are the sums of the photoelectric and the Compton absorption coefficients of the materials in t h a t phase,i, for each energy, j. The r a d i a t i o n t r a n s m i t t e d from each source will be therefore be different and, as discussed in chapter 2 for narrow beam geometry, there will be two equations for Ij, the t r a n s m i t t e d radiation, as given by eqs. (8.10) and (8.11) below:

I1 = Iol e-((~tol Po%1 + ~wl Pwaw + ~gl pgag)D);

(8.10)

I2 = Io2 e- ((~o2 Po % + ~w2 Pw aw + ~g2 Pg ag)D); and

(8.11)

ao +aw + ag = 1

(8.12)

390

Chapter 8

where ~ij is the mass absorption coefficient for each phase at energy j, p is its density, and a is its volume fraction. The three phases are: w = water, g = gas, and o = oil. The high-energy beam is denoted by j = 1, the low-energy beam by j = 2, D is the inner diameter of the pipe, and Ioj is the radiation level from each source when the pipe is empty. Three equations are required to solve for ai, the three-phase saturations; these consist of eqs. (8.10) and (8.11), giving the radiation transmitted from each of the sources, and the saturation condition, given by Eq. (8.12). The volume fraction of each phase can be calculated from these data using the mass absorption coefficients tabulated in the literature for the components of each phase, given the density and phase composition. While little seems to have been published on it, this procedure is a commonly used laboratory technique for measuring three-phase saturation in cores. It appears to be a semicommercial technique for measuring pipeline saturations in Australia and has been reported elsewhere for this purpose. A dual gamma source for this purpose is illustrated in Fig. 8.12 (Rebgetz et al., 1991). . . . . .

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9!i![ p'p Figure 8.12. Dual gamma radiation for three-phase saturations Two sources commonly used for these measurements are the 7.5-yr half-life 133Ba and the 240-yr half-life 241Am. Rebgetz et al. (1991) have discussed results obtained using the 59.5-keV gamma ray from 241Am in conjunction with the 356-keV gamma ray emitted by 133Ba. The estimated precision and long-term counting stability for the 59.5keV and 356 keV sources using a scintillation detector was 0.1percent (1~). The errors in determining the oil volume fraction due to counting statistics are shown in Fig. 8.13 as a function of pipe diameter for salt concentrations varying from 0 to 20 percent. The errors decrease with increasing pipe diameter (path length) and with increasing salt concentration (density). No error appears to be induced by changes in convective flow in the

391

Tracers in Facility Operations

pipe, though no sudden changes in flow regime were tested. Other experimenters (Tomada et al., 1987) have worked with the 17.4- and the 59.5-keV g a m m a rays, both emitted by 241Am, which provide higher sensitivity at a loss in penetrating power. Relative penetration of the two low-energy gammas for a 50/50 wt percent oil/water mixture are shown in Fig. 8.13b (Rebgetz et al. 1991), at salinities of 0 to 20 percent. The p a t h length of the g a m m a ray method is limited by the absorption of the lower-energy member of the gamma-ray pair, in this case to 50 m m or less, below the diameter of many oilfield production lines. The sensitivity of the measurement is, however, greater at the lower energy.

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-

300

Figure 8.13. Transmission of 17.4- and 59.5-keV gamma rays through liquid To monitor three-phase flow under field conditions, it is necessary to measure saturations as a function of time under conditions where saturations m a y vary abruptly with both time and location in the pipe. The effect of a small perturbation in time was tested by inserting short bursts of air in a three-phase system. The errors induced by these rapid changes were small, providing the activity was high enough to give a statistically valid count over an interval shorter t h a n the burst interval. The effects of large shifts in flow regime were not investigated. These m e a s u r e m e n t s cannot be made through the steel pipe walls used in high-pressure pipe or gathering lines in the field; however where fiberglass or other types of plastic pipe are used, it is a viable procedure. For steel pipe it is necessary to insert the source through the pipe wall using a high strength beryllium or aluminum window. For narrow-beam geometry, the window should be of relatively small diameter so that the total force exerted upon it is minimal. The

392

Chapter 8

NaI detector can also be enclosed and inserted through the wall using a lubricator. The low energy of the sources chosen places a limit of about 10 in. on the thickness of the fluid column that can be scanned at these energies. For scanning liquids in pipes of greater diameter, higher-energy gamma sources are required, which will cause some decrease in sensitivity to photoelectric absorption. For energies below 400 keV, however, this may still provide adequate separation between water and oil. The energies required for any given thickness of water and oil can be estimated from tables and charts such as those given in Fig. 1.12. The response from two different g a m m a ray energies, transmitted in narrow-beam geometry, can be described by eqs. (8.10) and (8.11). By adding the s a t u r a t i o n condition, Eq. (8.12), the individual phase saturations can be calculated. Additional energy channels can be used and the error minimized by a least squares procedure. An inverse of this concept was used in chapter 7 to estimate the distance from source to detector down hole using the ratio of radiation arriving at the detector in two different energy regions from a single-energy source. In this case, the higher energy region represented the arrival of relatively unscattered g a m m a radiation, while the lower-energy region represents the arrival of radiation degraded by Compton scattering. The downhole geometry was poorly defined, and distance estimates obtained from this procedure ~vere very approximate. If the distance from source to detector is fixed, and good geometry is used, it should be possible to monitor the location of one or more radioactively tagged phases in tanks and pipes. Such work has not been reported.

Dual-detector dual-energy systems for three-phase flow In the procedure described above, gamma radiation of two different energies was used to measure oil and water saturation in a three-phase system. The use of a pair of such dual energy density meters has been proposed as a means of m e a s u r i n g the velocity of oil and water in a three-phase system. Such a procedure was tested and described by Watt et al. in a recent paper (1991) in which simple laboratory experiments and computer modeling were used to investigate the possibilities of the method. In this procedure, the response function, R, of the two dual assemblies is defined as the ratio R1 to R2, where:

R1 In(Io/I)l

R- R2- In(Io/I)2

(8.12)

Here, Io refers to the transmitted radiation when the pipe is empty or gas filled, I to the same when oil or water is present, and subscripts 1 and 2 refer to the two dual-energy stations. Cross correlation of the response function, R, from the two

Tracers in Facility Operations

393

dual-energy pairs shows that it is proportional only to the mass fraction of the liquid phases and independent of the mass fraction of the gas.

ipe

Lead shields/ collimators

~

Scintillation

~!

detectors

,5~

,ooo,

Gas

Water

,

,,

!

Ax

=

~ooo~ ~

i!!I~4~

!

mm

I 0 mm

25001

5 mm

20001 1500!

Radioactive

15

1000

.

.

.

.

.

.

.

.

300 r

| , 0% 'o.'~ o.',|

o.'| , ,i" o.,|

,

.o

i1

Time delay, seconds

ZX Compressed air

Figure 8.14. Dual energy pairs cross correlated for flow velocity Two kinds of tests were described, one on the effect of gas in monitoring the velocity of water, and the other on the effect of brine on monitoring the velocity of oil. The laboratory test procedure for monitoring the effect of gas is shown in Fig. 8.14a, and the results obtained from the test are shown in Fig. 8.14b. This test compares the cross correlation from two-phase flow of air and water at velocities of 1 and 5 m/sec, for different thicknesses of air in a 150-mm diameter pipe, using stations 500 mm apart. The cross correlation of the single-energy gamma (Am-241) from the two stations is shown in the upper part of Fig. 8.14b, where minima in time correspond to both the oil- and gas-phase velocities. The dual-energy function in the bottom part of the figure shows a minimum only for the liquid phase velocity. Similar tests measuring oil velocity in the presence of brine showed good agreement between dual-energy and single-energy stations.

394

Chapter 8

To obtain useful velocity numbers, it was necessary to keep counting rates high enough to m a i n t a i n the counting error below 0.1 percent. F u r t h e r work is being planned using flow loops.

Gamma-ray backscatter The alternative to g a m m a - r a y scanning through the pipe walls is to use a b a c k s c a t t e r device inside the pipe by mounting it through a sidearm. Such a device, containing both a g a m m a source and a detector shielded from the source, should produce a signal due to the backscattered (Compton) radiation proportional to the density of the fluid in the pipe. A low-energy g a m m a ray source can provide a high-intensity field with no external radiation h a z a r d and simple shielding of the detector. By using two different energies, it m a y be possible to measure oil and water saturations in small-diameter pipes using the same principles discussed earlier for t r a n s m i t t e d radiation. Assuming t h a t there could be large v a r i a t i o n s in the local s a t u r a t i o n s as a function of time, such meas u r e m e n t s m u s t be made at a high enough counting rate t h a t small changes in s a t u r a t i o n can be monitored in the presence of noise (counting statistics). No such work has been reported. THREE-PHASE SATURATIONS Most pipelines are buried and not very accessible for gamma-ray transmission except where special areas have been exposed for this purpose; however the top of the pipeline can easily be made available to monitoring by g a m m a - r a y backscattering. Most such pipelines are too large for saturation m e a s u r e m e n t s by backscatter, but one can take advantage of special situations. If the fluids are gravity segregated, or if the fluids are highly dispersed, saturation m e a s u r e m e n t can be used in small regions to estimate the entire flow. It should also be possible to combine radioactive methods with nonradioactive techniques such as electrical and acoustic methods to improve the flow measurements; unfortunately, however, there seems to be relatively little cross-fertilization between these technologies. PIPELINE WALLS G a m m a - r a y backscatter can be used on a pipe wall (or other facility wall) in the same m a n n e r as it is used on casing down hole. The penetration distance is relatively short, with the major effect caused by material adjacent to the wall. As a result, it can be a useful method for monitoring deposition of material inside the pipe walls, and of corrosion or erosion of the walls. It might also be useful for determining flow regime if there is a distinctive flow layer along the wall. This seems to occur when certain mixtures of heavy crudes and w a t e r are shipped in pipelines; it may also occur in some qualities of steam flow. As in borehole

Tracers in Facility Operations

395

logging, the depth of penetration is related to the spacing between source and detector. A variable detector distance may have some advantages here. Another procedure for examining the inside of a pipeline is by backscatter g a m m a radiation from a source-detector pair on a pipeline pig. This would locate any unusual buildup of sludge or scale as the pig traveled down the pipe.

Gas v

?-

Foam

Oil Neutron response

Tank

I

Neutron backscatter tool

Figure 8.15. Neutron backscatter measurements

Neutron methods

The use of a neutron transmission device for monitoring s t e a m quality in pipes was described in chapter 7 in the section on steam injection. This procedure is not restricted to steam in pipelines but is applicable to hydrogenous material in any vessel, since the steel walls are relatively t r a n s p a r e n t to fast neutrons, which are moderated by the hydrogenous material inside pipelines, storage, and separation facilities. Measurements are most conveniently done by neutron backscatter, where the neutron source and the detector are outside of the vessel wall, a n d the detector responds to the cloud of slow n e u t r o n s formed by the moderating material inside the vessel. The difference between hydrocarbon gas and liquid would show up as a sharp difference in hydrogen density; whereas the difference between oil and water would be relatively small. Foam would show up as a zone of distinctly different hydrogen density, a useful monitor for separation vessels and storage tanks. Zones of high or low liquid (hydrogen) content moving in a pipeline would also be visible. Portable neutron backscatter tools for looking

396

Chapter 8

at flow distribution in pipes and tanks have been made commercially (Charlton et al., 1981). A schematic showing the detection of a foam zone between gas and liquid in a t a n k using a neutron backscatter tool is shown in Fig. 8.15. These tools use small chemical neutron sources and are well shielded for use by hand. N e u t r o n s have an advantage over g a m m a radiation for use as a backscatter source because the pipe walls are much more transparent to neutrons. Another possible application of neutron backscatter or transmission is the (n,7) reaction, leading to a prompt or delayed g a m m a response from the high neutron cross section of chlorine to differentiate between saline water and oil. The same techniques used in neutron logging down hole are available for pipeline use, except t h a t the geometry can be a lot better in the neighborhood of a pipe or storage vessel than down hole, and small, chemical neutron sources can be used.

Combined methods In downhole logging, it is traditional to combine m a n y logging tools in scanning a hole. It would be equally useful to do the same thing in working on pipes and gathering lines. The combination of neutron and g a m m a backscatter and transmission measurements with tracers, acoustic, electrical, temperature, and other types of m e a s u r e m e n t s might reveal a lot more detail t h a n would any method alone.

U N D E R G R O U N D GAS S T O R A G E Underground storage of gas is common in the collection and distribution of gas to the public from a flowing gas supply. It is particularly important for balancing the variable needs brought on by seasonal demand. Stored material can come from m a n y sources and have different compositions. Tracers can be used to determine how these gases behave in storage, and to answer the question always associated with this kind of storage: how secure it is against leakage from underground or surface paths?

Tracers for underground gas storage Several studies have been performed on the security of gas in such storage. Tracers, both radioactive and chemical, have been used for evaluating gas loss by tagging the stored gas. Early work assessed the use of helium (Frost, 1946, 1950) and radioactive tracers (Armstrong et al., 1951) for tagging gas. There was some fear t h a t these were not suitable for long-term monitoring of gas in storage. Helium was thought to be too mobile, and radioactivity was not suitable for use in gases for public consumption. One study of produced gas (Walker et al., 1966)

Tracers in Facility Operations

397

proposed the use of ethylene as a tracer for stored gas, since it did not occur in n a t u r a l gas. A series of tests in both w a t e r - s a t u r a t e d and dry sandstone cores showed t h a t ethylene had some losses but was suitable for use as an identifying tracer. PROCEDURES IN CURRENT USE Vogh et al. conducted a literature search and survey of all the storage-facility operators in the U.S. and published a report (1987) listing tracers and other procedures used to identify gas from an underground storage cavity. The three tracer methods for identification of injected storage gas in c u r r e n t use are 1) addition of tracers, 2) compositional analysis of the stored gas, and 3) isotope ratios of selected components in the gas. Operators had little knowledge of tracer gas migration characteristics or of the stability of m a n y tracers under reservoir conditions. All operators depended on inventory or pressure methods to monitor the integrity of their storage systems. Tracers were likely to be used only when specific questions came up, although there has been a decrease in use of radioactive tracers because of public opinion. Olefins are often used as gas tracers (Walker et al., 1966) but have recently become suspect because of the possibility of biogenic olefins, as reported for ethylene (Cole et al., 1985). Sulfur hexafluoride and chlorofluorocarbons are also commonly used tracers. Compositional analysis may have some problems as a gas identifier because of the possibility of compositional alterations due to mixing with other gases on passing through the formation. Specific concentrations of such gases as He, Ar, N2, and CO2 have been used as gas identifiers but these may also undergo compositional changes. The ratio of C-13 to C-12 in stored gas has been used to differentiate stored gas from "swamp" gas or other biogenic sources (Coleman, 1985). The i n d u s t r y seems to be relatively unconcerned about the lack of monitoring, probably because there are no other storage options.

Kr-85 for pretest of storage integrity Tracers of various kinds were used for studying some of the problems associated with underground gas storage. Krypton-85 was used as a tracer (Teumer et al., 1973) for verifying the tightness of an aquifer storage under operating conditions before using it for storage. Air was tagged with Kr-85 at a constant level by adding tracer in pulses at thirty-minute intervals. The tracer concentration was kept at the maximum permissible concentration (MPC) for Kr-85 of 10-5 Ci/m3. The unit was carefully designed to ensure that tracer concentration was maintained at the correct level. An air ionization chamber was used to monitor the Kr-85 beta emission. About 15 x 106 m 3 of air was injected into the formation at a pressure of 70 atmospheres. No leaks were found, and the system was approved for gas storage.

398

Chapter 8

Hydrogen tracer for gas mixing in underground storage Underground storage frequently involves a number of operations beyond those of receiving, holding, and delivering, including such operations as 1) use of a storage unit for selective storage of gases having different compositions; 2) conversion of native working inventory to pipeline quality dry gas; and 3) replacement of part of the gas cushion by an inert gas. For these reasons, and to gain a better understanding of how flow of gas is affected by mixing and dispersion in underground storage, several tracer tests were made (Carri~re et al., 1985). Hydrogen was used as a tracer in this series of tests designed to answer some of the above questions. This tracer test was undertaken in an underground gas storage reservoir at Germigny-sous-coulombs in France. This reservoir is being developed for high BTU gas storage while part of its cushion gas will be of low BTU content. The purpose of the test was to determine the dispersive characteristics of the gases in order to calculate the respective amounts of each gas to inject.

Pressure valve

.r===== Chromatograph

l

Nozzle>~ 9

I~

I

/

/ ' ~,r os

9 I.

Computer

~llhe Tracer

Pressure reducer o

~1r J , ~ ~' t

o

Gathering Pipe

'~ Well

Figure 8.16. Hydrogen tracing for storage leaks The hydrogen tracer was injected at a constant rate and concentration using a sonic nozzle. It was injected with 5 x 106 m3 of natural gas at a constant gas flow rate of 720,000 m3/d. The hydrogen concentration of the injected gas was maintained at 270 ppm and monitored by a computer-controlled gas chromatograph. Figure 8.16 is a schematic showing the equipment used. The gas was injected

Tracers in Facility Operations

399

into well CR23, the geographic center of the "gas bubble." The concentration profiles were monitored at three observation wells, CR03, CR24, and CR26, located at distances of 200 m, 200 m, and 320 m, respectively, from the injector. This was followed by the injection of 16 x 106 m 3 of a chase gas. (All gas volumes are given at 0~ and 1 bar). The results, presented in terms of reduced concentration, are shown as points in Fig. 8.17. A numerical simulator was also used to model the flow. The results obtained from the s i m u l a t o r were modified to improve the flow model by fitting the field tracer data as shown in Fig. 8.17.

1.0

1.0

8o

o3 0

10

o

8ot

20 Days

30

.

.

.

.

10

_

-

0

_.4 ee

CR26

0

0

.

.

Days

.

20

, ~

|

10

Days

20

30

Experimental Simulated

.

30

Figure 8.17. Simulated and measured tracer profiles

Troubleshooting with tracers One of the most common uses of tracers in underground gas storage is for troubleshooting when gas-loss problems arise. One i n t e r e s t i n g application of tracers is described in a paper (Araktingi et al., 1982) giving a case history of leakage problems in a gas-storage cavity in Utah. It shows how problems are solved by combining m a n y different kinds of information. In this case, reservoir simulation, well logging, tracer surveys, surface monitoring and engineering evaluations were used together to arrive at a solution to the problem. The avenues of gas leakage were identified by using a different tracer for each path. In this case, t r i t i u m gas, Kr-85, tritiated methane, and sulfur hexafluoride were

400

Chapter 8

used as initial test tracers. Tritiated ethane was used as a final t r a c e r when m a n y of the well problems had been solved. OIL, WATER, AND GAS S E P A R A T O R S Oil, water, and gas are separated at the facility because of the difference in their densities, aided to some extent by the difference in other physical properties. Separation is done in a continuous manner, frequently in staged separators, with each p h a s e - oil, water, and gas - - s u b j e c t to further separation. There are factors involved in phase separation by gravity separators t h a t are not subject to investigation by the use of tracers and are not discussed here. An import a n t factor t h a t is subject to such examinations is the amount of time the fluids spend in the separator. Ideally, the incoming fluids should move through these separators by plug flow, with a long enough residence time in the separator for the phases to separate in the gravity field; however, in practice plug flow does not occur, and instead of a single residence time there will be a distribution of residence times about some mean. The injection of a pulse (or step function) of tracer is used in the chemical process industry to study the distribution of residence times for nonideal flow. There is a large literature on the subject and a well-developed tracer methodology and nomenclature (Levenspiel, 1972; Himmelblau and Bischoff, 1968). The residence time distribution of the fluids moving through the vessel is determined by injecting a tracer pulse at the inlet to the vessel and monitoring the tracer response as a function of time at the outlet. The mean of this distribution is the m e a n residence time, which is used as its locator and is given by the first moment of the distribution. The spread of the distribution about the mean is given by the second moment. This was discussed earlier in chapter 4 in relation to a distribution of swept volumes based on the work reported above on residence time distributions in vessels. The first moment of a distribution was also used in chapters 5 and 6 in discussing residual oil measurements by tracer delay.

Residence time distribution (RTD) in oil/water separators OIL/WATER SEPARATORS Oil and w a t e r are separated in various kinds of gravity separators, which share a variety of names. Many include auxiliary features such as injected gas, heat, and an electric field for aiding the separation. All ultimately depend upon the difference in their densities for the separation. Vessels used to separate gas, oil, and w a t e r are called three-phase separators. Those separating w a t e r from oil are called free-water knockouts (FWKO). Other terms for the oil/water separator are gun barrel, wash tank, settling tank, skim tank, flotation tank, and chemicalelectric tank. In m a n y cases, either water or oil forms a continuous stream with the opposite phase entrained as droplets.

Tracers in Facility Operations

401

One of the principal functions of the separator is to allow enough residence time in the unit for the individual droplets to rise or fall in the gravity field and form a continuous phase that can then be removed. Analysis of a tracer response curve, as used in the chemical process industry to describe flow behavior in vessels (Levenspiel, 1972), will be applied here to analyze flow in separators. This is the basis for the analysis used in chapter 4 to estimate the m e a n swept volume between wells. In the ideal case of plug flow, all the elements of fluid spend the same amount of time in the vessel and have the same residence time. In the extreme case of fully mixed flow, there is an exponential distribution of residence times with a maximum at zero time. Real flow in separators lies between these extremes, usually, with an asymmetric distribution of residence times about the m a x i m u m (mode). All three of the above cases may share the same mean residence time but have widely different distributions. HYDRAULIC BEHAVIOR OF API SEPARATOR Two of the earliest studies using tracers to study hydraulic behavior in gravity separators were performed on the passage of liquids through percolating beds (Clifford, 1907) and on the flow of sewage in precipitating tanks (Clifford, 1922). Clifford used both dyes and salt (NaC1) as tracers and observed that one-third of the volume of most tanks is not used in the separation. The first investigator to report oil/water separation with rising instead of falling particles was Hart, who in a series of papers (1938, 1947) provided most of the basics for design of the American Petroleum Institute separator (API, 1969). The separation of small amounts of oil from relatively large amounts of water remained a problem in the separator. This led to an API-sponsored study of the hydraulic characteristics of the API separator at the University of Wisconsin in 1948. In t h a t study (Rohlich, 1951), phosphate ion was used as a tracer to follow the behavior of the water. The tracer was injected as a pulse at the inlet to the t a n k model. The outlet water was sampled for produced tracer concentration. Results were expressed in the form of dimensionless response curves. Rohlich analyzed the data by plotting dimensionless concentration (C/Co) versus reduced time, = t/t,, where c is the measured concentration at time t, Co is the initial concentration of the injected tracer pulse, and t is the mean residence time for the tank. The study considered the effect of various outlet and inlet configurations, and of single-stage vs. two-stage models. HYDRAULIC BEHAVIOR OF OILFIELD SEPARATORS Many years later, Zemel and Bowman (1978) examined the hydraulic behavior of both water and oil in several different separators in common oilfield use. While these were not API separators, the principles of separation were the same. These tests were made under normal operating conditions, except t h a t every effort was made to maintain a constant flow rate during the test. Different kinds and amounts of emulsion treatment were in use at the time but were ignored for

402

Chapter 8

this purpose. Tests were made on free-water knockouts of different design and on several different wash tanks and flotation cells. In each of the tests, a pulse of tracer was injected into the line at the input of the separator and the tracer response measured at the output on an exit line. The field test procedures had been described in an earlier report by Zemel and Burton (1977). The tracer response curve, C = f(t), was characterized in terms of the first two moments of the distribution, defined here as the mean residence time, t, and the variance, o2, respectively (Levenspiel, 1972). The tracer response curves were expressed in terms of dimensionless time, ~, plotted against dimensionless concentration, E(r to make comparisons between separators independent of capacity or dimension, where the dimensionless parameters are given by: = t / t ; and

(8.13)

i

E(r

=

~Ct ZCt At

(8.14)

where Ct is the measured tracer concentration at the elapsed time, t, At is the interval of measurement, t is the mean residence time, and the value at ~ = 1 is the m e a n residence time for the separator. Operational constraints often terminated these field tests before they could be completed; however the tail of the curves was found to fit the exponential decline for fully mixed flow, as described in chapter 4, and the equation for the m e a n residence time, calculated in the same m a n n e r as for the swept volume in Eq. 4.14, is given by: te ~Ctdt + aCe(a+te) ~= o te ~ C d t + aCe

(8.15)

o

where a is the inverse slope of the exponential decline, te is the time at which it is applied, and Ce is the tracer concentration at that time. The second moment of the tracer response distribution is its variance o2. It is given by: oo

~ C ( t - t )2At O2 = 0

(8.16) oo

~CAt o o2 is a measure of the width of the distribution and in some cases can be related to the Peclet number, the ratio of convective to dispersive forces. It is important here as a measure of deviation from plug flow. This equation can also be fitted to

403

Tracers in Facility Operations

an exponential decline by s u b s t i t u t i n g the time-equivalent of Eq. (4.8) into Eq. (8.16) and integration by parts.

te ~Ct2At (~2 =

0

+ a C e ( t 2 + 2 a t + 2a 2) te ~CAt + ace 0

. ~2

(8.17)

Variance of the dimensionless residence time distribution, ~(~)2is given by: (~2 a ~ -

=

_

t

(8.18)

This kind of analysis provides a general picture of how fluid moves through the vessel but gives no details about the spatial distribution of flow inside the vessel. Tests were performed on the flow of both oil and water using an appropriately soluble tracer, of different gamma energy, for each phase. Only a few of the m a n y kinds of separators available are discussed here. Most had a spreader system to distribute the incoming fluid uniformly through the tank. In m a n y cases, unfortunately, these were plugged by solids deposited in the tank, so t h a t their effectiveness could not be judged. The separators tested here were judged on how well the flow through the separator approximated plug flow. In general, the narrower the distribution of residence times about the mean (the smaller the standard deviation, (~,), the better the separator performed. In those cases, as discussed below, where the standard deviation, (~, was not a good operational criterion, it was because of the presence of other factors.

Free-water knockout This horizontal free-water knockout (FWKO) was equipped by the manufact u r e r with removable internal baffles. Tracer tests were used to determine how effectively these baffles functioned. Fig. 8.18 is a schematic of the FWKO showing its internal construction. Tracer tests made with the baffles out gave the response curves for oil and for water shown in Fig. 8.19a. The effect of inserting the baffles is shown by the response curves in Fig. 8.19b. These data show t h a t the FWKO, with or without baffles, has a reasonably narrow distribution about the mean. Removing the baffles had two effects: it broadened the distribution about the mean and it increased the mean residence time by a factor of two. The effect of the baffles seems to be t h a t of shielding a large section of the vessel from flow, which seems to give a narrower distribution of flows, but at a cost of vessel capacity. In either case the vessel capacity was adequate for the separation.

Chapter 8

404

Emulsion inlet ( L F ~ ~ ~ _

Oil outlet ~_

Water "9 ~ out 3 R~emovablebaf/fles /- Weir box

Figure 8.18. Schematic of free-water knockout

2.4 ~"

1.2

FWKO a.Baffles out Water ,,--,, ,oil

0.81 /~,, 0.4

I/,,,"

.., ,,n.nV""-

0.0 0.4 0.8 ,

I

1.2 1.6 2.0 2.4 ,.

0

2.4 I

F~,

~.o /

f ",

~KO

FIX o.8L

/,,~, oil

0.4It / / o.g.o

i o.~

0.8

water

~ ~.~

~.o

.o

~:~

0

Figure 8.19. Effect of baffles on operation of free-water knockout

405

Tracers in Facility Operations

15, O00-barrel wash tank This vessel was intended for a primary separation of a heavy oil (12~ from produced water. It is a large tank, about 52 ft in diameter and 40 ft high. A schematic of the t a n k showing its internal configuration is given in Fig. 8.20.

i f

r "~

_~ 0 0 .Q

__~__~s pot /

fill

4-*-

// i_ ~'' to spreader/// "--..~16" spreader~..~

Figure 8.20. 15,000-bbl wash t a n k with spreader detail At the time of the test it contained 6000 bbl of oil and 7500 bbl of water. The input flow rate was 3200 BOPD and 6800 BWPD. Hence, a mean retention time of 45 hr was expected for the oil and of about 33 hr for the water. The actual tracer responses obtained for the oil and water are shown in Fig. 8.21. In each case, tracer broke through immediately, peaked in minutes, and then decreased to near background before a meaningful extrapolation could be made. This behavior represents an extreme case of short-circuiting. Oil and water had probably separated in the gathering lines before entering the tank. The wash t a n k functioned only as a storage vessel for old oil and water. Short-circuiting, although not usually so extreme, is a common failing of large-volume t a n k s of this type. The spreader design is shown in the figure to indicate the sort of efforts made to spread the inlet fluids in the tank. In this case, the spreader would have

406

Chapter 8

made no difference, but it was largely covered by sand deposited at the bottom of the tank.

15,000-bbl wash tank Tracer response (in arbitrary units) II II II ql

._~

11

9 ",i~

II II

L_

o

', ,,

e

1 I. , i

0

I

4

8

12

16

20

24

28

Elapsed time (minutes)

Figure 8.21. Tracer responses for 15,000-bbl wash t a n k

Sequential dispersed gas flotation cell One of the most efficient oil-water separators used in these California fields was a sequential, dispersed-gas flotation cell. Fig. 8.22 shows a schematic of the separator. It is composed of an inlet chamber, four completely back-mixed flotation chambers, and an outlet chamber. The flow passes sequentially from the inlet, through each of the flotation chambers to the outlet chamber. Gas is drawn down by the vortices formed in each chamber by rotors (inductors) and is dispersed into the fluid. The experimental t r a c e r response curve is shown in Fig. 8.23. This is a well-balanced distribution, closer to plug flow t h a n any other tanks tested in this study. The tracer response data were fitted to a tanks-in-series model (Levenspiel, 1972), which t r e a t s linear flow through a separator as though it were passing through a serial combination of fully mixed chambers. As shown in Fig. 8.24, the n a t u r e of the flow varies from fully mixed flow to plug flow as the n u m b e r of

Tracers in Facility Operations

407

chambers increases. The residence time distribution, E(r as a function of ~, for this model, depending upon the number of tanks, n, is given by: E(r =

O~)

n(no)n-1 e-nO (n-l)! and

(8.19)

1 n

(8.20)

2 = --

where o~) 2 is the variance of this distribution, and ~, the dimensionless time, is defined by Eq. (8.13). The variance of the tracer response distribution can be calculated from the second moment using Eq. (8.16) or, if needed, the extrapolated form using Eq. (8.17) and the dimensionless residence time (~(~)2 obtained from Eq. (8.18), related to the number of tanks in series by Eq. (8.20). Separation of oil from oily water by dispersed gas flotation is a complex process and its mechanism is not fully understood. The good fit betwen the tanks-inseries model and the vessel tested verifies the high degree of mixing in each compartment but sheds no light on the actual separation mechanism. Nevertheless, it does show that high mixing forces and rapid through-put are not necessarily bad for such separations.

._ J--I

inlet

~--I

rh

II ..4, k..

Inductors

I

I

I

I

I

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/41

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Figure 8.22. Schematic of sequential, dispersed gas flotation cell

Clean water .

Chapter 8

408

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~

~

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/

/

f

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Figure 8.23. Tracer response with sequential, dispersed gas flotation cell The n u m b e r of t a n k s in series for the sequential dispersed gas flotation (SDGF) cell, calculated from the variance of the tracer response data, was 5.17. Fig. 8.23 shows the curve calculated for 5 tanks in series as a dashed curve and the experimental data from the SDGF tracer test as a solid curve, to show how closely they match. The mean residence time of the water moving through the system calculated from tracer data was 5.8 min, in agreement with the flow rate and the volume of 214 bbl. This was a very effective unit, handling 53,000 barrels of fluid per day and efficiently separating oil from oily water, despite the short residence time. The flotation cell discussed above fits the tanks-in-series model physically and, as shown in Fig. 8.23, accounts for the hydraulic behavior of the cell.

Tracer test procedure The procedures used in these tests were described in a separate paper (Zemel and Burton, 1977). Three tracers were used, the 8-day half-life 131I, the 36-hr half-life 82Br, and the 5.2-yr half-life 60Co. Iodide, bromide, and the hexacyanocobaltate ions, introduced as potassium salts, were used for water tracing. Iodobenzene and an iodinated kerosene, tagged with 1-131, were used as oil tracers. The tracer injector was inserted into a flow line leading into the test vessel by means of a lubricator mounted on a full-opening valve, as shown in Fig. 8.25. The tracers were carried to the field in small glass vials inside a lead carrier designed to permit direct transfer of the tracer vial into the injector by a shielded pushrod, identified in the figure as the tracer loading system. Once the tracer vial is

Tracers in Facility Operations

409

i n s e r t e d into the injector, the latch plate is closed and a r e m o t e h y d r a u l i c drive is used to force the vial into the flowline and s m a s h it a g a i n s t the "Carbaloy" knives.

-~

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0.5

i

o.s

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o.s

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Figure 8.24. RTD of tanks-in-series model as function of n u m b e r of t a n k s The produced t r a c e r was monitored by m e a n s of a N a I scintillation crystal m o u n t e d on top of the outlet line from the separator. A small, b a t t e r y - o p e r a t e d count r a t e m e t e r was used to collect the counts and drive a b a t t e r y - o p e r a t e d strip c h a r t recorder. This is a cost-effective method for monitoring tracers in the field, consisting of a survey m e t e r fitted with a scintillation detector and modified to accept a chart drive. The availability of portable m u l t i c h a n n e l analyzers (MCA) has simplified this kind of operation and m a d e it more flexible, a l t h o u g h at a n increase in cost. W h e n operated in the multiscaler mode, the MCA becomes a digital r a t e m e t e r w i t h at least a t h o u s a n d channels of capacity. The r a n g e of counting t i m e s on such i n s t r u m e n t s is variable and can be set to allow p r e s e t counting times from milliseconds (10~) to kiloseconds (103) per channel. This is more t h a n a d e q u a t e to complete a t r a c e r response curve for almost a n y facility operation. If t r a c e r s of different g a m m a energies are used to tag the oil and water, both fluids

410

Chapter 8

can be monitored simultaneously. Each of these counters has its place in oilfield tracer studies, and they are discussed in chapter 2.

piston stop

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Tracers in Facility Operations

411

E R O S I O N AND C O R R O S I O N Erosion and corrosion are not restricted to pipelines or gathering lines. They can be major problems in any part of the oil field from the borehole to the facilities and sales unit. The occurrence of these problems is associated with handling high volumes of brines, oil, gas, solids, and, occasionally, corrosive materials but often has no apparent cause. There are two parts to the solution of this problem: the first is identification and location; the second is treatment. Tracers have been used in both. Corrosion and erosion problems are rarely visible from the outside and m a y show up in unexpected locations after considerable damage has been done.

Corrosion a n d erosion monitoring Identification of the problem is one of the more difficult oilfield tasks. The corrosion products of iron alloys are usually hydrous oxides or sulfides t h a t are not water soluble and not easily identified in produced fluids. Analyzing the iron dispersed or dissolved in the produced water (iron counts) is still, however, used for monitoring corrosion. Corrosion itself is often nonuniform, leading to a pitting attack r a t h e r t h a n a uniform removal of metal, and the locations attacked are often relatively inaccessible. The presence of excessive iron in solution is always suspect, but the lack of it is no assurance that corrosion has not taken place. Preventative measures can be taken, but detection of corrosion depends upon making a positive search, which is rarely done without reason. The methods used include corrosion coupons, sonic methods, x-rays, and special corrosion probes. Erosion is sometimes predictable, but detection of unexpected erosion is limited to m e a s u r e m e n t of wear, either of the wall thickness or of a coupon placed in areas of potential wear. The principal application of tracers has been in coupons, which provide a signal when the material is corroded or eroded. They occupy a special niche for use in remote locations such as subsea or downhole installations where other methods may be difficult to apply. CORROSION COUPONS

Conventional coupons A corrosion coupon is a metal piece, usually of the same composition as the pipe wall or other area of concern, which can be placed in suspected locations to release identifiable material when it corrodes or erodes. It can be monitored for loss of activity at the coupon site, or released material can be monitored in the produced water downstream. Some of the early uses of coupons were a variation on the iron count method using radioactively tagged steel coupons. In a technique used to monitor corrosion down hole (Gordon et al., 1966), a complete section of well tubing was constructed for use as a downhole corrosion

412

Chapter 8

monitor in an oil well. The section was constructed of a J55 steel to which cobalt was added to a concentration of 0.07 percent by weight. The piece was machined and threaded to fit the tubing string and then irradiated in a nuclear reactor. Cobalt-60 was generated in the tubing section by the 59Co(n,y)60Co reaction to serve as a corrosion monitor for several years. The coupon (section) was placed in the tubing string and lowered to a depth of about 3600 ft. Corrosion was monitored by counting the produced water for cobalt activity. Results of the test with no corrosion inhibitor t r e a t m e n t down hole showed a very sporadic distribution of corrosion activity with a m e a n of 120 _+ 30 mills/yr, in reasonable a g r e e m e n t with the previously m e a s u r e d r a t e of 150 _+ 50 mills/yr. A n u m b e r of corrosion inhibitor t r e a t m e n t s were evaluated by the authors using this corrosion monitor. Laboratory and field tests showed that the tubing section had the same corrosion properties as the s t a n d a r d J55 and t h a t the cobalt activity accurately followed corrosion of the section. The method was shown to be sensitive to a corrosion rate of 1 mill/yr.

Thin layer activation N e u t r o n activation of the mass of metal used in the experiment described above generates a great deal more activity than is desirable or necessary. In most situations, only the material lost from the coupon surface is important; activation of bulk m a t t e r produces undesired additional radiation. A method developed to avoid activation of the bulk m a t t e r is thin-layer activation. In this procedure, the coupon is bombarded by positive ions from a particle accelerator. Because of the limited path length, only a surface layer (Konstantinov et al., 1971) is activated, the thickness of the active layer depending upon the particle and the energy of activation. For a 13-MeV proton beam on iron, the layer thickness (Finnigan et al., 1982) is on the order of 300 microns (~m). This method is commonly used in wear and corrosion studies (Evans, 1979) in reciprocating and rotating machinery. The nuclides generated by this procedure depend on the material irradiated, the accelerated particle, and the particle energy. A method for using thin-layer activation to identify pitting corrosion was proposed in a patent (Conlon et al., 1983). The authors defined a dual i n s t r u m e n t using a resistance probe whose surface is made radioactive by m e a n s of thinlayer activation. Corrosion is monitored independently by both methods. The loss of radioactivity is measured in combination with the change in resistance. The difference between the loss of material according to each method is used to identify pitting (nonuniform) corrosion. OTHER CORROSION AND EROSION DETECTION PROCEDURES A tracer method proposed for automatic warning of pipe thinning (Hopenfeld, 1990) suggested t h a t tracers be imbedded in the pipe walls at suitable locations. The method is based upon a procedure in use by the steel industry to monitor furnace liner thickness in furnaces continuously exposed to molten steel. In this

Tracers in Facility Operations

413

procedure, small holes are bored into the pipe wall to different depths. A small a m o u n t of a suitable tracer is placed in the hole and backed up with a plug t h a t is screwed or welded into place. When the wall thickness is eroded or corroded out, the tracer is released. A monitor is situated on the pipe or at a suitable distance downstream. The author presents equations used to ensure t h a t the diameter of the hole bored does not reduce pipe strength. The presence of small amounts of sand and other fine particulate materials can be a problem in cleaning hydrocarbon pipelines, particularly long lines. A set of experiments (Lingelem et al., 1990) was performed to study how these particles are transported. Small (30~tm to 200~tm) spherical glass beads were activated in a nuclear reactor. Particle velocities in very dilute solutions were measured by following the radiation. The particles showed a dune-like behavior. A critical velocity t h a t was found for suspending the particles in a fluid increased with fluid viscosity. Corrosion inhibitors interfered with particle transport.

Corrosion treating The usual t r e a t m e n t for unavoidable corrosive conditions is to t r e a t the system with a corrosion inhibitor. The function of the inhibitor is to provide a film of active material on the pipe walls that prevents corrosion of the metal. All inhibitors work well in laboratory tests before they are t a k e n out to the field. The problem is how to get the film to the pipe wall under field conditions. Oil and gas wells are commonly treated using one of three application methods: 1) continuous application though the tubing and r e t u r n up the annulus; 2) squeezing inhibitor solution into the formation down hole, from which it is slowly fed back as the well is produced; and 3) frequent batch treatments. The active agents in these formulations are amino derivatives of complex n a t u r a l products t h a t are difficult to analyze, particularly at low concentrations. As a result, tracer tagged inhibitors have played a large part in optimizing these field applications. Iodine-131 is also a common tag for such materials as corrosion and scale inhibitors, which are usually based on materials derived from cheap natural sources t h a t contain enough u n s a t u r a t e d bonds to permit easy addition of radioactive iodine. The g a m m a radiation m a k e s 1-131 tagged inhibitors easy to monitor t h r o u g h the pipe or down hole (Patten et al., 1970), but the short (8-day) half-life limits their use. The m a n n e r in which tracers are used to optimize field t r e a t m e n t is indicated in some of the papers discussed below. In an early test on inhibitors in oil wells (Barr et al., 1965), tritium tagged inhibitors were used to optimize conditions for squeeze inhibition. Two common inhibitor formulations were tested. The tests showed t h a t for the conventional method used, most of the inhibitor was produced back in a relatively short time, and concentrations quickly dropped to levels too low for corrosion prevention.

414

Chapter 8

Subsequent tests showed t h a t the injection of much larger initial amounts of inhibitors and a greater overflush gave significant improvement. A test on the batch t r e a t m e n t of gas wells with corrosion inhibitor reported by Annand et al. (1971) used 1-131 and tritium to tag the corrosion inhibitor. In this set of experiments, the authors compared the effects of inhibitor viscosity and flow constrictions on the inhibitor film thickness down hole. Film thickness was e s t i m a t e d by monitoring the 1-131 tagged inhibitor down hole with a wireline g a m m a tool. Minimum flow rates to obtain good film thickness were noted. The authors determined that a good batch treatment provided inhibition for 60 days. An extensive set of tracer tests was used to develop an empirical equation for optimizing well circulation times (Cameron et al., 1988) in continuous inhibitor treatment. Loss of corrosion inhibition was noted if the wells were either undercirculated or overcirculated. The equation and other field t r e a t m e n t data were put into a computer program for field use. Tracers were used (Baker and Asperger, 1988) to establish the travel time required to move water from an off-shore platform to land, a distance of about 100 miles, to establish whether onshore or offshore corrosion rates should be used for corrosion inhibition. The travel time was long enough t h a t corrosion inhibitor for offshore conditions was needed, which led to readjustment of the corrosion inhibitor pumps.

S C A L E M O N I T O R I N G AND T R E A T M E N T In the present context, scale is meant to include only the carbonates and sulfates of the group IIA cations: calcium, strontium, barium and radium. These form insoluble deposits upon pipe and tubing walls and in the near-wellbore area. This can occur whenever the solubility product, Ksp, is exceeded, where: Ksp = [cation] [anion]

(8.20)

and [ ] represents the molar cation or anion concentration. The solubility product can be exceeded whenever w a t e r t h a t has a high concentration of any of the group IIA cations comes in contact with w a t e r having a high concentration of sulfate or carbonate. These are referred to as incompatible waters. This can also occur when the solubility product is lowered due to changes in temperature, pressure, pH, or ionic strength. The chemistry of these interactions has been extensively studied, and the conditions under which scale formation is likely can be predicted. The precipitation of scale is, however, frequently delayed and can occur in pipes and tubing remote from the original source. The problem with monitoring for scale is t h a t the conditions that actually prevail either down hole or in the facilities are often not known in detail. As a result, scaling is often discovered long after its deposition.

Tracers in Facility Operations

415

Scale can be monitored by m e a n s of scale coupons, by downhole radiation emitted from radioactive scale, by the Ba(n,2n) reaction with 14 MeV neutrons, and by physical m e a s u r e m e n t s t h a t are affected by scale deposits. The latter include loss of flow, x-rays, back-scattered g a m m a rays, caliper measurements, etc. The deposition of carbonate and sulfate down hole is often associated with emission of radiation due to the coprecipitation of radium. No reports of the same association with radiation have been noted for scale deposited downstream from the wellbore, but it seems likely. The radiation associated with downhole scale was discovered because boreholes are routinely logged with g a m m a - r a y detectors. We do not routinely log the facilities for radiation. The possible use of a neutron generator for monitoring barium scales down hole was described in an earlier chapter. Barium sulfate scale is so difficult to remove t h a t early warning should be valuable.

Tagged scale inhibitors The principal application of tracers to scale problems has been in t r e a t m e n t to p r e v e n t scale. Scale deposition can be prevented by the presence of trace amounts of materials called scale inhibitors t h a t act to inhibit crystal formation. A wide variety of compounds has been used for this, including phosphonates, organic and inorganic phosphates, and hydrocarbon polymers such as polyethylene and polypropylene. As in the case of corrosion inhibitors, m a n y of these m a t e r i a l s are very difficult to analyze in the field. As a result, tracer tagged inhibitors have been important in evaluating and optimizing field t r e a t m e n t and in the analysis of residual concentrations. Scale inhibitor t r e a t m e n t s are applied much like corrosion inhibitor treatments. The same kinds of tests have been applied in the field, but for some reason, much less has been reported on the use of tracers for scale inhibitor treatment. A recent report (Suzuki et al., 1989) described a t r a c e r test of a scale inhibitor squeeze t r e a t m e n t in the field. A carbon-14 tagged scale inhibitor was used in conjunction with tritium tagged water in an inhibitor squeeze. The produced w a t e r was analyzed for both tritium and carbon-14. The samples were also analyzed for inhibitor r e t u r n by three other methods, including ion chromatography, thorium titration, and total phosphorous analysis. None of the chemical methods agreed with each other or with the radiochemical method. The authors concluded t h a t the concentration levels were too low for the chemical methods to give good results. About 67 percent of the injected water was recovered, but only 16 percent of the injected inhibitor returned. No reason was proposed; however it is known t h a t these inhibitors can form insoluble compounds with calcium and m a y have reacted with the dolomite surfaces. The success of the t r e a t m e n t was judged by pump run life; in this case, run life was extended by a factor of 3x over the untreated case.

416

Chapter 8

PIPELINE LEAKS Tracers include some of the earliest methods used for leak detection. They are still a common method for detecting leaks. Both radioactive and nonradioactive tracers are used. A French paper (Hours, 1979) gave a s u m m a r y of the development and status of radioactive tracers for pipe leak detection. The author divided leak detection by means of radioactive tracers into two classes: 1) detection of tracer t h a t has escaped the line, and 2) detection of tracer during its displacement along the line. The latter requires a gamma-emitting tracer with sufficient energy to traverse the pipe wall and the soil of burial. Detection of the tracer can occur at the surface of the soil, in holes drilled down to the pipe for this purpose, or by t r a n s p o r t i n g the detector through the pipeline. Many variations on these methods are described, with considerations of safety inherent in any work with radioactive substances. This kind of work requires a specialist in handling radioactive m a t e r i a l s and suitable equipment for monitoring the progress of the tracer. The choice of the most suitable isotope and detectors depends upon m a n y parameters. Tracers for pipeline leaks are not confined to radioactive materials. By far the largest share of tracers used are not radioactive. They include any gas or liquid for which reasonably sensitive, simple analytical methods are available. Odorproducing compounds such as mercaptans are still in common use, but generally restricted to large leaks. SF6 and the halofluoro compounds are popular because of the ease with which they can be monitored by portable electron capture detectors at the surface, or even by simple flame color tests. Volatile hydrocarbons are also common tracers and can be monitored by simple flame ionization detectors; however the volatile hydrocarbons, particularly methane and ethane, are easily confused with ground-generated hydrocarbons. Dual tracers, e.g., an argon/methane mixture, are sometimes used to avoid the n a t u r a l hydrocarbon problem (Heim, 1980). The list of reported and unreported tracers used for identifying pipeline leaks is virtually endless. Carbon dioxide (dry ice), helium, argon, and nitrogen are used as gas tracers; and dyes, volatile organic compounds, and a m m o n i a have all been used in liquids for leak tracing. In addition, physical methods such as t e m p e r a t u r e changes and sonic effects have also been used with success. The real problem in locating leaks occurs when they are deeply buried, subsea, or otherwise difficult to access, and when the pipelines are very long. Many sophisticated physical methods are in use for locating leaks in such situations; however they are not a proper subject for this book. All have their successes and failures; a tracer method t h a t has had some success in subsea application is the t r a n s p o r t of a radioactive source in the pipe. In this method (Bryngelson, 1987), the pipe is filled with liquid and shut in. The liquid and source are then pumped towards the leak until the source becomes stationary at the leak. It is located by a scintillation detector mounted on a subsea vehicle.

Tracers in Facility Operations

417

ENVIRONMENTAL PROBLEMS Tracers are used in a large n u m b e r of environmental problems, m a n y of which have had only a marginal impact on the oilfield side of the industry. Increasingly, these marginal impacts are moving into the m a i n s t r e a m of oilfield operations. Air and w a t e r pollution from oilfield activities are affecting an increasingly u r b a n environment. It is impossible to do justice to all of these tracer applications in this chapter; we will restrict ourselves to a small group of problems uniquely related to the oil field. In this section, we will discuss the incidental production of naturally occurring radioactive material, which has become a political problem in several areas. We will also cover pollution from oily water (as distinct from major oil spills) and from drilling fluids on offshore platforms.

Naturally Occurring Radioactive Material (NORM) Naturally occurring radioactive material (NORM) impacts the oil industry because of the concentration of either radium-226 or its d a u g h t e r radon-222 in normal oilfield operations (Gray, 1990). Radioactive scale has become a handling problem in m a n y areas where sulfate scales are common. In areas where the scale is brought to the surface for removal, the concentration of radioactivity is often high enough t h a t special handling is required (Smith, 1987). The handling and disposal of "low level radioactive waste" is considerably more expensive than conventional disposal. The problem is not restricted to the scale but may cont a m i n a t e pipe yards and reclamation areas. NORM is now under regulation in most industrial nations but has not been specifically regulated until recently in the United States. Unlike most other nations, the U.S. has left regulation of this kind of radioactivity to the individual states, rather than to the federal government. The state of Louisiana was the first to specifically regulate NORM for the oil and gas industry. Equipment and pipes are considered to be radioactive if the radiation level measured at 1 cm from the surface exceeds 25 mR]hr. Soil is monitored at 10-m intervals, and if a high background is detected, samples are analyzed. Soil exceeding 30 pCi/gn~100m2 is declared radioactive. Louisiana imposes a costly set of license fees on operations declared to be radioactive. Arkansas and Mississippi are the only other states that currently address this problem. Most states t h a t address this issue will probably accept the guidelines Louisiana has used; however fee structures and areas of emphasis will probably differ. In addition to the scale problem, the occurrence of radon in association with natural gas has raised environmental concerns. The existence of radon in natural gas from North America has been known since the early part of the century. (Satterly and McLennan, 1918). The problems of radon production had surfaced

418

Chapter 8

from time to time but did not attract attention until radon contamination set off the level gauges in a chemical plant propane t a n k in Houston in 1971. This propelled an industry-wide examination of natural gas production and treatment. Radon-based activity was found in wellheads, transmission lines, gas plants, and storage units. The radon in natural gas does not present a significant health hazard to either homeowners or workers (Gesell, 1975); the problems lie in the fact t h a t the end product of radon decay is lead, including lead-210 (half-life = 22 yr) and the daughter activities in equilibrium with it, Bi-210 and Po-210. These activities are particularly high in gas plant pumps. The separation of natural gas liquids (NGL) seems to separate radon as well and to concentrate it in the pumps and in long-time NGL storage units. The principal hazard will be associated with maintenance and decommissioning of those units that have built up contamination over the years. Other environmental

concerns

Oil production impacts the environment in a great m a n y areas. Much has been written about this in the form of papers and regulations. In the current regulatory climate, virtually everything produced from an oil field has been, and is being, subject to environmental regulations. In addition to produced hydrocarbons and water, this includes the production of a great m a n y associated materials such as NORM (discussed above), other gases produced with hydrocarbons, and constituents in produced brine. Emissions from flared gas and from the exh a u s t of motors, heaters, and furnaces used in secondary operations are also regulated. Although the subject is vast, and tracers have played a significant part in it, only two aspects will be discussed here: 1) small, accidental spills of oil or oily water into environmentally sensitive areas; and 2) the handling of drilling fluids in such areas, particularly from platforms OIL SPILLS AND OILYWATER As in all industrial operations, accidents can happen during the production or transportation of oil. Major oil spills are rare and self-tracing; they are not considered here, nor is oil contamination from such deliberate acts as t a n k cleaning operations and dumping oily ballast. This discussion will focus on the use of tagged oil to detect the release of relatively small amounts of oil in the presence of other oil sources in order to identify the path and the source. The principal development in tracers for oil has been for and by regulatory agencies, and its main targets have been oil companies. Increased population density near oil-producing areas in the industrially developed nations will only increase the regulatory pressure. In this climate, it also behooves oil producers and carriers to be aware of how and where the oil they produce or carry impacts

Tracers in Facility Operations

419

the environment. It is generally cheaper and better to find and repair small leaks t h a n to wait for a suitable regulatory response. Oil tracers for this purpose m u s t meet three criteria: 1) they should not be found in oil naturally; 2) they should be stable in the environment; and 3) they should have a high sensitivity for detection. A list of compounds t h a t have a high sensitivity for detection by electron capture has been proposed for this purpose by Landowne and Wainright (1971). Similar lists can be put together using other sensitive detectors, provided they meet the criteria above. Fluorescent tracers can be used in aerial surveillance with laser detectors to monitor thin oil slicks (O'Neal et al., 1981). This can be valuable in documenting the fate of such slicks. In areas where runoff from rain and other sources can carry oily w a t e r into undesirable locations, w a t e r tracers can be used to map the likely p a t h of the flood runoff (Pilgrim, 1976), thus allowing remedial actions in advance of the flood. It also allows emergencies to be dealt with in a more organized manner. DRILLING FLUIDS The fate of drilling fluids and cuttings in sensitive areas has been investigated in a number of studies, m a n y of which were comprised in the Joint Governm e n t I n d u s t r i a l Symposium on E n v i r o n m e n t a l F a t e and Effects of Drilling Fluids and Cuttings (Lake Buena Vista, FL, Jan. 21-24, 1980). In almost all cases, the effects of normal drilling operations were shown to be minor, although the same questions are resuscitated periodically. A number of tracer studies were included in this symposium, some that used barium (barite) as a tracer to follow the p a t h and effect (Chow, Gettleson, and Laird). Several used trace metals as indicators of the presence and effect (Kramer; Kalil), and one used radioactive tracers to follow three separate components (barite, bentonite, and mud water) of the mud plume in the neighborhood of the platform (Zemel). A later symposium (International Drilling Wastes Conference, Calgary, Alberta, Canada, April 3-8, 1988) addressed the same kinds of issues. Barite barium is still the most popular t r a c e r for the effect of drilling fluids on sediments in the neighborhood of platforms (Jones, 1988). Other drilling mud chemicals such as lignosulfates have also been proposed as tracers (Sauer et al., 1988) in a marine environment. OTHER TRACER APPLICATIONS It is not possible to cover all the applications of tracers to oilfield problems in a book of this kind. We have omitted the laboratory applications of tracers in oilfield research, although this covers a large class of work including core flow studies, m e a s u r e m e n t s of core properties, petrophysical measurements, and logging applications, as well as others. X-ray CAT scanners are widely used in oilfield laboratories for monitoring fluids in cores; so to a lesser extent are NMR scanners, used in studying the movement of fluids at the pore level. Neither application is covered here. There are also m a n y common applications, such as the use of tracer tagged m a r k e r s for monitoring subsidence in a well or m a r k i n g the

420

Chapter 8

entry of perforation shots, that have not been covered here, as well as many less common ones for special applications that did not easily fit the classifications used in this book. Our main concern here has been to cover those tracer areas in which tracer technology can or does impact general oilfield practice, to point out the use of tracers for quantitative oilfield measurements, and to transfer technology developed in biomedical and other fields to the oil field.

REFERENCES

Anderson, R.P., and Vogh, J.W, "Gas Identification: Pt. 1: Various Tracers Identify Injected Storage Gas," Oil & Gas J. (March 13, 1989) 87, No. 11, 52-54, 56. Annand, R.R., Farquhar, G.B., and Michnick, M.J., "Batch Treatment of Gas Wells with Corrosion Inhibitors: Tracer Experiments," preprint 68 presented at Intl. NACE Corrosion Forum, 1971. API, "Oil-water Separators Process Designs," chapter 5 in API Manual on Disposal of Refinery Wastes, Volume on Liquid Wastes, Amer. Petrol. Inst., New York (1969). Araktingi, R.E., Benefield, M.E., Bessenyei, Z., Coats, K.H., and Teck, M.R., "Leroy Storage, Uinta County, Wyoming: A Case History in Attempted Control of Gas Migration," preprint SPE 11180 presented at 57th Ann. SPE of AIME Fall Tech. Conf., New Orleans, Sept. 26-29, 1982. Arino, H., and Kramer, H.H., "A New Cs-137/Ba-137m Radioisotope Generator," Intl. J. Appl. Radiation and Isotopes (1968) 19, 816. Armstrong, F.E., and Lovelace, K.B., "A Study of Core Invasion by Water-Base Mud Filtrate Using Tracer Techniques," in API Drilling and Production Practice, Amer. Petrol. Inst. (1961) 104. Baker, M.A., and Asperger, R.G., "Assessment of Multi-Phase Movements in a Gas-Gathering Pipeline and the Relevance to On-line, Real-time Corrosion Monitoring and Inhibitor," preprint 185, NACE Corrosion 88, St. Louis, March 21-25, 1988. Barr, C.L., Guinn, V.P., Lilly, D.L., and Raifsnider, P.J., "Radioactive Tracer Studies on Squeeze Inhibition of Oil Wells," Mater. Protect. (July 1965) 4, No. 7, 18-22. Bryngelson, RH., "New Methods Detect Subsea Flow Line Leaks," Petrol. Eng. Intl. (April 1987) 59, No. 4, 35-38.

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422

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Evans, G.V., Spackman, R., Aston, M.A.J., and Clayton, C.G., Measurement of Gas Flow by Radiotracer Methods, Peter Peregrinus Ltd., London (1971) 245260. Evans, R., "Radioactive Methods for Measuring Engine Wear," Wear (1980) 64, 311-325. Fediw, T.J., Nemeth, E.J., and Caram, H.S., "Tracer Study to Measure Deposits and Dispersion Coefficients in Large-Diameter Gas Lines," Chem. Eng. Sci. (1981) 36, No. 9, 1575-1577. Field, E.L., Nucleonics (1953) 11, No. 9, 66--68. Finnigan, D.J., Garbett, K., Woolsey, I.S., "The Application of Thin Layer Surface Activation to the Study of Erosion-Corrosion Behaviour," Corrosion Sci. (1982) 22, No. 4, 359-372. Frost, E.M., "Helium Tracer Studies in the Elk Hills, California, Field," Bureau of Mines Rept. BM-RI 3897 (1946). Frost, E.M., "Helium Tracer Gas Studies," Petrol. Eng. (March 1951) 87. Gettleson, D.A., and Laird, C.E., "Benthic Barium Levels in the Vicinity of Six Drill Sites in the Gulf of Mexico," Proc., Res. on Environ. Fate and Effects of Drilling Fluids and Cuttings Symp., Lake Buena Vista, FL, Jan. 21-24, 1980, 2, 738-788 (1982). Gilath, C., "Ventilation and Air Pollution Studies Using Radioactive Tracers: A Critical Review," Intl. J. Appl. Radiation and Isotopes (1977) 28,847-854. Gesell, T.F., "Occupational Radiation Exposure Due to Radon-222 in Natural Gas and Gas Products," Health Physics (1975) 5, No. 29, 681-7. Gordon, B.E., Raifsnider, P.J., and Lilly, D.L., "Corrosion Monitoring in Oil Wells with a Radioactive Specimen," Proc., 22nd Ann. Natl. Assoc. Corrosion Engineers Mtg., Nov. 25, 1966 (pp. 21-23). Griesseir, H., and Makowski, J., "The Use of Generators of Short-lived Radioisotopes in Hydrology and Hydrogeology," Pure and Appl Geophys. (1974) 11~ No. 1, 192-203. Gwyn, J.E., "Fast Response Pulse Tests Use Of Gamma Milking," Ind. Eng. Chem. (1961) 53, 908. Hall, C., "Monitoring Drilling Mud Circulation," U.S. Patent 4,807,469 (1989). Hart, W.B., "Elements of Wastewater Separator Design: Report of an Investigation Using a Model Separator," Proc., Amer. Petrol. Institute 8th Midyear Mtg. (1938), Sect. III, 19, 8-22. Hart, W.B., "Industrial Waste Disposal for Petroleum Refineries and Allied Plants," Petroleum Processors, Cleveland OH (1947).

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424

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Levenspiel, O., Chemical Reaction Engineering, John Wiley and Sons, New York (1972). Lingelem, M., and Nuland, S., "Propagation of Solid Particles in Single- and Multiphase Flow Pipes and Pipelines," Proc., 22nd Ann. SPE et al. Offshore Technol. Conf., Houston, TX, May 7-10, 1990 (3,623-630, paper OTC 6412). Ljunggren, K., "Review of the Use of Radioactive Tracers for Evaluating Parameters Pertaining to the Flow of Material in Plant and Natural Systems," Proc., Symp. Radioisotopes in Hydrology, IAEA, Vienna (1963) 303. McCloud, W.R., Rhodes, D.F., and Day, J.J., "Determination of Linear Velocities of Materials in Multiphase Pipeline Streams," paper presented at 71st Ann. Mtg. A.I.Ch.E., Dallas, TX, Feb. 20-23, 1972. McCloud, W.R., Rhodes, D.F., and Day, J.J., "Radiotracers in Gas-Liquid Transportation Problems: A Field Case," JPT (Aug. 1971) 939. Millar, R.H.G., and Buckles, R.S., "Tritiated Water as a Drilling Mud Tracer in Beaufort Exploration Wells," JPT, April-June 1975. Nederween, N., Washington, G.V., and Batstra, F.H., "Wet Gas Flow Measurements," paper SPE 19007 presented at SPE Gas Technol. Symp., Dallas, TX, June 7-8, 1989. Newacheck, R.L., Beaufait, L.J. Jr., and Anderson, E.E., "Isotope Milker Supplies 137Ba from Parent 137Cs," Nucleonics (May 1957) 15, No. 5, 122. Patten, C.C., Deemer, D.A., and Hilliard, H.M. Jr., "Field Study of Fall Rate Oil Well Inhibitor Effectiveness," Mater. Protect. (1970) 9, 37-41. Rau, R.J., "Pipe Line Flow Efficiency and Gas Flow Tracer Systems," Proc., 2nd Gas Process. and Transmiss. Short Course (1966, 50-71). Rebgetz, M.D., Watt, J.S., and Zastawny, H.W., "Determination of the Volume Fraction of Oil, Water, and Gas by Dual Energy Gamma-Ray Transmission," Nucl. Geophys. (1991) 5, No. 4, 479. Rohlich, G.A., "Hydraulic Characteristics of Gravity Type Oil Water Separators," Proc., Amer. Petrol. Inst., 31MV, 111, 63-85 (1951). Russow, R., and Becker, F.J., "Radiometric Methods for the Determination of the Effectiveness of Corrosion Inhibitors Used in Petroleum Processing," Isotopenpraxis (June 1966) 2, No. 6, 258-262. Satterly, J., and McLennan, J.C., "The Radioactivity of Natural Gases of Canada," Trans. Royal Soc. Can. (1918) 12, 153. Sauer, T.C. Jr., Brown, J.S., Boehm, P.D., and Requejo, A.G., "Evaluation of an Organic Chemical Method for Drilling Fluid Determination in Outer Continental

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425

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426

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APPENDIX

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APPENDIX

ANALYTICAL FLOW MODEL FOR DESIGN AND ANALYSIS OF TRACER PULSE TESTS Maghsood Abbaszadeh

INTRODUCTION Interwell tracer tests are performed by inserting a pulse of tracer into the injection stream and monitoring the tracer response at the producers. Since this response is the result of tracer movement through the reservoir, it contains implicit information about the reservoir characteristics affecting flow. In order to extract this information, the produced tracer response curve must be deconvolved into its components. Such tracer tests usually involve multiple tracer injection wells in repeating patterns. The flow model proposed by Brigham and Smith (1964) and since modified and extended by Abbaszadeh and Brigham (1982), is a mechanistically based analytical model for flow in a pattern waterflood. It relates the amount of tracer injected in the pattern to the peak tracer concentration produced at the wells and provides a logical mechanism for tracer response as a function of pattern geometry and reservoir properties. This model allows deconvolution of the tracer response curve in terms of reservoir heterogeneity, at a given pattern geometry, and provides a base for estimating the amount of tracer to inject in order to produce a maximum peak tracer concentration. This appendix describes the model in six main topics: 1) areal dilution of the tracer due to pattern geometry, the resulting breakthrough (BT) curves, and their correlation into a single generic curve independent of geometry; 2) the effect of superimposition of dispersion on areal dilution for a closed homogeneous pattern; 3) the predicted response from developed homogeneous patterns as a function of Peclet number, adsorption, and tracer decay; 4) extension of the model to irregular and open patterns; 5) tracer response in layered reservoirs as a function of layer number and characteristics, and of the Dykstra-Parsons coefficient; and 6) design of tracer tests based on predicted maximum produced concentrations from homogeneous and multilayer reservoirs. Several numerical examples are included to illustrate the application of the method for the design of tracer tests and the analysis of the tracer response.

A n a l y t i c a l base for tracer movement Brigham and Smith (1964) describe an analytical model for predicting tracer breakthrough times and peak concentrations in a five-spot pattern waterflood.

430

Appendix

Although this model has since been modified and broadened in scope, the basic concepts have not changed significantly. In their model, the reservoir is treated as a layer-cake composed of homogeneous, noncommunicating layers. The injected tracer pulse is distributed among the layers in accordance with the flow conductivity (permeability thickness, kh) of each layer. The tracer material in a layer moves out radially at the interface between the injected water and the water in the reservoir, and is broadened by longitudinal dispersion in the direction of movement. When it arrives at the production well, the dispersed tracer pulse is diluted further by untagged water arriving from unswept regions in the same layer. The combined tracer response from all of the layers makes up the response curve of tracer concentration as a function of the cumulative volume of water injected or produced. The peak height, the breakthrough time, and the shape of the produced tracer response curve can be computed from the amount of tracer injected, the formation properties, and the pattern geometry. In effect, this proposes a means of calculating the amount of tracer required to produce a given maximum response at the producers. The Brigham and Smith model has two main limitations" first, it is only applicable to five-spot patterns; and second, mixing is treated as due only to divergent flow, the main source of inaccuracy of the model. That model was expanded in 1982 by Abbaszadeh and Brigham, who presented analytic solutions of tracer b r e a k t h r o u g h curves for a number of balanced patterns, with a rigorous treatment of the effects of tracer dispersion. The Abbaszadeh-Brigham model will be referred to as "the model" in the following discussions. In this model, tracer flows along individual streamlines of a flooding pattern with longitudinal dispersion occurring in streamtubes as tracer moves toward producing wells. The production of tracer from a layer is the volumetric sum of tracer concentrations from all the streamlines flowing into a producing well for t h a t layer. The tracer response curve from a single layer is the basic element in generating tracer breakthrough curves from multilayer systems. For a given pattern geometry, the tracer response curve, C(v), from a homogeneous layer is a function of the Peclet number, a/a, where a is the distance between producers and a is the dispersivity of the formation. In addition, the tracer response curves from all homogeneous and balanced patterns discussed here can be correlated into a single curve using a dimensionless pore-volume parameter. This correlation allows a tracer response curve to be estimated for any balanced pattern. A nonlinear optimization technique was introduced for deconvolving a field tracer response curve into a set of responses from n layers; each layer, j, having a flow conductivity, (kh)j, and fluid capacity, (r This allows an estimate of the heterogeneity of the reservoir in terms of a noncommunicating-layers model. The inverse problem of calculating a set of pseudolayers from the Dykstra-Parsons coefficient of variance is also addressed. m

Analytical Flow Model

431

The model contains a number of implicit and explicit assumptions, including 1) flow in parallel noncommunicating areally homogeneous layers, 2) a mobility ratio of unity, 3) constant water saturation, Sw, and 4) a single dispersivity, a, for the reservoir. Although the layer-cake model may appear to be a restrictive assumption, it need not be so. Many reservoirs are layered; those t h a t are not may act as though they are for fluid-flow calculation purposes. The assumption of unitmobility ratio displacement is not far from reality, since m a n y waterfloods are conducted with a mobility ratio near unity. Assumptions 3 and 4 are for convenience only and can be readily removed from the model. It should be noted that the original Brigham-Smith t r e a t m e n t of mixing deals only with divergent flow, which is valid for observation wells located near the injector. Such wells only observe flow passing along radially divergent streamlines and are not influenced by the effect of convergent flow at the producing wells.

AREAL DILUTION FROM PATTERN GEOMETRY

The t r a n s p o r t of tracer material in any flow system is subject to convection and mixing. Convective transport is the gross movement of fluids in the system. It represents displacements in which sharp fronts between fluids are preserved. Mixing is a local phenomenon that spreads and dilutes the tracer concentration at the front as it moves through a porous medium. Even if convection is the only transport mechanism, the tracer material at a producing well will undergo dilution due to the pattern configuration or well arr a n g e m e n t effect. Unlike linear flow geometries, where the shape of a produced tracer pulse imitates the shape of the injection, the effect of two-dimensional flow geometry is to dilute the tracer arriving at the wellbore of a producing well by mixing it with tracer-free fluid entering the wellbore from other portions of the flow plane. To illustrate this point, we will demonstrate the displacement in a five-spot pattern initially filled with fluid A, into which fluid B is injected. P a t t e r n b r e a k t h r o u g h c u r v e f o r a five-spot

We will first examine the single displacement case, in which fluid A (tracer) replaces fluid B in the reservoir. This is equivalent to a continuous or step function injection of tracer, as shown in Fig. A.1. Next, we will consider the double displacement case, wherein a small amount of fluid B (tracer) is injected into the reservoir containing fluid A and is itself replaced by the injection of additional fluid A. Shown in Fig. A.2., this is equivalent to the injection of a pulse of tracer. DISPLACEMENT OF ONE FLUID BY ANOTHER In this case, fluid B (tracer) is injected continuously into the pattern. It displaces fluid A with a sharp front, since the movement is piston-like and there is

432

Appendix

no mixing between fluids. The location of fluid B in the system after the injection of a certain volume of fluid B is shown in Fig. A.lb. At the producing well, therefore, a mixture of fluid A and B is produced. The fractional flow of fluid B produced, fB (or fA for fluid A), plotted against the cumulative volume injected is called the breakthrough curve, shown by the solid curve in Fig. A.la. This breakthrough curve is characteristic of the five-spot pattern and defines the way these fluids are produced. As the figure shows, there is no production of fluid B until breakthrough occurs, after which its production rises sharply and approaches 100 percent asymptotically. The produced fraction is always less than unity because of pattern dilution effects. Evolution of the breakthrough curve is described exactly by the flowlines of the pattern. The fraction of flow of fluid B produced is given by the angle of the streamline that has just broken through at the producing well.

a. Breakthrough curve

,..loo

b. Front location

~

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Figure A.1. Front location and breakthrough curve for continuous injection DISPLACEMENT OF A SMALLSLUG If a small slug of fluid B is injected into the pattern, initially filled with fluid A, and then displaced by re-injection of fluid A, each displacement can be treated independently. The location of the tracer bank in a quarter five-spot is shown in Fig. A.2b as the hatched region around the well. The fraction of fluid B in the producing stream is determined by the angle at which fluid B enters the well. The same breakthrough characteristics describe the displacement of fluid A by fluid B. The net production of fluid B is given by the difference between two angles, one for fluid B displacing fluid A and the other for fluid A displacing fluid B. Therefore, the breakthrough behavior of fluid B is defined by the vertical difference between two identical pattern breakthrough curves that are displaced from each

Analytical Flow Model

433

other by a volume equal to the volume of the slug of fluid B. Each individual pattern b r e a k t h r o u g h curve, t h a t of B displacing A, followed by A displacing B, is identical in shape to that in Fig. A.la. They represent, respectively, the leading edge and the trailing edge of the displacement of fluid B through the reservoir, as shown in Fig. A.2a. The resulting hatched breakthrough curve in Fig. A.2a describes as a function of total injected volume the fraction of fluid B produced at the well. Again, the well always produces fluid B at a concentration below 100 percent, even though the displacements in the reservoir are piston-like. This dilution is a property of pattern configuration effects and is a consequence of the geometry of the flowlines. The dashed b r e a k t h r o u g h curve in Fig. A.2a shows how dispersion would affect the tracer breakthrough response if the mixing of fluids in the reservoir were also considered. The effect of mixing added to pattern geometry is to spread the curve out. It causes an earlier breakthrough and a more diluted tracer peak. The areas under the dashed and hatched curves, however, are identical and equal to the volume of tracer slug injected, if the tracer is conserved. In order to give a quantitative description of a tracer elution curve from a pattern, whether or not mixing effects are considered, it is first necessary to describe the pattern breakthrough curves.

100 "O

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b. Front location

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Figure A.2. Front locations and breakthrough curves for a tracer pulse

G e n e r a l p a t t e r n b r e a k t h r o u g h curves Any mathematical description of fluid movement in a flow system requires a knowledge of a potential field for that system so that movement of particles can be tracked through the system. For single-phase steady flow, the potential field can u s u a l l y be obtained either from a solution of the Laplace e q u a t i o n with

434

Appendix

appropriate boundary conditions, or by application of the superposition principle as indicated by Muskat (1949) and Prats et al. (1955). Generally, it is simpler to solve the problem in a complex plane and derive an expression for the complex potential of the geometry. This expression can be decomposed into a real part and an imaginary part. The real part is the equation for the potential distribution (proportional to pressures), and the imaginary part is the stream function. The flowlines or streamlines are constructed from stream functions and are perpendicular to the potential lines. Morel-Seytoux (1966) gives the complex potentials for a variety of flooding patterns. Although he does not give the pressure and stream functions for all patterns, they can generally be derived from the pertinent complex potentials. Since stream functions are available or can be constructed, it is feasible to describe mathematically the displacement of fluids in different patterns. The displacements are assumed to be of unit mobility ratio and piston-like. Fluids are assumed incompressible, and gravity and capillary effects are neglected. The following general procedure is used to derive the analytic expressions for the breakthrough curve, defined as the displacing fluid cut, fD, versus pore volumes injected, Vp, of any pattern: 1. Compute the time required for a particle to travel from an injection well to a production well along a streamline of the pattern. This is the breakthrough time for that streamline. 2. Multiply the breakthrough time by the injection rate and divide by the pattern area to obtain the pore volumes injected into the pattern at the breakthrough of that streamline. 3. Compute the angle at which the considered streamline enters the production well. This angle divided by the total angle subject to flow at the production well of that pattern element is the displacing fluid fraction at the producing stream, since the total flow rate is proportional to the total angle from which each fluid enters the well. The calculated fluid fraction corresponds to the pore volume determined in item 2, thus a relationship for the pattern breakthrough curve is constructed. The details of derivation of the equations for the pattern breakthrough curves are illustrated in the last section of this appendix. These are complex expressions whose forms differ for different flow geometries. Pattern breakthrough curves for a variety of repeated systems at unit mobility ratio are shown in Fig. A.3a.

Correlation of p a t t e r n breakthrough curves Because of the complexity of the breakthrough expressions, a simpler relationship applicable to many patterns was sought to correlate pattern breakthrough curves. The breakthrough curves of developed patterns for various geometries were found to fit a single curve by using a dimensionless pore volume, VpD:

435

Analytical Flow Model

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Figure A.3. Pattern breakthrough curves and their correlations Vp -VpBT VpD - 1-VpBT

(A. 1)

This is an empirical transformation, where Vp is the total pore volume injected and VpBT is the pore volume injected at breakthrough. The result of such correlation, shown in Fig. A.3b, should work for any balanced pattern. The key parameter is the breakthrough pore volume, VpBT, which can easily be calculated from the breakthrough time for a well in any balanced or repeated pattern. This can also be estimated for field problems from the measured breakthrough time and the known fluid volume injected, if certain approximations regarding flow geometry and drainage boundaries can be made. The curve in Fig. A.3b can be fitted by a regression procedure to give the following equation for fD, the fractional flow, as a function of dimensionless pore volume, VpD: fD = 1- 2{exp(- 1.810(VpD)0.530) + exp(-0.715(VpD )0.972) }

(A.2)

Thus, the entire breakthrough curve for any balanced pattern can be predicted from Eq. (A.2) using only its breakthrough pore volume. When a slug of tracer with a pore volume equal to VpW and an initial concentration of Co is injected into a pattern, the effluent tracer concentration profile from the reservoir is the difference between two pattern breakthrough curves in the absence of mixing or any other transport process. That is: C = fD(Vp)- fD(Vp- VpT) Co

(A.3)

436

Appendix

where fD is given either by the correlating relationship of Eq. (A.2) or by a more exact pattern breakthrough curve. This accounts, however, only for pattern dilution effects under convective forces. Other processes, such as mixing, adsorption, chemical reaction, and partitioning into oil, can affect the tracer breakthrough curve. In dealing with ideal tracers, which do not adsorb, react or partition, the only process t h a t occurs, and occurs in all tracer flow tests, is mixing of tracer material with reservoir fluid. Other processes may or may not be significant, depending on the physical and chemical characteristics of tracer material, reservoir fluid, and reservoir rock. We will describe the mixing effects first, and then present a mathematical t r e a t m e n t when adsorption effects become important.

A R E A L D I L U T I O N BY MIXING E F F E C T S

Mixing in p o r o u s m e d i a FUNDAMENTALS Mixing of a tracer with reservoir fluid during its transport through a porous medium is due partially to molecular diffusion and partially to mechanical or hydrodynamic dispersion. Diffusion is primarily driven by concentration gradients and is independent of bulk flow velocity. Fick's diffusion law describes the molecular diffusion component of tracer mixing (Crank, 1957). Dispersion is caused by the uneven movement of fluids due to variations in velocity of tracer material around the spreading and rejoining pore passages, consequently tracer material gradually spreads beyond the region due to fluid convection alone. The amount of spreading depends on the dispersivity characteristics of porous media, the fluid velocity, and the geometry of the flow system. Two types of dispersion are to be considered: longitudinal and transverse. Longitudinal dispersion occurs in the direction of gross fluid movement, whereas transverse dispersion is perpendicular. Longitudinal dispersion is therefore more significant for our purposes, because fluid velocity in the principal direction of flow is greater than that in the transverse direction. As a result, more spreading occurs in the direction of flow. The total mixing in either direction is the sum of molecular diffusion and mechanical dispersion. The following relationship for total mixing has been established experimentally (Brigham et al., 1961) in a variety of laboratory sand packs and natural sandstone cores as: D + au 1.2 K = ~-~ where: K = effective mixing coefficient

(A.4)

Analytical Flow Model

437

D = molecular diffusion coefficient F = rock's formation resistivity factor = porosity a = dispersivity of porous medium u = pore flow velocity, bulk flow divided by porosity The first t e r m on the right side of Eq. (A.4) is the a p p a r e n t molecular diffusion, and the second term is the mechanical dispersion. The dispersivity, a, depends on the n a t u r e of the porous medium as well as the viscosity ratios of the fluids involved in the displacement. For consolidated formations, values of a are 10 to 100 times larger t h a n those for unconsolidated cores. Based on experimental results (Brigham et al., 1961; Blackwell, 1962), the effect of molecular dispersion on mixing in field tracer tests can be neglected with good approximation. Also, because longitudinal dispersivity is at least an order of m a g n i t u d e larger t h a n t r a n s v e r s e dispersivity, transverse mixing is neglected as well. F u r t h e r m o r e , to simplify the derivation of tracer mixing expressions, without losing much accuracy, mixing is considered to be related in a linear fashion to the bulk velocity in Eq. (A.4), so that: K = au

(A.5)

MIXING IN LINEAR SYSTEMS

We will first t r e a t mixing in linear systems and t h e n extend the r e s u l t i n g tracer t r a n s p o r t equations to a r b i t r a r y flow geometries. When one fluid miscibly displaces another in a linear porous medium, and the displacement is stable, the convection-dispersion equation describing the displacement, and the fluid concent r a t i o n in a long system, is given by (Aronofsky-Heller, 1957; Brigham, 1961; Bear, 1972): ~}2C

~)C

~)C

K~ - u = 3x 2 3xx 3t

(A.6a)

where C is the concentration of displacing fluid, K is the effective mixing coefficient, and u is the interstitial pore velocity equal to q/Ar (q = injection rate, A = cross-sectional area, and r = porosity). For a semi-infinite m e d i u m with zero initial tracer concentration and the tracer injected at a concentration of Co, the initial and boundary conditions are: C(x,t) = C o, for x = 0

(A.6b)

C(x,t) = 0, for x = oo and for t = 0

(A.6c)

438

Appendix

The solution of Eq. (A.6) with the above conditions is (Aronofsky-Heller, 1957; Ogata-Banks, 1961): C c0(X't) _- !2 erfc ~/X2(K--t-at + 12eux/K erfc ~/X2(K-t + ut)

(A.7)

The second term is usually small compared to the first term, except at small values of x or large values of K. Under these simplifying conditions, the concentration profile becomes symmetrical around the x = ut plane. Therefore, the solution for tracer concentration at any location and at any time for continuous tracer injection is given by the first term alone" C (x,t) = ! erfc /x - ut Co 2 ~ 2(K-t

(A.8)

For a small-slug tracer injection whose length is infinitesimal compared to the distance between wells, concentration is described by the derivative of Eq. (A.8), given below: C(x,t) _ Ax Co - ~ 2 ~ 2

[ (x'x) 2] exp[-2~2]

(A.9)

where Ax is the tracer slug size, ~ = ut is the tracer front position corresponding to the 50 percent concentration location, and r is the variance of the tracer distribution profile, where r = 2Kt = 2 o~ Eq. (A.9) is a fundamental equation that can be extended to any flow geometry as long as the variance, ~2, can be defined. A general flow geometry of interest is a streamtube of an injection pattern. MIXING WITHIN A STREAMTUBE For an arbitrary streamtube shape, of length s = L, as shown in Fig. A.4, the tracer concentration within the streamtube is given by the following expression, in analogy to Eq. (A.9): C(s,t)=

Co

As

~2n~2

cx

-

(A. 10)

where As is the width of a streamtube occupied by an undiluted tracer slug at distance ~, the position of the volumetric front of the injected chase fluid, since the tracer slug is of negligible thickness compared to the system length. In contrast to a linear system, where mixing is due only to dispersion, variations in the flow passage geometry of a streamtube contribute to the mixing of tracer in a streamtube (Lau et al., 1959; Brigham, 1973). The change in the size of the tracer pulse within a tube depends on two effects: 1) the change due to local mixing as tracer moves through the porous medium; and 2) the change due to the

Analytical Flow Model

439

zone becomes narrower since the volume remains constant. Therefore, the total spread of the mixed zone is the sum of two spreading factors" do = dos + dog

(A.11)

Production well

A B s=L S

re ,~

Flow'~"~ S

B

a

Figure A.4. A general streamtube geometry and the location of a tracer pulse The first term on the right side of Eq. (A.11) represents the distance effects and the second term accounts for geometry changes. In this manner, d(~s is computed from the mixing equation of the linear system discussed earlier, where o 2 = 2as. Differentiating this relationship results in d~s = ads/~. The geometry effects are obtained by noting that, since the volume of the mixed zone remains constant, irrespective of the shape of the flow system at that location, (~v is constant. This is shown in Fig. A.4a, where w is the width of the flow system at a location of interest, and w = q/CSwh. Differentiating the relationship that mv equals a constant yields do g =-odw/w. Substituting both dos and dog in Eq. (A.11) and integrating over the flow domain yields the following result for mixing variance, where u is the interstitial velocity: SB 4 = 0"2A+20: u2

u2

ds .,sA ug(s)

If there is no mixing at the entry, then aA = 0 at s = 0 and

(A.12)

440

Appendix

m

s

~2 = 2 ~ u 2 ( w

(A.13)

u2(s) 0

Eq. (A.13) is a general expression for mixing in any geometry. For example, in r a d i a l flow in which ds = dr, u(s) = q/2nrO, and u(~) = q/2nro, it follows t h a t ~2 = 2a~/3. For spherical flow, ~2 = 2a~/5. Eq. (A.13) involves a line integral of inverse velocity s q u a r e d along a s t r e a m l i n e t h a t can be evaluated from the m a t h e m a t i c a l definition of s t r e a m l i n e s of a pattern. W h e n eqs. (A.10) and (A.13) are combined, an expression for tracer concentration within a s t r e a m t u b e is obtained. These two equations, however, are expressed in t e r m s of d i s t a n c e ; t h e y need to be f o r m u l a t e d in t e r m s of volume since tracer information is used on a volumetric basis. The volumetric conversion is carried out by noting that: s - w = u----(v - ~) qs

(A.14)

U

(A.15)

As = ~ssVt where: u = interstitial velocity at point vt = tracer volume in streamtube, vt = (Vw)(qs)/q q = flowrate into p a t t e r n qs = flowrate into s t r e a m t u b e v = displaceable pore volume of s t r e a m t u b e up to location s ~r = displaceable pore volume of s t r e a m t u b e up to location VT = volume of tracer slug injected into p a t t e r n The resulting expression for tracer concentration within the s t r e a m t u b e is:

cs/v/ CO

vt = 2qs~eXp

{ - 4aIq 2

(A16)

w h e r e I is the line integral in Eq. (A.13), computed from the knowledge of s t r e a m functions of the pattern.

TRACER RESPONSE FROM DEVELOPED HOMOGENEOUS PATTERNS Formulation Tracer concentration at a producing well in a given p a t t e r n is a volumetric average concentration of t r a c e r flow from all the s t r e a m l i n e s t h a t e n t e r the well.

Analytical Flow Model

441

This results in a superposition integral of individual streamline tracer concentrations C(~,). The superposition integral for a variety of injection pattern configurations has been derived (Abbaszadeh, 1982). These are complex expressions, and for the five-spot pattern the equation is: exp{-

0.Y(V)645776aT[VapB

(~)

- Vp]2}

C--D(Vp) = 0. 577266 4Y(v)

(A17)

0

Here, the Y(~) term is a hyperelliptic integral that results from the mixing integral of Eq. (A.13) for streamline ~,, and VpBT(~) is the pore volume injected at breakthrough of streamline ~. It is important to note that VpBT(~) represents the characteristic breakthrough curve of the pattern that was described in the earlier discussion of dilution due to geometry effects. Note that developed pattern in a mathematical context means a system of repeated well arrangements in which all injection wells receive the same volume of tracer slug simultaneously. Eq. (A.17) includes the combined effects of both pattern configuration (area swept), and mixing on tracer flow. CD(Vp) is the dimensionless tracer concentration produced at the injected pore volume, Vp, and defined by Eq. (A.18) below: C--D =

C Co Fr ~ a a

where: C = a = a = Fr =

(A.18)

produced tracer concentration, mass fraction distance between like wells dispersion constant tracer slug size expressed as a fraction of displaceable pattern pore volume, defined as:

VT Fr = A(~hSw

(A.19)

where VT is the tracer slug volume injected into the pattern, A is the area of the pattern, r is the porosity of the layer, h is its thickness, and Sw is its water saturation. Correlation of tracer production curves

These complex equations of tracer breakthrough do not have a single solution but for any given pattern will have a different solution for each value of the Peclet

442

Appendix

number, a/a. As a consequence, a set of dimensionless tracer breakthrough curves is generated for each pattern, as a function of Peclet number. An example of this is shown for the tracer breakthrough curves of a developed five-spot pattern for different Peclet numbers in Fig. A.5a, and for three different patterns compared at the same Peclet number in Fig. A.5b.

a

0.2

b .2

"

O

~

-

"

"

|

"-

pol Direct line drive "~ d/a =1

0 t-

9

5-spot

5

r

0

0.1

.~ 0.1

i5

' ~

.

C

0.5

1.0

Pore volumes injected, Vp

0

A,aioele,ie

.

.

|

.

0.5

1.0

Pore volumes injected, Vp

1.5

Figure A.5. Dimensionless tracer breakthrough curves All the curves in Fig. A.5a show tracer production at a pore volume less than the breakthrough pore volume for piston-like displacement (0.717), illustrated in Fig. A.1. This is due to tracer dispersion in the porous medium, as shown by the dashed line in Fig. A.2a. The sets of tracer profiles from the various patterns can be correlated into a single set of curves (sda being the parameter) that represents the tracer production curves from repeated homogeneous patterns. If the peak data (maximum tracer concentrations and the corresponding injected pore volumes) of tracer production curves for different patterns are plotted against a/a on log-log paper, the data for each pattern yield a straight line with the same slope. Fig. A.6a is the graph of dimensionless peak (maximum) concentration, ( CD)max, vs. Peclet number, and Fig. A.6b is the graph of the corresponding dimensionless injected pore volume, (VpD)max, at which the m a x i m u m tracer concentration occurs. This is the same dimensionless volume p a r a m e t e r group used to correlate the pattern breakthrough curves in Eq. (A.1). A vertical shift of lines in Fig. A.6a and a horizontal shift of lines in Fig. A.6b correlate the respective sets of lines into a single line for each figure.

Analytical Flow Model

.00

. . . .

'

.

.

.

.

.

.

.

a

443

,

.

9

'.

9 ."'...,,'"

D i r e c t line dr.

9 ' .

,

. . . . .

.

S t a g g e r e d line dr.

9 d/a = 2 9 d/a=1.5

O d/a = 2 A d/a=1.5

9d / a = 1

D d/a=1

.10

.01

........ 102

.00

' '

. .......

~ 103

9 .......

......... a/a

~ , =,: . . ~ i r e c t line dr.

b

I .......... 104 . . . .

,

<> d/a = 2

9 d/a = 1.5

z~ d/a = 1.5

9 d/a=1

~----~"--.~"~o~

,

S t a g g e r e d line elf'. ' ' '

~I, d/a = 2

I

105

[] d / a = 1

0 5 spot

0.1 'X

=.

$

.01

............

10 2

J- . . . . . . . . . . . . . 103

'-

10 4

105

Figure A.6. Peak tracer concentrations and locations vs. Peclet numbers

Adsorption and decay In addition to hydrodynamic mixing, tracer adsorption and radioactive decay m a y occur as tracer material flows through a reservoir. (Most data from radioactive tracers are provided to the user already corrected for decay; where this is not done, radioactive decay can be treated as shown here.) These two effects can be superimposed on the previously developed tracer flow solutions. The superposition relationship is obtained first for a linear system and then generalized for pattern flow geometries. The tracer transport equation in a linear

444

Appendix

geometry w h e n both adsorption and decay processes are considered is (Satter et al., 1980): ~2C

OC

(

C§

1- r

prCr

"~ OC = ~+ ~t

)

1- r

@

()Cr Pr - ~t

(A.20)

where: K = mixing coefficient C = tracer concentration in the flowing fluid stream Cr = tracer concentration adsorbed on the rock surface Pr = reservoir rock density ~, = tracer decay constant

Adsorption refers to a process wherein a flowing tracer m a t e r i a l in the aqueous solution is absorbed on the surface of the reservoir rock. Two limiting cases m a y exist: i n s t a n t a n e o u s adsorption (equilibrium) and t i m e - d e p e n d e n t or ratecontrolled adsorption (nonequilibrium). For an equilibrium adsorption, the concentration on the rock surface is generally described by the L a n g m u i r isotherm: aC Cr = 1 + bC

(A.21)

where a and b are constants related to the ratio of the adsorption and desorption r a t e constants. The L a n g m u i r equation, however, can be a p p r o x i m a t e d by a linear expression at low concentration levels. Because the tracer concentration levels in most interwell tracer tests are low, the linear relationship of C r = aC should provide a useful model for tracer adsorption effects. Therefore, considering only adsorption, Eq. (A.21) becomes: Cr = aC

(A.22)

and therefore,

Krt~2C ~ ~)x2 - u ~ - = R ~Ot

(A.23)

where the retardation factor, R, is defined by R = 1+

( 1 - @)Pr @ a

(A.24)

This suggests t h a t the adsorption-free solution given by Eq. (A.9) also applies to Eq. (A.23) but is reduced by a factor of 1/R. Thus, for a slug of t r a c e r t h a t

Analytical Flow Model

445

undergoes adsorption in addition to mixing, the effluent concentration in a linear system is: C(x,t) = ]2~ a2

exp{- (x- ut) 2 2~--~

}

(A.25)

where Ax

Aft- R

(A.25a)

t =R

(A.25b)

Hence, the effect of adsorption is to retard a tracer response and reduce the level of effluent tracer concentrations. For a pattern flow, such as a five-spot, Eq. (A.17) still applies, but with adjustments to both the dispersivity and the pore volume injected, in analogy with the linear flow geometry, as given in Eq. (A.26) and shown in Fig. A.7"

0.15. R=I.0 /r,~, 1.10 i0.1o

/

Analytical solution ..... UTCHEM solution 125

I

I Ii I

Pore volumes injected, Vp

Figure A.7. Tracer production retardation from five-spot at Peclet number a/a = 500

446

Appendix

u/4

exp -

0.645776 a -- Vps T (~/) Y(~) a

~Y(~)

C% ( V p ) = 0. 577266 F--LrR

d(v)

(A26)

0 Radioactive decay effects are simply accounted for by multiplying a nondecay solution by e -xt, where ~. is the decay constant of the tracer. This is applicable to any geometry. Thus, multiplication of Eq. (A.26) by e-~V/q will account for both decay and adsorption effects. Here, t = V/q, where V is the volume injected and q is the injection rate.

T R A C E R FLOW IN I R R E G U L A R AND O P E N PATTERNS The theory and formulations provided so far consider developed and balanced pattern geometries. This may not be always the case in field practices. The wells may be drilled in irregular patterns, produced at different rates, or the existing pressure gradients in the reservoir may cause flow in directions away from the pattern of interest. A robust method for handling such nonideal cases is first to construct the proper flowlines of the system of interest, and then to superimpose the tracer flow and tracer mixing on the streamlines, exactly in a fashion that was described for regular patterns. The streamlines can be generated either analytically or numerically by solving for the pressure or the velocity field under steadystate conditions. Fig. 4.12 in chapter 4 showed an example of computed streamlines for a field tracer test. Modeling tracer flow in this configuration would require evaluation of the line integral of Eq. (A.13) along each streamline and proper superposition of concentrations from all the streamlines entering a producer. This approach is different from a full finite difference or finite element numerical simulation of tracer flow, where the tracer transport equation is discretized in both space and time and solved by numerical techniques. Useful approximate results for tracer flow in irregular and isolated patterns may be based on sound engineering approximations combined with the equations discussed earlier. Such irregular and unbalanced patterns are shown in Fig. A.8. The central well injects at rate qi, while each of the producing wells produces at rate qpj. Each producing well is thus draining a different area and receiving a different quantity of injected fluid. Distribution of injected fluids among the four producers is proportional to the wells' producing rates, based on Deppe's (1961) approximations:

447

Analytical Flow Model

outside w

q

pl

qp4

qA? . . . . . . . o i ! ! e e e |

qpi

e

qpa

i ! !

o i

|

|

!

I

!

I

qB ~

~ b

Figure A.8. Irregular and unbalanced tracer injection patterns

4 qp = ~__,qpl, ~lpl = qXqp, 1=1

= vi

qpl

VTX =

-~p

=

A

qpl qp

where: qp = cumulative production rate ~lpl = rate of injected fluid flowing towards well 1 V] = actual produced volume from well 1 Vi = total injected fluid volume V1 = produced volume from well 1 for equivalent developed pattern VT = total tracer volume injected into pattern VTI = tracer volume injected flowing towards well 1 A1 = area of pattern associated with well 1 A = total area of pattern Tracer production from well 1 can be approximated by the production of a developed p a t t e r n according to Eq. (A.17), with adjustments made to fluid and tracer volumes and equivalent area according to the definitions above. As a result of flow from outside the pattern, the tracer concentration is diluted and the corresponding produced volumes are increased. Therefore, the computed tracer concentrations from an equivalent developed pattern should be multiplied by a factor of ~tpl/qpl and assigned to an injected volume, VTI, which is increased by this factor. Such a d j u s t m e n t s are necessary to model correctly the tracer breakthrough history of the unbalanced pattern in Fig. A.8.

448

Appendix

T R A C E R R E S P O N S E IN LAYERED R E S E R V O I R S

One of the common ways of simulating flow through a heterogeneous reservoir is to treat the reservoir as though it were composed of parallel, noncommunicating layers. There is a reasonable geological base for this, and a number of successful reservoir engineering calculations (Dykstra and Parsons, 1950; Fitch and Griffith, 1964) have been based upon this concept. The concept is developed here as a means of predicting tracer response from a producing well.

Layering Layering is one of the major forms of heterogeneity in reservoirs. Cross flow between adjacent layers occurs because of vertical pressure gradients between layers. These can be caused by gravity, capillary forces, viscous forces, and diffusion or dispersion. For unit mobility ratio and fluids of equal density, there should be no vertical pressure gradient between layers; however cross flow between adjacent layers can still occur because of transverse mixing. As can be seen from Fig. A.5, the pattern breakthrough curves do not depend strongly upon dispersion constants. If transverse mixing is assumed to be negligible, the reservoir can for this purpose be treated as though it were composed of noncommunicating layers. A waterflooded reservoir fits the above conditions when the density and viscosity of the tracer solution are the same as those of the reservoir water. When flow through layers occurs in the reservoir, the tracer production from the well is the sum of the tracer production from all the layers. The tracer flow process in each layeris predictable by the techniques described earlier for homogeneous patterns; however the tracer arrival time at the production well and the tracer concentration contributed by each layer are functions of the porosity, permeability, and thickness of each layer. The fraction of injected tracer entering each layer, j, depends on the conductivity, (kh)j, of that layer compared to that of the total conductivity, Zkh, of the reservoir. COMPUTATION OF TRACER RESPONSE FROM A LAYEREDRESERVOIR If VFL is the total volume of displacing fluid injected into a layered reservoir, the pore volume of fluid, Vpj, injected into layer j, is given by: (kh)j VFL kjCj VFL Vpj = ~ A((~h)jSwj - Swj AZkh

(A.27)

This pore volume is based on the displaceable fluid volume in layer j and not in the reservoir. Similarly, if VTL is the tracer volume injected into reservoir, then the fractional pore volume of tracer, F rj, injected into layer j is given in analogy with Eq. (A.28) by:

449

Analytical Flow Model

VTL

h

Frj = Ekl~ A(Oh)jSwj = OjSwj A]~kh

(A.28)

The tracer concentration, CL(VFL), from the producer when the fluid volume of VFL has been injected is the volumetric sum of the tracer concentrations from all the layers:

CL(VFL) = ~ (kh)j Cj(Vpj) Co j=l

(A.29)

where" n = number of layers C--j(Vpj) = contribution of tracer concentration from layer j, computed at a (kh)j

layer pore volume of Vpj injected into layer j. = flow capacity of layer j

The individual layer concentrations can be computed from an equation for the appropriate homogeneous pattern, such as that given for a five-spot in Eq. (A.17), with Vpj and Frj replacing the Vp and Fr terms in them. If the number of layers, n, as well as the thickness, h, porosity, ~, and permeability, k, of the layers are known, the tracer concentration profile for the patterns can be constructed. A numerical example is shown in the table below to illustrate the procedure. Generally, a computer algorithm is used for this kind of calculation; however distinct peaks corresponding to each of the layers may be masked by interference effects between layers.

NUMERICAL EXAMPLE OF LAYEREDRESPONSE COMPUTATION Given a three-layer reservoir with a five-acre repeating five-spot pattern, with reservoir parameters as shown in Table A.1 and a dispersivity of a = 0.466 ft, if a 500-bbl tracer slug is injected into the pattern, the tracer concentration, CL/C0, produced from the reservoir after injecting 100,000 bbl (5.61 x 105 cu ft) of fluid (VFL) is calculated as shown in the following table: TABLE A. 1 Three-layer reservoir k,md h,ft 1 2 3

100 400 1000

10 5 5

~ 0.2 0.23 0.3

Sw 0.7 0.75 0.85

kh

k&Sw

Vpj

F~

1000 2000 5000

715 2320 3920

0.23 0.75 1.25

0.00115 0.00365 0.00632

CDj 0.0 0.112 0.026

Cj 0.0 0.0129 0.0052

450

Appendix

The known reservoir parameters, k, h, ~, and Sw, are entered into the first four available columns. Numbers derived from these occupy the next two columns and are used to calculate Vpj according to Eq. (A.27), for the injected volume, VFL, given above. Frj is calculated from Eq. (A.28). For a five-acre five-spot, a = 466 ft, hence" (a]a) 0.5 = ~]1000 = 31.62. The CDj values are obtained from the homogeneous pattern response shown in Fig. A.5a and used to calculate Cj from the equation Cj = CDj Frj (a/a) 0.5 (in analogy with Eq. (A.19)). Hence, from Eq. (A.29): CL/Co = (1000 x 0+2000 x 0.0129 + 5000 x 0.0052)/8000 = 0.0065.

Heterogeneity definition by layers STATISTICAL BACKGROUND Permeability measurements on cores from petroleum reservoirs frequently exhibit log-normal distributions. This means that a plot of core-sample frequency versus the logarithm of measured permeability results in the bell-shaped Gaussian distribution, g(z), given by Eq. (A.30). This is also known also as the probability density function (pdf), and is characterized by two parameters, the mean, ~, and the variance, ~2. The integral of the pdf plot is the cumulative distribution function (cdf), which is the error function, G(z), given by Eq. (A.31) and found in s t a n d a r d tabulations. These functions are shown in Fig. A.9. Note t h a t the parameter z represents the natural logarithm of permeability, In k, and ~ is the s t a n d a r d deviation of p a r a m e t e r z. One can equivalently use the common logarithm of base 10 instead of the natural logarithm. .

z-z

g(z) = ~2 ~ 2

g(z) i

G(z)

,

Z

Figure A.9. Probability and cumulative distribution functions

Analytical Flow Model

451

G(z)= 11 1+ err(z-~ where g(z) represents probability t h a t the p a r a m e t e r value (ln k) is equal to z, and G(z)gives the probability t h a t the p a r a m e t e r value is less t h a n z. The probability t h a t the p a r a m e t e r value is larger t h a n z is simply: ^

G(z) = 1- G(z) =

1

1- err ~

(A.32) A

We can compute the p a r a m e t e r z from the inverse of the probability, G(z): z = 5 + ~/-2~erf "1(1- G(z))

(A.33)

where erf -1 is the inverse of the error function whose a r g u m e n t is (z-5)/X/2~. This equation can be used to compute z = I n k where the probability of having a larger permeability is given by p = G(z).

0

g, _J

0.1

1

5

50

90

Cumulative thickness, %

Figure A.10. Dykstra-Parsons cumulative probability plot DYKSTRA-PARSONS COEFFICIENT TO CHARACTERIZE LAYERING HETEROGENEITY If z follows a normal Gaussian distribution, it will yield a straight line when plotted on a probability scale. The slope of the straight line is a function of the s t a n d a r d deviation ~ and reflects the degree of variation in core permeability. Dykstra and Parsons (1950) took advantage of these properties of a normal distribution and introduced a heterogeneity variance parameter, VDP, to characterize the layering heterogeneity of a reservoir. The Dykstra-Parsons coefficient of variation is defined as" VDp =

k50 - k84.1 k- k~ k50 - ~

(A.34)

452

Appendix

where k50 is the median permeability, k, and k84.1 is the permeability at one s t a n d a r d deviation, kg. This is illustrated on the probability-scale plot of Fig. 9.10, which is a plot of logarithm of permeability versus percentage of permeabilities larger than that particular permeability value. This plot is usually prepared by arranging the core permeability values in descending order (from high to low) and computing the related percentages or probabilities. The Dykstra-Parsons coefficient of variation lies within 0 < VDp _1; hence a value of VDp = 0 indicates a homogeneous system, whereas VDp = 1 corresponds to extreme heterogeneity. CONSTRUCTION OF LAYERSUSING DYKSTRA-PARSONSCOEFFICIENT, VDp If the Dykstra-Parsons coefficient of variance is known, the layering composition of a reservoir can be constructed. The calculation of layer permeabilities may be accomplished as follows. The probability that the permeability is equal to that of I n k from Eq. (A.30) is given by the probability density function for a lognormal distribution: 1 {_(lnk -ln 1~)2.} p(z = In k) = ~]2x~2 exp 2(~2

(A.35)

where a = In k50 - In k84.1 = -In fi[84"1~ [ ks0 J = -ln(1 -VDP)

(A.36)

The probability that the permeability is larger than the value of In k is obtained from the cumulative distribution function, Eq. (A.32): In (k/k ln(1- VDp)

(A.37)

If the reservoir consists of n layers, each with thickness hj and porosity (~j, then on a porosity-thickness cumulative basis, the probability that the permeability of layer j is greater than k is: J Z (~h)i i=l PJ= n (r i=1

(A.38)

which for equal porosity and thickness reduces to:

pj-

(A.39)

Analytical Flow Model

453

Thus, the permeability of layer j from Eq. (A.37) is obtained as follows: kj = (l_VDp)_~r~ erf-1(1-

21~)

(A.40)

where e r f -1 represents the inverse of the error function whose a r g u m e n t is (1-2pj), and the pj terms are given by Eq. (A.38) for each layer, j. When the number of layers is small (fewer than 20), a more accurate procedure is to assign an average probability to the midpoint interval, as shown in Eq. (A.39), and use it in Eq. (A.40): 1 Pj = ~(Pj + Pj-1)

(A.41)

NUMERICAL EXAMPLE OF LAYER CONSTRUCTION FROM VDp The process is illustrated for a ten-layer reservoir (n = 10) with Parsons heterogeneity parameter, VDP, equal to 0.5 in Table A.2 for thickness and porosity values. The value for ~j is obtained from Eq. the reciprocal of the error function is calculated by interpolation from error functions provided at the end of this appendix. This is a useful those with limited experience in such calculations.

a Dykstraequal layer (A.41), and the table of exercise for

TABLE A.2 Ten-layer reservoir Layer 1 2 3 4 5 6 7 8 9 10

p = j/n

~j

1-2 ~j

err" 1(1_2 pj )

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95

0.9 0.7 0.5 0.3 0.1 -0.1 -0.3 -0.5 -0.7 -0.9

1.163 0.733 0.477 0.273 0.089 -0.089 -0.273 -0.477 -0.733 -1.163

kj / 3.14 2.05 1.59 1.31 1.09 0.92 0.77 0.63 0.49 0.32

B

The knowledge of average permeability, k, will allow computation of individual layer permeabilities. Once the layer permeabilities are obtained, the tracer breakthrough curve from a multilayer reservoir can be constructed for a given

454

Appendix

number of layers and the layer permeabilities, thicknesses, and porosities according to Eq. (A.29).

D E C O N V O L U T I O N OF TRACER BREAKTHROUGH DATA

The consequence of tracer flow in a stratified reservoir, where each layer is areally homogeneous, is a tracer-response curve with a specific breakthrough profile. This noncommunicating layer-cake model is the most common and simplest model of a heterogeneous reservoir. The objective of a quantitative tracer data analysis is to compute the properties of those layers that make up the observed tracer breakthrough profile. Two approaches to deconvolving a tracer breakthrough profile have been employed. One assumes that any observed peak in a tracer breakthrough profile corresponds to an individual layer. Layer properties are calculated from the layer concentration assigned to each peak and its volume location. This approach works well when the peaks are so widely spaced that they do not interfere with each other; however when the peaks are close to each other or when some of them are masked by interference effects from the more dominant layers, it is only an approximation. To correct for the discrepancy, one needs to revise the peak locations and concentrations by trial and error until a satisfactory match is obtained. This trial and error approach can be cumbersome and in some cases may prove impracticable. An alternative to these manual adjustments is to use a nonlinear regression approach (optimization technique) to determine layer properties more systematically.

Nonlinear regression The nonlinear regression procedure is a least-squares method for curve fitting that minimizes the squares of the difference between the measured tracer breakthrough data and those computed from the multilayer theoretical model. Computer programs capable of nonlinear regression analysis are widely available, even for use with personal computers. Those algorithms with better convergence properties and those that are more closely compatible with the form of the tracer equations are most suitable for the regression process. Mathematically, an objective function, F, is minimized and the unknown model parameters are determined at the minimum point. The objective function here is defined as the difference squared between measured and computed concentrations: N

F= ~ i=l

where:

(C~- CLi) 2

(A.42)

Analytical Flow Model

455

Ci = measured tracer concentration at sample data point i CLi = computed tracer concentration from the layered model at point i N = n u m b e r of m e a s u r e d sample data points in the tracer b r e a k t h r o u g h curve.

The larger the value of F, the poorer the match between the model and the measured tracer breakthrough data. The best match to the measured data occurs when F reaches its m i n i m u m value. The theoretical developments presented earlier for tracer flow in layered reservoirs show that the layered model response as a function of the injected volume is given by: n

CLi (V FLi) = ~ F(Tj,VFLi) j=l

(A.43)

where F is a function relating the tracer breakthrough curves for a single layer (e.g., Eq. (A.17)) with the layer distribution; VFLi is the total volume injected into the reservoir corresponding to observation point i; and the unknown parameters are: 1~

(kh)j

= ~S~tkh Zkh

1~ ~=~S~Zkh

(A.44a)

(A.44b)

The functional form of F(yj,VFLi) in Eq. (A.43) suggests that the minimization process is nonlinear with respect to the parameters yj and linear with respect to parameters ~j. Therefore, initial estimates are needed only for the nonlinear parameters ~ in the minimization algorithm. Reasonable estimates of yj may be calculated from the volume locations of peaks in a tracer response curve, assuming t h a t the measured peak locations are the same as those from the individual layer tracer responses, expressed in barrels: ASwjVpmax (Tj)est = 5.615VFLj max

(A.45)

where VFLjmax is the volume corresponding to the jth peak in an observed tracer profile, and Vp max is the pore volume at the peak location of a tracer response curve from a homogeneous pattern. Vp max can be calculated from curves given in Abbaszadeh (1982) and reproduced here as Fig. A.6, and from the pattern breakthrough areal sweep efficiency, VpBT.

456

Appendix

The nonlinear regression program computes the parameters ~j and yj, resulting in the best match of the model to a measured tracer profile. The layer properties are then obtained from these computed parameters as follows: (kh)j _ fkh

(A.46a)

- 1,J

YJ (+hSw)j = (~j)2

(A.46b)

A computer program designed to analyze a tracer elution curve is given in Abbaszadeh (1982). The regression method is general and can be applied to a variety of tracer flow problems. An application of the method to a field example is illustrated next, and implications of the resulting reservoir description are discussed.

Interpretation o f Loco field tracer test An interwell field tracer test was conducted in a heavy-oil reservoir waterflooded to its economic limit to measure travel times and breakthrough characteristics of the reservoir (Brigham and Smith, 1964; Martin et al., 1968). Two chemical tracers, thiocyanate and iodide, were co-injected in an inverted five-spot pattern. The layout of the pilot pattern and its important characteristics are illustrated in Fig. A.11. The pattern is unbalanced because of unequal production rates and the nonunity injection-to-production ratio.

A

C

160 BWPD ()s Pattern area 2.5 acres Injector Thickness (h) 12 ft 600 BWPD Permeability (k) 1500 md Porosity (r 0.26 Water saturation 0.55 330 ft - - > Mixing constant (a) 0.05 ft D

260 BWPD )

)

140 BWPD

C

240 BWPD

Figure A.11. Pilot pattern and flood parameters, Loco field

Analytical Flow Model

457

Most of the tracer production occurred at wells A and D. Well C produced a far smaller volume of tracer and had breakthrough at a later time t h a n wells A and D. During the one-month period of the test, no tracer at all was produced from well B. The tracer production curve from well D is shown in Fig. A.12. The nonuniform behavior could be attributed to such factors as permeability anisotropy, nonuniform pressure gradients, and/or existence of n a t u r a l barriers within the pilot area. A rigorous analysis of the tracer t r a n s p o r t mechanism requires computer simulation of flowlines and augmentation of tracer flow process on the flowlines in a multilayered reservoir. However, with sound engineering approximations for imbalance patterns, the tracer test from each well m a y be analyzed using the theoretical developments discussed in this appendix. For this purpose, the actual cause of unequal tracer distribution within the p a t t e r n is not important and should not matter.

30 IlI ~" 20

~ .k~ ...... Iodide I~.!,kJ~ Injection I / v ' ~ . ~. down ~ I I

E.

~

................-.~..

8

,

o,

;

....

;

......

,,;

, ...... ;

,

,

Volume produced x 1000, bbls Figure A.12. Tracer response, well D, Loco field

ADJUSTMENTS FOR OPEN PATTERN Before the tracer d a t a can be analyzed, the relative flow from the injector toward each producer must be estimated by the approximations described in the section on tracer flow in unbalanced patterns. Because no tracer was produced from well B during the test period, it is clear t h a t the flow in t h a t direction is small. For lack of additional information, such as interference pressure t r a n s i e n t tests, to better estimate the distributions of fluids in the pattern, it is assumed t h a t 50 barrels of water per day (BWPD) is flowing toward well B. This somewhat

458

Appendix

arbitrary figure allows for the fact that no tracer has yet appeared but still permits some flow in that direction. The remaining 600-50 = 550 BWPD from the injector is divided among the producers according to their producing rates. This proportioning method is also consistent with the times of tracer breakthrough and the cumulative volumes of tracer from these wells. Thus, 225 BWPD flows toward well A, 120 BWPD toward well C, and 205 BWPD toward well D. Similarly, out of the total of 200 lb of ammonium thiocyanate tracer material injected, 68.3 lb (200 x 205/600BWPD) is flowing toward well D, 75 lb (200 x 225/600) toward well A, 40 lb (200 x 120/600) toward well C, and only 17 lb (200 x 50/600) toward well B. Dilution effects from production outside the pattern are taken into account by the contrast between a well's actual production rate and the amount of injected fluid flowing toward that well. For example, for well D, the total producing rate is 240 BWPD while the flow rate from the injector is 205 BWPD, as calculated before. Therefore, the observed concentrations at that well are multiplied by 240/ 205, and the produced volumes are divided by 240/205 to make the corresponding tracer breakthrough curve approximately equivalent to that of a developed pattern. If the pattern were completely balanced, this ratio would have been 4/1, because 3/4 of the fluid flowing from outside of the pattern would not contain any tracer. This sort of scaling and proportioning is necessary because the formulations and procedures presented in this appendix are all based on the precise repetition of developed patterns. The final adjustment is made to the drainage areas of wells. For well D, the corresponding drainage is estimated as 205/600 x (2.5 acres x 43560 ft2)= 37,207 ft 2. LAYERANALYSISBY NONLINEAR REGRESSION Once a consistent relationship is established between the open pattern and the developed five-spot pattern, the nonlinear regression method is applied to the adjusted tracer data to determine the permeability and thickness of the responding layers. It is important to realize that the layers showing early breakthrough are the high-permeability or fast layers of the reservoir. Matches of the tracer data with seven and ten layers are shown in Fig. A.13. Although the match with the ten-layer model is somewhat better, both models are satisfactory for practical purposes. The computed layer permeability and thickness values are given in Table A.3. All calculated permeabilities are higher than 1500 md, the average permeability from pressure transient tests. The layering definition obtained from the tenlayer model is only a refinement of the seven-layer model; hence, the basic reservoir characteristics are established by a small number of layers with more detail added as the number of layers is increased. The total thickness and the permeability-thickness products from the two models are almost the same. The thickness of the reservoir investigated by the

459

Analytical Flow Model

Well D, 10 layers

Well D, 7 layers .

.

.

.

30

I

-

"

"

I,,,

I

.

.

.

.

I

.

.

.

.

I

30

.

2O

9 ',,

I-

10

i1~...

0 2000

3000 Volume produced, Bbls

4000

/

/

2000

~

-

Computedcuw.e

;

~ Computed peaks i . Selected peaks 3000 4000 Volume produced, Bbls

Figure A.13. Layer analysis of tracer response from well D, Loco field tracer flow is only about 14 percent (1.692/12) of the total thickness of the reservoir. The total kh from the analysis, however, is about 33 percent (6000 md/18000 md) of the average kh of the reservoir. Only a small portion of the total thickness of the reservoir is investigated, while a much larger portion of the

Table A.3 Computed permeability and thickness, well D, for seven and ten layers Values for seven layers Layer 1 2 3 4 5 6 7 8 9 10 suin

Values for ten layers

h

k

kh

h

k

kh

(i~)

(md)

(md-ft)

(i~)

(md)

(md-ft)

m ~

294 788 1,313 756 783 1,091 981 m m m

0.0439 0.0530 0.1342 0.2716 0.1028 0.1839 0.2050 0.3256 0.2910 0.0811

4,926 4,531 4,285 4,070 3,902 3,681 3,490 3,253 2,947 2,768

216 240 575 1,105 401 677 715 1,059 858 224

~

6,006

1.6921

~

6,072

0.0602 0.1824 0.3247 0.2036 0.2241 0.3357 0.3351 m

1.6658

4,890 4,320 4,045 3,712 3,492 3,249 2,928

460

Appendix

reservoir kh was seen. Thus, the high permeability layers are emphasized from this or any other tracer test. The ability of a tracer test to provide definition of highly productive layers is a key feature, because it is crucial to know the high permeability zones to predict the flow performance under any injection process, such as a more expensive EOR.

Dykstra-Parsons analysis of test results Because of economical and operational considerations, tracer tests may not be run long enough to investigate larger portions of the reservoir. In that event, only the definitions of high conductive regions of the reservoir are obtained. This is not a limitation of tracer tests because extrapolation of the definition of lower productive zones can be made from the tracer-derived information, using the DykstraParsons permeability heterogeneity parameter. Fig. A.14 is a Dykstra-Parsons analysis of tracer test results from well D with the ten-layer model.

10 4

~ 1 0

~

V

=

~

15O0

~

- 890

= ~----7g~--

(1.

=0.41 10 2 ~*

o 1

~

1

~

'

~

SLO2O

Cumulative

9 9 L A L

5o

l

l

8o 9o

thickness,

99

%

Figure A.14. Dykstra-Parsons analysis of well D tracer response This plot is based on percent of cumulative thickness, because uniform porosity is assumed for the formation. The 100 percent point would correspond to the total thickness of the reservoir: i.e., 12 ft. The open circle at 50 percent represents average permeability value of 1500 md from pressure transient data. The pressure transient information is very useful for this analysis because it anchors the entire graph. The Dykstra-Parsons permeability coefficient of variation, VDp, is calculated from the straight line to be equal to 0.41. This value can be used in further reservoir engineering studies of this field.

Analytical Flow Model

461

Areal heterogeneities Undoubtedly, heterogeneities exist in the layers that would affect the tracer flow to some degree. The mathematical model and the analysis procedures discussed here, however, assume a layer-cake model for the reservoir with homogeneous layers. Such a model may geologically fit some of the reservoirs; however it may not fit others. Nonetheless, it may still be possible to consider an actual reservoir as though it were layered and behaved as a stack of noncommunicating uniform layers. This concept has been quantified by Mishra (1987), who investigated random permeability distributions with short- and long-range spatial correlations in a two-dimensional, single-layer, developed five-spot pattern. The results of his studies indicate that if variations in the permeability distribution of the layer are correlated only over short ranges of distance, the tracer response will appear homogeneous, with an apparent increase in dispersivity, a; however, if the permeability variations are correlated over long ranges of distance, the multiple tracer peaks that are produced result in apparent layering with a pseudo-Dykstra-Parsons coefficient. Whether apparent layering or increased mixing occurs depends largely on the correlation length scales and the variability of the permeability field. Examples of tracer breakthrough profiles for both short-range and long-range correlations with different degrees of permeability variations in the plane are shown in Fig. A.15 (adapted from Mishra, 1987). Fig. A.15a shows the tracer response curve for a single-layer, five-spot pattern with short-range correlations and a relatively low Dykstra-Parsons coefficient. Fig. A.15b gives the breakthrough response for the same pattern with a high Dykstra-Parsons coefficient and long permeability correlation range. In the second case, the effect of long-range correlations, combined with a high degree of heterogeneity, shows up as an apparently layered system. This is primarily caused by formation of preferential flow paths due to the alignment of high permeability regions. The results of Mishra's work support the idea of apparent layering as a possible substitute for areal variations in permeability. Referring back to Fig. A.14, which shows a Dykstra-Parsons permeability layering of 0.41 for this field test, the reader should remember that the reservoir may not actually be made up of distinct homogenous layers that give this value of permeability variations; it merely acts as if it were. This point is important, because as far as the modeling of the flow behavior is concerned, it is much easier to work with a simpler but equivalent layer-cake model than with a three-dimensional, fully heterogeneous reservoir. The concept of equivalent layering presented here is analogous to the generally accepted approach of pseudofunctions in multiphase-flow reservoir simulation studies.

Appendix

462

4~176 F

~

Matched model

aJ=z2s

3001-

/

/ t Heter~

2ool-

400[k1hl/Zkh = 0.56,

k 1hl/Y.~h = 0.48 k2h2/Zkh = 0.38, k2h2/Z~ h = 0.45

ao0I-

!

/

I1 Vow=oas 2OOl-

|

~

Matched model

l~t ~n"= ~

/

~

Heterogeneity

,~ i!

vDp = 0.65 t'~, (~'nk= 1"92

100

o/

0

~! "~ I /

J

JJ

"

~l : < : : . .

I

0.5 1.0 1.5 0.5 1.0 1.5 0 Volume injected, bbl x 105 Volume injected, bbl x 105

a

Figure A.15. Effect of layer heterogeneity on a five-spot tracer pattern D E S I G N OF T R A C E R T E S T S

A major problem in designing an interwell tracer test is to determine the amount of tracer material to be injected, in order to yield effluent tracer concentrations above the detection level, below a maximum environmentally safe level, and at an affordable price. In addition, tracers must often be injected in a relatively unknown flow environment. Even limited reservoir data, however, can be used to improve the estimation of required tracer. The Abbaszadeh-Brigham model allows at least three approaches for estimating the amount of tracer required, depending on data available, the level of complexity, and degree of accuracy desired. These three approaches are based on: 1) a single layer analysis, 2) layer capacity (Oh) or layer conductivity (kh) distribution, and 3) the Dykstra-Parsons heterogeneity parameter, VDP. These approaches are discussed in the following sections. It should be remembered that the reservoir is not a well-understood environment, that these design values are just estimates and not facts, and that as a rule of thumb, no design estimate is better than a factor of two in predictability. D e s i g n b a s e d on a s i n g l e

layer

The original test by Brigham and Smith (1984) was performed in the Loco field in Oklahoma. The amount of tracer required for the test can be estimated by

Analytical Flow Model

463

using the equations and curves developed here for a closed five-spot p a t t e r n , a s s u m i n g a single layer, with the test p a t t e r n and field p a r a m e t e r s shown in Fig. A.11. F r o m eqs. (A.18) and (A.19), the peak-produced tracer concentration, Cmax, is related to the dimensionless calculated peak concentration, CD,max for the pattern. Since the mass of tracer, M, in pounds is related to volume by: M = C oPVW

(A.47)

where" C O = injected tracer concentration (mass fraction) p = solution density, 62.4 lb/ft3 VT = tracer volume Combining Eq. (A.47) with eqs. (A.18) and (A.19) yields: M =

Cmax pAOhSw

(A.48)

CD max Let us a s s u m e t h a t the desired peak concentration, Cmax, in the field data is 50 ppm. The a m o u n t of tracer required to produce this peak concentration is obtained from the curves for dimensionless m a x i m u m concentration, CDmax , as a function of the Peclet number, as shown in Fig. A.6. The other p a r a m e t e r s needed are obtained from Fig. A.11. For this example the reservoir parameters are: A = 2.5 acres at 43,500 ft2/acre, the Peclet number, a/a = 330/.05 = 6600, the layer thickness, h = 12 ft, k = 1500 md, Sw = 0.55, p = 62.4 lb/ft3, the porosity, ~ = 0.26 and CD,max = 0.07 obtained from Fig. A.6 for the calculated a/a = 6600. These n u m b e r s are s u b s t i t u t e d in Eq. (A.48) to yield an estimated requirement of 103 lb of thiocyanate.

M

=

(50 x 10 -6) (62.4) (2.5 x 43,560) (0.26) (12) (0.55) 0.07~]6600

= 103 pounds

This calculated a m o u n t of tracer compares adequately as a design criterion with the original injection of 200 pounds, a s s u m i n g t h a t neither the unbalanced p a t t e r n nor the layering data were known.

Design based upon layering If a plot of incremental kh versus incremental Oh of a formation is available from core data, the design of tracer tests can be refined to account for the layering effect by a s s u m i n g t h a t layers are either of equal Oh or equal kh, and by using a

464

Appendix

graphical approach. For an n-layer system, we define fractional flow conductivity and fractional storability, respectively, as:

Equal kh case

Equal Ch

Fk

Figure A.16. Equal kh or equal Oh case for calculating layer properties

J Fk =i=l

(A.49)

n

i-1 and J ~r Fr = i=1

(A.50)

n

i=l thus,

k) = Fkj - Fkj-1 j

(A.51)

Fr - Fr 1

Individual layer parameters, (ldr can be calculated from either the equal Ohbased or the equal kh-based approach, for a selected number of layers n, as demonstrated in Fig. A.16.

Analytical Flow Model

465

Once layer parameters become available, tracer flow calculations in an n-layer reservoir can be performed using the equations and procedures described in the section on tracer flow in layered systems. For these calculations, it is necessary to specify the required total tracer volume, VTL. The resulting tracer-response curve for a selected VTL value is examined not only for criteria of detectability and safety level, but also for its general appearance. If the results are not satisfactory, another VTL value is selected until an acceptable tracer response curve is obtained. This is the most straightforward approach to the design of tracer flow in layered reservoirs; however the method requires a computer program that can calculate tracer response curves in layered reservoirs. A simplified version of this approach that does not require computer calculations is to assume that each tracer peak from a layered reservoir corresponds to a peak from tracer flow in each of the individual layers. This assumption neglects the interference effects and contribution of tracer flow from other layers when considering only layer j. That is:

(kh)j (CL)max,j = ~

~jmax

(A.52)

Cj, max = C0 Frj

~ C D,max

(A.53)

k] VTL Fr = -~ J ASw~,kh

(A.54)

therefore:

(CL)jmax=C0 -~ jASw~,kh y.,kh. CD,max

(A.55)

where: (CL)max,j = jth peak in layered response Cj,max CD,max

= contribution of tracer from layer j corresponding to layer peak volume -- dimensionless tracer peak concentration from single layer, Fig. A.6

The tracer mass is calculated from tracer volume as:

M=

(CL)max,j pASw

(Oh)j

(Xkh/2

(A.56)

466

Appendix

There will be n values of (C L)max, j corresponding to n layers. One can design a tracer test based on the desired maximum and minimum peak concentrations. The mass, M, of tracer required is then computed from Eq. (A.56) for these selected peak concentrations, using the calculated layer properties and pattern geometry.

Design based on the Dykstra-Parsons VDp coefficient This design approach uses the concept of the layer-cake model. The DykstraParsons coefficient of variations, VDp, can be calculated from core data of available wells in the field. Given the VDP value and the selected number of layers, permeability distribution of the layers is computed by the procedure described for the ten-layer case of Table A.2, although any number of layers may be used. Equal porosity may be used for the layers, because layer porosities often do not vary significantly and the contrast in layer permeabilities has a more significant impact on the tracer breakthrough curve. Once layer permeabilities are calculated, the design procedure for the layered reservoir is followed.

D E R I V A T I O N OF P A T T E R N B R E A K T H R O U G H CURVES

When formulating the equations for fluid flow in any pattern, potential equations or stream functions are required. Some of the basic methodology used is described in the following paragraphs. The relationship between produced concentration and injected volume is only a function of the number of wells and their arrangement in the reservoir. A pattern breakthrough curve is obtained by tracking particles along the streamlines of the flow system and by keeping account of those streamlines that break through. The method requires knowledge of the mathematical relationships for streamlines of injection patterns. In general, the streamlines are constructed from the imaginary part of the complex potential in a flow domain of interest: •(z) = O(x,y)+ i~P(x,y)

(A.57)

where: f~(z) = complex potential O(x,y) = velocity potential (pressure equation) tY(x,y) = stream function For a system of nl injectors located at points Zai (i = 1,...,nl) and n2 producers located at points zbj (j = 1,...,n2), the complex potential at location z = x + iy, (a complex number) is given by:

467

Analytical Flow Model

nl n2 ~(z) = )_Wai ln(z - z ai)- )_Wbjln(z - z bj ) i=l i=l

(A.58)

where Va and Vb are the flow strengths of injectors and producers. Thus, the stream function q~(x,y) can be obtained from the imaginary part of Eq. (A.59) for any well arrangement. Morel-Seytoux (1966) gives compact forms of the stream functions for m a n y frequently encountered regular patterns. For repeated patterns, such as a staggered line drive system shown in Fig. A.17, the streamlines are in terms of various elliptical integral functions. In this pattern, the breakthrough time, tBT(~), for streamline ~ is obtained by tracing a particle along it:

tgr(W) =

f

K(m~

dx

(A.59)

Vx(V)

JO

where K'(m)/2K(m) = d/a, d is the distance between unlike wells and a is the distance between like wells of the pattern. K(m) and K'(m) are complementary and uncomplementary elliptical functions of the first kind. Fluid velocity is calculated from the complete pertinent stream functions as: Vc (~)= r

I

y= y(~,~)

(A.60)

k. . . . . .

K' (m)

K (m), K' (m)

o II

~ II

III

-0,

K (m)

Figure A.17. Element and coordinate system for the staggered line drive pattern

468

Appendix

The pore volume injected into the pattern at time of breakthrough of streamline ~ is equal to: Vp(W) =

tBT (~t)q 4 O h K ( m ) K ' (m)

'(A.61)

where q is the injection rate into the pattern; this rate is set equal to q = 2n kh]~ for arbitrary unity pressure gradient. The concentration or fraction of displacing fluid in the production stream is proportional to the angle at which the streamline, y, enters the producing well. Referring to Fig. A.17, this is given by: fD(~) =

7~

4

V = 1

4~ ~:

4

(A.62)

Therefore, the pattern breakthrough curve, fD vs. Vp, can be computed from the knowledge of expressions for streamlines. Abbaszadeh (1982) derived pattern breakthrough curves for a variety of developed p a t t e r n s using the streamline tracking approach described. For a repeated five-spot pattern, the pattern breakthrough curve is: Vp = 0.228473(1 + rl)K(1 - ~2)

(A.63)

rl = t a n 2 [ } ( 1 - fD)]

(A.64)

where K is a complementary complete elliptical integral of the first kind with an argument of (1- T12). The pore volume injected at breakthrough is calculated from eqs. (A.63) and (A.64) for fD = 0 to be equal to VpBT = 0.71777.

NOMENCLATURE A a

Ci eL (CL)maxj Co

Cr

Cs(v) C(~) C

= = = = =

cross-sectional area distance between like wells in a pattern measured tracer concentration at sample point i layered reservoir-produced tracer concentration peak tracer concentration in layered reservoir corresponding to layer j = initial tracer concentration = tracer concentration absorbed on the rock surface = tracer concentration within a streamtube at volume location v = tracer concentration flowing into well from streamtube = produced tracer concentration from homogeneous pattern

Analytical Flow Model

CD Cmax

D d erfc(z) F

Fk FO Fr

fD g(z) G(z) h I J K K(m) K'(m) k k m

k~ L M N n P q qp qs A

qra qpe R Sw S S

tBW U

VDp VFL Vp VPBT

469

= dimensionless produced tracer concentration = p e a k t r a c e r c o n c e n t r a t i o n from single l a y e r r e s e r v o i r = m o l e c u l a r diffusion coefficient = d i s t a n c e b e t w e e n like wells in a p a t t e r n = c o m p l e m e n t a r y e r r o r function = 1 -erf(z) = f o r m a t i o n resistivity factor = fractional l a y e r flow capacity = fractional l a y e r s t o r a g e capacity = t r a c e r slug v o l u m e as a fraction of displaceable p a t t e r n pore v o l u m e = fractional flow or displacing fluid cut = probability d e n s i t y function = c u m u l a t i v e d i s t r i b u t i o n function = thickness = line i n t e g r a l of velocity t e r m s for m i x i n g in s t r e a m t u b e = index of l a y e r i n g = effective m i x i n g coefficient = c o m p l e m e n t a r y complete elliptical function of t h e first k i n d = u n c o m p l e m e n t a r y complete elliptical function of t h e first k i n d = permeability, md = m e d i a n p e r m e a b i l i t y , k50 = p e r m e a b i l i t y at one s t a n d a r d deviation, k84.1 = well index = c h a r a c t e r i s t i c s y s t e m length, d i s t a n c e from injector to p r o d u c e r = tracer mass = n u m b e r of d a t a points in a field t r a c e r b r e a k t h r o u g h curve = n u m b e r of layers in t h e m u l t i l a y e r r e s e r v o i r model = probability = flow r a t e into p a t t e r n or flow s y s t e m = c u m u l a t i v e flow r a t e of p r o d u c i n g wells = flow r a t e in a s t r e a m t u b e = r a t e of injected fluid flowing t o w a r d s well = flow r a t e of p r o d u c i n g well = r e t a r d a t i o n factor or rock's a b s o r p t i v e capacity = w a t e r s a t u r a t i o n , fraction = d i s t a n c e along a n a r b i t r a r y s t r e a m l i n e = location of a t r a c e r front in a n a r b i t r a r y s t r e a m t u b e = breakthrough time = i n t e r s t i t i a l pore velocity, b u l k velocity divided by porosity = D y k s t r a - P a r s o n s coefficient of v a r i a t i o n = fluid v o l u m e injected into l a y e r e d r e s e r v o i r = pore v o l u m e injected or p r o d u c e d = pore v o l u m e of t r a c e r injected at b r e a k t h r o u g h

Appendix

470

VPBT(~) VPD VPT VT VTL VFLj, max

Vpmax V v

Vc v

vt x

Ax z w

= = = = = = = = = = = = = = = =

pore volume injected at b r e a k t h r o u g h of s t r e a m l i n e dimensionless pore volume group pore volumes of t r a c e r injected into p a t t e r n t r a c e r volume injected into p a t t e r n t r a c e r volume injected into layered reservoir volume corresponding to the j t h p e a k in m e a s u r e d t r a c e r profile pore volume corresponding to the p e a k location of a t r a c e r response from a homogeneous p a t t e r n produced volume equivalent to developed p a t t e r n displaceable pore volume of s t r e a m t u b e up to location s bulk fluid velocity displaceable pore volume of s t r e a m t u b e up to location g t r a c e r volume in s t r e a m t u b e t r a c e r front location corresponding to the 50 p e r c e n t c o n c e n t r a t i o n t r a c e r slug size in a l i n e a r s y s t e m l o g a r i t h m of p e r m e a b i l i t y w i d t h of s t r e a m t u b e at locations

= = = = = = = = = = = = = =

objective function complex potential p r e s s u r e function s t r e a m function dispersivity c o n s t a n t porosity, fraction s t a n d a r d deviation of t r a c e r distribution profile mixing s t a n d a r d deviation due to distance t r a v e r s e d m i x i n g s t a n d a r d deviation due to g e o m e t r y change t r a c e r solution density reservoir rock density t r a c e r decay c o n s t a n t dimensionless correlation range, fraction of s y s t e m l e n g t h (L) flow s t r e n g t h of injection or production wells

SYMBOLS

F

q~

~g

P PR

XD 1)

Analytical Flow Model

471

E R R O R F U N C T I O N S (National B u r e a u of Standards, 1965)

x

erf x

x

erf x

x

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44

0.00000 0.01128 0.02256 0.03384 0.04511 0.05637 0.06762 0.07885 0.09007 0.10128 0.11246 0.12362 0.13475 0.14586 0.15694 0.16799 0.17901 0.18999 0.20093 0.21183 0.22270 0.23352 0.24429 0.25502 0.26570 0.27632 0.28689 0.29741 0.30788 0.31828 0.32862 0.33890 0.34912 0.35927 0.36936 0.37938 0.38932 0.39920 0.40900 0.41873 0.42839 0.43796 0.44746 0.45688 0.46622

0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.70 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.80 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.90 0.91 0.92 0.93 0.94

0.52049 0.52924 0.53789 0.54646 0.55493 0.56332 0.57161 0.57981 0.58792 0.59593 0.60385 0.61168 0.61941 0.62704 0.63458 0.64202 0.64937 0.65662 0.66378 0.67084 0.67780 0.68466 0.69143 0.69810 0.70467 0.71115 0.71753 0.72382 0.73001 0.73610 0.74210 0.74800 0.75381 0.75952 0.76514 0.77066 0.77610 0.78143 0.78668 0.79184 0.79690 0.80188 0.80676 0.81156 0.81627

1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1.20 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.30 1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.38 1.39 1.40 1.41 1.42 1.43 1.44

erf x 0.84270 0.84681 0.85083 0.85478 0.85864 0.86243 0.86614 0.86977 0.87332 0.87680 0.88020 0.88353 0.88678 0.88997 0.89308 0.89612 0.89909 0.90200 0.90483 0.90760 0.91031 0.91295 0.91553 0.91805 0.92050 0.92290 0.92523 0.92751 0.21923 0.93189 0.93400 0.93606 0.93806 0.94001 0.94191 0.94376 0.94556 0.94731 0.94901 0.95067 0.95228 0.95385 0.95537 0.95685 0.95829

x 1.50 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.60 1.61 1.62 1.63 1.64 1.65 1.66 1.67 1.68 1.69 1.70 1.71 1.72 1.73 1.74 1.75 1.76 1.77 1.78 1.79 1.80 1.81 1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.90 1.91 1.92 1.93 1.94

erf x 0.96610 0.96727 0.96841 0.96951 0.97058 0.97162 0.97262 0.97360 0.97454 0.97546 0.97634 0.97720 0.97803 0.97884 0.97962 0.98037 0.98110 0.98181 0.98249 0.98315 0.98379 0.98440 0.98500 0.98557 0.98613 0.98667 0.98719 0.98769 0.98817 0.98864 0.98909 0.98952 0.98994 0.99034 0.99073 0.99111 0.99147 0.99182 0.99215 0.99247 0.99279 0.99308 0.99337 0.99365 0.99392

Appendix

472

Error functions (concluded from page 472) x 0.45 0.46 0.47 0.48 0.49

erfx 0.47548 0.48465 0.49374 0.50274 0.51166

x 0.95 0.96 0.97 0.98 0.99

erfx 0.82089 0.82542 0.82987 0.83423 0.83850

x 1.45 1.46 1.47 1.48 1.49

erfx 0.95969 0.96105 0.96237 0.96365 0.96489

x 1.95 1.96 1.97 1.98 1.99

erfx 0.99417 0.99442 0.99466 0.99489 0.99511

REFERENCES

Abbaszadeh-Dehghani, M., "Analysis of Unit Mobility Ratio Well-to-Well Tracer Flow to Determine Reservoir Heterogeneity," Ph.D. dissertation, Stanford University, Stanford, CA (Aug. 1982). Abbaszadeh-Dehghani, M., and Brigham, W.E., "Analysis of Well-to-Well Tracer Flow to Determine Reservoir Layering," JPT (Oct. 1984) 1753-1762. Aronofsky, J.S., and Heller, J.P.H., "A Diffusion Model to Explain Mixing of Flowing Miscible Fluids in Porous Media," Trans., AIME (Sept. 19, 1957) 210, 345-349. Bear, J., Dynamics of Fluids in Porous Media, Elsevier Sci. Pub., New York (1972). Blackwell, R.J., "Laboratory Studies of Microscopic Dispersion Phenomena," SPEJ (March 1962) 1-8. Brigham, W.E., "Mixing Equations in Various Geometries," paper SPE 4585 presented at the 48th Ann. Fall Mtg. of SPE/AIME, Las Vegas, NV, Sept. 30Oct. 3, 1973. Brigham, W.E., Reed, P.W., and Dew, J.N., "Experiments on Mixing During Miscible Displacement in Porous Media," SPEJ (March 1961) 1. Brigham, W.E., and Smith, D.H., "Prediction of Tracer Behavior in Five-Spot Flow," paper SPE 1145 presented at SPE Conf. on Production Research, May 3 4, 1965. Brigham, W.E., and Abbaszadeh-Dehghani, M., "Tracer Testing for Reservoir Characterization," JPT (May 1987) 519-527. Cranks, J., The Mathematics of Diffusion, Oxford at the Clarendon Press, New York (1957). Deppe, J.C., "Injection Rate raThe Effect of Mobility Ratio, Area Swept and Pattern," SPEJ (June 1961) 81-91.

Analytical Flow Model

473

Dykstra, H., and Parsons, R.L., "The Prediction of Oil Recovery by Waterflooding," Secondary Recovery of Oil in the United States, Amer. Petrol. Inst. (1950) 160-174. Lau, L.K., Kaufman, W.J., and Todd, D.K., "Dispersion of a Water Tracer in Radial Laminar Flow Through Homogeneous Porous Media," Progress Rept. No. 5, Sanitary Engineering Research Lab., U. of Calif. at Berkeley (1959). Martin, W.L., Dew, J.N., Powers, M.L. and Steves, H.B., "Results of a Tertiary Hot Waterflood in a Thin Sand Reservoir," J P T (July 1968) 739-750. Mishra, S., "On the Use of Pressure and Tracer Test Data for Reservoir Description," Ph.D. dissertation, Stanford University, Stanford, CA (1987). Morel-Seytoux, H.J., "Unit Mobility Ratio Displacement Calculations for Pattern Floods in Homogeneous Medium," S P E J (Sept. 1966) 217-227. Muskat, M., The Flow of Homogeneous Fluids Through Porous Media, McGraw Hill, New York (1937). National Bureau of Standards, Table of the Error Functions and its Derivative, Applied Mathematics Series 41, 2d ed. U.S. Government Printing Office, Washington, D.C. (1954). Ogata, A., and Banks, R.B., "A Solution of the Differential Equation of Longitudinal Dispersion in Porous Media," U.S. Geol. Surv. Prof. Paper 411-A (1961). Prats, M., Strickler, W.R., and Mathewes, C.S., "Single-Fluid Five-Spot Floods in Dipping Reservoirs," Trans. AIME (1955) 204, 160-174. Satter, A., Shum, Y.M., Adams, W.T., and Davis, L.A., "Chemical Transport in Porous Media with Dispersion and Rate-Controlled Adsorption," S P E J (June 1980) 129-138.

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INDEX

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INDEX Abbaszadeh-Brigham model 160 for Golden Spike D3 "A" pool 261 in Rainbow Keg River "B" pool 266 in Big Muddy field 151 waterflood tracer design by 105 Activation analysis 77 Agreement states 81 ALARA 83 Alcohols as tracers 90, 96, 117, 150, 153, 210, 211,213, 243 Alkyl esters 203 hydrolysis to alcohol 203 Alpha particles 11, 13, 14, 18 Analog count rate meter 65 Analytical strategy 107 Annual Limit of Intake (ALI) 83 Anticoincidence counting 50, 64, 253 API oil/water separator 401 API gamma units 218 Atomic mass 1 Atomic number 1 Ba-137m isotope generator 73 for line metering 384 for production logging 353-356 Background 50, 53, 64, 332 Bacterial decomposition 159 Beam and source geometry 24 Becquerel (Bq) 3 Beryllium alpha reactions 13 Beta decay 10-11, 15-16 by positron emission 10 by electron capture 11 Beta particles 9, 14, 19, 43, 50

brehmsstralung from 19, 55, 99 characteristic energy of 19 energy spectrum 14 emission of 10, 58 energy discrimination 107 Big Muddy field 150-153 Binomial distribution 5 Borehole processes 362-69 Boron tracer, neutron-activated 310 Breakthrough (BT) 166 Bremsstrahlung 19, 55, 99 Brigham-Smith model early breakthrough times 147 for detection sensitivity 148 for Golden Spike D3 "A" pool 261 injected pulse width 146-148 Brunei observation well 220 as Brigham-Smith model 226 as total dilution model 222 Co-60 as K-40 222 hexacyanocobaltate 220 C-14 tagged hydrocarbons 244 Capillary imbibition 141 in Ekofisk field 141 in Gulfaks field 144 Capture units 33 Carbon monoxide (CO) 245, 253 Cationic reservoir 164 Chlorine-36 95, 71 Chromatography 91, 108-125, 193-195, 246-248, 258-264. Coalinga tracer test test procedure used 256 Coincidence counting 59 Collimator 331

478

Compositional changes 201 Compositional simulator (UTCOMP) for Big Muddy pilot 151 for Ranger field waterflood 157 swept pore volume by 174 Compton scattering 19, 20, 22, 55, 64 Compton edge 21 Continuous field sampling 126-131 by gas counting 254 gas tracers used 254 using additive method 127 using differential method 130 Control of radioactive materials 82 Conventional field sampling 125 at separator 251 at wellhead 252 by solid absorber 252 Corrosion and erosion monitoring 411-413 by Co-60 tagged coupons 412 by thin-layer activation 412 Corrosion treating by 1-131 tagged inhibitor 413 by tritium tagged inhibitor 414 Count rate 40 meter for 49, 66 plateau 48 Counting radioactive atoms 70 accelerator mass spectrometry 71 resonance ion spectrometry 71 Counting statistics 5-6 signal vs. noise in 5 zero count rate 6 Counting systems 48

Tracers in the Oil Field

figure of merit 40, 53 energy-sensitive counters 49 scalers 48 NIM bins 48, 53 Cross section for flow from flow measurements 379, 382 Curie (Ci) 3 Delay factor ~ 193, 194, 247, 259 Henry's law constant for 262 distribution coefficients for 192-195 Delay time 193, 246 Design of gas tracer test 250 Brigham-Smith model for 251 buoyancy correction in 250 dilution by gas lift in 250 Peace River steam pilot 279 pressure corrections in 266 Rainbow Keg River "B" pool 266 reservoir pressure effect in 251 sample collection needs 266 by total dilution model 251 Detector efficiency of 40 geometry, relative to source 40 Detectors for gas tracers electron capture detector 244 gamma counters 254 helium leak detector 284 proportional counters 253 thermal conductivity detector 253 Dicyanoaurate ion 95, 117 as gold-195 95 Diode detectors 63

Index Directional downhole tools focusing collimator 332 slit collimator 330 Disintegration rate 40 Distributed sources 26-29 external cylinder 28 internal cylinder 28 Monte Carlo procedure 26 Distribution coefficient 193 by Henry's law 247 by transit time 248 chromatographic method 198 classical method 195 effect of composition 200, 201 equilibrium conditions 196 FIA method 197 gas tracers, North West Fault Block 248 reservoir conditions 195 temperature conditions 195, 200 temperature correction 199 three-phase 247 Dose build-up factor 25 Dosimetry 78-81 Downhole cementation tracing 333-336 cement behind casing 335 Downhole tracer logging capture gamma radiation 294 depth of penetration 320-322 gamma-emitting tracers 293 hydraulic fracture tracing 326 injected radiotracers 294 multiple gamma energies 319 multistage acid tracing 328 neutron-activated tracers 294

479 radioactive scale 332 tagged gravel packs 328 wireline tools 293 Downhole tracer procedures 238, 322 tracer test design 322-326 Drift velocity 204, 233 Drill-bit wear tracer for warning of 364 Dynamic range 106 Einstein mass energy relation 2 Electron capture detector (ECD) 244, 254, 272 for cyclic halofluoro compounds 252 for cyclic perfluoro compounds 246, 252 for halofluoro compounds 245 for N20 -245 for SF6 244 Energy-sensitive counters 49 Environmental problems from drilling fluids and cuttings 419 from naturally occurring radioactive material (NORM) 417 from oily water spills 419 Fast neutron reactions 29, 32, 295 138Ba(n,2n,)137mBa 306 160(n,p) 16N reaction 295 69Ga(n,2n)68Ga reaction 306 with barite in drilling mud 307 for oxygen activation log 295306 Fenn-Big Valley MI flood 274 cationic water tracers in 274 Field gas tracer tests 257

480 Coalinga tracer test 256 gas tracer response in 256 Judy Creek field 273 miscible injection (MI) 265 Mitsue field 271 other field tests noted 257 of Rainbow Keg River "B" pool 266 for residual oil by gas tracer 258-264 tracers used in 256 Finite difference simulator Big Muddy field 150 Gulfaks field 145 Niitsu field 161 oilfield data 150 Ranger field 153 UTCOMP 151 Fission 13 Flow rates using tracers 76, 371386 by isotope dilution 371 by pulse velocity method 378 tracers used for 371 Flow through fractures temperature monitor for 238 tracers used 237 Free-water knockout (FWKO) 400404 with removable baffles 403 Gamma ray attenuation 19 backscatter of 394 dose from point source 79 emission 12 energy discrimination of 107 exposure rate constant for 79

Tracers in the Oil Field

interactions of 19 tracer methods 333-36 Gas counter 41 in current mode 43 in pulse mode 43 ion pair 41 Gas flood tracing injected gas velocity in 247 injection procedures for 267, 271 interwell tracers used 244-246 partitioning tracers used 246248, 258-260 phase behavior in 243 reservoir constraints in 244, 246 residual oil saturation 247 solvent flooding 243 tracer delay 247 tracer velocity 243 Gas tracer analysis of beta emitters 253 of chemical tracers 252 by conversion to water and CO2 253 using low-level counting 253 quality control in 255 radioactive tracers in 253 Gaussian distribution 5, 55 Geiger-Mueller (GM) counters 43, 46, 294, 359 Germanium detectors 64 Golden Spike D3 "A" pool 261 Gravity oil/water separators 400409. See also Hydraulic behavior of separators. plug flow in 401

Index Gray (Gy) 78 Halide ions 114 Helium 244, 245,254, 284 Helium-3 245 Henry's law constant (*H) for residual oil saturation 260 volume peak plot by 260 Hexacyanocobaltate ion 94, 99, 100, 114, 277 Co-57 94, 156 Co-57and Co60 139 Co-58 228 Co-58 and Co-60 153 Co-60 94, 97, 220 Co-60, Co-58 217, 229 preparation of 98 High-performance liquid chromatography 118 Hydraulic behavior of mud 364 Hydraulic behavior of separators API separator 401 free-water knockout 403 short-circuit flow 406 tracer test procedure for 410 tracers used in 409 wash tank, 15,000-bbl 405 1-131 217 1-125 142, 163 Injected water distribution 142, 165 interwell extrapolated from 171 mass balance in 172 North West Fault Block 181 Injectivity logging by conventional tools 338 by oxygen activation 302 in steam wells 357 by tracer loss log 338

481 by velocity shot log 342 Internal dose from ingested beta 79 Ion chamber 42, 43, 358 for C-14 and H-3 tagged gases 45 guard ring used for 44 quartz fiber electrometer for 44 saturation current from 43 solid state type 63 Ion chromatography 116, 118 Ion-exchange chromatography 108-125 for chemical tracers 114-125 for radioactive tracers 108-113 Isotope dilution procedures 74-76, 344, 345-357, 372-379 by constant rate injection 372 by pulse injection 373 by split stream method 376 by total count method 374 mixing needs for 373 Isotope generators 71-74 for constant rate injection 355 for downhole tool 354 for line metering 384 for production logging 352-357 for pulse injection 354 JOBO steam drive 277-278 Judy Creek field MI flood 273 tritiated toluene in 274 Kern River steam flood 278 Kr-81m isotope generator for production logging 357 for steam injectivity 361

482 Kr-85 71,244, 269, 271,276 Kr-85 and tritium 269 Landmark method for residual oil Golden Spike D3 "A" pool 261 Henry's law constants in 259 Judy Creek Beaverhill Lake "A" pool 210 laboratory experiments 258 Leduc field 211 peak-produced concentration 263 Leaks behind casing 295 by log-inject-log 310 by oxygen activation log 295 by tracer loss log 341 Licensing radioactive material 81 LIL. See Log-inject-log. Line metering by tracers 383 Linear attenuation coefficient 22 Liquid scintillation counter 58-63 cocktail for 59, 105 in Peace River steam pilot 280 quenching effect in 61 Logging observation well test design by Brigham-Smith model 226 K-40 as Co-60 used in 226 by Monte Carlo procedure 227 by total dilution model 225 Logging observation wells 217 API units used in 218 Brunei observation well 220 design of 222-227 Maljamar unit 230 Means San Andreas unit 227 minimum detection limit 217

Tracers in the Oil Field

tracer response width 218 Logging, production 336-61 Log-inject-log 307-311 borehole background in 310 by boron activation 310 by chloride activation 308 for residual oil 308 Low-level counting 50, 59, 64, 253 Maljamar observation well Co-58, Co-60 230 Maljamar unit pilot 163 swept pore volume in 164 Marinelli beaker 70 Mass attenuation coefficient 22 Maximum annual radiation dose 83 Maximum permissible concentration (MPC) 83, 104, 224, 271 Meter proving by tracers 383 Midway-Sunset steam pilot 278 Minimum detection limit (MDL) 104, 106, 116, 117, 124, 217, 250, 266, 271, 272 Miscible (MI) injection. See solvent injection 264 Mitsue field 270-273 Moment analysis first moment and mean in 168, 169 second moment, variance of 171, 407 Peclet number by 151, 168 simulation of 174 Mudwater invasion 227 by tracers 362 Multichannel analyzer (MCA) 53, 67

Index multichannel scaler in 69 NaI(T1) scintillation detector 52, 53-56, 294 figure of merit of 56 NaI(T1) gamma spectrum 55-58 downhole gamma tracers 318 least-squares procedures 58, 315 natural gamma radiation 313 spectrum stripping 58, 314 Natural gamma radiation Ge detector spectrum 317 NaI spectrum deconvolution 316 Naturally occurring radioactive material (NORM) U.S. regulations 417 Neutrino 14 Neutron 1, 9, 36 Neutron absorption 30 attenuation 32 capture gamma emission 32 cross sections 32 detectors 65 fast neutron capture 32 thermal capture 31 slowing down 31 Neutron backscatter for detecting foam 395 Neutron reactions with matter 2933 Neutron sources 12-14 Niitsu oilfield 159-163 Abbaszadeh-Brigham model 160 simulation of 161 tracer behavior in 159

483 NIM bin 48, 53 Nitrate ion 114, 116, 277 Nitrous oxide (N20) 245 NORM. See naturally occurring radioactive material, 417 North West Fault Block 139, 176186 injection distribution in 177 interwell pore volume swept 176-186 interwell water distribution 176-186 kv/kh ratio of 141 production profile in 139 vertical segregation in 140 Nucleus 1 Observation wells 215-232 drift velocity in 234 logging wells 216-230 sampling wells 215, 230 Oilfield facility operations 371-426 Offshore drilling fluids fate of in environment 419 Oxygen activation log 295-306 continuous activation 297 injectivity profiles 302 short pulse activation 298 Pair production 19, 21, 55 Particle accelerators 14 Partitioning tracers 192, 246-248, 258-261 C-14 isoamyl alcohol 210 H-3 n-butyl alcohol 211 H-3 t-butyl alcohol 210, 211, 213, 215 phases of 194 residence time of 194

484

Peace River steam pilot 278 condensate tracers for 279 data analysis of 280 exponential tracer decline in 281 Peclet number 151, 168 Perfluoro compounds 117, 122 Phase saturation 194 by Ba-133/Am-241 paired source 390 by gamma ray absorption 387 saturation condition 389 Phase velocity by dual-energy pairs 392 Photoelectric absorption 19, 20, 22, 55-57, 331 Photomultiplier tube 52-53, 59-60 Pipeline leaks by chemical tracer 416 by radioactive tracer 416 Poisson distribution 5 Positron 10-11, 19 annihilation of 10, 19 emission 10-11 Potassium-40 35, 220, 314-317 Production logging by conventional means 337-357 by tracer dilution logging 344 Proportional counter 43, 45, 50 field tubes in 45 gases 45 SF 6 interference with 254 South Swan Hill field tracers in 269 Proton 1, 9 Prudhoe Bay field 139, 177-186 Pulse height 42, 43, 49

Tracers in the Oil Field

plateau 48 Quality control 96-98 Mitsue field 271 Rad 78 Radioactive decay 3 decay constant 3 decay rate 3 equilibrium 6-8 half-life 4 isotopes 2 scale 332 sequential decay 6 Radioactive tracers for downhole use 313 multiple gamma energies 318 Radioactivity 3 average life (~) 4 from cosmic sources 37 from manmade sources 35-37 from primordial sources 34 Rainbow Keg River "B" pool 265 Ranger field waterflood compositional simulation of 215 field data from 153 normalized data from 154 residual oil in 213 simulated tracer response of 157 streamtube model of 156 tracers used 153 Rem 78 Residence time distribution 168, 400 dimensionless form 403 first moment of 400 second moment of 400

Index Residence times 192 Residual oil 191 by dual completion single-well test 206 by neutron activation, LIL 308 by core analysis 192 eliminating temperature effect of 199 flow path 195 injected gas velocity 250 interwell gas tracer for 249-250, 258-261 local equilibrium 193, 247 landmark method for 210 log-inject-log methods for 192 single-well tracer test for 201207 tracers required for 250 two-well tracer test 192, 208, 248 Roentgen (R) 78 Sample collection 125-131, 147148, 251 by solid absorbent 246 gas partition in separator 267 Sampling observation well 230, 272 Saturation condition three reservoir phases with 247, 263 Scale monitoring and treatment 414 by scale coupons 415 by tagged scale inhibitor 415 Scintillation detectors inorganic 52 organic 51 Secular equilibrium 7, 73, 74

485 Sequential dispersed gas flotation cell tanks-in-series model 406 variance for number of tanks 407 SF 6 252, 254, 271 interference with gas counting 254 Sievert (Sv) 78 Signal-to-noise ratio 41 Single-channel analyzer (SCA) 49 Single-well test for residual oil 201-207 asymmetry by linear drift 205 asymmetry by reaction 202 correction for drift 204 dispersion in 202 in-situ reaction in 203 minitest for 204 symmetry problem in 201 simulation of Sludge in pipes by flow rates 382 Solid state ionization chambers 63 Solvent flooding 249 Solvent injection tracing miscibility loss 264 solvent-tracer separation 264, 265 tracer response analysis 265 WAG procedure 264 South Swan Hills field MI WAG injection 268 production logging 269 field injection 268 Spectrometry 71 Spectrum analysis 56

486 Split stream isotope dilution by chemical tracers 376 Steam behavior 276 Steam flood tracing condensate tracers 277 effect of phase 275 sample collection and analysis 283 vapor tracers 276 Steam injectivity survey 359 Steam quality at wellhead by neutron transmission 361 Steam wells gas phase tracers 358 quality downhole 357 Streamtube model 150 Sulfate conversion to H2 S 234 liquid scintillation counting 236 sulfur-35 tracer 235 Survey meters 49 Swept pore volume 163 by first moment 172-175 Maljamar unit pilot 164 mean volume injected 166 North West Fault Block 176186 simulation (UTCOMP) 174 Tanks-in-series model 406-408 Tc-99m isotope generator 73 for line metering 386 Tetracyanonickelate ion 95, 117 Ni-63 95 Thermoluminescent dosimeters 64 Thiocyanate ion 99, 114, 151, 153, 163,213,277, 278 carbon-14 99 sulfur-35 99

Tracers in the Oil Field

Three-phase flow by dual gamma ray 389-392 by dual-detector dual-energy gamma rays 392-393 by low-energy gamma rays 389 Tia Juana steam drive 278 Total count isotope dilution method calibration 375 Total dilution moctei~for design 271 Total sample isotope dilution method 377 Tracer dilution logging by constant rate injection 348 in Devonian shale gas well 349-352 pulse tool used 346 pulse injection pump 345 Tracer enrichment 105, 107, 124 Tracer injection for waterfloods 100-103 Tracer pulse 193 Tracer response curves 166-167 analysis by moments 168 BT response of 167 exponential decline of 170 extrapolation of 170, 402 landmarks 166 noise in 168 variance of 403 Transient equilibrium 7, 72 Transport of radioactive materials 83 Trifluoracetic acid (TFA) 117 Tritiated hydrocarbons 244, 271, 273 by catalytic exchange 244 conversion to water 266

Index counting as water 266 Fenn-Big Valley MI flood 275 quality control of 255 retention times of 244 Tritiated water 94, 150, 153, 163, 177, 199, 210, 213, 215, 227, 235, 273 preparation of 98 Tritium 2, 14, 45, 59, 244, 245, 261, 269 Two-phase flow 378-382, 387-388 Br-82 tagged condensate 380 by gamma-ray absorption 379, 387 in condensate lines 379 Kr-85 tagged gas 380 phase velocities in 381 Two-well test for residual oil at start of waterflood 208 gas tracer test 249 in Judy Creek field 210 in Leduc field 213 in Ranger field 213 residual oil measured 230 in watered-out fields 208 U-238 series 11, 35, 315, 317 Unconventional reservoirs gas tracing in 284 Underground coal gasification 284 Underground gas storage mixing of gases in 398 tracers for stored gas 396 troubleshooting in 399

487 UTCOMP (simulator) 151, 174 WAG (water alternating gas) procedures 264, 268 Waterflood tracer design 103-108 Abbaszadeh-Brigham model for 105 maximum permissible concentration in 104 minimum detection limit in 104 total dilution model for 103 Waterflood tracers alcohols in 95 cationic tracers in 91 chemical tracers used 114-125 constraints of reservoir 90 history of 90 ideal 90, 91-92, 93, 165, 166 quality control 97-100 radioactive tracers used 93-113 reactions with reservoir 91 tracer exchange 91 Waterflood tracer field tests Big Muddy field 150-153 Ekofisk field 141-142 Gulfaks field 142-145 Maljamar Coop Unit 163-164 Niitsu field 159-163 Northwest Fault Block 139141, 176-186 Water injection logging 337-42 X-radiation 11, 12, 55 Xe-133 244, 276

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