Production Optimization TM Using Nodal Analysis
H. Dale Beggs
Production Optimization Using NODALTM Analysis PHAM HOÁNG
mí ANH
H. Dale Beggs
OGCI and Petroskills Publications Tulsa, Oklahoma
I
I
Production Optimization Using NODALTM Analysis
COPYRlGHT 1991, 200~. 2003 by OGCI, Inc., Petroskills, llC. and H. Dale Beggs P. O. Box 35448 Tulsa, Oklahoma 74153·0-148 AH rights rescrved. No part of this text may be r~produced Oc transcribed in any fonn oc by any mcans withoUl ¡he written pennission of OGCI and Pelroskills.
lts use in adult training programs is specifically reserved for OGCI and Pmoskills. Printed in the United States of Americ. Libr.ry of Congress Catalog Card Number: 90·064081 International Standard Book Number: 0·930972·14·7 Second printing-Febru.ry, 1999 Third printing-November, 2002 Second Edition-May, 2003
Contents
1
Introduction 1 Systems Analysis Approach Applications 7 Summary 7 References 7
2
1
Production Systems Analysis 2
Reservoir Performance Introduction 9 Well Performance Equations 9 OarcyOs Law 9 Factors Affecting Productivity Index 15 Factors Affecting Inflow Performance 15 Orive Mechanisms 17 18 Oissolved Gas Orive Gas Cap Orive 18 Water Orive 18 Combination Orive 19 HJ Orawdown or Producing Rate Zero Skin Factor' 19 Non-zero Skin Factor 20 Effect 01 Oepletion 20 IPR Behavior 01 Gas Wells 20 Predicting Present Time IPRs lor Oil Wells 21 Vogel Method 21 Application 01 Vogel Method-Zero Skin Factor 23 24 Saturated Reservoirs UndersOaturated Reservoirs 24 Application 01 V0gel Method-Non-Zero Skin Factor (Standing Modification) Undersaturated Reservoirs 29 Oetermining FE from Well Tests 29
9
'
26
1°
Fetkovich Method 30 31 Flow-After-Flow Testing Isochronal Testing 31 Modified Isochronal Testing 32 Jones, Blount and Glaze Method 35 Constructing IPRs When No Stabilized Tests Are Available 37 IPR Construction for Special Cases Horizontal Welis 37 Waterflood Welis 37 Stratified Formations 38 Static Reservoir Pressure Unknown 39 Predicting Future IPRs for 011 Welis 40 Standing Method 40 Fetkovich Method 42 Combining Vogel and Fetkovich 42 Predicting Present Time IPRs for Gas Welis 43 Use of the Back Pressure Equation 43 Jones, Blount and Glaze Method 45 46 Predicting Future IPRs for Gas Wells Weli Completlon Effects 47 48 Open Hole Completions Perforated Completions 48 Perforated, Gravel-Packed Completions 53 Innow Performance Summary 54 Oil Welis ·54 Gas Welis 54 References 55
3
36
Flow in Pipes and Restrictions Introduction 57 Basic Equations and Concepts 58 The General Energy Equatlon 58 Single-Phase Flow 62 64 Two-Phase Flow Two-Phase Flow Variables 64 Liquid Holdup 64 No-Slip Liquid Holdup 65 Denslty 65 65 Velocity Viscosity 66 SUrface Tension 66 Modification of the Pressure Gradient Equation for Two-Phase Flow 66 Elevation Change Friction Component 67 Acceleration Component 67 Two-Phase Flow Patterns 67 Pressure Traverse Calculation 67 Procedure When Temperature Distribution is Unknown 69 Fluid Property Calculations 72 Fluid Density 75
vi
57
66
Gas 75 Oil 75 Waler 75 76 Fluid Velocity Gas 76 Oil 76 Water 76 Empirical Fluid Property Correlalions 76 Gas Compressibility Factor 77 Salution or Dissolved Gas 78 Formation Volume Factor 79 Gas 79 79 Oil Water 79 Isothermal Compressibilily 79 80 Viscosily Oil 80 Waler 80 80 Gas Interfacial Tension 81 Gas/Oil Inlerfacial Tension 81 GasN'laler Inlerfacial Tension 81 Predicling Flowing Temperatures 81 Flowing Temperature in Wells 82 82 Flowing Temperature in Pipelines Well Flow CarrelaClons 83 84 PoeHmann a"d Carpenler ~lethod 85 Hagedorn ane Brown Method 86 Duns and Ros Melhod Orkiszewski 1'.lethod 86 87 Bubble Flow Slug Flow 87 Transition Flow 87 Misl Flow 87 Aziz, Govier and Fogarasi Melhod 87 88 Chierici, Clucci and Sclocchi Method Beggs and Brill Method 88 MONA, Asheim Method 90 Hasan and Kabir Method 90 Flow in Annuli 90 Hydraulic Radius Cancept 90 Cornish Methad 91 Evaluation al Correlations Using Field Data 91 Elfects 01 Variables on Well Performance 93 93 Liquid FlolV Rate Gas/Liquid Ralio 93 94 Waler/OiI Ratio or Water Cut Liquid Viscosity 95 Tubing Diameler and Slippage 95 96 Flow in Gas Wells 97 Flaw in Direclional Wells Use 01 Prepared Pressure Traverse Curves 98
di
Preparation of Pressure Traverse Curves Generalized Curves 98 Application of Traverse Curves 98 Pipeline Flow Correlations 104 Horizontal Flow Pattern Prediction 108 Eaton, et al., Method 109 Dukler, et al., Method 110 Seggs and Srill Method 111 Flanigan Method for Hilly Terrain 112 Hybrid Model 114 MONA, Asheim Method 114 Evaluation of Pipe Flow Correlations 114 Effects of Variables on Pipeline Performance Liquid Flow Rate 116 Gas/Uquid Ratio 116 Water Cut 117 Liquid Viscosity 117 Pipe Oiameter 117 Single-phase Gas Flow 117 Use of Prepared Pressure Traverse Curves Parallel or Looped Pipelines 122 Pressure Orop Through Restrictions 123 Surface Chokes 123 Gas Flow 123 Two-Phase Flow 124 Subsurface Safety Valves (SSSVs) 127 Gas Flow 127 Two-Phase Flow 127 Valves and Pipe Fittings 128 Eroslonal Velocity 129 References 129
4
116
118
Total System Analysis Introduction 133 Tubing Size Selection 135 Flowline Size Effect 136 Effect of Stimulation 139 Systems Analysis for Wells with Restrictions Surface Chokes 141 Subsurface Safety Valves 143 Evaluating Completion Effects 143 Nodal Analysis of Injection Wells 146 Effect of Oepletion 148 Relating Performance to Time 150 Analyzing Multiwell Systems 151
5
98
133
141
Artificial Lift Design Introduction 155 . Continuous Flow Gas Uf!
155 155
l'iii '.
Well Performance 156 Valve Spacing 160 Gas Uf! Valve Performance 165 Otis Design Procedure 167 Submersible Pump Selection 174 Sucker Rod or Beam Pumping 177 Hydraulic Pumping 183 Summary 183 References 185
Nomenclature
187
Appendix A
191
Two-phase Flow Correlation Examples Hagedorn and Brown Method
197
Appendix B Pressure Traverse Curves
191
197
Production Systems Analysis
1
INTRODUCTION .-\ny procluctioll \Vell i~ drillcd :lnd completcd lo mQVC Ol" g"l~ fnJl1l irs original iocatioll in the rescrvoir
(;-:(' oil ¡~...
¡he stock tank or sales line. ~foYel1lcnr or {rampart of !luids rcquircs ~ncrgy to t)V('rcol11c friction losscs ::1 Ihe syslcm and lO !in (he products to lhe surfJcc. The (uids mus! travel Ihrough rhe rescrvoir and lhe piping
¡:-,¡;';C
~~ ~tem
and ultinltHe]y 110\\1 into J scparator for gas-liquid Thc produclion system can be relati"cly simr!c or can ínelude many components in which energy al' fíessurc losscs occur. Far cxample. íl diagram of:1 COI11rkx production systcm, which ¡Ilustrares a numbcr of ~('rJration.
l:-;e componcnls in which prcssure losses OCCUf, is shown ioFig.I·1. Thc prcssurc drop in thc fotal syslcm al any lime will ~ the iñitial nllid prc!'surc minus Ihe final nuid pres~:Jre, pI{ ~ P...",. This pressure drnp is the slIm of the rressure drops occurring in all ol' lhe componcnts of the ~~ stem. Since the pressure drop through any component yaries with producing rate, the producing rate will be cQntroJled by Ihe components selecled. The selcction and ~izing of the individual components is very important, r:Jt because of Ihe intcraction í.lmong the components, a ch.:lIlge in the prcssurc drop in one Il1
perfonnance and handled independenlly. The amollnl ol' oil and gas no~ing inlo the \\'ell fram the reservoir depen,-!s on the pressure drap in the piping sY:'lem . and the pressurc drap in the piping system dq:-ends on the amount of fluid tlowing through il. Ther-=,iore, the t:nlire production system mus[ be analyzcd J:; a unir. The production rale ar delivcrability of a \\'ell can aften be sevcrely restricted by the perfonnancc of on!y one component in the system. If the effcct of cach component on Ihe tot<'l.1 system perfannance can be isoIalcd. the systern performance can be optimized in the rnost economical way. Past experience has sho\\'n thtH Jarge amounts of moncy have been wasled on stimulating lhe [onnation when the we¡¡-s producing capacily \\'3:' acrually bcing restricted because the mbing or Oowline was [,-X, smal!. Another cX3mplc of errors in completiC'n design is to install tubing that is too largc. This often happen, on wells Ihat are expected to produce at high rales. lt will be shown thar this practicc not only was[es Illoney on oversized equipmcnt. bUI tubing that is too large ('an actually reduce the rate at which a well will no\\'. This can cause the wcll to load up with liquids and dic. which ncccssitatcs lhe early ínst.tllation of artifici.tl lift equip~ menl or comprcssion. A mcthou for analyzing a wel1. which will alk'!\\' dck'mlination of the producillg c;:IracJty for any C'llmbin:ltion of componcnts, is desnibed in lhe following st::ction. This melhod may be uscu (o delcnninc locafit1rts of c.\(:essive Oow rcsislance or prcs~urc drop in any p~lrt of the systcm. Thc crfcct of changing
I
Prodllctioll Oplimi=alioll Usillg Nodal Allalysis
2
f<-A PB =(P wh -i'sep)4 rr===::::::;;--~SALES UNE PWhO lAPB=(Posc-Psep)r' GAS
T2
;~~;~~-
~p~se~p~S~EP~A~R~A"iO~R~~~ lIQUID
Pose
Posv
STOCK TANK
AP4=(PUSV-r-uov'P_' pI,
I
t.p, t.P2
AP7= Pwl-Pwil
AP3 PUA-POA AP4 = Pusv-Posv A Ps Pwh -PDse c> P6 = POSC-Psep c> P7 Pwf-Pwh c> PB = Pwh-Psep
BorrOMHOLE RESTRICTION AP3= (PUA -POA)
PR-Pwfs Pwfs-Pwl
Á
LOSS IN POROUS MEDIUM LOSS ACROSS COMPLETION " "RESTRICTION " SAFETY VALVE SURFACE CHOKE IN FLOWlINE TOTAL LOSS IN TUBING " FLOWlINE
~;""';;'7\,
t. P, =(Pw's - Pw,)--1
I ....------1
A P, =(PFi - Pw's)
Fig. 1-1. Possible pressure losses in complete system.
SYSTEMS ANALYSIS APPROACH
The systems analysis approach, oflen caHcd NGDAL'" Analysis, '" has becn applied for many years to analyze the perfonnance of systems eomposed of interacting eomponents. Electrical circuits. complex pipeline networks and centrifuga! pumping systems are a11 analyzed using mis method. lts applicadon to well producing syslems was firsl proposed by Gilbert' in 1954 and discussed by Nind' in 1964 and Brown' in 1978. The procedure consists of selecting a division poiot or node in lhe well and dividing the syslem al lhis point. The locations of lhe most commoruy used nodes are shown in Fig. 1-2. AH of the components upstream of (he nade comprise (he inflow section. while the ou(f1ow section consists af all of lbe componenLS downstream of the node. A relationship between fiow cate and pressure drop must be availabJe foc each component in the system. The flow rale lhrough lhe system can be delermined once the following requirements are satisfied:
1. Flow inlo lhe node equals flow out nf lhe node. 2. Ooly one pressure can exist at a nade. ·"NODAL Analysis" is a uademark oC Flopetrol JohnSlon, a di8 'IisiDn oC Schlumberger Technology Corporation, and is proteeted by . U.S. Palent #4,442,710.
At a particular time in the Efe af (he well. there are always [wo pressures !.ha( remain flxed and are not fun.:tioos of ilow rateo Ofie of these pressure~ is (he aver.lge reservoir pressure PRI and (he other is the s)lstem audet pressure. The outlet pressure is usually (he separaror pressure Pup' bU[ if the well is cOnlrolled by a surface choke the fixed oullet pressure may be the wellhead pressure P...IJ. Once the nade is selected. the nade pressllre is calculated from both dírections starting at [he fixed pressures. inj10w fo the node:
fiR - t:.p (upstream componen!s)
= P"..J<
Outflow from the lIode: PUP
+ l1p
(downstream eomponents) ::::: P""dc
The pressure drop, IIp, in any component ,varies wilh flow rale, q. Therefore. a pJot of nade pressure versus flow rate will produce two curves, the intersection of which will give the canditions satisfying requiremenlS 1 and 2, given previously. The procedure is illustrated graphically in Fig. 1-3. The effect of a change in any of the eomponents can be analyzed by recalculating the nade pressure versus flow rate using the new characteristics of the componenl
3
PrOdllcliOIl Syslems Allalysis
NODE 1
2 3 4 5 6 7 B 1A 1B
LOCATION SEPARATOR SURFACE CHOKE WELLHEAD SAFETY VALVE RESTRICnON PWF PWFS
PR GAS SALES STOCKTANK
,e,g. 1-2. Localion 01 various nades. rhat
waS
changed. Ir u changc was made in
I ,~(l(}H'
ro
Hode:
(oll1poncnt. lhe Gutllo\\' curve wil1 rCI1l3in unchanged.
Ho"ve ....er. if cithcr curve is chang:cd, lhe intersection \ViII Pt: shifteu. and a IlCW !lo\\' capadty and node pressure \\'¡II cxist. Thc CtlfVCS \ViII also be shifted if eithcr of the fixcd prcssures is changcd. which may occur with depletion or a chunge in separatioll conditions. The procedurc can be furthcr illustrnted by considcring the simple producing systcm shown in Fig. 1-4 3nd ~elccting
the wellhcad as ¡he nade.
Qutj70w from nade:
The effect on the flow capxity of changing. the tubing size is illustrated in Fig. 1-:'. and thc crfce! l.."'If <1 dwnge in flowline size is shown in Fig. 1-6. The effcct of increasing: thc tubing sizc. :.1:' long as the
I•
g
Oulflow from node
~
w
OC
::>
(f)
~ oc
:
o... W
1
,
Inllow lo node
-----~:~-
L: °z
VERTICAL :-::; INClINED· .'9ING
I
1Syslem Flc-... I CapacUy
FLOW RATE, q -
,C¡g. 1-3. Oeterminalion
o( ffow capacity.
.:::'g. 1-4. Simple producing
s.'stem
Productioa Optimizalioa Using Nodal Analysis
4
OUtflOIV from node: Pup
Pwh
q-=.---=J
L
Fig. 1-5. Ellecl 01 lub{ng size.
tubing i5 not too large, is to give a higha node or wellhead pressure ror a gi\'cn flow rate, bec3use the prc.ssure drop in [he tubíng wiB be decreased. This shifts the ioflow curve upward and lhe intcrsection te the right. A lar'2.er tlowline will reduce {he pressure drop in (he nowline~. shifting the outtlow down and (he ¡ntceseerian to the right. The erfeer of a change in any component in {he system can be isolarcd in lhis manoa. Also, {he ef~ feet of declining reseryoir pressure or changing separator prcssure can be determined. A more frequently used analysis procedure is to select (he node betwecn (he reservoir and me piping system. lllis is labeled as paint 6 on Fig. 1-2, and lhe nade pres5Ufe is P..f' Selecting the node at Ihis point esséntially divides lhe well ioto a reservoir dominated eomponent aod a pipiog system dominated eomponenL The inflow and outf1ow expressions for the simple system will theo
be: Inflon'
10
nade:
+
!J.Pllwli.<
+
:'J.p,",;., = P-t
The effect of a change in tubing size 00 the total systcm producing eapacity when P..f ¡s the node pressure is illustrated in Fig. lo?~ A producing systcm may be optimized by selceting {he eombination of component characteristics that will give the maximum production rate foc {he lowest cost. Although the overall pressure drop available for a system, PR - PUP' might be fixed at a particular time, the producing capacity of rhe system depends 00 where the pressure drops occur. If too mueh pressure drop occurs in one component or module, there may be insufficiem pressure drop remaining for efficicnt perfornlance of the other modules. This is illustrated in Fig. 1-8 for a system in which (he tubing is too slllal!. Even [hough the reservoir may be capnbJe of praducing a large amounl of fluid, if too much pressure drop occurs in (he tubing, the well perfonnance suffers_ For this eype of \Vell eompletion, it is obvious (ha¡ improving the reservoir performance by stimulation \\'ould be a waste of effort unkss larger tubing were installed. A case in which the well performance is controlkd by the inflow is shown in Fig.·1-9. In rhis case, the exccssive pressure drop could be caused by fOITn
Pwf
q-
Fig. 1-6. Ellecl oOlowline size.
Lt
q_-_-
Fig. 1-7. Elfect 01 lubing size..
_
5
ProdUCliol1 Syslellls Allalv.sis
, I
,I I
Pwl
, I I
Im¡ I
I ,~
m
__
:~:
mm q
Fig. 1-10 Efleel 01 lubing size. Fig. 1-8. \.'Iell res/rieled by plping sys/em.
cusscd in dctail in Chaptn J. Thc nuid \'eloeity is the produClion rate divided by lhe area of lile lubing. A qual~ itative cxample of selccting lhe optimu11l tubing size ror
a well
th~H
is producing both gas
in Fig. 1-10 and 1-11. As tubing sizc is increased. ¡he frictiL'1l losses dccrt:
innow. H<Jwevcr. as rhe ltIhlng sizc is runher ¡ncreaset!. the wcll hegins loading with liquid ami th~ rlo\\' bccoll1cS inlamittent nr unst'lhle. As lhe liquid k\'el in lhe \\'el1 huilds Ihe \\"ell will c"cntllally die. Fig. 1·11 illustratcs
Ihis graphically. Once a \\'ell lhat is producing liqllids ail10g wiril [he ga;; rcaches Ihe stagc in \\'hich it \Vil! nl~ longer tlow natur
crease the required tlawing ballom hale pressure. Hawever, as the gns rate is incrcas.ed, lhe nuid \'clocity and, lherefore, th~ !'rictian lasses alsa ¡nerease. A paint \ViII cvcntually be reached ~uch that the frictian losscs ¡ncrense more lhan the density or hydrostatic losscs dccrease with an ¡ncrease in gas rate. This can be dctcrmincd using NODAL n, Analysis as ilIustrared in Fig. 1-12. A plot of liquid productil11l rale vcrSU5 gas injection rate can
PR ---------------------------------------
1
I
UNSTABLE
q
REGION
I
p
l----------t!
d FOR MAXII.IUM q~
sep I
q--~
Fip. 1-9 l'lelf rcsfricled by inf!ow.
d~-
Fig. 1-11. Finding optimum tucing size.
6
ProducliO/l Optimiza/ion Using Nada/ Ana/ysis
lnflow
ExcessivQ GlA
/
P
N2
"
,1"
t
Oullbw
A
> N1
P.1
NJ
N,
Pwl
> N2
GlR
\
/" l'l/Iow
Fig. 1-14. Elleel o/ per/orating densily en inflow.
Fig. 1-12. Efleel 01 gas rale on outflow.
IllfloU' lO /Jode:
OU{/7ow ¡ro", Ilode:
Since ¡he perforation pressure drop is a function of the number of perforations open, as well as prodüction rate, a different ¡nnow curve would exisl [or each perforating density. This is illuslraled qualitatively in Fig. 1-14. As [he numba of perforations is increased. a point will eventually be rcached such (hat the perforation pressure drop is ncgligible, and, therefore, a further ¡necease in perforating density would be useless. A pIar of the production rate resulting from various perforating densities, that ¡s, lhe intersection af the various inflow curves
L:~· t I
q L __
:~I Avail~ble ! I l·
l. Determine which eomponents in (he system can be changed. Changes are limitcd in some cases by previous decisions. For example, once a cert:lin hale sizc is drilled, the casing size and, thcrclorc, (he tubing size is limited.
2. Select ane component lo be optinlized. 3. Select lhe node location thar will bes! emphasize (he effeet of the change in lhe selectcd componcnt. This is nol critica1 because lhe same ovcrall resuh will be predicted regardless of the node local ion. 4. Dcvelop expressions ror the infiow and oulOow. 5. Obtain required data to calculare prcssure drop versus rate ror aH [he components. This may require more dara than is available, which may necessitate per-
=---c:-__..
I I I I
I I
with the autflo\\' curve, i5 shown in Fig. 1-15. M~thods ror calculating perforation pressure drop ar~ discusscd in ehapler 3. A suggested procedure for applying NüDAL '" Analysis is given as follows:
T q Gas Voluml!'
Economlc optlmumqlnJ
i
q
lo'.
Fig. 1-13. Efleet 01 gas injeclion rate en liquid rate.
N~mber 01 p~rlorations
--'to
Fig. 1-15. Elfect 01 perlori!ting density on rate.
Producriol1 S.1'",rems Ana~)'sis
7
the
13. Analyzing a multiwell producing SystClll.
6.
Oelenninc lhe cITect of ehanging (he characteristics of ¡he selcctcd eomponent by plotting innow versus out~ now alld reading lhe intcrscctioll.
I..!. Relating ficld pcrfonl1ancc to time.
7.
Repeallhc proccdurc ror ench component tlwt is to be optimizcd. 111. APPLlCATIONS
The nodal systcms analysis approach may be uscd to
l.
Selccting tubing sizc.
i
Sckcling nO\vlinc sizc.
_'o
Gran'l pack designo
..1..
Surrat'c chokc sizing.
"
Sub~urrat'c ~arely
('.
..\nalyzillg:ln
\"I\'e siling.
C\i~lillg
syslclll fl)r abnonnal
lll)\\'
rc~trictil)!l~.
IV. SUMMARY
Thc nodal systcms analysis approach is a \'cry ncxihlc melhod that can be uscd to impro\'c lhe perfonmlllcc of many "'el\ systems. To apply Ihe systcl11s analysis proccdure to a \Vell, it is nrCeS:':i3ry to be ablc to calculnlc thc prcssure drop tl13t wiJl (lCcur in al1 the sy:-Iem CL.nlponcl1ts listed in Fig. 1-1. These. prcssure drops depcnd not only on now mte. bUI on the sizc and other charaCleristics of Ihe eomponents. Un1css accuratc Illcthods can be fOUlld to cnlculalC thcse prcs:-ure drops. lhe systems analysis can produce crrOllcous rcslllts. The following sections in this book prcscnt Ihe l<1tcsl and Illost accurate 111cthods for calculating lhe rci::lliollship bctwcen now rnte ane! pressure drop fol' <111 Ihe COI11p0nelHs. This rcquircs a thorough rcvicw of rescr\'oir ell~ ginecring concepts to dClcrmine rescn'oir intlow pcrf(lrl11~nCe; an underslanding of Illultiph~sc nO\\' in pipes 1(" ca1culatc tubing and nowlillc pcrlorm'ance: procedures Il) dct12'rminc the performance 01' pcrlor
.\nillt'iallirt designo
V. REFERENCES
:\
\\'cll stilllulation c\·:llllatioll.
9.
Delcrmining Ihe clrcet ofcomprcssil)il on gas \\·cl1 pcr(onn:1I)cc.
10..-\naIY7.ing cllccts
l)r
pcrli.mlling dCJ1::;ity.
11. Predicting lhc c1Tccl paclli .' l~.
01'
dt'plctioll
l)ll
producing ca-
AJloc<1ting injeclion gas among ga:- hit wells.
1. Gilbcrt, W. E.: "Flowing and G,b-Lirt \Vell Performance," API Drill. Prod. i'raclicc. \95-J.. :\ind. T. E. W.: Pril/ciples (?( Gil IIdl ProdUcliol1. 'IcGraw-f1ilJ. 196~ . .. Bro\\'n, K. E. tl!ld Beggs. H. D.: rhe Ti:cllllology (~( .irr(/icia{ L~¡; '\/er¡'od\. Vol. 1, Pelln \\'ell Publ. Co.. Tuls<1. Okl<1homa. 197fl.
Reservoir Performance
2
1. INTRODUCTION Oile of thc m(l~l illlJ10rlrllll componenl:, i'n llll' 1\11;11 \\"cll
s\"~;('m is Ihe rc~\?r\"oir. Ulllc:,s tlCCllr;J{C pn'dil'tl\Il\:' l':1I1
\0 \\ lut will I1tH\ ¡nltl ¡he lltlrt'llt11t' 1"("111 ¡!lL' Ihe pcrl'llrll1¡lllCC (Ir {he Systclll (';1(lfln! l·,' ,111;1h ;:;:J. As disCllS:,cd in lhe prC\"i0US s,xlinll. IJlI" ,>1 111\..' 1~\~'J pn:ssu["c:-,. ¡JI :lllY lil1lc in ¡he 1ire l,ftlll' 11",\'1\,'11. IS 111;: J\'cragL' rcscr\ nir prcssurc Ji". T11I..' 1111\\" l111t' 1111..' \\(':', dcpcnds 011 lhe dra\\"(1L1\\"Il or prl..'Ssun.: 111111' 111 lh\.' rc~:rq)ir. />R -/\". The rclati\lIlship b\'I\\",11 1!l1\\" rí1¡~ ~\Ild prcssurc drop occurring in Ihe ptlrtlll" 111,\1111111 cm be vcry cOlllpkx and dcpcnds 011 parallll'lL'IS :--11,-11 as rl~~"~ propcrtics. !luid propcrtics. !lo\\' !"l',t:.illll'. I1l1hl :,;~Ill r~I1:\ms in IhE: rack. comprcssibility 01' Ihe 1l11WIII!: llllllb. ft1¡-::wtion dam
rC':';:;-\L,ir.
prc":,surc Pub is sOllletimcs selccted. This \\'ill ISI1!:lh' [he ctl'c,,:ts of ihc prcsslIrc drop
~('d in Charter l. The in!low to l!le. node l':lll llh'llId~ fhe !low Ihrollgh oll1el" eomponellls. dC¡ll'ndill!~ \'11 lhe ll'~'.ltiOIl of the IlDlk selccted. !;] this chílplcr Ihe \\'el! pcrform:111cc eqll:llillll...; \\ dI be
prc:,('nted for various r~ser\"oir types and drive I1lcehanisll1:'. Thcse equtl\iOll5 \\"ill pcnnit Ihe calculation of J.Pt fJll:f.~ or. if Ihero:;- is negligiblc prcssure 105s across the ~·~'ltlrlctioll. ÓI'I = P.I? -1'". where Pu'- is the ll(l\\'ing \\·c¡;·:'~'rc_pressurc. The I.:'ffl.:'c\:' ~1( ch:lllging conditit111s (In the ::..:'cllfncY 01' Ihe cqualil1 n:, ",jI[ be disclIsscd :llld clllr::-i~'alll1cthOlls lo (\lrrc'(l fN failurc nI' {he lhenry \\-il1 be ;':-~'sl'[lIcd. \lclhods rOl' prt'Jieling IPRs rnr l1lllh Ihe IWC5;,';lt 01' re;,'~i. l30th oil tlnd g:lS rcsl'f\l)ir pl'rformancc \\"ill he ¡m::'(':l1cd. Fi¡ully, mcthods for obtaining the nccessary roc.k and fluid rropcrties rOl' use in the equatiolls \\'ill be ollllincí.l, ane. ¡he accuracy of the data \\-ill be disCllsscd.
: : ro: -
11. WELL PERFORMANCE EQUATIONS T\' ..:::tlctdate the prcssure tiror occurring in a ITsc[\·oir. all ;,'..:juation that cxpresscs the cncrgy al' prcssurc losscs du\:' w viscous shcar or frictit'!n forces as a funclion al' ve!L'..::ily al' f10\V rate is requircd. :\1though lhe form ofthc cqu~liol\ can be quite difierenl for various typcs offluids, the [,Js.ic cqllation on which all of lhc variolls form5 are ba::~d is Darcy's law. A. Darcy's Law
Ir. 1856, whilc pcrforming ('.\pcrill1~nts for {he dL'sig.n of s.md filler beds for \\'alcr purifi(',ltion, Ileury Dan:y pmrl':,ed an cquatioll rclating arparcll! lluid vclocily lo prc:,:,urc drop aeross Ihe filter bed . .\ithough the c.\pcril1l~I1IS \\'crc performcd with tlll\\' only in the dO\\"ll\\"ard veni.:al dircction, the c.\prcssi011 is abo val id ror horizoll-
PJVdUClioll Oplimizalioll UsiJlg Nudul A¡;_I~rsi.\
JO tal flow, which is of mast ¡nterest in lhe pctroleum industry. It should al so be noted that Darcy's experiments involved only one Huid, water. and that the sand [¡{ter was completcly saturated with the water. Thercfore, no effccts of fluid properties oc saturation were involved.
Darcy's sand tilters wece of constan! cross-sectional arca, so lhe cquation did nol account roc changes in vclo~¡ly with localion. Writtcn in diffcrentiai form, Darcy's law is: kdp
v=--
(2-1)
!l ti,
=_ kA dI'
(2-2)
!l el,
wherc
k v
q A P dpld,
=
Units
Variable
Symbol
Darey
Field
cc/sec
bbl'day
Flow rate
q
PermeabHity
k
darcys
md
Area
A
cm'
ft' psi
Pressure
p
almo
Viscosity
~
cp
cp
Lenglh
L
cm
ft
Thc gcol1lctry of ¡he linear systclll is illllstr[\ted in Fig. l. It can be obsaycd from Eguatían 2~J lhat a plot on c3rt~sian coordillJleS of p vs. L \ViII pr.oduce a srr¡:üglli line of constanl slop~, -qW'kA. TIJat is, the variarion al pressure with distance is linear. If the nowing tluid is compressiblc, lhe in-siru 00\\ rate is a fUl1ctiol1 01' pressure. Using the t:1et lhal lhe mas~ now rate pq mus! be constant and ~xpressing the dClIsity in tcnns of prcssure, temperatun: and ga:i specinc gravity, it can be showll thut Equation 2-3 be-comcs' 1~
or in tcrms oh'olumctric now rate q
q = vA
TABLE 2-1 Units for Darcy's Law
pc.:-rrncability oflhe paraus medium, appararcnt fluid vclocity, volurnctric flow rale, afta open lo now, fluid viscosity, and pressure gradient in lhe direclion of flow
,
,
JI, - Pi
8.93ZT¡tL kA '/."
(2·:' .
(llL'gati\'c).
J. Linear Flol\" For linear now. that is [or constant area flO\y, the cquation may be intcgratcd to gívc the pressure drop occurring Qver some Icngth L:
l' T ft L k A
P' kdp = -qJ1 - fL el,
J
J.l
PI
kA o
PI
qp JL elr -dp=-kA o
ep,
ti, md,
fe, scf / day
If it is assum~d that k, ~ and q are independent of pressure, or that they can be cvaluated at lhe average pressure in the system, the equation bccomes
JP'
pSIJ.
°R.
(2·3)
FOl" high-velocity f10w in which turbulcnce or 0011Darcy Oow can exist, Darcy's la\\' must be moditied lo accaunl for the extra pressure drop cJused by the tUfbulcnc~. Applying [he turbulencc corrccti,on to Equatians 2-3 and 2-5 givcs: Oil Flow
Integration givcs:
-q¡.¡
p,-Pt =--L kA
(2-4) (2-6)
or
q
e
CkA(p,- 1',)
J1L
where is a unit conversioo factor. The correet value for is 1.0 for Darcy Units and 1.127 X 10-3 for Field Units (See Table 2"1).
e
where
1', 1', !lo
Bo L
upstream pressure, psia,
do\,·mstream pressurc, psia, oil viscosity, cp, üil fonnation volume f"ctor, bbl/STB, Length of flow path, n,
11
J. Radial FIOlI' Darcy's law
q~
----L---~
F"f;. 2-1. Geometry for linear tlo','/.
lío A
pcnncability to oil. md,
arC
Po ~
(1"
l;.'
=-:
c~n be us.cd to calculatc the no\\" into a \,"eH whcrc lhe fluid is convcrging radially into a rclati,"cly small hale. In this cnsc, Ihe arca open lo now is nat constnnt amI mllst ¡herefare be included in lhe integrntion 01' Equation 2-2. Rdcrring lo Ihe no\\" geomclry iIIustratcd in Figure 2-2. the cr05s-scclion~1 arc~ apcn lo lhe now ~t any radius is A = 2Itr". .-\150, dcfining the changc in prcssure wilh localion to be negalivc \Vith rcspcct lo lhe dircction of no\\". dl'ldr becomcs -dpldr. ~Iaking thcsc substitutions in Equatioll 2-2 gives:
n=. q:::o
oi! dcnsity. IbnlitV. \"Clocily coclliciClll. n-l. and oil llo\\' raleo STB day.
2¡rrhkd[J
'
~
FIfJ\\"
.:, Oil Flan: \\·hcl1 applying the Darcy cqualion lO !lo"," ,,1jl in a IT~Cf\"ojL il is a~sumcd that lhe oil is only :-li-;¡Hiy comprcssiblc. lile small, changc in q wilh prcs~ur~ i::; halllllcd with lhe oil fOrlllJ::ion "olume factor B", so {h~t Ihe Ilo\\" rate can be cxprcs5cd in surnlce llr stock ud: '"olullle:-i. For oil Oo\\', EqUJlion 2-9 b,,:coll1c::;: \)f
:
'2
I't -P:::::
+
S.l)3Z~1..LT Cjg
kg.1
(2-7)
1.247 xl ,)-J('PZTLy " , ~
r
q:
el B = 2rrrhk,,_i dp ~t,,; .Ir ,1
g'IZ dL'\i'llillll l;h.::~'r 1.,'\'1111:llct! ;11
"
g;l:, gr:n'ity (~lir;=; : J. gil:' 111..1\\ rate ¡It :,:. - psi
k
2rrh J "" --"- el" . p"B"
\n cstimatc l~lr Ihe \'c!oci¡~ ClldliciCll! [3 Clll be ob-
fr'. md. and a and b
Formation Type
Consolidtlled Uncorlsolidaled
approximalcd ¡'rom:
3fC
a
b 10 10
1.2
1.J7 X 107 ,
0.55
2.329
X
\llhough lincar !lo\\' rafe!y L1ccurs in tl n,::sL'r\-t1ir, Ihese .:Jtinlls ",ill be llscd blter 1\1 .:,\!culalc lhe pre~:\urc drop ",'-,)~~ ;1 gr¡¡n~l pack COlllplcli,,111. Ihal i:-;. ófJ = / 1 ,,; - pur.
. d,-
=.r"1~'r
1';-11 )
\\"h.. . ll inlegraling: Ihi~ cqutllioll. it i:-; u~llally assulllcd that lh,:- prcssurc rUIlClioll . .tfl'J oc:: k P.,B,. is indcp('ndcnt ('Ir rr~~~lIrc or lhílt il ":-tln be c\';lll1J~cd al avcrngc prc""urc in
";:d rrom:
k
I I
T. .!'.
J1l)\\ing [l'mpl.'ra:::r;.'. ~ 1?
P
12-9)
dI'
~'':
F;), 2-2" Rad;aJ (fow sys{em.
ProdllClioll 0plimizotioJl UsiJlg Noda/ .-lll,:~rsis
12 Ih~ w~lI's
drainuge volumc. This is ne..:essary beca use no
which gives upon inlcgration:
simple ílllalytical equation for this tenn as a functiol1 oC pressllr~ can be forll1ulm~d. Utilizing this assumption and inlcgrating Equation 2-11 Qyer the drainagc radius of the wcll gin~$: 2¡r.k.,h(p, - 1'''1)
llaBlJ
11'1 (1~
(2-12)
/1"11')
2
qsc =
kg
where
1'.'
p,,,. r
"
h
i,,!lo\\' ml<, STB / day cn~ctivc oil pcnneabiliIY. md, rcservoir lhickncss, n,
prcssure al r = 1"1" psia, wdlborc tlowing pressur~ al r wdl's drainage radius, fL
pR Puf ~l.!:
=
Z T
r,.., psia
\Vcllbore rJdíuS, n, oil \'iscosiry. cp, and
oil fonll:Hiúl1 volulllc faclI..)f. bbl/STB. Equatian 2-13
applie~
foe stcady-sr:.:.¡t
703XIO-6k"h(p~ - 1',:,) _ '
(2-17)
gas tlow rate, Mscl'd, penncabililY lo gas, md, n::scn'oir thickness, n, . averagc res,,:rvoir prcssurc. !)sia wcllbor~ t10Willg prcssur~. psia, gas viscosiry al T, Ji =.5 (PR + PI')' cp gas compressibility factor at T, p , rescrvoir lcmperalurc, o R, drainuge radius, n, and wcllbore mdius, ft.
c. Resermir Pressure Profile. The behavior ol' th~ presin lhe rcscn'oir as a fUllction ol' radius can be ,:m3Iyzed by plouing pressurc verSus radius as predicleJ b~ Equatiol1 }-14. Assuming a fixed average rescn·oir pressurc Px al r:= 0.472 r~ and solving for pressure. Equarion 2-14 gives: SlIfC
(PI' =
constant),
laminar tlo\\' 01' a \\'dl in lhe ccnter of:.I circular drainngc arca. It is mOfe useful if exprcsscd in I~nns of averag~ rescr\'oir prcssur~ PRo and for pseudo-s:r~3dy s.tate or stabilized !lo\\' (PR - Puf:= constant) as: O,OOIOSk)~PR - 1'",)
t2·16)
.1'('
where qsc
..
k /1'
JI g 1
IlgLTln (.472 1;/1;,,) (2-13)
/¡
=
Modifying Equalion 2-16 for stabilizcd no\\", a\"t~rag~ reservoir presslLfc, defining Psc = 14.7 psia and T,•. =. 520 °R givcs un cquation for gas inf10w rate in ficld units.
For fidd units, Equation 2-12 bccomes:
i/" k
qS(}lgZTpsc(lnJ~/r,,)
2
Po: - P"f
(2-14)
1l0B" ~1 (.4721~ / r,)
l~-IS\
whcrc
average pr~$sure in Ihe drJinage volume of th~ well. The other tcnns are the same as rhose defined for Equation 2-13.
'PR
b, Gas floa: To inh:grate Equation 2-9 for flow of gases, the faet that pq is constant is used along with the gas cquation of state . pM
p~ ZRT
(2-15)
A plOl of prcssure versus radius for typical wcll con-
ditiOllS, Figurc 2-3, shows thc large increasc in pr~ssurc gradient
m, where
or
111
141.2qu~UB(l
(2-19)
k)l
This type oC plol is illuSlratcd in Figure 2-4_ !I should be emphasizcd that the slope remains constant only if all oC the [erms on Ihe righl-hand side oC Equation 2-19 remain constan!. A different slope and, therefore, a differ-
Resen'uir Pc/formollce
/3
versus qf) on Cartcsian caardinatcs rcsu'¡is in a straighl
line having" slopc of -IIJ and an ¡ntercepl of al qo = O.
'"I!
p
r_\'I---c_~
(2·33)
-::cr - __
~ I
.~_7_2_r_e-,
Fig. 2-3. Reservo;r pressure profile. en!
PR
"aloe of P\l/' \Vould be obtaincd for each flo\V rate
Ir cond;tiolls are such tha[ J is constant ",illt drawdO\vl1, once a valuc of J is obtaincd from one production lest or calclIlated using Eqllation 2-20, it may be used to predict inflow performance ror other cOllditions. Examp/e 2-1: A wel1 that is producing from a reservoir having an average pressure of 2085 psig produced al arate of 282 STB/day when bottomhole flowing pressure was 1765 psig.
q".
A. similar anaiysis of Equation 2-17 for gas flo\V rc\'('als thnt a 1'101 of P~ \'crsm'" r rcsu\ts in a strnight lille
Calculate: 1. The productivily index J. 2. The producing rate ir Pwf is decreased lo 1485 psig. 3. The bollomhole pressure necessary lo oblain an inflow 01 400 STB/day. 4. The inflow rate if p\~J is reduced to zero, Le., Absolute Open FlolV polenlial (AOF) or
of :-.Iope:
3. Producrid(1' hule.\' Conccll/ The rclnlionship bctWCCll m:ll inflo\\' ralc and rrcssure
dLl\\-clo\\'11 hns o((cI1 been t'xprcsscd in Ihe form of a r,.u)ucr;l·il.l· ¡lIdex./,
qo(max)'
So/ution: J =
00070:'k"h ~L"B"
, ~-2())
1. J
111 (.--F~J:.I r".)
PR - P.,_
282 2085 -1765
=0.88 STB/day-psl.
2. qo =JÍPR - p",) = 0.88(2085 -1485) =528 STB/day
Thc inflc'l\\ equn(;on for oil !lo\\' cnll l!len be \\Tilten as
qo =JCPR-P,,/)
0, =-_-=
(2-21)
=PR -o,1J =2085-400/0.88 =1630psig 4. qo(mo,¡ =JIPR • O) = 0.8812085) =1835 STB/day
3. P",
.1 = -=--,-<Je-'_
(~-12)
PR - Pul
$0lving rOl' p,,(in
tel'IllS
('Irq" rcv(,
Tlle predictiolls llliJdc in "Examplc 2-\ are val id only if J rcmains constan!. This implies tll
, ¡ r
tion./{p) = k,/p"B" remains constant, which ;s scldol1l the case, as will be discussed further in following sections. Tlle productivity index can also be exprcssed as:
01
/
J
Pwfl
0.0070817
(Pn -1"'l)ln (.472r,. r,) I
sr,
I"if
k"
--dp ¡I j3"
(2·2-l)
',>"1
lr~/
I
L--------~cc!
'In ce: ~~'
In r....
The producli\'ity index concept could
Fig 2-4. Semi-Iog plot of pressure
VS.
radius.
or
Prodm.:t;oJl Optinú::otiolJ Using Nodo!
14
Jg
and
703xlO-6 kgh (2-26)
J.lgZTln
703xlO- kg/~ ¡i~ - P ~/) 6
(.472I;II~.)
A plOI of p~\fversus liJe would not be linear 011 Cartesian coordinalcs. A more commoll procedure roc gas well anaiysis \ViII be discussed in following scctions.
(2-28)
q" = ~JT [In (.472rJ r,,) +S']
The ski n faclor S' inciudcs the crrccts uf both turbukncc ami actual fanuncion damagc as:
S' ~ S + 0'1 4. Permeability Altera/ion Clnd Turbulem:e Darcy's law was bascd 011 the assumptions that permeability 10 (he nowing fluid was con~tant in lhe enlice drainage area ol' the well and that only laminar flow existcd. The effcctivc pcrmeability lo oil is lhe product of lhe fclativc permcability to oil and lhe absolute penne~ ability al' lhe reser\'oir, thal ¡s, k.. . =k k ro
Thc absohuc pcrmeabilily k, can be either increased around [he wcllbofe by wcll stimulation oc decreased by fonnation damage. such as clay swelling oc pore plugging. This would changc Ihe slope of lhe pressure profile out to the radius lO which the pcrmeability was altered. This is illuSlrated in Figure 2-5. Figure 2-5 illustrales that foe a CDIlSt.1nt flo\\' rate, less prcssure drawdown ",ould be cequired if the weJl had bccn slimulatcd and mor~ drawdowll would be requircd for a damaged wel!. The bottomhole tlowing pressure required for 110 changc in permcability is labelcd P~lf' II is oftcn impossibk 10 delennine either the aItered mdius r. , 01" lhe alten.::d permeability k... In this. case it is assumed Ihat the prcssure change due 10 the altered permeability oceurs al the wellbore in Ihe fonn of a skin cffee\. The skin effecl is defincd as a d!mensionless quantity and can be includcd in Equ3tions 2-14 and 2- t 7 as:
(2-29)
whcre ski n factor due lo pcrmcability change,
S
turbulence cocfficicnt
D
The tcrm S wil! be positivc ror damage, ncgati"c for improvemcnt, Dr zero for no changc in pcrmeability. The turbulcnce cocfficient. D, will be citller púsitivc 01' zera. Thc effccts oC S' on lhe pressure profik for an oil rescrvoir are illllstratcd in Figure 2-6. Althollgh a sudden large prcssurc drop cDuld occur al lhe wcllbore as indicated for a posilive 5', if, ror cxamplc, a small l1umber of pcrforations are open, it would be physically impossible for a pressure ¡necease lo occur as illustrated for a negative 5/, The actual siluarían is illu~tratcd in Figure 2-5. Equl.ltiDns 2-27 and 2-28 are cDl11l11only lIscd to describe psC'udostcady s{ate Oow in a circular drainagc area. Ir rhe drainage radíus is not circular, [hen Ihe use 01' Equations 2 27 and 2-28 rnay !cad to appreciablc errors. Odch 2 dc\'elopcd (h~ following equations to describe pseudostcady ::italc: t10w in a noneircular Jrainilgc ar~a. w
0.00708 kjl (P R - P ,,¡ )
J.l,B, (In (472 x) +S')
0.00708k)I(PR - p,,¡)
q,
J.luSu [In (.4721; 11;,.) + S']
(2-27)
J = -::-q-"",-p, - p,¡
J.luSo (In (.472x) + S')
.... ~'.!~i ~!..]
1 P
"¡II
.
Pwl
/
P;'"
__-i'--k.
>ti
\ '..
P
<, -~s'>o
Pwl(+}
PwI
k.
In Cw
In (.472 r.)
In ra
Inr-Fig. 2-5. Effects of allered permeability.
In (.472 r.)
In rw
In r - -
Fig. 2-6. Effacts of skin factors.
• Reservoir Pef/Onnance
15
where x is givcn in Figurc 2-7 for diffcrcnt dr<'linagc arca shapcs and well locations. The l11
be decreascd around the wellborc. This siluation can occur cven though PR may be wcll aboye 1"'. As pressure deplction in the reservoir occurs. PR will likely drop bclow Ph and free gas \ViII exisr !hraughout the reservoir.
(2-30)
can be ca1cul
(2-31 )
k(lh :\ value for S' can be oblained from allalysis ofvarious types of prcssurc transíent tests.
B. Factors Affecting Productivity Index The cxpress ion for the prodllctivity inc;?x for Lln oil wel!. including ski n cffcc!, can be writtcll 35: J~
O.00708kh
(PR - Puf )[ln(.-I72r/ r,) +Sl
Si', --(1' k. I 1'",
~ ,B"
(2-32)
From this exprcssion, il can be observcd ¡h~t.l willllot be constant uJlless lhe flressur~ fUllction is ír:dcpcndcnt of rrc5surc. In arri\'ing ti! Eqllation 2-14. it 'Xas assul11ed Ih:Jt kili \Vas ('(lllstant ami that ~I" tlnd B/I c(lu1d be evalu
J. PITase Be}¡ul'ior in Reserl'Oirs .-\ thorough discussion of lhe pllase beha\ ior of oil resc'fyoirs \ViII no! be giycn herc. bu! may be f..1tllHI in books \.111 tluid prop~nics'~'uch as ~IcCain3 and Ai":lYX. Bass and \\·hiting.-t _. Thc conccpl of bubblcpClint prcssurc and dewpoitH pressure wil! be rcvie\Vcd bcctlusc of lhe importance of gas saturation on Ihe rchltiyt: pcrmc(lbility to oil. A typical pressurc·lcmperalure phase diagram f('lf nn oil res(,Iyoir is sho",n in Figure 2-8. Thc liquid. gas and tworhase regions arc 5hoWI1, <'lnd lhe bubblepoinl pressurc is indicated as the prcssurc al \\'hich free ga~ first forms in Ihe reservoir as rrcssurc is redllced at COll5tanl rescrvoir lemperaturc. Thc rcscrvoir nuid dcpictcd in figure 2-8 is aboye lhe buhblcpaint pressurc p". at initial l"Csc,,·oir pressurc 1'_:;; élnd. thcrefore, no free gas \yould.exisl anywhcre in lh;: rcscrvoir. Ho\\'c"er, if lhe prcssurc nI an)' paint in lhe rcs.en·oir drops below I'h , free gas \ViII form ami km ",ril' ~(' relluced. Thcrcforc, if n \\'cll is produad al
l. ReJative Permeability Bellm"ior As free gas forms in lhe pores of a Tesen·oir rack, the abilily uf lhe ¡iquid phase lo no\\' is decreased. Evon though Ihe gas saturalío n may not be great enough to allow gas to Oow, (he space occupied by the gas rcduees the effective flow area for the liquids. The behavior ofthe rclative pcrrncability to oil as a function ofliquid saturalion is ShO\Vl1 in Figure 2-9. The relativc pemleability is delined as the ratio of effectiye pcnncability to a particu· lar fluid to the absolute pcrmeability of the rock, km = k" k. The absolutc permeability. k, is the permeability to a tluid when the nuid completely satura tes the roe k and is independent ofthe fluid as long as the fluid is :\ewtonian. The rclative pcrmeabiliry to g3.$ wil1 be dCCrC3$ed if liquid saturation develops in a gtls reservo ir. eilher as a result of retrograde condensalÍon or water ii.-¡mlatioll in ¡he pores.
., Oi¡ l'i.'icosi~\· Bellador The viscosity of oil 531uriltl~J w¡lh gas at c('n~tallt tcmJ:'c-r.Hurc will d('clTase ;1$ Pl\.·~~urc is decl'ca~;?¿ from illi~ ¡i::JI prcssurc lo bllbbkpoinl r~~ssur~. 8cI0\\-?, the vis("osilY \ViII increase as gas cor~~('s out uf SOlu!l011. lcaving lh? hcavicr molccllles in th(' :i(Juid pllasc. Fi~urc 2-10 iJlu5tmles qllalilalively the bchavior of 11" \-('[sus prcs5Ufe al constant tempcraturc. Equations for cJlculating bcha\·ior of vi$cosity with pressllrc
:\5 pressurc is decrcascd (ln a liquid. the liquid will expJnd. Whcn the bubblcpl1int pressure \.lf .111 oi! is reachcd, gas coming out ol' sC'lution \ViII cam~ the oil lo shrink. The behavior of 8 0 \'ersus ]J al C011:'13nl tcmpcrature js shoWIl grapllically in Figure 2-11. The oil fonnalion voJume factor is dcfincd 35: B 11
Vollll11e of oil plus ils dissoh'cd gas
al
p. T
Volull1e of oil <Jt stock tan" conditiol1s. P.'~·. r.~("
e, Factors Affecting
Infiow Performance
The lnno\V Pcrfonnnncc Rdationship (IPR) for a \\'ell is the rclalionship bet,,"ccn now rate into Ihe wcllbore and H'ellbore llowing prcssmc Pllf' The IPR is illuslrated graphically by plolting]J",.vcr511s q. (flhe IPR can be rep.resentcd by a constant productivily indcx J. lh~ pl01 \vill be linear and th~ slope of the line will be -1 J. wilh inlcr-
ProdllclivlI Optimiza/ion Using :\fui/u! Al1í1~D'¡S
16
SYSTEM
X
O D O
--
X
SYSTEM
I
re rw
0.966A'"
EJ~}
-
rw
2
0.571 A'" rw
t--j~j 1
1.44 A'·' rw
2
0.565 A'" fw
t-~~+
2.206 A'I'
rw
2
--
.-
0.604A'" rw
8 -ti! --
f --
-!.----JI
1.925 A'h.
rw
4
0.61 A
ll1
L-f-~--II
fw
6.59A" fw
4
9.36A"
0.67BA'" fw
I[~ "3" ¡---'
E-~--~--JI
fw
4
.. 0.66B A'" fw
[~} 2
[
.-~
--
•
1.36B A'" fw
1
1.724 A'"
D
~--
-
fw
[.:f:::+
1
4
2
2.066 A'"
I
• 5
rn m
1.794 A'h fw
1
4.072A'"
H+8 2
fw
1
0.884 A'I'
1
~¡;,!, - r - r - -I ~II
fw
I
, . : 1 I
fw
9.523 A'" fw
2
1.485 A'" rw .
Fig. 2-7. Factors for differenl shapes and wel1 posiUons in a drainage 8(ea. 2
!2.
10.·135 A'I' rw
Rese,,,oir Peljormonce
17
uauro
I Po
---------------,
I I I
Po --------------~ ___4~
T = CONSTANT
CRlTICAl PQ1NT
ri'<:-
c,'l P
GAS
o p-
Fig. 2-10. Oil viscosity behavior. TWO·PHASE
T-Fig. 2-8. Oil reservoir phase diagram.
cepls of P"f =PR and q = (jm3x at valucs of q = o and p...-¡ = o, respectively. In the previous scction the Iheorctical express ion for J was gi\'en in Equation 2-32. and it W
A dccreasc in km as gas saturalion incre3scs. An increase in oil viscosily as prcssure deereases and gas is evolved.
-
1.0
>>-
:J~
¡-....
ms «wg
:';.0
I
I o
.6
U>~
ii~ 0:«
-u
"O
tt~
...J'=-
w
a:
w~
I
z'" OW (JO:
I
0.0 O
20
An ¡ncrcase in Ihe lurbt11ence lcrm Dq{l4 as qo increases.
Thcsc faetors can change either as a rcsult of drawchange at a constant \-alue of PR or as P.;: declines b-:l'ausc of dcpletion. Chang,;';, in the skin fJl'wr can rcsult from formation darnage t... r stimulation. The em:cts on ¡nllo\\' performance ofdifferent drive mechanisms, drawd(,wl1 and dcplclion are discussed qualitilti\-ely in this section. Mcthods lo quantitativcly predict these ef-fecls wiJI be presentcd subsequently. dO\\"1l
/. Dri\'e A1echoflisms The sourcc of prcssure ent'rgy to c"use the ('jI and gas lo flow into lhe wcllbore has a substantial ctleer on both lhe performance of Ihe rcscryoir and the tolal production
60
T
/
~
CONSTANT
¡
¡
,
\
......
,/ 40
5.
L
11\
20
Formation damage or slimulalion around lhe wcllbore (5" O) as reflecled in lhe lerm S' ~ 5 ~ Dqo
I
t;;:~
.2
-.1.
k,tI--
I
1\ 1 \1/
w'" I;,;::::!
.4
Shrinkagc of Ihe oil as gas is evolvccl when pressurc on the oil decrcases.
I
,
~,g
"o:
w>'';::
I
!
\
2
a:'"
,,-o e Wo
"-
,
.8
_ID
l
1
3.
80
j 100
o UQUID SATURATION
=
Fig. 2-9. Gas-oil relative permeabilily data.
So + 8 wc ,%
p-
Fig. 2-11. Oi/ formation vo/ume factor behavior.
ProducliO/l Optimization Using Nodal ;llltl~rsis
18 -5yslcm. General dcscriptions of lhe thre~ basic types of drivc mc:chanisms are prescnted. Thc bchavior of rcservoir pressurc PR' lhe pressure function evaluated al p = ¡iR'/ (PR)' and surfacc producing gas/oíl ratio, R. Vt::fSUS cumulalivc n:covcry, Np , is presenlcd graphícaHy foc cach drive mcchanism.
a. Dissolved Gas Drive. A dissolved-gas-drive rcservoir is closcd from any outside source of encrgy, such as water encroachment. Its pressure is initially aboye bubblepoint pressure, and, therefore. no free gas exists. The only source of material lo replace lhe produced fluids is lhe expansion ol' lhe fluids remaining in the reservoir. Sorne smal! bU{ usually ncgligible expansion of the connatc water and rock may also DCCUr. The reservoir prcssurc declines rapidty with prod~lc ¡ion ulllil PIl = PI» since onl)' the oil is expanding to r~place the produced fluids. lile producing gas/oíl ratio wiII be constanl at R=R~.¡ during this periodo Also. sinee no free gas exisls in {he reser\'oir,j( PR ) will remain fair1)' constan!. Once PR declines below Pb free gas wilI be available to expand, and PR will decline less rapidly. However. as SOOI1 as tlle gns satumlion exceeds tite critical gas satur:Hion, R will ¡nerease rapid!)', funher depleting the res... rvoir energy. As abandomnent conditions are reached, R will begin lo dccrease because Illost of lhe gas has becn producco, and, at low resen·oir prcssures, the rcservoir gas volumes are more nearl)' egual to lhe standard surface yolumes. Rcco\"cry at abandonmcnt conditions will range belween 5% and 30% of original oil in place. However, in most cases, some type of pressure maintenance is applicd to supplement the reservoir energy and ¡nerease recoycries. Typícal dissolvcd-gas drive performance under primary depletion is shO\\'n in Figure 2-12.
b. Gas CClp Driw. A gas cap drj\,~ rcscrvoir is also c10scd from any oulsidc SOllfce of cncrgy, but ¡ht: oil is sarura(¡;d wilh gas at its initial pressurc and, thcrt:rore, free gas wil! cxisl. As oil is produccd lile gas l:é1(l will expand and hc1p to maintain the rescr\'oir pressure. Also, as the rcscrvoir prcssure declines fmm production, gas will be evolvcd from the saturated oi!. The rcscrvoir pressure will decline more slowly than ror a d¡ssolvcd~gas drive. but as the free gas cap expands, some of !hc llpstructure wclls wiIl produce <.It high gas/oil ralios. Under primary conditions, the rccovery may be bctwecn 20% and 40% of the initial oil in place. This may be increascd by rc-injecling the produced gas inlO the gas cap. Also, lhe effccts of gravity may in-crease rccovery, cspecially if producing rales un: low <.Ind the formarion has un appreciable clip. Primary performance for a gas cap drive reservoir is showi1 in Figure 1-13. C. Water Dril'e. 111 a watcr-drivc rcscrvoir, lhe oil zone is in cOlltact with an aquifer that can supply the material te rcplace the prodllced oil and gas.. The water lhat CIlcroaches muy come from expansion of the water onl1', or the aquifcr could be connccled to a surface OUICWp. Thc oil wiJl be undcrsalurateu initinlly, but ir the prcssurc declines bclow the bubblepoint. free gas will form and the dissolvcd-gas ch·ive mechanism will also eontribu!e lo the encrgy ror produclion. The rccovcry 10 be expected from a waler-dri\·e rcser\"oir may v.\ry from 35% to 75% of lhe initiZlI oil in pl:J.ce. 1f lhe producing rate is low cnough to allow water to movc in as rapidly as oil and gas are produced 01" if lhe water drive is sllpplemented by watcr injeclioll, rccovcry may be even higher. Ir reservo'r prcssurc rcmains aboye bubblcpoint, no free gas will form ane! the prcssure fUllCw !ion. based on PIl' \ViII remain fíJirly conslant. lhe perronnance of a strong water drive is illustralcd in Figure 2-14.
R
R
Np
Fig. 2-12. Dissolv~d gas drive performance.
N-
•
Fig. 2.; 13. Gas cap drive performance.
Reservo;,. Pel!ormol1ce
19
~
I
. / PR
. 1
------------
I
I
/ ' ( P R)
I I
------------..
Pwfl
PRO R. ((PR)
I
R
,./
•
N
--
Flg. 2-14. Water dnve performance.
TFig. 2-15. Phase diagram.
d. Comhinatioll. Dri"e. Jn many cases, an oil reservoir will be both sattlf
D1"0ll'dm1"ll 01" Producing Rote 11 W<1S showt1 carlier that the principal reason ror a changc in the productivity indcx was the change in the prcssurc function, flp) = k,iJloB o' If the pressure anywhere in lhe reservo ir drops below bubblcpoint prcssure, gas will cvolvc and the pcrrncability to oil will dccrease, causing a decreasc in J. Evcn though the average reser\"oir prcssure may be aboye p", to attaio a reasonable inflO\.... rate- it muy be necessary lo reduce Puf below p". \Vhen this happens, a zone of rcrluced km exists around the wellbore out lo the radius at whích the pressure in {he res~rvoir equa]s p". The pressure profile in a reservoir in the drainage area of a well depcnds on the weJl's skin factor, as was iIIustraled in Figures 2-5 and 2-6. lhe cffeets of drawdown on inflow performance will be discussed firsl for a well with zero ski n factor. The efTccts ofboth posilivc and negative skin factors wiII then be discusscd.
n. lera Skin FncIOI: Thc effects of drawdown or production rate on inflow performance can best be illustrated gmphically. The first case considered \ViII be one in which the re~crvoir pressure is aboye bubblcpoint prcssurc, tlwt ¡s, PR > p". The locátion of all of the prcssurcs
referred to are shown on a phase diagram, Figure 2-15, a pressure profile, Figure 2-16, and an ¡PR, Figure 2-17. If the desired inflow rate can be obtained with Pnj1?¡J", lhe value of fip)will be fairly eonstant at all values of radius, and the value of J will be csscntially constant. Ir a~production rate greatcr than lfo! is rcquircd, P"f musl be decreased further. If P""fl is less than Pb' free-gas sJluration \ViII exist out to radius r~, lhe "alue of km will be decreased and the slope of the pressure profilc will be increased over the distance 1"2 - r lt·• Since J dcpends on !.:,,-,. it will also be decreascd as p ..-{drops bclow p". This is illuslrated in Figure 2-17. . Furthcr rcduction in p,,¡ to P"f3 will extend the zone of reduccd km out to radius rJ and will further increase the ,Iape of the inflow perfonnancc plol. Methods to quan-
Pwll
p Pwl2 m
In
Tw
In
T2
= 141.2 q" ( ' , " ' ) kh k.,.
In r3
In (.472 re)
In'-
Fig. 2-16. Reservoir pressure profife.
ProdllClioll OplimizuliulJ Using Xudal AI/alysis
20
P.,I
;~~:c,~=",---J ,,, ,, P"fZ .... ------:--------, ' 1, l , P,,'3 ------,--------4, ' , ,, ,, ,, , ,, ,
QOl
I
.- CONSTANT J
1P
Pb Pwl ~Pskin<
O
P;"
,
qo2 Qo3 qo~-
In rw
Flg. 2-17. Inflow performance reJatlonshlp.
In (.472 r,) In ( - -
Fig. 2-19. Elfect 01 negati\'e skin.
tífy these cffccts will be presented in a subsequent section. b. NOIJ-:=ero Skin Fact01: In Figure 2-6, rhe concept of a zera-radius skin cffcct was illustrated by assuming that Ihe e:ora pressure drop caused by damage oc the d~creascd prcssure drop caused by stimulation occurred al dIe wcllborc. Thc con:itruction of ao IPR roc a well wilh a non-zcro skin factor can be more complex., espcciully rOl' lhe case whcre PR > Pb' For lhe case 01' a dal11a~cd well (S' > O), it is possible thal essentially no gas s;turation \Vould exist in the reseryoir even.though p,,¡< p,. for lhe case of a slimulated well (S' < O), there may be a ncgligible pressure drop through a highly stimulated zone out to a signifieant radius. Ihis wil1 distort the aS5umcd pressucC' profile. These phenomena, which are illustratcd in Figures 2·18 and 2-19, can cause difficullies in eon~ml1ctillg an IPR from test data, especially ror cases in which PRo); Pó'
P, P
p.,
I}---------------4Pw~-P;.,1-P""
In rw
In (.472 (e)
10'--
Fig. 2-18. Elfeet o/ positive skin.
3. EjJecl of Deplelion In any rescrvoir in which the average reservo ir pressure is not maintained aboye the bubblcpüillt prcssure. gas saturation will inerease in the enlire drainagc volumc of the wells. This will cause a uccrease in the prcssurc function in .the form of d.:creascd kw' which will cause an inerease in the slope of lhe prcssure proEk aad (he IPR. Therefore, to lnaintain a constant inflow rat~ lo a welL it wilI be ncccssary [O ¡nerease the drawdown as PR declines 1'rom dcpletion. Thesc cf1'ccts ar~ illustrated qualitatively in Figures 1-10 and 2-21.
4. IPR Behal'ior ofGas Irells The IPR foc a gas wdl will not be linear becallsc rhe inflow rate is a function of rhe sqllare of P"l For dry-gas. and wet-gas reservoirs, in which no ¡¡quid condenses in lhe reser\'oir, gas saturation and, thcrefore, permeability to gas will rema in constant as PR declines. Ir turbulent flow exists, lhe pressure drop due to turbulence \'>'il! increase with f10w rare, causing a deterioration in the inf10w performance. If no liquid forms in the reservoir, lhe effect of depletion will not cause a decrease in k,x' but lurbulence may ¡nerease due to the higher actual velocity required to maintain a conslanl-mass flow rateo Also, the value of the product JlZ will change as reservo ir pressure changes. In lhe case of a retrograde condensa te-gas reservoir, that is, wherc TR is between the critical temperaturc and the cricondenthenn, if the pressure anywhere in lhe reservoir drops below Ihe dewpoint pressure Pd, liquid wiIl form and decrease krg. This can oecur from cither reducing P.¡ below Pd or as P. declines below Pd from depletion. Prediction of retrograde-gas reservoir behavior or
Resen'o;r Performance
21
¡SAl PR2
Pb
PR3 PA4 PR5
Darey's law eould be used lo quanlify' ¡he IPR. Unfortunalely, sufficient information rarely exists to accomplish this and, therefore, empirical rnethods must be used to predict the inflow rate for a well.
Several of the mosl widely used empirieal melhods for predicting an IPR ror a weH are presented in tbis section.
Most of lhese methods require al least one slabilized test a well, and sorne require several tests in which pwfand q(J were rneasured. A procedure for estimating the IPR 011
when no stabilized tests are available is al50 outlined.
Methods to aeeounl for lhe effeels of drawdown only are first presented, 'that ¡s, PR is assumed constant. Mod-
ification of lhe methods for deplelion \ViII lhen be discussed.
A. Vogel Melhod m
Vagel' reporled lhe results of a sludy in whieh he used
141.2 qo
kh
In (.472 re)
In rw Inr-
Fig. 2-20. Effecl of deplelion on Ihe pressure profile.
a mathematical reservoir model to ca1culale lhe IPR ror oil wells producing rrom saturaled reservoirs. lhe study dealt with several hypothetical reservoirs including those with widely differing oil cbaractcri5tics, relative permeability characteristic5. well spacing and skin factors. The final equation fOf Yogel's method was based 011 calculations made for 21 resCTvoir conditions.
..I,lthoilgh lhe method was proposed for salurated, dissolved-gns-drive reseryoirs only, it has been found to apply ror any rcscrvoir in which gas saturalion increases as pressurc is decreased. \'ogel's original method did not aeeount for the effects of a non-zero skin factor, bul a ¡ater modification by
Standing' exlended lhe melhod for applicalíon lo da maged or stimulated weIls.
The Vagel melhod was developed by using lhe reser-
Fig. 2-21. Effecl of deplelion an Ihe IPR. w3(er~drive
gas rescfvoir behavior is yery complex and, in most cases, rcquires lhe use of a reservoir model. FOrlunatcly. since the condcnsed Iiquid will occupy the small pare spaccs firsl, the rcduclion of krg may be smaIl.
This is illustroted qualitatively in Figure 2-9.
voir modcl propo'>ed by \Veller7 to genera te IPR'5 for a wide range of conditions. He then replottcd Ihe lPR '5 as reduced or dimcllsionless pressure versus dimensionlcss flow rate. The dimensionless pressure is defined as the flowing wellbore pressure dividcd by average reservo ir pressurc, Puf / PR' The dimensionlcss Oow rate is dcfined as the now rate that ,,"ould result for the value of P"'f
being eonsidered, divided by the flow rale lhal would qjqo(mar.)' It was found lhal lhe general shape of lhe dimensionless lPR was similar for all of lhe eondilions sludied. Examples of lhese plols from lhe original paper are iIIustraled in Figures 2-22 lhrough 2-25. resulL from a zero wellbore pressure, that is
111. PREDICTING PRESENT TIME IPR's FOR OIL WELL~.
After plotting dimensionless IPR curves for aH the cases considered, Vogel arrivcd at the following re1ationship between dimensionless flow rate and dimcnsionless pressure:
The factors affccting the inflow performance ror oil wells \Vere discussed qualitativcly in the prevíous section. If al! of the variables in the inflow equations could be calculatcd, lhe equalions rcsulting from integration of
~=l-O.2~'f -0.8[~·f)' PR PR qu(max)
(2-1J)
ProducliVJl O/)(imizalivll Usillg ¡\'odul ..I1/t1lysi.\"
22
1300 .---------~~---_,
1500
1400
1000
1000
1500
CUMUlATlVE RECOVERY,
A
B
PERC8,T Of ORI GI NAL
OIL IN PlACE 1000
500
O~~~~~-,-~_ O 50 \00
-
Fig.
300
2·24. IPR change with reselVoir condilions.
~
O "" O
110
'O
100
\60
140
PR
=
average reservo ir prcssure cxisting at (hc time 01' interest.
Fig. 2-22. IPR change with deplelion.
intlow rate- correspondillg f10wing pfl~SStlfe Phi'
lO
The pressurcs llsetÍ to calculute the dill1cnsionless prcs· Sllrc ratio should be gag,c prcssures. A piar of the dimen· sionlcss lPR rcprcsenlcd by Equation 2·33 is showll in figure 2·26, which ..:an be lISCU in lieu af EquJtiol1 2·33. The dimensionlc55 (PR [oc a well \Vith a constan{ pro-
wellbore
inflow rate corresponding lO zen? wellbore f10wing pressurc. (AOf). and
ductivity indcx can be calculatcd [rum
1.0
1.0
0.8
0.8
Pw< 0.6
0.6
PR
Pwl
'R
0.4
DA
0.2
0.1
OL-_-'--_ _.L-_--'-_ _-'---_--"
O
0.2
0.4
0.6
0.8
1.0
O~---;;'oC----';;7---'c';-----,!'o---c' O 0.1 0.4 0.6 0.8 1.0
'lo
qo
QO(max)
CIo(max)
Fig. 2-23. Dimensionless IPR lor Fig. 2-22.
Fig. 2-25. Dimensíonless IPR lor Fig. 2-24.
Reservoir Performance
23
1.00
0.80
0.60
0.40
I
1
-1-
0.20
1-
.. / O
0.20
O
0.40
0.80
0.60
1.00
----'!"- = 1.8ql '"',
qL(msxj
JpR
Fig. 2-26. Vogef's dimensionless IPR.
the permeabilíty lo water. Therefore, the ratio ~=:l_Pl\f qo(ma'{)
PR
(2-34)
\bgcl pointed out that in most applic3tions of his method, tJ,e error in the predicted inflo\\' ratc should be le5s than 10%, but could increase to 20% during the final stages of dcpletion. Errors made by assumiog a constant J (Equotion 2-34) were found lo prod~cc errors on the arder of 70% to 80% at low values of PUf. lt has al50 beeo shown that Vogel's method can be applied to welIs producing water a10llg wilh thc.oi1 and ga5. sincc Ihe incrcascd gas saturation wilI also reduce
qjqo{max)
ean be replaced by q¡jqL(mul where qL = qo + q._ This has proved to be valid for weUs producing at water cuts as high as 97%. Applieation of Vogel's melhod is olmost os simple os the constant J method in that only one actual weH test is required. The applieotion win be illustroted by examples for conditions in which PR S Pb and for cooditions. in which JlR > Pb·
1. Application oJlógel Method-Zero Skin Factor lo the original paper by Yogel, only cases in ",bich the rcseryoir was saturated were cOllsidered. Thc mcthod can
ProdUCliol1 Oprimíz :Iioll Using Nodo/ AJla~rsis
24 be applicd to undersaturatcd reser'Ooirs by applying Vogel's equlltion only foc values OfPtl.~·
Salurated Resf!li'oirs.
Example 2-2: A welt is producing (mm a reservoir having an average reservoir pressure af 2085 pSlg. A stabilized production test on the well resultad in a producing rate af 282 STB/day when (he flowing botlomhole pressure was 1765 psig. The bubblepolnt pressure is 2100 psíg. Using Vogel's melhod calcula te: 1. The producing rate jf pwf is reduced to zaro (qmax or AüF). 2. The producing rate if Pwfis reducad to 1485 psig. 3. The bottomhole pressure necessary lo oblain an inflow rate of 400 STB/day.
Solution: 1. q,(max)
=q'/[1-0.2 ~I _0.8(~w/ '1'] PR
PR ,
From the test, for q, = 282 STB/day. Pw//PR =1765/2085=0.847 ,
2
q, (max) = 282/[1- 0.2(.847)- 0.8(.84 7) J
q,(max)= 282/0.257 = 1097 STBlday 2 q, = q,(m,,¡ [1-02
~~
-08[
t JJ
Far the new valua af Pwt.
Pw//PR =1485/2085=0.712
qo = 1097 [1-0.2(.712)-0.8(712)'] = 1097(0.452)
q, = 496 STB/day 3. Solving Equation 2 - 33 for
P./PR:
~w/ = [1.266-1.25qiq,(m,,¡J'-5
qo
2085 1800 '1765 1618 1300 1000 700 300 O
253 282 400 618 790 923 1046 1097
o
The same results could havc bCCIl obtaincd by using
Figure 2-26 ralher lhan Equalion 2-33. Tlle \Vell describcd in this example is the same well tha! was analyzcd in Exall1ple 2-1 using Ihe constant J concepl. The results of the t\\'o analyscs are summarized
as follows: Conslant J
Voge/
528 1645 1835
496 1618 1097
q for Pwt = 1485 psi9 pwt lar q = 400 q(max) or
AOF
lhe diffcrcnce in the results from
th~ (WO
methods is
small as long as the drawdown is close 10 lhe test condilions. Howcvcr, as P... ¡" is reduced to LdO, a substantial diffcrence is calculated ror q(m;¡¡.¡)' This C;ln be fin importl1l1t eonsideratiol1 if Ihe well is beillg cOllsidcred ror artificiallift where PIl¡ean be reduccd lo a !L)\\, valuc. b. Undersafllrated Resen'oirs (PR > Pb)' 1wo test cases must be considered for upplying '·vgd's m.cthod hJ undersáluratcd reser\'oirs. The tlowing wcllbore pressure [oc the test can be either aboye or bclow bubblepoilll pressure. The equations can be dcrivcd by considering lh~ productiyity inde.\. lO be constant for PI\j ~ Pb and assuming that Vogcl's equation applics for Pnf< Pb' Also, il is assumed that the complete IPR is continuous. that is ~the slopes of thc two segmenls are equal at Pllj= Pt>. Figure 2-27 is used to illustrate lhe lPR for an undersaturated rescryoir.
Applying Vogcl's equation for any now rale grcaler -0.125
PR
~w/ = [1.266 -1.25(400)/1 097Jo.5 - 0.125 PR
~w/
Pwt
than the rate qb. corresponding to PJ<j
q. -q, qO(Ill
1-0.2
:=
Pb:
p"! -o.s(p"! J'
qb
Pb
Pb
=0.901-0.125=0.776
PR
(2-35)
Pw/ =2085(0.776)=1618psig
The reciprocal slope is defined as lhe change in flow rate wíth respect to lhe change in Puf' oc
A complete IPR could be construeted by assuming olher values o~ p,¡and ealculaling (he corresponding qo:
dq. _
d-(qot=,¡-qb) 'P,!
1.6p..¡ l -----'-J Pb Pb
[-0.2
25
Reservoir Pelformance
and (2-39) •
Pb
• 1
TEST. CASE 1
If the test is such lhat P.f < Pb, the calculation for J is more complex since qb wí1l nol be known. This is iIlus-
r--------··,---
trated as Case 2 in Figure 2-:27. An expression for J to use
in Equation 2-38 can be obtained by combining Equations 2-38 and 2-39: ' •
J~
TEST, CASE 2
qo PR-Pb+
Pb
L8
[¡-0.2
P f • -0.8[P'/J] Pb Pb
(2-40)
Case J Procedure (Tesl P"I? pJ
q, (max) q,Fig. 2-27. IPR for an undersaturated reservoir.
l.
Calculate J using test data in Equation 2-22.
2.
Calculate qb using Equation 2-39.
3.
Generate. the ¡PR for values of P4 < Pb using Equation 2-38. The IPR for Puf"?' Pb is linear.
Evaluating the reciproca1 s10pe at P"f= Pb gives
Examp/e 2-3:
_ dqo ~ qo(m«)-qb (0.2+1.6)
The following data pertain to an ,ulldersaturated reservo ir: 4000 psig, Pb 2000 psig, S O
Pb
dPuf _ dqo
PR =
1.8(qo(m,,) -qb)
dplIj
(2·36)
"?,
So/ution:
~
=
1. J
Pr' Equation 2-36 beco mes:
J
=
Generate an IPR.
Pb
The productivity index is dcfincd as the negative of the reciproca! slope, and if J is cva!uated at any value of P"f
=
Test data: Pwr = 3000 psig for qo = 200 STB/day
qo PR
~
Pwf
-,.,--=2,,-00,--_ 4000 - 3000
=0.2
STB day - psi
1.8(qo(m,,) -qb)
---'-'-="---'-
2. qb=J(PR-P,J=0.2(4000-2000)=
Pb
400STB/day
or (2-37)
3. qo
This equátion also establishes a relationship between J and qo(milx) for saturatcd reservoirs, that is for Pb ~ PR and qb ~ O. In this case:
q
qo(m.1.X)
=
=q,
~ qb +
Ji5R T8
¡
JPb -0.2 P"f -0.8 [P'f 1.8 [ Pb Pb
p,
1.8
l
)2 ]
4000 3000 2000 1500 1000 500 O
(2-38)
(2-22)
P,
Case 2 Procedure (Test P'I<
0.8P';']
2000 (2000)' qo
p";'
Once a valuc of J at Puf f;: Pb is dctermincd, Equation 2-3S can be used to genemte an IPR. If the well test is taken with Puf"?, Pb, J and qb can be cálculated dircctly, sillce: q J ~ -=-20,,"-_ PR - Puf
1.8
=400+ 0.2(2000) r1- 0 .2..E:!!!....
o
Substituting Equation 2-37 into Equation 2-35 gives: qo
Jp, p", -0.8( -P", )'] + - [ 1-0.2-
O 200 400 489 556 600 622
pJ.
l.
C~lculate
2.
Calculate qb using Equation 2-39.
J using tesl data and Equation 2-40.
PruductiO/1 OptimizaliolJ UsiJlg Nodal tlllo/ysis
26 3.
General" lhe IPR using Equation 2-38 for P..¡ < pb· rhe IPR for Puf ~ Pb is linear and can be calculated using q, = J ( Jir p,,¡).
Example 2-4: The well descrjbed in Example 2-3 was retestad and the following results obtained:
FE . fiN - P;l! -t1p~J.¡'1
pK - Phi
In(.472J~.ll~J In(.472'; 11;,.) + S'
(2-42.)
Using the previous definilion for flow efficicllCY, Vogel 's equation becom\:s:
---""-=1-0.2 p:,¡ _0.8[P;,¡ fE-'¡ qU{Il~a..,) PR PR.
Pwf = 1200 psig tor qo = .532 STB/day
J'
(2-43)
Generale an IPR using this test dala.
q,
where
1. J - _ _ + &[1-0.2 1'., -0.8 pR P. 1.8 p.
(pwf )']
(2-40)
P.
532 J = 4000-2000+ 2000 - [1-0.2 (1200) - - - 0.8 (1200 - - )'] 1.8 2000 2000
532 STB J = - - =0.20-2658 day - psi 2. q.
O8[ -p"f )']
JI'. P., - . 3. qo = q. + - [ 1-0.2-
1
p.
p.,
0.2(2000) 0.2 1 q = 400 + 1.8 2000
l-
,,:,¡
or
~,¡ ~'I-FE+FE(p"flJiR)
1.
Seleel a value for FE.
2.
Assumc
3.
Far ench "alue assumed in Step 2, calcula le the COfrcspouJing value of P;lj / PR usillg Eqllution 2-45.
0.8 P:,]
(2000)'
4.
range of values for PHI / PR'
FEol Calculate 'Iv / "IlI(ma.x) for eaeI1 va Iue o f Pltf 1PR assume d in Step 1 L1sing Equation 2A3. Plot P"I! PR versuS FE=\
4000 3000 2000 1500 1200 700 500 O
O
5.
200 400 489 532 585 600 622
did not considcr an absolute penneabílity change in the
reservo ir. Standing6 proposed a procedure lo modify Vogei's method to account rOc either damage Oc stim~~a lion around the wellbore. lhe degree of permeabIltty alleration can be expressed in lerms of a Productivity Ratio PR oc Flow Efficiency FE, where: ideal drawdown
actual drawdown
.
'ID 1'I 0 (1I1a.:-..)·
2. Applicatian al Vage! Method-Non-Zera Skin Factor (S/unding Modifica/ion) Ihe method for generaling an IPR presented by Vogel
FE
(2-45)
lhe following procedure was uscd by Standing to construct dimcnsionless IPR curves for flow cl1ícicncies llor equal ta one:
400STB/day
p.
o(max)
pR
=J(PR - P.) =0.2(4000 - 2000) =
1.8
the maximurn intlow which could be obtaincd for the well if FE = 1 or S' = O. A relationship among PI1/' P~'I and FE can be oblained by solving Eqllation 2-4l for P~f: = JiR - FE(JiR - p,,¡) (2-4-1) =
qFE=;1
ti J' J --=qI J J'
(2-41)
Seleel a new FE and go lo Step 2.
The dimensionless IPR curves as presenled by Standing are shoWIl in Figure 2-28. The faet thal Standing seleeted the maxiInum intlow based on a tlow efficiency of one as the normalizing now rate limits the inflow rate that can be calculated by this method tú qu == q:;;;;~"(). This can be seen by consid~ ering the value of p;¡ 1 PR ealeulated by Equalio~ 2-45. If FE is greater than one, negative values of P;'f / PR e Otl 1d be obtained al large drawdowns or small values of P.,.¡. Vogel's equation would no longer apply, since lhe square of the negative would become positive. The actual value of qo(m
The relarionship between P",¡ and P;I! is shown in Figures 2-5 and 2-6. The flow efficien.cy can also be expressed in terros of /),Pskin- ami SI as:
FE.
J,
Standing's graph, Figurt: 2-28, can be !1ul ji} eq1l8tion focm by eoínbining Equalions 2-43 and 2-45. Ihis gives:
Reser..oir Performance
27
I .
0.8
~"''''''(Q "O~ 'If.1'0..I
¡~.¡.s
'f".)
0.6
L.f.¡
O-~
'1.¡
O '..>
PR
O '.J" _
-_'0
. f-' O+-
l+
.~
."
'.1'
Pwf
.¡
~
'",
1'1
0.4
O '".
0.2
ú O
0.2
0.4
0.6
0.8
1.0
qL
or - - -
Fig. 2-28. IPR for damaged or stimu/ated we/ls. 11
-08(FE)' [1-
~: J
Because of the restriction that P:vj !?; O. Equation 2-46 is valid only if or
~ = 1.8(FE) [1 _P"f ) FE=\
qll(max)
-
PR
This restrictiOll will al\Vays be satisfied if FE"; 1. For
28
Prodllctioll Oplimizafio/l Using Nod,¡f Analysis
vah.¡es of FE > 1, an
actual
q{max)
approximat~
Example
relationship bctwcen lhe
and
q(n",)
~
q[.,';;\<0.624 +0376 FE)
2085 1800 1765 1600 1300 1000 700 300
One of thc principal applicatiolls of the Standing graph or equation is lo predict (he improvement in int10w perfannanee that would be attained ir a wcll were stimulated. Once a value of q;~:x.)is obtained using data from one test. either Figure 2-28 or Equation 2-46 can be used to calculate int10w valu~s ror any value of FE. The proc~dure is:
Using test Jala (p,,¡and q,J and lhe value of FE existing when the test was conducted, calculate q~~~a~x.) w;ing Equation 2·46. This value can a150 be obtalllcd from Figure 2-28.
2.
Results Using Equation 2-46
Pwf
(2-47)
For the case of FE ~ I (p,,¡ ~ p;,¡ J, Equatíon 2-46 is identical to lhe Vogel equation, Equalion 2-43.
l.
2~5A
¡;'E""'l . Q(l1li1X) 15
Assumc various values of Puf and calculate qo for each Puf from Equalion 2-46. Other values of FE may be used to determine the cffeet of increasing FE
by slimulalion. Figure 2-28 may also be used if prefened.
O
PR = 2085 psig, Pb = 2100 psig,
FE = 0.7. From Ihe test, for qo = 202 STB/day, Pwf = 1765 psig.
0.137 0.153 0.233 0.376 0.520 0.664 0.856 1.000
FE -1.3
o
o
181 202 300 461 604 730 871 955
324 360 518 758 937 1054 1224
The minimum value of Pw( that may be used for FE = 1.3 is Pwr = 2085(1 -1/1.3) = 482. Therefore, qo cannol be calculated for the last two values of Pw( in the tableo However, an eslimale of the actual· q(max) can be obtained from Equation 2-47. That is q(max) = 1100
[0.624 + 0.376(1.3)]
=1224 STB/day. A piol 01 the IPR
far Ihe two ftow efficiencies is shown in Figure 2-29.
Using Figure 2-28: 1. Using P./PR = 1765/2085 = 0.847, Ihe correspondjng value of qo/q~t:~X) obtained from Figure 2-28 using Ihe curve for FE =0.7. This value is approximalely 0.18.
Example 2-SA: Using the following data, construct an IPR for thjs well for the present conditions and for a value af FE = 1.3.
FE = 0.7
o
q~¡;;;,) = qo/q~¡;;;,) = 202/0.18 = 1122 STB/day 2.
Various values are assumed far pw(, the ratio of Pwr fi5R is calculated, and the correspondjng ralia of o js obtained from Figure 2-28 from the appropriate FE curve:
q lq;ffn=1x)
Solulion: The ¡PR's will be calculated by using Equation 2-46 and also by using Figure 2-28. Using Equalion 2-46: 1765 1. (1_~fPR '=1_ =0.153 J 2085
FE" _ qo(max) -
1500
pwf
202 . 2
f[ • 1.3
1500
I
2
1_8(.7)('153)-0.8(.7) (.153)
= 11 00 STB/day
l 2085 J
2·qo =1100[1.8(FE)(1- Pwf
-0.8(FE)2 (1- Pwf J2] 2085
1000
500
FE • 0.7
o .L----::'=-_-=-_--:-':-_~_~---:~ o 3D 400 600 800 lOCO lt'úO
l
Fig. 2-29. Examp/s 2-5A solution.
Reservoir Pe,fonnance
29
Example 2-SA Resulls Using Flg. 2-28 FEpl Pwr qo I qo{rf.a<) q.
Pwt 2085 1600 1000 700 300 O
PR 1 0.767 0.480 0.336 0.144 O
FE=O.7
O 0.267 0.550 0.668 0.792 0.870
FE-1.3
O 0.472 0.852 0.963
FE =0.7
O 300 617 750 890 976
Eguation 2-48.
3. FE=t.3
O 530 956 1080
or high values 01 Pwr /i5R .Use 01 lhe equallon is therefore recommended. G. Undersatúraled Reservoirs with FE:té 1.0. Slanding's modlfieation ofVogel's melhod lo be used when the flow efficiency is nat equal to one may also be applied to
undcrsaturated reservoirs. EquatioT1 2-38 may be modified for a nQnzero S' or FE
1.8
Since Pwf fer the test is below Pb. use Case 2 Procedure.
1_ Pwt J=1- 1200 =0.4 Pb 2000 378 1. J= 2000 4000 -2000 + 1:8[1.8.4 -0.8 P )(4 )'] [
J=
378 =0.14 2000+ 700
Pb
1.8
J
<;: J]
.[1.8[1-~J-0.8(0.7)(1~J'] 2000 . 2000 (2-48)
The following proccdures may bc used to genera te ao IPR for any value of FE, including the case for FE = 1.
2. ForFE =0.7: . 1500 For Pwr = 1500 ps'g, 1- - - = 0.25 2000 qo = 280 +156 [1.8(.25)- 0.8(0.7)(.25)2] qo = 280+156(0.415)= 345STB/day
Case 1 Procedllre (Test Puf"P¡.)
l.
Calculate J using test data in Equation 2-22.
2.
Gen~r~te
the IPR for valllcs of Puf < Pb using the known vatuc of FE in Eguation 2-48. The IPR for Puf ""2:. Pb is linear. For valucs ofFE other than that which existed during
the test, the value of J is modified by J, = J, (FE), /(FE) ,
ForFE =1.4: J 2 = J, (FE),/(FE), = 0.14(1.4 YO.7 = 0.28 qo = 0.28(2000) + 0.28(2000) [1.8 (1- Pwr J
1.8
2000
-0.8(1.4)(1- P., J2] 2000
For Pwt = 1500 psig , qo ='560 + 311 [1.8(.25) .. 0.8(1.4)(.25)2] = 678 STB/day
where
J, (FE)I (FE),
So/ution:
qo = 0.14(~000 - 2000) + -'.:...--'.:..cc.:.é
JP. [ 1.81-[ P"f qD=J(PR-P,)+-
12
¡iR = 4000 psig, Pb = 2000 psig. FE = 0.7 From a test, qo =378 STB/day, Pwt = 1200 psig
0.14(2000)
not equal to one to oblain
~,.
Examp/e 2-58: Using the lollowing data, caleulate the flow rate which will result il Pw/ is 1500 psig for this well lor the present conditions and tor a value of FE ;::; 1.4.
There is sorne difference between the values obtained using the equation and those obtained using lhe graph. Most 01 thls is caused by lhe 22 STB/day difference obtained in the value of q~r:~X) u s í n 9 the test which was conducted at a low drawdown. The curves are difficult to read at low values of drawdown
-08(FE{1
For other values of FE, modify J as discussed previously.
new value for use in Step 2.
value ea1culaled from test data using (FE), flow efficiency ~xisting during test, and any other f10w cfficiency.
b. Determining FE/rom Well Tests. A value for the flow etliciency can be calculated if the skin factor is known from a pressure transient test, us.ing Equation 2-42. Ifvalues of rp and r.... are not known cxactty, an approximation
for FE can be made by assuming that In(.472 rIru .) Then:
Case 2 Procedure (Tesl Puf < p¡.) eq~uation
L
Ca1culate 1 using test data in
2-48.
2.
Generatc the IPR for values of Pllf ~ Pb using
FE~_7_ 7+S'
~
7.
(2-49)
Productioll Optimiz(ltio/l Usi/lg Nudal AIIOJy:iÜ'
30
lf two correel stabilized tests are available and PR is accurately known. FE can be cakulated directly. FE··1 Solving Equatioll 2·46 forqu(~):
q~r:,~;<)
) 'lo
(
L8(FE)(I- : ; -0.8(FE)'
I-~:
)'
C. SUfIllJIWY ol/!Ie Voge/-S/mufing EqHa/ions. Equation 2-48 can be used [or all of the cases considcred prcviously, that is, foc both saturated and undersaturatcd reservoirs and roc weHs having formation damagc or th3t have beeo stimulated. 'In this scctian it will be shown that Equation 2-51 degenera tes to aH af the simpler cases. _ Jph qL ~J(PR - Pb)+-
1.8
Thc para meter q~(~:dx) is a constant and, thercforc, must be equal foc any twa tests. That is:
.[18(1-::
'101
~/I)'
1.8(FE)(¡- P:./I )-0.8(FE)' (1PR. PR
For FE
__ _ _ _ _ _---"''lo''''~
~
L8(FE)(I-
P;"
~
- P;"
1 (S'~ O): 1.8
J
where subscripts 1 alld 2 refee lo the lwo tests. Simplifying and sol\'ing foc flow efficiency gives:
<;: J]
_ Jpb qL ~J(PR - Ph)+-
____o_
}08(FE)2 (1
)-08[FE{1
('-51)
(2-52)
For FE
~
1 and Pb 2:
PR
Ph/2) ]
FE ~
2.25['1- P"/I - ¡- Q2 %1 PR PR _-"'_--'--"----'--__"--------',-,,--O-L---""
(
1- P"il )' qtJ"J. PR
-(1-
(2·50)
P"i')' %1
t~-53)
PR
B. Fetkovich Melhod Example 2-6: Twa stabilized tests were conducted on a "well that was producing from a reservoir in which lhe average pressure was 2085 psig. Calculate the f10w efficiency
tar Ihls well. Test
1 2
Pw¡' psig 1605 1020
'lo' STBlday
3000 6000
Fe(kovich 8 proposed a mcthad ror cateulating the inflow performance for oil wdls using the sume type of equation that has becn used far analyzing gas wells [or many years. The procedure was yerified by analyzLng isochranal and flow-after-Oow tests conductcd in reser· vairs with penneabilities ranging from 6 md to greater than 1000 rnd. Prcssure conditions in the resen'aies ranged from highly undersaturated to saturated at initial
pressure and to a partially depleted field with a gas saturatian aboye the critica!. [n aH cases, ail-weH back-pressure curves were found
So/ution:
1
~ 1- 1605 =0.230 [1- P-"" PR 2085
lo follow the same general fonn as that used lo exprcss the int10w relationship for a gas well. That is:
=0.511 ( 1.Pwf,I~1.1020 PR) 2085 FE=
2.25 [(0.230)(6000)- (0511)(3000)]
2)" 90;;: C(-' PR - P.,.,¡
(2·54)
where =0.74
(0.230)' (6000)-(0.511)' (3000) Equation 2-50 is extremely sensitiye to smaH changes
in pressures. lt should be emphasized Ihat the value for FE calculated by this melhod is only approximate and requires accurate test data. Obtaining values of FE using the skin factor from a transient test in Equation 2-42 is much more accurate.
qo
producing rate, . average reservoir pressure, Plli flowing weIlbore pressure, flow caefficient, and 11 exponent depending all well characteristics. The value of n ranged from 0.568 to 1.000 for the 40
PR
e
field tests analyzed by Felkovich. The applicability of Equation 2-54 lO oil well analysis \Vas justified by writing Darcy's equation as:
Re.tervoi,. Pelformance
q
31
00708kh In (.~721~ Ir.,)
+ S'
f
P,
P..¡
(2-55)
f( p) dp
wbere
For aD undersaturated reservoir, the integral is evaluated over two regions as: qo~C'
f
P'
j,(p)dp+C'
fh f,(p)dp
P~I
(2-56)
Three types of tests are eommonly used [or gas-well tesong lo detennine e and n. These tests can also be used for oil wells and \\ill be deseribed in this seetion_ The type of test to choose depends on the slabilization time of lhe ",ell, which is a function ofthe reservoir permeabili!y_ If a wcll stabilizes fairly rapidly, a conventional flowafter-flo\V test can be condueted_ For tight \Vells, an isachronal test may be preferred_ For wells with very long stabilization times, a rnodified isochronal test may be more practical. The stabilization time for a weIl in fhe center of a circular or square drainage area may be estimated from:
JI,
I ~
= _38_0___',,¡to"-C-'A --f_ k
(2-59)
o
where _00708kh
C' ~ .,------:--=~:::,-...,..,
\'·..here
In (.472r,I/;,.)+S'
h was assuIned that for p > Pb, kro is equal to Dile and that ~o and Rv could be considered constant at P = (PR ~ pY2_ It \Vas also assumed that for p < p"j[p) could be expressed as a linear function of pressure, that is: j,(p) ~ ap+b
(2-57)
\Iaking thesc substitutions into Equatioll 2-55 and integi2iing gives: qo=C,(p;-p,'vJ+C,(PR-P,)
(2-58)
F~tkovich then stated Ih(lt the composite effect rcsu1ts in :-., equation of lhe form:
2)" qo:::: C(-2 PR-P":f
(2-54)
Once va]ues for e and 17 are determíned from test data Equation 2-54 can be used to generate a complete IPR. A~ ¡h;?re are t\Va unknowns in Equatian 2-54, at least ~\'0 tests are required to evaluate and 11, assuming PR 15 bown. Howevcr, in testing gas wells it has been cuslC'IT'.;uy to use' at least four flow tests lo determine e and TI ~ecause of the possibility of data errors. This is also re..:-C'rnmended foc oil well testing. By laking the log of bolh sides of Equalion 2-54 and 2 5-Clhing for log CfiR - PII/)' {he expression can be wnnen as:
e
stabilizntion time, hrs.. porosity, total fluid compressibility. ps¡-I, drainage area, n:!, penneabilily lo oil, rnd, oil \iscosity, cp f. Flow-After-F!ol\' ft'5tillg A. tlO\v-after-now test bcgins with Ihe well shut in so th.:u lhe pressure in lhe entire drainagc area is equal to P..... The well is rth.'c-d on production al a constant rate umil lhe flowing wcllbore pn::ssurc beco mes conslant. Th~ tlowing pressure should be me::tsured with a boltomhC'k prcssure gage. cspecial1y for oil-well tests. Once p,,¡ has stabilized, the produclion rate is changed, and rhe pri..~edure is repeated ror several rates. The idealized behavior of production rate and wellbore prQ,sure with time is shown in Figure 2-30. The test may als;ü be conducled using a decrcasing rate sequence. 2 2 The test is analyzcd by plotting ¡iR - p",¡ versus qo on lag-lag coordin:ltcs and drnwing [he best straight tine through the points. The exponent 11 is determined frOln the reciprocal ofthe slopc ofthe lineo Thar is:
log q~ ,,= t;, lagt;, (Pi< "- P~j)
(2-60)
Ir is cornmon pnctice to rcad the change in qo ayer one 2 log cycle of change in PlIf , sioce the difference in lhe lag value over one cyclc is equal lo one.
p/ -
A plot of p/ - p"j versus qo On lag-lag scales \ViII Te5-11lt in a straight line having a slope of I/n and an intcr- 2 2 cept o f qo = C al PR - Puf = l. The valuc of can also be calculatcd using any point 011 the linear plot once n has t><--ro dclcrmined. Thal is: '
e
c~
q, 2)" ( PR2 - Pl\:f
2. lsochronal Tesfing If the time required for the well lo slabilize on each choke size ar prooucing rate is cxccssive, an isochronal or cqual time tesl 15 prcferrcd. The procedure for conducting 30 isochronal test ls:
ProdllClioll OplilJlizulioll Using Noda/ ..ll1ulysis
32
"~t~
¡iR
a period of lime equ:li to lhe producing (ill1~. The Sl:.llic well bore pressurc P"'!i' muy nol rcach PR. > but ti plot of p.. p..,j? versus qQ wiIl usualIy produce a 51raighl line, from which n mal' be obtaincd. A stabilized test is still requircd to calcu'lale a value foc C. Thc lt..:sting proccdure is illuslrated in figure 2-32.
:i -
-'-'-'-'-¡~~~'-'-'-r'-'-'-'-'r'-'-'-'-'rv-'-'-'-'-'-'
r-
1
IPwI2:
:
:
I
1
1
\
I
1
..
P
I
1
lp-"jJ
1(
Example 2·7A: A flow-after-f1ow test was condueted on a welJ producing from a reservoir in whieh PR:::' 3600 psia. The test results were:
1
1
P,.t4
qo. STB/day
Hg. 2-30. Conventionallest-producmg rate and pressure diagrams.
a:
Starting al a shut-in condition, open the wel! 011 a cOllstant production rate alld mensure Puf al specific time pcriods. Thc lo tal production period foc each
rate l11ay be less than rhe stabilization time. b.
q¡I(Jl\:I .... )·
Shul lhe well in and allow the pressure to build up to
PRo c.
d. e.
Solution: q,. STB/day
Open the \vell on anothcr producing rate and mensure the pressufC al the same time intervals.
Shut lhe well in again
Ulllilpll'S
Rcpcat Ihis procedure ror several rates. 2
al lhe
specific
time periods are plottcd versus C/u and 11 is oblained frem ¡ht slope of lhe lineo To determine a value for e, one lest must be a stabi 1ízed test. The idealized behavior of producing rate and pr~ssure as a function oftime is shown in figure 2-31.
Pwf' psia
263
=PR'
The values of PR 2 - PI,j detennined
Pw{o psia
263 3170 383 2897 497 2440 640 2150 Construct a complete IPR for this well and determine
3170
2.911
383
2897
4.567
497
2440
7.006
640
2150
8.338
ro
The dala are ploned on Figure 2-33. calculate 11, the producing rales cQrrespondillg to a changc in ó.p 2 OVCf ane cycle are used. 610gqQ
log750-logl05
Lllog"P'
log 1O7 -lag 10 •
e : ~--2q!!.o~_
3. Modified lsochrollal Teslillg If the shut-in time required for the pressure to build back up 10 PR between flow periods is excessive, lhe isochronal test may be modified. The moditication eonsists of shutting the wetl in between each flow period for
(p~ - P;'¡
750
J
q q
EXTENDED RATE
EXTENDEDRATE
",-->p
0.854
JI=
q,
,, ,,, ,IPa1.O
'-'-T'-'-'-'-'-'-'-'-'-'-'-
p J ~ JPwl4 -
P..... $
Fig. 2-31. Isochronal test-producing rate and pressure diagrams.
'
..
t ___
Pwt5 _
1
Fig. 2-32. Modill(jd isochronal test-producing rate and pressure diagrams.
Rese",o¡r Pelformance
33
• 2.5_
1.5_g---m-·
_
, .'
1.5
100 " 105
FIf}-
2-33. Flow-after-flow results.
~0.00079
STB day-psia 1.71
The inflow equation is thcrcfore:
q, = 0.00079 (3600' _ p"j).854 = 0.00079(3600' - 0)·854
q,(m,,)
=
' 937 STB/day
Tú gcnorate the data for an ¡PR, assume values of PHi a:::d ca1culatc the corresponding qo:
Pwt> psia 3600 3000 2500 2000 1500 1000 500 O
qo' STBlday
The IPR is sha,," in Figure 2-34.
O 340 503
684 796 B75
922 937
Protlllclion Opliflli::alio/l Usin:; ¡\1m/u/ ,lnalysis
34
4000
3000
1000
OC--_----'--_ _---'---_ _-'-----_-----'_ _----'--_ _L . -_ _L . - _ - - - ' O
300
200
lW
400
600
¡W
-------'
1000
800
Fig. 2·34. IPR for Example 2·7 A.
The Fetkovich eguatían can be modified to a [onu similar lo Vogells e.:¡uation and stated in terms of Producth"üy Index J oc qL(mil.x) (AOF). ')" = C(-' PR -PlI! '! L(ma.. , = AOF = C(p~ - ot
qL
Eliminating the .:oefficient ~=
qL(ma.,)
e gives:
10g~L)~IOg[~R }nlog[I-[;:
e' ')" pf.-Paj -R')" (P
It can al50 be :,howo that as drawdown approaches
zcro, tha! is as Pl1i approaches PR' q L(max)
.
A plot of[I-(p,,¡ip,)'] versus qL on lag-lag scales
exponent 11. A valuc of J can then be calculated using aoy point on lhe linear plO\ from:
-2-
2qL
Therefore, the FClkovich equatioll can be expressed as: qL
~ ~R [1-( :~
JJ
(2·6l)
Fetkovich also suggesled Ihal lhe analysis could be furthec broken down foc undersaturated reservoirs as: qL ~J
- )+Tl Jp, rl - [p,¡)2 (PR-P, ¡;;
n
will result in a straight ¡ine having a slope equul to the
ljiR
;=
results from the faet [hat there are two unknowns in the equarions, eithcr e and n or J and /1. It should be pointed out that if only one stabilized test is ayailable, 11 is oHen assume to be one and either e or J can be calculated directly. This method ofanalysis llsually gives more conserva¡ive rcsults tlun [hose obtaincd using th~ Vogel melhod with FE ~ 1. Taking the lag of bOlh sides of Equalion 2-61 gives:
r
(2·62)
Applicalion of either Equation 2-54 or Equalion 2-61 lo analyze a flow-after-flow test requires al least two stabilized production tesiS. For isochronal testing at least two transient rates and one stabilized rate are required. This
Example 2-78
The well described in Examples 2-1 and 2-2 Is lo be analyzed using lhe Fetkovich equation with the assumption that n == 1. One production test on the
well resulled in arate of 282 STB/day for pwt ~ 1765 psig = 1780 psia. The static reservojr pressure is 2085 pslg = 2100 psla. Calcuiate: 1. Produclivity Index J 2. The new producing rale il Pwt ~ 1500 psia
35
Reservoir Pelfonnance 3. The value 01 Pwf required for q, = 400 STB/day 4. q'(m,,) or AOF.
where A=
So/utíon:
141.2¡t B
•• [ln(0.472r,/ rw ) + S]
k.h
2.3XIO-I4~B;p.
B
14L2¡t.B. D koh
2
2(282)
h rw
Po = 011 density evaluated at TR and 0.51h + P'f ),Ibmlfl J, and
13
J = 564 = 0.95 STB/day-psi 591 2 q, =
~R +-[;:
r
2
velociry coefficient, ft- I
The other terros in Equation 2-63 have becn defined previously and ~ can be estimated froro Figure 2~351O or caleulatcd using Equalion 2-8.
J
= 0.95(2100) [1_(1500
=
1']
~ = 2.329xl0 kt.2
•
2100/
q, = 489 STB/day 3. Solving Equation 2-61 for
10
pwf
and assuming
n = 1:
where ko is in millidarcies. The contribution to the pressure drawdown due to laminar or Darcy flow is expressed as Aqo while the 1100Darcy or turbulent contribution is expressed as Bq}. Dividing EquatioD 2-63 by q. gives: PR::; Pnf
5
2(400) ]°0 Pwr =2100 1=1625psia [ 0.95(2100)
A+Bq.
q.
('-6-1)
10H 4.
qL(ma,,):=
AOF =
.}pR
2
=
Q SANOSroNE5 .. • CARBONATES
o (l-
0.95(2100) 2
10 10
= 998 STB/day
., o
The values for QL(maxl obtained from the three methods used to analyze tMis well test may be comparad:
Method
q'(ma,¡
Constant J
1835
Vo~el
1097 998
Fetkovich (n = 1)
10
9
"
;=¡
""~
z~
o
•
<-
"Q
~
C. Jones, Blount and Glaze Melhod
",jI "'-"
'2>
.'.,
$ o 103
00
<>
00
v
o v >-
~
",°o. l?.-¿"
~
10
7
(2-63)
u
6 ~ 10 >
"<8 o
o
o
ú1< POROS ITY 33~ r'04'So 36~ Z/()-1 3911 0J
Ir? 10
o.,
o. <-
~
In 1976 Jones. Blount and Olaze' established a paper discussíng the cffects of turbulence or non-Darcy flow on well performance. Methods were presented to analyze weH complctiolJ cfficiency and to isolate the rate-depend~ enl component oflhe total pressure drawdown. Although thls papcr will be discussed in greatcr detail in the section on \Vell COmplclion Effeets, use of lheir plotting proeedure to determine real time IPR's wiIl be presentcd here. Equation 2-27 can be written with the turbulcnce tcrm indudcd as:
.,
4
to
I 100
I llXXJ
10, IXXJ
PERMEABllITY, MllllDARCl[S Fig. 2-35. Velocify coefficienl correfation. 1O
tOO, 000
36
Producthl/l Optimiza/ion Usil/g Nocla!
Aplot Of("PR -p"'¡)/C¡o versus q<1 on Cartesian coordinatcs should yi~ld a straight line of slopc B and intercept A as qu approachcs zcro. Once A and B are detcrmincd. a complete IPR can be conslructed using Equation 2-63 Of 2-64. Allcast 1wo stabilized lests are required to cvaluate A and B, ~ut usuaUy more tests will be used lo smooth out Ihe cffcets 01' errors in measurcments. Equation 2-63 can be solved for flo\\' rale to yield:
q. =
-A +[A' +4B(PR - p,,¡) 2B
AIJ(J,~rsis
1.5
..
..
1.0
r
Examp/e 2·8A: The test data presented in Example 2-7A are to be ana-
Iyzed using lhe Jones melhod. Reservoir pressure
PR
is 3600 psia. Using the data from the four tesls, find B and qo(max)'
A.
So/ution: qo,STBlday 263 383 497 640
l.0
P...f' psia
(jiR -Pwt Vq.,psia/STBlday
3170 2897 2440 2150
1.635 1.850 2.334 2.266
0.5 l---,-'-c--7--.,-L----'~--'--~-~
Tlle test data are plattco in Figure 2-36. The slopc B is ~.~ X 10- 3 psia/(STB 'd):! ami Ihe ill(CrCept at qu ='" O gi"cs a \"aluc of A = 1.05 psiaíSTR'd. Tú determine qo(max)' set V,( = O:
-1.05 +[1.05' +4(".2 XIO-')(3GOO -D) q
100
?:ú
300
400
500
600
,-':0
CI", STB/Day
Fig. 2-36. ExampJe 2-8A soJulion.
t
~--------------
_'lm:L"()
O
2(1.2xlO- J )
qvlm.'1 = 1063 STB'day
The value obtaincd for qu(ma.>;) using rhe Fetkovich melhod IVas 937 STB/day. As can be observed in Figures 2~33 and 2-36, lhcrc is considerable scatter in the data, and lhe choice of which points to use for constructing the lines is questionable. If a least-squares procedure had b«n used to oblain the slopes, lhe results would likely have been in closcr agreement. This melhod may give optimistic results for oil wells because of the assumption that the A t~rm is constant. As th~ A lenn includes the reciprocal of the pressure funclion, reducing PI.! below bubblepoint pressure wiII increase A.
D. Conslrucling ¡PR's When No Slabilized TesIs Are Available 1l is frequently necessary lo estima te the inflow performance of a well before the well has been completed, and therefore no stabilized tests would be available. AIl of the previously deseribed methods for constructing ¡PR's require at leas! one stabilized test.
rhe consLruclion of an IPR before compktion is required to detennine the lllbing sizc. lhe numbcr of perforaliúns, the Ileed for stimulatiol1, and for sizing of SUfface equipment. Ir all the parametcrs in Equation 2-38 could be delermined. and if lhe bubblepoint prcssure Pb, foc [he reservoir were known. CJb could be ciJkulaled, and rhen the Vogel mcthod could be uscd to construcl an IPR. using Pllf= Pb and lfu = qb as a test point. Ira lluid sample is 3\'ailable, then Sú and ¡...lu can be dctermined. The wellbore radius rll" will be known [rom lhe bit slze and recan be eSlimated, depending 00 anticipated wcll spacing. This leaves the permeability LO oil k u ' and Lhe skin factor S' lo be determined. These can be dctem1incd from transient well tests such as a drill stcm test. Rcscrvoir pressure, PR can also be obtained fmm the drill stem test. The procedure is:
1.
Using fluid property data and lhe values of klJh and S' from the transicnt test, calculate: J
2.
0.00708 k),
floB.[ln(.472r, 11;,.) + Sl Generate Ihe IPR for valucs of PI!f < Pb using Equation 2-48. If Pb :?: PR. use Pb = Pn in the equation. The IPR is linear for values of Pllf";:. Pb. Ir Pb is
37
Reservoir PelformaJlce unknown, assume Pb on page 27.
= PR. Then use Equation 2-46,
L
E. IPR Construction for Special Cases
h
AII the methods for eonstructing present-time IPR's diseussed previously were based on aoalysis of wells dril1ed vertically through a single zone. It was also assumed that the wells had reached pseudo steady state or stabilized flow. Construetion of IPR's for sorne special cases will be discusscd in this section. These cases are: horizontal wells, wel1s in waterflood projects, wells producing from stratified formations and cases in which PR is unknown. l. Hor;zonta! Wells It is becoming more common to complete wel1s by drilling a long horizontal hole ioto the producing formation. This mcthod of completion can have several advantages whcn comparcd to conventional vertical completions. The produced fluid does not have to converge into such a small area, and, therefore, the veloeities and friction losses are rcduced. It has becn found that water and gas coning tendcneies are lower for horizomal wel1s and that a larger volume of the reservoir can be drained by each well. The actual production mechanism or reservoir flow regimcs are more complicated th311 those for a vertical well, espccially if the horizontal section is of considerable length. Some combination of both linear and radial Oo\\' actualIy exists, and the well may behayc in a manner similar to that of a well that has becn extensively fractured. Generatian of data to construct ao IPR is best accamplished with a numerical reservo ir modeI, and this has becn discussed by Sheriard, et al. 19 They also reported that the shapc of mcasured IPR 's for horizontal wells completcd in the Prudhoe Bny field \Vas similar to those predicted by the Vagel or Fctkovieh methods. That is, the Productiví"iy' Indcx J decreascd with increased drawdown. The productivity indcx for a horizontal weJl in which perrncabiJity diffcrcnce in the vertical and horizontal directions is small was described by Giger, et a1..:o as: (2·65)
J
whcrc
I [ X=-ln 1+
h
2 JI+(Ll21~)2] +-(h,2r".) B ,
Ll2r,
L
effective penneability to oír in the hori/zontal direction, md, effective permeability in the vertical direetion, md, and, length of the horizontal section, ft, and vertical thickness of the formation, ft.
.
Sherrard, et al., 19 found that productivity gains of from t\Vo to four times those for vertical wel1s could be oblained for L values of I500 ft. The complex flow regime existing around a horizontal wellbore probabIy precludes using a method as simple as that ofVogel to construét an IPR. However, ifat least two stabilized tests can be obtained, the Fetkovich equation, Equation 2-62, could be used. With two tests, vaIues of both J and n couid be calculated. Inthis case, these values would not only aecount for effects of turbulence and gas saturation around the wellbore, but also for the effects of the nonradial f10w regime existing in the rescrvoir. Bendakhlia and Azíz24 used a complex reservoir model lo generate IPR's for a number of wells and found tha! the Vogel equation ",ould fit the goneraled data if expressed as:
~jl.O-V~'f l PR -(I-V)(~'fJ'I PR qo(ma.'()
In arder to apply t!lis equation to well test data, at least three stabilized tests are required to evaluate the three unknowns, Qo(m3..'()' V and 11. J. Waterflood ¡rells The inflow performance of a well producing from a reservo ir that is being waterflooded can be influenccd by the facts that the sta tic reser\'oir pressure, PR' usually remains constant and bubblepoint prcssure may be fairly low. Also, the water saturation in the reservo ir will change with time. causing the liquid productivity index to change. If the reservoir was deplcted to a fairly low pressure befare water injection was started, soiution gas will be lo\\', aod the bubblepoint prcssure depends on solution gas/oil ratio. A waterflood bubblepoint prcssure can be calculated using the solution gas/oil ratio existing at the start of water injection and by .assuming that sorne of the free gas existing at that time wiII be reabsorbed in the oil as pressurc is increased. 1t can be assurned that Ihe IPR will be linear for valucs of Pllf;::' Pb· For Pl\f< Pb' Vogel's equation may be used to account for the cffcet of gas saturation developing around the wellbore whenp,.¡is beIow
Po· The total liquid Productivity Index is: . 0.00708kh
J
[ln(.472I~/r",)+Sl
[km
1l0Bo
k~.] + Il",B.
(2-66)
As water saturation inereases, km will decrease and km
ProdllcrioJl OptimiwfioJI Lsill!; NudaIAl/alY:;1
38
will ¡necease. Tbe sum of k¡V and J:Y\1.' will first dccrease 3nd then ¡necease. Therefore, J \lo ¡U follow lhe S:llne trend, and evcn though PR muy remuln constant, both producing water fraction/w and J will change wirh time. '\'al~rf1ood theor)' can be used lo predict lhe change in water saturation and, thercfore.fw \\ith time.
Consider the case where PR2 is greqtcr than PRI- l j p"/ is greater (han PRI. liquid will Oo\\" ¡nlo Zone 1 from Zone 2, Thcre \ViII be no net produclion UJ1til lhe \\'cllbofl' pressure is low ~nough :iD that no\\' [rum thc higha zonL is more than th~ ral~ that will flow into the lowcr prcssur.: zone. This vaJue 01' \\"ellborc prcssure at which nd production begins lllust be determine::d lO construct a coo1-
3. Slratified Formalions AH the prcvious discussion on constructing lntlow Performance Relationships [oc producing wells has been conccrncd with \lOells that are producing from a single fonnatioll. In many cases lhe produ~d liquid will conlaio wata, and lhe walee fraction may in.:rease during the ¡ife of lhe well. This is true espccialIy of water-drive reservoirs oc rcscrvoirs uodergoing pressure maintenance by walcr injection. A1so, same wells ar~ perforated into two or more Zon~5> and the production [mm aH zones is comminglcd in lhe wellbore. This can cause both the producing wat~r cut "no gas/liquid ratio (GLR) to change with drawdown if the commingied zones have different chafaClcrislics. As will be shown in Chapler 3, ca1culalion of lhe outtlow or piping system pcrfonnance requires accufal< values fOf J. and GLR. Analyzing lhe performance of a commingled well can b~ illustraled by considering Ihe case where t\Vo zones ha\·ing different \·alues OfPR ,¡;,., GlR, and Qll13X or J are proJucing iota a cammon weUbore. This is illustrated in Figure 2-37.
-
posite
Of
totí.ll IPR. Ir can be cakulatcd by sctting q"1
and assuITIing that ¡he productivity drawdowns.
ind~x
q, = J,Cp" - p:¡) = q, = J,(p;¡ -
P.,)
Of
PHI + PR,(J,IJ,) l+J,/J, When Pnf is lowcr than PlIj*' fiel production will OCCur. p.,.l witl correspond [O the:: conditioll of zera inflo\\' ún the total IPR. Con:;tructioo of lhe tOlal IPR requires calculation of lhc iorlow from each zone at various Puf \"31lles. The inflow from each zone is added for the tolal q[. corresponding to each PlIf. The characteristics 01' each zone would have lO be known frorn eore and log data 01' fram production log:ging. The individual and lOlaI IPR '5 are illustraled in Figure 2-38. Valllcs for total/, and GLR applying at any value ofp,,; can be calclllalcd from: p.,
:;-
P" , JI, qmox¡
: ~
F-
Pwf
/ / / / / / / / / / / / / / / / / / / / / / / /T.
/ / / ////// /// /// / ////
-
--
P'2 , J2
1J
Qmox2
Fig. 2-37. Slra¡!fíed reservo!r.
= ql·
is linear at smal!
Reservoir Pelformance
39
P"
Fig. 2-38. Composile IPR.
+ qM" Field experience has shown that this method of handling water production is vatid in wel1s producing al 97% water cut.
q/qL(milx) where qL = q(l
N
¿qUJ.,., JII' = ~'=.-I,--_N
¿qu GLR , GLR = .!-'="'I
_
qT AII of the previously disclIssed IPR methods for oil welIs can be applicd to wclls that are producing considerable amounts of water along with the oiL This can be accomplished by rcplacing the oil rate q" used in the graphs and equations with total liquid rale qL' This is valid beca use the change in J is caused rnostly from the reduction of relative permeability to liquid as gas saturation forms in the reservo ir. The gas will reduce the perrneability to water in the same way that ít reduces the permeability to oil. IfVogcl's rnethod is uscd, his graph or equation can be considcrcd to be a rclationship between PII! I fiR a n d
4. Sta/ic Reservo;,. Pressure UnknowIJ Cases frequenlly arise in which an analysis. must be roade on a weIl at is producing from a rcservoir in which PR is not accurately known. PR can be obtaincd by measuring pressure in a wcll that has becn shut in for a long period of time or from a pressure buildllp test. Obtaining ao accurate value for ¡iR may be expensive and time consuming. lfit is unknown, IPR's may be constructed for a possible range of static prcssures, and the rnaximum and minimum production rates can then be determined through Noda1 Analysis™. However, ¡fseveral stabilized production tests are available, the value of PR required to force one of the IPR equations to repro~ duce the test data may be calculated. the simple form of Vogel's equation, Equation 2-33 is used, there are onIy two unknowns, that is q{ma;l:) and PR' Therefore, iftwo tests are available, both may be cal-
Ir
ProdllCtiOll Opli/1/i::atioll U"iug Nuclal .·ü;~I(rsis
40
cultllcd. lIowcvcr, as disclIssed prc\·¡ollsly, this model ¡1%Uml.:S Ihat lhe.: now cflícicllcy is 0ne or that S/ = O, which is rarcly the aclUal case. Ir me Fetkoyich equatiou. Equation 2-54, is used, th~re will be three unknowi\s: PR. e ítnd n. Solving for aH of these Ullknowll$ wauld requirc three slabiliztJ tests. Ir only tWQ tests an:: available. JI could be assumcJ to be one and ¡iR alllt could be calculated. This woulJ give results similar lo lhose obtaincd using Vogcl 's equ:Hioll, bUI would be
Thc two values for ¡iR are approximaldy equa] ror 11 ::::: 0.85 and ¡iN. == 3606 psia. Using lhe largesl tlow rate to calculate gives:
e
~ ')" ( P"R' - P"I
c= .
C = 0.00083 STB/day-psia
e
lJtl1\;lX) =
caskr to salve rol' ¡iR' Sc\'aal mClhods could be used to salve for lhe three unknowlls, bUI a simple trial and error 01' iterative method will b~ suggcstcd hefe. Assuming that available test data include- three producing cates and three corresponding ""Iucs of PI'f' can be climinated ¡rOm the Fetkovich cqu31iün to gi"c:
e
c-=
ql
')' (-' fJR - Pl~fl
')' PN. - Puf) ( -2
Ji.,: u~il\g
can be calculated using tests 1 and 2 and also ksts 1 and 3 to yield: 2
-2 P/{(l-2)
-2
p
R(I-J)
(
1
)1/11
!
Pufl q2 (11 - P-../2 = (q21 lJ, )1/11 - I 2 ( I I/n .:: - :"~iJ =PlI'iI . q3 {jI) . (1 )"11 , lJ3 q\ -1
PR actually exisiS. and a value for 11 t>(' dctcrmined that will give PR(;-:, = PRO"::))' This can k accomplished by trial and eIT0r. Ihis procedure will b~ illustrated by choosing thrce (lf the tests reported Only one valuc for
f,"~Hl
in E:\:lmple 2-7 A and assuming Ihat
PR.
'." STBlday
AOf -= Q.00083 (3606 2 -O) 0.:\5 =
N. PREDICTING FUTURE IPR's FOR OIL WELLS As Ihe prcssure in an oil rcscrvoir declines from d~ple tion, lhc ability of th~ reservo ir to transpon oil wiH also dcclin~. Ihis is causcd from the dccrease in lh~ prcssure fUllctioil as relati\'c p~rmcability to oi! is dt:crcascd due lo incrcasing gas saluration. Planning the dc\'elopment ofa rcscfvoir with respccl lO sizing equipmcnt and planning for artiticíallift., as well as evaluating lhe project from an ccollomics standpLlint, requires lhe ability to pr..:dict rcscrvoir performance in the future. Ihe effcct 01' dcplction was discusscd prc\'iously, and in this section several Illclhods to qU3ntify this cffcet will be presentcd.
A. Standing Method Standing ll published n procedurc that can b~ used to predict the decline in lhe value of q,,(m:J;>;) as gas saturntian in the reservoir inereases from dcplelion. Yogel's equation (Equation 2-33) can be rcarrangcd lo yicld:
~=[l_~'f'(1+08~"f)
263
3170
2897
Jl
(2-67)
PR
Substituting [he expression for rhe productivity index (Equation 2-22) imo Equation 2-67 and rearranging gives:
pw{tpsia
2150
J = q',-='I [1+0.8
Use this data loestimate PR,n, e and C;D(max)or AOF
PR
~'f J
(2-68)
PR
Standing lhen defined a "zera drawdown" produclÍvity index as:
Soludon: _, P
(3170)'(3831263)"0 -(2897)'
"'''l =
_, P
PR
CJu(nl':'L\)
383 640
1.7
925 STB'da}'
is unknown:
Example 2-88: Test Data:
MO (3606 2 -2150')°."'
,(1-'>
=
J* -=
(3170)'(640/263)"0 -(2150)' (640/263)"0-1
Eslimaloo n
1.00 0.50 0.75 .0.85
lim J::;; _1.8Qo(m a.'I) PR
(2-69)
p ... f--tpl.
(383/263)"0 -1 or
jiR(J-2)
PR(1-3)
3699 3395 3549 3609
3719 3339 3526 3604
If the change in J' with depletion can be predicted, then the change of qo(ma~) can be calculated. Standing observed that another dcfinition of J* is:
Reservoir Peiformance
J*
=
41
.00708kh ([Ch))
(2-70)
In(0.472r,} . r..
where _ ) _ 'k [( PR - -m-
}loBo The pressure function will change with depletion since Jlo and Boare functions of PR' and km is a function of oH and gas saturation. The relationship between the present or real time J* and sorne ruture time value of J* can be expressed as:
J~
[Cfi RF )
(2-71)
J; - [(PRP)
value of J* when PRP has declined to PRF value of J* at the present reservoir prcsSUre. This fulure J may be used directly in Equation 2-48 or if the vcrsion requiring a value for q(maxl' Equation 2·33, is used. combining Equations 2-71 and 2-69 gives a relationship bctwecn qo{m:H)f and qo(m:lx)p as: qo(m~xlF ::: qo(m'J..v..)p
PRFICfíRFl] ) [ PRP [ ( PRP
(2-721
3.
Calculate J*F using Equalion 2-71 or qo(mu)F using Equalion 2-72.
4.
Generate lhe future IPR using Equalion 2-73 or Figure 2-26.
Examp/e 2-9: The lollowing example was used by Slanding lo iIIusIrale lhe melhod al generaling a future IPR. Present Time
Future Time
PR i!o 80
2250 psig 1800 psig 3.11" cp 3.59 cp 1.173 bbflSTB 1.150 bbllSTB So 0.768 0.741 km 0.815 0.685 Presenl lime test dala: qo ; 400 STB/day, Pwf; 1815 psig Generate IPR's for botti the present and future times.
So/ution: 1. q,,(m,,¡p;
q+-
0.2 ; : - 08 ( ; :
J)
q,,;m,,¡p; 400/[1_0.2(1815 )_0.8(1815
2250
2250
J]
q,,(m.,¡p ; 400/0.318; 1257 STB/day
Once a valuc of Q,¡(m3x.)p is determined from a \Vell test conducted at the prcsent or real time, future values of qo(ma...) can be prcdicted at PRF' The value of the oil saturation as a function OfPR can be estimated using a material balance calculation or other rcservoir model, and then k1T) can be determincd if relative pcrmeability data for the reservoir in question are availablc. The fluid propertics ¡Jo and So can be obtained from a fluid sample anaiysis or from empirical correlations. Once the "yaluc of qo(m.,:"l) or J has been adjusted, future lPR 's can be gencrated from
[P"'f PI.! q"(F> =q,,(mu)F 1-0.2-::-:--0.8 -::-:[
PRF
PRF
J']
(2-73)
The present or real time IPR can be calculated (rom: 2. q,,(p¡ ;1257[1-0.2 PwI -0.8
2250·
/!PRP ); (km/i";, Bo J" ; 0.815/(3.11 )(1.173) /(j5RP) ; 0.223 I(j5RF); (km/i";,B,,} = 0.685/(3.59)(1.150) I(j5RF);0.166 .
1800(.166)] . 3. q,,(m")F ; 1257 ; 749 STl3lday , [ 2250(.223) 4. The future lime IPR can now be calculaled Ironi: q
or
0(F)
q,,(F) =
J~PRF l 8 [1-0.2 -p,,¡ -0.8[ -p"¡ J'] .
PRF
PRF
The procedure for generating a fllture IPR is: l.
Calculate qo(max)p \Ising prescnt-time well test data and either Equalion 2-33 or Figure 2-26.
2.
Using fillid propcrty, saturation and rclative permcability dala, calculale both1(PRP) and 1(PRF)'
p;' ,] (2250)
; 749[1-0 2 P,., -O
, PwI
2250 2000 1800 1600 1400 500 O
•
8~]
1800
. (1800)'
qo(P)
q,,(Fj
O 197 378 542 690 1148 1257
O 142 270 661 749
The réal time and future ¡PR's are'plotted in Figure 2-39.
Pradue/ioll Optimiza/ioll Usillg Noda/ ..tn..!(~'sis
42
130th the pn,::scllI time and future IPR's are plou.:d in Figure 2-40.
"'"
C. Combining' Vogel and Felkovich
Thc I1lcthod proposcd by Fetkovich ror adjusling e can also be used to adjust qa(m:lx) ifa value ror the expon~nt 11 is assumed. The cxprcssiolls ror qU(IlUI:\:)p and (jv(l\lal..I<'" can be cxpl'cssed using [he f-'etkovich equation as: (2-75) q¡j(mou)f;::: CP (-2 PRP )"
HES~T
"00 P.1
']
fUTUR[
Cj,)(m:l.\\F;:;:: Q Q
M
400
""
1M
800
1M
1400
q,
-=--- )(-2
PRP JO
CP (PRF PRP
(2-76)
Combining Equalions 2-75
gi\Ocs
Fig. 2-39. Example 2-9 solution.
If a value of n equal to ane is assulllcd, then:
B. Fetkovich Method
The lllcthod proposed by Fetkovichs lo construct future lPR's consiSlS of adjusting lhe flow coefficient e in Equ:ltioll 2-54 Coe changcs in,/CPR)' He assulllcd tlHH ¡<¡iR) was a linear function of PR ando therefore, lhe valuc of e can be:: adjusted as CF = Cp(/iRF / /iRP I
A \'aluc of e" is obtaincd from pre5ent lime production tests, thm ¡s, tests eonducted when p,'? :::; PRf" -Fctkovich assumed that lhe value of Ihe exponcnt JI would IlOl change. Future IPR 's can thus be generaled from
golF) = Cp(PRF / /iRP)(P~C - p;¡)"
qO(lIlJ.x¡r = qu(max)p
- / _)3 (PXF PRP
(2.78)
Use of this Illcthod is analogou,s to using lhe Fetkavich method Cor both prescnt and futurc IPR construction if ir is assul11cd [hat 11 = lo Adjustl11~nt of qdmax) for dcclining PR L1sing ¡his m~thod is illustratcd in th~ following example: Example 2-11: In Example 2-2,it was found that
qo[max)
was e qual to
=
1097 STB/day for PR 2085 psig. Usin9 this data and Equation 2 - 78, calculate: 1. qo(maxl when {iR =: 1900 psig = 19 15 psia 2. qo when PR = 1900 psig and Pwr = 1485 psi9
(2-74)
The Fetkovich method foc gcnerating fulure lPR'g is illustraLcd in the following example.
So/ufion:
Examp/e 2-10: Using the data from Example 2-7A, construct an IPR for the time when PR has declined to PRF = 2000 psia. The following data were obtained in Example 2-7A: PRP = 3600 psia, n = 0.854, Cp = 0.00079.
So/ulion: qo(F) =0.00079 (2000/3600) (20002 _pd)O.854 qo(F) = 0.00044 (2000 2 _pdJO.854 Pwl 2000 1500 1000 500 O
1. q,(m"1F =1097(1915/2100)'=832 STB/day
2.
qO(~
= qo(m,,+-02[;:: }08[;::
n
Pwl
"'" o 94 150 181 191
)00
400
seo
" Fig. 2-40. IPR for Example 2-10.
bOO
lOO
ro:..
r¡OJ
¡COl
Resenoir Performance
=832[1
A. Use of lhe Back Pressure Equalio'ñ
0.2(1485)_ 0.8(1485)2] 1900 19002
qo(F) q'(F)
43
= 295 ST8/day
Note that the correction factor is calculated using the ratio of absolute pressurcs since these were used by Fetkovich. The pressures used in Vogel's equations should be gage pressures.
V. PREDICTING PRESENT TIME IPR's FOR GAS WELLS Darcy's equation for radial gas flow including perrneabiliry altcration and turblllence was derived previously as Equation 2-28. This equation may be expressed as follows:
703xI0-6kg"(p~ - p,;!)
q." = JlgZT[ln(.472I~/ 1~)+Sl Solving for PR 2
-
(2-28)
p;'¡ and collccting terrns yields:
,
P"R -
2
p,\¡ = AqJC
'
+ Bq.;(
(2.79)
A = 14""~JT[ln(.472I~/I;,) +5]
kg h
3.161 xl 0- 12 PYgZT B = --~--'-=-~ ¡,2 '~I'
Examination of Equation 2-80 reveals that only two flow tests would be required to evaluate e and n whenPR is known. However, due to the possibility of errors in measuring values of qJC and PMf it is customary to use at least fom flow tests and to determine 11 by constructin~ the best straight line through the four tests. Many regulatory agencies require multirate tests to establish allow2 able production rate:,;. A plot of PR 2 - p",¡ versus qsc 00 log-Iag coordina tes will result in a slraight line having a slope of l/n and an intercept of e = qJC at a value of 2 PR - Pnf equal to one. There are essentially three types of multipoint or backprcssure tests that can be used to evalualc e and n. These are the flow-after-flow, the isochronal and the modified isochronal. Each of these tests, including the advantages and disadvantages of each, was described in detail in Sectioll lIl-S of this Chapter and will therefore nol be repealed here. The test requiring the least amount of time is the modified isochronal and will be illustrated for a gas well by means of an example. It should be recallcd that al leas! ane fully stabilized test is required to evaluate C even for the modified test. A procedure for conducting a modified isochronal test on a gas weH consists of: l.
Start al a shut-in condition (P":fl = PR), open thc well 011 a constant no\\' rate and measure Pllf at specific lime pcriods. The tOlal flow period rnny be Icss than lhe stabilization time for lhe well.
2.
Shut the well in for the same pcriod of time nt which it was allowcd to now. The bottomhole pressure will nol necessarily build back up to PR but lhe static pressure at the end of the shut-in period (Pws2) is assumed lo be the reservo ir pressure for the second now periodo
3.
Repeat Steps 1 and 2 unrillhe data are obtaincd for at least two flow rates. A plol of p".i--p":fi'l versus qoteon log~log coordinates will produce a straight tine of slope equal to lln for each time at which Puf was measured. A value for C ean be calculated from the stabilized test, whieh ;s usually eonduetcd afier the transicnt tcsts are runo The procedure is ilIustrated graphically in Figure 2-32.
T~¡s
definition of B includcs the assumption that re is much grcater fhan r..... Thc cfrects of turbulence can also be 3.:countcd for by incll1ding an exponent in thc pressure term of Equation 1-28. This reslllts in the familiar backpres5ure form of the equation. q,_~
-' - PlIf ')' = C( PR
(2·S0)
ObservatíQn' of Equation 2-80 rcyeals that for negligible rurbulcnce (B = O). lhe valuc of 11 is 1.0. For a negligible contribution from the laminar or Darcy term (A = O). me valllc of n is 0.5. The acluí:l! value of n usually ranges betwecn 0.5 and f.O for gas wclls and is an indication ofthe degree ofturbulcncc or non-Darcy f10w taking piare. AJthough the value of 11 is usually considered to be independcnt of no\\' rate, it actllafly \ViII be rate dependent since it is a Il1casure of the turbulence effccts which depwd on fiow rateo Manar, el a1. 12 have shown that errors in AOF inyolved in considering 11 to be constant are usually less than 0.1 percent if the test data do not hayc to be extrapolatcd too lll11ch to oblain the AüF. Either Eqllation 2-79 or 2-80 Ill~Y be \Jsed to genera!e a pre-_scnt-time IPR for a gas well once thc coefficients and exp.:ment are cvaluatcd from test data. Use of both cquatiC'ns will be illustratcd ill this scction.
Example 2-12: A modífied isochronal test was conducted on a well completed in a reservoir having an average pressure of 1948 psia. The flow and shut-in periods were six: hours long, and only lhe values of Pwf measured ar the end of each flow period are to be used to determine a value for n. The extended f10w test was run for a period 01 72 hours al a fiow rate 01 8 MMscld, al which time Pwf had stabilized al 1233 psia. Using the
following dala calculate:
Production Optimiza!ioJ1 Usillg lÚh/ul Allillysis
44 1. e and n 2. AOF 3. Producin9 rate for Pwl ~ 800 psia Test No.
PWSI
1 2 3
psia
1948 1927 1911 1887 1948
4
Extended
Thc test data are plottcd in Figure 2-41. 1.
Pwr. psia 1784 1680 1546 1355 1233
4.50 5.60 6.85 8.25 8.00
To calculatc n, rcad lhe now rate changc o\"er cyclc of pr~ssurc squarcd changc: 11
!1log qs,
lag 74 - lag 6
6. lag (P;"I - P'~Ji)
iog 10 - iag 1
-
Dile
lag
=0.60
Use the stabilized test to calculare C: e= q" 8.00M,}h:fd (p~ - P;f)" (2.274 xiO 6) 0.6
So/u lían:
= 0.00123 iI4,\{sc/d
psia 1.1 Test No.
qsc,MMscfd
1
4.50
2 3
5.60 6.85
4
8.25
Extended
8.00
2.
0.612 0.891
1.262
3.
1.725 2.274
AOF ~ C(PR-O)" AOF ~ 0.00123 (1948')0.6
~
iO.9 MMscfd
q.". = 0.00123 (1948' - 800')°·6
~.
9.76 M~lscfd
As notcd prcviously, at least üne stabilized test must be 10.0 ----
TRANSIENT
"u;
'o."
STABIUZED
•
o
1.0
x .10
,
Q.
"~
S
I 0.1
L-
0.1
Fig. 2-41. Example 2-12 solution.
•
......L
1.0
AOF
-!-_IL.-/_--L.. 6
10.0
24
Reservoir Pelformonce
.- .....
45
mn during a modified isochronal test to detennine a value for the coefficient C. Tbis sometimes requires an extended testing time and, ifthe gas is being flarcd, can waste a considerable amouot of energy. Referring to- Equation 2-28, if the efTects of non-Darcy flow are inclucted in the exponent n, the definilion of e is: 703)(\o-{; k
"
g e ~ --------'---
(2·81 )
bOlh linear and radial f1ow, but the defioiúoos of A aod B would depeod 00 the type of f1ow. The defioitioos of A aod B for lioear f10w are given io Equatioo 2-7. To have sorne qualitative measure of the importance of the turbulent contribution to lhe total drawdown, Iones et al. suggested eomparisoo of the value of A e'aleulated al the AOF ofthe well (A) to the stabilized value of A. The value of A' ean be ealeulated rrom:
Pg ZT[ln(.472r, I rw ) + S]
A'~
If aH the tenns in Equation 2-81 can be evaltiated, a value of can be calculated and the extended test can be delayed until the well is connected to a sales line. The principal unknowns in Equation 2-81 are permeability to gas k g , and skin factor S. Both kg and S' ~ S + Dq can be obtaincd from a drawdown or buildup test on the welL The shut-in periods during the modified isoehronal test can be estimatcd. AIso, if S' is different for the different flow rates, both S 3nd D can be calculated using two values of S'. Altematively, values for A and B in Equatioo 279 can be calculated and the inflow performance evaluated using {his fOrol of the equalion.
e
B. Jones, Blount and Glaze Method
Thc method of plotting test data, which was proposed by lones, et al. 9 dm be applicd to gas-well testing to determine real or prcsent time inflo\\' performance rclationships. Tlle analysis procedure allo\\'s dctermination of turbulcnce or non~Darcy cffrets on completion effieiency irrespective of skin cffcct and laminar flow. Thc procedure also cvaluates (he laminar flo\V coefficient A, and ir k/1 is knowll, ao estimate of skin ctTect can bc mndc. The data requircd are either two or more slabilized no\V tests. At kast one stabilized flo\V test is requircd to obtain a stabilized value of the laminar coefficient A. No transicnt tests are rcquircd to evaluate the completion efficieney if this mcthod is applied. Jones, el al., also suggestcd methods to estíiúate the improvement in inflow pcrfonnance thílt \Vould result from reperforating a well to lengthen the complction interval or increase the perforating density and prcscnted guidelines to dctennine ir the turbulent effecls \Vere excessive. Equation 2~ 79 can be written 8.S:
-,
,
.P-'R'------'-P-'''z.-f
-
= A + BqJC
(2-82)
where A and B are Ihe lamina, and turbulcnt cocfficicllts rcspcclivcly and are defined in Equation 2-79. From Equation 2-82, it is apparen! that a plet of(p/ - Pllf2) /qJ(. or (Ó p 2/QJC ') versus qsc: on Carfesian coardinates wil1 yicld a line, which hns a slope of B, and an intcrccpt of A = o.p2/q,\,t' as q.te' approaches zera, These plots apply to
A+B(AOF)
(2·83)
-A+[A'+4BP~]O'
(2-84)
where
AOF
28
Jooes, et al. soggested that if the ratio of A' lo A was greatcr than 2 Or 3, lhen it Is likely that sorne restriction in the cornpletion exists. They also suggested that the formation thíckness ¡, used in the definition of B could be replaeed by Ihe leogth of the compleled zone /ip' sioee most of the turbulent pressure drop occurs very near lhe wellbore. The effect of changing cempletion zene leng!h on B and, therefore, on inflow performance can be estimated from:
(2-SS)
where \
B,
turbulence cocnlcient after recompletion, turbulcnce-coefficient before recompletien, new eompletion length, and old completion le,nglh
BI
hp2 hpl
Example 2-13: A four-poinl test was conducted on a gas well that had a perforated zone of 20 ft. Slatic reservoir pres-
sure is 5250 psia. Using the Jones et al., melhod, determine:
1. ,2.
3. 4.
A and 8 AOF
Ratio 01 A'lA New AOF il the perloraled interval is inereased to 30 ft. Test Data Tesl No.
q,C' Msefd
1 2 3 4
9300 6000 5200 3300
Pwr. psia 5130 5190 5203 5225'
ProJm:/¡ol/ Oplimizaliofl Usillg Nodal Anul)'sis
46 8, Solution: Test No.
1.
AOF ,
qsc,Mcsfd 9300 6000 5200 3300
1 2 3 4
133.9 104.1 94.5 79.4
3.
= -48 +[48' +4(4.1 xI0-))(5250) '1 05 2(4.1 xlO J)
th~
prcvious cX
cffect of increasing lhe perforated ínlerval on the AOF is substantial. 11 has also been fOlll1d thar the cffect on B ol' increasing lhe total number of perforations opcn can be eslimaled from 8, = 8,(N,IN,)' whcre N represenls the number of perforations open. Further implications of Ihe cffccts of well complction efficíency will be discusscd in lhe section OIl \Vdl Completioll Effeets.
'105
2(9.24xlO ))
= 52,080 Mscfd
C. Predicling Fulure ¡PR's for Gas Wells
As reservo ir pr~ssure declines fram dcpl~tion in a güs reservo ir, the change in tlle IPR is p.ot as significant as il is for an oil reser\'oir. Tllis is due primarily to tlle fact that elfective permcability to gas rCll'l.ains fairly conslant since the gas saturation remains constant. This is truc for either
A'= 48 + 914 x 10') (52080) ~ 529 A'/A
4.
4.1 x 10')
The valuc of A'lA culculntcd in
8 = 9.14 X 10') psia'/Mscfd'
AOf
~
j'ndicatcs a large dcgrec of turbulent prcssurc drop. The
A ~ 48 psia'/Mscfd
-48 + [48' +4(9.24 xlO- J )(5250)
9.14 x 10')(20/30)'
AOf, = 76,3-10 Mscfd
The dala points are plolted in Figure 2-42, from which it is found that:
2. AOf
~
= 519/48
~
11
8, ~ 8,(hp ¡lhl',)'
180 160 140 120 100
• 80 B=133.9-48 9300
A 48 o
9.24 x 10- 3
60 40 '---_-'-_ _-'--__...L.,--_.:'--_--'-_ _-'-_---''---_....L.._ _-'--_--' O 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 qsc,Msctd Fig. 2-42. Example 2-13 solulion.
47
Reservo;r Pelformance lO
a dry or wet gas rescrvoir, but not for a retrograde condensate reservoir. The factors that will change as pressure changes can be seen by referring to the definition of C, Equation 2-81. The only tenns depending on pressure are lhe gas viscosily ¡.tg and the gas compressibilily factor Z. These same terms appear in the definition of A in Equation 2-79, with only the Z-factor appearing in the definilion of B. If no changes are made in re, Sor h, the values of C, or A and B can be adjusted for reservoir pressure changes as folIows:
= Ap(¡.tZ)pl(¡.tZ)p
(2-86)
Cp =Cp(¡.tZ)pl(¡.tZ)p
(2-86A)
Bp =BI'ZpIZp
(2-86B)
Ap
where the subscript p rerers to present or real time and the subscript F refers to some future time.
VI. WELL COMPLETION EFFECTS In many cases. the inflow into a well is controlled more by the completion efficiency than by the actual rescrvoir characteristics. This \Vas disctlSSed brieny earlicr whcn the inflo\V performance equations \VeTe modified to include a skin factor or flow efficiency. There are basically lhree types of completions that may be made on a weIl dcpending on the type ofwell, the well depth, and the typc of reservoir or formation. In sorne cases, lhe wcll is completed open hole. That is, the casing is set at the top ofthe producing formation and the formation is not exposcd to cemcnt. AIso, no pcrforations are required. Tltis typc of completion is not nearly as common as it was several years ago. Most wells are now compleled by cementing the casing tbrough the producing fonnatioll. -:.. The most widely t1scd completion method is one in which the pipe is set through the formation, and cement is used to mI the annulus belween the casing and the hole. Ihis, of course, requires perforating the well to establish cornmunication with the producing formatíon. This type ofcompletion pemlits selection ofthe zones that are to be opened. The efficiency of the complelion is highly dependent on the number of holes or perforations, the depth to which the perforations extend into the formation, the perforation pattcrn. and whethcr there is a positive pressure diffcrcntial cxisting from the well to the fonnation or vice versa during the perforating opcration. Compaction of the formation immediately around the pcrfor
lhe reservoir allows sand lo be produced inlo the well. When completing wells in which the formation is incompetent or unconsolidated, a gravel pack completion scheme is frequenlly cmployed. In this lype of completian, a perforated or slotted liner or a screen liner is set inside lhe casing opposite lhe produeing formation. The annulus between the casing and the liner is then fil1ed with a sand that is coarser than lhe formation sand. The size of the sand or gravel depends on the reservoir sand characteristics and on the type of gravel pack. The gravelpack sand also fiHs the perforation tunnels and, in sorne cases, a zone is washed out behind the pipe, which is alsa filled with pack sand. Even though lhe pack sand is looseIy packed and has a high permeability, non-Darcy or turbulent flow through the sand-filled perforation tunnels can cause a considerable pressure drop across the gravel pack. This pressure drop nat only decreases inflow into the welIbore but also creales high velocities lhal may deslroy lhe gravel pack if lhc veloeities are too high. To calculate the extra pressure drop caused by the complction, the general inflow equations can be modified to include the completion efficiency for any type of completion. The equations for both oil and gas flow were derived earlier and are given as 0.00708k"l~ PR - p"!)
qo =
~.,Bo([ln(0.472I;II;,.)+S1
q,c =
~03xIO-ó kgh(p; - p,:!) 1 I ~gZT[ n(0.472 1;. 1;,.) +S1
(:?-27)
(2-28)
where S'~
S+ Dq
2-29
The value of S' can be obtained from a single transient test, but obtaining valucs ror S and D requires transieot tests conducted al two different rates. Equations 2-27 and 2-28 may be written in a different form as (2-63) (2-79)
where A is the laminar coeflicient and B is the turbulencc coefficient. These coefficients may be written as composites of several tenns that depend an the complctioll characteristics. (1-87) (2-88)
laminar reservoir component, laminar perforation componcnt,
48
Prodllcliul/ Oplimi::aliol/ Usil/g Nudo/ Al1ulysis The actual calculation oC an accuratc yuluc ol' SI! is difficult beca use valucs of k d and rel musl be estimalcd. If a value of S can be obtilined from a transicnt test, this wlll be cqual to SI! fo.[ an opcnholc cOll1p(ction. The valuc of EH. may be calcuhllcd rrom
laminar gra\'cl-pack component, turbulcnt reservoír component, turbulcnt p~rforation component, alld turbu!ent gra\"cl·pack component. Thcsc components have dilTcrent dcfinitions for oil and gas Jlow, which wiII be gi\'l'1l as eaeh is discusscd. Onl)' values of the overall coetlicients A and B can be obtained from production tests 01\ wells 111at are already completcd. Thcrcfore, cquations for estimating the valuc of lhe components must be availablc if the efTects of each are to be isolatcd.
Oil (~-92)
Gas (2-93)
A. Open Hole Completions The only cffcet of lhe compktion on ¡nllow performance of an opcnholc complerion will be caused by alteration oflhe rcscrvoír pcrmt:ability by damagc oc slimulalioll. Thc inflow cquations becomc
PR -
p¡¡/
= A'.rrJ/o + BRq;
(2-79)
lhe laminar rescrvoir component includes Ihe effeet of Darcy or lamil1
Gas
kg. Sd
~
unallered res~rvoir permeability to oil, unaltered resen'oir permeability to gas, and skin factor due to permeability altecation around Ihe wellbore.
A value foc S¡J may sometimes be estimated from the following equation 11
SJ~(~:-I}n(/Jlr ..)
P. ~
(2-63)
or
where k o•
Values of the velocity cocfficient ~ may be calculatcd frolTI
(2-91)
2.33x10 IO
k 1.2
•
A value for BR can be calculatcd ifa valuc oC D is available from a transient test 00 an opcnhole completioll. The units to be used in aH the equations prescnted in this chapter are the ¡¡cid unils describcd earlier.
B. Perforated Completions Dile of lhe problems in volved in dcsigning a pcrforatcd completion is cstimating the efficiency of the perforatiOllS to transmil fluid from the resefvoir lo tht: wellbore. lhe efficiency depends on condilions such as the number of perfarations actually open, perforation diameter, penetration dCplh, degree of damage around the pcrforation, and phasing. Figure 2-43 from Be1l 21 i!lustrates tlle perforating process when shapcd-charge perfocating is used. A zone of reduccd permeabililY, caBed the crushcd zone or compactcd zonc, is formed around the perforation, This crushed zone can be the source of considerable pressure drop because of the high fluid velocilies caused by the fluid convergíng iota the perforations. Underbalanced perforating, in which the pressure in the wellbore is less than reservo ir pressure, results in an immediate backflow or surge through the perforation, thus minimizing plugging from debris and crushed-zone damage. EssentialIy three perforating techniques, as described by 8cll" are available for achieviog uoderbalance while perforating. These are illustrated in Figure
2-44. reservoir penneability altered zone penneability, wellbore radius, and ahercd zone radius.
Advantages and disadvantages of each method are discussed by Bell 21 but the conscnsus is that the tubing-conveyed method, even though considerably more expensive, is the best method. Almost any degrec of underbal-
• Reservoir Peljormance
49 ance can be created, perforating density tan be high, long zones ean be perforated ahd lhe well can be produeed immediately afler perforaling. A typical, lubing-eonveyed perforating operation is shown in Figure 2-45. One problem faeed in designing an underbalaneed perforaling job is lhe optimum degree of underbalanee pressure lo use. A field study eondueled by King, el aL'" resulted in correlations between reservoir penneability and required underbalance pressure necessary to obtain perforation performance which was not improved by subsequent acidizing. Figures 2-46 and 2-47 ean be used lo estimate lhe requir~d underbalanee. In lhese figures; lhe minimum underbalance pressurc" for various perrne~bili ties can be obtaincd from the tioe dividing improved and unimproved perforations. They observed thal a higher degree ofunderbalanee is generaIly required for gas ';'ells asopposed to oil wells. Regalbuto and Riggs 2J conducted extensive laboratory tests on eores lo dctennine the optimum degree of underbalance. The tests included pressure difTerentials from 500 psi overbalanee lo 1000 psi underbalanee. They defined a radial now ralio (RFR) as the now rate through the core after perforaling dividcd by lhe now rate before perforating, both rncasured wilh the same pressurc drop across the coreo Thc cfTects of surging ar backnowing fluid through the perforations \Vas also slUdied. In 5QIlle
CASINO
BEFORE
A
. /. . './"
.
','
flRING
:, ... ::
SHAPEO CHARGE
OUAiNG
B
PENETAATlON CRUSHEO SANOSTONE UNOAMAGEO SANO, K.,
,AFTER
e
OIRTY PERFORATION
PERFOAATlNG, BEfDRE FLOW
D
·CLEAN-
AFTER
PEAFORATION
fLOW
Kc/Ko·O.l-O.2l tRUSHED ZDNE, I
Fig. 2-43. Damage lo lormalion due lo jet penerrating process (API-RP 43 Berea sandsrone).21
_. :110111
i1JlIl.
.,. _o.
- --
..
•
-..
'
WIRELINE THROUGH - TUSING
WIRELlNE CASING GUN
TUBING CONVEYED
A
B
e
Fig. 2-44. Melhods 01 underbalaneed perloraling. 21
Productioll Optimization Using Nodal Al/d.l"sis
50
1000 SEAL~
LOCKIHG
ASSn
"
,
o 100
I
I
I
MOl' 84R
,I I
RAOIOACTIV[
W,
,.AC)(ER
~
,<
w
•" ,~
10
flJLL OPEH f>ACKEft Ofl,
"ii'
VALV[
1
"
\~
o
w
Z
'SR
V(NT
STUCK PACKER
\\
>
te
~
~
o o o o
6--.~
~:......CASING COLLAP~
1
'.\ <-
fllllNG
HfAO
0.01
legend 6
100
1000
1:1).)0
TOTAL UNDER8ALANCE PSI
Flg. 2-47. Underbalance pressure used on tubmg-conveyed perforaling in gas zones in sandstone. 22
,"N
" •
A YENT OPEN-
e
o
GUN
THROUGH
RELEASED
PACI<ER
GUN flREO
BAR OROPPfO
~ISU~c.E_
lO
:
~
,-r-
~
Fig. 2-45. Tubing-conveyed perforating techniques. 21
,. l' ~
o
cases, the surging was delayed, and, in other cases, the surging was immcdiate. Their results are summarized in Figure 2-48. 1t was also obscrvcd that a high degree of underbalance followed by surging increased the perforation size, thus rcmo\'ing sorne of lhe crushed oc compactcd zone surrounding the perforation. These results are ShOWll in Figure 2-49.
01:
,
0 100
~
>
S
o
,~ • •" ,~
10
1"'.
~
"".
<
ji
, ,
.""
•
-so•
-1000
PRíSSUItE PIHHfllTlAL lPHI
1
o
.. • •
~
o o
lOO
.8
~
SURGE.
"
o o.o;"'n "
~
w
Z
""o
"'lo
Flg, 2-48. RFR as affecled by test condllions. 23
1000
"'
~
~
11".
1-
1
. .\
o
"9'""
~-
l>. Acid Dld NOlImpfO~1l I'rodYelion
o Ac.id Okllmprove Produtto'l
lO
1
n.o 1100
-
l.-
1
1000
10000
lOTAL UNDER8ALANCE PSI
n "00
Fig. 2-46. Underba/ance used on tub/ng-conveyed perfo-
rating in oil zones in sandstone.
11\'1.
"L. !--
~
o
-soo
-1000
PllE:ssuRE DlfFtR[IIt1A/. (?Sil
Fig. 2-49. Hole vo/ume as affected by tesl condilion. 23
Reservoi,. Performance
.'
......
51
A modcl that can be used to estima te the prcssure drop through perforations was presenled by MeLeod. 14 Thís model is in tended to be used for wells that have not been stimulated through the perforations and requires estimates of several parameters that canoot be measured. McLeod prescntcd equations for gas welIs only, but simlIar equations for oil wells are also presented here. The oil flow equations do not take into account aoy reduction in pernneabílity that may be eaused by two-phase flow below Ihe bubblepoínt pressure. The efficiency of a perforated completion depends on both the reservoir and perforation components in Equalions 2-63 and 2-79. That ís
kR
reservoir permeability in the horizontal direction, anq k, vertical pernneabilily. The nomograph presented by Loeke t6 is shown in Figure 2-50. Loeke presented Ihe following procedure for obtaining a value for Sp from Ihe nomograph:
1.
Enter with the perforation length Lp on the ~pper lell stem. .
2.
Proeeed borizonlally lo Ibe appropriate perforation diameter. .
3.
Proeeed vertieally lo tbe appropríale damage or invaded zone thickness. f\·leasure a}ong the damaged zone tine honzontally from the vertical axis to the appropriate k,jk. line. This is distance b-c in Ihe nomograph. Shift Ihe vertical line from Ihe perforation diameter to the right by the distance b-c and proeeed lo Stop 4.
4.
Go verti.ally to the appropriate, crushcd-zone ratio
and (2-94A)
The laminar perforation component ineludes the effects orthe number and types ofperforations, and the effects of compaction around the pcrforations, These effects were discllssed in dctail by McLeodl" tlnd the discllssion on perforated complctions prcsC"lltcd hcre is based largcly on :'IcLcod's work. The equ
Gas (2-96)
IfsufficiC}lt data rcgarcling lhe pcrforations are known, v;:l.lucs for Sp and Sdf) may be calculatcd. Sr is a function of perforating density, pcrfoTíltion Icngth. perforation diarnctcr, phasing, wellbore radius, damaged-zone permeability, ratio of vertical~to-horizontal pcrmeability, and damaged-zone radius. Valucs of Sp may be oblained from nomographs published by Hong l5 or Lockc l6 . An equation for estimating Sr that requircs a value for vertical perrneability, was giyen by Saidikowski. 17
or relatíve-penneability lineo 5.
Proeecd horizontally lo lhe shol-density linc. Note that for 8 spf two lines exist. one for zera phasing and another for 90 0 phasing.
6.
Procced vertically to the angular phasing line.
7.
Procecd horizontaIly and r~ad the Productivity Ratio or FIO\v Efficiency, ifrequired, and the ski n factor Sr
The nomograph is drawn for a borehole size of six in. Howevcr, the effects of borehole size are partially compensating. An additional correclion for a 12-in. borchole with 160 aere spaeíng is shown. To apply this correction in Stcp 7 the horizontal linc is shifted up or do,vn befare proceeding to th~ skin factor scale. McLcod deriycd an equation for ealc"ulatíng the cffeet of flow through the compactcd zone as
. h Lp
N kR kdp rp
J¡
hf1
total fonnation thickness pcrforatcd-intcrval length
r
(2-98)
where
r(~J
wherc
1
SJp = -h- Ik ...!!..._~ k In(Id¡,/lp) LpN kdp kd
tolal formation thickncss perforation ¡ength, lotal number of perforations una1tered reservoir penncability, compactcd or crushcd zone permeability, perforation radius, and compaeted zone radius.
Figure 2-51 (reference 14) shows a schemalie ofa perforated completion and the relationship aniong the various parámeters in Equalion 2~98. Thc largcst par! of thc pressurc drop Ihrough a perfora-
Prvdllctioll Optimization UsíJlg Xvdal.-ll/.lf.\"sís
52
........ e '--'
..c +-'
O>
e
Q)
-.J
e
O
+-'
ro o .....
ll-
ID
o..
ductivity Ratio
0.5 0.25 P~rf.
18 15 ~ 12 .§..-
9 ::l ~ 6 f3- O 3 ~3
Dlam. (in.)
11.8
I
i'
l i
04 •
ji
0
I I
'. .
/
180 0
rI
1-+-+--+++- k /k l Id ~
VV
(1.0)
~ ~ ::;::.V
¡:::;;.-
o.. (f)
0
I
01
0.5
O?
~
O ~ ~"" ~b' ,c'l ¡g, ~: ~9 ~\..... ¿;¡ b- e~,,'
¡...--~
7.9 ~ 0.6 5.3 120 1.1 Borehole 3.4 ~~ol PhaSing~~ 90 Phasing ~~' 0.8 2.0 / -0.9 0.9 l-20° : ~~; 0.0 I /)' 1.0 90 ~, 1.1 -0.7
I~~
0
/6
I
Angular Phasing
o
Borehole
1.2
I
.
I
.
I 8 ?hots/Ft.,
..
't: /
0
0
-1.3
Phasing
V
J~.,.~+~~2,,¡oo/"-j--'/-+---+----+---+------i
~
Perforations Per Foot
Fig. 2-50. Loeke's nomograph. 16
lion is eaused by lurbulent or non-Darey flow lhrough the eompacted zone. The equations for calculating this effect are Oil (2-99)
Gas
B p
=
3.l61xlO-
12
Pdp ygZT
rp L2p N 2
(2-100)
The value of lhe velocity coefficien! mus! be ealeulaled using lhe eompaeled-zone permeabilil)'. The equalion is
2.33x10 10 {3dp =
k\.2 dp
(2-101)
There are ~~veral variables in the equalions for perforated completions that are difficult to delennine. These include the altered-zone permeability. Ihe compactedzone radius, the perforation length and the altcred-zone radius. Sorne of these parameters can be eslimatcd froro APr RP-43 test dala published by lhe perforaling eompanies. The following guidelines have becn rccommended by MeLeod: 14 For we/ls perforated in mud (2-102)
-. 53
Reservoir PerfomlanCe
C. Perforated, Gravel·Packed Comprétions Tbeequations for a gravel-packed completion are
PR -'Poi = (AR +Ap +.40)% +(B. + Bp + l\-;)q;
(2-94)
and
For mosl gravel-packed wells 'the formation will have a high permeability because.of lhe unconsolidaled nanire of lhe sand. This will also resull in negligible damage [rom the compacted zone around the perforations. However, lhe effed of lhe linear 1I0w lhrough lhe perforation tunnel that is filled with pack sand can cause a significant non-Darcy-flow pressure drop. The equations for A G and B G are· Oi/ (2-19")
(2-I05)
Gas Fig. 2-51. Flow into a performation. 14
12-106)
For 'wells perforated in brine
kdp kd
=
(2-107)
kc
(2-103)
k
where
where k/k values are obtained from the API test data. Guidelines for estimating k/k when no tests are available were a1so ~~.sentcd by McLeodl-l in Table 2-2.
N kG L
total number of perforations, grayel penneabilill', perforation tunnel length, and
13 - 1.47x10
TABLE 2-2
G -
Fluid in Hale
(2-108)
G
Perforating Parameter Guidelines
high solids mud low solids mud unfiltered brine fHtered brine cJean fluid ideal fluid
7
k O.55
Pressure Conditians
k,lk
overbalance overbalance averbalance overbalance underbalance underbalance
0.01-0.03 0.02-0.04 0.04-0.06 0.08-0.16 0.30-0.50 1.00
The following table, from Gurle)',18 mal' be used lo estimate. tl~e gravel permeability based on its size. Sieve Size 1()..20 16-30
2040
4MO McLeod al so suggesls lhat the compac(ed zone (hickness is usually abaut 0.5 in. That ¡s, r0/1'= rp + 0.5 if rp is in inches. If no informalion is a".ilable regarding lhe altered-zone radius, a vallle of r ti = r". + 1 may be lIsed, wherc r w is gí;;·en in ft.
5.00 X 105 2.50 X 105 1.20x105 4.0 X10'
A schematic ofa gravel-packed completion is iIlustrated in Figure 2-52. As iIIuslraled in Figure 2-52, lhe tunnel lenglh is defined as the radius of the hale minus the outsidc radius
\
ProdUCfiulI Oplimi:::alioll UsiJ)~ Nodol AJla(rsis
54
and mcthods foc qu~ntifying these en"eelS \Vece prcscntcd. A summary of thcsc methods will be prcscnlcd in {his scction.
_ - - f w ----->1
A. Oil Wells fp
An expression Cor lhe productivity \Vas presentcd in Equation 2-32 as
;b~----"_1_
h
JDiri==~-I-
J =
O.00708kh (PR -P"f)[IIl(.472I~/r ... )+S1
ind~x
r'
foc an oil well
-""'-dp p,¡lluBo
(~·32)
Any phcnomenon that causes a change in aoy parameter in this equation win cause a change in J and thus afreet intlow performance. The main paramclcrs that can ehangc are the pressure function,j{p) = klT/~
1.
Drawdown, which affects km around the wcllbore and al50 affccts Dqo'
2.
Formation damage or stimulation, which affecrs S,
3.
Depletion, which arrects h) in rhe cntire drninage volume 01' the well as PR declines below po. and
4.
Pcrforation effel:ts.
Fig. 2-52. Gravel-pack schematic.
of lhe scrcetl. In sorne cases, it is .idined as the hole radius minus lhe inside radius of lhe .:-asing. In allalyzillg perforated completi0:1.5. it is sometimes cOI1\-enient to break down lhe total pressure drawdown ¡nla (WQ separa te eomponents, thar i~. lhe prcssure drop in Ihe rcscfvoir and lhe pressurc dr('~ across lhe gnnoel pack. This can be expressed as
PR - Puf = PR - Puft + (Pl<.-:: -
Pllf) (2-109) where PlI'fs is Ihe pre-ssure existing al lh~ sand face, as iIlustrated in Figure 2-52. Mast operators agee that lhe prcssure drop across a gravel pack, Pl¡js - PII/_ 5hould be less than abour 300 psi. The equmions for lhe [wa pressure drops may be wrjlten as
Oi/
PR - P....fs PII./s -
;;;;
p.,.j =
AR % + BRu...~
(2-110)
Ac% + BG¿
(2-111)
Methods \Vece pres~I1led ror calculil[ing eaeh of thc:it cffeets. The methods thar may be applicd are:
l.
DrawdO\.... n cfTecls: a. vogel; (Equatioll 2-33) b. FClkovieh' (Equalion 2-54) e. 101l0S, el al 9 (Equatioll 2-63)
2.
Fonnation damage or stirnulation: a. Standing modification of Vogd (Flow Efficiency) (Equalioll 2-46 or 2-48) b. Fetkovich (5 is included in the cocffieicnt C) c. Joncs, et al. (5 is included in lhe coefficicnt A)
3. Depletion: a. Standing (adjustment 01'
lJo(ma\l
or J) (Equation
2-710r2-72)
Gas -2
PR 2
2 p"js 2
' = ARqsc + B Rq;
P,,¡, - P.f =
,lL "G q"
¡:L!
+ "G 'l,c
(2-112) (2-113)
The effeels of eompletioo melhod on a well's produeing capacity will be illustrated in a subsequent chaplee.
VII. INFLOW PERFORMANCE SUMMARY Melhods have been presented for eonstrueting for real oc present-time conditions foc both oil and gas wells.
Prediction of lhe effects of depletion oc decreasing reservoir pressure- 00 the inflow perfonnance was discussed,
••
b. c.
Fetkovich (adjustment of C) (Equalion 2-74) vogel-Felkovieh eombilled (adjustmellt of qo(m,,) O[ 1) (Equation 2-78)
4. Perforation Erfeets: a. Loeke b. MeLeod (Equalioll 2-94)
B. Gas Wells The inf1ow-perfonnance equation for gas wells is not as sensitive to pressurc as that for oil wells because lhe gas saturation and therefore the penneability to gas rernain fairly constant except for the case of retrograde
.',"
Reservoir Pe/formalice
55
condcnsate rcscn'oirs. The following methods were presented for accounting for various cffects. l.
2.
_.
Drawdowll efTects: a. Baek-prcssure equation (Equation 2-80) b. Jones, et al. (Equation 2-79) c. Darcy radial-Oow equatíon (Equation 2-28)
9.
10.
Formation damage or stimulation: a. Back-prcssurc cquation (S is included in the cocfficicnt C) b. Jones, et al. (S is included in the coeffícient A) c. Darcy (S is included in lhe cquation) Turbulence effects: 3. Baek-pressure equalion (lhe vatue of lhe exponent 11 is an indicalion ofturbulcnce) b. Jones, el al. (lhe cocfficicnt B or the vaJuc of A'I A indicates lhc cffccts of lurbulence) c. DaTe}' (Ihe turbulence coemcicnl D is ao indication of turbulence)
--l.
Depletion-thc ,·;:tllIes of e ar A and B can be adjusted fOI" ehanges in ~g and Z-faclOr witll pressure change. (Equation 2-86)
.:;
Perforation Effects: a. Locke b. McLcod (Equation 2-94A)
11. 12.
13. 14. 15. 16. 17. 18.
VIII. REFERENCES
19.
Gilbcrt, \\'. E.: "Flowing and Gas-Lift \Vcll Performance:' API Drill. Prod. Pmctice, 1954. Odeh, A. S.: "Pseudo Steady-State Flow Equation and Productiyity Index for a \Vdl with Non-circular Drainage Arcíl," Mobil Rcscarch and Development Corporalion. McCain, A" E.: The Properfies o[ Pefroleum Flllids Petroleulll Publishing Co., Tulsa, Okla., 1973. Amyx, J. w.. Bass, D. M., and Whiting, R. L: Pefroleum. Reservoir Engil1eering, McGrnw-HiJI, Ncw York, 1960. Vogcl, J. v.: "innow Performance Relationships for Solution Gas Orive Wclls," JPT, Jan., 1968. Standing, M. B.: "lnOow Pcrronnance Relationships fOl" Damaged \Vclls Producing by Solution Gas Drive," JFT. Nov., 1970. \Vcllcr, \v. T.: "Rescrvoir Perfonnance During TwoPhase Flow," JFT, Feb., 1966. Fetkovich, M. J.: "The Isoehronal. TestMg of Oil Wells": Paper 4529, 48th Annual Fall Meeting of
20.
2L
j
5.
7. 8.
22.
23.
24.
SPE, Las Vegas, Nev., 1973. Jones, L. 0., Blount, E. M., and Glaze, O. H.: "Use of Short Tenn Multiple Rate Flow Tests to Predict Performance of Wells Having Turbulence," SPE 6133, presented at SPE 51st Annual Fall Meeting, New Orleans, LA, 1976. Firoozabadi, A. and Katz, D. L: "An Analysis of High Velocily Gas Flow Through Porous Media," JPT, Feb., 1979. Standing, M. B.: "Conceming the Calculation of InOow Perfonnance of Wells Producing frolll Solution Gas Drive Reservoirs," JPT, Sept., 1971. Mattar, L. and Lin, G.: "Validily of Isochronal and Modified Isocbronal Testing of Gas Wells," SPE 10126, presented at 561h Annual Fall Meeting, San Antonio, TX, 1981. Matthews, G. S. and Russell, D. 0.: PresslIre Bllildllp and Flow Test ill IVells, SPE Monograph 1, 1967. McLcod, H. O.: "Thc Effect 01 Perforating Conditions on Well Perfonnance:' JPT, Jan,.1983. Hong, K. G.: "Producti\'ity of Perforated Completions in Formalions With and Without Damal!e" JPT, Aug., 1975. - , Locke, S.: "An Advanced Method for Predictin. the Productivity Ratio 01 a Perforated Well," JFT, Dec., 1981. Saidikowski, R. M.: "NulTIcrical Simulations of the Combined Effects of \Vellbore Damage and Partial Penetration," SPE 8204, Sept., 1979. Gur1cy, D.G.. Copeland. C. T. and Hendrick. J. O.: "Dcsign Plan and ExecutiOll of Gravel-Pack Completions:' JPT, Oet.. 1977. Sherrard, D. \\'.. Brice, W. B.. and ~lacDonald, D. G.: "Applieation of Horizontal Well5 at Prudhoe Bay." JPT, Nov., 19$7. Giger, F. M., Combe, J., and Reis.5, L. H.: "L'inlerest du forage horizontal pour I'exploitatíon des guiserncnts d'hydrocarbures," Rel'lle dt? /'JI/sf. Fral1cais de Petrole, May-June, 1983. Bell, W. T.: "Perrorating Underbalanceu-Evolving .. Techniques," JPT, Oct., 1984. King, o. E...~nderson, A., and Bingham, M.: "A Field Study of Undcrbalance Pre5sure~ Necessary to Obtain Clcan Perforations Using Tubing-Com"eycd Perrorating," JPT, June, 1986. Regalbuto, J. A. and Riggs, R. S.: "Underhalanced Pcrforation Characteristics 3S Affcctcd by Diffcrential Pressure," SPE Prado Engineering, Feb., 1988. Bendakhlia, H., and Aziz, K.: "lnOow Perfonnance Relationships for Solution-Gas Orive Horizontal Wells," SPE 19823, 64th Annu,1 Fall Meeting of SPE, San Antonio, Texas, Oct., 1989. ~
Flow in Pipes and Restrictions
3
1. INTRODUCTION In Chapter 1, it was pointed out that lo determine the perfOrmíll1Ce of any producing wel!. it is necessary to be ab1c lo ca1culate Ihe prcssure losses in aH ¡he componcnts in ¡he systcm. Thesc prcssure losses and
wh~rc
they occur
in the systcm are illuslratcd in Figure 3-1. Proccdures ror ca1culating lhe prcssure 1055 in Ihe reservoir, Cpl = PR - P"'fs' \VeTe prcsented in Chapler 2 ror both Di) and gas \Vells. Calculation of pressure 1055 acfOSS the compJetion, fJPl = Pnj.i - p,,¡. was also outlined. In this Chapler, methods to calculate yalues for ÓP3 through ÓPg \VIII be prcsented. These pressure losses may occur in cither lhe inflow lo the node or lhe outf1ow from the Hode. In many cases, Ihe node pressure will be select~ ed as nowing bottomhole pressurc p,,{, Calculation of the nade prcssure for lhe olltflow would (hen take the following form:
p."1' + ópJI. + ¡'j,PrM~ + Ó.Plt\'r,¡~~
whcrc P.H!P
¡jPjI
J[J..ho/';e !Jpwhing
:J.p.v.
separator pressllrc, pressure drop in the flowline, prcssure drop in the surface choke, pressure drop in the tubing, prcssure drop in lhe subsurface safety val ve, and pressure drop in 311Y olher rcstriction.
As \\'as discusscd earlicr aH these prcssure drops are fu 11 ct lons of producing rate 2nd the characteristics of the cOl1lponcnts. In the case of single-phase flow, either liq~
uid or gas, Ihe pressure drops can be calculated easily, as long as component characteristics such as size and roughness are knmvn. Cnfortunately, most producing oil or gas wells operate under multiphase conditions. There will usuaHy he sorne free gas produced along wilh the 011 in an oi! weH, and most gas wells will produce cithcr waler' or condcnsate al(1ng with the gas. The presence (lf both liquid and gas in lhe component complicales the rressure 1055 caIculatiolls immenscly. As average pressure existing in a component ehanges, phase changcs occur in the Ouids. This causes changes in dCJ\sities, velocities, ...olumes of eaeh phase, and fluid properties. Also, temperature changc.s accur for flo\V in the piping system and restrictians. This was not a problem in calculating the reservoir performance, since reservoir temperature remains constanL Calculatian ofthe pressure changc with dist3nce, or pressurc gradient, at any point in the systelTI, requires knowledge of the tcmperaturc existing at that point. Therefore. procedures to estimate heat or temperature l05ses must be available. Design and analysis of a system Ín which two-phase flow is occurring requires a thorough understanditig of lhe physical phenomcna as weH as lhe basic theory and equatioos. In this chapter, the basic equalions and concepts will first be presented in considerable detail. Procedures to estimate the necessary fluid properties as functions of pressure and tcmpcrature will then be givcn. Empirical correlations for calculating pressnre losses in both wclls and pipeline will be presentcd and suggestions of which rnethod to use for particular conditions will be made. The use of prepared pressure traversc curves for making rough estima tes 0[. press'ure losscs in wells and pipclincs wilI be discussed, and the effects o"r changihg conditions in wells or fields will be presentcd. Finally,
57
PruductiOll Oplimizalioll Using l\'odal.·JJlalysis
58
r;=:::::::::~-~ SALES L1NE GAS
SEPARATOR
BonOMHOLE RESTRICTION
Ó.P3 ~ (PUR - POR) Á
Ó. Pl ilP2 il P3 Ó.P4 il Ps il Ps il P7 Ó. PB
LOSS IN POROUS MEDIUM PR-Pwfs LOSS ACROSS COMPLETION Pwfs-Pwl RESTRICTION PUR-POR " " SAFETY VALVE Pusv-Posv " " SURFACE CHOKE " P"h -Pose " FLOWLlNE IN Pose -Psep = " TOTAL LOSS IN TUBING P\'ñ-Pwh Pv.!I-P sep = " " " FLOWLlNE ~
~
~ ~
~
~
~
~
~
~
Fig.3-1. PossibJe pressure losses in complete system.
lUclhods for caIculating pressure losses in short restríctions, sueh as ehokes, SSSV's, and pipe fillings, will be
gi"cn.
11, BASIC EQUATIONS AND CONCEPTS Pressure gradients occurring during two-phase flow in pipes can be ca1culated ir aH the energy changes that take place in the fluids can be predicted. In lhis section, thc basic pressure gradieol equalion will be derived thal will be applieable for flow of any fluid in any piping system. This equation will then be adapted fOfo various piping systcm conditions and fluid conditions.
cnergy of a fluid cntcring a control volumc, plus any shaft work done on ar by the fluid. plus any hcat cnergy added lo or takcll from lhe fluid, must cqual lhe energy leaving the control voIumc. Figure 3-2 may bc used lo illuSlratt:: this principie. Considering a steady statc system, lhe cnergy balance may be written as lm'~
mgZ
,
I
UI'+PIVI+-' + __1 +q +H~ 2g,· g, ~
mgZ v ' +p,Vz +/tly; 2 -+-2
2
-
g....
(J-2)
ge'
where
A. The General Energy Equation The theorctical basis for most fluid flow equations i5 the general energy equatioo. an expression for the balance or conservation of energy between two points in a syslem. The energy equation is developed first and, using thermodynamic principIes. is modified to a pressure gradient equation formo The steady slate energy balance simply stales that the
V'
intemal energy, energy of expansion Dr comprcssion, kinetic energy, potential encrgy, heat energy added lo fluid, and work done on lhe fluid by lhe surroundings
pV nn;J./2gc mgZlgc
q' ,
w,
Dividing Equation 3-2 by m to obtain an energy per unit mass 'balance and writi~g in differential fonn gives:
.'
Flow in Pipes ol1d ResfricfiollS
59
-1
I
Heat Exchanger
I
-11 11
q
Iz
I
Pump or
¡-
Turbine
z1 I
I
0(c!:==::::::,
ll__ __
2
_----'Reference Plane_1
L
_
I
Fig. 3-2. Flow system control volume.
I'J [
I'
and
For an irreversible process. thc Clausis incquality statcs that:
dS? -dq - T '
or TdS
~
-dq +dL"
where dL w =: losses duc to irre\'ersibiJities, such as friction. Using this relationship and assuming no \Vork is done on or by the nuid, Equation 3-5 becomes:
dp ~'dll o-+-+"'-dZ+dL P g< g, •
dI'
dh~TdS+
~O
p
If\Ve consider a pipe inclincd at some angle izontal, as in Figure 3-3, sincc dZ =: dL sin e:
or
dI' dU~TdS+p-d
r¡; IJ p
(3-4)
whcre
h
enthnlpy,
S T
entropy, and tcmpcrature.
ni" g + - + "--dZ +dq +dW, ~ O p g" g"
rlp
TdS + -
(3-5)
e to the hor-
dpvdvg _ -+-+-dLsmS+dL ~O p gc g" ..
Mu!tiplying !he equa!ion by p/dL gives: dI' pvdv g dL -+--+-psinS+p-' ~O dL g
Substituling Equntion 3-4 into Equatipn 3-3 and simplifying rcsulls in:
(3-6)
(3-7)
Equation 3-7 can be so¡ved for pressure gradient, and if a pressure drop is considered as being positivc in the diree!ion of !lo,," dI' dL
g
, 8 +--+ pnfv (dP) KdL dL ~
-~-psm
g<
(3-8)
Prodllctioll Optimiza/ion Using Nodul AJ1l1~D'jS
60
- (tldLP )
I
which. is thc well-known Fanning equation. In tcnns of a Darcy-Wiesbaeh or Moody frietion faetorJ~ 41', oud
I
ó'-:/;:
// /'
;::::; ~
I
i
dZ
e
//
-dP) ( dL ~
I
1
~
2f' p/ g,d
.JI
fpv' 2g,d
(3-11)
The [rictian factor foc laminar flo\\' can be dctennined analytically by combining Equation 3-11 with lhe HagenPoiseuille equation foc laminar flow:
dX Fig. 3-3. Flow geometry.
d'g, (dP )
v~ 32fl dL
f
oc:
whcre
dP) dL. ( dL f =P dL i$ lhe pressure gradient due ta viseous shear oc friction 1055es.
In horizontal pipe f1ow, lhe energy losses oc pressure drop are caused by change in kinetic energy and friction
Equating the cxpressions foc [riclional pressurc gradient gives
the
32flv
pipe wall, lhe ratio of wali shcar stress (t,J lO kinetic energy per unit volumc (pv2l2gJ reflects lhe relativc importance of wall shear stress lO Ihe totallosses. This ratio fornls 3. dimcnsionless group and defines a frictian factor.
g,d'
losscs only. Since mast of the viscous shear occurs
.r:::;
L".
pv'i2g,
2t",,·K
PT
al
[PI -( P, - : dL )]
oc:
f ~ 64fl ~ pn/
(3-9)
Tú evaluate lhe waH shear stress, a force balance between pressure forces and waH shear stress can be fonned. Refening lo Figure 3-4:
~' ~ '. (nd)dL
or (3-10)
fpv' 2g,d
64 N Rc
The dimcnsionless group, NRe = (p \' d)/fl. j~ (he ratio of fluid momentUlTI forces to viscous shear [orces and is known as the Reynolds number. It is used as a parameter lo distinguish betwtecn laminar and turbulent fluid no\\'. Foe
engineering calculations. the dividing poinl between laminar and turbulent flow can be assumed to occur al a Reynolds munbcr of2100 for flow in a circular pipe. The ability to predict flow behavior under tmbulent flow conditions is a direct result of extensive experimental studies of velocity profiles and pressure gradients. These stud¡es have shown lhal bOlh velocily profilc and pressure gra-
Subslituting Equation 3-10 inlo Equation 3-9 and solving ror the pressure gradient due to friction'gives:
dient are very sensitive to characteristics ofthe pipe wall. A ¡ogical approach to defining friction factors is to begin with lhe simplesl case, i.e., lhe smoath wall pipe, proceed to the partially rough wall and finally lo the fully rough wall .
. Only the mast accurate empirical equations availab!e fOí friction factors are presented here. For smooth wal! pipes, several equations have beeo developed. each valid over difIerent ranges of Reynolds numbers. The equation that is now used mast commonly since it is explicit in f and a1so covers a wide range of Reynolds numbers, 3000 < N., < 3 x lO', was presenled by Drew, Koo, and ~cAdams.1 Fig. 3-4. Force balance.
f
~ 0.0056 +0.5N;;:"
(3-12)
Flow in Pipes and Restrictions._ .....
61
An equation proposed by Blasius may be used for Reynolds numbers up lo 100,000 for smoothÍJipes.
j=0.316N;:"
(3-13)
The inside wall ofa pipe is not normallysmooth, and in turbulent flow) the ronghness can have a definite effect on the frictioo factor and thus the pressure gradient. Wall roughness is a function of the pipe material, the method of manufacture, and lhe environment to which it has beeo exposed. From a microscopic sense, wall roughness is not uniformo Individual protrusions, indentations, etc., vary in height, width, length, shape and distribution. The absolllte roughness of a pipe, t, is lhe mean protrudíng heighl ofrelati"ely uniformly distribuled and sized, tightIy packed sand grains that would give lhe same pressure gradient behavior as the actual pipe. Dimensional anarysis suggests that lhe crfect of roughncss is not due to its absolute dimensions, but rather to its dimensions relativc lo the inside diameter of lhe pipe, Eld. In turbulent flow, the effect of wall roughncss has been found to be dependent on both the relalive roughness and on lhe Rcynolds numbcr. If the laminar sublayer that cxists within lhe boundary layer is thick enough, then the bchavior is similar to a smooth pipe. The sublayer thickncss is directly relatcd to the Reynolds nllmber. N¡kurndse's~ famolls sand grnin expcriments formed the basis for obtaining friction factor data for rough pipes. His correlalion for fully rough wall pipc is still thc hes! onc availablc. The friction factor may be calclllated explicitly from:
J7I = 1.74 -2 log ('"~I J Thc cquation thal is used as the basis for rnodern frietion factor charls \Vas proposed by Colcbrook and White) in 1939.
_1_=1.74-2l0gr2E+~J J7 ,d y,JJ
(3-1~)
The [rielion factor cannot be extracted rcadily from the CoJebrook equation. By rearranging ¡he cquation as fo1lows, a trial and error procedure may be llsed to solve the equatioll for friction factor.
r;=
1.74 -2lo
(
2E + 18.7 gdNTf.
J
K~"JI:
\'alucs of/g are estimaled and thenf: is calculated until
J. andJ., agree to an aeeeplable toleranee:Üsing the Drew, K.oo and McAdams. equation as an initia\ guess is rccommended. Afler eaeh unsuceessful iteration, the ealculated va1ue beco mes the assumed value for the next iteration. AIso, if more than ene pressure 105s calculalion is lo be made as in the case of the iteratíve procedures discussed in la1er chapters, lhen the "converged" value of the previOHS ealculation should be used for the initial guess in the next calculalion. Convergence using this method is rapid, normally taking only 2 or 3 iterations. The variation of single,;phase friction factor with Reynolds number alld relative roughness ·is shown graphieally in Figure 3-5. The Colebrook equation may be applied lo flow problems in lhe smooth, transition and futly rough zones of turbulent flow. For large values ofReynolds number, il degenerales to the Nikuradse equ.ation. An explicit friclion factor equation was proposed by .Jain 4, and compared in accuracy to the Colebrook equation. Jain found that for a range of relative roughness between 10- 6 and 10-' and a range of Reynolds number between 5 x lO~ and lOs the errors were within ±I.O% when eomparcd wilh the Colebrook equation. The equation gives a maximum error of 3% for Reynolds numbers as low as 2000. The equation i5:
I [E- +21.25 -=1.I4-2log -d N;,'
J7
J
Thc dctcrmil13lion of the value to use for pipe wal! roughness in. the friction factor equations is sometimes difflcult. Jt is imrortant to emphasize that E is not a property that is physically meas\lred. Rather, it is the sand grain roughness that \Vould reslllt in the sallle friction factor. The only way this can be evaluated is by comparison of the behavior ('Ir a normal pipe with ene that is sand roughened. Moody has done this and his results, givcn in Figure 3-6, are still the accepted values. These valucs should nol be considered inviolate and could changc significantly because of such things as paramn dcposition. eros ion or corrosion. Thus, ir measured prcssure gradi~ cnts are available. a friction factor aud Rcynolds number ean be ealculated and al1 effeeti"e ,Id obtained from the Moody diagram. This value ofvdshould thenbe used for future predictions untiI updated agaio. If no information on roughness is a"aHable, a "alue of, = 0.0006 fI is reeommcnded for tubing and tine pipe that has been in service for sorne time.
Examp/e 3-1: A IiQuid 01 specifie gravity 0.82 and viseosity 01 3 ep (.003 kglm see) fiows in a 4 in. (101.6 mm) diameler pipe at avelocity of 30 fUsee (9.14 mlsee). The pipe material is ne"N commercial steel. Calculate the friction
PrvducIiol/ OplilJlizlllivlJ Csillg Nodal AI1.:!ysis
62
O. 1
, ..I
0.09
lamll'~~~'bC.'¡.1 !lo..., tone
o.oa
, ,.
0.0 1
~
,
•
0.0
.~
¡" ..!.' 111 Wholly IQuCh
Tr¡nllllOl1 tOUlh
:
I
..
<
,
"
,<
,
t
0.0
,
2
..
,
~
..
.--<
J:t 0.01 5
0.00
•
10
,
1110 J
,,
..
,
,
.. , ,
•
I
I ",'
,
" • 10 •
2{IO; :1
•
..
O O
8 10'
0.000\
,~
ZIlcl1J
"•
i
0.000.2
I
...,
Ul Ul
O.OOO~
"1
,.
(}j
O~~'ill
i""'i~II
,
lOO') 1
°002
I
, I I
,1 • lO'
O.00",
.. "
~
O.006
, , .', , ..
j!
,
" 0.009
O.01 O.008
,"
Smoolh
0.0 1
O.015
.. ,.
o,
o. 02
,, ,
,
-
/ti 0.02 5
'I-l
§
o.O,
..,
<.
"!mJ ,: ; 00
O 05
I1II I 11 I
o.
0.0 5
~
"
1
,
;
o.ooo.o~
I
..
• IOl ......... l la ¡Jo
•
..
0.000.01
• 'O •
N = pvd R
e--~
¡.L
Fig. 3-5. Friction laclors lor pipe flow.'
factor using bolh the Calebraak equalian and lhe Jain equation.
A lhird trial using 19 = 0.0182 gives 1, = 0.0182. Jain solution:
1=[1.14 - 2 Lag (rfd + 21.25/N~;')r' Solutíon: Fram Figure 3.6, for cammercial steel, ./d = 0.00045. Colebrook Solution: Use the Drew, Kao and McAdams equalian for a first guess. N•• = P vdf~ =(820)(9.14)(.1016)1.003 = 253,82 4 1, = 0.0056 + 0.5N••-O· 32 =0.0056 + 0.5 (253.824)
-0.32
1,=0.015
,ff,r'
1, = [1.74 - 2Log(2f1d + 18.7/N ..
/, = [1.74 - 2 Lag (2(.00045)+18.7/253,824
J.015r'
f, =0.0183 This value is not clase enough to 'g. therefore. another trial is required using f9 = 0.0183: f, = [1.74 - 2 Lag (2(.00045)+ 18.7/253.824 .J.0183 )1"
f, ~ 0.01.82
I = [1.14 - 2 Lag (0.C{)045 + 21.25/(253, 824) o')]" 1=0.01826
B. Single-phase Flaw
Now that equarions and procedurcs have becn presented for evaluating the frietion factor in single-phase flow, the pressure gradieOl equation deri ved previously can be furlher develaped. Combining Equalians 3-8 and 3-11, lhe pressure gradiem equation, which is applicable to any fluid at any pipe inclinarion anglc becomcs:
dp g . -=-p Sin dL g,
e+--+-jpv' pl'dv 2gc d
KdL
(3·16)
wherc the frietion factor, f. is a funetion of Reynolds number and pipe roughness, This relationship is shown in
63
Flow in Pipes and Restrictions" .....
'\,J
0.05
::
I
I
I
1"- . I
"'-1 11'l
j
11
~
I~
I
I
I
: I
! -¡
II I I
I "1 I
lOO
JOO
Fig. 3-6. Pipe fOughness.5
the Moody diagram (Figure 3-5). The total pressure gradicnt can be considered lo be camposed of three distinct componcnts, that is:
where (dpldL),.¡ ~ gp sin S/g, is the eomponenl due lo polentia! energy or clevalion changc. It is aIso ,referred to as the hydrostatic component, as it is the only componcnt that would apply at conditions of no flow. (dpIdL)¡ ~ fpv'/2g,d is the eomponent due lo frielion lo~es.
(dpldL )aee ~ p"dvlgedL is !he eomponent due lo kinelic energy change or convective acceleration. Equation 3-16 applies for any fluid in sleady stale, onedimensional flow for which j, p, and v can be defined. Definition ofthese variables is what causes most ofthe diffieulty in deseribing two-phase flow. In two-phase flow, f may be a function of other variables besides the Reynolds number and relative roughness. Sorne aspects of the pressure gradient equation as it applies lo single-phase flow are diseussed lo deve!op a Ihorough underslanding of eaeh componen! bcfore modiIYing il for two-phase flow. The elevatíon change or hydrostatic component is zero for horizontal flow only. It applies for compressible or
Producrion Oplimizatioll Using Nodal A/l..Jlysis
64 incompressible, steady 5tale oc tcansient f10w in both vertical and inclincd pipes. Far downward flow, Ihe sine of the angle is ncgatíve, and the hydrostutic prcssure ¡neceases in the dircction of flow. lhe frielion los5 eomponent applies for any type of flow al any pipe angle. It always causes a drop of pressure in the direction of nO\"'. In laminar flow, the friction losses are linearly proportional lo lhe fluid veloeity. In turbulenl flow, the [dettan losscs are proportional lo yn. where 1.7~n~2. The kinetic encrgy change oc acceleration component is lera foc constant area, incompressible flaw. Far any flow caodilion in which a velocity change Decurs. 5uch as COInpressible flow. a pressure drop will oceur in the direction of the velocity ¡ncrease. Although sing1e-phase f10w has beco studied extensively, it still involves an empirically detennined friclian factor for turbulent f10w calculations. Thc dependence ofthis friction factor Oll. pipe roughness, which must usually be estimaled, makes lhe calcuJal~d pressure gradienES subject to considerable error. Single-phase, incompressible or slightly compressible liquid flow is a trivial solulion of the pressure gradient equation. Single-phase compressible flow of gases is a more complcx problem to solve and ís covered in dctail later. Single-phase, compressibLe transient flow is an extrerncly complex problem and is beyond Lhe scope ofthis book. The preceding descriptions are not meant to be an exhaustive coverage ofsingle-phase flow ofNewtonian fiuids in pipes. As stated previously, the principal xeason for including the material is to fonu a finn foundation for the more complicatcd analysis of two-phase flow.
Example 3-2: Caleulale the pressure drap that oecurs in a 200 m (656 ft) seelion 01 100 mm (3.94 in.) diameler line pipe when a liquid having a viscosity of 0.05 k9/m-see (50 ep) and a density of 900 kg/m 3 (56.18 Ib",lft3) ftows al arate of
(a) 3.93 x 10·3m3/see (0.135 ft3/ see) (b) 2.355 x 10·2m3/see (0.83 ft3/ see).
So/u/ion (a) v
~ q/A ~
NRe
~
3.93 x 10· 3/n (0.1)2/4 ~ (900)(0.5)(.01)/0.05
P v d1J.
~ ~
0.5 m/see 900
8ince N Re < 2100, the flow is laminar, and f is jnde-
pendenl of pipe roughness. (~
64/NRe
~
64/900
~
.
0.071
bp~( P v2U2g¿J ~ 0.071 (900)(0.5)2(200)/(2)(1)(0.1)
bp ~ 1597? N/m2 ~ 15.975 k Pa (2.31 psi)
(b) v ~ q/A ~ 2.355 x 10·2 /n(0.1)2/4 ~ 3.0 m/~ec NRe ~ P v dl~ = 900(3.0)(0.1 )/0.05 ~ 5400 Since NRe > 2100, the flow is turbulent and f dep<.;nds on Reynolds number and relative roughness. As.sume E~
0.183 mm (0.0006 fi).
Using the Jain equation fer frktion factor, (~[1.14-2
Log Eid+21.251N;;')'
(=[1.14-2 Lag (0.183/100+21.25/(5400)")]"' ~ 0.0393 bp ~ ( p v' V2g,d =0.0393 (900)(3)'(200)/(2)(1 )(0.1 ) óp ~ 3.183 x10'
Nlm' ~ 318.3 kPa (46. 2 psi)
C. Two-phase Flow Introduetion ofa second phase into a fiow stream complicates the analysis of the pressure gradient equation. Thc pressure gradient is increased for the same mass flow rate, and the flow may devclop a pulsating naturC. The tluids may separate because of differences in dcnsities and flow at dilferent velocities in the pipe. A rough interface may exist between the liquid and gas phases. Propertics sLlch as densities, velocity, and \"iscosity, which are relatively simple for ~ndividllal fiuids. become very dinicult to dctenlllile. Befare modifying [he pressure gradienr equation for twophase flow conditions, certain variables unique to a twophase, gas-liquid mi:xture must be dcfined and cvaluat~d. l. Th'o-Phase Plo,,· Variables CalcuJation of pressure gradients requires values of flow conditions such as velocity, and fluid propcrties sueh as density, viscosity, and, in sorne cases, surface tension. When these variables are calculated for two-phase flow, certain mixing rules and definitions unique 10 this application are encountered. This section will define and analyze sorne of the more important properties that must be undersload beforo adapling lhe previously derived pressure gradient equation for two-phase eonditions. In lhis text, two-phase flow implies gas-liquid f1ow; however, the liquid phase may include t\\'o immiscible fluids 5uch as water and oi!. Methods for analysis of a ¡iquid phase that consists of any two eomponents are discussed Iater. a. Liquid Ha/dI/p. Liquid Holdup H L• is defined as the fraction of an element of pipe that is occupied by ¡¡quid at sorne instant. Ibat is
HL = Volume ofLiquid in a Pipe Element Volume ofthe Pipe Element
Flow in Pipes and Restrictions., ......
65
EvidentIy, if the volume eIement is small enough, the liquid holdup will be eilher zero or one. It is necessary lo be able to delermine liquid holdup lo calculate such things as mixTure densíty, actual gas and liquid velocities, effective viscosity and hcat transfer. In the case of fluctualing Oows, such as slug Oow, lhe Iiquid hoIdup al a point changes períodically and is taken as the time-averaged value. The value of liquid holdup varies from zero for singlephase gas Oow lo one for single-phase liquid flow. Liquid holdup may be measured experimentally by several methods such as rcsistivity or capacitance prohes, nuclear densitorneters, or by trapping a segment of the flow stream between quick-closing valves and measuring the volume of liquid trapped. A value for liquid holdup cannot be calculated analylically. 1t must be detennined from empirical correlations and is a function ofvariables 5uch as gas and Iiquid properlies, flow pattern: pipe diamcter and pipe inclination. Thc relativc in-situ volume of liquid and gas is 50rnetimes expressed in terrns ofthe voIume fraction occupied by gas called gas holdup H g , or void fraction. Gas holdup is expresscd as :
evaluate because of the gravitational separation of the phases anc\ lhe slippage between lhe phases. The density of an oil/waler mixture mal' be caleulaled frum the oH and water densities and flow rates ir 00 sJippage betweeo the oil and water phases is assumed.
p, = Po/" +P./w
(3-19)
where
¡.=~ qo+qw
(3-20)
and
/.=1- ¡. Calculation of the density of a gaslliquid mixture requires knowledge of lhe liquid holdup. Three equalions for twe-phase density have becn used by varíous investigalors of two-phase Oow. p. =.p,H,
+ p,H,
(3-21) (3-22)
H,=I-H, (]-23)
b. No-Slip Liquid Holdup. No-slip holdup, AL, sometimes callcd input liquid content, is defined as the ratio of ¡he volume of liquid in a pipe clement that would exist if the gas and liquid traveled al the same vclocity (no slippage) divided by the volume of the pipe cIernen!. It can be calcuIatcd directly from the known gas and liquíd ínsitu flow rates from:
Equation 3-2l is t1sed by most in\'estigators to deter~ mine the pressure gradient due to elevation changc. Sorne correlations are based on the assumption of no-slippage and therefore use Equation 3-22 for t\Vo-phase densily. Equation 3-23 is used by sorne iovestigators to define the mixture density used in caIculating the friction-loss tenn and Reynolds number.
(3-18)
where qL is thc sum ofthe ín~situ oil and water no\\' rates and qg is the. in-situ gas flow ratc. lhe no-slip gas holdup or gas void fraction is defined as:
d. Veloei/y. Many two-phase flow correlations are based on a variable called superficial velocity. The superficial velocity of a fluid phase is defined as lhe vclocity lhat phase would exhibit if it Oowed lhrough lhe lotal cross sectional area of the pipe atone.· The superficial gas velocity is calculated from:
q,
VJg=-
(3-24)
A
c. Density. AH fluid flow equations require that a value of tbe density of the fluid be available. The density is inyolved in evaluating the total energy changcs due to potential energy and kinetic energy changes. Calculation of density changes as prcssure and temperature changc requircs an equation of state for the fluid under consideralion. Equations of state are readily av,ailable for singlcphase fluids and are prescnted latero When two irnmiscible liquids sueh as oil and water Oaw simultaneausly, the definition of dcnsity becomes more complicatcd. The dcnsity of a l10wing gas/liquid mixtur~ is vcry difficult to
The aclual area through which the gas Oows is reduced by lhe presence of lhe liquid to AH.. Therefore, lhe actual gas velocity is caIculated from: (3-25)
where A is lhe pipe area. The superficial and actual'1iquid velocities are similarIy calculated from:
Prodlfctiull OplimizatioJl Usillg Nocla! Analysis
66
qL
(3-26)
V=~
(3-27)
V'L
=A AHL
L
Since H g and HL are less than one, the actual velocities are grealer than the superficial velociries. The two-phase oc mixture velocity is calculated based on the total in·situ flow rate from the equation.
110 =1l,A L +1l,A,
(3-32)
~, = I1~L XJl~·
(3-33)
11, =1l,HL +1l,H, (3-34) The viscosity of an oilJwater mixlur~ i5 usually calculatcd by using the fractions of oil and water tlowing in the mixture as weighting [actoes. The mast commonly used equation is (3-35)
(3-28)
As has been stated previously, the gJ.5 alld liquid phases may travel at different velocítíes in lile pipe. Some investigators prefer to cyaluate the degree of slippage and thus the liquid holdup by determíning a slip vclocity vS ' The slip vclocity is defined as the diffúence betwecn the actual gas and liquid velocities by:
v,
Vsg
r¿
= \'g -vL =H-H
,
(3-29)
,
Using the previous definitions roc lhe yacious velocities, altemate fonns of lhe cquations foc no-slip and aclual liquid holdup are: (3-30)
This equation i5 not valid if an oil/water emulsion is formed. The viscosities of natural gas, erude oil and water may be estimated from empírical correlations, deseribcd in the next seetion, if measured viscosities are no-' available.
f Swface Tension. Correlations for the int~rfacial lensian between water and natural gas and eructe oil and natural gas as functions of temperature and pressure are given in the next section. Tile interfacial tension depends on other fluid properties such as oil graúty, gas gravity and dissolved gas. When the ¡iquid phase contains borh water and oil, the same weighting factors as used Cor calculating density and viseosity are uscd. That is: a, = ajo +a"J.,
;lIld
v-\' • m
2
[
+ (\'m -\') +4\",· S J sL 2v,
(3-36)
where
J"2 (3-31)
Examp/e 3-3: Show lhal lor lhe condilion 01 no-slippage between phases (vL = v,). lhen H L = AL. So/u/ion: By definilion,
=qL/A HL• Vg =q¡A{I-HJ and since VL =Vg tor no slippage, VL
qL/A H L = q¡A(1-Hd
", (JI\'
oil surface teosian, and water surfacc teosian
2. ModificG(ion o/ (he Pressure Gradielll Equation for Two-Phase Flol1' The pressure gradient equation, which is applícable to any fluid flowing in a pipe inclined at a given angle 8 from horizontal, was given previously as:
dp =(dP) dL dL w + [dP) dL / + [dP) dL ~<
(3-17)
a. Eleva/ion Change Componen/o For two-phase !low the elevation change component beeornes
qL (l-Hd = qg{HJ HL
=q¡l{qL + q,) =AL
e. Viscosily. The viscosity of the flowing fluid is used in determining a Reynolds number as well as ather
dimensionless numbers used as correlating parameters. The concepl of a two-phase viscosity is ruther nebulous and is defined dilferenlly by various investigators. The folJowing equations have been used by various investigators (o calculate two~phase, gas/liquid yiscosity:
(3-37)
where p, is lhe density of the gaslliquid mixture in lhe pipe elernent. Considering a pipe element that contaíns liquid and gas, the densily of lhe mixture can be calculated from Equalion 3-21. If no slippage belween the gas and liquid phases is assumed, lhe density term is defined by Equation 3-22. Use 01 Equation 3-2t involves the
Flow in Pipes and Restrictions .....
67
detennination of an accurate value of liquid holdup HL> whereas the density defined in Equation 3-22 can be calulaled from the in-situ gas and Jiquid flow rales.
b. Frietion Component. The friction component becomes:
(3·38)
where f, p and vare defined differenlly by different ínvestigators. The friction component is not analytically predictable except for the case of laminar, single-phase flow. Therefore, it must be detennín'ed by experimental means or by analagies to single-phase flow. The method that has received by far the mast attention IS the one rcsulting in two-phase friction factors. Among the mast camrnon .definitions are the following:
J = !,p,v;,
dp ( dL:r
dPJ (dL ( dP)'
f
dL
f
(3-39)
2g,d
=!,p,v~ 2g,d
=J,Pfv~
(3-40)
(3-41)
2g,d
In general. the two-plwse friction factor methods differ only in the way lhc friction factor is dctermined and to a large extenl on the flow pattem. For example, in the mist flow pattcm, Equation 3-40, which is bascd on gas is normally used; whereas in the bubble regime, Equation 3-39, which is based on liquid, is frequently used. The definiti(ln of PI in Equation 3-41 can differ widely depending on the investigator. \[ost investigators have attempted to corrclate friction factors with some fonn of a Reynolds numbcr. The varíous Reynolds numbers uscd to evaluate friction factors are definéd when the friction factor correlations are discussed for the individual correlations. One variation, which dcseryes mention, is that severa1 correlalions for predicting vertical flowing pressure losses make use of only the numerator of the Reynolds number. c. Acceleralion Component. The acceleration componenl for two~phase flow is represented by:
dPJ,~ (dL
(pvdv ),
(3-42)
g,dL
The acceleration component is completely ignored by sorne invcstigators and ignored in sorne flow patterns by athers. When it is considcred, various assurnptions are made rcgarding the relative magnitudes of parameters
involved to arrive at sorne simplified piocedure to determine the pressure drop due to kinetic energy change. From the discussion af the vatíous eomponenls contributing lo the total pressure gradienl, it follows lhat the principal considerations for developing pressure gradient equalions are developing melhods for predicling liquid holdup and lwo-phase friclion factor. This is the approach followed by almost all researcheTs in the study of twophase flowing pressure gradients. d. Two-Phase Flow Patlerns. Whenever two fluids with different physicaI· properties flow simultaneously in a pipe, there is a wide range of possible flow pattems. By flow pattem, reference is made to the distribution of eaeh phase in the pipe relative to the olher phase. Many investigalors have allempted to predict the flow pallem lhal wilI exist for various sets of conditions, and many different names have becn given to the various pattems. Of evcn more significance, sorne of the more reliable pressure-Ioss correlations rely on a knowledge ofthe existing now pattern. Also, as a result of the increase in the number of two-phase Iines from offshore platforms to onshore facilities, concem has grown regarding tae predic~ tion of not ooly flow pattem, but expectcd liquid slug sizes and frcquencies. Prcdiction of flow patteros for horizontal flo\\' is a more difficult problem than for vertical flow. Far horizontal tlow, the phases tend to separate due to differellccs in density causing a form of stratified fiow to be commono Govier7 has presented a series of flow pattem descriptions for horizontal air/water flow and vertical air/water now. These are sho""n in Figures 3-7 and 3-8 lo iIlustrate the various pattems that can result and also to show that aH depend to sorne cxtent on the relativc magnitudes of vsL and vsg ' Whcn flow oeenrs in a pipe ínclíned at sorne angle other than vertical or horizontal the flow paltems lake other forms. For inclined upward flow, the pattcrn is almost always slug or mist. The effeet of gravity on the liquid precludes stratification. -For ill~lined downward fIow the pattem is usually stratified, Intst or annular. e. Pressure Traverse Calculatioll. The calculation of a two-phase flowing pressure traverse involves use oC 3D ilerative or trial-and-error procedure if temperatures or pipe inclination change with location or distance. In calculating a travcrse, the flow conduit is divided into a number of pressure or length increments, and the fluid properties and pressure gradient are evatuated al average conditions of pressure, temperature and pipe inclination in the incremento The accuracy oC the pressure traverse calculation inrreases as the number of increments increases, but so does the number of ca1culations that musl be performed. This presenls no problem if a computcr is availabJe, but the time im:Olved may be signifi-
68
Produc/iOtl Optimization Using Nada! .-1I1l1!ysis
mine the neccssary fluid and PVT propcrties at conditions of average pressure and tempera tu re determined in step 3.
fLOW OIREcnON
o
o
~
o
~
o 10 o
~
" '"
¡ ¡I 1
~
:::
..J
.1
'J
>
~
~
a
O Q
'9'0 IQ'Vr;/R
~
\~\
A
Q.
=>
01
1
Compare the estimated aad calculated values af "L obtained in steps 2 and 6. If they are not sufficiently clase, estimate a new length increment and go lo step 3. Repeat steps 3 through 7 untif the estimaled and calculated values are sufficiently close_.
8.
Set L ~ L, + r. "L andp ~ PI + í. "p.
9.
Ifí. Mis less lhan the total conduillenglh, relum la step 2. If í. ó.L is greater than lO tal canduil !englh, interpolate between the last two values of L lo obtain the pressure at the end af the conduit.
B
o ",
'D,~I
11 10
,
l ..
bJ
'!; :\
A
¡ ~
100
Superficial Gas Velocily, VSG, fl.! seco Fig. 3-7. Two-phase vertical naw pallems.
canl foc hand calculations. The increments should be sma1Jer al lower pressures where the pressure changes rapidly with distaace. Far computer calculations, the pressure incremenls should be no larger Ihan one-tenth of the average pressure in the increment. Algorithms are given both foc incremenling 00 pressure and incrementing on length.
Procedure [ar lncrementing Pipe Lenglh
'
7.
.sr/,v I
rJ
,
..
Calculate the length increment corresponding to lhe selected pressure increment, M ~ "p/(dp/dL).
..
~~~ ,~
;.
~
01
6.
i b\
),.t. ~6' "
'0
Calculate the pressure gradient, dp/dL in lhe increment at average conditions of prcssurc, lCmpC'T3ture and pipe inclinalions using the apprepriate prcssure gradient correlation.
L
n ' . ' I l'l
j!!
'"
5.
o·
o
¡
R
1.
Starting with the known pressure value, P 1> al localion L J select a pressure increment, 6.p.
2.
Starting al the location where the pressure i5 known, estimate a length increment, M, corresponding to the pressure increment ~.
3.
Calculate the average pressure and, far non-isothermal cases J the average temperature in the incremento Temperature may be a function of locatlon.
4.
From laboratory data or empirical correlations) deter-
This procedure is iterative if either temperature or pipe inclination are functians of length or location. For isothermal, constanl pipe inclination cases, steps 2 and 7 may be omitted. This procedure must be used with caution for calculating two-phase pressure lrJverscs fOf downward flow. In lhis case, the hydrostatic pressur~ can ¡ncrease in the direction of flow, while the frictioo 10ss component causes a pressure decrease in the direction of flow. This can create conditions of eithcr a ncgative or zero pressure gradient, which will cause problems in step 6 of the procedure. The result would be either a negative or infinite length increment. Ihis possibility is eliminated iflhe follnwing procedure is used. A flaw charl for calculating a pressure traverse by dividing the pipe iota length increments is shown in Figure 3-9, Procedure for lncrementing Pressure Drop 1.
Slarting Wilh ¡he known pressure value, p ¡, at location Lb select a length increment, /lL.
2.
Estimate a pressure increment, D.p, corresponding to the lenglh increment, M.
3.
Calculate the average pressure and, for non-isothermal cases, the average temperature in the incremento Temperature may be a function of location.
4.
Frem laboratory data or empirical correlations, determine the necessary fluid and PVT properties at conditions of average pressure and temperature de termined in step 3.
5.
Calculate the pressure gradient, dp/dL in the increment at average conditions of pressure, temperaturc,
69
Flow in Pipes and Restriclions. .'"-
2 0 r - - - - - - - - - - - - - - - - - - - - - - --.------,
...J UJ
>
2.0
Fig. 3-8. Two-phase horizontal flow patterns.
and pipe inclination, \lsing the appropriate pressure gradient correlation. 6.
Calculate the pressure increment corresponding to [he seleeted length increment, 6p = 6L (dpIdL).
7.
Compare the estimated and calculated valnes of obtained in steps 2 and 6. If they are not sufficienlly close, estimate a new pressure increment and go to stcp 3. Repeat steps 3 through 7 until the estimated and calculated values are sufficiently clase.
S.
Sel L
9.
If L 6L is less than the total eonduillength, retum to step 2.
= L I + L 6L and p = PI + L 6p.
Using this procedure, the length increments can be sclectcd so thal their 3um is exactly egual to the total conduit length, and interpolation is not required in the ,last step. Also, the calculation of a negative or zero pressure gradient in downward flow prescnts no problem in step 6. This method is always iterative even if temperature and inclination angle are constant, since fluid properties in an incremcnt depend on the unknown pressure. Also, it is not possibJe to sclcct !1p as sorne fraclion of pressure in the pipe. If the length incrcments are set equal, large pressure drops may occur in the low-pressure high-vclocity segrncnts. A flow charl for calculating a pressurc traversc by dividing the pipe into prcssure drop increments is shown
in Figure 3- IO.
f Procedure When Temperature Distriblltion is Unknown. When a more rigorous method of detenninillg temperature distribution is desired, it is necessary to account for heat transfer to or from the flowing fluids. Heat transfer calculations for two-phase no\\' can be very important when calculating preflsure gradients in geothcrmal wells, stcarn-injection wells, wet-gas pipelines in offshore locations or in cold elimates, now of high pourpoint crudes, etc. In general, heat transfer calculations are always preferable to assuming knov.'n temperature distribution, but for multicomponent systems, they require that either the ¡nlet or outlet temperature be known. To perform hea! transfer ealculations, it is first necessary to change the energy balance equation to a heat balance equation. Combining Equations 3-3 and -3-3a and assumingno \York is done 00 or by the fluid (dWs = O): dh + vdv +JL dZ + dq =0
gc
(3-43)
gc
If specific enthalpy and the heat-added lerm are exprcsscd as heat-per-unit mass, then the mechanical energy equivalent ofheat constant, J, must be introduced.
J
Jdh+ vdv +JLdZ +Jdq =0
gc
gc
(3-44)
70
Prodllc¡ion Optimiza/ion Using Noda! Analysis
lnilia~ul
Lnilia~le
L¡.p,
L¡,PI 1_1
¡.. ¡
Sel IIp
P"-p¡ ± 6PI2 l' ..
IIL) & .. I{L)
Calc. PVT prOPillies
C~lc.
PVT
p:cperti~$
-l(p,l)
.. IIT.Pi
Calc. dp/dl ALe" LlP/{dpldL}
Calc. dpfol Llp, _ 6L{dpldL)
Fig. 3-9. Ffow chart for calculaUng a pressure traverse (incrementing on /ength).
Expressing elevation in tenns of pipe ltmgth and angle and solving for specific enthalpy gradient: dh -dq g sin vdv -=---------(3-45) dL dL g, J gJdL
e
The heat added to lhe system per unít length dq/dL is negative since heal is ]ost to the surroundings when the fluid temperature is greater than the surrounding temperature. The heat loss gradienl can be expressed as:
dq = U(J
(3-46)
wT
where T Tg
U
average fluid temperature ayer dL average ground or surrounding temperature over dL overaU heat transfer coefficient
Fig. 3-10. Ffow chart for calculating a pressure traverse (incrementing on pressure).
d wr
pipe inside diameter total mass flow rateo
Heat Transer Coefficient
The overalI beat transfer coeffícient can be a combination of several coefficients that depend 00 the method of heat transfer and the pipe configuration. For unburied pipelines. there will be coovective heat losses between the tlowing fluids and the pipe wall, conductive losses through the wall and through aoy insulation or coating material. and conduclive losses to the environment. Tbere can also be significant thermal radiation transfer. A ca mplex mixture of heat losses can exist in wellbores due to the variely ofmaterials through which the heat must flow. For example, a well may be cased and the annulus cao be cemented, liquid filled or gas filled .
••
Flow in Pipes and Restrictions
7/
In general, the ovcrall heat transfer coefficient is the reciprocal of the SUtnS of lhe individual resistances to heat transfer. Consider a buríed pipeline. Then: (3-47)
where
R¡
resistan ce to conductive heat transfer from lhe pipe lo the ground resistance to eonductive heal transfer lhrough lhe pipe wal\ and eoalings resístance to convective heat transfer belween lhe flowing fluids and the pipe wal\
R = ,
and (3-52)
lhermal cond\lelivily of fluids Prandll number ~ ~ e/k¡ specific heat at constant pressure
In(4D Id) '
2k,ld
(3-48)
where
kg d
(3-S1)
where
For steady-stale heat transfer, Rg can be expressed as .
lhermal conduetivity of lhe wetting film on lhe pipe wall. NNu in rum depends 00 the flow characteristic-laminar, transition or turbulent, aod is nonnally correlated with three coromon dimen,sionless groups: Reynolds number, Grashof number, and Prandll numher. In turbulenl and transition flow, convective heat transfer can be significant so lhal lemperalure differences belween lhe fluid and the wall are ignored. In almosl all lwo-phase flow probIems, flow is turbulent. A commonly used approximation of lhe Nusselt factor is:
deplh from surface lo eenlerline ofpipe (Freq\lently taken as depth of fil\ on lop of pipe) thermal conducti\"ity of earth pipe insidc diameter
For flow in a welIbore, heat transfer is a combination of conveetion in the casing-tubing annulus and conduetion into the eaTth. The time dependent function in Equation 3-49 for intervals longer than a week can be expressed as:
re - ) -0.290 /(I)=-In - ( 2"¡;:;¡
For unsteady state heal transfer, Rg • can be cxpressed as: R
,
=JJrL
,
2k Id
(3-49)
where
re
whcre J(t} is a time depcndcnl, dirnensionless function. The conductíve resistance duc to lhe pipe wall is nor tn31ly exprcssed as the steady-state, radial, one-dirnen~ sional conduction equation:
(3-5]:)
outer radius of casing lhermal diffusivily of the earth time since well began flowing.
=
8
8
R = In(r 11') p 2k p Id D
,
(3-50)
where rQ,J'¡
kp
ouler and ¡nner radii of lhe pipe lhermal eonduetivity of lhe pipe
Typieal values of/(I) range from 0.5 lo 3.0. Equatioo 3-53 is totally inadequate for short-time, healtransfer applications or when non-steady flow Dccurs. This is the case for transient well tests, cyclic steam injcction, e1c. lo most two-phase design calculatíolls involving buried pipelines or wellbores, R g is hy far (he largesl of lhe possible resistances-to heat transfcr. The result will then be U == l/Rg If a pipeline is insulatcd, however, Rp can beco me the largest term, resulting essentially in U = l/RpSeldom is com'ective heat transfer comparable to the conductive terms. Howevcr, for unburied pipelincs, the thermal radiation losses can make this tenn very importanL Magnitudes of overall heat-transfer coefficients can vary widely. Insulated, buried pipelincs can ~ave U values as low as O. l BTU/(hrOF n')_ Uninsulated, unburied lines can have values highcr than 100. o
Rp can require modifications to account for seaIe or paraffin buildup on walIs or to account for insulation or conrosion proteetion coatings and wraps. The convcction tenn, Rj , is extremely complex in two~ phase flow, and depends on flow pattern in additioo to normal\y aeeepted single-phase flow.parameters. Heat transfer due 10 thermal radiation is frequently combined with the convcclion termo The convective resistance is invcrsely proportional to the NusseIt factor, NNII' and the
Pmt1ucrioll Optimizcilioll UsiJlg NOL"" A,;.¡{ysis
72 wherc Examp/e 3-4:
FkNI in a weiibore is oontrolled by unsleady heat conduction lo \he 910000. Calculate \he overaii heat transfer ooeflident after 30 days (720 hours) it
re = O.
The qua lity mal' be related to Ihe no-slip holdup by:
5 ft
x
kg = 1.4 BTU/(hr ft °F} ~ = 0.04 ft2/hr.
=
P,A., p,A., +P,A.,
(3-55)
A simplified nolV ehart of a eomputing algorilhm for simultancous pressure and tcmperaturc travcrse calcula-
So/ution: ((1)
specific enthalpy of the mixture, liquid and gas, respectivcly
=-In(re/2.,J:,t}-0.290
= -ln(0.5/2J(0.04}(720)) -0.290 =2.78 R g ((1)/2krJd
=
= 2.78/(2)(1.4)/(1.0) = 0.992 hr ft2 °F/BTU
U = lIRg = 1/0.992 = 1.01 BTU/hr ft2 °F Examp/e 3-5: Estimate the value of R, tor hat water injection ¡nta a well if:
tions is given in Figure 3-11. Convergence on beth pressurc and temperature: in íl givcn pipe lenglh incrcment requ¡res a double iteralÍvc procedure. Most efficient results are obtained when COllverging on the least sensitive variable first. Normally, mixture enthalpy is more sensitive to tcmpcrnture lhan to pressure. This is shown -in Figure 3-12 in which h (BTUI IDO-mol) is plotted vs. T for several isobars and foc a specific feed compo5ition. Similar curves can be dc\-eloped foc any feed composition using results from vapor-Iiquid cquilibrium flash caJculations and cmpirical cnthalpy correlations. The Duter loop of the tlo\\' chart is ¡hus the temperatu re loop. and the inner loop is lhe pressure loop.
k¡ = 0.4 BTU/hr ft °F
111. FLUID PROPERTY CALCULATlONS
d¡=1.0ft
wr = 200,000 Ib",lhr ~
= 0.3 ep = 0.726 Ib",lft hr
T = 300°F
cp
= 0.5 BTU/lbm °F
So/u/ion: Np
,= ~eplk¡= (0.726)(0.5)/(0.4) = 0.908
N R8
=(w.,l~}(4/nd)
= (200,000)/(0.726) . 4/n(1.0) = 3.51
N,.
x 105
= 0.027N:'·N~" (0.027)(3.51 x 10' )"(0.908)'"
=714 R¡ = d¡ /k¡ NNu R¡= 1/(0.4)(714) = 3.50 x 10-3 ·ft2 hr °F/BTU Mix¡ure Enrhalpy
The total mixture enlhalpy of a two-phase, gas-liquid mixture at a given pressure and temperature can be calculaled from a knowledge of lhe in-situ mass or mole fraelion of eaeh phase and lhe enlhalpy of eaeh phase. If x is lhe no-slip, gas, mass fraelion (quality), lhen lhe no-slip mixture enlhalpy is:
h=h,(l-x}+h,x
(3-54)
The general pressure gradient ~quation (Equiltion 3-16) was derived in lhe previous section. and it was pointed out that al! the temIS in this equation I11USt be evaluated at in-situ conditions. That is, during the ca1culalion of a pressure traverse. the pressure gradient Illust be calculated al several points in the piping syslcm at the pressurc and temperature existing at this poinL This is step..f in the proeedure [or calculating a pressure traverse. Also. as will be seen in the following secrion, it \ViII frequently be necessary to en.luate various in-situ fluid propenies el' fluid velocities te calculate no"" patteen, frictian factor and liquid holdup. The variables in the pressure gradient equation are fluid density, mixture velecity and friclion faclor. Calculation of these variables for the gas/liquid mixture requires values of the individual components at the conditions of interest. The mixture can be composed of natural gas, erude oil or condensate, and water. Also, evaluation of the frictien factor usually rcquires a value for the viscosity of the individual eompooents at various pressures and temperatures. The fluid properties required to caleulate che neeessary pararneters eould be obtained from a labóratory analysis ofsamples ofthe fluids, ifthese are available. Frequently, a pressure-volume-temperatue (PVT) analysis will have been conducted 00 the reservoir fluid to obtain data [or reservoir eogineering calculations. Unfortunately, these
73
Flow in Pipes and Restrictions .
READ DATA INITIALlZE~
L¡, PI ,Ti ,h,~L,I" I IT" O GUESS TI+I,9
NO
'>-"()-----~:::::~i=::_..J CALe T
IT )MAXT "...
IP "
o
GUESS Pi+l,g CAle ji
NO
CALe PVT PROPS.
(');;,1
CALe.
dp/d L,
.
PI+f,e "Pi +~ .o.L
dL
L-
-'-'N-"-O<:
lo?
~==::¡==-:(3-45) h¡+I" h¡+
~t·~L (3-54)
1"1 +1
NO NO
VES
Fig. 3-11. Heat transler calculation algorilhm.
analyses are usu3.lIy conducted at reservoir temperature only and are not applicable to piping system calculations, since the temperature ofthe fluids in the piping system is constantly changing. This fact has made it necessary to resort to empirical fluid property correlations for calculating pressure traverses, to account ror temperature change effccts.· Howcvcr, ir mcasured values are available at one tempcrature, these may be used to improve the accuracy of the
empirical corrcialions by forcing lhe cmpirical melhods
to match the measured values at tbis temperature. In any design situatíon, the flow or production rates of the fluids will be known at standard conditíons. Also, the fluid densities at standard conclitions will usually be
known in the forro of specific gravities. Thesc must bc converted to flow rates or velocities and densities at insitu conditions before a pressure traverse can be calculBt-
ed. The equations necessary for máking these conversions
will first be giveo for each of¡he three fluid components.
ProducJioll Optimiza/ion Usillg Noda! Analysis
74
I ,:rI1 11I 1ii 1:¡II
~: :!
i 11'
'
li .' 1: ,1. 1
I! "
L. _
1 11
. ..I I
"·1
,i
.
...,'. ':t 11;-.. ,
..
~ ! :r11.II'.-(r. 'Kb.'¡~;' Y' .. ~ ~I}.-' ,_ Vi,.fl !':XJYi(".Vo , 7 .. 1 ."/. .
' .•
:rli%
'j)• ~:tm':¡::! 611':-' l-Yí';' ~ Y~ ,,' !-l. ,:¡;¡. . 1".'{Y,:r" , .
l'
1/ . -I-('j.
~./
t;/' 'f'f.
1
. '+i'l$.j0.J' Víl/~f V' U1 }",,'>,y, \(7,/1. r(. •J
, ;'1·
4~
l.
,t.:
, l>F i
.::
-. ;1:
'J?ilr
'1 ~.IX fi
.¡. l
,·1-
17Ir~,(I;
¡: .,tl1l'..r.'
'Pi·fU- Y.'vPth
'1· I:H···t -.. ¡:r:¡.: '11,
~r0~i:I"jl:""':"I::::::--:o:rt!--: .:: ':'1" ·'~I/o.,.-fi '.' 1 r' . 'o.... . ·",II::IIJ ~I.I:I:¡: '1'1'1:' ::1:1-: . '.' :Ij:·o .. --
j ...
.
'HIT"
1~:I<~il W! jll. ,I} .. I !'ll . , 11 .. 111: t ¡q! 1'1'1 11 rllH rl!IIII·II.
.'
C1
-
~~
4.301:
1·\
--. --
,.. .
111
..
W
H¡ ¡.i.i-!-
2.9n2 100.00f1.l,
·111
",1+'
1: '~:~:f·:l ! ¡j1,:,'UT H:II' '11 r ,1 q ;·1· 1· I~ '-(11 I 1-1{. <>: i l' .. 1111'.1 111 [1'1:1:1 .1 11 . II'!I 111 1·111-11 j. . IllHl I 1 I '.
111
1.718 1.405
C7+
,.:
'r' 11'
¡
3.0GO'~
C4
C5 'CG
,
11-- :I.I 'Y.r
COZ
o
.. r 1),Yi/:1Y,j.1"
n'
L 375% Z
"j.
.: ,l' :rjV¡;Y»~ '2l'
N
,;.;r j' . :11'. --:. I:l:..
1!V¡I1;¡m~
Mol %
Componen'
. -1'.:--.1 . " . ,.
. :.:. i IX) r :nYiXJ1),1:' . : ,iy,:'/¡Y.'rVI) /¡ " .... :' --
'
1/~1.
:'. '-ji ~I:b¡; .r'. ':0" "1 ¡
.~'
jl~
.
,
1- -I!/: :)"1 L1 f/L .
'lliJ (;'1 1: :1)", K"~r Y,)'; '< I
'~
I
[III'H'
:
JriHilT
[TIT ¡ r:
I~ll!'j :¡"if' ell tf:'¡
I
,if~,'f
U
. 111 I JI:! I (rr~ 11, 11 IJ:U:L ,1
Fig.3·12, Vari,ation of mixtura enthalpy with prassura and temperature.
..
•
Flow in Pipes and Restrictions .........
75
These equations wilI require knowledge of various fluid
PVT properties, which will then be presented. The equalions will be presenled in the customary field units, but
In the petroleum industry, it is comm6ñ to express the
gravity in terms of lhe API gravity of the oil, or: 141.5
may be easily converted to rnetric or SI units if required.
A. Fluid Density
Y. = 131.5 +API
(3-59)
where
Calculation of a two-phase fluid density requires values for the densities of the gas, oil and water. The equations for converting the densities from specific gravities to in-situ values wi 11 be presented.
Y. API
oH specific gravity, and oH API gravity.
The density of the oil plus any gas dissolved in the oil at the pressure and temperature of ¡nterest may be calcu-
l. Gas The specific gravity of a gas is defined as the ratio of the density of the gas to the density of air, both measured at standard conditions of pressure and temperature; that is, (3-56)
lated by dividing lhe weight or mass per stock tank barrel by the in-situ volume that would be occupied by a stock tank barrel of oH and its solution gas.
P.
Po
where
350 0.0764 5.615
gas dcnsity,
A-fg Psc
air dcnsity, gas molecular weight, standard pressure (14.7 psia),
T"
standard tcmpcrature (60°F =520 0 R), and
Pair
Yg
gas gravity
Using the engincering equation of state for a gas, it can be shown that the relationship among gravity, pressure and temprature is:
P,
-
2.7y, P
ZT
(3-57)
P
T
P. = p.,EXP[C. (p- P.)J
~
gas comprcssibility factor.
Methods to estimale Z as a function of P, T and Yg will be prcsented subsequently.
(3-61)
where
P
gas gravity (air = 1), and
n3lbbl
is above the bubblepoint at the temperature of interest, incrcased pressure wiII merel)' eompress rhe liquid and increase its density. For the case of P ;::: Pb' the oil density is calculated from:
Pb Co EXP(X)
prcssurc, psia, tcmperalurc, °R
conversion factor,
Ifthe pressure and temperature conditions are sueh that
Pob
Pg ",' gas dcnsily atp and T,lbmIft 3 ,
oil density, IbmIftl, solution or dissolved gas, scflSTB, oil formation volume factor, bbIlSTB, density ofwater at s.c., Ibm/STB, density of air at S.e., IbmIsef, and
all of the available gas is in solution, that is, rhe pressure
Po where
(3-60)
5.615B.
where
R, Bo
P,
350y. + 0.0764 Y, R,
density at p, T, densily al Pb' T, pressure, psia, bubblepoint pressure at T, psia, and oil isothermal eompressibility at T, psi- I
e'
= (2.7183}'
Correlations for ca1culating Rs ' Bo ' Co and Pb at various conditions wiII be prcsented later.
3. Water For purposes ofcalculating two-phase flowing pressure
2. Dil
The specific gravily ofa liquid is defined as the ralio of the dcnsity oflhe liquid to the density ofpure water, bolh rncasurcd at standard conditions. That is:
gradienls, the effeet of gas in solution in the water is afien ignored since it is very low compared to Rs in the oil. However, the effects of dissolved solids and temper-
ature must be eonsidered. The density of water may be y
-(&)
L -
P...
p.....T..
estimatcd from: (3-58)
P". 1... 62.4,,"" P = --=-... B... B... SC
(3-62)
Prouuclioll OprimizQtioJl Using Nodo( AlU¡(ysis
76 T p
where
Pw Pwsc
Yw Bw
water densily at p and T, lbm/ft', density ofpure water at s.c. = 62.4 lbm/scf, water spccific gravity. and water formation volume factor, ft 3/scf.
The value af Y.. depends an the dissolved solids in the water. Equations foc calculating B w wilI be giveIl subsequently.
tempcrature, °R, and pressure, psia.
2. DiI To calculate the in-situ superficial vdocity of the oil, the expanded volume of the oH must be accounted fOL That is: (3-66)
where
B. Fluid Velocily
Vso
10 calculate the in-situ velocities of the gas, oH and water from surface flow cates, the actual volumetric flow rates must fíest be calculated. The foHowing equations can be uscd to correet standard 110w rates lo in-situ now rates, from which the velocities can be calculated.
qo Ba A
superficial oil velocity, ftlsec oil flow rate, scf/scc oil fonnation volume factor, ft 3/scf pipe area, ft2
Ir the oil rate is given in STO/day, the equ3tion becomes:
6.5xlO-' g,B,
J. Gas
The gas-producing rates are usually stated in standard volumes per unit time, 5uch as standard cubíc feet per day, sef/day. These may be converted lo cubie feet per second al in-situ conditions, rrom which the superficial \'clocities in ft/sec can be obtained. qg q~cBr v =-=-J,g A A
A
(3-66)
where STB/day ft/scc ft2 ft'/scf ar bbJlSTB
(3-63)
\\'here
superficial gas velocity, n/sec, free gas fiow rate, sef /see, gas fonnation volume factor, ftJ/scf, and cross-sectional arca of the pipe, ft2
3. Water The in-sitll, superficial water velocity is calculatcd from: (3-68)
Ifthe gas is in eontact with ail in the piping system, the solution gas must be subtracted from the measured separator and stock tank gas befare the in-situ velocity is calculaled. A convenient equatian foc making this calculatían is:
q.(R-R,)B q, = 86400'
The superficial ¡iquid velocity is the sum of the oil and water velocities. and the superficial mixture velacity is the sum af lhe liquid and gas superficial velocities; that
= gas flaw rate, ft'/sec, = oi! praducing rate, STB/day producing gas/oil ratio, sctlSTB, = 501utioo gas/oH ratio, scf/STB, and gas formation volume factor, ttJ/sef. = secands/day
B = p~ZT t
TICP
0_0283ZT p
where
Z = gas compressibility factor,
A
watcr rate, STB/day water formation volume factor, ftl/scf or bbllSTB pípe area, ft2 superficial water velocity, fv'sec
(3-64)
where
qg q. R R, Bg 86,400
where
, lis, (3-69) (3-28)
C. Empirical Fluid Property Correlations (3-65)
The mos! widely ased empirical fluid propertyeorrelalians for-estimating the parameters required to calculate densities and velocities will be presented in this section. Many of these correlations .were originally published in
'
•
..
Flow in Pipes and Res/rie/ions
77
graphical form only, but where possible lhe correlations will be given in equation formo This will greatly facililale
l. Gas Compressibility Factor The gas compressibility Or Z-faclor is a function of lhe
calculation of pressure gradients using computers or prograrnmable calculators.
pseudoreduced pressure and temperature of the gas. The correlation shown in Figure 3-13, froro Standing and
Mosl of lhe equations presented here are available for Hewlell-Packard 41-C programmable calculators in the forrn of a plug-in module called the Pelroleum Fluids
Corrections to the pseudocritical pressures and temperatures can be made to account ror impurities such as N1,
Katz' gives good values for hydrocarbon gases.
CO" and H,S. The pseudoreduced values are defined as:
Pac. 7
•
1.1
o.•
0.7
1.6 N
.
__
.- -
-
~
,l!1
,-
1.5~
:zi
q¡
~
"-
E
o
O
" 0.25
I.l
1.0
• Fig. 3-13. Gas compressibilily facfor.
•
10
11
12
Pseudoreduced pressure
"
"
0.'
IS
Production Optimiza/ion Usillg Nadal A.nalysí
78 P
T~. =Tpc
Ppr:::;-
-e,
(3-74
Pp<
T~I-.-
(3·70)
P;'
Tpc
pr
Pie T'/,,:
where
where p T
Ppc Tpe
Iflhe gas composition is known, lh.:: pseudocriticals are calculated from: -"
P",
= L.Y;Pú ;=1
(3-71)
y
T~ ~ L.y;1;; ¡,,¡
where y¡
Pci Td N
mol fracrian of i lh componen! critical pressure of i lh component critica' temperature of j lh eomponent number of components
If the gas composition is unknown. [he pscudocriticals may be estimated [rom T~ = 170.5 +307.3y,
2. So/u/ion 01' Dissolved Gas Vasquez and Beggs l2 presentcd correlations for several fluid properties, which were bascd on data from mOfe than 600 measured PVT analyscs. The corrclation for R. gives Rs as a function of pressure, tcmpcrature, oil API gravity and gas gravity. The gas gravil)' resulting [IOm a flash separatioll of oil and gas dcpends on the separatol pressure and temperature. Vasquez and Beggs based their gas gravity on a reference pressurc 01' 114.7 psia and prcscnted an equation [or correcting Yg fUf othcr separa tal pressures. If separator conditions are unknown, the uncorrected gas gravity may be used in rhe correlations for R t and B". The gas gravity correction equation is: y~.
(3-75)
xlO-' (AP1)T\og( pi 114.7)J
corrected gas gravity gas graviey resulting from a separation at p, T separator tcmperature, °f separator pressure. psia oil gravity, °API
Ygc
"tg T p
psia °R
Several equations or algorithms are available "[oc repro-
ducing Figure 3-l3, and the most accurate anes are trial and error Oc iterative. Oue of the simplest equations, which gives values sufficientiy accurnte for two-phase flow calculations, was published by Brill and Beggs9 and modified by Standing. lO The equation js: z ~ A +(I-A)EXP(-B)+Cp~
=y,[1.0+5.912
where
where Tpc
These correctcd pseudocritícal valucs are then used 1(1 calculate the pseudoreduced values for use in Equation 3-73.
(3-72)
P" = 709.6-58.7y,
Pp<'
120 (AU9_A 1.<) + 15 (BU5 -B') mol fraction H,S mol fraction CO, + B
E B A
pressure oC interest temperature oC interest pseudocritical pressure pseudocritical temperaNre
(J-73)
where
A = l.39(T". _0.92)'5 -0.36 TI" -0.101 B = P,.. (0.62 -0.23 TI") + p~[0.066/( TI' -0.86)
-0.037] +0.32 P~ / LXP[20.723( TI" -1)]
API
The dissolved oc solulion gas at any pn::ssure less than oc equal to bubblcpoint pressure is calculared from: R, ~C,yJCpc, EXP [C,(API)/(T + 460)]
where
Rs p T
solution gas, scf/STB
pressure of interests psia temperature of ¡nrerest, °F
Tne valnes of tne constants depend on the API gravity of rhe oil and are given by:
C = 0.132 -0.3210g TI" D ~ EXP(~.715 -1.l28T". +0.42 T/)
If the gas contains impurities, corrections can be made lo Ppc and Tpe according lo Wichcrt and Aziz ll as:
(3-76)
Constant
API <{ 30
API >30
C1
0.0362 1.0937 25.7240
0.0178 1.1870 23.9310
C2 C3
Flow in Pipes ol1d Restrictions·· .......
79
Ibis method for estimating Rs is used in the HP Petroleum Fluids Pac.7 Other correlations for Rs were
where
Bo R,
published by Standing" and Lasater."
Ir the initial solution gas, Rsi = Rsb is known, Equation
3-76 may bc solved for bubblepoint pressure, Pb. A1though frequently ignored in two-phase flow calculations, an equation for caIculating gas in solution in
volume/standard volume, e.g. bbl /STB solulion gas at P, T, scflSTB temperature of interests °F
T
pressure of interest, psia
P
API
oil API gravity gas gravity
Yge
water as published by eraft and Hawkins I5 is given.
The constants are deterrnined from: (3-77)
where
Constant
AP/< 30
AP/> 30
Cl
4.677 x 1()-4 1.751 X 10-5 -1.611 x 10"
4.670 X 10" 1.100 x 10-5 1.337 X 10-9
gas dissolved in brine, scf/STB gas dissolved in pure water, sef/STB 3.47 IT-o.B37
Rsw Rswp X y T Rs .... p
C2 C3
water salinity, ppm temperature, °F
The oil formation volume factor decreases at pressures aboye the bubblepoint pressure and is calculated from:
C , + C,p + CJP'
where
(3-80)
Bo = B"" EXP [C.(P. - p)] where
C,
2.12 + 3.45 x 10·'T- 3.59 x 10-'T'
C,
0.0107 - 5.26 x 10-'T+ 1.48 x 10-"T'
C,
-8.75 x lO·' + 3.9 x 10-'T - 1.02 x 10·"T'
Bob
oil FVF atpb
Pb P-
Ce 3. Formatioll Valume Factor Toe formation volulTIc factor of a fluid is a convenient parlmetcr to use for converting from standard volumes to actual or in-situ volumes existing at any pressure and temperature in the systcm. Equations are given for gas, oil and water.
c. Hatel: The equation given in the HP Petroleum Fluids Pae is (3-81)
where formation volume factor for brine in con-
a. Gas. The gas formation volume factor is dcfined as
the actual volumc occupied by a given quantity of gas at sorne pressurc and temperature, divided by the volume which the gas would OCCUpy at standard conditions. It is ca1culated fram:
=
bubblepoint pressure, psia pressure of interest, psia oil isothemlal compressibility, psi- I
Bv.p
y
X
taet with gas, bbl/STB = FVF for pure water, bbUSTB water saIinity, ppm
5.1
x
X
Bg
=
0.0283ZT
b. Di/. The Vasquez and Beggs method may be used to estimate Bn as a funetion ofy" API, R,.and T. The equation is:
= C, +C,p+C,p'
(3-82)
C, C2
0.99Il + 6.35 x 10-sT+ 8.5 x 10-'T' 1.093 X 10-6 - 3.497 x 10-9T + 4.57 X 1O- 12 T' -5 x 10- 11 + 6.429 X 10-I3T - 1.43 X lO-1ST'
T
°F
P
psia
4. Iso/hermaI Compressibility Bo = 1+ C,R, + C,(T -60)(APII Y,J
+C,R, (T - 60)(API / Y,,)
-
10-8 + 8.5
where
C,
P
X
10-"p)
B,p For pressure in psia and temperature in °R, using Psc 14.7 psia and Tsc = 520 °R, Equation 3-78 becomes:
x 10-'-1.95
10'p + (T-60)(5.47
x 10·lOp ) + (T-60)'(-3.23
,~'-
.
(J- 79)
The isothermal compressibility for oi! saturated with gas can De calculated using lhe following equation presented by Vasquez and Beggs.
}Jj-OdUClion Opl;m;zalúJIl Using Nudo! .in.. l!ysis
80 C
= SR, + 17.2T -1 I80 y.. +12.61(AP1) -1433
.\; YT-l.1bl Y 10l Z 3.0324 - 0.0203(AP 1) A 10.715 (R,+ 150)-051' B 5 44 (R, + 150)-0.338 R, scflSTB T 0p For Pressurcs greatcr tIlan Pb.
(3-83)
pxlO'
o
where Co R T p j
"'{gc
API
oil compressibility, psi- I solutioll gas/oil ratio, scC/STB temperature oC ¡nterest, cF pressure of interest. psia gas gravity oil API gravity
(3-87)
where
An equation foc estimating water iSQlhennal compressibility. ignoring the corrections foc dissolved gas and solids is:
Iloh P Pb
C. =(C¡ +C,T+C,T')xIO"
C,
viscosity at Pb pressur~ of ¡nterest bllbbl~point pressure C I pO EXP (C] + C4P) 2.6 i.l87 -11.513 -8.98 x 10·'
111 (3-84)
C, whece C, C,
C, T P C\\
C] C,
3.8546 - 0.000134 P -0.01052 + 4.77 X 10- 7 p 3.9267 x 10-' - 8_8 X 10. 10 P
b. Watel: A graphical correlation for water viscosity which was publishcd by Matthews and Russell,J7 has been convertcd to equation [orm by Meehan. ls The correlation accounts for bolh [he cffccts of prcssurc and sal inity.
'F pSIa psi· l
Thc isothennal compressibility foc gas is seldom requircd foc two~phase tlow calculations. Hawever, iI may be calculated from:
C
,
=:.._:.. az p z ap
I! = I! .. o [1 + 3.5 X10-' p' (T -40)] I! .. -o ~ A
+ BIT
A = -4.518 (3-8;)
where
B
(3-88)
X 10-'
+ 9.313
x 10-lY -
3.93
x 10- 12 ]'2
= 70.634 + 9.576 x 10-'oyo
where
Cg p
psi-) psia
~ ... =
5. Viscosjty To calculate lhe losses due to viscous shear oc friction, a value foe lhe viscosity of the fluids is required. Calculation of a Reynolds number always requires viscosity. Equations are presenled for the viscosity of oil, both aboye and below bubblepoint, for water and for nalural gas.
Dil. Equations for oil viscosity were presented by Beggs and Robioson_' 6 For p ;;; P•• Q.
(3-86)
where
Jlo J.loD
I!,D
oil viscosity at the pressure and temperature of interest, cp dead af gas-free oil viscosity, cp lOX - 1.0
brine viscosity at p and T, cp p = 14.7, T, cp psia temperature of inlerest. °f water salinity, ppm
~lU'D = brine viscosity at P = pressure of interest,
T
=
y
=
The effects of pressure and salinity are often neglected for two-phase flow ca1culations. A simpler egualion, which considers only temperature effects, was presented by Brill and Beggs.' ~w =
EXP (1.003 -1.479 xIO-'T
+I.982XIo-'T') where T is in °F and Jlw is in cp.
(3-8')
c. Gas. The most widely used rncthod to estimate gas viscosity was presented by Lee el 01. 71 The equation is applicable to natural gases containing impurities if the corrected Z-factor is used to calculate the value of gas density required in the equation. (3-90)
·"
"
Flow in Pipes alld RestricJions .......
81 where
where
A B C ~g
Pg' M T
"T
(9.4 + 0.02M)J1'/(209 + 19M+ 7) 3.5 + 0.01 M + 9861T 2.4 - 0.2B gas density at p, T, cp gas density at p, T, gmlcc gas molecular weight temperatu re of interest, °R
interfacial tension at 68 < T <100
The effeet of gas going ioto solutioo as pressure is increased 00 the gas/oil mixture is to reduce the interfacial teosioo. The dead oil interfacial tension can be correcled by mu!tiplying it by the following correction factor. C = \.0 -0.024 pO"
The gas density in gmlcc may be calculated from: 0.0433y,p
P,
ZT
(3-91)
psia
T
°R
Pg
a • =CaT
gm/cc
6. lntelfacial Tensioll lhe interfacia! tension existing betwecn the gas and ¡iquid phases has very little efTect on t\Vo-phase pressure gradient calculations. However, some of the pressure gradient prcdiction mcthods require a value for interfaciai tension ta use in calculating certain dimenpionless numbcrs~ Empirical graphs for estimating the gas/oil interfaciíll tensino werc presented by Baker and Swcrdloffl9 and gmphs for gas/water interfacial tension weTe published by Hough.:!O Regression ana!ysis was used ta fit equations to these graphs for spccific temperatures. The cffeet of tempera tu re can be estímaled by linear interpolation. o. Gas/Da Imelfada! Tension. Grapns \Vere prescntcd for dead oil intcrfacial teosíon measu red at temperatures af 68°f and 100°F. Equatians which fit these graphs are:
"" = 39- 0.2571(API)
(3-92)
""" = 37.5- O.2571(API)
(3·93)
where 0"68 O" 100
API
interfacial teosian at 68°F, dynes/cm interfacial tension at 100°F, dynes/cm gravity of slock tank oil, °API
It has becn suggested thal if the temperature is greater than 100°f, lhe value al 100°F should be used. Also, if T< 68, nse the yalue calculated at T = 68. For interrnediate temperaturcs, use linear interpolation between the values abtained al 68 and 100°f. That js:
"T = 68
where p 1S in psia. The interfacial tension at an)' pressure is tben obtained from:
where p
(3-95)
(T-68)("" -0,00) 32
(3·94)
(3-96)
The interfacia! Icosion beco mes zero at miscibililY pressure, and for most systems this \ViII be al any pressure greater than about 5000 psia. Equalian 3-95 will give a value of zero al a pressure of 3977 psia. Ir this occurs, a limiting value af I dyne/cm should be used lo calculate the dimensionless numbers in the following scction. b. Gas/Wa/er In/el/acial Tellsioll. Equations Were fittcd to grapfls of inlerfacial teosioo versus pressure at two temperatures. These equations are: G .. (14)
a."""
= 75-1.108p'])·.l9
(3-97)
= 53 - 0.1 048 pom
(3-98)
The same limitations 00 temperature as stated for the gas/oil case apply for gas/water interfacial tensioo for interpalation purpases. That is, for 74 < T< 280: (T - 74)( 0.""
- a.o"',)
(3·99)
206
D. Predicting Flowing Temperatures AII the fluid property carrelalions presented previously require a value of fluid temperature' to calculate lhe required fluid property. The f10wing temperature profile in a gas well or an oil 'oJell is usually assumcd to be linear betwecn the surface temperature and the bottomhole temperatu re. A linear temperature profile is also usually assumcd for surface flowline calculations. The linear assumption for weH flow will usually not introduce significant errors ifa good yalue for surface flowing temperature can be obtained. The heat loss from a fluid in a pipe is a function of the mass flow rate io the pipe and will therefore change with a change in producing rate. An algorithm for coupling pressure and heal loss calculations was presented earlier in tbis section. The iteratiye solution was necessary because both the oyerall heat
82
Prodllclion Opri1llizarioll Using Svdo! ..Ino!ysis
transfer cocfficicnt and lhe enthalpy change depend on
Cl
pressure. If sorne an:rage heat lransfer codlícient can be
C,
detcnnined, an approximate tcmperature profile can be calculatt:d indcpcndenlly of the pressure 1055 calculation. This will of course be less accurate, but in many cases lhe amouot of data available \ViII not be sufficient to perform the more accurate calculation.
C,
1. Flowing Tempera/l/re ill Wel/s An equation foc tempera tu re in a weH as a fu~ction of lacatian L, as derivcd by Ramey,21 can be weittco as: T,
~
1; - gT[L - A(I-EXP( -L/ A)]
(3-100)
where T, TL gr A l\'
el' d U L
C, C, C,
Eql1ation 3-101 is applicable for flowing oi! wells only, although a similar approach could be used for gas wells if insufficient data are available to calculate A. Equation 3-101 has been found to give good eesults foe dry gas wells (no liquid produerion) by using values foe liquid density and oil geavity of 62.4 and 50, eespeetívely.
2. Flowing Temperalure in Pipelines To calculate a temperature profile i1\ a pipeline, it is usualIy assumcd that the remperature 01' the surroundings is constant. Modification of Equation 3-100 to account for this results in:
tempeeature at fluid ente)" (L ~ O) tempt:rature at location L, geolhermal gradient, relaxation distance = wC/tcdU mass f10w rate, specific heal of the flowing fluid, pipe diamt:ter. overall heal transfer coeft1cient, and distance from fluid entry.
(3-1021
When the equation is \Vriuen in this fonn it assumes that the fluid and surroundings temperature are equal at lhe inlet to lhe pipe. This will be lhe case foe flowing wells, where TI is lhe reservo ir temperarure. AIso included is the assumption lhar the heat los5 is independent of time. This assumption limits application of -Equation 3-100 lo weHs that ha ve been peoducing foe a consideeable length of tíme. When multiphase f10w is occurring in a \Vell. the variables involved in evaluating lhe relax.ation distance, A, are \'cry difficult to detennine, especially {he overatrheat transfer coefficient U. In view of mis fact. Shiu and Beggs:!2 devdoped an empirical method to est¡mate A based 00 measured temperature prefiJes from 270 wells. Using lhe measuI'ed temperatuI'es TL at various locations L, a value of A foc each test was calculated from Equation 3-100. An equalion lo estímate A was lhen developed as a function of data which wiH usually be known. The equation is:
where Ts is the surroundings tempcratur¡; and the other variables are defined in Equation 3-100. For flow of gases, the Joule-Thomson efrcct may be included, but since this crreet depends on pressure, an iterative solution is required. The more rigorous equation ¡s: T,
~
dp/dL
PL d APl
19
rela\:ation distance, ft lolal mass flow rate, IbmJsee liquid (oi! and watee) density at standaed eonditions,lbmJft' p'pe 1. D., in. oil geavity, o API gas geavity (air ~ 1)
-c •
EXP (-L/ A)
(3-103)
Joule-Thomson cocfticient, and pressure gradient at L.
As was discussed earlicr the data necessary to calculate the heal transfer· coefficienl U is seldom available. A simplified approach to estimaling flowing temperatures in either wells or pipelines may be used if at ¡east one measured set ofinlet and outIel temperatures is available along wilh one measured !low cate. This appeoaeh ean be used foe oil and gas wells. A proceduee ¡s: 1.
Using the measured temperatures and flow rates, solve the flowing temperature equation for A. Equation 3-100 applies foe weHs, while Equation 3102 applies foe pipelines.
2.
Considering aH the variables in A excepl f10w rate lo be constant, solve foI' the constan!. A ~ wCp/lfdU ~ Cw
where
A
=T, +}lA(dp/dL) +[1; -T, -fL.j(dp/ dL)]
where
(3-101)
W
0.0149 0.5253 2.9303 0.2904 0.2608 4.4 t46
oc C=A/w
Flow in Pipes and RestrictioJlS......
3.
83
Use this value of e to estimate a value for A for other flow rates.
IV. WELL FLOW CORRELATIONS One of the most important eomponents in the total well syslem is lhe well lubing. As much as 80 percen! of the total pressure loss, that is PR - P.ftp' can beeonsumed in lifling lhe fluids from lhe boltom of lhe hole lo lhe surface. The tubing pressure loss is expressed in Figure 3-1 as P....f - PlI"h' The flow may exist in tubing or in the aonulus betwcen the tubing and the casing. The wells may be vertical of can be drilled at large deviation angles, especially in thc casc of offshore wells or weIls drilled in urban arcas. The general pressure gradient equation, which will apply to flow of any fluid in a pipe at any inclination angle, was given as Equatioll 3-16.
dp pgsin8 Jpv' pvdv -= +--+-dL g< 2g,d g
(3-16)
If the angle from vertical is used in the equation, it becomes
cljJ
~:::C
dL
pg cos<jJ + __ Jpv' + __ pwlv
g,.
2g,d
g,dL
(3-104)
wherc $ = émgle of the well from vertical. Equation 3-16 was wrilten as the composite of Ihree componcnts in Equation 3-17 as:
(;n"", =(:}/(: l+(: L
(3-17)
The numbers given in the table are" of course only approximations, since sorne oi! wells produce at high gaslliquid ratios (GLRs) and sorne gas wells produce considerable arnounts of liquid condensa te or water. Many correlations have been developed in the lasl 30 or 40 years for predicting two-phase flowing pressure gradients in producing wells. A list of the many methods and a briefreview ofeaeh can be found in Brown. 13 Sorne investigators chose to assume that the gas and Iiquid travel at the same velocity so that the mixture density can be calculaled based on lhe no-slip liquid holdup A.L (Equalions 3-22 ahd 3-30). In this case a correlalion for H L would not be necessary, and if acceleration is ígnored, on(y a correlation for two-phase friction factor is neccessary. This is, of course. a gross oversimplification of the problem and generally does not give good results. No methods presently exist for analytically evaluating eilher liquid holdup or friclion factor. Therefore il has been necessary to develop empirical correlations for these two pararneters as functions of variables that will be k.nown or can be calculated from known data. This requires an experimental facility from which values of H L and two-phase friction factor fTP can be measured under a wide range of now conditions and flow geometries. A general pro cedure for accomplishing this is described that will aid in the understanding of how the various correlations were de\·eloped. An experimental facility is requircd from which measurements can be made of qL' qg. 6.p, H¿, and in ~ome cases now pattern. The experimental data are then o'brained by the following proccdure: l.
Establish st3ble flow conditions at particular valucs of qL' q¡;. pipe diameter, pipe anglc, etc.
2.
In a test sex'tion of length M, measure HL and Ap. Methods f(lf rncasuring HL ¡nelude nuel~r den sitometers, caJ'Jcitance devices, quiek elosing valves, etc. Flow rattern may be observed ifthe test section is transparento
3.
CalcuJate mixture density and elevation component.
The rangcs of contribution of each of tbese components to the total pressure drop in the well can be sccn from the following lnblc, whcre the contributions are listed as per(cnt of total óp in the tubing, p,,¡- PII'/¡' for both oil and gas wells ... Componenl
Elevation (Hydroslalic) Friction Acceleration
Percenl 01 Total dp üil Wells Gas Wells
70-90 10-30 0-10
The dcnsity of lhe fluids in oil wells is usually much greatcr than for gas \Vells, and since the hydrostatic component dcpcnds on liquid holdup, the most important parmnctcr tha! must be cvaluatcd is thc liquid holdup. In gas "'elis, 1he fluid density is smaller, but the gas is usually moving at a rclatively high vclocity, which generales more rriction loss in the pipe. This necessitatcs havlng a good valuc ror pipe roughness from which fo obtain 3 friclian factor.
1
p, =p,H, +p,(I-H/.l
20-50 30-70 0-10
dP ( dL 4.
= p,gsine g<
Calculate 30 aFceleration component (if it is to be consideredl aod the fricrion component.
(:), = ~~ -( d~ 5.
1-(:t
Calculate a two-phase friction factor.
f, = 2g ,d(dP ) rp
pI"
"
dL
,
Pl'Oduclion Optimization Using Noda/ A Jlolysis
6.
Change test conditions and retum {O Step 2. HL>frp and flow pattcen should be obtain~d over a wide range of condilions.
7.
Dc"clop empirical correlatians for H¿'!TP and perhaps flow pattcm as a functian of \'ariables lhat will be known for design cases. These variables ¡nelude vsL' l's!." d, fluid properties, pipe angle, etc.
producing through tubing sizcs ranging from 2 3/8 in. lo 3 112 in. Most of the wells were proaucing at liquid rates less lhan 500 STB/day al GLRs Iess than 1500 scf/STB. Only a correlation for two-phasc friction factor was developed sincc the only rncasurcmcnts made \\'cre surface and battamhole pressures and fla", rates. Liquid haldup was not measured, and the wells were nol divided into short lenglh incremcnrs. The mixture density was ca1culated using the no-slip holdup. and aceeleration was ignored. A plal of lhe frictian factars calculated from the measured field data is showll in Figure 3·14. The correlating parameter for the frictian. factor was the mas s flow rate dividcd by nl4 times the pipe diameler or pvd in Ibmltl-sec. This simplificd approach, in which the energy losscs Ilat included in the hydrastatic term or Ihe acceleration lerm were absorbed in the frictim\ term, \\'as used for many years, mainly because of the diffículty al' measuring 1iquid holdup. In 1961, Baxcndell and Thomas" extended the frietion factor correlatian to hígher rates and larger pipe sizes using data oblained in VcnezuelJ.. Fancher and Brown:!6 used the same approach in an
The well flow pressure gradient melhods described in this section will he discussed from the point of view of their development. Some investigators did not measure H L, sorne did not measure flow panem, and others ignored the contribution of the accelcration component. In some cases, seperate correlations for H¿ andfTP were dcvelopcd for cach ofthree separa te flow patterns. Use of lhese methods requires (hat the flow p:.Htem ~xisting at the loealion of intcrest in the well be detennined first. This, of course, requires a HO\"" pattcrn map or sorne other means of predicting flo\\' paHerns. Several ofthe most widely used well no\\' methods will be diseussed in litis section. The discussions will be limited ta: l.
Ha\\' lhe experimental data were obrained.
')1 .
Ha\\' the corrclations far H¿ and/7? werc dcveloped.
100
'DClaikd equations and example calculations for each af thesc mClhods may be found in References 9 and 23. Computer subroulines [ar most of the melhods are given in Referenee 9. After discussing the development and application of tite various methods. several evaluation srudies of tite methods using measured field data will be described. This will aid the engineer in choosing whieh method to use for particular conditions existíng in a well or ficld. The effeets of changes in conditions that can exist from fidd lo field or from weU lo well in a field wiU be presentcd. These conditions include variables such as GLR, pipe size. water cut, etc. The preparation and use of pressure tr3\"erse curves for quick estimales af pressure drops in flowing weHs will also be described. These curves can aften be used for preliminar)' evaluation of a well or field prior to a more detailed analysis, which usuaHy requires a computer.
10
The principal reason for including this melhod in the discussians is the faet tbat this was the first serious anempl al solving Ihe multiphase weU flow problem. Alsa, this method was widely uscd for many years far design of flowing and gas lifl weUs. The Paettmann and Carpenter24 method was dcveloped using measured field data from sorne 334 flowing wells and 15 conlinuous flow gas lift weUs. The wells were
\
-
.-
..
-
!
1.0 o
.,. ....
"u
o
0.10
.. t,:
.¡
A. Poettmann and Carpenter Melhod
==. -
.
0.01 : : t;¡o
Flowing wells
=.
Gos litt wells
-
-
" -
\
Bureou 01 Mines doto
I I I 111111 0.00 I 0.1 1.0
I I 1111111
I
10
pvd. 1bm/ft-see
Fig. 3-14. PoeNmann-Carpenter friction factor.
100
• Flow in Pipes and Resfríetions
85
attempt to isolale the effeets of gasfliquid ratio on the pressure gradient. These methods, although easy to apply, will give erroneous results wllen applied to wells that are not producing under conclitioos very similar lo those from which lhe developing data \VeTe obtained.
B. Hagedorn and Brown Method The Hagcdorn and Brown 27 rnethod was developed by obtaining experimental pressure drop aod Oo\\' rate data from a 1500 ft dcep instrumented \,"ell. Pressures weTe measured for flow in tubing sizes ranging from 1-1/4 to 2-7.'8 in. O. D. A wide range ofliquid rates and gas/liquid ralíos \Vas included, aod the effects of liquid viscosity \VeTe studied by using water aod oil as the ¡iquid pilase. The oils llsed had viscosities al stock tank conditions of 10.35, and 110 ep. ¡\cilher liquid holdup llar now paltero was measllred during the Hagcdorn and Erown study, although a correlation for the calculaled Iiquid holdup is presenled. The correlations \Vere developcd by assuming that the twophJse friclion factor could be oblained from the Moody diag:ram bascd on a two-phase Reynolds Number. This Reynolds Numbcr reqllirc~ a value for H L in the viscoslty termo Thc proccdurc used for obtaining the calculaled H L i:5: 1. 2. 3.
Measurc t'1p/fl.L. Estimate a valuc for liquid holdllP, H L*. CaIclllatc N Rl•rp and find Irp from the Moody dia-
4. 5.
Calculalc (dpldL)fand (dpldL)",. Caleulate (dpfdL)d ~ t'1p/t'1L - (dpldL)f -(dpfdL)." and p, ~ (dpldL)" g!g. Caleulate IfL = (p, - Pg)/(PL - p,) amI compare with H L *. Ir not c1ose, sel IfL* ~ If L and go to Stop 3. Continue until convergence is obtained.
gramo
6.
Nd NL
diameter number liquid viscosity number
The other parameters have beeo defined previously and the units must be seleeted so lhat the numbers will be dimensionless. The three empirical correlations required for obtaining a value of H L are shown in Figure 3-15. Two modifications have beeo made to the original Hagedorn and Brown melhod that have extended the valid range of applieation eonsiderably. It was found that for sorne cases the value ca1culated for HL was less than the no-slip holdup AL' This js physically impossible in 0.0SI-
0.0 l
~
J
Z
E 1-
()
f-
.,,,.
,
0.00
0.001
~ .
0.01
I
V ,"
."
0.10
1.0
(8) Corralalfon ter Viscesity Number Coefficient .0
~
1/
o.S
~o
"
..
/
' c.
~O .4 'O
/
./
:<
O
O
10
10
.~ .,
..,
...
10 10 (N IN .575)(_)·10 CN L LV ev Pe N D
p'.o
10
,
(b) Holdup Factor Correlallon
The value of HI. obtained is nol necessarily lhe actual liquid holdup, bul it is lhe vaiuc requircd to balance the pressure losses once a friction factor has beeo sclected. SC\Tral dimcnsionlcss llUlllbers \Vcre uscd to corrclate H L and t\Vo secondary correetioo factors. These dimension¡css numbcrs had bccn dcfincd earlier by ROS28 and are gi\"cn as follo\\'5:
O
,.
• ,
1.
2
,.OO
-
k-
1.
,. (3·105)
S
I/)
l>:'
..> 0.02
0.04
0.06
0.08
0.10
(NovNl.·~tNo:r·1-4
(e) Correlallon for Secondary Correctlon Factor
whac liquid vclocity l1umber gas vclocity numbcr
Fig. 3-15. Hagedom·Brown ho/dup Corre/alions. (a) Cor-
re/afian for viscosity number coefflcient; (b) Holdup factor corre/afian; (e) Correlation for secondary correetion factor.
Productioll Optlmization Usillg Nodal Analysis
86 upward two-phase f10w so a lowcr limil \Vas imposcd 011 the HL " Ihat ¡s, N L must be greatcr than oc equal lo AL' The second modification involvcs d~termining if the flow faHs into lhe bnhble-flow pallem as defined by Orkiszewski.'. If buhble flow does exist, the GriffilhJO correlation is used lo determine the pressure gradient in lile pipe increment under consideration. The Orkiszewski and Griffith corrclations are described in a subsequent
Frgth no... IlfGlcrl 1
R(GIOll 1I B"bbl~ II~
section. The Hagedorn and Brown method has been fonnd to give good results ayer a wide range of well conditions and is Dne ofthe mast widely used weU t10w correlations in the industry. A detailed calculation procedure and example may be found in lhe appendix.
• 1.0
PI1I9 11"",
0.2
10·1c...,~_~--"'---'-'--_~~~_--"---' . .~_~--' 10. 1
lO Hg • • VSg
C. Duns and Ros Method
..
~-
..
Fig. 3-16. Duns and Ros31 flow patlern map:
Duns and Ros31 published the resultS 01' an experimental study of vertical two-phase flow. The experiment, which consistcd of some 4000 runs and 20,000 data points, was conductcd in a labaratary facility at low pressure using air, oil, and water as the tluid companents. The test section was lO m long and me: pipe diameters ranged from 3.2 to 8.02 cm. Sorne annular flaw tests wece also conducted. Liquid holdup \Vas measured with f3dioactive tracers, and flow pallern was obscrved through the transparent test sc:ction. Thc expl.:rimcntal \York and the prcliminary development of the correlations were reported eacliee by ROS.2S Thrce no\\' patterns \vere defined, and p. f10w pat~ tcm map was conslrllctcd from which [he f10w pattern can be detem1Íne:d based on the superticial velocities of the liquid and gas phases. The flow paue:rns are described as follows: Region 1: Ihe liquid phase is continuous, and the gas movcs as discontinuous bubbles or plugs. This region is ofien refen·ed to as the Bubble-jlow Pallern. Region H: 80th the liquid and gas phases are discontin1l0US. Ihis is sometimes called the Slug-j1ow Pa/fern. Region m:The gas phase is continuous, and the liquid moves as droplets dispersed in the gas or as an annular ring around the inside of the pipe. This region may be caHed the Misl-flow Pallem. A transition zone between Regions II and III was a150 identified. The f10w pattem map is sho",n in Figure 3-16. Equations \Vere presented for determining the bounderies of the various flow paUems as functions of dimensionless numbers. Separate correlations for ¡iquid holdup and friclion factor were prescnted for each of the flow regiDns. Acceleration was considered important in Regioo JII only. The liquid holdnp was correlaled in lerms of a dimensionless slip velocity, which was defined as
N, = v, (p, I ga)o."
10]
IPl'g~l"
(3-106)
where Ns Vs
dimcnsioniess slip vdocity actual slip velocity
Once Vs is detemúncd, H L can be calclllatcd from Equation 3-29. \',.0.:
\'_,L
l-H,
H,.
\' = - - - - -
,
(3.:>;1)
The slip velocity was considered ncgligible in Region 11I, and Ihercfore H L= AL' Both the dimcnsionlcss slip velocity and the fríclion factors were correlated as functions 01' the dimensionless numbers presentcd earlier in Equation 3-105. The correlatians were presented as a series of complex graphs thar must be transfomled to either equation or tabular form for computer application. The Duns and Ros rnethad is cOllsidcred to be applicable over a wide range of well conditions, especialIy an updated, proprietary version commonly known as the SheH Method. The correlation for Region 11I, lhe Mistflow Pattern, is recommended by both Orkiszewski29 and Aziz J el al.3 2
D. Orkiszewski Method Orkiszewski 29 performed a comparisan study on sorne 148 measured well conditions and found that none ofthe correlations existing at that lime (1967) adequately predicted the measured results. He thcn used the data 01' Hagedorn and Brown 27 and the field data fram the 148 oil well conditions lO develop a new correlation lo be used in the Bubble- and Slug-flow palterns. He recommended using the Duns and Ros method for Mist-flaw. The flow patterns considcred by Orkiszewski are
• Flow in Pipes and Restriclions
87
shown in figure 3-17. Orkiszewski's descriptions of these flow patterns are included.
Bubble Flow The pipe is almost eompletcly filled with liquid, and thc free gas phase is prescnt in small buhbles. The bubbies move al difTerent veiocítícs and, except for their density, have Iiltle effeet on the pressure gradicnt. The wall of lhe pipe is always contacted by the liquid phase. Slug F10w The gas phase is more pronounced. Although the liquid phase is still continuous, lhe gas bubbles coalesce and form plugs or slugs that almost filllhe pipe cross section. The gas bubble velocity is greater Ihan tha( of lhe ~iquid. The liquid in lhe film around lhe bubble may move downward al low velocities. 80th lhe gas and ¡iquid have significant effects on lhe pressure gradienL
In the Slug-flow pattem the Iiquid density was calculated using a so-called Liquid Distribution Coefficient, rather than the liquid holdup. A dislinclion was made as tú which equations are used to ca1cuIate the liquid distribution coefficient depending on whether oil or water was the continuous Iíquid phase and ir the mixture velocity was greater than JO fl/shsec. The Orkiszewski method can be computerized and has beeo widely used in the pelroleum-industry since its pub!ication. It is applicable over a wide range of well condiliaos, but in sorne cases, a mixture density less than the no-slip density will be ealculated. This is probably the resuit of using the Hagedom and Brown data to develop the equations for Slug-flowo AIso, discontinuities in the calculated pressure traversc can occur as the mixture velocity exceeds 10 fl/sec. This resuits from changing equations for mixture density at this velocityo
E. Azíz, Govier and Fogarasi Method
Tro17silion Floll'
The change from a continuous liquid phase to a continuous gas phnse occurs. The gas bubbles rnay join and liq~ uid may be entrained in the bubbles. Although thc liquid effects are significant. the gas phase effccts are predominant. Afisr Flow
The gas phase is c('Intinuous. and the bulk of the liquid is entraincd as dropkr:; in tlle gas phase. The pipe wall is cmned \\'ith a liquid film, but lhe gas phase predominantly controls (he prcssure gradient. Equations were presentccl for determining the flow patA (em exisling under \'arious eonditions. and methods for calcul
Aziz, el. al.,32 proposed what they referred to as a mcchanistic mode!. They proposcd a new vertical flow pattern map and presented new equations for calculating lhe liquid holdup occurring in thc Bubblc- and Slug-flow patterns. No ne\\' equations were proposed for the Annular-rnist paltern 8nd the Duns and Ros cquations \Vere recommcnded fm this no\\' pattem. The no\\' paltcrn was corrclatcd with dimcnsionlcss numbers which depend primarily 00 the gas and I¡quid superficial velocities. The now pattcrn map is shown in Figure 3-18. The coardinates, Nor. and N.,., are defincd from:
N~
='" V,t
N =v ,.
i[
.
~
iI , ,
I
o
o
,
1
.
1'
o
1,
• o
•
il , , o
" •
g
(;
z o ¡=
• • • o
BUBBl~ '-
¡(J ~ ~
"
o=(
Gi~. ~~l,~r t
lli' Irl .,
Q °T:o
o
~
\ O,,,
(;
17'~
¡:: ~
l·' '~
.;!
SLUG
I
3'1
Pl,O"...
p... aL
J"
(J-107)
Ji,
PI.O ...
(P...o r. J
where '.
¡ji
Pg PL aL
o\\'
· °r¡I1
"
.11
•
(..
,\ ...
··1
Pobo
l ')!I1:
Pw
in-situ gas density, in-5itu liquid density, in-situ gas-Iiquid interfacial tcosion, interfacial teosion between water and air at soc., dcnsity of air at S.C., and density of water at s.c.
oz ( o. . oo o,! ~
"
'.
j"
1, •
o
1
· '1' ··.1: · . ti
ANNUtAR - 5~UG ANNULAR - Ml5T TRANSITfON
Flg. 3-17. Verileal flow pattems.
03)) (
O,"
.
r~ l, '.
(EL P..;, J
The liquid holdup \Vas calculatcd as a fUl1ctíon of a bubble-rise velocity. The bubble-rise velocity was caleulatcd using eguations proposed earlier by Zubcl, et <"1. 33 The new equations \Vere uscd in a comparison study utilizing measurcd data from 48 wells. Thc difference in Ihe accuracy of the new equations and the Orkiszcwski mClhod was negligiblc,
88
Prac/lIdion OjJlimization UsiJlg Nodol A/w/ysis
2G. S
10
"1
1.0 BUBIHE
SlUG
Ny
ANNUlAR-MI S T
",
"
.1 TRANSIT 1Ot-
.01 .1
1.0
10
100
measured at angles from horizontal of 0, plus and minus 5, lO, 15,20,35,55,75 and 90 degrecs. lhe eorrdations were devclopcd from 584 mcasured tests. Different corrclations foc ¡iquid holdup are prcsented for each of !luce horizontal fiow regimes. lhe liquid holdup that would exist if the pipe were horizontu/ is fiest calculated and thcn corrected for lhe actual pipe inclination angle. The horizontal-fiow patterns are illustraled in Figure 3-19. The variation of ¡iquid holdup with pipe inclination i5 shown in Figure 3-20 fOI" lhrec 01' lhe tests. The holdup \Vas found to be a maximum at approxi~ mately +50 degrccs from horizontal and a minimum at approximate\y -50 degrees. The original flow-pattem map has becn slightly modified to include a transition zone between the segregated ami intermittent f10w regimes. lhe modified Oow-pattern map is superimposed on rhe original in Figure 3-21. A two-phasy friclion factor
111 X Fig. 3-18. Aziz flow regimes.
Sll-gregalod
F. Chierici, Ciucci and Sclocchi Method Another modification of the Orkiszewski merhod was proposed by Chierici, et al. 34 lhe modilication consistcd ~5scnlially of eliminating rhe discontinuilY inher~nt in the Orkiszewski equations for mixture density in slug flow. Chicriei, el al., found lhal the fluid ph)"sieal properties, which must be dcterrnlned al each stcp in Ihe pr~ssure traverse calculation, had a considerable efTect 011 the accuracy of the pressure drop calculation. They. thcreforc, specified which fluid property corelations were to be used with thcir pressure gradient method.
Annular lnlelmlrtcnl
G. Beggs and Brill Method lhe Beggs and Brill 35 eorrelalion was developed from experimental data obtained in a small scale test facility. lhe facility consisted of 1 in. and 1.5 in. seetions of aervlie pipe 90 ft long. lhe pipe eould be inclined at anv angle. The parameters studied and their range of variation were: (1) gas flow rate (O lo 300 Msef/D); (2) liquid flow rate (O lo 30 gaVmin); (3) average svstem pressure (35 lo 95 psia); (4) pipe diameler (l and 1.5 in.); (5) liquid holdup (O lo 0.870); (6) pres,ure gradienl (O lo 0.8 psi/fl); (7) inelination angle (-90' lo +90'); and (8) horizontal flow pattem. Fluids used were air and water. For each pipe size, liquid and gas rates were varied so that aH flow paUems were observed when the pipe was horizontaL Afier a particular set of f10w rates was set, the angle of me pipe was varied through lhe range of angles so lhat me effeel of angle on holdup and pressure gradient eould be observed. Liquid holdup and pre,sure gradient were
~=t;;:::::~::;::22:::::~r Slug
Dlstrlbulod
Fig. 3-19. Horizontal flow palterns.
.
.
Flow in Pipes and Res/ric/ions .
89
50 6~~264
+,
40
= 156
O, = 010
z
O
~
30
LL
ri. ::> a -'
O
20
I
Q
::> O
:::;
10
00 -90
-70
-50
-30
-10 O
10
50
30
70
90
ANGLE OF PIPE FROM HORIZONTAL
Fig. 3-20. Liquid holdup vs. angle.
is calculated using equations that are independent of no\\" rcgimc but depend on holdup. The cquations prescntcd by Beggs and Brill apply to fl0,," in a pipe al any anglc of inclination, illcluding
dt.."'Iwnward no\\'. Allhaugh ¡he lllethod has bccn [aund to slight!y over-prcdict pressure gradienls in n:rlical wells in :::"..1me cases, il gives good results for pipeline ealculati(ln:;. The faet that Ihis method can be used for pipes t\t
any angle and the faet that it is presented entircly in equation form make it an ideal mcthod for use in handheld. prograrnrñable calculalors. A program of the Bcggs and Brill method for calculating él. pressure lraversc in wells or pipclincs \Vas publishcd by Hcin 3(..37 in 1982. The program is ror use in the HP-4! e calculator and must be used in conjunction with the Pelroleul11 Fluids Pae dcscribcd earlíer.
111 100
\',
\',-
oc
z
~ ~
.o
\"
\"
10
E
e
~ ~ ~
,,
\,
"" '- ,
--Original map - - -Revised map
~
l
o
\,
2
Symbo 1
~
~
11
\"
~
IV O. 1 L 0.0001
Segregated lntermittent Oistributed Transition
3~21.
Horizontal flow pattern map.
\,
"
\
"
IV \ \
~---'--------'-------'----'>.--'---~
0.001
0.01
Input liquid contento Al Fig.
\, \,
1.0 1 11 111
,
\
0.1
1.0
ProdllCliOll Optimízatjoll Usillg Nodal.-lllal.l"sis
90
... A dctailcd calculation procedure and an example utilizing the Bcggs and Brill mcthod mar be found in the appendix.
H. MONA, Asheim Method Asheill178 dcscribed a model that was used in a computer program caHed MONA for two-phase l10w calculations. Thc program was developed at the Norwegian Instüute of Technology and was proposed foc use in both surface pipe and wells. No experimental data were used in the development. The morlel dOes not distinguish 8mong flow pattems. Liquid holdup was not directly predicted but a lincarized funcrional relationship between gas and liquid velocities was assumed lo calculate two-phase density. This rclationship, which was similar to earlier work by Nkklen, el al./ 9 requircs knowledge of two constants oc no\\' parametcrs. An extension of the Dukler55 equation was used to obtain a frictian factor. Anolher adjustable no\\' parameter was included in lhe [riction fflctor equalion. The program is conslructed so that measured field data can be used 10 adjust and optimize flow parameters that can then be used to make predictions for other tlow conditions for cases similar to thoses that were used to calibrate the ffiodel. This procedure, of course, could be used in aH oC the other rwo-phnse flow models describcd pre\'iollsly. \Vhen no calibration data are availablc, Asheim proposcd using values for rhe flow paramelers lhal were developed by Nicklen. 79 '"IONA was used to calculate lhe pressure deop for 50 caSeS of w~lIs producing from the Ekofisk fi
among scveral flow pattems [or both circular pipes and anllular flow. CorrelJtions for gas \"oid tj'aelioll \Yac given for the varioU$ flow patterns, and friction losses were calculatcd using "standard charts or corrdations in terms of Reynolds number." Thc propuscd model was tested using rield dala [rom ten offshore wells. Comparison of the proposed modcl wi¡h lf!JI of Beggs and BriHJ5 suggested [hat it performcd s~ightly bener. No claim was made as to the new modcl's :iUpcriority a"er existing methods because of the small dala base used in the test.
J. Flow in Annuli Many situalions arise in rhe pclrúl~um industry in which a wel1 must flow through th~ <111nular spacc bctween the tubing and casing. Example::: ofthis are dual completions with onl1' one tubing string: wells equippeJ wilh a kili string, and gas-lifting high-r;"l.(c wells in which the gas is injected clown lhe tubing. Nune ofthe previousl)' discusscd well tlow correlntions was developed specifically [or annular tlow, althaugh Hasan aod Kabirso includcd anJ;lular tlow prcdiction capJbilüy in their model. The correlations d~vclopcd for cir· cular pipes are sometimes used rol' anllubr Oow by applying the hydraulic radius concept. This mdhod and a proceduce proposcd by Comish,38 \ViII be discussed in Ihis sec¡ioll. l. Hydruulic Radills COllcept Aecording to lhis concept, the d¡am~tcr of a conduil of circular cross scction is equal to tour limt.:s the hydraulic radius, where the hydraulic radius is defincd as lhe eros::> sectional area open lO flow divided by ¡he \Vetted perimeter. That ¡s,
,
r
Hasan and Kabir" proposed a mode! lhat is to be used especíaHy for dírectional or devialed welis. The model predicts both flow pattero and pressure gradient. H was bascd on experimental dala obtained [rom a five in. circular pipe and from annular flow channels [oc deviation angles up to 32 degrees from vertical. Equations were presented for calculation of flow pattern transitions
d rrd
wened perimetcr
4
When applied to an annulus, this becomcs:
',=
lr
(di -d;)/4
d, -d"
lr(dj + dol
4
where
do dj rJ¡
1. Hasan and Kabir Method
eross sectional area
outside diameter of the rubing inside diameter of the casing hydraulic radius
r"
Setting the two expressions for equal implies lhat the correct express ion for hydraulic diameler d" is: d, = di --d" To calculatc superficial velocities, the actual cross sectional area open to f10w should be used. Using this concept, any of the pre\·iously described well-flow methods can be applied to annular l1ow.
Flan- in Pipes and Restrictions
91
The no-slip density \Vas used [or the elevation component and the fríction factor was obtained rrom a Moody diagram. The method has not found wide use in the industry because of the limitations stated previously.
JI is generally assumed thal the hydraulic radius concept is valid for annular flow if djd; <; 0.3 in the case of single-phase flow. Ihis limitation has not been confirmed [or two-phase flow. 2. Comish Method Comish 38 presented a method ror calcularing pressure traverses [or annular flow wells in which the Iiquid flow rate exceeds 5000 STB/day. No experimental data were used to develop the method, and il applied only to cases where there is essentially no-slippage between the gas and liquid phases; that is. ror the case where H¿ = AL' Cornish assurncd this to be the case ir his two-phase Reynolds numbcr was greater than lOS. The Reynolds number is defined as:
K. Evaluation of Correlations Using Field Dala The only meaningful procedure foc evaluating the V3Cious pressure-gradient prediction methods is by comparison ofthe pressure drop in a well predicted by the method with actual measured field data. Evaluation studies have been performed by several investigators, but in many cases the study was performed primarily to demonstrate the superior performance of sorne newly proposed pressure-gradient method. The results of several evaluation studies are su mm arized in this seclion. Also, atable is prcsented that gives infonnation regarding the developrnent of the well-flow rnethods evaluated in sorne of the studies. Table 3-1 summarizes the ranges of data used, the type of data, the pipe sizes and the fluids used lo deveIop the various methods.
(3-t07D)
where
mass flow rate hydraulic di ame ter A = area open to now ~"= mixture viscosity = (~l1t )(~~
11'
=
d~ =
)
TABLE 3·1 Well
Year
Flow
Correlations
Presenled
Type of Study
Pipe Sizes, in.
1952
Field. Experimental
2,2.5,3
oil, water, gas
Correlation developed frem well tests with q' > 420 STB/D, GlR < 1500 scf/STB.
Baxendell & Thomas
1961
Field, Experimental
2.5,3.3.5
oil, gas
Based on well data trom Lake Maracaibo Field. Very high flO'N rates.
Fancher & Brown
1963
Field, Experimental
2
water, gas
Data from or.e well, used GLR much high* er Ihan Poettman & Carpenter.
Hagedorn & Brown
1963
Inlermediate, Experimental
1,1.25,1.5
oil, air, water
Dala from 1500 ft. experimental well. Used wide range of oi! viscosity.
Duns & Ros
1963
Laboratory, Experimental
1.5. 2, 2.5, 3
oil, water, gas
Correlation developed from large number of laboratory data poinls.
Orkiszewski
1967
Field, Experimental
1,1.5,2,3
oil, water, gas
Utilizad sorne fip.ld data and Hagedorn* Brown data. New method ror slug flow only.
Az.iz. et al.
1972
Theoretical
Chi~rid.
1974
Laboratory, Experimental & Theoretical
0.5,0.75, 1_0
water, ail, gas
1973
Laboralory, Experimental
1.0, 1.5
water, air
A5~im
1986
Théoretical
HSXln & Kabir
1986
Laboratory, Experimental & Theorelical
Ir.esfigalors Po€"~ann
& Carpenler
et al.
Be9Js & Brill
Ffuids Used
Remarks
Revised Orkíszewski extenslons of Griffith-Wallis data. New f10w pattem map. Usad Wal1is & Nicklen data. New method for slug f1ow. New f10w pattem map. Method is primarily for inclined flow. Large number of low pressure data poinls. Based on work done previously by Dukler. 5, with some annular cases
Primarily for dírectional wel1s.
PrOd¡¡C:liOJl Optimization USil1g Nodal AI/o/ysis
92
TABLE 3-2 Well Flow Comparison Studies No. Wel/s
Authors
or Tests
8rown
Ibe
Rossland Asheim
Hasao
Well Ds-plh Rangf;;. n.
Pipe Diameter Range, in.
35
Aziz 48 Espanol 44 OrKisz.ewski 148
lawson
GORRange
726 892 130 50 10
2.5-7 140-10000 140-10000 185-7000 20-80000 0-78800 480-19000 300-500
4000-12500 4300-12500 3800-$)00 920-12500 1000-12000 5000-11000 6900-10000
37295 37264 1.0-8.8 2.6-5.1 3.958-6.184
The type of ficld data used in several comparison stud¡es is dcscribcd in Table 3-2. Rcsults of these studies foc the various wcll-flow corrclations comparcd are given in Table 3-3. rile comparison p3.ramcters are average pereent error 3nd standard deviation of the peccent enDes. The standard deviation is a measure of Ihe scatter of the calculated eeroes. Sorne of the comparison studies failed to calculate the dcgrce of scatter, bUl presented only average errors. A comparison is, of course, incomplete without sorne measure ofscaner. A positivc percent error indicates that the correlation predictcd a greater pressure drop than was measured.
TABLE 3-3
Comparison Study Results Comparisan Study Aufhar
Brown
Azjz, et al.
Vertical Corre/afien
Beggs-Brill Orkiszewski AziL et al. No-sjp
Avg. Pareent Error
-3.45 -2.41 -9.9 -6.84
Aziz.. al al. Orkiszewski Hagcdorn-Brown Ouns·Ros
8.9 8.9 -20.5 -11.1
Espanol, el al.
Hag==dorn-Brown Orkiszewski Ouns-Ros
-24 -15.5 -16.6
Orkiszewski
Orkiszewski Ouns·Ros Hagedorn-Brown
-0.8
Lawson, et al.
Ibe
Rossland
Asheim
Poettmann & Carpenter Baxendell & Thomas Fancher & Brown Ouns-Ros Hagedorn·Brown Orkiszewski Beggs·Brill Aziz. el al. Chierici, et al.
107.3 108.3 5.5 15.4 1.3 8.6 17.8 -8.2 42.8
Hagedorn-Brown Orkiszewski Duns-Ros Beg9s· Brill
1.24 -0.75 13.62 19.17
Hagedorn-Brown Orkiszewski Duns-Ros Beggs-BrilJ Poettrnann·Carpenter
-3.5 8.4 -5.5 10.7 14
MONA
Baxendell & Thomas Hasan, et al.
2.4 0.7
Hasan, et al. Beggs·Brill
Standard Devialion
7.39 16.22 13.95
868 14.7 14.8 2-1.0 1~_9
10.8 27 24.2 195.7 195.1 36.1
50.2 26.1 35.7 27.6 34.7 43.9
23.3 34.4
n.6 31.8 8.5 28.4 12.8 15.5 12.3
-2.38 -13.32
2.92 2.96
0.89 3.22
10.12 11.71
Flow in Pipes alld Restrictiolls ._ ......
93
It should be Doted that sorne bias exists in the results of 5()me of the evaluation studies reported in Table 3-3. In the Aziz and Orkiszewski studies, the data used in the comparison were also used to devclop the author's corrclations. In the Lawson sludy, of the 726 eases ealeulated, 3~6 were from lhe dala used to develop lhe Hagedorn and Brown rnethod. These tests were laler eliminated, and 3Ithough the accuracy of the Hagedorn and Brown method was diminished, it still gave the best results of all !be methods tested. The lbe'. study ineluded data from 300 direetional wells, and aJl of the wells used in the Rossland 41 and Hasan 80 studies were directional. The results of these evalualion studies cmphasize that DO one rnclhod is best for aH wcll cases. One rncthod may re best in one ficld whilc anothcr may be best in another :field. Therefore. the best procedure for determining which method to use in a particular field is to gather as much measured field data as possible and make a com::arisan study using lhat data,
L. Effects of Variables on Well Performance During the producing life of a ",eH or field many concan c113n~e that wilI affect [he \ve\l's flowing per~·omHmce. Also. ~onditions can change from welI to welI ::1 J field at a gi\"cn lime, and conditions can ccrtainly ., Jf\' among fields. Sorne of these variables that can ':JJ.-nge are liquid flow rate qL' gas/liquid ratio GLR, -.l."3tt':r/oil ratio "'OR (or water cut/J, oil or liquid viscos=':- !lv and fubing size d. As will be seen in the section on total system analysis, pl3nning for future wetl performance requires accounting :or the changc in pressure drop in the tubing (PIIY P'Il'h) as r:.1;ese variables changc_ The cffects of changes in these yariables can be calculated using any of the well-flow ..:orrclalions discussed previously. In this section. lhe effccts ofvariablcs wil! be discussed ,;u3litalively .lid iJlllstrated graphicaJly. This will lead lo 2 bettcr understanding of changes in wcIl performance as L'bserved in the fidd. Most ofthe examples in this section were calculated by Brill, et al.,4~ using the Hagedorm and Brown correlation. Similar results would be obtained l!5ing any of Ihe other rncthods. Bcfore discussing the changes in individual variables, ir will be infonnative to write the pressure gradicnt equaiion in a slightly different formo Ignoring acceleration, Equation 3-16 can be written as: ~:tions
dp = H + (I-H)+ Cjp.(q, +q,)' dL p, ,P, L d'
where C is a constant depending on the ttllits used. The olher terms have been defined previously. This form of the equation witl be referred to in the discussion of the effects of changes in variables.
1_Liquid Flow Role The effect of inereasing liquid rate will be an increase in both H, and fluid velocity. This will cause an increase in both the hydrostatie and frietion terms of Equation 3108. The effeet may be seen graphieaJly in Figure 3-22 that was constructed. by choosing sorne general well conditions and holding everything constant except 9[.. 2. Gas/Liqllid Ralio Thc GLR has more effect on two·phase flowing presSUfe gradients lhan any other variable. In a dcplction-typc field the gas/oil rati~ wi-lI usually inerease with time until late in the-Jife ofthe reservoir: The GLR may deerease if water cut ¡nereases. The GLR has the most effeet on the hydrostalie eomponent of the pressure gradient equation because H L will decrease as GLR increases. However, the tolal flo\\' rale will increase, and thc friction loss depends on the tlow rale squared. This means that as GLR inereases, (dp;dL)" deereases.but (dp.JL)/inereases. One ofthe best me,hods
2 Hr\\\1~4c---+---+--+--I-31--\'rl¡w,m~~--t--+-+-
:c
>-
~61---+--'t-'r-ft---\-'t+-'r"""+---''<-+--',.+----1
o
9 1----11---1---\----\l-----',r-l-'n 3-108
IO.L-_-'------:L----':'::-"--:':'--'-:'::'------=-"-_:
or
O
dp (dPJ dL = dL
,,+ (dPJ dL
f
4
8 12 16 20 PRESSURE (100 PSI)
24
Fig. 3-22. Effect of production rate on pressure gradienrs.
94
ProduClioJl Oplimizatjol1 Using Nodal
of artificial lift, i. e.) gas/lin: invoh-~$ the artificial increase of GLR by injccting gas into the tubing string. The
.-fmJ~\'Sis
component has increased more than tht: hydrosI3tic componenl has dccrcascd. The cffcet of
g:lS
rale on Ihe indi-
vidual componcnts and lhe total pressufe- gradi~nt is iUustrated in Figure 3-24.
as GLR ¡neceases. the cequired tlowing bottomhole pres-
SUfe decrcases up to a point. As the GLR ¡neceases from 3000 to 5000 sefiSTB, the required p.¡aetually inereases. This means that in going from 3000 to 5000 the frietion
3. Water/DiI Ratio or Water Cllt The total pressure gradient in the wdl will ¡necease as f..v ineceases. This rcsults from an incr¡;ase In liquid densiiy if ihe water is heavier than the oil and alsa fram a dccrcasing GLR, since the free gas in lhe tubing comes primarily from the oil anly. These effects can be expressed in Equations 3-19 and 3-109. The effee! mal' be expressed graphieaJly in Figures 3-25 and 3-26. Figure 3-25 shaws only the eITect of incrcased ¡iquid densit) while the total effect is shown in Figure 3-26.
p, = Po (J - lo) + p"Jo
(3·19
GLR = GOR(J - f.,)
(3-109.
where
PL Po
liquid density oil density,
0.--.---------------,
Rate - 600 8/0 2" Tubing Depth ·9000 Fl.
2
GIL", 600 scf/8 (Constant)
3 ;¡ .'!?
15
4
~
Fig. 3-23. Effecl of gaslliquid ratio.
"roe
~ ~
O
-S
5
.S ~
a. '"
Cl
6 7
_ "".....
P,..... ~
8 9 !;-_:----_:-_-:'::-_-"::--"---'~"--...J
O
4
8
12
16
20
Pressure in hundreds al psig
Fig. 3-24. Pressure-drop components in two-phase f1ow.
Fig. 3-25. Effect o( water.cut on required ffowing pressure.
•
FlolV in Pipes and Reslriclions
P... /" GLR GOR
95
water density, water cut = qv./(q.. . +qo), q!(q, + qw), and
q!qo
4. Liquid Viscosity The cffeets of liquid viseosity on prcssure drop are very dimeu!t to iso!ate. This resuits from the faet that the eoneept of a gas/liquid mixture viscosity has no physical meaning. Thc liquid viscosity wiII affect IfL to sorne degree and will also increase [he shearing stresses in the liquid and, thcreforc, the friction pres!st1Te drop. Ir an oil/water mixture is present, dispersions or ernulsions may form and cause a very large- increase in lhe pressure gradient. At the prescnt time, lhere is no mcthod to aCCllratcly predict the viscosity of an oil/water mixlmc, much less the viscosity of a gas/oil/water mixturc. The viscosity term does nol appear explicitly in Equalion 3-1 OS but it is uscd lo calculalc a Rcynolds numbcr fram which the friction factor is detennincd. It also appears in sorne of lhe ¡iquid holdup correlatiol\s. The combined effects of decrcasing API gravity and incrcasing viscosity for a gas/oi) mixture are shown qualitati\'cly in Figure 3-27. lfwater \Vere prescnt, the cffccts would rrobably bc even more pronollllccd.
5. Tubing Diameler and S/ippage The selection of the proper tubing size to install in a well is one of the mos! critical and the most neglected functions of a production engineer. In many cases the tubing size wiII be selected based on such criteria as what has been used in Ihe past or whal is available on the pipe rack. A total system analysis, which combines the reservoir and piping system perfonnance, is required to select the proper tubing size, but the effccts of tubing size on veloeity and s!ippage will be diseussed here. As can be secn in Equation 3-108, as d increases, the frietíon loss and thus the total pressure gradient wilI de crease up to a point. This can be observed qualitativeIy in Figure 3-28. However, as the tubing size locreases, the velocity of the mixture decreases and cventually the veloeity will be too low to lift Ihe liquids lo Ihe surfaee. The well will lhen begin to load up wilh liquids and may eventually die. The tubing sizc at which a well will begin to load or thc 1113ximum tubing size which will sustain no\\' can be detennined from a plot such as Figure 3-29. The effect of declining production rate and, therefore, "clocily for a particular tubing size can be shown qualitatively in Figure 3-30. For a particular tubing sizc, \vell
O Pressure, 100 psi
4
8
12
16
20
24 2
Rale - 600 bpd 2-in. Tu!)ing
3
Oeplh " 9,000 tt
2
Changing GIL
lnitial GOR " 600
3 =' o o
0_ oC
o.
o"
=' o o
0_
<; o.
4
4 5
w
o
6
S
7
6
B
7
9
B
10 O
4
8
12
16
Pressure. 100 psi
Fig. 3-26. Effect ef water cut en required flowing pressure.
F~. 3-2~ EffecIDrV~COS"~
20
24
28
96
Produclioll Oprimization UsiJlg NodalAl!alysis
o I
~\
2
1\\
3
-
1-
"-
4
--
5
o o o
~~
,~~\
\
,
'"""
~\ \
'"
1-
a.
\
6
Fig. 3-30. Effect of tubing size on minimum production rateo
\\\~\ \"
\\ \\\ \ ~~ -'\~ R
7 8
'"
;;;"u'o..
,/
~$Al ~¡
9 ...
- 10
O
5
10 15 20 25' PRESSURE (100 PSI)
/.
\
d
\
30
35
Flg. 3-28. Effect of tubmg slze.
Fig. 3-31. Effect of tubing size on minimum production rateo
The type of infoffilation dcpictcd in Figures 3-30 and 3-31 can be calculated using the multiphase tlow corrdalious discussed previously. A simpler procedure for estimating this data for a gas well will be discussed in a subsequent section.
i
M. Flow in Gas Wells
. I
As was stated previously, the general pressure gradient
I
equation, Equation 3-16, applies for any fluid for which
Fig. 3-29. Determining maximum tubing size.
depth, wellhead pressure and gas/liquid ratio, lhere will exist a mínimum production rate that will keep the wel1 unloaded. Figure 3-31 shows lhe effecl of lubing diame-
the variables on the right-hand side can be determined. Therefore, a pressure traverse for a gas well can be calculated by dividing the well into short increments, just as was proposed for oil wells. This amounts to the numerical integration of Equation 3-16. This was necessary ror two-phase flow case, since no analytical expressions are
ter on the mínimum rateo This type of ínfonnation is valu-
available for density and velocity. In the case of single-pha,e flow, lhe in-situ density and
able in determining al what rate a well will begin to load foc various tuping sizes.
velociry can be expressed as functions of pressure and temepraturc, using the gas equation of statc, pV = ZnRT.
Flow in Pipes and Restríctions. .....
97
If acceleration is ignored, and tcmperature is assumed constant, Equation 3~ 16 can be integrated over the tubing string to give the fol1owing equation.
P;f
= p;, EXP( S)
(3-110)
C,"I,q;,7%f(MD)(EXP(S) -1)
+---'-"-'-=--'---'-Sc-""'-'---'----'-----'a where
s
~ C,Yg (TVD)/(T Z) Cl> C2 = constants depending on units A set of consistent units is: P.. .-¡; Pwh pressure, psia q", flow rate, MMscfd T average flowing temperature, °R TVD troe vertical depth, ft MD measured deplh, ft d pipe inside diameter, in. C, 25 C, 0.0375 In this equation, Tand Z are the average temperature and Z-factor existing in lhe well, which makes the solution iterative sinee Z ~ f(p). An equation similar to Equation 3-11 O was presented by Cullender and Smilh." They chose to divide the well into t\Vo incrcments of Icngth HIJ and evaluate the integral using a series expansiono The Cullender and Smith mcthod \Vas uscd extensivcly \\lhen most calculations \Vere madc by hand l ami its use has carricd over into computcr applicatiolls. Actually, if the well is divided into short enough incrcmcnts, the same results \ViII be obtained from Equations 3-16, 3-110, and the Cullender and Srnith method. Equation 3-110 amI the Cullender and Smith melhod are applicable for csscntially dry gas only; that is, a fluid in which the specific gravity of lhe fluid is constant. These methods have becn used for wells producing small amounts of ¡iquid along with lhe gas by making an adjustment on thc-gás gravity. The mixture gravity can be estimaled fmm:
"1, +459Iy,/ R "l. =
(3-111)
1+1123/R
where
1111 "Ig "IL
R
mixture gravily (air = 1) gas gravity (air ~ 1) liquid gravity (water = 1) produeing gas/liquid ratio, sef/STB
If the OLR is less than about 10,000, whieh eorresponds lo a ¡iquid loading of greatcr than IDO bblslMMscf, or ir the rate is lcss than that required to kecp lhe liquids unloadcd , lhe two~phase now correlatÍons should be uscd for gas wells.
Another method for taking into aceoúnt the effects of liquids in gas wells was developed by Ora"'" and is reeommended by the API in their manual for sizing subsurfaee safety valves, Manual 14BM, API 14B. The liquid holdup was correlated with two dimensionless numbers and the no-slip holdup. The accuraey of the Oray method was stated to be questionable if:
> 50 ftJsec
I.
Vm
2.
d> 3.5 in.
3.
Liquidlgas ratio> 50 bbllMMsef
4.
Water/gas ratio> 5 bblIM.Vlsef
In practice, the Oray method has been found lO givc good results for conditions weIl out of these ranges. An equation for estimating the minimum gas-producing rate required to keep a weU unloaded if water or condcllsale is being produced was presented by Turner. et a t..J5 The minimum rate for a particular tubing size and wcllhead pressure is calculated from qu(min)
=
3.06"min 12
AP...h
(J-112)
whcrc
q.".
M,[scfd minimum velocity, ft/scc area of tubing. ft~ surface flowing tempcraturc, °R gas deviation ractor at T, jJ".1t wellhead flowing pressurc, psia
"m;1I
A T Z
PlI'h
Two equations were given for v min dcpcnding on whctner the liquid is water or condensatc. 5.62(67 -0.0031 P ,,) 0.)5 (O.003IP.,)o,
=
v.
lO
m",o
v
4_.0_2('-4_5_---'0--'.0_0_3~1P:c"""):"o_" - _ (0.003 1 PII"h) 0.5
min(rond<=:Ile) -
(J-IlJ)
(3-114)
The Turner method was originally stated to be applicnbJe for LOR less than 130 bbl/MMsef, but has been found to give good resuIts for rales as high os 250 bbllMMsef.
N. Flow in Directional Wells Thc general pressurc. gradient equation applies to directionaIly drilled wells if lhe effeets of pipe angle on flow pattern and liquid holdup can be aeeounted foro Equation 3-16 may be written in tcrms of the pipe angle measured from vertical <1> rathcr than (he anglc fram horizontal 8.
ap . pgeos~
_.= aL
g,
fpv' 2g,a
p\'
+~-+--
g,aL
(3-115)
Prvdlluio/l OptimizutioJl Usillg Nodlll.·/I/O(l·sis
98 The only well-flow methods disCllssed prcviously in which lhe crCcet of angle 011 liquid holdup is considcred wece lhe Beggs and Brill mcthod and lhe Hasan and Kabir melhod. lnclusion of the pipe angle in lhe pressure-gradicnt equation accounts fOf the faet that the hydrostatic oc etevatian component aels only Dver lhe (fue vertical dCplh (TVD) of lhe well while lhe friction 10$$ oceurs ayer the entire pipe lenglh ar measured depth (MD). Therefare, any of lhe previously discusscd methods can be used in dircctional wclls if [he wcll is dívided into incremcnts in which lhe angle is fairly constant. The feasibility of this approach is demol1straled wirh lhe results of lhe evalu3tion sludy by RossJand:H AIl the wells used in this study were dircclional. but low crrors were obtaincd using fhe vertical mcthods. In Ihe case of directional gas wells, Eqllalíon 3-110 may be applied.
o.
Use of Prepared Pressúre Traverse Curves
Almost all the prl'viously discussed well flow corre lations require the use of a computer to calculatc a prcssure lrJvcrsc or to calcula te the prcssure drop occurring in lhe lubing string ror g¡\,cn no\\' conditions. Before !mgc amounts of money are inycsled in a project, the most aCClIrillc design m~thods Jyailable should be llsed to Jcsign (he project. This will almosl always inyolvc COI11puter application, bur in some cases it is not feasible ror the ficld engineer lO condllct an inyol\'cd computer sludy. In some cases, it 11l3Y be advantageous to construct a set of pressure lravcrse curves for hypothclical values of rhe variables such as qL' GLR. d, ¡;,., etc. These curves can then be used to c:)[imale the pressure drop that would occur in a well producing under similar conditions. Use of travcrse or graditnt curves will nOI be as accuratc as compllter calculations, but the more c10sely tile curves match the actual well condítions, lhe more accurate the results will be. In this section, tlle preparation ofworking curves will be discussed and Sourc~s of curves prcpared far general candilians will be listed. Applicatian af the curves lo well design prablems will be outlined, and several example problcms \ViII be worked using sorne general curves. Finally, sorne of the sources of errors which can accur !rom using the curves will be discussed.
l. Preparation 01Pressure Traverse Curves lhe curves are usually prepared in a fonnat similar to Figure 3-32, which was calcul.ted using the Hagedam and Brown correlation. a set of curves is to be prepared far a particular field, lhe earrelalion used shauld be the one that most closely matches any field data available. To prepare a curve such as Figure 3-32, the fol1owing parameters are selected:
Ir
l~
2. J. 4. 5.
Pipe inside diamelCf, d Liquid no\\' rate, qL Waler fraction,hr Average flowing tcmpcratUl"C', T Oil, gas, and water grnvilies
A pressure lraverse is then calculatcd ror several values of OLR, starting at zera pressurc at zera wcU depth. The maximul11 value ofGLR used is lhe OIlC Ihal \ViII givc the minimum pressurc gradient for the chos~n conditions. Figures will be prepared Cor the full range of pipe sizes, Iíquid cates and water fractions expected to occur in the fidd undel' considcration. The avcrage tlowing tcmpera[me and fluid properties can be selected rrom fluid sampies takcn in the field. 2. Gcnerali=ed OIlYt.'.s Sets of gradicllt or traverse curves, which were prepared using ,\\"crage tluid propertics ¡lnd tlowing lcmperaturc, aro.:: '.lYailable from scveral sourccs. Thcsc curves wcrc usually prcpared using an oil API gmyity of 35°. a gas gravity oC 0.6 to 0.7, and a water gf
3 Applicatioll ofnm'erse Citrves rhe application of the curves Cor estimating either a bottornhole flowing prcssure from a known flowing wellhead prcssurc or vice versa will be demonslrated with several example problems in this sectioll.
99
Flow in Pipes anel Res/f'ic/ions.
8
oO
12
16
20
PRESSURE, 100 PSIG 24 28 J2 36
40
48
44
52
56
1 TUBING SIZE, IN.: 2.441 2
LIQUID RATE, STBL/D: 300 WATER FRACTION:
O
3 GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY:. 1.07 AVERAGE yLOWING TEMP.,F: 150
4 5 6
I
,,
,,
'oo"
1 I
,,
,,
,, ,
t-
9
,
~ 10
111
, ,,
8 E-<
¡ :
,,
, ,,,
~1l\
7
, . ,
,f-
,, H+.:; I I
~
"
.,
,, ,, , ,,
'"~ 11
,
"'o
"
,, ,
-++ ,
I+H+ , f-f-I+
, +I-..L
1
-1+1-
++',
12 13
1+,
14 "
15 16 17
I
18
20 Fig. 3-32. Vertical flowing pressure traverses.
ProductiOlcOptimi:zatiQ!l U.\'il/g Nod(d AlI(/~\'5is
100 Far a parlicul,u" case the tubing size, liquid flow rate, water fraction and producing gaslliquid ratios will be k.nown or assumed. Thcrefore. only ene curve on a graph will be of interest. Several curves for various GLRs were plotted on the same graph lo save spaee. It has already been demonstrated that lhe pressure gradient cxisting at any location in a pipe is highly dependent on the average pressure cxisting al that lacalian in lhe pipe. This occurs because the density and thaefore, lhe velocity of lhe fluid both dcpend on pressure. This requires that lhe sec-
Example 3-6: Finding the Requlred F/owing Bottomhole Pressure The 101l0w1ng data are known lor a particular well: d = 2.441 in. (27/8 lubing) qL = 1000 STB/day fw = 0.50 GLR = 400 sel/STB H = 12000 ft Pwh = 160 psig
tion of the travcrse curve corresponding to lhe average prcssure conditions existing in lhe well of inlerest must
Find the flowing bottomhole pressure, Pwr. required lo lift this fluid to the surface_ This could represent one point on an outfJow curve if Pnode = Pwf.
be used. That is, lhe loealion of lhe lop or bottom of lhe well must be selected al a poiot on lhe curve that corresponds to the known wellhead or bottomhoJe pressure. Therefore, the numbers on the depth axis are rcference numbers only_ That is, zero dcpth on the curve does not actually represent lhe v.l cllhead unless the wellhead pressure is zero. Ifthe actual wellhead pressure js greatcr than zera, then sorne number greater than zerO an the depth axis will represent the wellhead. This means that sorne number on the depth axis greater than the actual well
So/ution: The curve that most closely corresponds to the given conditions must first be selected. Figure 3~33 is sel~cted. The steps in the solution are:
1.
enter'lhe pressure axis at 160 psig, proceed vertical-
depth will represent the loeation of the bottom of the
Iy unlil lhe appropriate GLR line, whieh is 400 scf/STB
well. In other words, the cunres must be "shiftcd" vertical1y to correspond to actual weH conditions) unless the actual wcllhead pressure is zero. A procedure for estimating an unknown pressure i$:
•..
1.
Seleel lhe ehart lhat most closely eorresponds to the known conditions of tubing ID, liquid production rate, and water fr?-ction. In rhe appendix. charts for
water fraetions of O, 0.5 and LO are provided for
fer this case, is intersected. From this intersection
proeeed horizontally lo lhe depth axis, whieh locates the equivalent depth as 1400 ft. This point represents the surface.
2.
3.
Enter the pressure axis at the known pressurc_ Proceed vertically from this pressure to the intersectian of the appropriate GLR curve. Proceed horizon-
Add lhe well deplh, 12,000 ft, to the surface equivalenl deplh 01 1400 ft to ob\ain 13,400 ft. This polnl represents the bottom 01 the well. Proceed horizontally and interseet the same GLR line. Proceed vertically upward fro'!l this intersectian and read the pressure al 12,000 ft as 3320 psig.
each tubing size and flow rateo For other water fractions, interpolatían would be required. 2.
Find the equivaienl depth corresponding to the known pressure, which ls 160 psig lor this case. To do this.
Example 3-7: This example demonstrates the use of the vertical curves to find the maximum permissible wellhead pressure that wil1 result in a required production rate. The well is equipped wlth 2 7/8 tubing. Other data are:
tally to the lcfl to lhe interseelion of lhe depth axis. This locates the number on the depth axis whích represents the equivalent depth of which the known pressure exists, Le. either the \\'ellhead or bottom-
Required oil rate H
GOR
hole. 3.
well deplh from lhe number found in Step 2. This gives lhe axis deptb lhat 1s equivalent to the actual wellhead pressure. From lhe point loealed in Step 3, proeeed horizontalIy lo lhe right lo the 1nterseetion of lhe same GLR line. From lhis point proeeed vertieally upward to the pressure-axis. Read the unknown pressure.
=
500 STB/day 12,000 ft 800 sel/5TB 4000 psig
fw =
0.5 J 5 5TB/day-psi Find the required valve tor Pwh.
lf the known pressure is the wellhead pressure, add lhe actual well deplh lo lhe eqúivalenl depth 10eated in Step 2. This represenls lhe axis depth which is equivalenl lo lhe actual well depth. lf the known pressure is bottomhole pressure, subtract the actual
4.
PR
= = =
=
Solution: 1.
Find Pwf necessary to satisfy the reservoir requ¡re~
ments. This can usually be oblained using Vogel or Fetkovieh. Use the Voge! method and assume the reservoir is saturated, that is Pb ~ PRo
...
101
Flow ín Pipes and Restriction! ......
O
PRESSURE. 100 PSIG oN
lO 0-
12
8
4
-
-
24
20
16
.
28
!]
-
::l 36
40
52
48
44
mm.
1'lij:\:t'I:Ht-!:I:l-t~\: --:
1
1400
-
TUBING SIZE, IN. , 2.441
-
2
-
.
.5
GAS GRAVITY, 0.65 OIL API GRAVITY, 35 WATER SPECIFIC GRAVITY: 1. 07 AVERAGE FLONING TEMP.,F: 150
4
-
S
~
-
,
~
6
, , ,, ,",
-
-
7 \
o e
--
-
~lO
.
,
,
,
-
.
9
,
o
-
-
12
13
.
-
-
,
'.
17
.
-
-
18
- -
20 Fig. 3·33. Example 3·6 solution.
'.
- -
.
-
,
,
-
-
-
--
-
-
.
·
·
-
---
·
-
-
.
-..
·
--
,
· --
-
-- -
--
-
- --.. -.. -
·
- .-- - . ... - · -. - . · - ..· . - - - '.-
--. - ----- - --- ;~~ ." _. '.. -
-
-
-
<
- ,
· -.
.'-
-
· ·
. -
-
+
± +
-.
·- - -
, -
- - . , --
- . ·
- -. ,.
-
·-
.L
-
,
-
.~f
,
·,•,
,
, J+ r"T - , , H=' ,, ·
.
-
-
·
-
,. , •.• ,.
-
-
--
,.
-
-
-, -
.' ,.
-
-
16
·
•, ,
.
'.
-
·,
-
-
-
14
-
,
-
.
, -- ,.
·, ,
, .-
-
-
13400
.-
-
,
[.:.:
,
,,, , ,, ,, , , ',..... 1
-
-
,,
,
.-
-
t: 11
19
- ,
I
..
- - -
-
, ,,
,
15
-
",
,
,
-
- 1+,
8
t
lOaD
LIQUIO RATE, STBL/O, WATER FRACTION:
3
56
oO'
- --
.
- -, - -
..
" - - -
- ....
"'._._~:'<'
·:1: _:
· ... , .. "
"1: .
1112
PrudUClioll
.íp
q,(max)~_R ~
5(4000)
A plol 01 lhe values 01 qL VS. Pwl (Figure 2-35) reveals -11,111STBLlday
that Pwt reaches a minimum at a produclion rale oí about qmin = 500 STB!day. Plotting the dala for rates
1.8 1.8 Solving Equalion 2-33 lar Pwt (see Example 2-2):
belween 200 and 2000 STB/day on en expanded scale would result in more accuracy, but it is. obvious
p, [(1.266 -1.25q/q"m../ ' -0.125] ~ 4000[(1.266 -1.25(1 000/11111 )J" P., ~
P.,
-0.125]
Optimiza/ion Usillg, Nocla! .·JIi.','.L'Ü
lhal lhis well will nol flow al a rale less lhan 400-600 STB/day under its presant conditlons. For other condilions of Pwh. GLR. fw • etc., the value of qmin would
,l.
change.
P.,
~
4000(0.949)
~
3800 psig
Example 3-9: 2.
Seleet the vertical curve lhat mas! c10sely matches the given conditions. This is Figure 3-34.
3.
Locate. the known pressure. Pwt = 3800, and the equivalenl depth. Use the appropriale GLR line. GLR ~ GOR (1 - fw ) ~ 800 (1 - 0.5) ~ 400. This equivalenl deplh is about 14,700 ft and represents lhe bollom of
4. 5.
This example demonstrates the applicatlon of the vertical curves in delermining Ihe minimum GLR that will allow a well to flow al a particular rate for given condilions. If the reservoir is nol producing the required volume ot gas, the well may be placed on gas lift. From a f10wing test on a well, it was determined that qL(ma.) ~
Determine lhe suñace equivalent deplh as 14,700 12,000 ~ 2700 ft. From lhe 2700 ft deplh, proeeed horizonlally lo lhe 400 GLR line. Read the pressure at lhis deplh as approximalely 360 psig.
data are d 1.995 (2-3/8 tubing) Pwh 400 psig H ~ 9400 ft
3100 STB/day, FE
fw = Pb ~
~
1.0 and PR
the well.
~
3200 psig. Olher
0.5 3200 psig
Find the GLR required tor this well to produce at arate 01 900 STB/day lolal fluid. Assume lhal Voge!" method is valid tor f w = 0.5.
Example 3-8: The v~rtipal curves may be usad lo estímate the minimum p'róduction rate for given well conditions tha! will prevenl" the well from loading up. Tt:lis demonstrates the eff.ect af slippage, as previously discussed. Using the givE:fl data, determine the production rate al which
Solution:
lhe lVell may load up. d 2.992 in. (3-1/2 lubing) H 8000 ft Pwh 240 psig fw = O GLR ~ 500 sef/STB
P,.,
Find the valua of Pwf required by the reservoir te inflow 900 STB/day. Solving Vogel's equalion (Equalion 2-33) for Pwt: (See Example 2-2)
1.
. [(
P,.,
~
-
PR
1.25q, 1.266 - - qL'''-4I1
J"'] -0.125
= 3200 [[1.266 - 1.25(900) J" 3100
-0.125] ~2640
Sofutlon: The f10wing bottomhole pressure will be determinad tar varlous production rates using the vertical curves. When the required Pwt begins to increase for decreasing qL. this means that qL < qmin' Plotting of PwtVs. qL will allow determination of qmin'
Depth
Hola Depth
800 1100 1300 1900 2000 2600 3000 3000 3100 3100 3200 3600 3400
8800 9100 9300 9900 10000 10600 11000 11000 11100 11100 11200 11600 11400
3.
Pwt 3040 2640 2120 2000 1760 1750 1650 1560 1510 1450 1460 1600 1640
•
Seleet lhe verücal curve for the appropriale conditions, Figure 3-36.
Find lhe equivalenl deplh al Pwh
~
400 psig, assum-
ing Ihe minimum gradient Une applies. This js approx-
4.
TABLE 3-3C Equiv. Sudace Equiv, Bortom
8000 6000 4000 3000 2000 1500 1000 800 600 500 400 300 200
2.
5.
imalely 2500 ft. Find lhe equivalenl deplh lar the bOllomhole as 2500 + 9400 ~ 11,900 ft. Draw a horizonlalline al 11,900 ft across al! of the GLR lines. Enter the pressure axis al Ihe required Pwf = 2640 psig and draw
a vertical lína lo intersect the horizon-
lal line drawn in Slep 4. The inlerseclion 01 lhese Iines indicales lhal lhe GLR required lo salisly lhe fixed pressure drop is approximalely 700 scflSTB. The 700 GLR line would merge lVilh lhe minimum gradient line before reaching a pressure 01 400 psig, so lhe assumplion made in Slep 3 is valid. lf lhe GLR line faund in Slep 5 had nal merged al lhe known Pwt>. a new surface equivalent depth would be fcund, and the procedure (epeated until the corre.ct GLR was obtained .
103
Flow in Pipes and Reslriclions
OO
iii M
PRESSURE,
4
8
12
16
20
24
100 PSIG
28
32
1
36
8
:!l40
5>
48
56
-1 +t++.1-H-1+I ++tH+tt f
o o
·. • ··o,,,
1
44
~
TUBING
IZE, IN.
2.441
LIQUID
ATE, STBL/D,
o
2
,,
2700
4 5
WATER F ACTION,
oo
3
¡\\¡
GAS GRA OIL API WATER S AVERAGE
,, ., • ,, , ," o o o
I
1000
.5
ITY, 0.65 GRAVITY, 35 ECIFIC GRAVITY: 1.07 FLOWING TEMP.,F: 150 • o
1: 1
•
o
6
8
'o"'"
9
,
o
, , ,
:c b": 11
'""
12
·
", ,
,"
o
•
o
~ 10
"
·,
-, l·.... •
I
I I
,,
+H+
II
,
,,, '-f
, I
, I
, .,
, ,,
, I ,., ,,
," o
13
o
," ,, ," ,
7
8~
,, .
,
"
, •
,
,,., , ,·, , I
" '14
14700
15
., 16
,o
17 "
I
18
.{
Fig, 3-34, Example 3-7 solution.
·1: ',,-
-l-f-~--
19
20
1+
'--I~~ -!-F'"
-
,
-Jo"-'+ -
Producri01¡ Optimizatioll Using Nodol Alla~rsis
104
3150,--,-~-~-.--.-
t1p¡ = {MD-TVDlLlp/ LlL 6.
2900
Estimule the tlowing boltomholc prcssurc for the dircctional wcll as:
2650 2400 p.. I,PSIG 2150
1900
~
1650
14oo!c O +',O!;OO;;;O--oc,,"'):O-C;3000f,;;;--;;'OOO~-o5f,000VC-'''OOO~~7000 8000 9000 10000 qmill Q,;,' STBlday
The average pressu(~ ca1culatcd in Step 2 could then bc rcfin<::d using the PI.¡calculated in SlCp 6, and Ihe procedure repeatcd. How~rer. the accuracy of the l1lelhod does oot warrant this step.
Example 3-10: Estimate Pwt tor the directional well described as follows:
Fig. 3-35. Example 3-8 solution.
Tile general pressure traverse curves were prcpared rOl' ,'ertical wclls ont)' in which bolh lhe hydrostatic tcnn and friction tenn aet ayer Ihe total tubing length. A rough approximation of lhe pressure drop in a directional well may be made by combining vertical and horizontal curves. This is accomplished by using lhe vertical curves 10 find lhe total pre55Ure drop over lhe TVD and using lhe horizontal curves ro estima te lhe extra pressure drop due
w fricliqn:¡Jlcting over lile tubing length MD-TVD. As will be discussed in more dclail subsequently. the hori~ zl'ntal curves \Vece prepared assuming an angle of zcro 1r0m horii.pntal. Thcrefore, Ihe hydroslatic term would be lero.
qL = 1500 STB/day GLR 800 sceSTB 160 psig Pwh MD = 9000 ft. Iw = O d 1.995 in. TVD = 6000 ft. So/ufion:
1.
p~ is found lo be 1520 psig frQm Figure 3-37.
2.
P = 0.5 (160 + 1520) = 840 psig.
3.
From Figure 3-38, which is a horizontal CUNe for the same conditions of qL' f W1 and d as Figure 3-37, the lenglh corresponding to a pressure of 840 psig is
This mélhod should be used only for making very Cl1Ugh preliminary 6limates, and a computer calculation should be used in final designo The procedure is Jimit~d to rclativcly low~pressure wells because the horizontal curves have much lower rnaximum pressures than the Y~rtical curves. The following procedure may be used to estimate the Howing bottomhole pressure in a directional wel1:
me
1.
Using the appropriate vcrtical curve, find the value of t10wing bonomhole pressure that would. exist in a
vertical well of depth
= TVD.
Labe! this pressure as
aboul 5700 ft. 4.
5.
Reading on the 800 GLR line, the pressure al 4700 ft is 760, and lhe pressure al 6700 ft. is 920. IIp 920 - 760 . - = = 0.080pSllft llL 6700 - 4700 llPI = (MD - TVD) IIp¡llL= (9000 - 6000)(0.80) = 240 psi
6.
Pwt =P~ + IIp¡= 1520 + 240 = 1760 psig
P:¡ .
2.
Calculate the a\·erage pcessure in the lubing as p = 0.5 (Pwh +P:¡ l· .
3.
Select a horizontal curve that was prepared for the
appropriate GLR line. Detennine the pressure gradient, J1p/!J.L existing at this pressure. This can be done by reading the pres-
PDSC- psep
sure change over a selected length, such as 2000 ft. 5.
PIPELINE FLOW CORRELATIONS
Procedures for caIculating the pressure losses occurtring in a pipeline are required in the petroleum industry foc designing flowlines oc gathering lines and for designing long distance pipelines. Ihis section wiII be concerned primarily with the effect of the flowline on oyeral! well performance, but the correlations discussed also
same pipe size, flow rate, waler cut and GLR as was used in Step l. Enter this curve 00 the pressure axis at Ti and draw a vertical line to iotersect the 4.
v.
Calculate the extra pressure drop due to friction over the tubing length not considered in Step 1.
apply to large diameler lines. The pressure loss in the flowline, expressed as 6p6 :::= in Figure 3-1, can be very small for short f1ow~ lines, such as might exist in an offshore situation if the separator is located near the wellhead. Conversely, in many producing arcas the distance between the wellhead
105
Flow in Pipes .and Restrictions·
PRESSURE. 100 PSIG
8
12
., 16
20
24
2640
28
32
36
40
44
48
52
56
II~+HHI-H H+H-JjJ.:JJI j-'HI~Añ TUBING SIZE, IN.: 1.995 LIQUIO RATE, STBL/o: WATER FRACTION:
900
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER'SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEHP., F:
150
,. '.
-'+4+
.,. , .,
, ,, f-H±I:-tf_·- --
, ,, ,
, ,,
, -
, ,, ,,,
--:*1::tl#=-==: -=
,",, , 'l' ,
,, ,, ,, , ,, ,,
,,
I
,
,,
,,
, ,, , ,,
h
_!.l_
,
.
, ~
,1+ ,,
,
I-H- .
1+1-,
,,
,, ,, ,
-
.. ·mI: :¡=¡= +
, ,,
. ,,
1+
1I
L GLA
- - '" -
700
, 16
- -
18 19 20
Fig. 3·36. Example 3·9 solulion.
.. p
f+ 'eI-
17
ItI .
'--
_ : "K¡' , I
-
.
Pmduclion Optimiza/ion U\'iJlg Xoda! Al1u(rsis
106
g O G~
8
4
6
12
,
1-
BOO
20
PRESSURE, 100 PSIG 24 28 32 36
40
'4
48
52
56
~tf ;,~:I :/tItj-.j::j:jttliLiJljJ}IJl±l1Ü'111
1
2
,"
,
,,
,
, ,,
,
:
5
x,
,,
7 8
,,
,, ,
,' ,
r++ , ,i+ 9 o o
~ 10
~ 11
'"
Q
'
, ,,
, ,
,, ,, ,, '
,,
, ,,, ,
12
13 14
15
1500
LIQUID RATE,
,, , ,,, , ,,
GAS GRAVITY: 0.65 WATER SPEClfIC GRAVITY: 1·.07 AVERAGE FLOHING TEMP .• F:
,,
, ,, ,'
1
", ,," , '1 ¡,.. , ,, ,, ," ,, ,, ,,
,, , ,,, , ,, , ,,, .., ,, ,,, ,, ,,
,,
l' I 1
,,",,
,.
-:/:/++1-:++7 1, :-11
,,
+
,,
I
l'
,~ ,, ,
,LL;, "
I l- j ' - - .
,, ,
,,
)+1-+ ,,,
, ,,. , , ,, , , ,, ,, ,
'
17
150
,,,
'-
, ,"
• ¡ I I
,
I
1
I
=r:-H+-
L
I-H+t" . -6H-+
.,
," , ,
,, ," , , ,, ,,
j
ill±
, ,
16
-~
.. "/-f
, ft-
~ e , -~"b
_,-.r, <\:~'~
19
- J-+----_:' _-,It: -tJ.:;J~: ~ rr~r
20
-, -I~ :-:::lm[r j~
18
Fig, 3-37, Example 3-10 solution.
•
o
OIL API GRAVITY: 3S
, ,, ; , "
6800
TUBING SIZE, IN.: 1.995
WATER FRACTION:
3
4
,
-B. '
'1'
i'l'lt
/07
Flow in Pipes al1d Reslriclions.
6
8
~ PRESSURE, 100 PSIG 10 12 14 16 lB
20
22
24
26
28
HJ+I-I;ljifIJ++I-I-H:I+ -- -- [Ef[I+H+I:rffillfn-FH-I-I-I"¡=¡:¡::¡: _-:¡::¡:::¡::¡
PIPELINE LO.,
-- - ....-I=¡' -f--- kt . ...L. ~I·
LIQUID RATE,
J
2
IN.:
~
~f1-l--I-
4
5 6
!
O
GRAVITY: 0.65· OIL PI GRAVITY: 35 WATER PECIFIC GRAVITY: 1.07 AVERAGE. LOWING TEMP.,F: 100 CORRELAT : BEGGS & 8RILL
3
§
1500·
STBL/D:
WATER FRACTION:
t
2
1-1' - _
,
,, ,
-1-,
-g -t
,'
7
,, - - -1:
"
- -rt> ,,
I
-' ,
, I
,
~
- r7-, -1,
,, ,,, ,,
,. -f-+, - Hj-, , , .-rn= ,, f
, I
, ,,
+
12 13
- H-, - , ,
,
I
14
-l .
15 16
:¡.:¡::¡:--¡::¡::¡:-:¡::¡::¡:H- \1*18
19
-H. J.
..L.
- --- -ll- :~-- -
¡j- lffi--~m::lLm_· --. - + -
rm- -lli- :I::¡m. -- m-
.20, ..
Fig 3-38_ Example 3-10 solution.
m-
- __ -
-- ---- -- "1+ - : --I*hlfj: Jt - -1I~9;-m-: - --lr H - :: --
-jmJ-m-:ffij: - m--
m-- --
Proc!uctioll Oplimizalio/l Using Noda!
JOS
and scparator may be several miles, and {he pressure drop in lhe flolVline might he 20 lo 30 per«nl of lhe lolal
prcssure lass, p
-Psep'
The general pr~ssure gradient equation \ViII apply roc flow in pipelincs, and aH three of lhe components will apply in most cases. Some pipcUnes can be considered to be essclltially horizontal, and in this case the hydrostatic component would be zeco. Tllus. it is important to have a good eorrclatioll roc [cíClico factor in pipeline designo The friclian factor foc rnultiphase flow can be several times greater than \\!ould accur foc a single-phase fluid traveling al the same velocity as the two-phase mixture. Although the hydrostatic oc elevatian component of the pressure gradicnt equation is not as important in pipeline tlow aS il is in wellnow calculations. a substantial part of the tota'l pressure loss in a pipeline can result from Iifting lhe fiuids over hills or inclines. AIso, ir has becn found that in most cases, hardly any 01' the hydrostatic pressure losl in lhe uphill seclion ofa line is regained in the downhilL scction. This is true if the flow panem in the downhill section is segregated, that ¡s, stratified, wavy, or annular. The flow lhen behaves as open channel flow. Therefore, it is still necessary to be able to predict liquid holdup 3;n~Jlow pattem in pipeline flo\\". Some a§pects of the pipeline design problem are not rclated to -p.ressure loss only, but include sizing lines and separationJacilities such that the sep:lrJtor will not be ovcrloaded or tlooded. Separatars are usually designed hased on a sleady rale of gas and liquid llo\\'. If extra liquid yolumes or slugs arrive at the separator periodicalIy, means musl be provided to handle lhe extra liquido This can be accomplished by installing slug catchers upstream of the separator. Befare separation facililies can be sized, the engineer must be able to predict the size or volume of the extra liquid and haw fast this volume must be handled. lhe extra liquid can result from changes in fiow conditions, such as adding or deleting wells, which will usually change lhe liquid holdup in lhe lineo If conditions are ehanged such that liquid holdup is decreased, then the extra volume of liquid removed from the system will eventually arrive at the separator. Designing foc this situation requires accurate holdup prediction methads. This typc of problem can arise al so during pigging operations. If flow conditions in a line are such that slug flow exists at the pipeline outlet, liquid and gas will arrive at lhe separator as altemating slugs of gas and Iiquid. Even though a separalor may be large enough lo handle lhe gas and liquid volumes al steady conditions, a large liquid slug can easily flood the separator. It is, therefore, necessary lo be ab!e lo predicl the horizontal or pipeline flow pattem existing at given conditions. Several flow pattern maps will be discussed in this section, but methods for predicting slugging characteristics. such as slug length,
.·!lId~\·sis
vclocity and frequency, will not be prcscnlcd. Procedures for accomplishing this can be found in Reference 9. Many correialions for pipeline flo\V prcdit.:tion ha ve been developed over the past 30 or 40 years. A rc\'icw of many of the corrclations ano the manncr in which they were developed can be found in Reference 23. Since the purpose of this book is to prescnt the best l11cthods to optimize production systcms, only the methods 1110st widely used at the present tim.e will be discusscd_ A limited number of comparison studies or evaluations of sorne of the methods has been conductcd. The results of sorne of these studies will be presented. lhe effects of changes in conditions that can exist in pipeline flow will be discussed from a qualitativc vic\vpoint. These condi~ tions inelude variables such as GLR. pipe size, liquid rate, etc. The cffccts of hilts oc inclines on ~he pressure loss will be included in this section, and a procedure for separating the friction and elcvation losses wil! be discussed. As in the section OIl well fiow correlations, the discussions wiII be limited lO how the experimental data \Vere obtained and how the corrclations for Irp, H L , and flo\\' pattem were developed. Detailed cquations and an exampIe calculation ror the Beggs and Brill ll1~thod wilI be induded in the appendix. DetaiIs ol' the other methods discussed here and sorne methods nol discusscd here can be found in References 9 and 23. Compurer subroutincs for sorne ofthe methods are Iisted in Reference 9. lhe preparation ano use of pressure tra\-erse curves for quick estimates of frictional pressure loss in pipelines \\'ill also be deseribed. Example prohlems illustratiug lhe application of these curves will be presented.
A. Horizontal Flow Pattern Prediction At least eight separate flow palterns thal can exist III twa-phase horizontal flow have been described. Man}' different na mes have been applied to these flow patteros, but the most widely accepted na mes and descriptions were presented by Alves,48 and are illustrated in Figure 339. The horizontal flow patterns wece c1assified into only three categories by Degance and Atherton,49 and these same ealegones lVere used hy Beggs and Brill. as illustrated in Figure 3-19. The Beggs aud Brill flolV pallern map is sholVn in Figure 3-21. One of the earliesl allempts to predicl flow patlern by the use of maps was made by Baker in 1958. 50 The coordinates of the map are dirnensionless, but the vertical and horizontal axes essentially represent gas velocity and liquid velocity. respectively. A map that was developed from extensive experimental data was published hy Mandhane, el al.'l in 1974. The
Flow in Pipes and Restrictions ._
/09
le) SLUG
(a) BUBBLE
GAS_
lf l
(b) PLUG
SEMI-ANNULAR
\
GAS _
GAS_
(q) ANNULAR
(e) STRATlFIED GAS
:=,'~ ....:,::r:."_Jf._, ,- ~: -, -.'.::.., .-- --:: ...' ~- ~. - .". '.:.:':-:'_:~"::'.: . . - '.,
~
::~.:~·~~:ii¿:::':_:-4":¿~·"¿.:-~-;;;~.:~:¡~ (d) WAVY
L
(h) SPRAY'
-'
Fig. 3-39. Horizontal flow patterns.
mJp coordina tes me superficial gas and ¡iquid velocities. This is one of Ihe most widely used horizontal now patI~rn IlWPS at the present time. The flo\\" patterns and Ihc::ir locations on the Baker and Mandhane maps are illustrat~ ro in Figures 3-40 and 3-4 L The flow patterns and maps dC5cribcd aboye apply for stTlctly horizontal flow only. It has becn obscrvcd that ~!T3tificd or wavc flow cannot exisl Ín a pipe that is lnclincd llpward at only a few degrecs. When upward inclination 5)CGurs, the ¡iquid is hcld back by gnn-üy
Baker Flow PaUet"n Map
100.000,-----.,----,---.,--,---,----, Oispersed Bubble
0'
0' Froth
Annular
,
forces and lhe flow pattern changes lo slug. Conversel)', if the pipe is inc1ined dowllward, stralified flow is prcdomínate, and slug flow wi11 not occur al Ihe conditiolls predicted by the horizontal maps. Very few srudies have beco made lo try to Ínelude lhe cffeet of pipeline angle 011 lhe flo\\' pi3ttem. An experi~ menlal sludy performed by Mukhcrjee 52 addressed this problem, but the maps produced haye not beco tested using field scale data. A theoretical slUdy of the inclined two-phase nO\\! pattem problelm was pllblishcd by Taitcl and Dukler. 5J The study involved the prediction of conditions under which the now pattero would change from stratificd lo intcrmittenl (slug) or annular. The basis of the equations presented was similarity and dimensional analysis, but several simplifying assumptions weTe made to makc lhe equatians applicable. AIso, no limits on lhe pipe angles for which the method is valid were given.
G
B. Eaton, et al" Method
Slralified
1000
100 'c----;----,';;---;;;;;---;-;!2'~_:c~
0.1
10
100
lJ,IV/G
Fig. 3-40. Baker f10w pattem map.
1000
',O,CCe:
The Enton, et al.,54 correlations for friction factor and liquid holdup resultcd from extensive data that were oblained from a lest facility thal consisled of twa 1700 f\ lines. Diarileters of 2 in. and 4 in~ were utilizcd, ano thrcc liquids werc use-d in each lineo Thc ,·ariables studíed and thcir ranges were:
Produ..'litJll Oplimizatioll Using Nod,d .11:,¡(l'sis
/la
I 10.0
-
o
w
(f)
'1-
-
,. .::
BUBBLE,
;.".
ELONGATED
SLUG
BUBBLE
FLOW
FLOW
-
~
lL
-
-
.
--J
>1o
o
-' W
/.0
...;
r
.
.-
11-
~?
= -
ANNULAR,
1-
>
o
....
5 o ::::; -' «
o
0.1 r 111-
::J
1-
W eL
(f)
FLOW
-
--=-
~
o::
lL
STRAT I F lE D
FLOW ,"
::}{..
:->:-:.;.
-
W.1VE
;.;.;."
;..... ;:';':'"
-
I
0.01 L_ _--'_--L--'--L...LLILILI 0.1 1.0
I
1 11 "
-
I 10.0
I 100.0
I
500.0
SUPERFICIAL GAS VELOCITY,VSG ' FT /SEC Fig. 3-41. Mandhane flow pallem map.
1.
Gas rate, O- 10 MMsefd
2.
Liquid rate, 50 - 5500 STB/day
3.
Liquid viseosity, 1 - 13.5 ep
4.
Syslem pressure, 70 - 950 psig
The frietion factor and liquid holdup were eorrelaled with dimensionless numbers using regression analysis. Liquid holdup was measured by Irapping a segment of lhe flow stream between quick-closing valves. Flow pattern was nal considered in the correlation. and 110 effect of pipe angle is ineluded. The friclioo factor and Iiquid holdup correlalions are shown graphieally in Figures 3-42 and 3-43, respectively. The liquid holdup corrclation is considere~ lo be one of lhe best available for horizontal flow, but the frietion factor correlation does not degenera te to lhe single-phase
case as lhe flo\\" approaches either aH liquid or all gas. In Ihe range of lo\\" gas-liquid ralios, lhe fr¡elion fílClOr becomes ve!)' iJrge. lt has bccn found lhar the friction [actors will be \'alid if (he value of lhe abscissa correJa!ing group fa lis belween abOUl lO. ano lO'. Detailed caJculation procedurcs and cxample calculatians for the Eaton method can be found in References 9 and 23.
c. Dukler, el al., Melhod The American Gas Association sponsored a study lo ímprove methods ror predicting prCS5ure drops occurring in two-phase no\\' pipelines under the direetion of Dukler at Ihe Universit)' of HoustOll, and the results were published in a dcsign manual.5 6 The study was conducted by first gathering more lhan
//1
Flow in Pipes and Restrictions
1.0
0.1
H,O 4" H,O 17" DISTILLATE
.01 10'
10'
(GR ¡-' ( ~.
10 '
la'
j''' W;~
Fig. 3-42. Eaton fn"ction factor correfalfon.
20,000 experimental data points from both laboratory and field scale facilities. After eliminating the doubtful data, only about 2,600 remaincd for developing the correlatians. Dukler used a combination of dimensional and similarity analysis te arrive at expressions for calculating the friclional pressure loss. A method for predicting in-situ 1.0 0.9 0.8 0.7
.-='8
"o " ~
, "
f!
¡ I
I ¡¡ I '1
¡
"1 1111 1
I
j
¡
I ¡¡ ¡II
I
WA1ER-GAS OATA Z' PIPE - 50-2500 BPO ~" PIPE - 50-5500 BPD '0 - 10 MM Sef/DAY
¡ I III
... "' ....
/
I
/
/
/
/
0.6 0.5
O. ~ 0.3 0.2
liquid holdup is required because the density (crm in this component requirt."s a value for H L. Liquid holdup was correla(ed with no-slip holdup AL and with a two-ph3se Reynolds number. Finding a value for H L is iterativc since the Rcynolds number ineludes H L in the density termo The holdup correlation is shown in Figure 3-44. A nonnalized metion factor, from which the two-phase friction factor may be obtained, is iIIustrated in Figure 3-45. The Dukler method has been widely used in the petro¡eum and pipeline industries and gi\'cs good rcsu!ts for both small and llrge diametcr pipelines. Although no effect of pipeline inclination is included in the method, it has becn succcssfully combined wilh a mcthod proposed by F1anigan'6 for hilly (errain pipelines. The Flanigan method will be discussed in a subsequent section. References 9, 23 and 56 contain delailed ealculation procedures and examples using the Dukler method. A computer subroutine that combines Dukler and Flanigan is included in Reference 9.
O: 1 0.0 .001·
D. Beggs and Brill Method 10
0.01 1 64}l 0.515 ( ' )O'O~}l 0.1 L • Lv PP b
H
gv
H 0.0271
d
Fig. 3-43. Eaton liquid holdup corre/alfan.
The Beggs and Brill method wasdescribed earlier in the section 00 well flow correlations. Although it may be U$cd for pipes at ;my angle of inclination, its widest applieation has beco in the area of pipeline design as opposed lo tubing designo The fael lhat this method is presenled entirely in equation fonn and therefore requires that no
ProductiO/1 Optimizalion Usin!!. Nadal AJi.J(\'sis
Jl2
100
Fig. 3-44. Dukler liquid hafdup correfalian.
graphs oc charts be curve tit foc computer oc calculator applicatíon has increased its acceptance in lhe ¡nclustey. As was mentioncd eacHee, a program foe the HP41 CV calcu\ator utilizing lhe Beggs and Brill method is available. 36 Also, a detailed calculation procedure and exampie calculations are published in References 9, 23 and 36, as well as in. [he appendix of this work.
3.0
2.' 2.0
~
'o
1.5 1.0
o
0.0001
0,001
0.01
" Fig. 3-45. Dukler friclian factor cOffelalion.
1.0
E. Flanigan Method for Hilly Terrain A study of the effects of hills on lhe pressure drop in a t\Vo-phase pipeline was eonducted by Flanigan..56 The study was prompted by the obscrvation that a particular gas condensate pipeline thal was designed for a total pressure drop of about 30 psi exhibil~J. a gradual ¡ncrease in pressure drop with time even though the input gas and liquid rates were hdd fairly constanL lnvestígation of the souree of the extra pressure drap revea(ed that Iiquid was accurnulating in lhe low sections of lhe pipeline and causing an increase in both the elevation or hydrostatic and the frietion components. lt was found [rom experimentation that an ¡ncrease in gas rate al the same liquid rate caused a deerease in the total pressure drop. This was attribuled to the faet thal the increased gas velocity swept out sorne of the liquid accumulated in the low sections. After extensive investigatían of this 16 in. pipeline and several other Iines in which twa-phase tlow was occurring, Flanigan developed a method to account for both the increased [rietion and inereased hydrostatic pressure drops. The ¡ncrease due to friction caused by the presence oC the liquid phase was accounted for by a reduced efficiency factor to be used in the Panhandle equatioD_ lhe
Flow in Pipes and Restrictions
J13
100 90 ~O
70
;, óO
u
e
\0
u
40
~
~ ~
~
30
~
~
e
". ~
2\ 20
~
1\
10 0.1
0.2
O. J 0.40.\0.6
o.a
,
1.0
Gas 'Jelocity (1 ¡quid to /
gdS
J
ratio)
4
\
6 7 8 910
0.32
Fig. 3-46. Flanigan efficiency factor.
Panhandle equation wil! be prescnted in a subsequent section. The efficiency factor was correiated with superficial gas vclocity and liquid to gas ratio and is illustrated in Figure 3-46. The units to be used in calculating the abseissa value are ft/see and bbl/MMsef for lhe gas velocity and liquid-to-gas ratio respectively. Tile extra hydrostatic pressure drop due to liquid accumulation in the low sections of atine, which must be addcd to the friction loss, is calculated fram: (3-116)
whcre ÓPIt
PL
HL h¡
prcssure drap due to hills .Iiquid dcnsity at average pipeline condi~ (ioos holdup faelor the vertical rises of the individual sections of the pipeline.
Flanigan found that neither the angle of inclination of the uphiJI sections nor the difference in inlet and outlet elevation of the pipeline was important. He a1so fouod that recovery of hyclrostatic pressure in the downhill section:; of the lioe was ncgligible. The holdup factor was found to be a function of superficial gas velocity only. The relationship is shown graphically in Figure 3-47 and may be calculated fram:
where v.~.g is in ft/sec evaluated at average pressure and temperature existing in the pipeline. Since ca1culalion of the average pressure requires knowleclge ofthe inlet and outlet pressures, the calculation of pressure drop is iterative. The Flanigan equatjon fur calculating the extra presstlfe drop due lo hills has been combined with frictian los5 mcthods other than the Panhandle equation. As \Vas menfioned earlicr, the American Gas Association pipeline design manual recommends combining Dukler and Flanigan for hilly terrain pipelines. It has also beeo suggested that the Flanigan equation for hydrostatic prcssure drap be combined with friction loss obtained [rcm prepared horizontal pressure traverse curves for quick cstimates of pressure drop in hilly terrain pipelines. This praccdure will be illustrated with an example in a subsequent section.
o., 0.6 HL
H _
'
L
1+.J2ti4V:.oroS
0.4 0.2
0.0024 ti
81~12104161820222(''6283032J(3638(04''U464650 V"O,FeelPefSecord
I +O.3264v:~006
(3-117)
Fig. 3-47. Flanigan hoidup faelor.
Productiol1 Optimization USiflg Nodol A/Hllysis
114
F. Hybrid Model , A pipeline flow model which combines several of the prevíously published correlations ,,,·as published by Gregory, et a1.51 A data bank cont3.ining 2685 liquid holdup measurements and more than 10,000 pressure drop measurcmcnts was used to test existing 'pipeline corrclations. The experimental data poinI..S wece divided into no"" patterns according to Figure 3-41 and the mast accurate correlation \Vas selected [oc each now pattern. The methods judged to be best roc eaeh flow pattern are listed in the fol1owing tableo TABLE 3-4
Hybrid Model
'l,
FlowPattem
Holdup Corre/afian
Friction Loss Melhod
BubbJe
Chenoweth (62)
Stratified
Hughmark (58) Agrawal (59)
Wave
Chawla (60)
Dukler
Slug
Hughmark
Annular Dispersed
Lockhart (61)
Dukler Chenowelh
Beggs and Brill
Lockhart (Modjfied)
The correlations listed dcscribed in this book may papers. Application of this seven empirical correlations utilization of a computer.
Agrawal
ín the t9.ble thal are not be found in the referenced model requires the use of and would thereforc require
G. MONA, Asheim Melhod The model developed by Asheim" in Norway and discussed in the section on Wellflow Correlations can a1so be used for pipeline designo Details 01' lhe model can be found in Reference 78.
H. Evalualion of Pipe Flow Correlalions The lack of accurate field dala from operating pipelines or flowlines has made the comparison ofpipe flow correlatiaos difficult. Ahhough surface and bottomhole pressures are measured in wells for several reasans, once a pipeline is installed, performance measurements are seldom made. Only if the pipeline will not carry its designed rates is it likely lo be analyzed. Also, liquid holdup and flow pattern are extrernely difficult to measure, and almost no field data exists for these parameters. For these reasons, many of the comparison studies have beeo based on laboratory scale data, although sorne comparisons using field dala have been published. Sorne of the published studies wiU be discussed in this sectioo. Vohra, et al. 6] made a study using the data that were used to develop the Eaton correlation and the Beggs and Brill dala lo compare measured and calculated liquid holdup values: Six published correlations were used to
calculate the liquid holdup and compare it te lhe measurcd valuc for each test. A description oC lhe experimental data can be fÚlIl1d in the referenccd po.pers. 1'he result:; are reported in Tablc 3-5 as average pacent error and standard deviation. A bias in favor of rhe Eulon and lhe Beggs and Brill methods exists since {hese merhods \Vere developcd from the test data.. The same experimental data were used by Hernandez. el al.,64 to compare (he friction factor correlalions. Tbe values for experimental [rietion factor werC obtained by solving the frictioo pressure drop component of the general equation for frictían factor. The results are reponed in Table 3-5, and the same bias exi5lS in favor of lhe mcthods from which the data carne. In general, the errors in friction factor prediclion are larger than those for liquid holdup preJiclion. A dala baok assembled al lhe Ulü\"ersity of Calgary v."as used in a liquid holdup comparison sludy by Mandhane, et aL65 The data bank cOnl3ined more tha..r¡ 2600 rneasurcd holdup data points. The:;e dala were use-J to test cight publish~d ¡iquid holdup corrclations. Th.:data were divided inro tlow patterns bascd on the map in Figure 3-41, aod several rneasures of accuracy were cal· culatcd -for each correlation for each [IOW pattern. Onl:the overall results are reported in Tabk .3-5. A friction-factor comparison sludy was reported in .: later papcr66 by the same authors. Th( sarne data balú: was used, but more lhao 10,000 pressurc drop points \\'er~ uscd. The data breakdown by flow panem was also mad~ in this study, but onl)' lhe O\'eral! rcsu\ts are reported i:: Table 3-5. The data obtained from an operating: pipeline, which had an insidc diameter of 6.065 in. and a Icngth of alm05t 20 mi, were used in a comparison srudy rcporled b:Gregory, el a 1. 57 The pipeline was not horizontal, and the sum of aH the uphiH rises (Lh) was 8"9 ft. The Hybrid Model discussed earEer aod three other methods wer~ used to calculate the total pressure loss in lhe line taking into accouot the effects of the hills. The results reported in Table 3-5 show good accuracy for all of the correlations tested. The correlation labeled Dukler-Ealon mean> that the friction loss was calculated using Dukler's melhod, bUI lhe liquid holdup was evaluated using Eaton 's correlation. Fayed and Otlen&l performed tesIs al 13 different flow conditions, on both 12 in. aod aod 16 in. offshore pipelines. The lines were 1500 ft. long. Liquid flow rates ranged from 44 lo 134 STB/day, and gas rates were belween 23 and 110 MMscfd. Average pressure in lhe lines varied belween 635 and 1080 psig. Only l\Vo correlations were used to calculate the pressure drops and compare them with the measured values. These were the Beggs and Brill method and lhe Dukler-Eaton melhod. As reporled in Table 3-5, Beggs and Brill underpredicted the
•
Flow in Pipes olld Resfricfions ......
lJ5 TABLE 3-5 Pipe Flow Comparison Sludies
Comparison Study Aufhor
Correlations Compared
Avg. Percent Error
standard Deviation
Beggs and Brill Oukler, et al. Eaton. et al. Guzhoy67 Hughmark Lockhart, et al. No-slip
6.0 -25.4 -3.8 29.1 16.4 0.7 -42.1
17.2 25.0 11.4 35.9 23.9 25.6 23.1
Hemandez, el al. (Friclion)
Beggs and Brill Oukler, et al. Eoton, et al. Guzhoy
7.7 7.7 42.6 80.0
86.3 73.3 129.1 188.1
Mandhane, et al.
Lockhart, et al. Hoogendorn (68) Eaton, et al. Guzhoy Beggs and Bri1l Oukler Hughmark Chawla
8.0 9.4 12.5 8.5 10.4 9.3 7.4 9.5
11.5 13.9 16.8 11.7 15.1 13.8 11.6 13.2
Vohra, el. al.
(Holdup)
(Holdup)
Mandhane, et al. (Friclion)
Lockhart, el al.
Chisholm (69) Baker Dukler, et al. Chawla Hoogendorn Bertuzzi, el al. (70) Chenowi!h, el al. Baroczy (71) Beggs and Brin
4.7 4.7 -7.1 -7.9 4.8 -19.5 -15.8 -2.1 -1.7 -4.7
117.5 120.9 77.8 57.2 87.3 60.4 56.0 63.5 59.9 57.3
Gregory. et al. (TolaI6p)
Hybrid Model Oukler-Ealon Beggs and Brill Flanigan
-3.1 -0.4 2.0 -12.0
11.7 17.1 17.3 18.7
Fyed,etal. (TolaI6p)
Dukler-Ealon Beggs-Brill
16.2 -0.4
12.8 7.9
Asheim (TolaI6p)
MONA Beggs and Brill Dukler-Eaton
-4.5 1.5 14.7
10.4 15.2 16.6
Osman, el al. (To'aI6p)
Beggs and Brill Highmark-Dukler Dukler Hybrid Model
-2.1 -17.9 -7.0 -17.9
27.3 32.6 33.0 33.0
rncasurcd prcssure drops slightly on the average while DlIkler-Eaton ovcrpredictcd the Illcasurcd data. Osman and EI-Fck y 82 oblaincd field data from eight pipc1incs in a gas-condcnsatc gathering system to compare the prcdictive accuracy of four dcsign mcthods.
These mc.hods were those of Beggs and Brili, Gregory (Hybrid Modc!), Hllghmark-Duklcr", and Dllk!er. Thc pipeline insidc di,\I11clcrs rangcd from 4.026 in. to 10.02
in. A widc range of both gas and líquid rates was included, Thc pipelincs were not horizontal, and sorne werc charactcrizcd by esscntial1y downhill flow and othcrs by
essentialiy uphili now. The statislical rcslllls oflhe study are summarized in Table 3-5. A conclusion that was made in both of the ¡¡quid holdllp compar1son stlldies was that no availablc corrcla'tion can accuf3tely predict holdup valucs less than 0.1.
Prodllctioll Optimizatioll Usillg Noclal
JJ6 Another conclusion rcachcd in aH the srudics was that no one m.::thod is best roe aH ranges of par;:.meters. This conelusion is whal promptcd the developmenl of the Hybrid Model by Gregory, et al. Again, this en~phasizcs lhe nccd for obLaining as much ficld data as pos~¡bl~ befare dcciding which mcthods lO use foc further ddign in a particular ficId oc for a panicular pipeline.
o
AJIl¡~rsis
Effect of Flowrate
1
=-r----r----,--.-'~,~I·:
5 d = 2 in.
GLA = 1000~
STa
10
J. Effects 01 Variables on Pipeline Performance 15
As \\o'as pointed out in lhe section 011 wdl performance, many variabics can change from time to time or fram local ion to localioll in a producing ar~J. The effccts of ehanges in paramctcrs sueh as Ene sizc. gas/liquid ratio, ¡¡quid rate and water eut wiII be discus.-seJ brief1y in this sectioll. These changes will be illustrateJ qualilatively by graphs in SOIllC cases. When a graph is used. it will havc becn calcula red using one of the pipe-rlow corrclatioIlS diseussed prcviously. AIthough lhe results might differ slighrly among the methods, the general trend would bc the same. The general prcssurc gradient equation applies, but for horizontal condilions the elevation component \\fouId be zo.:[o. To enhancc lhe diseussion of the ~[re("ts of changing conditions, the equarion is rewcitten here.
C/p",(q,+q,r ti'
dI' dL
Lang!h Feel x 100
20
oo
25
o
~
o
o
30 N
o
o
35
4O;.'-'--';:-'--':';:---L':-'--:':c'---!c----:':-..Ll,--_J I o 5 10 1S 20 25 :;0 35 ':;0' Pressure
e·a
PSJG x 1
Fig. 3-48. Effect 01 flow rateo
or
or«"=C--
Er.2ct 01 Gas-liquid RallO 1
I-----¡-
HCfl,llC·,T~:. .=lOWlIiG
dI'
dL =
J dL f
). Liqllid Flow Rate An ¡necease in qL will cause an increas~ in the total fluid yeloeity, thcreby incr~<.lsing the pressure drop due to friction. Thus, the effeet is similar to (hat which will occur in flowing wells. This effect is illu5trated in Figure 3-48 ror f10w at a fixed GLR in a 6 in. line. A cOl11mon error committcd in d~veloping a field is to conneet new wdls inlo cxisling nowlines lha! are already overloaded. This, of course, inereases the wellhead pressure 011 aH the wells tied into the lineo
2. GasfLiquid Ratio The effect of a change in GLR on pipeline performance depends on whether the Ene is essentially horizontal or if hilIs or low sectians exist in the lineo If the linc is horizontal, ¡he ¡ncreased gas now wilI ha re (he oppositc effect on pressure drop campared to what wiH oceur in well flow conditions. For a horizontal line, the friction }oss wiIl ¡nerease approximately as the square ofthe flow rate. This effeet can be secn in Figure 3-t9. This meaos that if the GLR js increased in a gas lift weU to de crease
PRE~SI.';:¡~ ~'l':'¡)IErn:::
2 -
(dI'
I':"LL "~'~T!::i'll P.o'"I.tle
4
S'l~
J. I c. :K:.:l ==~:;~y
?:COucinc¡ Rile \·'i:e, S;t"r,c G:J":I G.Js Sp.:c,:.c G'l"')
O.a:
;""",¡¡;e f,"·.·.".;
I~O' F
TtC':~.
',01
6
8 Lenglh
10
Feet x 100
12 14
16
"" r
18 20
O
2
.1
6 Pressure
Fig. 3-49. Effect 01 gasfliquid ratio.
8 10 PSIG x 100
12
Flow in Pipes and Restrictio/1.~.......
117
the pressure drop in the tubing, the wellhead pressure wiJI be increased because of the increased D.p in the flowline. However, if the tioe is not horizontal, an in crease in gas velocity will sweep out sorne of the Iiquid accumulation in the low sections and may even decrcase the overaH pressure drop. Therefore, the effect of changing GLR depends on lhe pipeline profíle and would have lo be evaluated for eaeh line considered. 3. Water Cut The effeet of ehanging water cut or WOR is diffíeult to analyze for pipeline flow. As Jw inereases for a fixed gas aod liquid rate, the amount of gas in solution Rs will dcercasc. This happens because the gas is not as soluble in watcr as it is in oil. This will have the same effeet as ao inercased GLR, as diseussed earlier. However, if a very viseous oil is being transported in the line, the effect ofwatcr may dccrcase the prcssure drop. Ifemuisions are forlTIcd, thc pressurc drap may inerease several fold. 4. Liquid Viscosit)' The errect of oil or liquid viscosity on pressure drop in pipelincs during gas/liquid now cannot be aceurately calculated with the present technology. The effective viscosity of lhe mixture depcnds Oll whcthcr dispersions or ernulsions arc formcd nnd on the degrce of"tightllCSS" of thc cmulsion. Ficld observaliolls nave revealcd that the prcssurc drop does incrcasc \Virh incrc
J. Single-phase Gas Flow The pressure drop occurring in gas lines that are ncar horizontal can be calculatcd by mcnns of several equations. A11 thcsc \\'ere derived by integrating the general pressurc gmdicnt cquation, and lhe onl)' diffcrcncc lies in the typcs of simplifying assumptions made during the inlcgr<1lion. Eithcr the Duklcr or the I3cggs and Brill CQfrclntiolls will dcgcfleralc to the singlc-phnsc gtls case and
EUcct of Une Diameler
o 5
qL
:=
2000 STB day
GLR=1000~ 10
\5 Lenglh 20 Feel x 100
25
'°0L.L--!2-!-00=--''!0''0-.l-6~oLO-~8LOO=--'''0''OO+--''''200 f'fessure
PS1G
Fig. 3-50. Effeet 01 fine diameter.
can, thcrcforc, be used if the tille is dividrd into short incremcnts. Some of the most widcly used vcrsions 01' the gas pípeline cquations are prcsented as fol1ows,
(J·IIS)
where E is lhe cfficicney factor and lhe values of the ai constants uscd in the various equations are tabulatcd as follows. Equation
a,
a,
al
a,
a,
Panhandle A Panhandle B IGT Weymouth
435.87 737.0 337.9 433.5
1.0788 1.02 1.111 1.0
0.5394 0.510 0.556 0.5
OA604 OA90 OA 0.5
2.618 2.530 2.667 2.667
The following units are to be used in Equation 3-118. fll/day measured al Tb, Pb q T °R p psia L milcs . d inches The valueof the efficiency factor must be estimatcd from the condition of the pipe inside surfacc. It usually ranges bClweenabout 0.80 alid 0.92 for dry gas. An attcmpt to modify the efficiency factor for the presence of liquids was p~oposcd in Figure 3-46.
Prodllc/ioll Opfimiza/ion Uúng Nodol AJ/,dysis
118
read the upstream pressure as 790 psig. Fol!owing the same procedure on Figure 3-52 far a 3 in. line yields an upstream pressure af about 280 psig.
K. Use of Prepared Pressure Traverse Curves
Thc preparation and use ofprepared pressure curves foc flow in wells was discussed in a preYivus section. The same methods were used for preparing 5.:t5 of curves foc horizontal two-phase Oow) and lhe same types of errors will result froro using lhe generalizc"d curves. lf several fiow conditions are to be anJ.lyzed foc a particular pipeline, it might be feasible to prepare specific curves for that pipeline, but the pressure peafiles would depcnd 011 lhe pipeline profile being considered. Thereforc, it would be more feasible tú use a computer prograil1 to perform lhe calculations [oc various condilions. Howc\"er, ror preliminary estima(cs of lhe effect of flowlines on lhe o\'erall well performance, lhe gcncralizcd curves can be lIsed. Since lhe only curves available wcre prepared roe horizontal flow, ir ¡he pipeline under consideration conlains hills, some mean:; ol' accounting for the hydrostalic component must be used. The Flanigan melhod is suitabk for this ster. To Ihe aUlhor's knowledgc, there are (loly three sources of curves for horizontal two-phase tlow. The Eoton mClhod \Vas uscd lO prepare the cur\"e:i 8vailable from Brown. 47 These CUf\'~S \Vcre calculated (or /.,. = 1.0. The otiJa source, also published by Brown,:: cOlllains a much lnrger set of curves that wcre prepared using the Bcggs and Brill me[hod. The curves \Vere cakularcd ror water cuts of zcro and 100 percent. The cur.·es includcd in the Appendix of this book, which were ;lIso used in the example problems in this sectioIl, were prepared by the authar using rhe Bcggs an.d Brill carrelatiuIl. The camputer program used to prepare the curves can be modified for any possible flow conditions.
Example 3-12: A well thal is lo produce al a rale 01 1500 STB/day wilh a wellhead pressure 01 400 psig is localed 5000 ft from lhe separatar. The separator pressure is fixed al 200 psig. The well is producing no waler and Ihe GLR is 1000 scflSTB. Find lhe necessary fiowline size requirad for lhis well if the terrain between the well and the separator is relatively f1at.
Solufion: The solution consists of finding the minimum Hne size necessary to require ao upstream pressure of 400 psig or less. Figures are selected for ·various Hne sizes, and the required upstream pressure is tound using the same procedure as used in Example 3-11. Pwh. psig Une Size, in. 2 910 2.5 520 3 360 The results show that a line of size berween 2.5 al1d 3 in. wauld result in a value of Pwh ;:: 400 psig. Since only specific pipe sizes are available, the 3-in. line wouJd be selected.
Example 3-13: The following data apply to a pipeline constructed jo a hiJly terrain area. Use the horizontal traversa curves and the Flanigan method to find the required upstream pressure Pl'
A well 15 producing al a rale of 1500 STB/day wilh a GLR of 600 sel/STB. No waler is being produced and Ihe well is localed al a dislance of 6000 ti Irom lhe separator. If the separator pressure is fixed at 120 psig, find the required wellhead pressure for flowline sizes of 2 in. and 3 in.
1.
2.
3.
=
qw =
T
rg
-
10000 fi 3000 ft O 140°F 0.65
d
qo GOR Oil gravily P2
--
3 in. I.D. 3000 STB/day 800 sel/STB 35° API 200 psig
Solution: The solution will be trial and error or iterative sinca !'.Ph ((vsg!, vsg - I( p), and i5 - 0.5 (P2 + !'.PI + !'.Ph)· A suggested solution procedure when using the traverse curves is: Find P1 * using the horizontal curves Estimate llPh ~ For a first guess, use:
=
SolutlOn: Figure 3-51 represents the conditions for a 2 in. flowline. The sama solution procedure as described tor the vertical curves wm apply tor the horizontal curves. Locate!he known pressure, Psep - 120 psig on lhe pressure axis and the equivalenllenglh using lhe 600 GLR line. This lenglh is aboul 400 ti. Add lhe line lenglh, 6000 ti, lo lhe oullel equivalenl lenglh lo oblain 6400 ti. This is lhe equivalent lenglh correspondíng to the upstream conditions. Proceed horizonlally and inlersecl Ihe 600 GLR IIne. Proceed vertically upward lo the pressure axis and
-
Lenglh l:h
Example 3-11:
1. 2.
PL - 0.433 rL' HL = 0.2 3. 4.
Calculale p- 0.5 (p,' + tip,' + p~ Calculale, al p, f: R5 , 8 0 , Po,l, B g , v 5g' H(
•
Flow in Pipes ami Restrictions
JJ9 - ~
4
:111
400
-
:;:
§ 6
8
10
PRESSU RE, 100 PSIG .1'4 16 12 18
, .-1+, --
2
§
3 4
-
-1+
PIPELINE LO.,. IN. :
2
LIQUID RATE, ST8L/O: WATER FRACTION:
lS0Q·
O
•
-
5
2B
GRAVITY: 0.65· OIL PI GRAVITY: 35 WATER PECIFIC GRAVITY: 1. 07 AVERAGE LOWING TEMP.,F: 100 : BEGGS CORRELAT BRILL
-
-
26
24
~lmtl:H-I-H-H:~
..
-1+-
-
22
20
-
-
+!',
6
,
S400
7
8
'"
9
o o o
rl
,10
-
--- - .
E-<
-,
..
:¡.
'" E-<
-
-
-,
--
"
0-1
--
-
l511
.
-
-
. -
-
-
-. --
-
- 12
-
13
..
H
15
-
--
-
- - -.
-
-
-
16 ·17
-
18 19
.20
-
-
-
-
..
-.
- - - ... -
.+
-- -
I
Fig. 3-51. Exampfe 3-11 sofulfofl.
--
--
- - -
--
- - ..-
-- ct~
- ..
..
-
-
o •
o
,r
_ o
- -- - .. - . - - - - --
......
o
,
. ..L
..
.. . ... .- .
0_
-
ProduClioll Optimizarioll Using Nodal AJla/ysis
120
o ~
o ~
4
2
OO
a
10
PRESSURE, 100 PSlG 12 14 16 18
20
26
24
22
.: -~*rtl" 1
--I--t-:
1500
2
-!.. j~
¡ .¡
pIPELINE LD'
I
LIQUIO· RATE,
STBL/O,
WATER FRACTlüN:
3
1I1U1\\"1-
~~~mr
"
4
§
HL:
3
1500
o.
"GAS GRAVITY: 0:65" OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEr-1P., F: 100 CORRELATION: BEGGS & 8RILL
"
5
6
7 7500
_. - -" "1"""
"lfHHf
a
...
"'
o o o
9
mi"..
IJI.\L1
,,
rl
10
¡-; lO
~ 11
H
12
:IHIIIJI· -
13
14 15 16 ·17
la
.1
Fig. 3-52. Example 3-11 solution.
T
28
12I
Flow in Pipes ond Reslrictions .
,. o
§
:.
6
4
PRESSURE,
100 PSIG
101214
1618
-'}:t"::litlíldtmt1títlr-¡-HJm .I~l,:
PIPELINE 1. D. ,
.- 4+ -.
2
·2022242628
-l..
IN.:
LIQUID' RATE, STBL/D: WATER FRACTION:
3
GAS GRAVITY:
3000'
O
0.65'
OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
4
§
3
5 ..
l± - . 1
• -
-
6
7
8
.1f ... _: W:OOm.:J:lt
mn_:J:l.I:J:..1:1.:I:J ..
1:1:.
eJ--11-l->·1->-1--1-1-1-1
,
..
12
-'.
, ," 14
L
-±, -:
15
16
17
:1+ .
Fig. 3·53. Example 3·13 solution.
,
1ll 5. 6. 7. 1. 2.
3. 4.
5.
ProuucrioJl Optimizar/oll
Calculale ÓPh ~ PoH L [ h Compare ÓPh and óPh If nol close, sel óPh' =óPh and go to Step 3. Calculate p, = p,' + óPh From Figure 3-53, find p,' =810 psig 70 = 141.5/(131.5 + 35) = 0.85 Po ~ 0.433(0.85) = 0.368 psjlft óPh' = PoH L [h = 0.368(0.2)(3000) = 220 psi 15 = 0.5(810 + 220 + 200) = 615 psig = 629.7 psia R, = 96 sctlSTB (Eq. 3-76) Bo = 1 .093 bbilSTB (Eq. 3-79) Po =350(.85) + 0.0764(.65)(96)15.615(1.093) (Eq. 3-60) Po ~ 49.3 Iblft3 = 0.342 psiltl Z =0930 (Eq. 3·73) Bg =0.0257 h3/scf (Eq. 3-65) V,g = q,jA = qo(R-R,)B,j86400A (Eq. 3-64) V,g =3000(800 - R,)B,j86400(0.0491) = 0.7074(800 R,)Bg V,g =0.7074(704)(.0257) = 12.8 ftIsec H L = 1/(1 + 0.3264(12.8)1.006) (Eq. 3-117) HL = 0.19 ÓPh ~ 0.342(0.19)(3000) = 195 psi
,
;."
This t~.not clase enaugh to the initial eslimate, Ü.Ph* ;::.
220'.,!et 3. 4.
5.
6.
7.
"P," = 195 psi.
15 = 0'.'5(810 + 195 + 200) = 602.5 psig = 617.2 psia R, = 93, Bo = 1,092, Po = 0.342, Z = 0,9'30, Bg = 0.0262, V,g = 13.1, HL = 0.187 óPh = 0,342(.187)(3000) = 192 psi
L~s¡ng
Nodul
.-ll1o~rsis
lhae is no changc in cithet friction faLtor or fluid dcnsity betwecn the branchcs. Ihis conecpl is il1accura{~ for two-phase flow bccause lhe liquid phJ:ie lIoes 110t always split bctween the branchcs in the sume ratio as the gas. It has beco abservcd (hat in many cases all the l¡quid will go inta only ane of {he branches, while the gas wiII split in such a manncr as to create equal pressure drops in each branch. As has already becn disclIssed, to calclllate this pressurc drop. the: tlow rates and gas-liqllid ratios cxisting in a pipe mus( be known. Thcrefore, so me method to estimate the path 01' the ¡¡quid must be availablc. The flow-splitting problem was first discllssed in ddail by Orange. R3 He ob:it::rved that in a comptcx gas distribution system, uny condensate that fonncd in thc s)"stem eventually rcached a single location, cvcn though the gas may have encountered nUlllerous branchcs up.s(rearn of that lacation. Aflc:r paforming cOl1lpreh~nsi\'e studies of the phenomenon. he suggested tha( if [he braneh took off less than 20 pcreent of the total 00\\", núnc of the liquid would divert ¡nto {he lateral. If more ¡han 35 percent of the flow was divencd iuto the lateral, all the ¡iquid would divert into the la¡eral. Lutcr sludies by J-Iong34 and Bcrgman, et al.~~ rc\"caled that undcr otllc!' no\\' conditions, particulnrly high rales al which mist Oow might exist, the liquid 111JY also split al lhe branch. They $uggesled procedurcs ID estimate the degree of liquid splitting as a function 01 gas splitting and gas RCYllolds number in the m.ain lineo Their relalionship is shown grJphically in Figure 3-5~. The Reynolds numbcr for the gas in the main line can be calculated from: where
2001Iq".I',
N Ro
(3· ti SF)
¡Id
Y¡.;
Since two successive values of tJPh agree, the solutian has converged. P, 810 + 192 = 1002 psig
q~c
=
d Jl
gas specific gravity, gas now ratc, MMscfd. pipe inside diameter, inchcs, nnd gas \·¡scosity, cp
L. Parallel or Looped Pipelines
AlI the previous discussion regarding pressure drop calculations in surface lines has been wilh respect to flow through a single pipe of constant inside diameter. However, when the flow capacity of an existing pipeline or gathering systern becornes too srnall, it is comman praetiee to construct another Hne alongside or parallel to existing lines to inerease the flow capacity or reduce the pressure drop. Ihis is sorne times caJled "looping" the line. Calculation of the pressure drop occurring in parallel lines is f.irly simple in lhe case of single-phase flow beca use the flow corning into the branching point wiII split or divide such that the pressure drop is equal in the two pipes. The two pipes of diarneters dI and d1 can be replaced by a singie pipe having a diameter of d, ~ (dI''> + di')""· This eoneept ineludes the assumplion that
100
:['<;~~-L_~~I:~'(~;:<~"OI>O'" o
"..u.L'.'-.-'-....L.LL.l.ll""='~~.ill'·""'7°"".. "'"",,,,,,,~,-,"
lO'
llf
106
Id
loe
=.rYNOLOS NUM8ER Al MAIN P:?E
Fig. 3-54. Generalized chart for route selectively based on Oranje's dala. 85
•
Flow in Pipes and Restrictions ." ..... The results obtained from this figure have not beeo extensively tested and may be too simple toactually describe the phenomenon. However, unless more accurate methods are available it can be used to detennine the " gas and liquid rates in eaeh braneh or lateral for nodal analysis purposes. The following iterative procedure is suggested for caIculating the pressure drap occurring across a looped section of a pipeline. It is assumed that the pressure is known at ane end of the section where the branches are joined and lhat this pressure is equal allhal point in both branches. TIte diameters and lengths of the two lines are known. Tbe total gas and liquid rates are al50 known. 1.
Assume a value for the fraction of the gas going into the lateral. This fixes the gas rate in each branch.
2.
Use Figure 3-54 to estirnate the liquia rate in each branch. This rncthod may not always give the correet liquid split, but it will be cIose enough for a nodal analysis.
3.
Using the gas and liquid rates detcnnined in Steps 2 and 3, ealeulate the pressure drap in each branch using the appropriate methods.
~.
Compare the pressure drops ealculated in Step 3. If they are egual, the assumed rates are correet and the prcssurc drop is correct. If they are not egual, adjust ¡he gas split and go to Step 2. Rcpeat until convergence on pressure drop is attained.
A more complex analysis of this phenomenon is beyond the scope of this book. More detailed methods for estimating the liquid split can be found in Reference 9.
123 that critical flow will exisl. A rule-of-tIiümb for distinguishing belween critical and subcritical flow states that if the ratio of downstream pressure to upstream pressure is less than or equa! to 0.5, then the flow will be criticaL This is a c10ser approximation for sing!e-phase gas tban for two-phase flow. Sorne engineers use either 0.6 or 0.7 as the critical pressure ratio in two-phase flow, although research perfonned at Tulsa University87 has shown that in sorne cases, the ratio must be as Iow as 0.3 befare flow becomes critical. The purpose of a SSSV is not to control lhe How rate, bul to shut lhe welI in when wellhead pressure becomes too low. Therefore, they are usually sized for minimum pressure drop and will be operating in sUDcrilical flow. Procedures rol' calculating the pressure losses in these three types of restrictions wiII be presented in this section.
A. Surface Chokes Equations for estimating the relationship among pressure, flow rate and choke size for both subcritical and critical flow through chokes will be presenled for both gas flow and two-phase flow.
1. Gas Ftaw A general equation for flow through rcstrictions can be derived by combining the Bcrnoulli equation with an equation of state. The irreversible losses are accounted for by use of a discharge coefficient, which depends on lhe type of restriction. The following equalion applies for gas flow in both the critical and subcritical regimes. For critical flow, the pressure ratio y = P;lPI is replaced by the critical pressure ratio J'c'
VI. PRESSURE DROP THROUGH RESTRICTIONS
~ C"(p,)(d)' [~k_)()~"
Although the principal pressure losses in the well system occur in the rescrvoir, the tubing, and the flO\vline, the pressurc lo·ss in restrictions can be substantial in some wells. The main typcs of restrictions are:
q"
1. Subsurfacc safcty val ves (SSSV's)
where
~(T.)Z Yg 1 1
2. Surface or bottomhole chokes 3. Yalves and fittings
d The losses occurring in SSSV's and pipe fittings cannot be 3 y oided, but the pressure drop across a surface choke can be climinatcd to obtain the maximum producing cap3.city from a well. The flow through a restriction may be eithcr critical (sonic) or subcritical (subsanic). Ifflow'is critical, a pressure disturbance downstream of the restriction will have no effcct on cithcr lhe flow rate through the rcstriction or the upstrcam prcssurc. Since one of the maio purposcs of a choke is to control flow rate, it wil1 usuatly be sizcd so
Yg k PI 1'2 T, ZI
k-l
-
_("')"1)
(3-119)
Y
volumetric gas flow rate coefficient based on systern of units, discharge coefficient and standard conditions LD. of bore open to gas flow gas speciftc gravity (air=l.O), dimensionless ratio of specific heats=C;C", dimensionless upstream pressure, absolute units downstream pressure, absolute units upstream temperature, absolute units compressibility factor at PI and T" dimensionless coefficient based on system of units discharge coefficicnt (empirical), dirncnsionIess
ProdllCfiol1 Oplil1lizalioJl Using Nodul Allalysis
124
standard absolutc tcmpcralure base, absolute
TABLE 3-7
unit!) standard absolute pressure base) absolute
Choke Constants Investigator
units
y,
criticaI pressure ratio, dimensionless
The pressure ratio al which fiow becomes critical dépends on lhe k value for lhe f10wing gas and is given by:
J,,
2
_ = [k+1
2.00 1.89 1.93 1.88
b 4.25 x 10- 3 3.86 x 10-3 3.12x 10-3 1.54 x 10-3
c 0.500 0.546 0.546 0.650
Example 3·14:
J'/(<-I) (3-120)
Using bolh lhe Ros and Gilbert equations, determine the choke size required to obtlin a liquid rate of 400
STB/day il wellhead pressure is 900 psia and R = 600 scflSTB.
TABLE 343 Coefficients and Units tor Eq.
Symbo/
a
Ros (72) Gilbert (73) Baxendell (74) Achong (75)
3~119
English System
S/ Metric System
Msctld
m 3 /d
in.
mm kPa "K 1.6259
psia "R 27.611
Solution: Solving Equalion 3-122 for d: d=
[b~~' ]'"
Ros:
lhe following equation can be used to estima te the d = [4.25 x 1O" (400)(600)" ]'" = 0.215 in.
relationship among flo\V rate, upstream pressure and
900
choke size Jor short restrictions wilh slightly rounded
openings operating in critica} tlo\\'. lhe units are obtained from Table.J-6.
Gilbert: d =
(3-121 )
lhe value to be used foc the discharge coefficient Có in Equations 3-119 and 3-121 depends on the shape of lhe
opening to the restriction and the length of the restriction as well as the Reynolds number. A value of Cd = 0.82 is recornmended if no infonllation is availab!e concerning [his data.
1. TIvo-Phase Flow The folh)wing equations rnay be used to determine the relationshil' among Pi, qL and d for gas/liquid f10w in lhe critical regime. These are empirica! equations and the coefficient and exponents may vary from field to field or well to well.
[
3.86' 10"(400)(600)o~. ]'"'' . = 0.218In. 900
Detennination of the boundary betwcen critica! and subcritical flow for the two-phase case is more complicated than that for single-phase f1ow. The sonic velocit)' in a two-phase mixture depcnds on both the gas and ¡iquid properties. Sachdeva, et al.,86 presented equations for determining the critical ratio of downslream to upstream pressure at the boundary, and proposcd a mcthod for calculating the flow cate through a choke for various pressure conditions. The critica! pressure ratio Yc = p/p/ is calculated iteratively from:
)', = (N/D)'/(H) where N=~+ (l-X,)p,,(t-y)
k-I (3-122)
where
D=~+!!.+ k-l
PJ qL
R d
upstream pressure, psia ¡iquid f10w rate, STB/day gas/liquid ratio, .cflSTB choke diarneter in inches
Valnes of a, b, and e proposed by different investigators are given in Tapie 3·7.
(3-l23)
X¡ Pgl
Pg 2 PL k
2
X,PL
n(l-X,)p" +!!.[(I-X,)P"]' X,PL 2 X;PL
mass fraction of gas at upstream conditions (quality), gas density at upstream conditions, gas density at downstream conditions ¡iquid density at upslream conditions, ratio of specific heats for the gas, CIC y
•
125
Flow in Pipes and Restrictions
(3-124)
where
specific heat uf the liquid
Equation 3-123 is dimensionJess, and any consistent set ofunits may be uscd. It is .solved by assuming a value for y and then ca1culating YC' Each calculated value of Yc is lised ror the next estimated y until convergence is rcached. A good first guess is y = 0.5. The quality is the ratio of the gas mass flow rate to the total rnass flow rateo Using field units, it may be ca1culated from
X =
0_.0_76_4....:Y-'-g(:....R_-....:/'.;:.oR....:,:....) _ 00764yg(R- J"R,)+5.615(J"BoPo + J"B.pJ (3-125)
where
gas specific gravity, produciog GLR, scflSTBL, fraclioo of oil ftowiog, qj(q. + qw), fraction of water Oowing, (1-1:), solution gas-oil ratio al PI' TI> scf/STBO, oil deosily al p" T" lbm/ft3, water density al PI. T¡,lbrn/ft3, oíl formal ion volumc factor at PI' TI' water farmalion "olumc factor at PI' TI'
ed at downstream conditions. If flow is subcritical, that is y> YC' use the actual downstream pressure, P2' If flow is critical, use y = Ye aod P2 = YeP,. It was suggested that if ao elbow is immediately upslream of the choke lhe value of CD is 0.75. If 00 fiow-perturbiog e!fects are upstream, use CD ~ 0.85. Examp/e 3-15: A wellhead choke is installed ín a well that is producing oil and gas. Upstream pressure is 1000 psia and dawnstream pre~sure is 600 psia. Estimate the oil producHan rate lhrough the choke under these condilion5. Other data are:
GLR = Yo = T, = T, = Cv = k =
GOR = 1165 scf/STBO 0.825 = 40' API 100'F = 560 R 90 F = 550 R 0.414 Blwlbm-'F 1.3 0
0
0
Yg = 0.70 d = 24/64 = 0.38 io. fw = O Cp = 0.537 C L = 0.55
Btu~bm-oF
Btu~bm-'F
Upstream Condifions Downstream Condi(íons
R" scf/STBO 80
140 1.08 48.9 2.32 0.891
250 1.14 47.3 4.05 0.834
Po' 1 bm/ft3 Po, 1 bmlft3 Z
So/ution:
Sachdeva, el al. also prcsented an equatian ta calculate the flo\\' rale through a chakc which can be used foc both critical and subcritical flow. For field units:
_ 0.525Cd d' { ,[(I-X,)(1- y) q, C P,P., M2
PLl
(3-126)
)]}'.5
where qL =
.+ X,k(l- /-". ". Pg,(k-l). Iiquid flow rate, STBLlday, X,
P",l
=:
[
Pgly11k
(1- X), ]-'
+~
co,' =8.84xI0-'yg(R- /"R,)
Calculate critical pressure ratio,
Ye:
x= , -0.139 0.0764(0.7)(1165-250) 0.0764(0.7)(1165 - 250) +5.615(1.14 )(47.3)
n =1+
0.139(0.537-0.414) -1_032 0.139(0.414) + 0.861 (0.55)
Estimale Ye = 0.5: N =...2.2...+ 0.861(4.05)(1-05)
1.3-1 (3-127)
+6.5 x W-'(foPoBo + J,.p.B•. )
4599 .
O = ~ + 1.032 + 1032(0.861 )(2.37)
0.3 (3-t28)
0.139(47.3) 2
0.139(47.3)
+ 1.032 [0_861 (2_37)]' 2 0.139(47.3)
0=5.219 Ye = (4.599/5.219),·313 = 0.578
where
d p]
Pe
p.,
X,
choke inside diametcr. inches upstream prcssure, psia, liquid dcosily, Ibm/ft3, gas dcosily atp" T" Ibm/¡\J, aod quality alp" T, (Equalioo 3-125)
Thc fluid propcrtics used to calculatc Cm2 are cvaluat-
Estimated Ye
0.5 0.578 0.556 0.562 0.560
Calculated Ye
. 0.578 0.556 0.562 0.560 0.560
Producrioll Optimi::aliol1
126 Since lhe value of y tor the given conditions is y :: P2'p, = 600/1000 = 0.6, flow is s""crilical (y> Ycl.
Caiculale qL: Cm' =8.84 x lO·'(0.7)(1165-140)
+6.5 X 10·'148.9\11.08\ Cm2 = 0.0041
0.139
0.861]·'
~-p, q L =3428C . ,'L
(
= 14.48 .bmlft' q = 0.525(0.75)(0.38)' {1000(14.48)' , 0.0041
'YL
" J
(3-129)
where q,.
• [0.861(0.4) + 0.139(1:3)(0.111)]}" 47.3 4.0:>,0.3)
p,
p, 'YL
qL = qo = 979 STB/day
C l ./. F,
An equation for calculating t10w rates foc subcritical flow lhrough multiple orifica valv", (MOV) or chokes el
Nodal AJlalysú"
consist of a stationary disk with 1wo h0{e~ and a mo\'-'" able disk wÍlh two holes. The size ofü:~ opl.:ning can b~ changed by rotating lhe movable disk. The chokc used in the Surbcy el al. study was lll.:iOut:1ctured by the Willis Company. A schematic of lhe thúkc is shown in Figures 3-55 and 3-56. The study rcs'Jltt:d in a mcthod to modify thc discharg~ coefficient for singlc-phase liquid flow so that it will apply for two-pn.:.1se flow through lhis particular type and size (2 in.) of ohoke. The equation is:
P., = [ 4.05(0.6)"" + 47.3
was prcsented by Surbey,
C~;'¡g
al. 87 Múst of these valves
flow rate, STBLlday \lpstream pressure, psia úownstream pressurc, psi.l ¡iquid spcLific gravily, anJ CI'//2Fc [sin (A,RA')]-"p,A.,IR
where CI'fP
R
CALIBRATION OIAL
A¡
two-phase dischal'ge cú~fficient Figure 3-57, gas-liquid ratio, scflSTB. anglc of choke opening.. degrees values are from Table ~-~
from
TABLE 3-8 Choke
Constants
Constanl
Valuf;
A, A2 A3
91.9039 -0.1458
A,
-20.25:0
0.2419
In sorne cases, it may be necessary lO ~$timate the presdrop through a choke in which a single-phase liquid is tlowing. This will almost always be subcritical f10w since the velocity of sound in a liquid ¡s very large. sure
Fig. 3-55. MOV wellhead ehoke design (after Willis8 8).
a
e
b
Fig. 3-56. Ceramie ehoke disk operation (after WiIIis8 8).
••
o"
Flow in Pipes ond Restrictions
127
Yg
35
o ó
WATER AIR
21
w
"'"
o: w ~
TI
upstr~am
d D C¿ y
"-
t
gas gravity (air = 1) gas eompressibility at 1',. TI
q" P
28
u
Z\
temperature, °R
gas flow rate, Msefd beta ratio = dlD bean diameter, in. pipe insirle rliameter, jn.
diseharge eoeflicient (API suggests 0.9) expansion factor, dimensionless
The expansion factor determination is iterative and 14
may be ealculated from Eguation 3-133. lts value ranges between 0.67 and l.0. For quick estimates, a default value of 0.85 is afien used.
7
y
O\·"'5-~"'--,'''O'-'-----C4;'5'-----·6tO;--~7;';5'-------':9·0
~ 1-[041 +0.35P,l 1'\- p,]
l "p, )
13-133)
whcre k is (he ratio of specilic hcals of the gas.
CHQKE ANGLE lDEGREESI
Fig. 3-57. Average Cv vs. choke sefting. 87
The following equation m~y be used: q,
~1022.7C"d'r p'.~p,
2. Tlllo-Pllase Flan'
r
(3-131)
\vherc q/.
d p
YL Unless
now ratc in STBL/day, chokc diamctcr, inches, psi. and Iiquid spccific gravity.
el! is known,
a valuc ofO.85 may be used.
A research project was sponsored by the APl in 1978 at the Ulliversity of Tulsa 76 that was designed to improve the equations for sizillg SSSV's operaling in (\\'o-phase subcriticn,' flo\\'. Sevcral of Ihe cornmercially available SSSV's \Vere U:;~d in the experimental phase of the fescarch, and speLific cql1ations for discharge coelTícicnt fOf cach valve testec! werc prcscnted. Howcyc'r. it has becn found that in practicc a single cqu~tion ror discharge cocfficient will give reasonable results for any type of SSSV Thcrefore. only (!lis equation will be prescnted here. For a more detailcd treatment of the problem. reference may be made to a report publishcd by Bcggs, et al.,
ín 1980.7 6 Thc equation fN pressure drop is:
B. Subsurface Safety Valves (SSSV's):
p. -1' = .
As was stated cmlier, thc flow through a SSSV will be 5ubcritical a!ld the unknown of intercst is usually the prcssurc drop eaused by a SSSV of a particular size. Thc solutlon is usual1y itcralivc bceause most ofthe cquations require cvalunlion of Ihe fluid propcrtics, eitbcr al upstream prcssurc or at avcrage prcssurc.
1048xI0"Y,Z,7;q;,(I-P') p,d'C~Y'
where PI
P2
llpstream prcssure, psia do\\'ns!r~~m prcssure, psia
1"
" '"
(3·134)
n
Pn
no-,lip density, Ibm/ft' (Eq. 3-22)
vm
mixture velocity through the choke, n/sec,
(Eg. 3-28) PI
P2 CD
upstrcam pressure. psia dO\\llstream pressure, psia discharge cocfTícicnt (3-1J5)
wherc (3-1l2)
C
whcre
1. Gas Flaw An equation publishcd by the API65 can be used to calcU]
p, - p, ~
1.078x10~p
2
CI
0.233
C,
8.4 X lO"
C,
6.672 -11.661'
C, N" AL
q/qL = (1 -Al.)/AL qL(qL + qK)
128
P
=
Co -0.233 + 8.4 x 10-4 (2.947) + 6.672(0,455)11.661(.455)2
dIO
choke diamerer lubing inside di ame ter
d D
Co
In the previous equations, aH the fluid propcrties ncccssary roc calculating the density and ydocities are evaluatcd al upstrcam conditions ofpressure and tempcrature. Solving roe PI fram a known P2 value ¡s. thacfore, iterativc. Example 3-16: A well thal is producing through 2 3/8 tubing is equipped wilh a 0.908 in I.D. SSSV. Pressure and temperature upstream of the SSSV were found to be 615 psi a and 140 F respectively. Using lhe following dala calculate the pressure downstream of the SSSv. Q
qo" 800 STB/day q\V ;: O R" 800 scf/STB Oil gravily " 35°API Yg " 0.65
=0.391
A "::'d' = 0.7854(0.908/12)' = 4.497 x 10" ft'
4
V
m
=q; +q; =0.057+0.168 -50fUsec
A 4497 x l0" 1.078xl0-4p v' P2 ;::; PI " '" C o
1.078 x 1O~ (13.92)(50)' = 615 - ------'---"'---''0.391
P," 615 - 9.6" 605.4 psi a
C. Valves and Pipe Fittings
Solution: The following PVT properties were calculaled at p " 615 psia and T" 140°F = 600 o R:
The prcssure losses occurring through \·arious types 01' valves and filtings can be approximatcd by lhe equivalent length concepto This involves rcplacing each fitting by an equivalent lenglh of pipe lhar would produce the same pressurc drop as rhe fiuing. This can be exprcsscd in equation form as: (3-1361
R, " 96 scflSTB Z" 0.93
or
Bo " 1.093 bbl/STB Bg
"
fL=K d
0.0257 ft 3/scf
, q, IR - R.JB, q, 86400
where
800(800- 96)(0.0257) 86400
d
q'g" 0.168 ft 3/sec q'o" 6.5
X
~
diameter of pipe fricrion factor foc pipe no\\' L length of pipe K :::: rcsistance cocfficient depcnding on the type oc size of fitting. I~
10.5 qoB o " 6.5 x 10.5 (800)(1.093)
q'o" 0.057 ft 3/sec 0.057 0.057+0.168
Solving roe [he length gives:
0.253
L =Kd 350(.85) + .0764(.65)(96) Po 5.615(1.093)
2.7y,p
.
(3-137)
49.3Ibmlfl'
2.7(.65X615)
1.934Ibmlft'
"ZT = 0.93(600) Pn =PaAL+Pg(l-Ad" 49.3(.253) + 1.934(1 Pn =13.92 Ibm/ft3 P,
N y = q'/q'o = 0.168/0.057 = 2.947
P =0.908/1.995 =0.455
I
.253)
An equivalent length, Le can be calculaled roc each fitting by using the [riclioo factor calculated foe flow in lhe pipe. AH lhe Le values can then be added to the actual pipe length [or the pressure drop calculation. Values of lhe resistance coeflicient have becn 'de termined for single·phase flow, and it has beeo found tha1 lhese values also apply for two-phase flo\\'. Tile friction factor for two-phasc flow ¡s, of course, usually larger than for singlc-phase-flow. The following average valucs for K can be llsed to obtain satisfactory rC$ults for two-
-
Flow in Pipes and Resfrictions ....... phase f1ow, aIthough in many cases the relatively small pressure drop in the fittings will be ignored. Fitting Type
K
Gate Valve Elbows Globe Valve Cheek Valve
0.15 0.2-0.3 3.0-5.0 6.0-8.0
Solution:
ror
(3-' 3S)
where erosion vcloeity, ftlsec fluid densily, Ibllllft J ~ PLAL + Pg (I-AL)
e rangcs between 75 and
150
A good average valuc far e has been found to be about 100. l fe is sel equal lo 100 and the gas equation of sta te is used to cxpress density, Equation 3-138 becomes 100
......f!.L ]05
v, = [29
ZRT
where p, T and Z are the conditions at which the velocity is to be dctermined. The equation may be cxpressed in tenns of gas f10w rate at standard conditions by:
q, = J.86xl0'
A[-P-J"
(3-139)
ZTy,
whcrc
q A" p T
at- Pt T
A gas weIl is producing lhrough 2 718 in. tubing al a weIlhead pressure 01800 psia. The weIlhead temperature is 140"F and gas gravily Is 0.65. Determine the maximum rale al which Ihis weU can produce withoul exceedíng the erosional velocity.
When fluid flows through a pipe at high veloeities, it has been foulld that erosion of the pipe can accur. This is especially true high capacity gas flow in which the insitu velocity may exceed 60 fo 70 ftlsec. Erosion is not as mueh of a problem in oil wells, although sorne high gas¡¡quid ratio wel1s may be subject to eros ion. lile velocity at which crosion begins to occur cannot be determined exactly, and ir some salid particles, such as sand, are in the fluid, erosion may oecur at relatively low velocities. The velocity at which crosion may occur has been related to the density of the fluid by the folIowing equation:
p
gas compressibility factor gas gravity
Example 3·17:
VII. EROSIONAL VELOCITY
Ve
129
crosional now rale, r-.·fscfd area of Ihe pipe, ft2 lowcst prcssurc in the pipe, psia ICmpCrJturc at point whcrc p is dctcnnined, °R
A = ~d' = 0.7854(2.441/12)' = 0.032 ft' 4 Al P = 800, T = 140"F the value 01 Z is 0.91. q. = 1.86 x 10 5 (0.032)(8001(.91)(600)(.65))0.5
q. = 8,936 Mscfd = 8.9 MMscfd This corresponds to an
¡n~silu
velocity of 62.3 ftlsec.
VIII. REFERENCES 1. Drew, T. 8., Koo. E. C. and MeAdams, W. H.: Tram. Am. Ins1. Chem. Engrs., 28, 1930. 2. Nikur-adse. 1.: Forsclumgsheft, p. 301,1933. 3. Colebrook C. F.: J. Jnsl. 0"';1 Engrs. (Lomloll). 1938. 4. Jaill, A. K.: "A~el1fale Explicit Equalion for Fric:tion Facl~lr,"
J. Hydl. Div. ASeE, NoHY5, May, 1976. 5. Mood)'. L. F.: "Friclion Factors for Pipe Flo\\'," Trans. ASME, YoL 66.1944. 6. Govier, G \Y. and Aziz, K.: The FlolV ofColllpli'x Mix/l/l"Cs in Pipes, Van Norstrand Reinnold Co., New York, 1972. 7. HP-4IC Petroleum Fluids Pae, Hcwlett·Pacbrd, 1000 N. E. Cirele Blvd., Corvallis, Ore., 97330. 8. Slanding.:'>.1. B. and Kalz, D. L.: "Density ofNatural Gases," Trans. AJ:\tE, 1942. 9. Brill, J. P. and Beggs, H. D.: Tu·o-Pllase Floll' in Pipcs, The Univ. ofT\11sa. Tulsa, ükla. 1978. 10. Standing.;\l B.: VolulIlcrric and Phasc Beharior o/Oil Field Hydrocorboll Syslems, SPE of AIME, 8th Printing, 1977. 11. Wichcrt, E. anJ Aziz, K.: "Calculatc Z's for Sour Gases," Hydrocarbon Proc., May, 1972. 12. Vnsqucz. M. and Bcggs, H. D.: "Corrclations for Fluid Physical Property Prediclion," JPT, June, 1980. 13. Standing. M. 8.:.
AIME,1958. 15. erafi, B. e, and Hawkins, M. F.: Applied Perro/eu", Reservoir Engineering, Prentiee~Hall, NJ, 1959. 16. Bcggs, H. D. and Robinson, 1. R.: "Eslimaling the Vi!'cosily ofCnlde Oil Systems," JPT, Sept., 1975. 17. Mattnews, C. S. and Russell, D. G: Pres.'iUre Blli/dllp and F/ow Tests in Wells, SPE Monograpn 1, 1967. 18. Mechan. o. K: "A Correlation for Waler Viscosity," Per,:
ProcillCtiCJII 0pfimbl/ioll Usillg
130 Eng/: /111., luly, 1980. 19. llakcr, O. anJ Swcrdlotl: W.: "Finding
Surra~~
Tensioo 01'
lIydrucarbon Liquids," OGJ, Jan 2, 1956.
20. Hough, E. W.: "Inlcrfaciu\ TCllsions al Rt:servoir Prc5surcs and Tcmpcralurcs," Tral/s. AIME, 195 L
2 L Rumey, H. 1.: "Wcllbore lleat Transmission," JPT, Apr.. 1962.
22. Shiu, K. C. and Bcggs, H. D.: "Predic¡ing Tcmperaturcs in Flowing Dil \Vcll.".," Trans. AIME, J. Ellelg.l' Res. TeL'h., Mur., 1980.
23. Brown, K. E. and Bcggs, H. D.: The Tedmolog)' of Arfijicial Lifi Ale/llods, Vol. 1, PcnnWdl PubL Ca., Tulsa, Okla., 1977. 24. Podtmallll, F. H. and Carpcntcf, P. G: "Thc t-,-fuhiphase Flow of Gas Dil and Waler Through Vertical Flow Strings," Dril/. & Prol/. PraC/ice, 1952. 25. [3axcllddl, P. B. and Thomns, R.: "Thc Calcululion of Pr~ssurc Gradicnts for f',{uitiphasc Flow in Tubing," SOCo Pel. EI1~. J, t\f:¡r., 1963. 1ó. Ikggs, 11. D.: Lindale, TX, p~rsonal communicillioll. 27. Hagellorn, A. R. and 8roWIl, K. E.: "Experimental Study of Pre::;sun:: Gr
•
•
Nodt.J! ,1J/ClI)'sis
43. ClIlIender, M. H. and Smith, R. y.: "PlaC\lL'JI Solulion orGas flow Eq1l31lons for Wdls anu P¡pdil\~s wilh Large Tcmll..:raturc Gr.loicllts," Trum'., AIME. IY56. 44. Gray, H. E.: ''\"erliC,ll Flow Corn:lalions in Gas \\'clls," Uscr Manual, API 14-8 SSSV Cümpuler Prúgram. 45. Tllrner, R. G., l-I11bbard, M. G., and Dukh:r, A. E.: "Analysis ' in Pipes," Cal/. J. CHE., 51, 1973. 60. Chawla, J. M.: -Liquid Content in Pipes in Two-Phase Flow 01' Gas-Liquid ~Iixtul'es," Chimie /Jlgellil!lIl' TecJmik, 69, 1969. "Proposed Corrclation 61. Lockhart, R. \r. and Mal'tinclli, R. of Dala for Isothermal Two·Phase Two-Component Flow in Pipes," Chem. ElIg. Prog., Jan., 1949. 62. Chcno",eth, J. M. and Martin, M. W.: "Turbldent Two-Phase Flow," Pe": Re/. Oct., 1955. 63. Vohra, 1. R., el al.: "CoOlparison of Liquid Holdup Corrclations for Gas-Liquid flow in Horizolllal Pipes," SPE 4690, Sepl., 1973. 64. Hcmandcz, F. anJ BrilI. 1. P.: "Comparisoll ofFriction Factor Correlations [ol' Gas-Liquid Flow in Horizontal Pipes," SPE 5140, Del., 1973. 65. API 148: Users Malllw/jorAPl148 SllbswflJce ron/mUed
c.:
FlolV in Pipes and Reslriclions ......
66.
67.
68. 69.
70. 71. 72.
73. 74.
75. 76.
77.
Subslfrjace Safety Valve Sizing Computer Program, API, Washington, O. e, Junc, ]974. Mandhane, 1. M., Gregory, G. A., and Aziz, K.: I
131 Aug.,1966. 78. Asheim, H: "MONA, An Accurale Two-Phase Well Flow Model Based on Phase Stippage," SPE Produc/;on Engineering, May, 1986. 79. Nicklin, D. J., Wilkes, J. O., and Davidson, J. F.: "Two-Phase Flow in Vertical Tubes," Trans. Inst. Chcm Engrs., 1962,40. 80. Hasan, A. R. and Kabir, C. S.: "Predicting Multiphase Behavior in a Deviated Wel}," SPE 15449, Presenled al 61 s1 Annual SPE Conferencc, New Orteans, LA, 1986. 81. Fayed, A. S. and Otten, l: "Comparing Measured with Calculated Multiphase Flow Pressure Orop," OGJ, Aug. 22, 1983. 82. Osman, M. E. and EI-Feky, S. A.: "Oesign Methods for Two~ Phase Pipelines Compared, E\"aluated," OGJ, Sept, 2, 1985. 83. Oranje, L.: "Conrlensate Behavior in Gas Pipelines is Predictable," OGi, luly 2, 1973. 84. Hong, K. c.: "Flow Splitting a T\Vo~Phase Fluid at a Pipe Tee," SPE 6530. 85. Bergman, D. F., Tce, 1\1. R.. and Kalz, D.L.: "Retrograde Condcnsation in Natural Gas Pipelines," Rcport on Projcct PR 26-69 of the AGA Pipc:line Rcsearch Comm., U. of Michigan,1975. 86. Saehdc\"a, R., Schmidt, Z., Brill, 1. P., and Blais, R. M.: "Two-Phase Flow Through Chokcs," SPE 15657, Presentcd at 6J~f SPE Fall Confercnce.. New Orlcans, LA, 1986. 87. Smvcy. D. \V., Kelk:lr. B. G. and Brill, J. P.: "Sludy of Subcricital F1Q\v Through ~rulliple-Or¡fice Val\'cs:' Sf"E Prod. Engl:, Feb., 1988. 88. "Instruc¡ions ilnd r"rts li!'t:' Willis Oil T001 Co.. Cal. 4230A. Long Beach, CA (19: 1).
•
Total System Analysis
4
1. INTRODUCTION The general proccdure for applying total system: or nodaI ana]ysis fo a producing \Vell \Vas dcscribed in Chaplee l. It \Vas potnted out thal methods musl be available to calculate lhe rclatiollship bctwecn pressure drap and flO\.... rate roc al! al' lhe componcnts in lhe S)'stCIll. The total system, illustrating the n.rious componcnts, was shown in Figure 1-1, which is rcproduccd as Figure ,+.1. The system analysis proccdurc rcquires first sclecting a node and ca1culating lhe nade pressure, starting al lhe
fixed oc constan! prcssures existing in the system. These fixed pressurcs are usualIy ¡iR and either Pll'h or psep. The nade may be selcctcd al any point in lhe system, and lhe mas! commonly selected points are shown in Figure 4-2. The exprc~sjons for the flow into the nade and for the 00'" out of the node can be cxpressed as:
/l1jlOH' Pinle! -
.óp(upstream components)
= Pnodc
Ou1}low Poutlet
+ 6p(downstream componcnts) =
Pnode
Pinle! = Pn a n d = Pscp or Pwh·' lhe two criteria that must be met are:
As \Vas statcd earlier, in most cases Poutlet
l.
Flo\V into the nade equals Oow out. of the node.
2.
0111y one prcssurc can exist at lhe nade for a given now ratc. Finding the now rate and pressure that satisfics lhe pre-
vious requirements can be accomplished graphically by plotting node pressure versus now rate, as described in Chaptcr l. Thc intcrsection of the innow and outnow curves occurs at lhe rate that satisfies the rcquirement that the inflow rate equals the outnow rateo This rate will be the producing capacity for the systcm for a particular set of components. To investigate lhe cffcct of changes in any of the components on the producing capacity, ncw inflow or outflow curves can be gencraled for eaeh change. Ir a change is made in an inflow or upstream component only, the outllow curve wiIl not ehange, and will therefore not require recalculation. Conversely, ¡fthe only change made is in a do\Vnstream component, the inflo\V will remain unchanged. This allows isolation of the effect of a change in any cómponent 011 the tolal systcm capacity. This method can be uscd for dctennining if existing systems are performing properly and a1so for designing new systems. Possible applications of nodal analysis are listed in Chapter 1. Examples of several of lhese applicalions will be presenled in Ihis ehapter, which will illustrale lhe l1exibilily of Ihe melhod. Many of lhe problems will be worked using Ihe prepared pressure traverse curves for the piping system perfonnance, but the same solution procedures would apply ifthe calculations were made by a computer. The simplest production system \Viii be considere~ first as an introduction to the application proccdures. More complex and realistic systems \ViII then be considered. . The examples in lhis chapler will be reslricled lo 110wing wells, eithcr oil er gas. In Chapter 5, the application ofsystcms analysis to artificiallirt wclls will be prcsented.
133
ProdllC! iUII OflJim i:::.uJioll U\ ill.'..! Sod,,1 . ¡ ti.:, ~ .<'
134
~"Pa ~(Pwh':: PS
PWhC
-r·~~
ep)--1
r;==~ ~ SALES
r/). ':
Pose
L1NE
GAS
lAP6=(Posc;-P",W
SEPARATOR O"C==-' L10UID
Psep
SURFACE CHOKE
"P4rpusv-¿~sv:f,,-:,:~~;,;~-::';:¡::; AP,=
- ose) AP, = P,,-Pwls
Pwf - Pwh
BOTTOMHOLE RESTRICTION
"Po = (PUR - POR)
1
6. P2
Pwts -Pwf
A Po AP 4 A Ps ó. P6 AP, A Pa
PUR -POR Pusv-Posv P,·.h -Pose Pose -P sep p.·.1-Pwh p," -Psep
~
LOSS IN POROUS MEDIUM LOSS ACROSS COMPLETION " RESTRICTION " SAFETY VALVE " SURFACE CHOKE " IN FLOWLlNE TOTAL LOSS IN TUBING " FLOWLlNE
Fig. 4-1. Possible pressure losses in co-;y/ete system.
l'lQQE 1
2 3 4 5 6
7 8 1A
18
LOCATION SEPARATOR SURFACE CHOKE WELLHEAD SAFETY VALVE RESTRICTION PWF PWFS
PA GAS SALES STOCK TANK
Fig. 4·2. Location al various nades.
.... ..
..
Total Syslem AlJolysis
135
JI. TUBING SIZE SELECTION One of the most important components in lhe production systcm is the tubing string. As much as 80 pcrcent of (ile total pressurc loss in an oil well can occur in moving the fluids from the bottom of Ihe hale to the surfacc. A cammon problcm in well complction dcsign i5 to sclcct a tubing size based on totally irrcJevant criteria, suth as what size tubing is on the pipe rack or what size has beeo instal1ed in the pasto The tubiog size selection should be madc befare a wcIl is drilled, because the tubing sizc dicta tes the casing size which dicta tes the hole sizc. Thi~ i5, of course, not possible on al1 exploratory we1l bccausc of lack of rescrvoir dala, bu! once the first weH has becn drillcd, enough data will be avai!able to plan othcr weJls in the field. Selection can also be made using: a p05sible range of expccted rcservoir characterislies 2nd Ihcn rcfincd as more data bccúme availablc. Tb~rc is an optimum tubing sizc for any wcll system. Tuh:ng loo small will restrict the production rate bccause of ex.cessivc friction lass, while tubing too large will cau~ a well to load up with liquids and dic. A common prar[cm that occurs in completing large capacity wclls is to ir:5ta\l vcry lnrgc tubing to be "safe:- This often rcsults in 3 jecrcascd flowing tife fOf the wells t1S reservoir prcssure declines
Solution: Use Vogel's melhod lo caleulale Ihe innow: qL
qL(m"l -
1-.2 Pwf_ -.8
()2
"..wf
PR
PR 320
1- .2(3445) _.8(3445)2 3482 (3482)2
qL(ma" '" 16810 STBlday To generale Ihe IPR:
q =16810[1_·2Pwf_ 3482
L
.8p~f
]
(3482)2
Inflow Pwr. psig
qL' STBlday
o
3482 3000 2500 2000 1500 1000 500
O
3930 7464 10442 12866 14735 16050 16810
TIle inflow data are ploltcd on Figure 4-3. Ir should be pointed out that the inflo\\' data also íncJude implicilly any cffccts of formation damage or stimulation and per· foralions. For this case rherc is inslImcicnt data to COI1sider Ihcse cffects scparately. To calculate the outnow, assume that the prcpared pressure travcrse curves in the appendix apply to this well. Using the proccdure dcscribcd in Chapter 3, the rollowing data are obtaincd:
PR -!'!.Prc.t = PII! OlltflOll'
q,. STBI
OIl;jlOlV
Pwll
+ !'!.PIII!Jillg :::: Pllf
Example
4-1
Determine the producing capacity of the well described below for nominal tubing sizes of 2-3/8, 27/8 and 3·1/2 inches. Other well data are:
PR = 3482 psig Deplh = 10,000 ft GLR = 400 sel/STB =0.65
'9
Pb=360o psig Pwh = 400 psig
API=35" fw =0.5 .
day
1.995 (2 3/8)
400 600 800 1000
3200 3280 3400 3500
1500
4400
(assumed, since only ane test is available)
2.992 (3 1/2)
3160 3200 3250 3400
3130 3200
2000 2500
3290
3400
The outtlow data are also plotted 011 Figure 4-3. The flow capacilics for the various tubing sizes are read from the intcrsections of the inflow and outnow curves as: Tubíng /.0., in.
Test data: qL = 320 STB/day. Pwr = 3445 psig. FE = 1.0
2.441 (2 718)
1.995 2.441 2.992
Producing Capacíly, STBlday
800 1260 1830
ProdllCfiol1 O/Jlilll;::a1iol/ Using Sodu/ .. llIo(I"Si...
136
2-3/8
2-7/8 3-112 (Pwh
3500
~
4001 3-1'2 (Pwh = 200)
( 3000 -
2500
800 2000 L 0
\
1260
1E:O
/
3350
--+.1-=J"OO,.--!'/~--+'2"0-=C::-:----;;3;C00;;;0;-+'----~40;;;O;;;O,----5~O'00 e . STB/day
Fig. 4-3. Example
4~ 1 SO/Li:
:Jn.
The performance ol' lhi~ wcll is sewrdy rcstrictcd by the OU(nO\~- p~rrürnlJl1Cl" (,~ piping sysh:m. EYCl1 with thl" ~-112 in. t(ibing, ¡he \\'er's producing ('~¡pacÍly 1::; only Jbout 11 pcrccllt of il~ LJ: __ .,,). Ir lhi~ wdl \\cre assigncd :m aIlO\\'abll" fale 01100(1 STBO da)'. lh.:' lL1tJI liquid r~Hl?' 10 obtain this oi! ratc w,"'uld be ~OO(J STBl/day. This cOlllú b~ oblain~d from th:~ wcll wilh (he .~-l "2 in.. tubing by d~Ln"'3sing qlC \\"cllhc.::.J prcssure s.j;gluly. bUI if Ihe water CUI incrcascs. other 5[CPS \\'úuld h3\"e 10 b~ taken to mainlain rhe allowable rat=. This could be accomplished by installing larger tubil)g •.)r placing the well on artificial ¡if.. The ¡arge effect of wel!hcad pressure on [he pressure drop in the lubing is illu5!rated by deCr~~l:5ing P"'J¡ lo 200 psig. Th~ efft:cl is illustr¡:,~cd in Figure -t-J which shows that lhe producing capacit)' wauld be increased from
could be obtnincJ by keeping lhe nade al lhe bottomhll!c nnd ciI!cul¡lIing lite 11Il'ing prcssun:: drop in (\\·0 stcps.
111. FLOWLlNE SIZE EFFECT Tlle l<Jrge cf!cct 01' \\'('llhcl1t1 prcssLlrL' on the' prc%ur~ drop in the tllbing was ilhbtraled in lhe' pr..:-yiUllS cxalllplc. in which a 200 psi dccrcasc in fJlliJ re'sultcd in an incn::asc in producing c3pacity of 1520 STO day. This is caused by the f<Jet lhat at lowcr avcrage prcssure in the tubing the incrt:ascd yoJume of the gas dCLn:~bcs liquid holdup ano, thus, lhe hyJrústatic prcssurc 105$. If 11 \\'el\
1830 lo 3350 STI3L1day 10r
Upper String Pnode
Lower String
Fig. 4-4. Tapered slrings.
Total System Analysis
137
PR = Pb = 2400 psig
2500
=
Flowllne size 2 in. Flowline ¡ength = 3000 ft Iw =0
2000 1500
ie
Innow
Test data: Pwf
~
=2000 psig lO( qo =710 STB/day
So/ulion:
1000
Using test dala, determine qc(max) "-wf
500 00
GLR = 800 sc!/STB Tubing size 2,441 In.(2-718) Tubing deplh = 7000 ft FE =1.0
=
P.ep = 100 psig
Tapered Slring
.PR 500
1000
= 2000 = 0.833 2400 710
1500
qo{max)
= 1-.2(.833)-.8(.833)2
=2556 STBOlday Fig. 4-5. Elfecl of upper slring me.
A. {Pnode
=
P.1) Calculale !he Innow data using Vogel's melhod:
q = 2556[1- .2P.1 is producing ¡nlo a Oowline, the wel1head pressure is equal to the sum of the separator pressure and the pressure drop in the Oowline, assuming there is no wellhead choke. A comlllon cause of low producing capacity in many wells, especially for wells with long nowlines, is Ihe cx.cessive flowline pressure orap. ~bny opcrators have a tendency fa use any size pipe thlil is convcl}ient or, in somc cases, tic t\Vo or more wclls in lo a common, small flowlinc. Ihis can be very detrimenwl, espccially for gas lin wclls, becausc the flowlinc pressurc drop incrcases as the gas rate increases. This effect will be demonstratcd in the section pertaining to artificial lift. The eITect of Oowlíne size will be demonstrated in the foml of example problems in this section. The node sclected can be eithcr node 6 or nade 3, as illustrated in Figure 4-2. As wiII be secn, node 3 is usua!!y more convenient ir tlle Oowline sizc cITcct is to be isoialed from the tubing cffect. The following cxamplc wil1 be solved using both node loc3lions. The cfTcct or sep
2400
o
Inflow Pwf
o
2400 2000 1500
710 1438 1988 2361 2556
1COO 500
O
These resuHs are plolted in Figure 4-6. The outftow is determined from Psep
+ /),Pnowline +
A. B.
The producing capacity as presenlly equipped using Pwr as the node pressure The producing capacity us;ng Pwh as the node pressure for the following conditions: 1. As presently equipped 2. Flowline size increased to 3 in. l.O. 3. Separator pressure aecreased to 50 psig with present equipmenl
jPfubing
= Pwf
When using the traverse curves, the following procedure is used: 1. Far various flow rates, find Pwh using {he pipeline curves (horizontal) and Psep ' 2. For each flow rate and the Pwh found in Step 1, use the wellftow (vertical) curves and ftnd Pwf. Outflow Pwh
Examp/e 4-2: The foHowing data pertain to a flowing well that has no surface choke. Calculate the followlng:
.8 P: " ] (2400)2
900 1200 1500
3808 510 640
Pwf 1450 1720 2000
A plot of the inflow and outOow data on figure 4-6 results in a producing capacity 011175 STBOlday and a value of Pwf = 1700 psig. To analyze the effect of changlng either flowline size or separator pressure, the entjre outflow calculation would have lo be repaated, even though the tubing remains the same. This can be avoided by selecling PWll as the node pressure.
ProdlKtiO¡i Opfillli::.oliuJI Usillg .vuc!a! AJld.>.,is
138
:-
,.¡+-
f-'-
1;+ :,
,,
¡+
hi" j ~ •.
j-d-
,,
,.
":.
outflow
zooo
f-n
,
~
¡J:
·1
,,
e
,
•
11
'H
inflow.
P.... f'
,, ,,.,
psi,;
,"
¡OOo
L' , , 1
, "
rt'
",
:i=l= o
, 11
'1:.t, i -:
,
1--l,
-4
.,.
,WCU.LJj:"_U
,
"
H
"
-
..,
~
,..
" .í-'-'.
. ·-1+
'L
~ ¡
J,
'1_' J+:". :.. j,!
.
, ·1
T:\:
*' 11'-
'-l' "
In j
.
•
-1
l.
_,'
1,
,::
T+~' . 'l • "
•
o
2000
1000
•
t
3000
G::.' STB/dd:f
Fig. 4-6. Example 4-2A solulion.
6. (Pnode
=Pwh) p,¡
,
IIUlo,,' PR - 8pl'<'.\' - ().p¡:. C;ng
Ol107oH' P.;,p
+ 6pj1f11l'fiIJ.
=:
= P,t'lJ
l.
Select various flow rates and c::lculate PI'! using Yogel.
2.
For each now rate andplIfdetermincd in Slcp 1, use the vertical tra\'Crsc curves to fine P,,/r Feom Voge!:
")
[[ L66
2556
p"./¡
10 expedile the inflo", calculation using the travcrse curves, it is convenient to salve Vogel"s equation for P"f and select flow rates. This results from the fact thal Ihe tra\'erse curves are available for speciric flow rates_ The procedure for gencrating lhe inflo\\' dara is:
_ _ P"f - PR
[¡
= 2400 L266 --'-1 2') Se J'" -0.125 ]
_ 1.25 q¡¡ C¡v(nJ;l:\)
_ ') O'5] 0.1-5
J
900 1200 1500
Pwl
Pwh
1880
640 480 240
1677
1451
The ",ellhead pres5ures obtaincd from the horizontal CUf\'CS in Solution A will bl: uscd for plolting lile oUlno\\, for the 2 inch line.
OurjlOH' Outflow, Pwh d
=2,
Psep = 100
900 1200
1500
380 510 640
d
Psep
=3, = 100
140 190 230
d - 2, PSflP
=50
365 500 610
139
Tota! System Analysis
expansiono This creates more frictional pressure drap. This m.y not apply ir the nowline is in a hil\y terrain arca, since the increascd velocity may decrease the pressure drop caused by the hills.
The following producing eapacilies were obtained froro Figure 4-7 for lhe three configurations considcrcd in Solulion B: Ffowline Diameter
Separator Pressure
Capacity
100 50 100
1175 1180 1500
2 2 3
IV. EFFECT OF STIMULATION Tile systems analysis approach can be used to estimatc the improvement in wcll capacity due to fracturing or acidizing. Even though Ihe reservoir capacity may be increased considerabJy by stimulation; in sorne cases the well's actual praducing capacity ¡ncrcase may be SITIal! duc to restrictions in the oulnow. Befare a decision is made on what steps to lake to increase lhe producing
Thcsc results indieate that the effect of reducíng the separalor prcssurc 15 small compared lo {he effecl of incrcasing flowIínc size. This resuIts from the faet that as average pressure in lhe flowline is dccrcased in a constant area pipe, (he fluid musí move fas ter because of its
,, ,
, , 1 , ,, ,,, -
,
,
, ,,
,,
,, ,
, , ,,
,
,,
, 'L '
too
=it±t+t•
~
-1
I
H
d 2, P..,p 100
l'
,, ,
,
I
,
H-' '
' , + .~~
:
,
200
-
-
1+
100
O
l!+ 1i l+1-1-
O
-
,
,
,
,
2.
SO
,
* '"
,, ,
--+ L+, f.J-J-++c, :
,i
1_ 1_
-
_!_+_++-..J
:l+ ,.f -
innow
,
,
d - 3, P...p 100
...j
,
-
1= 1--
-
,,
I
I
,
, ,, 500
1175
1500
t 180
1000
qL. STB/day Flg. 4-7. Example 4-28 so/u/IOn.
.
,, ,
,
I
-
,, , ,
,
,
,
, ,, , ,
P.,
,
,
I
, , ,
d
,,
.~+
I
-,
,
,
.w.' -4+.
,2"- ; ~ -+ , , , , ,, , ,
:
,,
,
II
, , ,
,,
, ,
, !
,,
lSÓO
2000
NO
PrvdllcrioJl Optillli:wtioll Usil1!,! Soda! A'"I(I'sis
capacity, the cxuct caus(' 01' the low p~l)ductivily should be deLcrmincd. This can be iJccomplish.:d ollly through a
Usiog Equalioo 2-46 aod Tesl 1 data:
qo
LUlal systcm i.lnalysis. Largc sums of moncy are oftcn
wasted on worko"crs becíluse lhe wrong component of lhe \\'ell systcm is changl:d. The followíng example illustratcs ¡he cfrcet of stimulating a wel! ulld how the bcnefits of an cffcctivc stirn.ulation can be nullificd by small tubing.
_
fE'\
-qo(m.ax)
PR " 3482 psi9
q,
GLR " 800 scflSTB
fw "O
Oeplh" 10.000 fl
Tubing diameter
~
2.441 in.
Test Data:
---_.
Test Pwh. psig qo' STBlday __ .------------- - -
1 920 2 630 _._-------
1000 2000
So/ution: The present flow efficiency can be calculated fram the t'NO tests jf the bottomhole pressures for each test are determined using vertical curves or correlations. Test
Pwh
2
920 630
Pwr
1000 2000
3240 2990
From Equation 2-50, 2.25 FE " _--'-'L---'-:'---'-_-'-----'-"::-'----'
(2-50)
1000 2
~ '2
1.8(.5)(.0695) -08(.5) (.0690) STB "16238day
preseotly equipped wilh 2-718 io. tubiog. Usiog Ihe fol-
C.
~~' JJ
FE"'l qo{max) ~
lowing data, determine: The flow efficiency of the well at present. The producing capacity al present conditions for 27/8.3-112. aod 4 io. lubiog ir wellhead pressure is maintained al 400 psig. The producing capacity tor the condilions stated in Part B jf the flow efficiency js increased to 1.3 by stimulalion.
I
1.8(FE)( 1- Pwll ¡SR )
-08(FE)' (1-
Examp/e 4·3: Two stabiJized tests were conducted on a weJl that is
A. B.
[
"16238[1.8(FE>(1-~) -08(FE)' (1-
~:
J]
In}lo)l'
Pwr
qo (FE" 1.3)
qo (FE" 0.5)
o
O
3482 3000 2500 2000 1500 1000 500
4839 1961 3863 6970 5631 12195 1!.515 7266 15930 8767 10134 O 11367 These \'alucs are plotted as inflow curw;; on Figure 4-8. Using a \\'cllhe:1d pressure 01' 400 psi~ ;ll1d a GLR = 800, lite following P4values are obtaincd ¡"[,,1m che yerlical curves,
OutjlVH' Pwr. psig
qo 1000 2000 3000 4000 5000 6000 8000
d" 2.441
d" 2.992
2220 2570 3040 3600
2100 2440 2680 3160
d" 3.476
2160 2320 2480 2710 3680
The outflow CUfyes fúr the theee tubing sizes are plottcd on Figure 4-8. The flow capacities for ¡he \'arious tubing sizes and f1o\\' etliciencies are tabulated as follow5.
where
1- 324013482" 0.0695 1-2990/3482" 0.1413 FE " 2.25[(0.0695)(2000) -(O.1413)(1000)] (0.0695¡2(2000) -(0.1413) '(1000) FE" 0.5 Calculale q~~~X) and generale an lPR for the two FE conditions.
Producing Capacity, STBlday
Flow Efficiency
2.441
0.5 2600 1.3 3160 lmprovement 560 rhe irnprovemencs in producing ous tubing sizcs are also tabulated
2.992
3.476
3610 4670 1060
4330 6550 2220 capacity for the vari~ in the pre\'iol\s table.
Notice that lhe improvcmcn~ is mínimal ror Ih..:: 2-7/8 tLIb-
Tola/ Syslem Ana/ysis
14/
3500,--------,----d ::, 2.441
3000 [-=O::::::;::::::::====-~T~----;ré=:cJ = 2.992
d = 3.476
FE
= 1.3
2000 Pwf' psig
FE =
1000
2000
4000
0.5
6000
8000
10000
qo' STB/day' Fig. 4-8. Example 4-3 sofufion.
ing. evcn though the no\\' cfliciency was ¡ncrcased by a rociar of 2.6. Hod this ",elI bcen equipped wilh 2-3/8 lub¡ng, which is not uncomlllon, the improvement would ha ve becn ncgligiblc.
V. SYSTEMS ANALYSIS FOR WELLS WITH RESTRICTIONS The anaJyscs pcrformed previollsly \VeTe bascd on \\"ells thal hado no restrictions in lhe outflow scgment. Many wells will be equipped with surface chokcs, and 11105t offshorc weIls and wclls locatcd in urban areas will be eqnippcd \Vith subsurface safety yalves. A surface choke wil\ usuolIy be sized such lhal now lhrough Ihe choke is crilical, while now Ihrough a SSSV will be subcritica!' In this sectioo, cxamplcs will be presented lhat show the cffcet of the rcstriction and lhe location of lhe restrietion on the producing capaeity of the wel!. AIso, the mas! convenicnt nade Ioeation for caeh analysis will be speci fied.
rate, the downstrearn pressure or prcssurc surges. Thcsc chokcs are usually locatcd al thc wellhcad. but in same cases they may bc localed near the separator. The locatíoll can have a considerable effect 011 the well's producing capacity, espccially if the wel! has a long flowline. The following e:
Examp/e 4-4: The following well is lo be equipped wilh a sunace choke operating in clitieal now. Determine the well's producing capacity and the choke size required for the following conditions: 1. No choke 2. Choke al wellhead 3. Choke al separator
R
A. Surface Chokes .. Most Oowing wclIs and some artificiallift welIs will be equippcd with surfaec chokes to control the producíng
Well Deplh = 7000 ft Tubing Size 1.995 in. PR = 2500 psia fw =0 STB
=
c=0.0023---..,.
day- psiaT'
Flowtine Lenglh = 30 00 ft Flowline Size = 2 in. GLR = 500 scf/STB Psop 120 psig
=
n=0.85
ProtlUclúJll OpfilJli~a{i()1I L'sill.J!, .\'()dal.·lllill~\·sis
143
Solution:
The horizontal curves are uscLl tu 11nd JI"./¡ rol' now ratcs unu PS"P = 120 psig.
Using Pwll as the nade pressure, the infJow expression will be identical fer al! three cases. That ¡s,
PR - tiPrrs -
tJ.Ptubing
= P....h
To calculate tJ.Pres. assume severa! ftow rates and culate Pw( using Fet~ovich's melhod:
Pw{
=[(2500)'
q, . STB/day
Pw(' psia
400 600 800 1000
2188 1973 1716
,-.
r~)r!JQ
cal~
5
3.
Figur~
Far n chokc /ocaled al Ihe separatar. Ihe prcssufc just upslrcam of ¡he choke. which is also ¡he oullel prt:;sure lor lhe l1úwlinc. \\'¡JI be equ<.lllll ¡wice thl' s~pa ralOr prcssllre. The \\"ellhead prcs::.ures for \'afinus no\\" rates C¡lll ¡!len bL' rOllnd U$l11g lhe horizontal
560 430 280 100 on
the \\'cllhL'ad, lhe prLS-
horizontal CUf\'CS, and will be idcllticat lO Ihe fJ"j¡ valllCS fülllld in S¡CP l. Ho",cvcr, lo :lSsure Ih,H th~ chokc is in critical now, lhe wcllhcad pr~S::iure \\'ill be cqual to twice {he Pa valuc. Tha! i:;.
Pwh' psig (vertical curves)
r~o(\cd
¡tI
surc dowllstrL'J,m of lhe chokc, p". is !0und lIsing lhe
0.0023
1397
Thc ínIJ.o\V cunc is l.
-(-q l""r·
Por a chokc in critical now
2.
Varil)US
CllI'''es.
Th~H
IS.
Tlle valuL's obl:1ined Cor the \'
4-9.
chokc in lhe well. lhe ounlún' cxpressioll is
700 ,-----,-------,-----,-600 -
Inflow
,v 500 -
Outilow
Pwh '
Wellhead (
400 psig
(
separa~
300
No Choke
200 100 -
o '-----'--=---:--:'-c:----c-.c...,-------'~~---L-___:-.L-~-__c_'I_,__~cc':I_=_~-! O
100
200
300
400
500
600
qo' STB/day Fig. 4-9. Example 4-4 solulion.
700
800
900
1000
Total Syslem Ana~vs;s
143
OutJlow
OUtJIOlV Pwh' psig
Psep
qo' STB/day
No Choke
Wellhead
Separatar
400 600 BOO
1BO 215 2BO
360 430 560
1000
340
6BO
270 300 350 400
Choke Location
PI
Choke Síze, 64fhs in.
Producing Capacity
275 800 435 595 22 Separator 240 730 34 The chokt sizcs \Vere calcuiated using the Ros coefficimls in Equation 3~ 122, The pressure upstream of the choke, Ptt is read from Figure 4-9, al the innow-outflow intersection. No choke
Wellhead
el = [
O.0045(q~,(GLR)Oó
r 5
For the case of the choke at the wellhead,
J.S
el = [0.0045(595)(500)"; 449.7 = 0,5 in. = 22/64 in. Comparison of ¡he results reveals that locating the choke at the separator rather than at the wcllhcad increase; the prodlleing capaeity by 135 STB/day or about 23 percent. Thcrc are l\vO rcasans for this effect. L
A lower downstrcam pressure is doubled to obtain the chokc upstream prcssure, and
2.
The average prcssurc in the flowline is highcr, resulting in leSos frictional pressure drop.
+ óPfloK'/ine + 6p(/Ubing' obOl't) =
P nQót
Using this analysis, lhe outnow curve will nol change for different SSSV sizes, and only the pressure drop across the SSSV will change in the infiow calcul.tion. A systems analysis plal that would result foc various size SSSVs is shown in figure Figure 4-10. The outf1ow curve for no SSSV is shown also.
VI. EVALUATING COMPLETION EFFECTS Nodal system analysis is a convenient method to use in comparing various well completion schcmes, such as perforating density and total perforated intc'rval. Methods for caI~ulating the pressure drop across the completion weTe prescnted cactiee foc open hale, perforated, and gravcl pack completions. As \Vas discussed earlier, the completion pressure drop, Pltft - Pltf> may be included in the reservo ir pressure drop component, or it may be isolated to compare efTects of various completion methods. If the complettan efTeet is combined with the reservoir effeet, the system analysis would be _identical to the exmnples prcsented carEer, where Puf was selcctcd as the node pressure. A differcnl inflow curve would result for each completian seheme, sueh as number of perforations uscd. This is illustratcd qualitatively in Figure 4-11. If gravel-packed complctions are being considered, ir is advantageous to isolate the pressure drop aeross Lhe grav· el pack. This is necessary so that the critical pressure drop, usually aboul 300 psi, is nol exeeeded. This is accomplíshed by lreating the completion or gravel pack as an ¡ndependent component and plotlíng pressure drop across the gravel pack versus flaw rale. To analyze a gravet~pack completion, the system is
B. Subsurface Safely Valves
Analysis of the effeet of a SSSV in the tubing ean be eonductcd in essentially the same manncr as itlustrated previously. However, lhe SSSV will be operating in subcritical flow, and, therefore, the pressure drop across the vslve must be calculated. Also, ir Nade 4 is chascn, the oulflow will inelude the seclion of tubing aboye lhe SSSV. It is convenient to choose the node pressure as the pressure just downstream of the SSSV, sincc lhe equaliaos foc pressure drop across lhe SSSV dcpcnd on upstream conclítioos of pressure and temperature. The inflo\v and ouino\\" exprc5sions are:
lTlfloW
IÍ! Inllow
P nooe
d, Qulflow
Q-
PR -ÓPrr-s -iJ.p(fllhillg beloll')-6[Jsssv == Pnod~
Fig. 4-10. Subsurfaee safeiy va/ve errec/.
q For No SSSV
llmdllctiofl Optimiza/io/l Usillg Sodal AII(I~l'sis
IN
t
q-~
Fig. 4-11. Elfect of perforating density.
Fig. 4-13. Gravel-pack analysis, producing capacity. divid~d al
tbe weltborc. lhe nade prcssure for {he inflo\\" is 1\,1-;" ,,"hile lhe node prcssurc foc lhe QUIllow is P"f That ¡s.
I¡¡j/oll' Pn
--~ró:::;: JJuft
Olllj/O\l" P.rt'1' + Ój> jlvllh,-.,' + !1.p wbillg ~ P lIf
Both P".is and Pillare d~tamincd foc \',1riou~ tlow ra[~s ;llld plotl¡,;od \"ersus no", r:u~" as illuSlrated in Figure 4-11. Tile inlcrsection of these curves gi\'cs rhe producing capacit)' that would rcsulr ir no prcssurc drap across (he gravel pack occurrcd. rhe rClluircd Pllls may be calculated using equatíons for oil al' gas rescf'·oirs. The pressure drop available for overcoming the gravel pack's resistance lo flo\\" for [ates lower Ihan the maximum system mle can be [('3d fmm Figure 4-12. These are designaled as !J.p¡. Values uf D.PI versuS q are plOllCd as illustrated in Figure 4-13.
Thc prcssure drop occurring across (he gra"d p<'lck for various no\\' rates can be calculatcd as a rUllc{ioll 01' [he l1umbcr of perfOralioll$. perforation size, pcrforation knglh, and grn\'cl penneabili{y, using Equation::i 2-111 or 2-113. ThcsC' pressurc drops, dcsignatcd as !J.p'!. ar.:: "Iso plotted Oll Figure 4-13. The intcrscction ol' lhe tlpl aud /1P2 curves gi"cs lhe producing capacity and pressurc dl'Op across tht: grave" pack fot" vario LIS L'omplction schemcs. This pennits detenninatioll of the maXílllllil"l producing rate allowcd [01' any I1lllnbcr 01' pcrforations l(' kccp D.p bt:lu\\" the crilical valuc. Example 4-5: Adrill slem test was conducted on an oil wellto be campleled in an uncansolidated formatian. lt was determined lhallhe well musl be completed by gravel pack¡ng. Using the following data, determine lhe producing capacity far perforaling densities af 4, 8 and 12 shots per fool. Also determine lhe maxímum producing rate fer each perforating density if the maximum pressure drop acrass {he gravel pack is 300 psi. Assume Ihat there is no compacted zone around Ule perforatians. From DST and PVT Ana/ysis:
k o = 100 md p R = 3200 psig S'=O fw =0 ¡lo = 0.803 cp } Po = 2200 psig Bo = 1.248 bblfSTB assume constant Po = 451bmlft3 GOR=400scf/STB TR =180°F API=35° Yg =0.65
I
'w1
'w1,
Complefion Data: = 6 in. W h"30ft Oeplh " 7000 ft Tubing I.D. =: 3.958 in. Perforation diameter = 0.5 in. f
Fig. 4-12. Gravel-pack anaJysis, system pressure drop.
•
re =750ft Sereen diameler = 4.5 in. Pwh =: 200 ps]g Gravel permeabillty =: 45 darcies Casing l.D. = 8.921 in.
e'. Total System Ana/ysis
145
Plotting both P.. .¡, and pwfversus qo on Figure 4-14 indicales a producing capacity of 4800 STB/day for no perfo-
Solution:
J
ration pressure drop. Read ó,p¡ = PlIft - PUf ror various values of q(l' This is
~ 11 B [[.472r.) In - - +$ ,] r
the pressure drop available to oyercome the perforation pressure drop al these flo\V rates. These values may be
o o
w
J
~
0.00708(100)(30)
ohtained by subtracting the requircd outtlow pressure from the required inflow pressurc at the same flo\\' rates,
(803)(1.248{ln(.472~50)}0]
or read from Figure 4-14. qo 1550 1000 2000 1180 3000 770 4000 390 4800 O
STB
~3.23--
D- psi
qb
~J(PR -pb)~
3.23(3200-2200)
STS
~3230-
D
q
Jpb .21'." .81';",] + - [ 1-~~---
~q
o
Pb
1.8
b
~
(2·38)
P;
+ Jpb ~ 3230 + 3.23(2200)
Qo(ml1x}
qb
q,(m,,¡ ~
3230+3948 ~ 7178
1.8
1.8
Plol lhis dala as f..p versus q, on Figure 4-15.
Use Equation 2-111 to dclcnninc values of IJ.P?=PMjj Pw( for
lhe gravel paek.
STS
ÓP2
= Pl\fs -
0
AG
Solvíng Equation 2-38 for Pwfs:
Pwfs
~ PI>' [[12656- 2.25(q, _Qb)]0.5 _ 125] J .
=
[[
1.2656
2 25( - 3230) . q, 3.23(2200)
.... fs
JO.5 -.125 ]
A
""G
~ ~ G
L
r;
=1.47XIO" k 0.55 G
1.47xlO' (45000)o.55
rp = 0.25 in.
~~.06xlO' fl- I
~
0.0208 fl
8.921 2 =1.54in.=0.128fl
L=¡;,,-rc.tg =6---
¡'~17ow
2890 2581 2271 1950 1572 1096
~v
N 2 rr4
~ p- _ q, ~ 3200-..'7..· R J 3.23
1000 2000 3000 4000 5000 6000
282.4~,B
1~-I12)
9.20 x 10-" ~(;B.,' P" L
This equation ;5 valid fer Pwfs < Pb' For Pwfs ~ Pb' use
p
= ~qo + BGq;
KGN
p,
p.,,~2200
Pllj
'~r'-l"P::'-";;)'-------------.., lnllow (P,.fs)
Oulllow
_!!'_"'.!t_
The valuc::; ofp,,!for the cutno,," are rcad from the vertical traverse curves roc 4-1/2 tubing, usingpwJr = 200 psig.
Outjlow
qo 1000 2000 3000 4000 5000 6000
Pwr
1340 1400 1500 1560 1650 1750
,~
__-- _._
_------!~
l~OOO~-;¡,"":;;-."""':;;-"""MC>~'"~)5.:U Producinr;¡
Fig. 4-14. Example 4-5 solulion.
R~l~
'000
,~ 5000 ~~
fSTB/dJ
W('(l
PrvdUCliol1 Optimizo/ioll Usil/!!, Nudol .·IJ/(I~l'sis
146
analyzcd in Chaplcr 5. Thc production enginccf musl somclimes dcsign compiclion configurations ar analyze pl:rformancc of yarious typcs of injc(rioll wdls. Thcse wells may be us~d t0r injl:cting watL:f or soml: olhl:(" tluid fOf enhanccd fCCO\"ay prújccts ar lhey could bc gas injccrion wells opcraling in gas storage rcscrvoirs. Nodal analysis may be p(:rformcd 011 injcction wclls by sekcting the nade al botwm-hole sudl lhat lhe inflo\\' to the nude will indude the injection pump Of compressor and rhe piping systcm, whilc (he outílaw will consist of the perforations aod reservoir. For exampk, if gas from a compressor is being inject~d ¡nto a \\'c 11 , (he iollow and outilow expressions would be:
,
.1" (psi) '000
."
~
-<1
."
SPF
-- -- --
'00
r-:
.
'" ,,,
a SPF --
---- --
'00
12SPF
100
--------------
, -
~-~:.: . --
c~~-
'000
l~O
2~-'J
~ --
=:=- -- --
--~.
-- ==- =-:=. , '''''' '''' ¡ro,;:
,~
,"-"
.~
,~
0000
Producing Rale (STB/dj
Injlu\\'
Flg. 4-15. Example 4-5 so/ullOn.
Ou(flow ,le
282.4(.803)(1.248)(.128) = (45000),\'(.0208)'
1.861
Px +:lp"".I':::: Puf
N
This type ol' analysis could be useu to determine lhe effects 00 injecI¡on r:.He of variolls cOlllpressof pressures, tlowlinc sizes Of !lJbing sizes. Thc crfeet oftubing size on injcction rate will be illustrated by an examplc. For (his e.xample, ir is assumcd rhar wcllhead pr~$$ur~ is COllstan( so lhat the ¡nllo\\" will include only th~ !)fCSSllr(: drop in (J1t:: tubiog. Thal ¡s.
B _ 9.20XI0-"(4.06xI0 4 )(1248) \45)(.128) 11"(.0208)'
G -
0.179 N? j,p, = 1.861 '1,: +0.179('1")' . " N .lp2' psi
'10 2000 3000 4000 5000
N - 120 (4SPF)
N = 240 (8SPF)
N - 360 (12SPF)
30 50 80 120
15 30 43 60
80 158 260 390
Pd, + /<.p" - óp J = P"i Equation 3-109 may be used to calculare p,,(far various rates. The outllow performance may be calci.datt:d using rhe backpressure equatioll for gas wells. That is,
Plolting both ÓPI and Ó.P2 versus qo on Figure 4-15 foc the three perforating densities indicates Ihe following
producing capacities and corresponding pressure drops: SPF
'lo
dp
'lo lar dp = 300
4 8 12
4200 4600 4700
260 100 40
4500
Out/lo\<'
PR + ó.¡Jr¡:s = Puf where qinj :::: 2
p"J
These resulls indicale lhal lhe 300 psi limit on óp would not be exceeded i f aH the data are correet. However, if fewer than foue shots per [001 are open, the
2 - PR -2)" e( Phi -2
q
= PR + (e
II"
J
Example 4-6: Using the following data, determine the rate al which gas can be injected into Ihis well for 2-318 in., 2-7/8 in.
and 3 112 in. tubing.
300 psi could be exceeded. VII. NODAL ANALYSIS OF INJECTION WELLS
AII lhe previous examples in lhis chapter have dealt wilh flowing produclion wells. Artificiallift wells will be
•
PR - 2000 psia
ro = 0.7
T,., = 150°f
E
=0.0018 in.
Injeclion Pwh - 4000 psi a = 150°f Well deplh, H =10000 ft T wh
Total System Analysis
147
•
This procedure was followed for the v"arious injection
From a previous injection test:
e = 2 x 10.
5
MMscfd/psia''', n
rales and tubing sizes to produce lhe lollowing lable 01
= 0.86
inflow pressures and rates:
Solution:
Inflow
The infiow performance can be calculated from:
p;" = p;"
EXP(S)
f H(EXP(S)-1) f Z q~J
25y,
Sd'
where
Inflow
Injection 2-318 /ubing
o
5050 4934 4580 3945 2910 1200 O O O
S= 0.0375y,H/(TZ) E 21.25 f= 1.14-210g - + - d N~:
[
[
4 8 12 16 20 24 28 32
4
J]
N Re = 20011Yg q¡n/v. g d
The soluJ.ion for Pwffor any injection rale will be iterative sin c e Z depends on the average of Pwf and pwh. The iterative procedure wiH be iIIustrated for one tubing size and one rateo lf a computer is available, the tubing can be divided into short increments of length, and the 501ution wiH be more accurale. The procedure for hand calculations is: 1. Assume a value for pwf.
15 = (Pwh + pwf)12.
Calculate Calculate
4.
Calculate Pwr and compare with the assumed value. If not close. use the calculated Pwras nexl estimate
Pwl =
5050 5010 4890 4685 4390 3985 3455 2735
5050 5035 4995 4925 4830 4700 4540 4350 4120
[p/ + (q/C)"O
r'
Pwl = [(2000)' + (q/2 x 1O") '.1628
al 15, f
r'
Outflow Injeclion Rate, MMscfd
o 4 8 12 16 20 24 28 32
The.procedure will be iHustrated by cakulating Ihe bot-
tomhole pressure lor the 2-318 in. (1.995 \.0.) tubing for an injection rate of 4 MMscfd. For this rale:
20011(0.7)(4)
28086
-~,
1.995~,
[ [
.0018 2125
f= 1.14-210g - - + - 1.995 N~:
. 0.0375(0.7)(10000) S= (150+460)Z
3-1/2 /ubing
The re5ervoir or outflow performance is calculated from:
and go lo Slep 2.
NRe =
2-7/8 lubing
GlltflOW
2. 3.
Z and Jig
Pwr. psia
Rate, MMscfd
J~
"
0.4303 Z
labulaled in the lollowing lable:
P;" =(4000)'EXP(5)
Tubing size, inches
25(0.7)(150 + 460)(1 OOOO)(EXP( 5) -1) f Z(4) , 5(1.995)'
p;" =(4000)'EXP(5) 5.405x10'(EXP(5)-1)f Z 5 Assumed
Cafculaled
p
Z
l'
N RiJ
4000 4991 4930 4934
4000 4496 4465 4467
0.879 0.921 0.918 0.918
0.025 0.027 0.027 0.027
1.1x10G
1.0 x 10' 1.0x106 1.0 x 10 6
S
JJ.019 0.019 0.019 0.019
2000 2336 2695 3039 3363 3671 3964 4245 4514
The intersecHan5 of the various lnflow curves w;lh lhe outOow curve in Figure 4-16 represent the injection rates possible tor the 3 tubing sizes. The results are
=~~
Pwf
Pwf' psia
0.489 0.467 0.469 0.469
PwI
4991 4930 4934 4934
2-318 2-718 3-112
Inj.c/ion Rafe, MMscfd
14.6 21.5 29.0
This well could al50 be, analyzed for other wellhead pressures. In gas storage operalíons, the sta tic reservoir pressure will ¡ncrease as gas is ínjecfed, and Ihis would cause an upward shifl in the outflow curve in Figure 4-16. This would result in a decreasing injection rate with time, as the inlersection of the innow and outflow curves would shifl to the left. The change in ¡njectíon rate with time could be determined by using a procedure similar lo thal discussed in Sections VIII and IX in this chapter.
NODAL ANALYSIS GAS INJECTION WELL
6000
5000
~-~-..-... ~ ... :: ••~~.~.~~~~~~~::.:...:.:.--~~~~~~;:.---..
:-~
--13••__
Pwf.
; .- >,.~,,::..
:
~DOO
<....
3000
psig
.-
2000
I j .. :
;
O
8
;
"""'0.
:
~
,-----_--,
..'.
. \
~.~
"a.
I
.
...l,
'
. :
<;>..,,<.~
.
'*
2-3/8
.Q.
2-7/8
I
. ••••••
. . . . . . . . . . .! . . . . .
"'r':
o-I-_ _-+-_ _---+
•
,...¡ : I
I : 1000
.
3-1/2 L....._OU_T_FL_O._'tI....J
I
.............
: I
I
I---_.l.--l--_ _--+--ll_ _~--+_'---_j 12 16 20 2~ 18 32 Injeclion Rate. MMscfd
F,g. 4-16 Gas ¡nje:ojon rale.
VIII. EFFECT OF DEPLETION .-\5 Ihe prcssurc in a rcs\.?f\'oir declines from dcp-Iclioll. bL1lh tlle innow anJ OlHlll)\\' condi¡jons. can change lile ch:1figcs occurring in Ihe n:scrvoir inflow capacily \\'cre discusscd in Chapl~r 2, and Illcthods for prcparing IPRs fúr the future were prcscntl'd. 11 is vcry Iikely that thl1 outflo\\' conditions will niso changc with dcplclion ar lime, cspccially in rhe case of
naHlrally fiowing \,,"¿lIs. Oltee a \\:'cll is ptaccd
Example 4-7: The following data pertaining to a welJ producjng from a reservojr with a weak water drive were obtained from a
material balance calculation and a PVT analysis. The reservo!r pressure at the present time is 225D psig and from a currenl test qo(max) ::;; 1257 STB/day. Using Standing's O1ethod for generating future IPRs. determine the oil producing capacity af (he weJl al the vari~ ous reservoir pressures given. Plol the producing capacity versus reservo ir pressure.
00 artif¡~
cial lin:, the ourllow condirions can be he Id fairl)' con~ SlJnt. The princip,,-t parametcrs rhat will change with dcpl~tion are gas/oil or gas' ¡iquid ratio and water cut. Thc eJfects that these parameters ha ve on rhe pressure drop in
lhe lubing were discussed in Chapler 3. The prodllCing gas/oil ratio will ¡nerease in any reservoir in which lhc pressure declines below bubblepoint pressure, and the water cut will inerease Wilh lime oc deplction if a water drive is active or ¡fwater is bcing injeclcd in lhe reservoir for pressure maintenanee purposes. Beforc any developmen! planning oc economic calculatiaos can be performed. il is nccessary to be ahle lo pn:dicr lhe producing rate of a weU or field as a function of ., time. The effcet of changing rescrvoir eonditions on the producing capacity of a well is eonsidt:rcd in this scclion. Relating lhis changing performance to lime wilI be dis· cusscd subsequenlly_
API = 35" Deplh = 5000 h qo(max)p
= 1257 STB/day
80 psig Tubin9 size = 2-3/8 in. PRP = 2250 psig
Pw!l ::;;
Yg = 0.7 ------'"
PR
J.101 cp
B o . bbllSTB
k ro
GOR. scflSTB
fw
2250 1800 1500 1000
3.11 3.59 3.70 3.80
1.173 1.150 1.130 1.110
0.815 0.685 0.580 0.430
400 600 800 1000
O O O 0.5
-------
Solution: To generate ¡he future IPR data, the followjng ships will be used to predicl qL{max)F:
relation~
Total Syslem Analysis
149
(2-72) 3000
where 2500
f(i5R) = kro/~oBo
2000 PwI.
p~1g
1500
2250 1800 1500 1000
0.223 0.166 0.139 0.103
501.8 298.8 208.5 103.0
1257 749 522 258
Vogel's equalion is now used lo generale the IPR data fer both the present and future times.
_
qLF - qL(max)F
[0.2 Pwt
0.8 P;" ]
(2-73)
1--_---~
PRF
qL' STBlday
P R=1000
PR - 2250
2250 2000 1800 1600 1500
1200 1000 800 600 400 200
O 239 412 570 642 837 947 1040 1118 1180 1227 1257
O 142 208 383 481 564 632 686 725 749
PR= 2250
950 1040 1120
The intersections of the inflaw and outflaw curves for the same conditians af PR give the produclng capacily for \hose concitions. These are
O
171 267 348 413 464 501 522
O
85 153 204 239 258
OutJlOH'
100 200 300 400 500 700 800 1000 1200
PB=1800
730 810 840
2000
Fig. 4-17. Example 4-7 sofufion.
2250 1800 1500 1000
O The node pressure for the analysis ¡s selected as Pwf. Thererore, the data in the previous t3ble represen! the infiow for the weH. These are plolted on Figure 4-17 as Pwf versus qL· The vertical traverse curves will be used to generate the outflow data for this example. A different outflow curve will'have to be prepared for each ¡nflow curve because the gas/liquid ratios and water culs are changing. It is assumed that lubing sjze and wellhead pressure remain constant. The outfloW' data are tabulated as follows and ploned on Figure 4-17.
q, ,S7B1day
1600 1SOC
PRF
Inflo1\' Pwr
1400
p-B=1500
510 640 7.10
P-R= 1000
600 660 730
940 590 410 140
940 590 410 70
A plol af the5-e results is presented in Figure 4-18. A similar anal}'s:s can be performed fm gas wells using the procedures outlined in Chapter 2 lo generate future IPRs. The out1aw conditions are nol as likely to change for a gas well unless ;t is producing from a water-drive reservoir, in which case the liquid loading may increase as dedines. lf this occurs, the minimum gas rate necessary to '<eep {he tubing unloaded will eventuaHy be reached. and the tubing s;ze may have to be reduced to k~p the well flowing. This siluation is ilIustrated qualita'i5vely in Figure 4~ 19. The minimum gas rate that will keep the well unloaded fer a particular tub-
PR
,= TOTAlllQ. RATIO
01l RATE
--
Proo"cing Capacíly. STBlday
=
""
"" "" "" ""
"" "" ,'" """
/ /
~
=
,,'" ,,'" "'" ,,'" ,..., ,,'" ""
STATIC RESERvorA PAESSUAE. pslg
Flg. 4-18. Exampoe 4-7 so/vlron..
2~OO
.!!!J; .•' -
•
/lmduCfio/l Optimiza/ion UsiJlg Nod(J! AII().'~~·sis
150
Th~ following pracedllrc may be used to relate rL'$Cfva ir and well perfonmmcc lo time:
Pm PA2
l.
Using dala frolll a material balance ur otiler fcscn'uit model, dctcnninc ¡iR' GOR,j;,., cte., vcr::;lIS cumulati ve productioll, Nv Typical bchavior oflhcsc par.uneters is illustralcd in Figufe 4-20.
2.
Construct inflow-outt1ow curves, similar to Figure 4-21 ror each welL This Slcp was iIluslraled in Example 4-7.
3.
Construct a graph of producing capacity QL = 'EqL versus PR, as illustrated in Figure 4-22 ami Example 4-7.
4.
Select a small incremcnt al' IHoduction, I1.NI" :.ll1d determine the average value 01' SI
5.
Using the \'aluc of PR¡;\\g) delL'fmincd in Skp 4. enter lhc graph of QL versus PR lInct uetermin= ¡he average producing c3pacity, QL¡;\lgl at this valu.-= ol'
PA3 ?wl
P R4
d,
Fig. 4-19. Future gas well performance.
ing size and wellhead pressure can also be estimated using Equation 3-112.
IX. RELATlNG PERFORMANCE TO TIME Methods for calculating lhe producing capacity of a wdl as n function DI' SI
..
PH(
6.
Calculate
Ih~
clln1t¡Jaliv~
lime increment rcquircJ to produ(;:, the produc(ion inCrCIllL'llL Thal is, 6.1 = J...\'¡J
QL(;I\'gj'
7
Rcpeat SlCpS 4 through 6 and plot PR(:I\'~I' and s." = I6.Np vcrsus f = I.ó.t, to obtain a graph such as r:gure 4-23. Tlle time at which the producing carJ(ily reaches some minimum value can thcl1 be li-=tt:fmined.
Example 4·8: The well described in Example 4-7 is producing fro:-rl an aO-acre drainage area. Using lhe following cumuiative production versus pressure data, determine whe:l the oil-producing capacity 01 the well will decline lo 150 . STBlday.
GOR
Fig. 4-20. Reservoir performance.
Total System Analysis
15/
PRl PR2
PR(avg)
I
PRJ
Np
PR{avg) QL{avg)
Pwf
O~avg)
Np PR4
------,.--
QL(min) -
t_
Fig. 4-21. Determining producing capacity.
Fig. 4-23. Performance versus time.
Np,STB
PR,psig
The data are plolted on Figure 4-25. Entering the graph al a value 01 0 0 = 150 STB/day, a time 01 930 days Is obtained. Al that time the cumulalive oil produced is approximate'y 300,000 STS and the reservoir pressure Is 1030 psig.
o
2250 1800 1500 1000
80,000 150,000 300,000
Solutíon: A plol 01 PR versus N p Is shown in Figure 4-24. The following table was constructed using the procedure outlined previously. üil-producing capacity, Qo(avg), was obtained from Figure 4-18 tar the values of PR(avg) cor responding to production increments of 50,000 ST8. v
MVpx10-3
50 50 50 50 50 50 50
Npx1Q-3
50 100 150 200 250 300 .350
P R(avg)
Q o{avg)
2100 1950 1630 1430 1260 1100 930
ót,days
t,days
66 74 100 132 192 333 1000
66 140 240 372 564 897 1897
760 680 500 380 260 150 50
X. ANALYZING MULTIWELL SYSTEMS The conccpts discussed fGr applying total system or nodal analysis to single \....ells Ciln also be applied to the analysis ofmultiwell systems, including cntire fields. The procedurc will b~ illuslratcd qualilatively b;" rercrring to the simple systetn shown in Figure -1-26. In ihis case, <1 ehange made in any component in the systcm wauld affect the producing capacity oflhe total systcm. Same of Ihe changes that couId be considcrcd are: 1.
Working
2.
Placing
3.
Adding new wclls to the system.
4.
Shutting in 50mc of the existing wells.
O\"e'T
som~
individual \,,·clls. wcIls on artificial lift.
::::~
°l(avg)
250+
-----~------
I
I
2000
P , R
p~19
A
1500
I I
1000
I
.I
500
oO~'S",'-'l-i;;OO'--"15"O--""'O-""'SO'--300""-"""'O-"OO""""'so..--d soo N" lII0- 3.5TB
Fig. 4-22. Fie/d producing capacity.
Fig. 4-24. Examp/e 4-8 solution.
Prodl/ctiu¡; OptilllizlIliuJl
U.'m~
Nodill.·l/l" ...."'..
~ooo
:::r\'
3500
600
500 Q~
~
o
)000
\
\
ST8/llily
o,
~IO-3.STa400
000 200 100
1500
'000
- - - - - - - - ,, I
SOO
l/:,"" ;':;:0,
OO"'----C,CC~:c-:"00';;--c6~0;;-0--;60~O:-'é,,;OO":-,",200;0,--;;""o~
"
TIme. days
Fig. 4·25. Example 014·8 so/ulion. Fig. 4·27. II1f1ow lo Painl A
5.
Chí\l\gCS in prl1Jucing cilaruclcrisli..:s wilh lime.
Ú.
Effec! of surface li!le sizcs.
7.
Installation ofpumps
8.
Effcct 01' lhe tinal outlct prcssure. PI)'
01'
sckctl'd at poi m C. Il1tenncdiutc nodes mus! be crcd
compressors.
The localion 01' lh.:- nade for lhe final analysis mUSI be
selcclcd al a point such lhat thcrc is no rllnhcr COl1Unillgling oC no\\' sIrCalll5 dOWllSlream 01' thl.' nade. Far {he systcm 5h\.1\\'11 in Figure 4-::~6. this \Vould be al eithcr poilH e al' !,1..1inr D. Intcrmedi3.(c nades must be s..:lcl'lcd al any point whcrl: no,," $ifl..'¡JI1\S COli1l11illgk upslrc
al
Tile
illnOW to
poim.-l will be calclllalcd from:
This exprcssion would be cvaluatcd f0r c¡¡eh wdl ing into POilH :1 for a range of producing rates. would rcslIlt in a plol such as illustralcJ in Figun,::
has oecurrcd.
e
l--------j o
,
Fig. 4-26. Multiwel/ syslem.
fc~'J
Thi~ ~-~
A similar plOI fOl" (he pr.:::'surc behavior;\t poinl B l:'¡1Il h: constructed by cOllsid¿oring wclb 4 and 5. This is illuSILHcd in Figure 4-::!8. TIle: gaslliquid ralics and \\'¡¡tcr frJ':tions us~d in calculating ¡hé: prcssun:: drops in lhe pir¡n~ system to {his point \\'ould be those corr~spond¡ng to Ihe individual wells, sincc no commingling of weH strc31l15
To illustrate lhe pro~cdurc, considaJEion wilI be gin~n to ci[her changing the prcssurc ,\t poin¡ D Ol" looping lhe surfacc line bctween points and D. The nade ",ill be
,
con~iJ
points .-1 and B.
"
Fig. 4·28. /nflow lo Painl B.
'.
• Total Syslem Analysis
153
o,
Fig. 4-30. Syslem capacily.
Fig. 4-29. Inifow lo Poinl C.
Moving downstrcam to lhe ncxt point at which
COI1l-
mingling occurs, poinl C. {he inflo"" exprcssiolls roc the flows comíng from points A and B are: Pe = p.., - !'JPAC and Pe = PR - ¿jPse
This will result in n rclatiollship betwccn prcssure at poin! e and the inflow rate into poin! e as illustrated in Figure 4-29. Thc calculation of the pressurc drops bctwccn points A "ud e, ó.P..¡c. and betwecn points B and C, ¡"PBC, is complicaled by the fael that lhe GLR and water fractions are functions of rate \f Ihe individu~1 wells have diffcrcnt valucs of these pafamcters. In thls case, lhe carree! GLR and.f.t. ror each cOl1lmingled Tate are calculated usillg:
GLR AC and
Similar cxprcssiolls are used to determine thcse values
roc calculnting E:.¡Jnc.
The expression for the outflow from point Pe
= PD
e is
+ L!.pco
Calculation of j,PCD for various rates would again require dctcnnining the corre<'t GLR and .{". corresponding to cach ºc = QA + Qo· .-\ change in cilher Po or the line sizc bctwe~n roints e 3nd D would rcsult in difftrcnt outflow curves and thus ditferent syslem capacities, as shown in Figure ..$-30. To determine the effcct of thesc changcs on indi\'idual well perfonl1ance, the pressurc at point e corresponding to an inlcrseclion 011 Figure 4-30 can be uscd to moye upstream to points A and B and thus determine the individual wen rates. The procedure outlined prcviously will also apply jf sorne of the wells are under choke control or on artificial lin. If a wel! is flowing through a choke in crilical fiow, the well's mte will be constanl unless lhe pressure downstrcam of lhe choke is increascd lo lhe poinl al which critieal flow no longer oecurs. The producing rate for a \Vell 011 a suckcr rod pump may be indepcndcnt ofthe pressure at the eommingling point, but ¡ts rate will arreet the pressure at the commingling point and thus the producing capacity of other wetls feeding into the same point. The producing capacity of wells on gas lift or elcctrical submersible pumps would be aO-ccted by lhe well-head presSUTe or the pressure at the cornrningling point. Analysis of wells on artificiallift will be discussed in Chapter 5.
I
I
Artificial Lift Design
5
1. INTRODUCTION In Chaptcr 4 it was shown that as the pressure in a reservoir declines fram deplction the prod'..1cing capacity ofthe wells will decline. The decline is c311sed by both a
decrease in the reservoir's ability
lO
supply fluid to the
we11borc, and, in SQn1C cases,
once the well has beco stimulaled te reduce reser\'oir pressure dTap to a minimum, is by pressure maintenance or secondary recovcry. litis will c\'entually be initiated in most oil rcscn'oirs, but methods are available to reduce lhe flowing wellbore pressure by artificial means, that ¡s, lo modify the outflow perfornlance of lhe wcll. AH the methods presented carlier fm calculating reservoir performance, or gencrating IPRs, apply equally well lo either Oo\\'ing or artificial !ift wclls. Thc rcservoir inflow perfonnance dcpends on p __! and js completely independent of wh3t methods are employed to obtain a parti-:::ular value of P"f. Therefore, no new procedures are required for reservoir performance in analyzing artificial lifl wells. Analysis of the outflow, however~ is changed considerab1\" from what \Vas presented earlier for sorne types of arti'ficial lifl methods. For other types, the outflow analysis \\'ill change vcry little, only requiring addition of a preS5.urc increasc term in the outflo\V exprcssion. The analysis is frequently expedited by choosing the node location as the point at which the artificial lift encrgy is introduced into the system. This point is usuaIly very clo$-c to the rcservoir, but for certain types of artificial lift :malysis, it may be sorne distañce aboye the reservo ir.
The four most commonly used artificial Jif\ methods are sucker rod or beam pumping, gas lift, submersible pumping, and hydraulic pumping. For a thorough diseussion of each type of system, its frequency of applieation and relative ad\·antages and disadyantages, reference should be made to Brown. 1 Descriptions of the rnethods discussed in this chapter will be given 3S the analysis }.1rocedures are presented.
11. CONTINUOUS FLOW GAS L1FT The operation ofa continuous gas lift well is very similar to that of a naturally flowing well. Gas is continuousIy injected into the tubing through a gas lift valve -al a fixed dcpth and (he inereased gas/liquid ratio from lhe valve lo the surface decreases the hydrostatic pressure gradient in the tubing) thus decreasing Pllf' The only difrerence between Ihis type of operation and a flowing well is that the gas-liquid ratio changes al some point in Ihe tubing for the gas Ji fl well. The depth at whieh the operating gas lifl valve can be loeated depends on the gas ~njection pressure available. rhe more pressure available the deeper the injeetion point can be. Also, as the deplh of inje~tion is increased, less iojeetion gas is required, to aehieve the same bottomhole pressure: A simplified schematic and pressurc traverse for a gas lift wen is shown in Figure 5·1. Other valyes are required aboye the working valve in order to un load the wclt, and the design and Iocation ofthese val ves will be discussed later. rhe design of a continuous flow gas fift system consists ofessenlially twa parts: (1) detennination ofthe perfomlancc"of the well once it is unloadf'd and in stabilizcd operation) and (2) spacing and pressure setting of Ihe upper gas lift val ves used in unloading the well.
155
/56
Produc¡iOlI O/)/il1li:::aliol/ LrsiJlg Nodd .·JJlu/ysis
flljlolV Pwh
PreSSU(e
,
OlltflOlV
1\
- --- -----~
PIt-lt
'" o•
-1---- -------
T
Fig.
5~ 1.
+ t1p(tubing aboye valve)
~
PI'
1i
Gas lift well schemalic.
Dctcrminatiol1 of the well's stabilized performance \\'il! discusscd first. In figure 5~J, there art cssentialiy two variables that can be controllcd by the dcsigner rol' a givcn tubing size and \\'ellhead pressure. These are the deplh at which the gas is' injccltd and Ihe \"olume of gas ¡hat is injected. Thcre can bt conslraints 011 these valucs thal must be takcll iuto accounL FuI' exampk, lhe amount 01' surface gas injeclion prcs~ sure control5 the depth lo injcction. As was il!ustrated in Figure 5~ l. Ihe deeper lhe injection deplh, the higher the pressure in lhe tubing al lhe point of injcction. rhe prcs~ sure in the annuJus al lhe injeclion point mUSl be bctween 50 aud 150 psi greater than lhe pressure in the tubing to be able to injeef the gas. Therefore, to iojecl at a decper point in lhe well, more injection gas pressure is required. As will be scen subscquently, there is an optimull1 injection gas yolume for a weH [hat wil! result in a maximum ¡iquid production rateo If this va1ume 01' gas is not available, the- . .vell will produce at a lower rateo If several gas lití wells in a field are utilízing a limited volume of injeetion gas, nodal analysis can be used to determine [he optimum voJume of gas 'to allocate to the various wclls. b~
A_ Well Performance
A plOl of PI' versus qL would yield th~ producing eapac~ ity al the intersectioll 01' the inflow and anUlow curves. A changc in injccted GLR would nol afreet the inflow curve. If the cffeet 01' d~pth of injcction were bcing analyz~d. it would be more cOllvcnient to selcct Pllj as the nade prcssurc, in whidl case only Ihe oUItlow curve would change with injcction dcpth c1wnge. Ihis is somelimes used lO d~lcnl1in~ which valve is the \\"lwking vn[vc in an opcnlling gas liú \\'ell. Ir a gas lin \\"el! has a nowlinc of considerable \englh. the \\'cllhead prcssurc \ViII not be constant, but wi\l incn::asc as the gas injcclioll rate is incrcased. This rcsuhs from lhe increJscd fricti~~lil loss in the llüwline. Therefore, an excessive gas injcction rate can actually cause an increa5c in pujtlnd thus decr~
[1/j/Ol1'
PR -ó.PI"t'~
=Pkf
Olltflol1'
P..p + !1PjlQ,,"IiM + !1p (lubing above ,·alve) + !1p (tubing below valve) = p,,¡
using system nodal analysis in the same manner as was diseussed in Chapter 4 for a flowing well. Any eonvenient node may be selected dependil1g on which para meter
Wirh Pllfas the node pressure, lhe int10w will be inde~ pendent of injected GLR, but the tlo\\'Jine prcssure drop and the pressure drop in the tubing aboye the valve wiII ehange as injccted GLR ehanges. Therefore, a differenl outf1ow curve \\"ould be obtaincd for eaeh injected GLR.
is being analyzed. If the effeet of the injeeled gas volume is being analyzed, it may be convenient to select the working vah-e as the node, parlieularly if wellhead pres-
The formalion GLR must be used to ealeulale óp (lubing below valve). and lhe tOlal GLR musl be used above lhe val ve. As the injeeted GLR becames too large, lhe
sure remains constant. In this case, the node pressure would be the pressure in the tubing at the valve Pv' and the inflow and outflow expressions would be:
inerease in piping system pressure drop due to friction wíll exeeed the decrease in the hydrostatic pressure in the lubing aboye the val ve. This is illustraled in Figure 5-2 .
The perfonnanee of a gas lift well can be analyzed
•
Artificial Lifi Design
157
Excessive GLR
/
,1
t
I
Pwl
"
GLR
\ qL-Fig. 5-2. Gas Ufl welf analysis.
The intcrseClions of Ihe inflow and oulflo\\" curves give the liquid production rate corresponding to each injected GLR. Thc required volume of gas lo be injected can then be calculated. and a plol of Jiquid production rate versus gas injection Tate can be constructed. This is iIlustrated in Figure 5-J. The maximum liquid Tate obtainable for Ihis \Vell and lhe corresponding gílS injection rate can be rcad from Ihis pIeL Injection al
than that required to obtain the maximum liquid rateo This is iHustrated qualitatively on Figure 5-3, but the actual value wiH depend on the individual weH being eonsidered. It can, of course, ehange iC the price oC oil or the cost of compression ehanges. The liquid production rate that can be expected from aoy limited available gas valume can also be estimated from a plot sueh as Figure 5-3. The ealculatians \required fo produce fhe plots in Figures 5-2 and 5-3 were based on a particular injeclion depth. As was discussed earlier, the possible injection depth is controHed -by the available injeetion gas pressUre. In most cases, the maximum liquid production rate is obtained by injecting the gas as deep as possible, possibly just above the packer. This could, however, require a high surfaee pressure if the weH is deep. The effeet of injection depth and, thereforc, injection pressure required on liquid production rate can be determined by repeating lhe procedure iIlustrated in Figure 5-3 for various injection depths. This would result in a different plot of qL versus q¡lIj for each injection depth, as il1ustrated in Figure 5-4. Once the liquid production rate and gas injection rate are determíned, lhe pressure cxisting in the tubing at (he injection depth C30 be deterrnined. The required surfacc opcrating_pressur~ for the injecled gas can then be cslimated from: (5-1 )
where
p" p,. ópv e X D,.
Y,
suriaceoperating pressurc, psi a tubing pressure at the gas lift vatve, psia pressurc drop across the valve, psi natural log base,
001875 D v Y! f
Z.
tme vertical depth lo injection point, specific gravity of injccted gas,
n,
Maxlmum InJ. Oeplh
...---~~
L~ax.qL -------
t
°L
----- I 1--I I I I I I o(
-
I I I I '
~
~-----i
Available Gas Volume
Economlc Optlmum CI
o In/. Flg. 5-3. Effect
j •¡¡ •
-
i
gas In¡eellon rateo
Inl.
q Inl. -
Fig. 5-4. Effect 01 injeclion depth.
Producrioll Op/imiz{/thm L'sillg Noda/
/58 T
aycragc tcmpcrature in the annulus , °R average gas comprcssibility factor.
Z
Solution of Equ3tion 5-1 is iterative since Z de p e n d s on the unknown pressure PJo' It also assumes no [ricI¡on loss in the annulus. 11' rcquircd injecti')Il rates are high oc the annular area is small, frictian may have to be considered. The proccdure ror calculating pressure drop foc Ihis case \Vas discussed in Chaplee 3. The prcvious discussion assumed that parameters such as separatar pressure, tlowline size, tubing sizc. water cut, fonnation GLR and static reseryoir pressure were fixed. The cffccts of changes in any (Ir these can be slUdicd foc a well on gas ¡ift by using lhe procedures dcscribed previously roc flowing wells. For example. if a
A/I.I~I·SjS
uid rates, and then using these wellhead pressures lo find the node pressure necessary lo satisfy the tubing and f10wline requirements.
/lIjlOII'
qo. STB/day 300 400 500 600
Pw(' psig
1277 1195 1107 1013
OI/Ij/OlV Flowline Requirements
wcll is lo be placed on gas-fift (and ;ide pockct mandr
llave not prcviously bccn installed). i.h~ tubing will ¡uve to be pulled. This prescnts an cxcell~nt opportuniry ro optimize tubing sizc. AIso, since rhe Ilowline will ha\"c lo transport additional fluid whcn gas ¡ift is installed. ir is often economically fcasible to either r~place oc loop [he
existing flowline. Examp/e 5-1: .~
..
An oil well that has died due to dedining gas/oil ratio is to be placed on gas lift. From a lest conducted on the well befaré it died, it was dete~ined that qo(mal I 15 1200 STSOlday. Using this test da:a and the 101l0ll
Injecled
Pwh"
Tofal GLR
Qo-300
qo=400
qo-500
300 500 700 900 1100 1400
400 600 800 1000 1200 1500
150 160 170 190 200 220
170 190 210 230 250 280
200 230 250 280 300 340
So/ution: Seleet the injection poiot, which is al50 al midpenora· lians tor this case, as the node location. The jnflow is calculated from:
[
1.25q,
Pwf =1500
U] -0.125
qo(max)
[(1.266-
125 ;20~'
J"
230 26C
300
320 360 400
Tubing Requirements
Injected
Pw.'J·
GLR
Tota! GLR
qo-300
300 500 700 900 1100 1400
400 600 800 1000 1200 1500
1040 890 840 830 820 810
Injected GLR. scllSTaO
_
q,]=6C.J
qo-400 1150 1000 960 950 940 950
psig qo-500
1260 1110 1070 1060 1070 1080
Qo-6:-')
136:) 1210 1180
118'1 1190
1220
The inflow and six outflow curves are plotted on Figure 5-5. The producing capacities for the various injected GLRs are read from the intersections of the inflow and outflow curves. The oil production rate, injected GLR. and gas injection rates are tabulated as follows:
Po
Pwf =PR (1.266---)
psig
GLR
-0.125
]
The outflow is determinad for each possible gas injection rale by first finding the wellhead pressure necessary to salisfy lhe flowline requirements for various liq-
300 500 700 900 1100 1400
Oil Rate,
S TaOlday
420 497 518 522 515 511
Injeclion Rale. Mscld
126 249
363 470 567 715
A plot of the oil production rate tor various gas injection rates is shown in Figure 5-6. It can be sean that the maximum oi! rate is approximalely 520 STSO/day and that injection at arate greater than about 360 Mscfd resulls in very little increase in oi! rateo II Ihe profit on oH and the gas compression cost were known, the economic optimum rates could be determinad.
Artificial Lift Design
159
/
::
.,.
1190
.........
1170
........... ··································0···················
::~
::...:
:
300
.
500 1150
Pwf. psig
--- 700
113D
~
900
1110
--+-
1100
~
1400
~
lnflow
1090
1070 lOSO +-~~
_~~~_~
__
..L....=-.L-Lf-----l--"..L-_~~----''----
~Oo
-l 600
500
Production Rote. 5180/0 Fig. 5-5 Example 5-1 resulls.
600
,
.
Production Rote. 300 5180/0 200
.
.
100
...
...............-¡-
~.-
~
·· ···
~
.. ...
~
:
:
O+-------t-------t------t------t--------/ O
125
250
375
500
625
Gas Injection Rote, Hscfd L ----=-c--=-----,----=-c-----,,-------------''------------------' Fig. 5-6. Example 5-1 resulls.
ProdUCfiOJI Opfil1liz(J(ioJl Usil1g Nodtd AIi.;"~\'sis
160
Once lhe procedures discussed abo\"~ have bccn 1'01{he following inronllution is kr.Jwn roe a particular well: tow~d,
Liquid production rate: CJL> Injcction gas liquid ratio, GLRitif• Injcction deplh. Di/l i ' Required bOHomholc tlowing pressure. P"f' Gas injection surface pressurc, Pso. Flowing weJlhcad pressure, Plt'/1' and Static rcscrvoir pressure, PR' Knowledge oc an estimate of aIl l:;~se paramcters is rcquired bcfore the unloading VaIH"'). can be spaced. Addilionai informal ion rcquired i~"'Ir valve spal.:'ing
indudes: StaLi~ grndicnt of load lluid, gs. Tubing pressurc during unloading per:_'J, PU'/p and tvlaximum lemporary gas pressure fm "kickoft~" Pko'
As can be obserycd frol11 lhe disc:,:s.5ioll on pcrfonnunce of a continuou:i tlow gas !ift we:l. once the well is prodncing in a stable condition, gas is jeing injccted al a colltinuous rate at onl)' ane point in [h:; :ubing. Therefore, only one gas !in \'al\'c is opon. and l:-,~ requircd surface operating prcssurc is known. Howc\ ~r. unlcss a mudl highcr pressurc source ol' gas is 3\'ai:,;ble to unload kili l1uids from the weH 10 gCl il into It:S strlble opcnuing condilion, other gas lin valvcs at st.:.:towcr tlepths are requir~d. The necessi[y toe ha\'ing the unloading valn~s will Hesl be illustea[~d, followed by s Jiscussion of procedures foc spacing the valves. As it ü necesservoir pressure so that no tlow is occurring. Tbe unloading peocess begins by injecting gas into the annulus and forcing the l¡quid iota lhe tubing. This is illustrated in Figure 5-7A. As can be seen from this figure, if thece were only one val ve in the well, that ¡s, lhe bottom oc operating val ve, enough casing gas pressure would have lo be a\'ailable lo support the hydrostatic pressure af the liquid in the tubing down lo the deplh of the valve befo re lhe ,"alve could be uncovered and gas injection ioto lhe tubing initiated. This wauld rcquire a very high gas pressure for deep wells loaded \Vith heavy liquid" For exampk, if gas is to be injeeted al a depth of 10,000 ft and the kili fluid gradielll
.
is 0.47 psi/ft, a hydrostatic prcssurc of 4700 psig \;"mld ... cxist in the tubing
B. Valve Spacing There are at least lhree distinct types of val ve spacing encountcred in lhe design of continuous tlo\\' installations. One case is that in which the val ves are 10 be spaced, and pressure-charged and run with the tubing in an existing wcll. A sccond case involvcs mnning side pocket mandrcls in a well that may not be placed on gas lift until sorne later time. Ihis case is frequently cllcountered in areas such as offshorc oc in remole !ocations where pulling tubing is inconvenient or expensive. The spacing of the rnandrels must be based 00 antici?ated future condit!ons. A third case is one in which the cpen-
'~'problems
.
"
Artificial Lijl Design
161
T. S.p•• ohr
T. S.'_",~"~"==_ Ch.h
Boll.", V.l... Opu
lrans~
(B) Fluid in tUbing being aarated lo
lerred inlo tubing Ihrough all valves
surface by ¡njeelion gas through lop
!.,d u-lubed by ¡njaclion gas pressure
valve 85 fluid in annulus Is transferred loto lubing through lower valvas. .-
(A) Fluid {rom casing bring
to surface.
To, Vol •• (el.ud)
(C) Injeelion gas enlering lubing through top and !lecondvalve immediately aflar second valve unCovered.
T.9 V.I ••
To, Vol.. (Clo.. d)
(el... d}
"\"'11>;"- Soc••d V.l••
o,...
Suud Vol.. (Ctn.dl
Th¡.d V.l .. Op...
Thi.d V.l.. Opu
, ~.
U"d Vol.. O,u (0'0101;"9 Vol~ol
, Bollo",
¡ ·l, ,.~
{t
(O) FluId In tubing OOlng serated to 5urlace by InJeeHon gas through second valve as fluId In annulus 15 lransferred loto tublng through thlrd and
bottom valvas.
Fig. 5-7. Unfoading sequence.
(E) Inleellon gas enterlng tubing through second end thlrd valvas lmmedlalely efter lhird valva 15 un-
coyored.
VQI~, OpOft
.,
,
(F) Produdng rala equals capaclty of tublng from third valva lor aVBllebiB Injectlon pre.!lsure. Therefore, bottom valva C8nnot be uncovered.
ProclUCliOI/ Oplil1lizaliv)1 Using Nocla! r/.//iI;>:sis
162 ing and closing conditions mus! be cakulated foe val ves to be run in cxisting mandrds. The mandrels may huye becn spaced same time earliee, and lhe existing conditions may be considcrably different from lhe
l.
Construct the casing prcssure travcrsc by locating rhe available surfare casing pressurc at zero dcp{h ano extcnding lhis line downward, taking illlo account th~ weight of the gas.
2.
Starting al lhe tlowing bottomhok prcssurc rcquired to intlow the design production rat~, plot the tubing Oowing pressure traverse llpward llsing the formalion GLR.
3.
Locate the inrersection of the tubíng pr~ssure line and the casing pressurc line as (he point of b3lance. This ¡s the depth al which gas could be injccted ifno pressure drap across lhe valve wcre requircd.
4.
Locate the tubing flowillg wcllhcad pressure al zero depth, and connect this point wi¡h a lill~ from ¡he paint of bnlancc. This represents lhe lubing pre:i:iure traverse aboye (he point of injcclion bascd on {he design liquid cate and the formation plus the inje . .' ted gas rateo This is ¡he theoretical cOlldition that would exist in lhe m~1l aftcr it is llnload~d and stabilized, assuming no pr~ssure drop across lh~ opcraling g.as lift valvc.
5.
Starting at the surface tubing pressure, ex¡cnd a line downward based on the kili or load fluid gradient. Tbis represents lhe pressurc in lhe lubing bdore an)'
surface bdore lhe valve is mn into the wel!. The spating and prcssure settings must be such as following:
10
accornplish the
l.
It must be possible lo displace liquid from the casing ¡nto lhe lubing clown lo the desired opcrating depth with lhe available gas pressure, and
2.
lt musl be possiblc ro open any \'al\'e undcr producing conditions without opening [he- valvc aboye it.
The spacing will be illuslrated qualitatively and graphically first. Then safet)' factúrs wiII be introduced and dctailed design procedures and examples will be prescnted. lhe procedure is illustrated graphical1y by making a pIar 01' pressure versus dcpth, such as in Figure S-S.
Pfi.ESSUAE. PSI
o
o
'00
.00
1200
1600
2000
"':::---------'~2530'
>-
'"'"
""'000
'.,,,----_--">\ .01600'
~
:i >o-
w
a
6000
'.,:::----"", 5900'
1500' 8000
10,000
Fig. 5-8. Graphica/ so/utian for va/ve spacing.
7900' 8250'
2000
2400
Artificial Lifl Design gas has entered the tubing. The intersection of this line represents the depth al which the pressures in the tubing and casing are equal as the load fluid is being U-tubed from the casing into the lubing. This is lhe location of the top valve. When gas is injected into lhe tubing al this poinl, the tubing gradient above the valve will lhen be represented by the flowing gradi-
ent lineo 6.
From the depth of lhe top valve on lhe flowing gradient line, eJtlend a line based on the load fluid gradienl downward to the intersection with the casing pressure lineo This locates the second valve. Repeat this procedure until the difference between the casing and tubing prcssures 15 abol!t SO psi. Figure 5-8 represents this proccdure ror a hypothetical case.
1\1051 design methods inelude sewra\ safcty factors, and these factors are recornmended ror the following rcascns: (1) an error in well data that would affeet injection gas voJume or injection gas pressure at depth; (2) an error in yalve operating temperaturc for temperature sensitive valves; (3) a slight error in setting the valve opening pressure in a tester, particularly if the valye opening pressure must be set in the field; and (4) lo overcome the load rate of the gas lift valve, which means that a given psi in crease in pressurc is required to OblJin sufficient slem tr:1.\"el in a gas lift \'alyc. Se\'cral safcty factors that are incorporatcd in the design of a conlíllllo\lS now inslallation as discussed in Reference 3 are: 1.
A pressure differenliaI across the valve of 50 psi is recommcndcd and uscd for detennining valve depths in most installations. Gencrally, only a few psi differentia! \VouId be requircd theoretically if aH assurned data were absolutely corrcct.
2.
The maXírn1l11l tllbing pressure at valve depth, used to ca1cula~e the reopeníng pressure of a valve, is based on the maximum flowing tubing pressure at this depth while lifting from the next lower valve with the assumed prcssure differential across the lower valve. Thc minimum flowing tubing pressure at valve deplh is opposite the upper gas lift valves at the instant a lowcr valve is uncovcred. However, gas lifling may occur fram the 10wer valve depth with the flowing tubing pressure equal to, or ncar, this maximum flawing tubing pressure.
3.
A prcssure gradient bascd on a flowing load fluid gradient curve is used to locate the valve depths. This condition should not exist for Ihe Jowcr valves when lhe flowing BHP is less than the static BHP and reservo ir fluid fecd-in occurs.
4.
The total producing GLR is assumed to be the injection GLR during unloading operations for the tra-
163 verse aboye the point of gas injection. In most installations, sorne formation gas will be produced before the unloading operations are co01pleted. 5.
Gencrally, the unloading traverse for locating the vaIve deplhs is based on tbe desired producing rate and injection gas volume available to unIoad the well. The actual unloading producing rate can be controlled by varying the injection gas volume. Decreasing the choke size in the injection gas lioe will decrease the injection gas volume and producing rate during liquid transfer from casing to tubing. Therefore, for high capacity wells, a minimum fluid gradient traverse 'for a lower producing rate O13Y exist unlil lhe deliverability of lhe well approaches the desired producing rateo
Not aH the aboye safety factors wil1 be recornmended for all installation design melhods. AIthough many of these factors may be used, the gas lift val ve manufacturers' literature seldom emphasizes this fact. Experience diclates lhat certain safety factors should be incorporated in the design calculations to assure unloading. One means of including a safety factor in the designo frequently caHed the Camco or Winkler method , is iIIustratcd ilf Figure 5-9. The saCet)" factor consists of reducing the casing prcssurc rcquircd to open the valve successively fOI" cach lower \'alve in the wd\. The casing pressure availabh:: ror U-tubing at each vah'c is reduccd, and thercfore, lhe valves must be spaced closer togcthcr. As can be seen from Figure 5-9 the point at which a 50 psi differential between the casing and tubing prcssure is reached is at a shallower depth in the wel!. This rneans that with the same available surface gas injcction pressure, lhe well would produce less liquid. When this methad is uscd, the location of the point of injection beco mes trial and error. That ¡s, the total reduction in casing pressurc depends on the number ofvalves required to reRcIl the paint of injection. The spacing of the val ves, and therefore the number required, depends on the flo\\"ing tubing pressure traverse, \vhich depends on production rate and point of injection. The production rate depends on flowing bottornhole pressure, which depends on the point of injection. Another means of incJuding safety factors is caBed the design gradient method and is iIIuslrated in Figure 5-10. Sorne pseudo flowing wellhead pressure higher than the expected wellhead pressure is selected. Ihis pseudo wcllhead pressure is generally selected as the expccted flo\\'ing wellhead pressure plus 20 pereent of the differcnce bctween surface casing and tubing pressurc. The rnethod is frequently refcrred to as the 20 perccnt design gradient melhod. A line is drawn between lhis pseudo wellhead prcssure and the point of injection. The val ve spacing is then carried out as i"f the pressure in the tubing during unloadíng were represcntcd by the pseudo pressure tine.
--'"
ProdUCliol1 Optimization Uxil1g Nodal Anu.-iis
164
PRESSURE, PSI
o o
.olCO
600
1200
1800
2400
2000
I
2000 "':-----
----''"\2530·
~
w w ~
4000
X
"':--------''''1\ "'''' BO'
~
~
w
o
!5850'
8000
6750'
7JOO' 7600' 7BOO'
BOOO
PWF :----..
"'-
q
= 2180 =
p~i
570 bpd
"
l',·.·.·_"
..l/g. 5-9. Exampfe design using casing d:op of 20 psi.
PRESSUAE. PSI
o
o
1200
600
1600
2000
'..-:-------'0>.\ 2530'
.. .. ~
w w
4000
"':-
""\4000·
",-
>-
'..-:------''"\ 5 100'
w
o
6000
8000
'.-:-----',\ 8000'
7100' 7500' 7800' 8050'
8250'
10,000
Fig.
5-io.
Variable gradienl designo
2000
2400
• Artificial Lifi Design
'
......
165
Using this method, full casing pressure is availahle at the depth of injection, and location afthe point of injection is Dot iterative. J Only two methods of inporporating safety factúes ínto [he design ha ve beco described. Mest gas lift valve manufacturers have rheir own methods, and sorne companies use a combination of the two described previously. It is also cornmon practice lo install additional valves below the anticipated inilial poinl of injection to be able to han-
dIe changing well conditions. Sorne designers a150 recornmend bracketing the design injection point with several valves aboye and below this point to handle changing conditions. 1. Gas Lifi Valve Peiformance As was disclIssed earlier, ane of the requirements foc gas lin valve design is that one must be able to open any \'alye withollt opening the valve abovc it in the wcll. Selection of the pressure at which to charge the bellows of a valve before ruoning it ioto lhe hale requires sorne knowledge as to how the valvc responds to various pressures and temperatures, particularly lhe casing pressure and tubing pressure. A very brief di seussion of lhe most eornm.only used valve is given here. For a more comprehensive discussion, see lhe APl Gas Lift Design Manual) A well may be equipped wilh either nonretrievable or retrievable vah"es. Thal ¡s, they mal' be mounted on the oUlside of thc lUbing or may be nm in sirle pocket mandrel:; inside thc lUbing. Figures 5-) J and SMl2 illustrate
both of these cases. The operation of the val ves is independent of the mounting but the temperature existing at the valve during unloading and producing operations may be different. For retrievable valves, the temperature is usually eonsidered to be the flowing fluid temperature. For nonretrievable valves, the temperature is considered to be earth temperature. The faet that neither of these may be correet is one of the reasons that safety factors are required in the spacing of the valves. Estimates of the fiowing temperature at any depth may be made using either the correlation given in ehapter 3 or Figure 5-13. Mas! gas!ift val ves can be placed into one oftwo broad categories for analysis. These categories are caBed Injeetion Pressure or casing pressure operated valves, and Production Pressure or fluid operated valves. The two types are shown in Figures 5-14 and 5-15. Only one type ofvah·e will be considered in this book, the unbalanced pressure charged valve that is primarUy responsive to injeetion oc casing pressure, Figure 5-14. The design of a valve spacing program for a con(inuous-flow gas }in well requires the ca1culation of several pressures. The pressures al which a valve will clase and reopen downhoJe are essenlial in spacing the val ves. It is necessary to calculate the required bellows or dome pressure existing do\vnhole that control:; the opening and closing pressures. Since the bellows must be pressured up or charged at the surface, lbis bcl1o,,"$ pressure I11USt be con verted to standard conditions. To be sure that the
VALVE MOUNTED OUTSIOE lHE MANOAEL (TUBING MUST BE PULLEO 10 HAVE ACCESS 10 THE VALVEI
CONVENTlONAL GAS UFT VALVE
o o
AEVEASE FLOW CHECK
THREAD FOA INSTALLlNG VALVE ANO CHECK TO MANOAEL .
Fig. 5-1,. De/aUs 01 conventional va/ve.
Produclion OptinúzalioJl Using Nodal Ana.:\sis
M6
1 r-n rl
VALVE MOUNTED INSIDE THE MANDREL (WIRELlNE RETRIEVABLE)
-
n
>-- LATCH
L~
'\ ;
¡;::: 1'-- .-
LAT CH RETAINING SHOULDER
PAC KING IVALVE TO POCKET SEAL)
a1-
POR T5 TO ANNULUS
,tr o
f:: -: -:"
I}-
1--
PAC KING (VALVE TO POCKET SEALI
LO.
-
SIDE POCKET (VAL VE RECEIVERJ
• 1-
[j -
~
>---- VAL VE
\¡;;
POR T TO TU81NG
t
Fig. 5-1i._9.~lails ofwireline retrievable \'alve.
\'
P, =
P" - P, (Al' I Ab ) ¡-(ApIA,,)
=
(5-2)
where
injection or casing pressure existing at the valve deplh. This is also ca1led Po or Pe. Pbr bellows or dome pressure at valvc depth. Also caIled Pdr' P"!. production or tubing pressme at valve depth. Also caBed production pressure PPI or tubing pressurc PI" Ap arca ofvalve port or seat. Ah area of the betIows. RAjA, p¡
Equation 5-2 can be rearranged as: _
Pb,
P, -l-(Ap ! Ab )
P, (A p I Ab ) I-(A p ! Ab )
Pb,- p,R l-R
P"
PI = l-R - P,,,·
where
Rp. . _ P", = __ = Productlon Pressure Etlect, ,
o
l-R·
P,,,
Ihis reprcsents the amouot that the opcning prcs5ure
P" - Rp, (-R
Qr
(PI) is reduced as a result of the assistance from P2' The
ratio R/(l-R) or (AjAb)/(I-A,IA,) is called the Production Pressure Effect Factor (PPF.F) or the Tubing EtTect Factor (TEF). lhe Production Pressure Errect (PPE) is "' also called lhe Tubing Errec! (TE). This equation can be rearranged to detcnnine the val ve charge (dome) pressure (PhI) required to obtain the specified opening pressure (P,). Pb' = p¡(I- Ap ! .4,,)+ p,(Ap I r\,) =p,(I-R)+p,R
1)'))
The dome pressure (PhI) in this case is at the temperature of the val ve in the well. When the valve is open, both PI and P2 are acting on the same area (Ah)' and, therefore, the theoretical injection pressure or casing pressure at which the valve closes IS
PI =fbt
(5-4)
•
Artificial Lifi Design
167
CHAAT TO BE USE O DIRECTLY fOR 2)\' TUB1NG. fOR 2' TUB1NG MULTlPLY THE ACTUAL FLOW RATe BY 2. FOR 3' TUB1NG DIVIDE THE ACTUAL FLOW RATE BY 1.5.
"
,., .,
GIVEHI
...
7QO lauI¡:'AYTOTAL 1'\.\110 To 111: ""'OOUGD 1HIlOO,lOH
.r
iv'IH
,\110.
DlnOlOlIHI 3l/1I'Act: ....OtnHO
SOI-UTlOH:
...
T~VlAruIlL
lU l'CiO . .".. slgAV 1M T ru"NCllS Al'f'tw:>D,U.TU.Y (¡UIV,u.El(T 10 1.olO • .....",0...1' ll! si" ru"Hll. UI A' nu: IHTUUECnOH 01' 1400 alOUJI>oloY JoItO 1,1 OItQnll!:I'IoU>I.. """,,OI.EHT I.lltlltU4 A lOlUo't:HT OH ntlE OIll)l>\ATI 01' 1" "ud ~TM.
,.,
nu:
... ...
UIIliIll'''Cr: I'1-OtnHO TOQ'[l\An¡¡u: ·In-ll.olllo&l
_1'"
•~ ... ~ i ...
l'
~
u
".1'0
.
,
..
" ,
~ ~
~
~
'. .• . ,.• ...
•• ••
'
~ ••
.,
'
•• ••
"
... u
...
•., •
IOllltnl~ll"17"U:¡g
101...1. 'LUID 1"1.0'0' """TI: _ 10> ULS/OAY
Fig. 5-13. Flowing temperature gradient for different flow rates, geothermaJ gradients, and tubjng sizes. 3
When the valve is in the test rack, as in Figure 5-16, Pl is equal to zero and the lest rack opening pressure is given by
p,@60°F
p,
l-(Apl A,)
I-R
(5-5)
Tables 5-1 and 5-2 lisl the valuos of'Ap and A, for two manufacturer's gas lift val ves. The spread of a gas lift valve is defined as the difference between Ihe opening and closing pressure of the val ve. '-
2. Olis Design Procedure The procedure that was descríbed qualitatively earlier, sometimes called the 20 percent design gradient method, was first used by Otis Engineering. It has the advantage Ihat aH the available gas injection pressure al dcpth can be used in spacing the valves, and, therefore, gas can be injected deeper for a fixed available pressure. Also, the pDiot of injectíon can be determined before the valves are spaced. The folJowing procedure may be used for localing the val ves and dctennining the pressure sctti.IlgS for a fixed production rateo
168
ProdllC;ivl1 Optimizotion Using Noc/al A",;:ysis
.......
~
~
'-
I p
l'
t
~. :b~
' ,
Z
o
~~
¡: u
"oo "'
I
~: ~:~
c 5ó P,
P,
"o<
-
P,
!A;1
~
¡
¡
P,
i
A
1
I
~PRESSl"E
, ,P" I
' P", ,
~
, , "!'\l' F
t
z
o
SOURCE.{P.J
ti
'"oo
"' I ~
Fig. 5-16, Test rack.'
:';;"
""
~'--
Produclion up Ihe lubing
Produc!IQn up Ihe annurus
(A)
(B)
D. Locate the imersection of the opcrating casing rressure line \\"ilh (he flowing gra.dicnt lineo This is thc depth at \vhich the casing and tubing prcssurcs are balanccd or egua!. E.
Fig. 5-14. Injecfion pressure operaled valves. 3
1. Selec! Deplh to Operaling Valve (Injection Depth)
Subtract the C'perating differcntial prcssurc, usually 100 psi, from rhe prcssure at the inlcrsectian faund in D. The depth al which this pressure occurs on the flowing gradient lioe is the operating valve dep!h.
A. Plol kick-off (P'o) and operaling casing pressure (P.'O) \·crsus.depth.
11. Determine the Necessary Injection Gas Rate
B.
Dctermine p"! required for desired production rate using Ihe Intlow Perfonnance methads.
C.
Ploe Oie flo\\'ing gradient from P....·upward using gradient curves for appropriate d r,' q(. and farmation gas/liquid ratio, GLR f
A. Using the tW(I-phase gradient curvcs, deter11lin~ the GLR line which connects the pressure at the inje.:-tion point to the wdlhead flowing pressure. I\,-fr This gives the rcquired lotol GLR, GlR r. B. Calculate the necessary injection gas rale.
q" = qL(GLR T - GLR¡). 111. Determine the Deplhs lo the Unloading Valves A. Draw a design gradient lineo
j
l. Locate the design surface pressure, P,,'J = P"., + 0.20(p" - Pwh)'
2. Connect this point to the point of injcction. A,
I¡
P,
J\...
Production up the annulus
Produclion up the tublng
(A)
(B)
Fig. 5·15. Producfion pressure operated valves. 3
B. Draw a kili fluid gradient line (usually 0.5 psilft) from P....h to intersect lhe Pifo line. This locates the lap valve.
C. From the tap \'alve depth on the design gradient line, draw a kili fluid gradient line to inlerseet the P, line. This is lhe deplh to the seeond val ve. Repeat this procedure unlil the operating valve depth is reached. IV. Seled the Por! Size for the Operating Valve. (This is necessary lo gel R = AlA.). The por! size should be large enough to pass the rcquired gas injection
• 169
Artificial Lifi Design
TABLE 5-1 SPECIFICATIONS FOR CAMCO PRESSURE OPERATED GAS L1FT VALVES TEF=
A.
ApIA. ] Effecüve Bellows [ Area al Port with Bevel (1- ApIA.) Port Size 1.0. Afea in. sq. in. AlA. (l-AJA,,) Tubing Effect Factor Type Va/ve sq. in. 3/32 0.0077 0.06 0.94 0.07 0.12 J50, JR50 1/8 0.0133 0.11 0.89 0.12 JP50 5/32 0.0204 0.17 0.83 0.21 13/64 0.0340 0.28 0.72 0.39 11/32 0.0955 0.80 0.20 4.00 1/8 0.0133 0.043 0.957 0.045 AK,AKR 0.31 3/16 0.0291 0.094 0.906 0.104 BK,BKF 114 0.0511 0.164 0.836 0.196 BKR,BP 9/32 0.0643 0.207 0.793 0.261 J40, J41 5/16 0.0792 0.255 0.745 0.342 JR40, PK 3/8 0.1134 0.365 0.635 0.575 ep, J20 3/16 0.0291 0.038 0962 0.040 0.77 114 0.0511 0.067 0.933 0.072 JR20, R20 5/16 0.0792 0.104 0.896 0.116 R21, R25 R28, R29 3/8 0.1134 0.148 0.852 0.174 7/16 0.1538 0.201 0.799 0.252 1!2 0.2002 0.262 0.738 0.355 NOTE: The valves are grouped according to their bellows size. A specific valve type may nol be available in alJ port sizes shown for a given bellows. This is particularly true ter valves wilh a crOSS-Dver seat. 1. The maximum part size far the AK series valves is 9/32-inch 1.0. 2. Valves with cross-Dver seats and their corresponding maximum I.D. port sizes are as follows:
AKR-2: 5/32-inch BKF-3: 3/16-inch BKR-l: 114-inch JR40: 3/16-inch R25: 5116-inch 3. The specifications apply lo lhe pilol seclion only of a pilol valve.
BKF: 1/4-incil BKF-10: 1/4 c nch JR20: 3/16-ir.ch JR50: 3/32-ir.ch R28: 5/16-inch
4. Port areas were calculated based on the nomínal I.D. plus O.005-inch far the beveL
rate correcled for temperature at the valve. The corrected gas rale is
e, is oblained [rom Table 5-3. E.
Calculate the test rack opening prcssure
V. Determine !he Required Dome Pressures lar alllhe Valves. A. Read the opening pressure (Po) al vaJve depth from the Po lineo
B. Read lhe design tubing load (P,) al a valve depth [rom the design gradient lineo C. Calculate the closing or dome pressure (PhI) al valve deplh. pbl = P.(1 - R) + p,R,
where R
= AJA b.
D. CalcuJate·-the dome pressure required at surface conditions lo give Phi at the valve temperature.
Example 5-2: Using the foUO'Ning data, determine: 1. Deplh lo poinl of injecllon. 2. Required gas injection rateo 3. Valva spacing ~nd test rack opening pres5ures.
Deplh to mid-pertoralions = 7500 ft. Oil gravity =35'API Gas gravity =0.65 Waler fraclioo = O Formalioo GOR = 200 scflSTB Pwh= 100 psi9 Twh = 100'F
-
'""
TABLE 5-2 SPECIFICATIONS FOR OTIS SPREAOMASTER PRESSURE-OPERATEO GAS L1FT VALVES R VALUES Bellows Afea and Sea! Area Relationships for Gfis Spreadmaster Valves
For 1-1/2" 0.0. O/ameler of Spread
Control Seat-in.
For 1" 0.0. Valves
Valves
1- R
R
1- R
3116 1/4 9/32 5/16
.0863 .1534 .1942 .2397
.9137 .8466 .8058 .7603
.0359 .0638
.9641 .9362
0996
.9004
11132
.2900
.1 lOO
3/8 7/16 1/2 9/16
.3450 .4697
.6550 .5303
-
-
R
R = ArlAb Where:
A,) ;: Area of srread control seat-in 2 Al} :. Ulucllvtl ¡ 11 ull tll UUJlIJW:1' -Jrl:.!
.1434 .1952 .2562 .3227
A b lor 1" 0.0. Valves-.32 ¡n 2 A b for 1-1/2" 0.0. Valves-.77 ¡n 2
.8566 .8048 .7438 .6773
TYPE S OTIS SPREADMASTER GAS L1FT VALVES WITH PILO-PORT TYPE NS OTIS CONVENTIONAL VALVE
Va/ve
Uft Port
0.0.
Diam.
Inches
Inches
1.000 1.500 1.500
7116 9116 114
PILO-PORT OIAMETER INCHES 118 8164 .125
114 16164 .250
1116
12/64
.187
Yl32
5/16
18164
20164 .312
.281
11132 22164 .343
318 24/64 .375
7116 28164 .437
112 32164 .500
9116 34164 ,562
221NSI017 221NS1018 221NSI001 221NS1003 221NS1005 221NS1004 221NSI512 221NS,5,4 221NS'524 22'NS'513 221 NSI525 22'NS'508 22,NS'507 221NS15,0 22'NS,5'1 22' NS'509
Thread
Valve
Connecrion {nchf;Js
Lenglh Inches
112 NPT 112 NPT 114 NPT
14718 20 114 20 114
0.0. Inches
Inches
Valve
'.000 1.500 1.500
7116 8/16 1/4
1116 12164
114 16164
9/32 18164
5116 20164
11132 22164
318 24164
7116 28164
112 32164
.187
.25(J
.2EJ1
.117
..14:1
..17.'1
.1.17
.!inO
221 RS1014 221 RSto15 221 R$lÚOl 221 HS100J 221 HS1005 211 [<S1U04
221RS'518 221RS1519
(Courtesy Otis Engineering, Dalias, Texas)
221RS1513 221RS,509
"~. ~:
PILO-PORT OIAMETER INCHES 118 8164 .125
"9-
f
TYPE RS 0TIS WIRELINE RETRIEVABLE VALVE Lift Port Diam.
:y
9116 34/64 Pack;ng 0.0. In. !i6?
Uppnr
'.032 1.562 221 RS'5,2 221RS1514 221 RS1508 221RSI507 221RS15'0 22,RS'511 1.562
Valve Length
Lnwor
Inr.hn:;
1.032 1.500 1.500
2013116 20 13116
131/8
~
~'
::
s:
'1~'
o-
..
~
§: '~ .".. .;;;. .;
171
Artificial Lift Design
TABLE 5-3
Temperatura Correction Factors far Nitrogen Based on 60°F
°F
C,
°F
C,
°F
C,
°F
C,
°F
C,
°F
CI
61 62 63 64 65
.998 .996 .994 .991 .969
101 102 103 104 105
.919 .917 .915 .914 .912
141 142 143 144 145
.852
.794 .792 .791 .790 .786
221 222 223 224 225
.743 .742
.849 .847 .645
181 182 183 184 165
.739 .738
261 262 263 264 265
.698 .697 .696 .695 .694
66 67 68 69 70
.967 .985 .963 .981 .979
106 107 106 109 110
.910 .908 .906
.844 .842 .841 .839 .638
166 187 166 189 190
.787 .786 .784 .763 .782
226 227 226 229 230
.737 .736 .735 .733 .732
266 267 268 269 270
.693 .692 .691
.903
146 147 148 149 150
71 72 73 74 75
.977 .975 .973 .971 .969
111 112 113 114 115
.901 .899 .898 .696 .894
151 152 153 154 155
.836 .835 .833 .832 .830
191 192 193 194 195
.780 .779 .778 .776 .775
231 232 233 234 235
.731 .730 .729 .728 .727
271 272 273 274 275
.688 .687 .686 .685 .684
76 77 76 79 80
.967 .965 .963 .961 .959
116 117 116 119 120
.693 .691 689 .867 .686
156 157 158 159 160
.829 .827 .826 .825 .823
196 197 198 199
236 237
.725 .724 .723 .722 .721
276 277 278 279
.683 .682 .681
200
.774 .772 .771 .770 .769
280
.679
81 82 83 84 85
.957 .955 .953 .951 .949
121 122 123 124 125
.884 .882 .881 .879 .877
161 162 163 164 165
:622 .820 .619 .817 .816
201 202 203 204 205
.767 .766 .765 .764 .762
.720 .719 .716 .717 .715
261 262 283 284 265
.678 .677 .676 .675 .674
86 87 68 89 . 90
.947 .945 .943 .941 .939
126 127 126 129 130
.676 .674 .672 .671 .869
166 167 166 169 170
.814 .813 .812
.761 .760 .759 .757 .756
246
250
.714 .713 .712 .711 .710
266 267 288 289
.609
206 207 206 209 210
290
.673 .672 .671 .670 .669
91 92 93 94 95
.936 .936 .934 .932 .930
131 132 133 134 135
.666 .866 .864 .863 .861
171 172 173 174 175
.807 .806 .805 .803 .802
211 212 213 214 215
.755 .754 .752 .751 .750
251 252 2>3 2Sl 255
.709 .706 .707 .706 .705
291 292 293 294 295
.668 .667 .666 .665 .664
96 97 96 99 100
.928
136 137 138 139 140
.860 .656 .856 .855 .653
176 177 178 179 180
.800 .799 .796 .796 .795
216 217 218 219 220
.749 .746 .746 .745 .744
250
.704 .702 .701 .700 .699
296
.663 .662 .662 .661 .660
.926 .924 .923 .921
.905
e I
.850
i
.810
233 239
240 241 242 243 244 245
247 245 249
2fiT
253 259 260
.740
Gas Uf! Valve Dome Pressure al 60 'F Gas Uf! Valve Dome Pressure al Well Temperalure
197
298 299 300
.690
.669
.680
Productioll Op,imizofiol1
Tms = 182°F Tubing LO. = 1.995 in.
l.J.~¡ng
Nodal Ana,~"'_,is
Pressure. pslq
400
00
800
1200
1 &00
Ps o = 870 psig
= 920 psig t.p across operating valve = 100 psi
Pko
1000
Injected gas sutface temperature = 1000F
Load ftuid gradient = 0.5 psi/ft Sta!ic liquid level 1s at surface
2000
Weli lo be unloaded lo Pwh = 100 psig Desired produelion rale = 600 5TBD/day 3000·
Valves will be 1 in. retrievable. From a previous test:
PR = 2000 psig. qo = 383 5TB/day for Pwr = 1850 psig
5000.
1.
A. Using Figure 5-18. determine the gas prcssure at 7000 ft:
B.
4001>
Ps
P al 7000 ff
920 870
1100 1050
6000
70<:0
-'o .
Using Vogcl"s Mcthod lo delcrmine p,,¡ rcquircd for a ¡iquid role af 600 STBO/day:
8000
Fig. 5-17. Example 5-2 sofufion.
From test: P"r/JiR =185012000 =.925
q,,',m) = 383/[ 1-.2(.925) -.8(.925)'] PH(=
C.
=
2935 STB/doy
2000[ 1.266-1.25(600/2935))-'-.125] = 1760 psig
Va/\'e No.
Oeplh
1
1700 2600 3300 3850 4300 4660 4950 5150
2 3
Inlerseelion is al 5400 f\ (from graph, Figure 5-17)
D. Opcmling valve deplh = 5100 ft (from graph)
4
5 6 7 8
11. A. Using the pressure traverse curves for 1.995 tubíng and 600 STBO/day eSloblishes lhe required GLR above lhe operaling valve as 400 sef/STB.
B. qg' = 600(400-200)
=
120,000 sefldoy
111. A.
IV. A part size must be selected which will pass gas al a rale af 120 Mscfd ",ilh an upslrcam pressure of 1000 psig and a downstrcam pressure of 900 psig. The tcmperature at the operating valve is
Pwhd =
100 + 0.20(770)
=
254 psig
B, C. The valve deplhs are found from lhe graph as:
T. =100+(I82-100)(5150)=156°F
,.
7500
173
Artificial Lift Design
GAS PRESSURE AT DEPTH FOR GAS GRAVITY =0.&5, TEMPERATURE OF GAS AT SURFACE = lOO 0F, AHD TEMPERATURE AT DEPTH = 70°F + I.6°F PER 100 FT. OF DEPTH. # # #
.
15
..§" ¡;;
.
~
. . " .f' l' ,¡P ~# ,,,, ,'1- ,"
" " l2 11
i:.
.. "
w u
\O
"
•
..
~
1-
w
"" ~ ~
.."
7
"
•
u
s
~
,
W
..
~
x o ¡:
!'<
2
3
2
s
•
• •
7
\O
11
12
"
"
15
IHJECTIOH GAS PRE.s.sURf AT DEPTH (p.. ) IN 100 PSIG
17
la
19
Fig. 5-18. Copyright, Carnco Incorporaled. Reprinled with pennission.
C. Pb, = pil - R) + poR Pb'= 896 Psig
The corrcclep gas volume is: . 120(l5~ +460) '1g;~ (60.¡-460)
142 MscJd
For the top valve:
A. Po
=
970
B. p, = 490
970(.8466) + 490(.1534)
(S-sC)
From lhe choke capacily char! (Fig. 5-22), a 16/64 oritice will pass gas at arate of 250 Mscfd. Although a srnaIler port size will sufficc, select tbe 0.25 in. port foc possible changing condilions. From Table 5-2: R = .1534, (1 - R) = .8466 A b = 0.32 in.' Use lhe same porl size for aH lhe valves.
v.
=
D. From Table 5-3: C, = .886 for T, = 120°F. The lable roc valve setting temperatures of 60°F was used. Sorne companies use 80°F.
Po = C/,pbJ
=
.886(896) = 794 psig
E. P.. = p;/(I -R) = 794/0.8466
~
938 psig
TabIe 5-4 summarizes the design: The example problem illuslraled lhe design for a vertical well. Ir a direclionally drilled weH is lo be placed on gas lift) the same design procedure can be used if the flowing prcssure traverses are calculated based on the measured depth and the measured depths are con verted to true vertical deplhs for plot· ting. This is convenicnl bccause the load fluid and
Producfion Oplimization [:')'¡"g Nodol
/7·/
A1i.. l!ysi.\
TABLE 5-4 OPENING PRESSURE CALCULATIONS FOR SINGLE-ELEMENT, UNBALANCED NITROGEN CHARGED GAS UFT VALVES Company Examole 5·2 Field Lease Wen No. _ Valve Manufacturer Otis Engineering Valve Type 1 ¡neh Date _
L
Valve No.
n.
1 2 3 4 5 6 7 8
1700 2600 3300 3850 4300 4660 4950 5150
Port Size
in. .25
Oesígn
ArlAb .1534
Po@L psig
p,@L psig
Pb' psig
T,@L 'F
e,
Pb psig
P,o psig
970 935" 955 970 980 990 1000 1005
490 600 680 750 800 847 882 906
896 884 913 936 952 968 982 990
120 128 136 142 147 151 154 156
.886 .872 .860 .850 .842 .836 .832 .829
794 771 785 796 802 809 817 821
938 911 927 940 947 956 965 970
Ihe injcctcd gas aroC under static conditions and are. thercforc, unaffected by hole angle.
111. SUBMERSIBLE PUMP SELECTION Many high-volume wclls are equipped with electric suhmersible pumps (ESP) to lift the liquid and decrease the flowing bottomhole pressurc. A submersible pump is a multisragc centrifugal pump that is dri\cn by an eiectric ¡üotor locnled in the wcll bclow lhe pump. Electric po\\"c: is supplicd by means of a cable from lhe surface. Submcrsible pumps are íl\'ailable for production rate5 ranging: fram about 300 ro 60,000 bblsiday and are idcz¡ for high water-cut, lo\\" gas/liquid ratio wells. Detailed dcsign procedures wiU not bc presented here, but the application of nodal syslems analysis in detcrmining lhe size and power requircments of a submcrsible pump wilI be describcd. A comprehensi\'c discussion of submersible pump 5clcclion can bc round in Brown. 1 The pump and motor are suspended 00 the tubing at a certain dcpth in the \\'ell. The aonu!us is either veoted or ticd ioto the well's Oowlíne, so that as much gas as pos,sible is scparated from the liquid befare it cnters Ihe pump, In sorne cases, a centrífugal separator will be placed between the pump and molar for obtaining maximuro gas-liquid separation_ Sorne manufacturers claim up to 90 perccnt gas separalion with a downhole separator. A schemalic of a wel! equipped with a submersible pump is. given in Figure 5-25, along with the pressure traverse ín lhe wetl. An iltustration of a typical pump assembly is presenled in Figures 5-26 and 5-27. To perforrn a nodal anaiysis on a submersiblc pumping well, the node is seleCled al lhe pump. The pllmp can be handled as .
sure gain [hat lhe pump must genefilte for a porticulal producing rate is ~:: POli - PUl" Th.cse pressurcs and thcil locations are illustrated in Figure 5-25. lile prcssure tra· verse below Ihe pump \Viii be calculated bas<:d on the formation gas/liquid ratio and the casing sizc. Thc Iraversl..' in tlle tubing above the pump \ViII be bascJ on the ga~ /¡iquid ratio cntering the pump and th~ tubing size. If 1l( information is a\'ailable regarding the amount of g:l5 sep· arated, it may be 3SSUlllCd to be about 50 pcrcent. Tilo.: inllow and out no\\" expressions are: Injlow
PR -
t'1¡J n'.~
-
óP c.
OlltflOlt' P
+ CJp jlolt"lil1f + I1pfub (above pump) ::::
P tllI
lhe foltowing procedure may be uscd to cslim~lte t!lo.: pressure gain and power required 10 achicvc a particula; producing capacit)'. Injlow
1.
Sclcct a value for Iiquid producing rate qL-
2.
Detennine the requiredpllffor this qL using the reservoir performance procedures described in Chapter 2.
3.
Detennine the pump suction pressure PIlP using the casing diameter and the total producing GLR to calculare the pressure drop below the pump.
4.
Repeat for a range of liqllid prodllcing rates and plo: P'lp VS. qL as íIlustrated in Figure 5~28.
Dutflow l.
Select a value for qL'
2.
Determine the appropriate GLR for tubing and flowtine pressure drop ~alculations.
,
Artijicial Liji Design
175
=
GAS PRESSURE AT DEP.TH FOR GAS GRAVITY 0.65, TEMPERATURE OF GAS AT SURFACE AHD TEMPERATURE AT DEPTH. 7O'f. t U'f. PER 100 Fr. Of DEPTH
=lOO'f.
.00
,so u ;;; L
!
'00
~
6SO
~
u
'" " ~ ~
600
~
...
'" ~
~
'SO
"::: ~
~
L
500
:¡ u
z
o
'"
¡:: u ~
!
'00
35.
lOO lOO
35.
.00
'"
500
SSO
600·
650
700
150
SOO
aso
900
950
1000
\050
1100
IHJECTIOH GÁ1 PRESSURE AT DEPTH (P",) IN PSIG
Fig. 5-19. Copyright. Carneo /ncorporaled. Reprinted with pennission.
a.
b. c.
d.
Determine Pllp and fluid temperature al the pump al this qL value from inflow calculations. . De~~nnine dissolved gas Rs • al this pressure and lemperature. Estimate fraction of free gas Es. separated at lhe pump. This wil1 be dependent on whether or not a downhole separatar is lo be used. If not, use E, = 0.5. Calculate the GLR downstream of the pump from GLR dn = (1 - E,)(R'~al- laR,)
where RIO/(J/
R,
l. 3.
total producing gas/liquid ratio, solution gas/oil ratio at suction conditions, and fraction of oil flowing.
Determine Pd" using GLRdfl to calculate the pressure drop in the tubing and the flowline if the casinghead gas is vented. If the casing is tied into the flowline,
lhe total GLR will be uscd to detennine lhe presiurc drop in the flowline. 4.
Repeal for a range of qL and plot PcJ" vs. qL on lhe same graph.
5.
Select various producing rates and determine the pressure gain óp required lo achieve an intersection of the inflow and outtlow curves at these rates. The suction and discharge pressures can also be delermined for each rate.
6.
Calculate tbe power requirement, pump .size, number of stages, etc., al each producing rateo
The required horsepower may be calculated from HP = 1.72 X 10.5 f1p(q oB, + q"B w) where HP f1p
horsepower required, pressure gain, psi,
176
Producliem Oplimizafirm Usillg
Nodal AI/a~\'sis
-.,-:~~;:
~
'"
..
-
...
.....
".-~ "'1'11:-
..•...
"
;~Is:· ·~i:/
.
CHOKE CAPACITY SQUAñE EOGE ORlflCE oft,nct
It:[
CHOKE CAPACITY
..
SQUARE EDGE eRlnCE _ ORlflcr S'Z(
;¡;
OOWH'3TREJl.l
, .:; ~bQ
X
PRESSUR!
PSIO
Jo
10<:.0
Jo
l'
Fig. 5-20. (Courlesy oas Engineering, Dalias, Texas.)
q, q" Sn
oil rale, STB day, water rate, STB/day,
oil formation yolume factor al suction
condilions, bbIlSTB, and
B.....
,"
i
,,~
water fonnation volume factor al slIcfion
condilions, bbIlSTB. The pressure gain can be converted to head gain if nec-
essary for pump selection. This is accomplishcd by dividing lhe pressure gain by the density of the fluid being pumped. The actual plotting of Ihe data is nol required if the pump is lo be sclected for specific rates, as all the necessary information is calculated befare plotting.
Other variables that could be analyzed using systems analysis include pump sctting dcpth, effect of a down-
!lH'
1_._'_ _~
:=
_
-.-. -"_._-
Fig. 5-21. (Courlesy oas Engineering, Dalias, Texas.)
is lo produce at a total iiquid rate of 3000 STBlI day.
PR = 3482 psig Oepth to mid-perfs = 10,000 ft R tota/ = 400 scf/STBL QL(max)= 16810 STBlIday Yg = 0.65 Yw = 1.07
Pb = 3600 psig Pwh
= 400 psig
=
fw 0.5 Tpump = 200°F Yo = 35" API
So/ution: The required Pwr lo inflow 3000 STBlIday ise Pwr = 3482 [(1.266
1.25(3000) JO.5 -0.125] 16810
=3120psig
hole separator and pump speed. Example 5·3:
Using the vertical pressure traverse curve for flow in the casing, entering at a pressure of 3120 psig on the 400
GLR line and moving upward 3000 ft gives a pump suction pressure 01 about 2040 psig. Use Equation 3-76 to
The well described in Example 4-1 is to be equipped with an ESP set at a depth of 7000 ft lrom the surlace. Assume that the 2-7/8 (2.441) in. tubing is run to 7000 ft and Ihat the casing ID. below the pump is 6.366 in. If
determine R s at suction conditions:
one-half af the free gas is separated at the pump, determine the horsepower and head gain required if the well
+ 460)) = 352 scflSTBO
Rs = 0.0178(0.65)(2054.7)1.187 EXP[23.931 (35)/(200
Anificia/ Lifi Design
177
"-'-'00
..00
Fig. 5-22. (Courtesy Olis Engineering. Dalias, Texas.) .
Calculale lhe gas whlch wlll go !hrough lhe pump and lhe lubing. GLR dn :
Fig. 5-23. (Courtesy O/is Engineering. Dalias. Texas.)
PL
~
P",o + P./w
PL
~
55.9 - - ~ 0.388 psilfl 144
GLRdn~(1-E,)(R'o'al- foR,)~(1 - 0.5)(400 - 0.5(352)) ~
112 scf/STBL
GLRdn~ 112 scflSTBL Using the vertical pressure traversa CUNe for flow in 2.441 ID. lublng al a rale 01 3000 STBUday and fw~0.5. enler al Pwh ~ 400 psig and using lhe GLR ~ 100 line. find lhe pump discharge pressure lo be approximalely 3200 pslg al 7000 fl. The required pressure galn across lhe pmp is !herefore lIp~3200-2040 = 1160 psi. Calculale Bo for Rs ~ 352 scUSTBO al 200°F: From Equalion 3-79:
Bo~1.0 + 4.67 x 10-4 (352) + 1.1 X 10.5 (200 X 10.9
. (200 - 60)(352)(35/0.65)
60)(35/0.65) + 1.337 Bo ~ 1.251 bbllSTB Assume Bw = 1.0 Use Equalion 3-60 lo calculale !he bil densily: 350(0.845) + 0.0764(0.65X352) 5.615(1.251)
Po ~ Po = 451bmlfl'
~ 45(0.5) + 62.4(1.07)(0.5) ~ 55.91bmlft'
HP ~ 1.72 x10·5 /1p(q o Bo +qwBw) HP ~ 1.72 x10· (1160)[1500(1.251) + 1500(1.0)] ~ 67hp 5
. 1160psi Head galn ~ = 2990 fl 0.388 psilfl
IV. SUCKER ROD OR BEAM PUMPING Although nodal syslcms analysis is nol as widely applied lo lhe analysis of welis equipped wilh sucker rod pumps, lhe effects of pump selting deplh or liquid level can be detennined using this method. AIso if the casing annulus is tied into the well's fiowline, the producing cate will have a direct effect 00 casing pressure and thus bot~ tomhole "f1owing pressure. Sucker red pumping is the most widely used artificial ¡ift melhod. Thal is, more artificiallift welis are equipped
Proe/ucriOll Oprimizathm c.;sillg Noe/al AII,}.''''.ds
Pump
..i-rl \=-:Q
.....
Ji,oo':*'"'-
Impe11 ers
iCc¡JHI-
Separator '-,.-'-L
7+
'~!~.~~_-::::::2~,-;':':':'
'~ ,~~i=~~0Z
~
J-
Pump-To-Separator Shafl Coupling
Motor
':',
~'~
,?
Separator Shall
'::=':2100 ': :~:~.~.-.:.:;- .-:-.' ';T" ----:-'-+:::r... -~-_. 1/ll:Xl
~~.-
Fig. 5-26. Submersible pump assemb/y
Fig. 5-24. (Courles)' Olis Engineering, Daltas, Texas.)
with rod pumps than any othcr type of artificial ¡ift method. This does not mean that more oil is produced by rl.-1d pumping, since rnany rod-pumpcd wells produce at \ ery lo\\' rates. A d:scussion of the relati\'e popularity of Ihe various methods can be found in 8ro,,"0.\
A suckcr rod pump is a posltlve displaccment pmnp. ílnd Ihus thc prcssure drop in the tubing docs not alTe.:'1 Ihe bottomholc flowillg prcssurc. Howe\·cr. Pul is al';";,'.:':ed by the surfacc ca50ing pressurc, the pump sctting dt'rth ano the working liquid level, usually referred to as rhe fluid Icve!. A schemaric of a rod-pumpcd wel! and the corresponding tran~'rse are shown in Figures 5-29 and 5· 30. A more detailed representation of the pump and the operating scqucnce is shown in Figurc 5-31. A method for
TRANSFORMERS MOTOR CONTROLLER ..~
AMP METER ~,¡",,+,.
Pressure
WELL HEAO
SURFACE/ CABLE
Gas.......---=
:: DRAIN VALVE
VENTBOX ,:~
TUBING
SPLlCE
.c
o. o" , P"p
Fig. 5-25. Submersible pump schemalic.
.',',
"
I
=
MOTOR FLAT
CASING
I
HECK VALVE
CABLE
.:¡. Pwf
Fig. 5-27. Submersible pump installalion.
PUMP
INTAKE SEAL SECTION
MOTOR
.• 179
Artificial Lift Design
---
1 -...
I
~
"
dO
.............
qL-
s.<..,
,""
1;
WorlU"l
bo."
ar.d Iintf
'O
""p",
_o-°,
Flg. 5-28. Submerslble pump seleelion.
Beam Counterbalance
J.
J.
Tubil'll: p~
lb)
(4)
Walking Beam
Horsehead
Id>
(,)
(a) Plunger moving (b) Plunger moving (e) Plunger moving (d) Plunger moYing
down, near bottom af stroke; up, near bottom of stroke; up, near top of stroke; down, near lop ot stroke.
Fig. 5-31. The pumping eyeie. Prime Mover
m~asuring the fluid level in a wdl is illu$(rated and described in Figures 5-32 and 5-33. ]fthe nade pressure sclected is Ph{lhc illflm\' and autnow expressions fol' ~ well which is Qc:ing rod pumped
Crank Counterbalance
are:
Sud',er Rods
Inflo\\'
Tr::veling
Valve
PR
Sub-Surface
~ ó.Pm· = PHI
Pump Standing _____ Valve"""Slylus Recorder
Fluid Level
Tubing Collar Reflections
Electrical Connections
Fig. 5-29. Beam pumping unil.
,~::::::::;:~1<~;;:;:;
" ,
~
Pe
,,
Pressure
~
Recording Scroll Explosiva Charge Oetonator and Receiver
Gas Column
Gas
----Oil
~---011 &
Fluid Level
---~---------
.c
15. Q)
Gas-Liquid Interface
"
O liquid (Oil, Water, ar bOlh) Calumn
Pump Deplh
------ -------------
t---
Wate
Pwf
Ftg. 5-30. Rod pumpmg wel/.
PR
Fig. 5-32. Measuring wetl fluid levet.
P/"oc/"criol1 Opfimiza/ion USiflg Noda{ Af/o!ysis
180
culate Ihe prcssure changc in the ¡iquid calumn.
Deep Collars Aeeenled Upper Collars (For Greater Aeeuracy in Deep Wells) Aecenled
Liquid Level Aeeenled
Shol
Shol 4
4
8
8
12
12
16
16
20 24 28 Fluid Level
Thcrcforc, Ihe prcssurc c
r
Liquid Level
1
28 Fluid Level
P"I Ca/euforian. P/lmping Well Thc following nOll1cllclalurc will be used in prcscnting a procedurc for cakulating ""f: Pe surf
Fig. 5-33. Reflecfions of sound waves.
t.
Measure Pe and fluid level DF , Calculate Pr using tlle gas weiglH rroll1
P,..
= r.EXP(O.01875¡, J),..i
This will be tri,11 and error, sinec 'p,. + 6.JI~'J.< - ..1p(nuid abo\"c pUlllpl - óp(nuid bo:low pump) = P,,:'
,
+
¡)"Pflúw/ill('
+
I1pJ:
Z =.!((PF + P, 1 2),
CalculatePr.1f!hc \\'ell is putllped down, that is i[D r =: D", t!len fJf-'
¡J¡ ; :
Casing fied ;Jlro jlO\\'lilll.' flH'P
TZ
p.: ;;:: Pr + Pog(D,,- D r ) -:-
.1plabo"c pUlllp) +
To determine P"li!: Estimate p,,-=: 0.433 y" Estimate F*x =: 0.95 c. Calculate P*",-, = p,,~>; d. Ca1culate P*fJ~= PF + PtJ./ (D" - DF ) e. Calcula,e Ji = (1'''' + l' ',,)0.5 f. Determine R" Ba aud p" al D. f g. Calculate Fy = q!a(p)(J.J, alld find F x from Figure 5-34. h. Compare F.l and F*x' lf not clase, sct F*.l "" Fx and go to step C, Continuc ul1til Fx =F*.l'
"p(bclo", pump) = P"l
a. b.
The prcssure drop in the gas is lIsual1y calculatcd l1sing [he hydrostalic pressure only and may be ca1culated using equations givcn in Chapter 3. lhe fluid aboye the pump will usually be oil ollly with gas bubbJing through it. The !luid bela\\' the pump will be ti mixture of oil, water and gas if !he well is producing an)' water. In mast cases, any
pressure drop duc to friction is ignored since the fluid will usually be moving at a lo\\' velocity in fhe casing bclow the pump. The effcel on lhe density of the fluid of the gas bubbling through lhe fluid and escaping ¡nto the annulus can be cstimalcd using an empírical curve prescnted by
Gilbcrt. 2 This is often refcrred to as Gilbcrt's "S" curve and is shown in Figure 5-34. The gas rate q in the group of tcrms on the vertical axis is lhe amaunt of gas bubbling tilrough a caIumn of ¡iquid occupying an area A. The pressure in this group of lcrms is lhe average prcssure in the liquid calumn. The liquid hydrostatic gradient tS multiplicd by F , and uscd to col-
4
Calculate P"i= Pp + PLg(D'''''l- D,,),
wl1cre
PI.Fe Po(l - /".)
+ p"./".
A value for Fx is found iteratively using the procedure described in Slep 3. Thc two-phase flow mcthods may a150 be tlsed to find P.. .¡ by assuming a \'ery low Iiquid flow rate in the fluid column aboye the pump.
A,.¡!ficial L!fi Design
181
10 ANNULUS GRADIENT CORRECTION FOR BUBBlING THROUGH STATIC lIQUID COLUMN
A - in 2 q - Mscf ID P - psia O.!:>
F =-qy
ApoA
0;/
O.~
0.01
O.OO!:>
J
Fig. 5-34. Gradienl correction factor, Fx'
I
'
..2
.3
.4'
.!:> .6 .7 .8 GRADIENT CORRECTION FACTOR,
.9
FX
1.0
182
ProdllClicl1I Oplimizaliol1 Using Nodal Ano::, sis
PIl .• Ca{ClI{Or;Ofl, Shur-il1 H'elf
\\'hen the \Vell is shut in, no gas will be bubbling through Ihe liquid, and, Ihcrcforc, F". will not be requircd. Howc\'cr, R.f
2. Eslimale Z' = 0.9
PF = 134.7 EXP (0.01 875(.7)(6000)1(595) Z'] PF = 134.7 EXP (0.132IZ') = 134.7 EXP(0.13210.9) PF = 156psia p =(134.7+156)0.5=145.4 Al P = 145.4 and f = 595, Z = 0.98 PF = 134.7EXP(0.1321.98) = 154 psia
p = (134.7+154)0.5 = 144.4, Z = 0.98 Z, PF = 154 psia = 139 psig
Since Z' =
Mcasure Pe and F L · C<1Iculate PF'
"'O
3. Calculale Pp
Calculate the rn.;ssure at the oil-waler interface, p" =
PF -:...
p,,(D m ,·
-
:
Yo =141.51(131.5+37)=0.84 a. Po' = 0.433(.84) = 0.364 psilfl
DF)
b. Eslimale F. = 0.95
ro df!lermil1e P,,:
'0.(.
c. Po; = 0.354(.95) = 0.345
Estimate p* v = OA33 Yo Cí'l\culatep*u,=PF+ p"'o{DoÓ\ -D F) Calculate p = O,S(PF + p*,..) Caleu Iate R." B{l" and Po at p, f Compare Pv and p* O' If not close, set p* n11l..\ go lo Stcp h. Rcpeat lInlil Po == p* (1'
a. b. c. d. r.
d. Pp ' = 139+ 0.345(6200 -60001 = 208 psig e.
(1
=
Po
f. R, = 25 scfiSTB, So = 1.081 _ 350(.84) + .0764(.7)(25) = J8.651blfl'
Po 5.515(1.081) Po = 0.338 psilft
Cnlculate P"'-I p", = jJ"
-
p,,(DI"":l-
p = (139 + 208)0.5 = 173.5 psi, = 188.2 psia f = (187 + 170)0.5 = 179°F = 639'R
D,,,J
g.
A=~(4.95'-2.375')=14.8ic: 4
\\ here
p"
_q_ =
F =
0.433 YIl"
Ap'"
y
The depth lO lhe oil-water intcrfaci: canno! be measurrd. bUI it can be calculated by using the pumping and sl,Hic fluid levels and Ihe producing waler fraction. The equ<Jtion is
25.2
-
e 21
14.8(188.2)-'
F. = 0.68 (Figure 5.34) h. Fx "# F"X .., therefore, F"X * = 0.68 P",,' = 0.338(.68) = 0.230
Pp ' = 139+.230(200) = 185
P = (139 + 185)(0.5) = 162 psig =176.7 psia R, = 24, S, = 1.081, Po = 0.338
where DFl'
pumping fluid level,
F = -q- = 0.21
D,..s = shut-in fluid level, tubing outside diameter. nntl dT casing inside diamcter d,.
F. = 0.68
Since Fx = Fx ",convergence is attained, Iherefo re. Pp = 185psig
Example 5-4: Using the following data, calculate the flowing bottomhale pressure for this welL qo = 70 STBlday Op = 6200 ft d T = 2.375 in. API = 37" TR = 187"F 'Iw = 1.0 qg = 25.2 Mscfd
ApO.4
y
Op,n = 7350 ft
qw = 83 STBlday de = 4.95 in. Yg = 0.7 Tp = 170'F Ts = 100'F
4. Calculate Pwr : f" = qwl(qw + qo) = 831(83 + 70) = 0.54 a. PL = 0.433(.54) + 0.338(.46) = 0.389 psilft b. Estimale F. ' = 0.68 C. PLg
= 0.389(.68) = 0.265
d. Pwr' = 185+ 0.265(7350 - 6200) = 489 psig e.
p = (185 + 489)0.5 = 337 psig = 352 psi a
f. Assume change in Po is negligible
So/ution:
g. A
=~(4.95)' 4
1. Pe =120+14.7 = 134.7psia,OF = 6000ft
:
=1g.2in'
Artificial Lifl Desigll
183
Shut Off and Bleed paWER alL UNE
L---
Pump In
Operate
Jfn.
Jfn.
(j
([
FLOW UNE
Pump Out
;fu
Engine _ _ Pistan
Pump 1 - - - Pistan ---IHI;:C
STANDING VALVE CLOSED
Down Stroke
Up Stroke
Fy
~
0.21
Since Fx ~
;1.
25.2
Pwt
~0.13
F,
~
19.2(352)°4 0.74
FII.
::t.
Fx ~,fherefore, sel Fx * = 0.74
p"
~
y
VALVE
GLOSED
~
F,
~
0.74
=Fx ., convergence is attained, therefo re,
516 psig
Anorher artificial lin mcthod that cmploys a posi¡i\"c displaccment pump is the hydLHllic pumping s)'.::aem. In
p.I·~516
this system, the powcr is transmÍtlcd lo a subsurface
P~ 351 psig ~ 365 psia
hydraulic motor that is coupled lo a pump similar to a
Power OilTank Stock Tanks
Triplex PLlffip and Prime Mover
-_.""
,uuo
<:> .......•..... ~••• ·O"
Bottom Hole Hydraulic Pump
Fig. 5-36. Hydraufic fiti syslem.
STANDING
V. HYDRAULlC PUMPING
0.389(.74) ~ 0.288
Bool
STANDING VALVE OPEN
Fig. 5-37. /nslalling and reldeving Ihe pump.
Fig. 5-35. Pump and engine 8ssemb/y.
F
STANDING VALVE GLaSEO
sucker rod pump. The power is transmittcd by hydraulic or power fluid that is pumped (rom lhe surface down an extra string of tubing. If the gas from a hydraulically pumped well is vented, the systems analysis would be identical to tha! for a rod-pumped well. A schematic of the pump and motor assembly is illustratcd in Figure 535. The power fluid system is shown in Figure 5-36 and the merhad used far inslalling and retrievlng lhe pump without the use of extra equipment is illustraled in Figure 5-37.
VI. SUMMARY A fcw of the mast widely used artificial methods were discussedJ and the application of systems analysis to the design of sorne of these methods \vas illustrated. Many ather methods exist for decreasing the flowing bottomhole pressure in a well to increase its producing ratt:. Some of these are plunger lin, intermittent gas lift, jet pumping, and hydraulically powered centrifugnl pump. Many of these methods are discusscd in Refcrence l. Regardless ofthe methods used to move the fluids from the wellbore to the separator, an analysis that considers
TABLE 5-5
Relative Advantages of Artifi~ial Lift Systems S. G. Gibbs -Nabla Corporation Rod Pumping
'Relatively simple syslem designo 'Unils easHy changed lo other wells with minimum casI. 'Efflcient, simple, and easy for fietó pea pIe to opera te. "Applicable lo slim hales and multiple completions. 'Can pump a well down lo very low pressure (deplh and ra!e dependenl). 'System usual1y is na tu rally vented tor gas separalion and nuid level soundings. "Flexible-can malch displacemenl rate lo well capabilily as weH declines. "Analyzable. 'Can Iift high temperature and viscous oils. 'Can use gas or eleclricily as power source. 'Corrosian and scale trealments easy to periorm. 'Applicable to pump-ofr control if electrified. •Availabitity of differenl sizes.
Hydr8ulic Pumping
'Nol so depth limited-can Iift large volumes from great depths (500 BPD (rom 15000 ft.). Have been inslalled lo 18000 ft. 'Crooked hales present minima1 problem. "Unoblrusive in urban locations. "Power source can be remolely located. ·Analyzable. "Flexible--can usually match displacement to well's capability as well declines. "Can use gas or electridty as power source. 'Oownhole pumps can be circulated out in free systems. 'Can pump a well down lo faírly low pressure. 'App!icable to mulfiple complelions. "Applicable offshore. 'Closed system will combat corrosion .
Gas Uft
Electri.c Submersible Pumping
"Can Ii« extremely high volumes {20000 BPO'" in shallow wells with large casing. Currenlly lifHng ±120,OOO BID from water supply wel1s in Míddre East wilh 600 HP unils. "Unoblrusive in urban locations. "Simple to operate. "Easy to instal! downhole pressure sensor for lelemetering pressure lo suriace via cable. 'Crooked holes presenl no problem. 'Applicable offshore. "Corrosion and scale lreatment easy to perform. "Availability in different sizes. 'Ufl.ing cost for high volumes general1y very low.
"Can handle largo volum€ of solids with minar problells. "Handles large volume in high PI. ,...'e1ls (conlinuous ]::'t) (50000 BLPD+). "Fairly flexible---convertible from continuous lo intermilte·ll to chamber or plunger fift as wel1 declines. 'UnobLrusive in urban loca:50ns. "Power source can be remotely localed. "Easy to obtaín downhole pressures and gradien:s. "Ufting gassy wells is no problem. "'Sometimes servicable \'':~h wireline uni!. "Crooked holes presenl ro:) problem excepl ror relrieving and running valves by wire line. "Corrosion IS not usually as adverse. "Appliezble offshore.
Relative Disadvantages of Artificial Uft Systems S, G. Gibbs -Nabla Corporation Rod Pvmping
"Obtrusive in urban locaHons. "Heavy and bulky in offshore operations. "Susceptible to paraffin problems. "Tubing cannot be inlernal1y coated ror corrosíon. 'Crooked hales present a friction problem. 'High solids production is troublesome. "Gassy wells usual1y lower v01umelric eflkiency. 'ls depth limited. primarily due to rod capabilily.
Hydraufic Pumping
'Nol easy for field personnel to Iroubleshoot. 'Difficurt lo oblain valid well lests in low volume welfs. 'Requires two strings of lubing lor sorne installations. 'Problemsin lrealing power water where used. "Power oi! systems are fire hazard. "Large oil lnventory required in power oil syslem which detracls from profitability. "Hígh solids production is troublesome. "Operaling costs are sometimes higher. "Unusually susceptible to gas interference; usuafly not vented. ·Vented inslal1ations are more expensive beca use of exlra lubing required. *Treating for scale below packer is difficult.
Gas Lift
Electric Submersible Pumping
'System is depth limiled (10,000 ft.±) due to cable cost and inability to instal! enough power downhole. 'Gas and solids produclion are troublesome. "Not easily analyzable unless good engineering -knOW M
how.~
'Lack of production rate nexibmty. 'Casing size limltation. 'Should not be sel below fluid enlry. "No! applicable lo multiple comptetions. "Onty appficable wilh elec\ric power. 'High vottages (1000V±) are necessary. "Impraclical in low volume wells and in welfs wilh deep lift. "Expensive lo change equipment lo match declining well capability. "Cable causes problems in handling tubulars. 'Cables deteriorate in high temperatures.
gas is no\ always aya :able. 'Not efflcienl in lihing small fields or one-wellleases. 'Oifficult to Uf! emulsions and viscous crudes. "'Not efficient for sOlall fields or one-wel1 leases ir compression equipment is required. "Gas rreezing and hydrale problems. "Problems with dirty suriace Hnes. "Difficulty in relrieving valves in highly deviated wells. ~lifl
Artificial Liji Des/gn the components of the system as completely separate and unrelated entities cannot adequately describe the total
185
published by Gibbs.'
system. Total system oc nodal analysis is necessary to
VII. REFERENCES
optimize the performance of any oil- oc gas-producing
well. lhe choice of the type of artifieiallift system for a well or field depends on many faetors, sueh as well depth, availability of gas, production rates required. hale de vi ation. etc. Some of (he relative advantages and disadvantages of the vacious methods are lisle:d in Table 5-5, as
1. 2.
3.
Brown, K. E.: The Technology 01 Artificial Liji Methods, Vol. 2, PennWell Pub!. Co., Tulsa, Okla., 1980. Gibbs S. 0.: "Predieting the Behavior of Sueker Rod Pumping Systems," lPT, July, 1963. Gas Liji, Book 6 of the Vocational Training Series, American Petroleum Institute, Dalias, Texas, 1984.
'. Nomenclature
Dimensions
A
Bg B" Bol>
B,
area gas fonnation volume faclOf
L2
oH fOn113lion volume factor
}¡
oil fonnation vol lIme faClOr al bubble-point condilions total (two-phasc) fomlalion
H
vaJume factor
B., Cl
cg c" cP' c".
C C
CL d D
E E,
f f fll' F F,o g
g,
e
water fornution volume factor formalion (rock) compressibility gas compressibility Dil compressibility pseudoreduced compressibility water compressibility coefficient of gas-well backprc:ssure curve conccllIration condensate or natural gas liquids content diameter depth efficiency volumetric efficiency fraction fr¡ctioo factor producing water fraetion force instantaneolls producing wateroil ratio acceleralion of gravity conversion factor in Newtoo's Second Law of Motian total inilial gas in place in reservoir
Dimensions
el' l1ep
L/2/m
Lt21m Lrl /m LJ-ln¡-lnlm 2/
HL Hg J(PI) J,
k kg ko k kro
'"
various
krll' kw
valious L L
K /11
log L In In
NI 11
mLlI] 11
I/j
Lit'
N N
mLlFl'
N;..
LJ
p
I1Np
cumulati\"e gas produced gas produced during 3n ¡nterval lhickness (general and individual bed) enthalpy (always wilh ph3:iC or syslem subscripls) liquid holdup gas void fractian
producti\"iry index specific productivity index absolute penneability effeclive permeability to gas
efTective permeability
lo
oil
relative permeability to gas relative penneability lo oil relative penneability to waler effective penneability to water equilibrium ratio (y!.<) naturallogarithm, base e cornmon logarithm. base 10 length . mass slope " molecular weight exponent afback-pressure curve, gas lI'ell total moles moles af component j initial oil in place in reservo ir cumulative oil produced Reynolds number oH produced during"an interval pressure
V V L
mU/,]
[411m
Vllm L' L' L'
L'
L m various 11/
V V
Ll miL"
187
Productivll Optimi::atioll U5ilig Yodo/
188
Oimcnsions
P" p¡,
Pe P'l Pes Pd
PD PI?
Pi Pr< fJl'r
p, Ps c
Psp P,,·h PI.< p,.. Pu/
Pul< PU'J
P PR p,.
q % fJ.>:
q" q" r
r"r, r., r" r""1
R R Rp R, R,b
Rsi R~.
s
S S, S,e
SI7 SL
S,
atmosphcric pressure bubblcpoint (saturation) prcssu.-~ crilic;:¡1 prcssure casing prcssure, flowing casing prc55ure, static dcwpoillt prcssure d;mcnsion!css pressurc external boulluary preSSllre initial prcssure pseudoeritical pressure pseudorcduecd prcssure reduccd prcssurc prcssUfc, standard conditions separator prcssure tubing pressurc. tlowing lubing prcssure. static bottomholc pressurc, general boltomhole pressurc, flowing bO(lOmhole prcssure, sandface bottomhole pressure, static average pressure pressure, rescryoir average capillary prcssurc productiol\ rate or no\V rate dimcns;onless production rale g
m/Lt2 m/U2 m/U2 111/U2 m/U2 mlU2 m/U2 111/[(2 m/Lt2
DimcnsiQlls Sur
S". Sw.< t
'vt, T Te Tr Tpe Tpr
111/L12 m/Lt2 m/Lt2 m/Lt2 m/Lt2 m/L{1 m/L12 I1I/Lt2 I1I/LI2 m/Lt2 m/L(1
VII
T, TR
T.
" "V
,
V
I-·~) 1\'
JI'
11' IV
IV,.
VI, VII VII L L L
rc.c;idllal oil saturation water salur;:¡tion crilieal water saturalion lime dimensionlcss time time for stabilization of a \\'cll temperalure critical lcmpcrature fonnation tcmperaturc pscudoeritical temperature pscudoredueed temperature rcduccd temperature rcservoir tempcrature tcmperature, slandard condilions spccific VOl\l111C veladty valume bulk volume pore vo/ume mass flow rate ínitial water in place in rcscryoir water (always with identifying subseripts) work cUITIulative water ¡nflux
(encroachment) JI~ LlIV, ¡\/J~
x
L L
.1'
L
z
Z mUll'T
A'll/~l'sis
ex y
Y, Yo 1,," LI 8
Ag AL Jl Jl, Jl, Jl..
cumtJlati\·c wa!~r produced water ¡n flux (cncroachment) during an interval water produced during an interval mole fraction of a component in liquid phase mole fmetion of a componcnt in vapor phase gas dcviation faeror (eompressibility factor, z ~ pVlnRI) elevation referred to datul11 alpha angle gamma speeifie gravity gamma gas specific gravity gamma oil specific graviry gamma water specífic gravit)o delta differenee theta angle lambda gas void fraction (no-slip) lambda liquid holdup (no-slip) mu viscosity mu gas viscosity mu oil viscosity mu water viscosity
I
T T T T
T T V/m
UI
mIl
LJ various mL2/t~
l.)
V I.'
V
L
miLi miLi miLi m/LI
Artificial lifi Design
189 Dim~nsions
Dimensions
P PL
p. Po
rha rha rha rha
density liquid density gas density ail density
mil' mil' mil' mil'
P"
cr
rha
water densit)'
sigma
(interfacial tension)
phi
mil'
surface tension
porosity
m/P
Two-phase Flow Correlation Examples Hagedorn and Brown Method
Appendix
A
The Hagedom and Brown method. ignoring acceleration, requircs solution of Eguatían 3-16 foc each increment inlo which lhe well is divided. .
,
dI' g (Pilleas,!, "')+ -,._'/p,l',;, -;::::-
(A-I) dh gc _g,.d Empirical corrclalions are pre5~nted fOf dClem1ining lhe mixture dcnsilY, Pm and lhe friction factor f The p3rameters in Equatioll A-l are detined by
PL HL + pi l - }JL), liquid density, gas density liquid holdup (fraelion ofpipe oeeupied by liquid), angle of well Oc segment [ram vertical,
Pm PL Pg HL
'P
Detennination ol' H L requires use of three empiricaJ correlations. These are prescnted in Fig. 3-15a) b. and c. To detemline H L from these figures, the following dimL'nsionless numbers must be evaluated from kno\Vl1 dat3: N/y
Ng \.
NJ NL where O" = gas~liqll¡d surface tension. These equations are valid for any consistent set of units. For field units, the equations are
+
V~L V sg ' . superficialliquid
\1 m \l
JlL = liquid viscosity, Jl g == gas viscosity.
vclocity =: qdAp. superficial gas velociry = q/Ap • arca of flow string now , string I.D.,
sL
v sg
Ap d
PI
p,;/Pm PLAL + Pg (1 - AL)'
P" :=
where
v~L/vn,.
l1SL.
vsg PL
a
The frielioo factor is calculated using the Jain equation oc found from the Moody diagram using the pipe relative roughness and thc l'ollowing Reynolds number:
d
l'L
ftlsee, lbm/eu ft, dynes/em ft, ccntipoise.
The procedure for finding H L is:
where
Jlm
1.
Caleulale N,
2.
Find CN, from Fig. 3-15a
3.
Calculate
/9/
Prvducrioll Optimizotion Usil1g Nodo! Anc:ysis
192
Determine HL
l. NL = 0.0024 2. From Flg.3-15a, eN, =0.002
whcre jJ" == base prcssurc (14.7 psia)
-
3. 4.
Find
-
11.52(0.002)(1500)°·1 42.56(69.14)0.575(14.7)0.1
7.53 x 10'; =
4. FromFig.3-15b, H, 1 '11=0.29
H /. from Fig. 3 -15b.
'V
5.
~H
Calculate
'1
¡.l.'"
NO. 38 L
,"
N"2.1
6.
Find 'V from Fig. 3-15c
7.
Calculatc H,. ~ 'V(H,/'Vl
5. X'V
69.14 (0.0024)°·38 = 2.28 x10" (42.56)"" 6. FromFig.3-15c, 'i'=1.0
7. H, =1.0(0.29)=0.29
Pm = 50 (0.29) + 8 (1-.29)= 20.181blfl' P, =(14)"20.18=9.71 Iblft' ~m = (0.45)°29(0.012)t 1- O '9) = 0.034 cp
N
A constraint
011
liquid holdup is H L ~ AL-
ance H L is determincd, "'Re rmd 111m/can be calculated. The pressurc gradicnt can then be calculated. This is Stcp 5 in lhe Proccdure for Calculating a Pressurc Travcrsc that \Vas pr~scl1ted c2.i1ier. AH the fluid
propcrties and yelocitics used in the 2.bovc cquations are cn.luatcd al lhe ;'1'..,crage prcssurc é1nd temperature in the tubing incrcmcnL
- 1488(14)(35)(0.249) = 5.29x10' 0.034
Rem
~ = 0.0072 = 0.0024 d
2.992
From Fig. 3-5 or Eq. 3-15 f = 0.025 dp =20.18+ 0.025(9.71)(35)' = 20.18+18.5-' dh 2 (32.2)(0.249) dp = 38. 721blft' = 0.269 poilft
dh
Beggs and Brin Method
Example A-1: During the calculation of a preSSl!~e traverse in a gas well producing Iiquid, the following condHions were
determined at lhe average pressure and temperature in the pipe incremento p = 1500 psia Vsg = 30 ftIsec f = 180 °F vsL = 5 ftlsec d = 2.992 in. E = 0.0006 ft ~g = 0.012 cp pL = 50 Ibm/cu ft ~L = 0.45 cp Pg = 8 Ibm/cu ft <J 25 dynes/cm
=
Using the Hagedorn and Brown method, determine the pressure gradient.
Solution: Befare finding H L and t, some preliminary calculations are made: v m = vsL + v sg ::: 5 + 30 = 35 ftlsec AL = 5/35 = 0.143 Pn = 50 (0.143) + 8 (1 - 0.143) = 14 Iblft 3 Ap = mf214 = 0.7854 (0.249)2 = 0.0487 ft2 PLlo 50/25 2 NLv = 1.938 (5) (2)·25 = 11.52 N gv o 1.928 (30) (2)·25 = 69.14 N d = 120.872 (0.249) (2)·5 = 42.56 N L = 0.15726 (0.45) [1/(50) (25)3].25 = 0.0024
=
=
The Bcggs and Brill mcthod requircs Ihe dCh.'nni:L<.lI.ion of lhe no\V pattt:rn that \Vould exist in lhe pipeline if the pipe wcre horizontaL Differcnl' cquations are uscd 1:0 calculate liquid holdup for caeh flow pattern. Thc no\\" patterns defincd are shown in Fig. ]·19. Dctermination of the correct no\\' regimc rcquir~:-; calculating severa! dimensionlcss numbcrs. inc1mling J tWDphase Fronde number. The foflowing variables are used to determine which now rcgime wouId exist if the pipe \\'ere in a horizontal position. This Oo\\' rcgime is a corrclating parameter and givcs no informatíon about the actual now rcgime un less (he pipe is horizontal. N
"
-~ g d
FR -
1
_
"L -
L,
v.~[,
vm
=316
Af'02
L2 = 0.0009252 AL'·4(," L,
= 0.1 O
AL'"''
L4 = 0.5 A¡:"7J8
Thc horizolllal now regime limits are:
AppendixA
193
'Ji = I + e [sin (1.8$) - 0.333 sin' (1.8$)]
Segregated: Limils: AL < 0.01 and NFR
where $ is (he actual angel of the pipe from horizontal, and
Transition:
where d. e,/. and g are detennined [oc each flow eendition
e ~ (l -
AL)ln [(d)(AL)"(NLvY(NFR)E]
from Table A-2.
Limits: AL" 0.01 and L 2 < NFR :;; L,
TABLE A-2
Intermiltent Uphill
Intermittent: Flow Pattem Segregated uphill Intermittent uphill Dlstributed uphiIJ
Dislributed:
Al! f10w pattems downhill
Limils: AL < 0.4 and N FR " L 1 or AL ~ 0.4 and NFR > L 4
e
d
Limils: 0.01 :;; AL < 0.4 and L) < N FR '; L 1 or AL" 0.4 and L) < N FR ,; L,
0.011. -3.7611 2.96 0.305 No correction 4.70
3.539 -<>.4473 e = o, '1' = 1
-0.3692
with with the restriction thaí
When the Ilow faJls in lhe lransition regime, the liquid holdup must be ealeulaled using bolh the segregaled and intermittent equations and interpolated using the follow-
(
0.1244
9 -1.614 0.0978 HL
* ~.)
-0.5056
e ~ O.
Once HL{~) is determined, the two-phase density is ca1culated from
ing weighting factors.
HL (transition) minent) where:
= A x HL
(segregated) + 8 x HL (inler-
The pressure gra(d~)nJt due ; elevation ehange is then
L, - .V'"R
A
-
dZ ,/
LJ -L'].
The same equations are used to calculate liquid holdup [or all flo\\' regimes. The eocflicients and cxponcnt.s used in lhe cquations are different for each flow regime.
The liquid holdup depends on Ilow regime and is ealculated [rom
H Lt.) = 'l'H L,O) whefe HL(fJ) is lhe holdup which would exist al the same conditions in a horizontal pipe aud \JI is the inclination corrcction factor.
aAt
=-,-
J
dP ( dZ ~ where
Pn = PL Al. + PgA.
J;p
N FR
Segregated
0.98 0.845 1.065
lntermittent Oistributed
fin
e 0.0868 0.0173 0.0609
The valne ealeulated for HLtO ) is eonstrained by HL(O)~ AL
Th. faelor for eorrecting (he holdnp for lhe effeel ofpipe inclination ís given by:
J
_Pnvl11d NR , - - fin
Flow Paltem b 0.4846 0.5351 0.5824
/'p ( /11
where
TABLEA-1
a
= /"
The no-slip frietion ractor'fn is delcrmined [rom the Moody diagram (Fig. 3-5) or from Equatioll 3-15 lISillg lhe following Reynolds number:
whefe a, b, aud e are dctcnnined for each flow pattem from Table A-1.
Flow Patlern
g,.
The pressure gradient dile 10 frictioll i5
8=1-04
HL(o)
= -tP, SIn '1»
~
fiL AL + fig Ag
The ratio of lhe two-phase to no-slip [riction factor is calculated fram:
Irp
-=e
J
in
where:
s
[In (y)]/(-0.0523 + 3.182 In (y) --<).8725 [In (y)'] + 0.01853 [In (¡.)]'}
Produc/icm Optimiza/ion USi11g Yodol AlIa~\'sis
/94
3nd
Po = 5Q.29Ibm/cu ft )'
[HI.(~J
J'
s ~ 1n(2.2)' -
2.7(410)(0.7) 0.925(550)
=1.52Ibm/euft
qo = 0.485 Ít'/see
3.27x10·' Z(q; .q~R,)T
q 9
1.2)
Although the accelcration pressure gradient is very smal\ cxccpt for high vclocity now, it úould be included for high flow rates.
ZT
-
qo = 6.49 x·I.O·s q~ 80 = 6.49 x1 O·s (7140)(1.047)
The vnluc DI' S bccomcs unboundcG JI a paint in the intcr\'al I < y < 1.2; and for)' in tbis in!~rYal, the function S is calculated from:
2.7py,
R = ,
=-----'------'--'--l'
q =
3.27 X 10" (0.925)(25.7 x10' - 7140(96)) (550) 410
9
qg =10.1ft'/see 4.
Calculate the in-situ superficial velocities
= qúA = 0.485/0.7854 (1)2 = 0.617 ft/see vsg = q/A = 10.1/0.7854 = 12.87 ftlsee
VsL
If W~ ddinc nn acceler3tion tcrm as. _ p.~ \'1/1 l'.tg Ek gcp
v m = vsL + vsg = 0.617 + 12.87 = 13.49 fVsec
5.
dI'
dZ
1- Ek
N,.
culate the ouUet pressure using t~-= 8egg5 and Brm method.
= 7140 STB/day
p,(inlet) = 425 osia
= 1.5'
L, = 316 ~,~);: = 12t.
i
L = 0.009252
Example A-2:
q~
~ 1938v" [::
L3 = 0.10
Using the following data fer a hilly ;:?rrain pipeline, cal·
r
N,. = v;/gd ~ (13.49)'/(32.2)(1) ~ 565
the lotal pressure gradient can be calc:::lted fmm:
(~1, +( ~n,
Delermine Ihe flow paUern v 0.617 )'l = -!!:.. = - - = 0.0457 vm 13.49
~,~\ ~~.~ = 8.82
Since )~L > .01 and L2 < NFR $ L3, flow paUern is TRJ\N· SIT10N, therefore interpolation is required.
6.
Caleulale liquid holdup a. Segregated
q~ =25.7 MMcf/day f=90 °F ":=0.70 d = 12 in. Yo = 0.83 = 40 °API .
H
-
L(O) -
0.98().,)0""
(N
)O.0868 FR
Divide the pipeline inlo two sectio~s. Section 1 rises
C = (1· Adln [0.011 p.,)
300 ft in one mite. Seetion 2 drops 3JO ft in 3000 ft.
$ = aresin (300/5280) = 3.257
'''1 N F# ""j
O
'V = 1+ C[sin(1.8$)· sin i1.8
1.
Estimate óp' and_ealeulate p óp' = 30 psi. P = 425 - 302 = 410 psia
2.
From fluid property correlations. at 410 psia and 90 °F:
3.
.' 761N lJ
,= 5.516
Solution: SecUan 1
R s = 96 sef/STB
0"0 =
8 0 = 1.047
Z = 0.925
~o=
~g
2.4 ep
0.189
19.6 dyne/cm
= 00105 c¡¡
Calculate flow rales and densities
350yo + 0.0764 R, Y, Po =
5.61580 = 350(0.83) +0.0764 (96)(0.7) 5.615(1.047)
H L1 " (se9re9aled) = H '101'1'= 0.189 (1.56) = 0.2 95
b.
Intermiffent 0.845(A )0.5351 HL(O) =
O_O~73
NFR
-0.157
C = (1- A,) In [2.96( A, )o"s( N"
)-<J4437 (N
FR
=0.1246
'V =1+C(0.1015) = 1.013 H'I" (inlermittent) = 0.157 (1.013) = 0.159 A = L, - NFR L, . L,
8.82 - 5.65 - 0.455 8.82 -1.86
8=1-A=0.545
••
)00978 J
195
Appendix A H, (Iransilion)= AxH, (seg.)+ BxHdinl.)
3,
= 0.455 (0.295) + 0.545 (0.159) = 0.221 7,
8,
= 50.28 Ibm / eu ft
Caleulale t he actual and na - slip dens ities p, = p,H, + p.H, + 50,29 (0,221)+1 ,52 (0,779)
_ 2.7 (392.8) (0.7) 0.925 (550)
p, =12,3Ibm/euft Po = p, A, + P,A, = 50.29 (0,0457)+ 1.52 (0,9543)
P, -
Po =3.75Ibm/euft
q, =
Caleulale the frietion faelor
NRen
=
1.047
°
= 10.61 ft' / see
4, v" =0.484/0.785=0,616 ft/see V,g
fn = 0,0126
_""A:.:;'~ [H, ($)]'
, .484 ft / see
7
J1L AL + ~gl..g
Y =
0.485 (1,046)
1.46 Ibm / eu ft
q = 3.27 x 10- (0.925)(25, 7) x 1 6_ 7140(90)(550) , 392.8
d _14_8_8-,P,-,o,-vf!!.m_ 1488 (3,75) (13.49) (1) = 6,29x10' 2.4 (0,0457) +0,0105 (0,9543) 0.0457 (0,221)'
= 10,61/0.785 = 13.52 fIIsee
vm = 0,616 + 13,52 = 14.14 fIIsec
0.936 5.
A, = 0,616/14.14 = .04356
X = In y=-0,066
N'R = (14.14)'/(32,2) = 6,21
S = X/[-0.0523+3, 182 X-0,8725 X'
N
+ 0,01853 X'] = 0,248
t,pPnv~1 --·psm$+-.dp = 9 c
dL
.
2
oS
Qc
d
Psvmv.s g 1-----
g,p
Sinca )'L > .01 and
a.
_ 0.98(.04356)°48<6
L(O)
-
(6.21}O.0668
0.183
C = (1- ;., ) In (4,n;3692 Ni;'" NF~o") = 1,75 $ = aresin (300/3000) =- 5.74 o
0,999
\ji = 1+ C (sin (1 ,8$)- sln'(1.8$)/3) \ji =1-1.75 (0,177) = 0,69
10. Calculate the pressure drop
= 0,0061 (5280) = 32,2 psi
H'(Q} = 0.183 (0.69) = 0,126 b.
lntermittent
HL(O)
This is clase enough lo the estimated t>p. of 30 psi far hand calculalions. If a computar program was being used, the calculated !1p would be laken as the new eslimated
L3 . flow patlern is TRAN-
Segregaled
H
dpO _.::.7.,:0:..-+:..-0::':'.:,1:...7 = 0,871 psflft = 0,0061 psi/ft
}L
N FR <
6,
32,2 (410) (144)
t>p ~ (:
L2 <
SITlüN,
1- ]2.3 (13.49) (12,87)
dI.
L, = 945
l., = 2.11
12,3(0.057) + 0.016(3.75)(13.49)' dp = . 64.4 (1)
dI.
1.51
L, = 316 (0,04356)°302 = 122,7
Ca1culate Ihe pressure gradient
9
= 1.51 (0,616) 0.617
"
f,p = ro EXP(S) = 0,0126 (1.28) = 0,016 9,
0.:..76:..4'.:(~9.:.0)é.!(.:.0:.:...é' 7) P = .:.35::.:0,,(0::..:.8::.:3",)",,+-=.0:.:., o 5.615(1.046)
_ 0,945 (,04356)°·5351 -
C=1.75,
óp· and the procedure would be repeated until
00173
(6.21) .
-0.153
\jI=0.69
H,(" =0.153 (0.69) = 0.106
the error was smaller. The pressure at the end of Seetian 1 is 425 - 32,2 = 393,8 psia, The same proee-
0.44 B = 0,56 9.45 - 2.11 H, (Iransilion) = 0.44 (0.126) + 0,56 (0.1 06) =
A = 9.45-6.21
dure musl be followed to calculate the pressure at the end of Section 2.
0,115 Section 2
1.
2,
Estimate
t>p. = O, ji = 392.8 psia
R, = 90
JI, = 0.0105 cp
B, = 1,046
o, = 19.6 dyne/cm
p, = 2.4 cp
Z = 0.925
7,
p, = 50.28 (0.115) + 1.46 (1 -0.115)
~ 7.07
Ibm /
cu ft
Pn = 50.28 (0.04356) + 1.46 (1-0,04356) = 3.59 Ibm/cu ft
PmduCliol1 Optimiza/ion Using Soda! AI1lJ(~·..sis
196
8.
N" . '" =
1488 (3.59) (14.1 l
=
)
-7.07 +0.189
2.4 (0.04356) + 0.0105 (0.9564)
0.999
6.59 x 10'
1, = 0.0125
Y
dp = -0.518 psflft = -0.0036 psilft dL •
0.04356 = 329 (0.115)'
X=ln y=1.192
10. 6p = (-0.0036) (3000) = -10.8 psi
5=0.319 Irp = 0.0125 EXP (0.319) = 0.017
9.
dp
7.07 (-0.10)+ (0.017)(3.59)(14.14)' 64.4 (1)
dL
0.999
The estimated t:J.p*' was zero. Iteration Ihrough lwo more trials gives a pressure drop of -8.6 psi. The pressure al the oullet end 01 the pipe is then 425 - 32.2 + 8.6 =
401.4 psia.
PHAM HOANG TRí ANH
,'O
•
Pressure Traverse Curves
Appendix
B
These pressure traverse (gradient) curves are included for making estimates of pressure drops occurring in both vertical and horizontal pipes in which two-phases are flowing. The accuracy of the values obtained from these CUIVes wíll decrease as the actual conditions diverge from the conditions used to prepare the curves.
Vertical Curves The vertical curves were prepared for water cuts of 100%,50%, and 0%. Tubing 0.0., in.
Tubing !.D., in.
Liquid Rates, STBlday
2-3/8
1.995 2.441 2.992 3.958
50-1500 100-3000 300-6000 500-10000
2-7/8 3-1/2 4-1/2
Horizontal Curves The horizontal curves were prepared for 100% oil flowing. Pipe 1.0., in.
2.0 2.5 3.0 3.5 4.0 5.0 6.0
Liquid Rates, STBlday
100-2000 100-3000 400-10000 600-10000 800-10000 5000-10000 5000-10000
197
Production Optimization Using Nadal Analysis
198
O
1
4
8
12
16
20
PRESSURE, 100 PSIG 32 36 24 28
40
44
48
52
56
tt++t-j ++Htttittttt ltl=ti=tttttt TUBING SIZE, IN.: 1.995
2 3 4
LIQUIO RATE, STBL/o: 50 WATER FRACTION:
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
5 6 7
, 8
,..
.
9
o o
~ 10 :t:
~1l
""' 12 , 13
,
14
, 15 16 17 18 -
19 20
'I~--~
= :::'.-:-.:. _. _ _
LW_J2·LL_
Pressure Traverse Curves
oO
4
199
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
H -j t-H-I t-H-f 1
44
48
52
1:t=ltl-I:t-ttJltml-tm
TUBING SIZE, IN.: 1.995 2 3 4 5 6 7
8
.."'
9
o o·
~ 10
'" !i:ll "' Q
12 13 14 15 16 17 18 19 20
56
LIQUID RATE, STBL/D: 50 WATER FRACTION:
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING. TEMP.,F: 150
Production Optimiza/ion Using Nodal Analysis
200
O
1
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
nl¡i#itfJI~M TUBING SIZE, IN.: 1.995
2 3 4 5 6 7 8
.. E-<
9
o o
;: 10
'i"í:ll
''"" 12 13 14 15 16 17 18 19 20
56
LIQUID RATE, STBL/D: WATER FRACTION:
50
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
Pressure Traverse Curves
201
12
16
20
PRESSURE, 100 PSIG 32 36 24 28
40
44
48
52
1 TUBING SIZE, IN.: 1.995 2 3 4 5 6 7 8
.....
9
o o ~ 10
,
o::
!i:ll
'"
" 12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
iDO
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Production Optimiza/ion Using Noda' Ana/ysis
202
OO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 1.995 2 3 4 5 6 7 8
.. E-<
9
o o
~ 10 o::
~11
''"" 12 13
14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
100
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
oO
4
203
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 1.995. 2 3 4 5 6 7 8 E<
r.. 9
o o
;: 10
'" !;;1l
"'" 12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
100
O
GAS GRAVITY: 0.65 OIL API GRAVIT~: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Production Optimization Using Noda/ Analysis
204
o
4
B
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
1 TUBING SIZE, IN.: 1.995 2 3 4
5 6 7 8 E-<
'ee"
9
;: 10
'f;:1l "
"''"
12 13 14
15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
200
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING. TEMP.,F: 150
Pressure Traverse Curves
OO
4
205
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
1 TUBING SIZE, IN.: 2
3 4 5 6 7 8
.. 8
9
o o
;: 10
'~"ll "'e 12 13 14 15 16 17 18 19 20
1.995
LIQUID RATE, STBL/D: WATER FRACTIDN:
200
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
Production Optimization Using Nada! Ana/ysis
206
OO
4
8
12
16
20
PRESSURE, 100 PSIG 24 36 28 32
40
48
44
52
1 TUBING SIZE, IN. : 1.995 2 3 4
LIQUID RATE, STBL!D: WATER FRACTION:
6 7 8
.
9
o o
;: 10
'" !i:.ll '" Q
12 13 14 15 16 17 18 19 20
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1. 07 AVERAGE FLOWING TEMP.,F: 150
5
€o<
200
.
-
.
56
Pressure Traverse Curves
oO
4
207
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 1.995 2 3 4
LIQUID RATE, STBL/D: WATER FRACTION:
GAS GRAVITY: 0.65 OIL API GRAVITY, 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
5
6 7
, 8
...
9
o o
;: 10
"' !l:11
""' 12 13 14 15 16 17 18 19 20
300
56
Production Optimization Using Nodal Analysis
208
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36,
1 TUBING SIZE, IN o,: 1. 995 2 3
4 5 6
7 8
.....
9
o o
;: 10
!i:ll .,'" el
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
300
05
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1007 AVERAGE FLOWING TEMPo,F: 150
Pressure Traverse Curves
oO
4
209
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 1. 995 2 3 4 5 6 7 8
....
9
o o
;: 10
o::
~11
"' e
12 13
14 15 16 17 18 19 20
LIQUID RATE, STBL!D: WATER FRACTION:
300
o
GAS GRAVITY: 0.65 DIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLDWING TEMP.,F: 150
56
Production Optimiza/ion Using Nadal Analysis
210
OO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 36 32
40
44
48
52
1 TUBING SIZE, IN. : 1. 995 2 3 4
LIQUID RATE, STBL/D: WATER FRACTION:
6 7 8 9
o o
;: 10
"' !i:ll "'"
12 13 14 15 16 17 18 19 20
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1. 07 AVERAGE FLOWING TEMP.,F: 150
5
....
400
-
56
Pressure Traverse Curves
oO
4
211
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 1. 995 2 3 4 5 6 7 8
. E-<
9
o o ::: 10
'" !i:ll 'e"l
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
400
.5
GAS GRAVITY: 0.65 DIL API GRAVITY: 35 WATER SPECIFIC GRAVITY. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
212
Production Optimization Using Nodal Analysis
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 1. 995 2 3 4 5 6 7 8
'o..."'
9
o
~ 10
'" !i:ll
""' 12 13 14
15 16 17 18 19 20
LIQUIO RATE, STBL/O: WATER FRACTION:
400
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE,FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
213
PRESSURE, 100 PSIG
oO
4
8
12
16
20
24
28
32
36
40
44
52
48
1 TUBING SIZE, IN.: 1.99S 2 3
4 5 6 7 8
..,..
9
o o
~ 10 tI:
.,~1l " 12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
sao
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
56
214
Production Optirnization Using Nodal Analysis
o 1
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
tltl1tt¡~tjjjjílJjt¡~
52
¡-mM
TUBING SIZE, IN.: 1.995 2 3 4 5 6 7 8
.. E-<
9
o o
~ 10
'!";;1l '" el
12 13 14
15 16 17 18 19
20
LIQUID RATE, STBL/D: WATER FRACTION:
56
500
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
Pressure Traverse Curves
4
oO
215
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36'
40
44
48
52
I+H-fl:t:ltmtiJlt+Htñrr
1
TUBING SIZE, IN.: L 99S 2 3 4 5 6 7
8 E<
r.. o o
9
~ 10
.,'i"í:ll " 12 13 14 15 16 17 18 19 20
56
LIQUID RATE, STBL/D: --ti\'
WATER FRACTION:
SOO
O
GAS GRAVITY: 0,65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY' 1.07 AVERAGE FLOWING TEMP.,F: 150
216
Production Optimization Using Noda! Analysis
oO 1
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
H tlH
40
44
48
52
-H-I:t UtttutlJtltttlf111
TUBING SIZE, IN.: lo 995 2
3 4 5 6 7
8'
.. 8
9
o o
~ 10
'a": 11 "'
" 12 13 14 15 16 17 18 19 20
56
LIQUID RATE, STBL/D: WATER FRACTION:
600
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
Pressure Traverse Curves
oO
4
217
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 1. 995 2 3 4 5 6 7 8
..
E-<
9
o o
;: 10
'" !;;11 "'
" 12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
600
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGEFLOWING TEMP.,F: 150
Production Optirnization Using Nadal Analysis
218
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
48
44
52
+H+H+l-H IH+UIH,IHtllttH
1
TUBING SIZE, IN.: 1.995 2
LIQUID RATE, STBL/D: WATER FRACTION:
3 4 5
6 7 8
.. E-<
9
o o
~ 10
"' !;:11 "' Q
12 13 14 15 16 17 18 19 20
56
I
BOO
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
Pressure Traverse Curves
oO
4
219
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
48
44
52
1 TUBING SIZE, IN.: 1.995 2 3 4
5 6
7 8
."'
9
o o ;: 10
'.,!"i:11 a 12 13
14
15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
700
1
GAS GRAVITY: 0.65 OIL API GRAVITY:"35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Production Optimization Using Noda! Analysis
220
oO
4
8
12
16
20
PRESSURE, 100 PSIG 32 36 24 28
1 TUBING SIZE, IN.: 1. 995 2 3 4 5 6 7 8
....
9
o o ;: 10
¡;:11 .,'" Cl
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: 700 WATER FRACTION:
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
Pressure Traverse Curves
OO
4
221
8
12
16
20-
PRESSURE, 100 PSIG 24 28 32 36
- -/--Ht+H
1
40
44
48
52
IJI±tttttm$
TUBING SIZE, IN.: 1.995
2 3
LIQUIO RATE, STBL/O: 700
11
WATER FRACTIQN:
5 6 7 8 E-<
r.. 9
o o
~ 10 o::
fi:ll
"' Q
12 13 14 15 16 17 18 19 20
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY. 1.07 AVERAGE FLOWING TEMP.,F: 150
4
I
~
56
Production Optimiza/ion Using Noda! Analysis
222
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
56
H-H+
-H
IH+HttHIi:lttlfJI L
TUBING SIZE, IN.: 1. 995 LIQUID RATE, STBL/D: WATER FRACTION:
800
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE· FLOWING TEMP.,F: 150
7
, 8
.-..
9
o o
~ 10
~
..
'" !i:ll
"'e
12 13 14 15 16 17 18 19 20
-
-
----
~: :-mlf'kLI:-.:
Pressure Traverse Curves
oO
4
223
8
12
16
20
PRESSURE, 100 PSIG 32 36 24 28
40
48
52
1 TUBING SIZE, IN.: 1.995 2 3 4 5 6 7 8
. E-<
9
o o
~ 10
¡;:11 "'
'"
o
12 13 14 15 16 17 18 19 20
LIQUIO RATE, STBL/O: WATER FRACTION:
BOa
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY:.l.07 AVERAGE FLOWING TEMP.,F: 150
56
224
Production Optimization Using Nadal Analysis
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 1.995
2 3 4 5 6 7 8
..
9
o o
~ 10
o:
!;;11
"'"
12 13
14 15 16 17 18 19 20
LIQUID RATE, STBL!D: WATER FRACTION:
800
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY. 1.07 AVERAGE FLOWING TEMP.,F: 150
Pressure Traverse Curves
oO 1
4
225
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
48
44
52
-H HH H-H"IJ-I-H Ilttl¡-ltli-liJi! TUBING SIZE, IN.: 1.995
2
3 4
LIQUID RATE,
STBL/D:
WATER FRACTION:
900
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
5 6 7 8
.. 8
9
o o
~ 10
'~11 "
'" Q
12 13 14 15 16 17 18 19 20
56
" - __Ul-LL.LI-t_LH_l_Ll'J
226
Production Optimiza/ion Using Nadal Analysis
OO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
1 TUBING SIZE, IN.: 1.995 2 3 4 5 6 7
8
..
o'"' o
9
;:: 10
'" !i:ll '" Cl
12 13 14 15 16 17
18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
900
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP"F: 150
Pressure Traverse Curves
oO
4
227
8
12
16.
20
PRESSURE, 100 PSIG 24 28 32 36
1 TUBING SIZE, IN.: 1. 995 2 3 '4 5 6 7 8
« 9
'"
o o
;: 10
"'~11 '" Q
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
900
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
228
Production Optimiza/ion Using Nada! Analysis
oO
4
6
12
16
20
PRESSURE, 100 PSIG 32 36 24 26
40
46
44
52
eI-!-I--+--J.-I-I--H-j-I" -H-I-II-I--111 I±H+ttlit
¡·t-t+H-!-t-t-H-I+H-j
(.j
f-I-IITfT{t-lJ'LJ.
1 TUBING SIZE, IN.:1.99S 2 3 4 5 6 7 6
.
,..
9
'"'"
~ 10
c::
¡'-:11
"' Q
12 13 14 15 16 17 16 19 20
56
LIQUID RATE, STBL/D: 1000 WATER FRACTION:
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
Pressure Traverse Curves
oO
4
229
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
1 TUBING SIZE, IN.: 1. 995 . 2 3 4 5 6 7 8
...
9
o o
;: 10
'" 1.:11 '" Q
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
1000
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
Production Optimization Using Nodal Analysis
230
o
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
1 TUBING SIZE, IN.: 1. 995 2 3 4 5 6 7 8
.. E-<
9
o o ~ 10
'~"11 "' Q
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL!D: WATER FRACTION:
¡OOO
a
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F, 150
Pressure Traverse Curves
oO
4
231
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 . TUBING SIZE, IN.: 1. 995
2 3 4 5 6 7 8
"o..
9
o ~10
o::
!i:ll
'" Q
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
1200
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
56
232
Production Optimiza/ion Using Nadal Analysis
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
48
44
52
1 TUBING SIZE, IN.: 1. 995 2 3 4 5 6 7 8
.. ó<
9
o o ~ 10
¡;:11 .,'" e
12 13
14 15 16 17 18 19 20
LIQUID RATE, STBL/D: 1200 WATER FRACTION:
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY:. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
OO
4
233
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 1.995 2 3 4 5
6 7 8 8
o""
9
o
;: 10
'~"11 "'" 12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
1200
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Production Optimization Using Noda/ Ana/ysis
234
oO
4
6
12
16
20
PRESSURE, 100 PSIG 24 26 32 36
40
44
46
52
1 TUBING SIZE, IN.: 2.441 2 3 4
5 6 7 6 E-<
'oo"
9
;: 10
,
'"f;;11
'"
Q
12 13
14
15 16 17 16 19 20
LIQUID RATE, STBL!D: WATER FRACTION:
100
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY' 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
oO 1
4
235
8
12
16
20
PRESSURE, 100 PSIG 2B 32 36 24
40
44
48
52
:H-I~Hjl+l¡tljjíttttthHH
IIJI-I
TUBING SIZE, IN.: 2.441 2 3 4 5 6 7 8
. E-<
9
o o.
~ 10
.,"'
¡';11 Q
12 13 14
15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
56
100
.S
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
Production Optimiza/ion Using Nada! Analysis
236
oO
4
8
12
,16
20
PRESSURE, 100 PSIG 24 28 32 36'
40
44
48
52
1 TUBING SIZE, IN.: 2.441 2 3 4 5 6 7 8
. ó<
9
o o
~ 10
'" !i:u "'" 12 13
14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
100
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLQWING TEMP.,F: 150
56
Pressure Traverse Curves
OO
4
237
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.441 2 3 4 5 6
7 8
..
8
9
o o
::: 10
.,'t";::11 Q
12 13 14 15 16 17 18 19 20
LIQUIO RATE, STBL/O: 200 WATER FRACTION:
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY:. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
238
Production Optimization Using Nodal Analysis
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
-1 TUBING SIZE, IN.: 2.441
2 3 4 5 6 7 8 ".. r.. 9
o o
;: 10
"' !;:11 "''"
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: 200 WATER FRACTION:
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY,. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
oO
4
239
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.441
2 3 4 5 6 7 8
....
9
o o
~ 10
'" "" 12
Íi:ll
13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: 200 WATER FRACTION:
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY:. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Praduction Optimizatian Using Nodal Analysis
240
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 2B 32 36
40
44
4B
52
·1 TUBING SIZE, IN.: 2.441
2 3 4 5 6 7 B
....
9
o o
;: 10 ti:
.,li:ll '" 12 13 14 15 16 17 lB 19 20
LIQUID RATE, STBL!D: 300 WATER FRACTION:
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY:. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
-Q O
4
241
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.441
2 3 4 5 6 7 8
,..
'"
9
o o
~ 10
" "'
1;:11 Q
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: 300 WATER FRACTION:
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY,. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Production Optimization Using Nadal Analysis
242
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
48
44
52
1 TUBING SIZE, IN.: 2.441
2 3 4 5 6 7
8 E-<
r.. 9
o o ~ 10 :x:
!;:11
"' Q
12 13
14 15 16 17
18 19 20
LIQUID RATE, STBL/D: 300 WATER FRACTION:
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
00.
4
243
8
12
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1
TUBING SIZE, IN.: 2.441 2 3 4 5 6 7 8
. &<
9
o o
;: 10
,
" .,'i.::ll Q
12 13 14 15 16 17
18 19 20
LIQUID RATE, STBL/D: 400 WATER FRACTION:
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY,. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Production Optimiza/ion Using Noda! Analysis
244
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.441 2 3 4 5 6 7 8
....
9
o o
;: 10
o:
a: 11
'" el
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: 400 WATER FRACTION:
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
oO
4
245
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.441 2 3 4 5
6 7
8
.. ó<
9
o o ~ 10
o:
~11
"' Q
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
400
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
56
246
Production Optimization Using Nodal Analysis
OO
4
8
12
16
·20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.441 2 3 4 5 6 7 8
..
8
9
o o ;: 10
'" 1;:11 '" Q
12 13
14 15 16 17 18 19 20
LIQUID RATE, STBL/D: 500 WATER FRACTION:
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
oO
4
247
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52.
1 TUBING SIZE, IN.: 2.441 2 3 4 5 6 7 8
. ¡.,
9
o o ;: 10
"' ¡;:11
'" Q
12 13
14 15 16 17 18 19 20
LIQUIO RATE, STBL/O: 500 WATER FRACTION:
.5
GAS GRAVITY: 0.65 OIL API GRAVITY:·35 WATER SPEC!FIC GRAVITY,. 1.07 AVERAGE FLOWING. TEMP.,F: 150
56
Production Optimization Using Nadal Analysis
248
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
.40
44
48
52
1 TUBING SIZE, IN.: 2.441 2 3 4 5 6 7 8
.. E-<
9
o o
;: 10
'" 1;:11 "'"
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
500
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
OO
4
249
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.441 2 3 4 5 6 7 8
,..
r.. 9
o o
~ 10
'a:" 11
"'" 12 13 14
15 16 17 18 19 20
LIQUID RATE, STBL/D: 600 WATER FRACTION:
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Production Optimiza/ion Using Nodal Analysis
250
PRESSURE, 100 PSIG
oO
4
8
12
16
20
24
28
32
36
40
48
44
52
1 TUBING SIZE, IN.: 2.441
2 3 4 5 6 7 8
. 8
9
o o
~ 10
'" !i:11 '" Q
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: 600 WATER FRACTION:
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
oO
4
251
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.:2.441 2 3 4 5 6 7 8
...
9
o o ;: 10
'" 1;:11
"' Q
12
13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: 600 WATER FRACTION:
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Production Optimiza/ion Using Nodal Analysis
252
o
4
8
12
16
20
PRESSURE, 100 PSIG 32 36 24 28
1 TUBING SIZE, IN.: 2.441 2
3 4 5 6 7 8
...
9
o o
~ 10
,
o: ~11
"' Q
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
700
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
253
Pressure Traverse Cur,¡es
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.441 2 3 4 5 6 7 8
....
9
o o
~ 10
'" !i:u
''"" 12 13 14 15 16 17 18 19 20
LIQUIO RATE, STBL!O: WATER FRACTION:
700
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE.FLOWING TEMP.,F: 150
56
254
Production Optimization Using Noda! Analysis
PRESSURE, 100 PSIG O
4
8
12
16
20
24
28
32
36
40
48
44
52
1 TUBING SIZE, IN.: 2.441 2 3
4 5 6 7 8
..
E-<
9
o o ~ 10
'" !i:11
'c"
12 13
14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTIDN:
700
O
GAS GRAVITY: 0.65 DIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLDWING TEMP.,F: 150
56
Pressure Traverse Curves
O
4
255
8
12
16
20
PRESSURE, 100 PSIG 24 32 36 28
40
44
48
52
1 TUBING SIZE, IN. : 2.441 2 3 4
LIQUID RATE, STBL/D: WATER FRACTION:
6 7 8 9
o o ;: 10
'" !i:ll '" el
12 13
14 15 16 17 18 19 20
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1. 07 AVERAGE FLOWING TEMP.,F: 150
5
..,..
800
.. -
- ..
56
Production Optimization Using Noda/ Analysis
256
o
4
8
12
20
PRESSURE, 100 PSIG 24 28 32 36
40
48
44
52
1 TUBING SIZE, IN.: 2.441
2 3 4 5 6
7 8
.. E-<
9
o o ~ 10
:c
!;;11
"'" 12 13 14 15 16
17 18 19
20
LIQUID RATE, STBL/D: WATER FRACTION:
800
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
56
257
Pressure Traverse Curves
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
48
44
52
1 TUBING SIZE, IN.: 2.441 2 3 4 5 6
7 8
'.."
9
o o ~ 10
'" !i:ll "'el
12 13 14 15 16
17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
800
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Production Optimiza/ion Using Nodal Analysis
258
O
4
8
12
16
20
PRESSURE, 100 PSIG 32 36 28 24
40
44
48
52
1 TUBING SIZE, IN. : 2.441 2
LIQUID RATE, STBL/D: WATER FRACTION:
3
5 6 7 8 €o<
9
o o
~ 10
a:
!i:ll ., Q
12 13 14 15 16 17 18 19 20
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1. 07 AVERAGE FLOWING TEMP.,F: 150
4
..
900
_.
-
--
56
259
Pressure Traverse Curves
oO
4
8
12
16
PRESSURE, 100 PSIG 20. 24 28 32 36
1 TUBING SIZE, IN.: 2.441
2 3 4 5
6 7 8
.. ó<
9
o o
~ 10
-
o:
!;;11
"'
el
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
900
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
260
Production Optimization Using Nada! Ana/ysis
o
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.441 2 3 4 5 6 7 8 E-<
o'" o
9
::: 10
'~11 "
""' 12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
900
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Troverse Curves
oO
4
261
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.441 2
3 4 5 6
7 .8
...
9
o o
~ 10
'¡;;U " "'
" 12 13 14 15 16
17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
1000
1
GAS GRAVITY: 0.65 OXL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
56
262
Production Optimiza/ion Using Nodal Analysis
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.441 2 3 4 5 6
7 8 8
'"
9
o o
~ 10
o:
li:ll
'" Cl
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
1000
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 .AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
oO
4
263
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.441 2 3 4 5
6 7 8
.....
9
o o
~ 10
"' !;:11
'e" 12 13
14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
1000
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 . WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Production Optimization Using Nodal Analysis
264
OO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
1 TUBING SIZE, IN.: 2.441 2 3 4
LIQUID RATE, STBL/D: WATER FRACTION:
6 7
,
..
« 9 o o
~ 10
:e
¡;;11 ., Q
12 13
14 15 16 17 18 19 20
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
5
8
1200
Pressure Traverse Curves
o
4
265
B
12
16
20
PRESSURE, 100 PSIG 24 2B 32 36
40
44
4B
52
1 TUBING SIZE, IN.: 2.441
2 3 4 5 6 7 B
« 9
'oo"
~ 10
"' ¡;;11 "' Q
12 13 14 15 16 17 lB 19 20
LIQUID RATE, -STBL/D: WATER FRACTION:
1200
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLQWING TEMP.,F: 150
56
Production Optimization Using Nadal Analysis
266
oo
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.441 2 3 4 5 6 7 ·8 E-< ¡.,
9
o o ~ 10
'" '"
l;:11 Q
12 13
14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
1200
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
oO
4
267
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 1. 995 2 3 4 5 6 7 8 E-<
'" "
9
"~ 10 :c
!i:1l
"'" 12 13 14
15 16 17 18 19 20
LIQUID RATE, STBL/O: WATER FRACTION:
1500
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 . WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Production Optirnization Using Nadal Analysis
268
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
48
44
52
1 TUBING SIZE, IN.: 1. 995 2 3 4
LIQUID RATE, STBL!D: WATER FRACTION:
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
5 6 7 8
.. E-<
9
o o
;: 10
"'~11 '" Q
12 13 14 15 16 17 18 19 20
1500
---t.-- -j-
56
269
Pressure Traverse Curves
PRESSURE, 100 PSIG
oO
4
8
12
16
20
24
28
32
36
40
52
48
44
1 TUBING SI ZE, IN.: 1. 995 2
LIQUID RATE, STBL/D: WATER FRACTION:
1500
O
3
4 5 6
7 8
....
9
o o
~ 10
"~ 11
'"
Cl
12 13
14 15 16 17 18 19 20
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Production Optimizatían Using Nodal Ana/ysis
270
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.441 2 3 4 5 6 7 8
....
9
o o ~10
'5"::11 " Q
12 13 14
15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
2000
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
oO
4
271
8
12
16
PRESSURE, 100 PSIG 20· 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.441
2 3 4 5 6 7 8
.. E-<
9
o o
;: 10
'f";:11 '" el
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
2000
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
56
272
Production Optimization Us;ng Nodal Ana(vsis
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
48
44
52
1 TUBING SIZE, IN.: 2.441
2 3 4 5
6 7 8
....
9
o o
~ 10
'~"1l fil
Cl
12 13 14 15
16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
2000
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY; 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
OO
4
273
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.441 2 3 4
LIQUID RATE, STBL/D: WATER FRACTION:
6 7
,
....
9
o o ~ 10
'~"11 '"
" 12 13 14 15 16 17 18 19 20
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
5
8
2500
56
Production Optimiza/ion Using Nadal Analysis
274
OO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
·1 TUBING SIZE, IN.: 2.441 2 3 4
5 6 7 8
..""
9
o o
~ 10
"'~11
'" Q
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
2500
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY,. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
oO
4
275
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.441 2 3 4 5 6 7 8
..
E-<
9
o o
;: 10
"' !;:11 "' Q
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
2500
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY:_ 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Production Optimization Using Noda! Ana/ysis
276
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
1 TUBING SIZE, IN.:2.441 2 3 4 5 6 7 8
. f«
9
o o
~ 10 :I:
¡;:11
'" Q
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: 3000 WATER FRACTION:
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
Pressure Traverse Curves
o
4
277
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
1 TUBING SIZE, IN.: 2 3 4 5 6 7 8 &<
'o"
9
o
~ 10
!"i:ll
"'o
12 13 14 15 16 17 18 19 20
2.441
LIQUID RATE, STBL/D: WATER FRACTION:
3000
.5
GAS GRAVITY: 0.65 OIL.API GRAVITY: 35 WATER SPECIFIC GRAVITY. 1.07 AVERAGE FLOWING TEMP.,F: 150
Production Optimization Using Nadal Analysis
278
o
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
1 TUBING SIZE, IN.: 2.441 2 3 4
5 6 7
8
....
9
o o
~ 10
o:
f;:11
"'" 12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
3000
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
Pressure Traverse Curves
oO
4
279
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
48
44
52
1 TUBING SIZE, IN.: 2.992 2 3 4 5 6 7
8
....
9
o o
~10
'" Íi:ll
"'" 12 13
14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
300
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Production Optimiza/ion Using Nadal Analysis
280
oO
4
6
12
16
20
PRESSURE, 100 PSIG 32 36 24 28
40
44
46
52
1 TUBING SIZE, IN.: 2.992 2 3 4 5 6 7 8
...E-<
9
o o ~ 10
'" I;:il 'O"
12 13 14 15 16 17 16 19 20
LIQUID RATE, STBL!D: WATER FRACTION:
300
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
oO
4
281
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
1 TUBING SIZE, IN.: 2.992 2 3 4 5 6 7 8 E<
'oo"
9
~ 10
,
'" ¡;;11
'"'" 12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL!D: WATER FRACTION:
300
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
Production Optimiza/ion Using Nadal Analysis
282
oO
4
8
12
16
20
PRESSURE, 100 PSIG 32 36 24 28
40
44
48
52
1 TUBING SIZE, IN.: 2.992 2 3 4 5 6 7 8
...".
9
o o ~10
'" 1;;11 '" el
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL!D: WATER FRACTION:
500
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY:. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
oO
4
283
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
48
44
52
1 TUBING SIZE, IN.: 2.992 2 3 4 5 6 7 8
.. E-<
9
o o
::: 10
'" !i:ll
"'a
12 13
14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
SOO
.S
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY; 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Produclion Optimiza/ion Using Noda/ Analysis
284
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
52
48
1 TUBING SIZE, IN.: 2.992 2 3 4 5 6 7 8
..
E-<
9
o o
~ 10
'~ll "
'"
Cl
12 13
14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
500
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
oO
4
285
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
52
48
1 TUBING SIZE, IN.: 2.992 2 3 4 5 6 7 8 E-<
'"' o
9
o ~ 10
,
'"f;:11
"'e 12 13 14
15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
7DO
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
56
286
Production Optimiza/ion Using Nada! Analysis
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.992
2 3 4 5
6 7 8
. E-<
9
o o
~ 10
.,"'oa: 11 12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
700
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY,- 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Troverse Curves
oO
4
287
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.992 2 3 4 5 6 7 8 E-<
r.. 9
o o
~ 10
'~11 "
'" Q
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTIDN:
700
O
GAS GRAVITY: 0.65 DIL API GRAVITY: 35 WATER SPECIFIC GRAVITY,. 1.07 AVERAGE FLDWING TEMP.,F: 150
56
288
Production Optimization Using Nada! Analysis
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
48
44
52
1 TUBING SIZE, IN.: 2.992 2 3 4 5 6 7 8
....
9
o o
~ 10 tI:
.,!i;1l Q
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
900
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
oO
4
289
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.992 2 3 4 5 6 7 8
..
8
9
o o ~ 10
,
:z: ~11
"'
",.
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
900
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY,. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Production Optimization Using Nada! Analysis
290
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
48
44
52
1 TUBING SIZE, IN.: 2.992
2 3 4 5 6 7
8 E-<
r.. 9
o o
~ 10
:z:
!l:11
'e"
12 13 14 15 16 17
18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
900
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY:. 1.07 AVERAGE FLOWING TEMP.,F: 150
. 56
Pressure Traverse Curves
oO
4
291
6
12
16
PRESSURE, 100 PSIG 20· 24 26 32 36
40
46
44
52
1 TUBING SIZE, IN.: 2.992
2 3 4 5 6 7 6
...O<
9
o o
~ 10
'¡;:11 "
'" Q
12 13 14 15 16 17 16 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
1000
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY,. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
292
Production Optimization Using Nodal Analysis
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1
TUBING .SIZE, IN.: 2.992 2 3 4 5 6 7 8
.. "'oo
9
~ 10
!"i:ll
'" Q
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
1000
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY:. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
oO
4
293
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
·1 TUBING·SIZE, IN.: 2.992 2 3 4 5 6 7 8
....
9
o o
~ 10
!i:u .,"' el
12 13
14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
1000
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY:. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
294
Production Optimization Using Noda! Analysis
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
48
44
52
1 TUBING SIZE, IN.: 2.992 2 3 4 5 6 7 8 E-<
'"
9
o o ~ 10
'" ¡¡:11 'e"
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
1200
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
o
4
295
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.992 2 3
4 5 6 7 8
.. 'oo"
9
~ 10
'"!;;1l
'" Q
12 13
14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTIDN:
1200
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY:. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Production Optimiza/ion Using Nadal Analysis
296
OO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.992 2 3 4 5 6 7 8
..
E-<
9
o o ~ 10
"' !i:ll "'" 12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
1200
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY,. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
oO
4
297
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.992
2 3 4 5
&
7 8 E-<
'o"
9
o
~ 10
"' "'" 12
1;:11
13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
1500
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
56
298
Production Optimization Using Nadal Ana/ysis
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.992 2 3 4 5 6 7 8 ó<
'" o.
9
o
;: 10
.,"i;:11
" 12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
1500
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAV¡TY:. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
oO
4
299
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.992 2 3 4 5 6 7 8 E-<
r.. 9
o o
~10
o:
tu
""' 12 13 14 15 16 17 18 19
20
LIQUID RATE, STBL/D: WATER FRACTION:
1500
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY:. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Production Optimization Using Nodal Ana/ysis
300
OO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.992
2 3
4 5
6 7
8
...
9
o o
~ 10
'" ii:1l 'e"
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL!D: WATER FRACTION:
2000
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
OO
4
301
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.992
2 3 4 5 6
7 8 E<
"'
9
o o
;: la
"' 1;;11
"'e 12 13 14 15 16
17 18
19 20
LIQUID RATE, STBL/D: WATER FRACTION:
2000
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY,. 1.07 AVERAGE FLOWING TEMP.,F' 150
56
Production Optimization Using Nadal Analysis
302
oO
4
8
12
16
20
PRESSURE, 100 PSIG 32 36 24 28
40
44
48
52
1 TUBING SIZE, IN.: 2.992 2 3 4 5 6 7 8 E-<
[<,
9
o o ~ 10
'~"11 '" Q
12 13 14 15 16 17 18 19 20
LIQUIO RATE, STBL/O: WATER FRACTION:
2000
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
OO
4
303
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
48
44
52
1 TUBING SIZE, IN.: 2.992
2 3 4 5 6
7 8
.."
9
o o
~ 10
'a"; 11 'o" 12 13 14
15 16 17 18
19 20
LIQUID RATE, STBL/D: WATER FRACTION:
3000
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY,_ 1.07 AVERAGE.FLOWING TEMP.,F: 150
56
Production Optimization Using Nadal Analysis
304
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
5'2
48
44
'1 TUBING SIZE, IN.: 2.992 2 3 4 5 6 7 8 8
r.. 9
o o
;: 10
'~11 "
'" Q
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
3000
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, , 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
OO
305
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.992
2 3 4 5 6 7 8
..
9
o o ~ 10
!"i:ll
"'" 12 13
14 15 16 17 18 19
20
LIQUID RATE, STBL/D: WATER FRACTION:
3000
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY:. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
306
Production Optimization Using Nadal Analysis
oO
4
8
12
H
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
·1 TUBING SIZE, IN.: 2.992 2 .3 4 5 6 7 8
..
¡.<
9
o o
~ 10 tI:
~ a
11
'" 12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
4000
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY,. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
307
Pressure Traverse Curves
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 2.992 2 3 4 5 6 7 8
.. E-<
9
o o ~ 10
'" i;::11
"'" 12 13 14 15 16 17
18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
4000
.5
GAS GRAVITY: .0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY,.1.07 AVERAGE FLOWING TEMP.,F: 150
56
Production Optimiza/ion Using Nada! Analysis
308
OO
1 2
4
8
12
16
mi
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
TUBING SIZE, IN.: 2.992 LIQUID RATE, STBL/D: WATER FRACTION:
3
4000
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY; 1.07 AVERAGE FLOWING TEMP.,F: 150
4 5 6 7 8
. O<
~
1 ti
9
o o
~ 10 tI:
~11
'" Q
12 13 14 15 16 17 18 19 20
-1+
56
Pressure Traverse Curves
oO
4
309
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 3.958
2 3 4 5 6 7 8 E-<
r.. 9
o o ;: 1~ tI:
¡;;1l .,
" 12 13
14 15 16 17 18 19 20
LIQUID RATE, STBL/D: 500 WATER FRACTION:
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY,. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
310
Production Optimization Using Noda/ Analysis
OO
4
8
12
16
20
PRESSURE, 100 PSIG 32 36 24 28
40
48
44
. 52
1 TUBING SIZE, IN.: 3.958 2 3 4 5 6 7 8
.. ¡..
9
o o
~ 10
!i:"' 11
"' Q
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
sao
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY:.l.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
311
100 PSIG 28 32 36
P~ESSURE,
oO
4
8
12
16
20
24
40
44
48
52
1 TUBING SIZE, IN.: 3.958 2 3 4
5 6 7 8
.
E-<
9
o o
~ 10
o:
.,t;11 el
12
13 14
15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
500
O
GAS GRAVITY: 0.65 DIL APIGRAVITY: 35 WATER SPECIFIC GRAVITY:. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
312
Production Optimization Using Nodal Analysis
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 3.958 2 3 4 5 6 7 8
. &<
9
o o
~ 10 tI:
~1l
'" Q
12 13 14
15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTIDN:
800
1
GAS GRAVITY: 0.65 DIL API GRAVITY: 35 WATER SPECIFIC GRAVITY:. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
oO
4
313
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 3.958 2 3
4 5 6 7 8
.. 8
9
o o
~ 10
'~"11 ""'
12 13 14
15
16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
800
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY' 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Production Optirnization Using Noda! Analysis
i14
oo
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40·
44
52
48
1 TUBING SIZE, IN.: 3.95B
2 3 4 5
6 7
8
.. E-<
9
o o
~ 10
'~"11
"'" 12 13 14
15 16
17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
BOa
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY,_ 1.07 AVERAGE FLOWING TEMP"F: 150
56
Pressure Traverse Curves
oO
4
315
B
12
16
20
PRESSURE, 100 PSIG
24
28
32
36
40
48
44
52
56
1 TUBING SIZE, IN.:3.958
2
LIQUID RATE, STBL/D: 1000
3
WATER FRACTION:
4
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
5 6 7 8 E-<
'oo"
9
;: 10
'" .,[;;11 el
12 13 14 15 16 17 18 19 201111111111111111111111111 tül1llJ't ¡I 1'11 le-tu L1J" UU l±ti 1I LJ 1I1sIILL I tfi;tl
Production Optimiza/ion Using Nodal Analysis
316
PRESSURE, 100 PSIG
oO
4
8
12
16
20
24
28
32
36
40
44
48
52
1 TUBING SIZE, IN.:3.9S8
2 3 4 5 6 7 8
.. E-<
9
o o
~ 10
o:
f;:11
"'" 12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: 1000 WATER FRACTION:
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY,. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
0.0
4
317
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN., 3.958 2 3 4 5 6 7
8 E-<
i><
9
o o
;: 10 tI:
¡;:11
"'" 12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION,
1000
O
GAS GRAVITY: 0.65 OIL API GRAVITY, 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Production Optimization Using Nadal Ana/ysis
318
o
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
48
44
52
1 TUBING SIZE, IN.: 3.958 2 3 4 5 6
7 8
'o" O<
9
o
~ 10
'Z;:11 "
'"" 12 13
14 15
16 17 18 19 ··20·
LIQUID RATE, STBL/D: WATER FRACTION:
1500
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
oO
4
319
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 3.958 2 3 4 5 6 7 8
..
«
9
""
~ 10
f'"i:ll
""' 12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
1500
.5
GAS GRAVITY: 0.65 OIL API GRAVITY, 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Produclion Optimiza/ion Using Nada/ Ana/ysis
320
oO
4
6
12
16
20
PRESSURE, 100 PSIG 24 26 32 36
40
44
46
52
-1
-1
1 TUBING SIZE, IN.: 3.958 2 3 4
5 6 7 6
.. E-<
9
o o
~ 10
'" .,¡;;11 el
12 13 14 15 16 17 16 19 20
LIQUID RATE, STBL!D: WATER FRACTION:
56
1500
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
Pressure Traverse Curves
oO
4
321
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 3.958 2 3 4 5 6 7 8
..
'oo"
9
~ 10
.,¡;:'" 11 " 12 13
14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
2000
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
56
322
Production Optimiza/ion Using Nadal Analysis
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
-t-
1 TUBING SIZE, IN.: 3.956 2
LIQUID RATE, STBL/D: WATER FRACTION:
3
6 7 8
. E-<
9
o o ~ 10 tI:
!;:11
"'" 12 13 14 15 16 17 18 19 20
2000
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
4 5
56
I
Pressure Traverse Curves
oO
4
323
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING· SIZE, IN.: 3.958 2
LIQUIO RATE, STBL/O: WATER FRACTION:
3
5 6
8
....
9
o o
~ 10
'" "'" 12
1;:11
13 14 15 16 17 18 19 20
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
4
7
2000
I
56
Production Optimiza/ion Using Nodal Analysis
324
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
56
1-4
1 TUBING SIZE, IN.: 3.958 2 3 4 5 6 7 8
.. E-<
9
o o
~ 10
,
'" !i:ll
., " 12 13 14 15 16 17 18 19 20
LIQUIO RATE, STBL!O: WATER FRACTION:
3000
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
Pressure Traverse Curves
oO
4
325
8
12
16
20
PRESSURE, 100 PSIG 36 24 28 32
40
44
48
52
56 .~
1 TUBING SIZE, IN.: 3.958 2
LIQUID RATE, STBL/D: WATER FRACTION:
3
6 7 8
... 'o"
9
o
;: 10
o: ~1l
''"" 12 13 14 15 16 17 18 19 20
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
4 5
3000
I
326
Production Optimization Using Nada! Analysis
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
56 -~
1 TUBING SIZE, IN.: 3.958 2 3
4 5 6 7 8
.. E-<
9
o o
;: 10 :z:
!i:ll
'" Q
12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
3000
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
Pressure Traverse Curves
oO
4
327
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 3.958 2 3 4 5 6 7
8
....
9
o o
;: 10
"' ii:ll
""' 12 13 14 15 16 17
18 19 20
LIQUID RATE, STBL/D:
5000
WATER FRACTION: GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Production Optimization Using Nadal Analysis
328
oO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 3.958 2 3 4 5 6 7 8
...
9
o o
;: 10
'g";11 'e" 12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
5000
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY, 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
OO
4
329
8
12
16
20
PRESSURE, 100 PSIG 32 36 24 28
40
44
48
52
+
1 TUBING SIZE, IN.: 3.958 2 3 4
LIQUID RATE, STBL/D: WATER FRACTION:
6 7 8 9
o o
;: 10
"'1;:11
"'" 12 13 14 15 16 17 18 19 20
5000
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1. 07 AVERAGE FLOWING TEMP.,F: 150
5
....
56
m
Production Optimiza/ion Using Nadal Analysis
>30
PRESSURE,
8
12
16
20
24
100 PS!G
28
32
36
40
44
52
48
1 TUBING SIZE, IN.: 3.958 2 3 4 5 6 7 8
....é<
9
o o
~ 10
.,'a": 11 " 12 13 14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
8000
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLDWING TEMP.,F: 150
56
Pressure Traverse Curves
oO
4
331
6
12
16
20
PRESSURE, 100 PSIG 24 26 32 36
40
44
46
52
1 TUBING SIZE, IN.: 3.958 2 3 4 5 6 7 6
.. O<
9
o o ~ 10
'¡;:11 "
"'"
12 13 14 15 16 17 16 19 20
LIQUIO RATE, STBL/O: WATER FRACTION:
8000
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY:. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
332
Production Optimization Using Noda! Analysis
OO
4
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1
TUBING SIZE, IN.: 3.958 2
3 4
5 6 7 8
'"
ro.. 9 o o ~ 10
o:
l;;11
"'Cl
12
13 14
15 16 17 18
19 20
LIQUID RATE, STBL/D: 8000 WATER FRACTION:
o
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY,. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Pressure Traverse Curves
4
333
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
44
48
52
1 TUBING SIZE, IN.: 3.958 2
3 4 5
6 7 8
....
9
o o
~ 10
"' !i::u
"'" 12 13
14 15 16 17 18 19 20
LIQUID RATE, STBL/D: 10000 WATER FRACTION: GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Production Optimization Using Noda/ Analysis
334
O
4
6
12
16
20
PRESSURE, 100 PSIG 24 26 32 36
40
44
46
56
1 TUBING SIZE, IN.: 3.958 2 3 4 5
6 7 6
.....
9
o o
;: 10
:x: ~11
'" Q
12 13 14 15 16 17 16 19 20
LIQUID RATE, STBL/D: WATER FRACTIüN:
10000
.5
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY:. 1.07 AVERAGE FLOWING TEMP.,F: 150
Pressure Traverse Curves
0.0
4
335
8
12
16
20
PRESSURE, 100 PSIG 24 28 32 36
40
48
44
52
1 TUBING SIZE, IN.: 3.958 2 3 4 5 6 7 8
...f«
9
o o
;: 10
'1";:11 ""' 12 13
14 15 16 17 18 19 20
LIQUID RATE, STBL/D: WATER FRACTION:
10000
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY:. 1.07 AVERAGE FLOWING TEMP.,F: 150
56
Production Optimization Using Noda! Analysis
336
OO
2
4
6
10
8
PRESSURE, 100 PSIG 16 12 18 14
22
20
24
28
26
H:H+f-FlI=¡~ -+t -.·.lHt/WJtWIi:t: - iIT· .. -. J--L: -1-1+1-1+ t
,-'+
1
PIPELINE 1.0. , IN. :
•ftJ=i • LIQUID
+-I...!.·
2
STBL/D:
RATE,
- - - - -WATER FRACTION:
3
2 100
1
GAS GRAVITY: 0.65· OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1. 07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
4 5
-
rtI
•
-
~
6 7 8
.....
9
o o o
~
,10
...o:
'"
¡;jll
-f
H
12 13 14 15 16 17 18 1 2
--
-
.
-
--r T
:
- ---
--
337
Pressure Traverse Curves
oO 1 2
2
4
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
20
l.
26
o.,
LIQUID RATE, STBL/D: WATER FRACTION:
3 4 5
6 7 8
.. E-<
9
o o o
....
10
"' ¡:j11 '" E-<
H
12 13 14 15 16 17 18 1 2
2 100
O
GAS GRAVITY: 0.65· OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
28
Production Optirnization Using Noda! Analysis
338
2
:1 2
4
6
8
10
PRESSURE, 100 PSIG 12 18 14 16
20
22
_
_ _ ___ _
-~tr
f-
~
.. (
--
-i+
-l-.
LIQUID RATE, STBL/D: WATER FRACTION:
2
200
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1. 07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
5 .-
tiI
6 7 8
E-<
9
.... • 10
"' "~ 11 E-<
-
f
..:l
12 13 14 15 16 17 18 1 - -r-
2
__
.l._
'-j-f- - PIPELINE I. D. , IN. :
4
o o o
28
-l~itlftrn:ltt~jitt~I:!-Irn'JI1 -I-f-I+++-I-I:--
L+_ ,___ _ _-> -¡ _. -
3
..
26
24
-1
+-r
--
Production Optimizalion Using Nodal Analysis
340
2
oO
4
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
-,-i j- -
1
-+i-l-
:1+$1.
2
22
20
26
28
liti 1tt:J::l:jt~:1 flFi I H-t+ HII:i:t -l:ill:n f-Fr¡:ll-f I1 +H+I-I:r1 PIPELINE 1. D., IN.:
2
LIQUID RATE, STBL/D:
300
WATER FRACTION: 3
24
1
GAS GRAVITY': 0.65 OIL API GRAVITY': 35 WATER SPECIFIC GRAVITY': 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
4 5
-H- --
. H- -6
7 8
.. 11 E-<
o o o
9
.-<
,10
'" E-< el
í;¡ll
..:l
12
f
13 14 15 16 17 18 11-
20
• • 1:
L
r -- --
,r
--
Pressure Traverse Curves
341
4
1 2
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
20
22
PIPELINE 1.0., IN.: LIQUIO RATE, STBL/O: WATER FRACTION:
3 4
7 8
O<
9
~
.10
'" ..," O<
¡ ;jll 12 13 14 15 16 17 18 1
- 1 ....
- - -\. - - lT·- ..
2
300
GAS GRAVITY, 0.65· OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS • BRILL
6
.
2
O
5
o o o
26
24
.
28
342
Production Optimization Using Nada' Analysis
4
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
1 2
20
PIPELINE 1.0., IN.: f~-
LIQUIO RATE, STBL/O: WATER FRACTION:
3 4 5 6 7 8
.. €o<
9
o o o
.... • 10
'" €o< Cl
¡;jll H
12 13 14 15 16 17 18 1 2
2
400
1
-GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
Pressure Traverse Curves
343
PRESSURE, 100 PSIG 4
6
8
10
12
14
,16
1 2
18
PIPELINE 1.0., IN.:
i~
LIQUIO'RATE, STBL!O: WATER FRACTION:
3
4 5 6
7 8
....
9
o o o
... • 10 '" "f:jll
. ..:l
12 13 14
15 16 17
18 1 2
2 400
O
'GAS GRAVITY: 0.65' OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
344
Production Optimization Using Nodal Analysis
4
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
1 1-
2
f-· +-
2
LIQUID RATE, STBL/D:
sao
5 6 7 8
E-<
9
o o o
~
,lO
'" ..,'f":111 E-<
12 13 14
15 16 17 18 1 ~
2
1
--GAS GRAVITY: 0.65OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
4
..
26
PIPELINE 1. D., IN.:
WATER FRACTION: 3
24
20
28
Pressure Traverse Curves
345
4
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
1 2
PIPELINE I.D., IN.:
-r-r
1-
-
-f -'-o
LIQUID RATE, STBL/D: WATER FRACTION:
3 4 5
6
7 8
.
9
o o o
~
,10
.."'
"~11 él
12 13 14 15 16 17 18 1 20
24
20
26
2 500
O
""GAS GRAVITY: 0.65" OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
28
Production Optimization Using Noda! Ana/ysis
146
4
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
1 1- -
2
-1-
~-
20
PIPELINE LO., IN.:
2
LIQUIO RATE, STBL/o:
700
WATER FRACTION: 3
-GAS GRAVITY: 0.65OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 ORRELATION: BEGGS & BRILL
4 5
6
7 8
.. 8
9
e e e ~
,la
'" 8
tí'" 11 ,..;¡ 12
13 14 15 16
17 18 1 ~
2
1
Pressure Traverse Curves. -
4
347
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
1
20
PIPELINE I.D., IN.: 1~"
2
5 6 7 8 9
....o
..
•10
tI:
"..,&1 11 12 13 14 15 16 17 18 1
--/ 2
O
"GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
4
'oo"
2
LIQUIDRATE, STBL!D: 700 WATER FRACTION:
3
..
24
Production Optimiza/ion Using Nadal Analysis
348
4
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
1 -
+~.
4 5 6 7 8
..
9
o o o
... ,10 '" "f;Jll E<
H
12 13 14 15 16 17 18 1 2
2
LIQUID RATE, STBL/D: 900 WATER FRACTION:
3
26
24
PIPELINE LD., IN.: f-
2
20
1
GAS GRAVITY: 0.65 OIL APr GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRrLL
28
Pressure Traverse Curves
349
4
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
20
24
22
26
.1.
1 +- -
2
f
+ -'--
PIPELINE 1. D., IN.: LIQUID RATE, STBL/D: WATER FRACTION:
3
5 6 7 8 9
o o o
~
.10
.."'
"..,~1l 12 13 14 15 16 17 18 1 . -j
,
2
900
O
- GAS GRAVITY: 0.65OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
4
.
2
28
Production Optimization Using Nodal Analysis
350
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
1 2
20
PIPELINE I.O., IN.:
+ -'-.
LIQUIO RATE, STBL/o: WATER FRACTION:
3
4 5 6 7 8
...
9
o o o
....
..'"
•10
..,'~"11 12 13
14 15 16 17 18 1 2
2 1200
1
GAS GRAVITY: 0.65· OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 VERAGE FLOWING TEMP.,F: 100 C RELATION: BEGGS & BRILL
Pressure Traverse Curves
351
4
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
1
20
PIPELINE I.D., IN.: +-
2
-1-
-'-.
LIQUID· RATE, STBL/D: WATER FRACTION:
3
5 6
7
.. o o o
9
'"
...
..'"
• 10
'-'
..,~ 11 12 13 14
15 16 17 18 1 2
1200·
O
GAS GRAVITY: 0.65· OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 ORRELATION: BEGGS & BRILL
4
8
2
~
Production Optimiza/ion Using Nada! Analysis
352
6
1
8
10
PRESSURE, 100 PSIG 12 14 16 18
24
26
LIQUID RATE, STBL/D:
1500
20
I.D. ,
2
WATER FRACTION: 3
GA RAVITY: 0.65 OIL A GRAVITY: 35 WATER S CIFIC GRAVITY: 1.07 AVERAGE F WING TEMP.,F: 100 CORRELATION. BEGGS • BRILL
4 5
6
7 8
...
9
o o o
... ,la ..'" <.!J
f:íll
H
12 13 14 15 16 17 18 1 2
1
, -1-
28
Pressure Traverse Curves
353
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
-, 1
.+ PIPELINE I.D., IN.: LIQUID RATE, STBL/D:
2
WATER FRACTION: 3
5 6 7
.. o o o
9
r..
.-<
.
,la
:c
,
'
f:í 11 ,..," 12 13 14 15 16 17 18 1
:,,- "
2
2 1500
o
GRAVITY: 0.65OIL PI GRAVITY: 35 WATER PECIFIC GRAVITY: 1.07 AVERAG LOWING TEMP.,F: 100 CORRELAT BEGGS & BRILL
4
8
26
24
20
.1
,
28
Production Optimiza/ion Using Nada! Analysis
354
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
20
24
22
26
1
2000
LIQUID RATE, STBL/D:
2
WATER FRACTION: 3
1
GRAVITY: 0.65I GRAVITY: 35 ECIFIC GRAVITY: 1.07 AVERAGE OWING TEMP.,F: 100 ORRELATIO : BEGGS & BRrLL
4 5 6 7
, 8
....
9
o o o
....
,
..'"
•10
.+
i":íll ..:1
12 13 14 15 16 17 18
~-
1 ----.__ --
2
+
.
r
28
Pressure Traverse Curves
2
355
4
6
10
8
PRESSURE, 100 PSIG 12 14 .16 18
20
22
24
26
-i 1
. 2
-~
- -1
--'-
PIPELINE l. o. , IN. :
2
LIQUID RATE, STBL/D:
2000
WATER FRACTION: 3
.
AS GRAVITY: 0.65· API GRAVITY: 35 O SPECIFIC GRAVITY: 1. 07 WA FLOWING TEMP.,F: 100 AVERA CORRELK ON: BEGGS & BRILL
4
~
O
5 6
7 8
..
- -
9
o o o
....
."'
,lO
el
~
¡;jll >-1
12 13 14 15 16 17 18 1
- - - -1 2
-1
--
- - -... - . - -
-
28
Production Optimization Using Nodaf Analysis
356
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
1 ~
2
¡. -'-.
20
24
PIPELINE I.O., IN.:
26
3
LIQUIO RATE, STBL/o: 500 WATER FRACTION:
3 4 5 6 7 B
.. E-<
9
o o o
.-<
.10
'" E-<
'" ¡;'jll >'l
12 13 14 15 16 17 18 1 .2
GAS GRAVITY: 0.65· OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
28
Pressure Traverse Curves
0 0
2
357
4
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
20
24
26
LIQUID RATE, STBL/D:
500
1 2
WATER FRACTION: 3 4
GAS GRAVITY: 0.65' OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
5
6 7
8
.,
.
9
o o o
.-<
.10
.,"' ¡";jll '"
12 13 14
15 16 17
18 1 2
O
r
28
Production Optimization Using Nodal Anolysis
358
4
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
1
22
f~-
LIQUID RATE, STBL/D: WATER FRACTION:
3 4
6
7 8 9
o o o
.... ,ID
..
o:
<.!J
..,f:¡11 12 13 14 15 16 17
18 1 2
26
3
BOa
1
GAS GRAVITY: 0.65OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
5
....
24
PIPELINE I.D., IN.: ,
2
20
,r
28
Pressure Traverse Curves
359
4
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
1 +- -
2
+1-· -'-o
20
22
4 5 6 7
8
.. E-<
9
o o o
~
,la
o::
E-<
<.O
f:111
H
12 13 14 15 16 17
18 1 20
26
PIPELINE I.D., IN.:
3
LIQUIDRATE, STBL/D:
800
WATER FRACTION: 3
24
o
GAS GRAVITY: 0.65' OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
28
Produc(ion Optimization Ur;ing Nada! Analysis
360
4
6
8
10
PRESSURE, 100 PSIG 12 14 16 18 ~
1 2
.1
~-
24
20
--
PIPELINE I.D., IN.: LIQUID RATE, STBL/O: WATER FRACTION:
3 4
+-
7 8
..
E-<
o o o
9
..-. .10
"' E-<
f:jll
..,
12 13 14 15 16 17 18 1 2
3 1000
1
GAS GRAVITY: 0.65· OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
5 6
26
r
28
Pressure Traverse Curves
361
4
6
8
10
PRESSURE, 100 PSIG 12 14 16 18 -r
20
24
26
_ ...L. ' •.
1
PIPELINE 1.0., IN.: LIQUID RATE, STBL/D:
2
WATER FRACTION: 3
5 6 7 8
ó<
9
o o o n
.10
"' ó<
'-'
¡;jll H
12 13 14 15 16 17 18 1 2
1000
O
GAS GRAVITY: 0.65OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
4
..
3
1-
28
Production Optimization Using Nodal Analysis
362
4
1 2
6
8
10
PRESSURE. 100 PSIG 12 14 16 18
20
PIPELINE 1.0., IN.: LIQUIO RATE, STBL/O: WATER FRACTION:
3
4
'" .~
24
22
26
3 1500
1
GAS GRAVITY: 0.65· OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP •• F: 100 CORRELATION: BEGGS & BRILL
5 6 7 8
...
9
o o o
., ,10
'.". 'f":íll
..:l
12 13
14 15 16 17 18 1 20
r·
28
Pressure Traverse CUrles
363
4
6
8
10
PRESSURE, 100 PSIG 12 14 '16 18
1
.
22
PIPELINE I.D., IN.:
- - -1
2
20
'
LIQUID RATE, STBL/D: WATER FRACTION:
3 4 5 6 7 8
.'"
9
o o o
.... ,la
'.". "..,¡;¡11
12 13 14 15 16 17 18 1 2
3 1500
o
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
Production Optimization Using Nodal Analysis
364
4
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
20
22
24
26
1 LIQUID RATE, STBL/D:
2
WATER FRACTION: 3
5 6 7 8 9
o o o
~
..'"
,
,la
t!J
¡:¡ 11
+
"' 12 13 14 15 16 17 18 1
:1
-c
2
1
GAS GRAVITY: 0.65OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 ORRELATION: BEGGS & BRILL
4
....
2000
28
Pressure Traverse Curves
2
365
4
6
8
10
PRESSURE, 100 PSIG 14 16 18 12
1 ¡.
2
-- -
3
-~
+ -'.,
20
26
24
PIPELINE l. D. , IN. :
3
LIQUID RATE, STBL/D:
2000
WATER FRACTION:
O
GAS GRAVIT'l: 0.65OIL API GRAVIT'l: 35 WATER SPECIFIC GRAVIT'l: 1. 07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & 8RILL
4 5 6 7 8
.. O<
9
o o o ~
,lO
"' O<
"
¡ ;jll H
12 13 14 15 16 17 18
-c 1
, 2
-1
"
r
28
Production Optimizarion Using Nada! Analysis
366
4
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
1 -1
~-
2
20
26
PIPELINE I.D., IN.:
3
LIQUID RATE, STBL/D:
3000-
WATER FRACTION: 3
24
1
GAS GRAVITY: 0.65OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
4 5 6 7 8
...
'"
9
o o o
.-<
.10
'"'-'...
-+
f;'jll ,..:¡
12 13 14 15 16 17 18
¡-
1 2
-1-
28
Pressure Traverse Curves
367
4
1 2
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
20
4 5 6 7 8
.."'
9
o o
o
.... ,lO
"''"
'-'
¡;jll
,..,
12 13 14 15 16 17 18 1 2
26
PIPELINE I.D., IN.:
3
LIQUID RATE, STBL/D:
3000
WATER FRACTION:
3
24
O
··GAS GRAVITY: 0.65· OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
28
Production Optimiza/ion Using Nada! Analysis
368
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
1 1- "1
2
-,
-l· -l..
PIPELINE 1.0., IN.: LIQUID RATE, STBL!D: WATER FRACTION:
3
5 6
7 8 E-<
r..
9
~
,lO
:c
-'
E-<
e>
..,¡;¡ 11 12 13 14 15 16 17 18 1 2
26
3 4000
1
S GRAVITY: 0.6501 API GRAVITY: 35 WAT SPECIFIC GRAVITY: 1.07 AVERAG FLOWING TEMP.,F: 100 CQRRELA ON: BEGGS & BRILL
4
o o o
24
20
-,"'
28
Pressure Traverse Curves
:. 2
369
4
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
1+
~
-=t: q:: 1:.
22
20
3
LIQUID RATE, STBL/D:
4000
~
5
-,~- - -I-f.-
6 7 8 E-< Ó<
9
~
,la
o: E-<
" 11 ~
H
12 13 14 15 16 17 18 1Ilr.-1-
1 -
2
o
GAS GRAVITY: 0.65 API GRAVITY: 35 WA ER SPECIFIC GRAVITY: 1.07 AVE GE FLOWING TEMP.,F: 100 . CORRE TION: BEGGS • BRILL
4
o o o
26
PIPELINE I.D., IN.:
WATER FRACTION: 3
24
:1- - . - - ~:~
r
28
Production Optimization Using Nodal Analysis
370
2
4
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
1
24
20
PIPELINE l. o. , IN. : ;-
2
-
1-
-'o
LIQUID RATE, STBL/D: WATER FRACTION:
3
5 6 7 8 9
o o o
.... ,la
"'E-< ..,'f";¡11 12 13 14 15 16 17 18 1
- :1· 2
3
5000
1
GAS GRAVITY: 0.65' OIL API GRAVITY: 35 TER SPECIFIC GRAVITY: 1. 07 AGE FLOWING TEMP.,F: 100 LATION: BEGGS & BRILL
4
.....
26
"
r
28
Pressure Traverse Curves
371
6
8
10
PRESSURE, 100 PSIG 12 14 16 lB
1 1- '1
2
e-f· .J..
20
3
LIQUIO RATE, STBL/O:
5000
5 6 7 8 9
o o o
~
.
,lO
c::
'f":jll
..:l
12 13 14 15 16 17 18 1
-1 2
O
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 VERAGE FLOWING TEMP.,F: 100 RRELATION: BEGGS & BRILL
4
...
26
PIPELINE I.D., IN.:
WATER FRACTION: 3
24
22
Production Optimization Using Noda! Analysis
372
8
10
PRESSURE, 100 PSIG 12 14 16 18
20
22
24
26
1 6000
2
FRACTION: 3 4 5 6
7 8
..
...
9
o o o
.... ,lO :::
...
I
•.¡.
"f:jll H
12
13 14 15 16 17 18 1
. ·1 2
"
1
28
Pressure Traverse Curves
373
PRESSURE, 100 PSIG 8
10
12
14
16
1
-> -f _1
2
-l-_
18
20
3
LIQUID RATE, STBL/D:
6000
5 6 7 8 9
o o o
....
.'"
,10
,
.+
'f":jll
H
12 13 14 15 16 17 18 1 2
O
S GRAVITY: 0.65 OI PI GRAVITY: 35 WATE PECIFIC GRAVITY: 1.07 AVERAG FLOWING TEMP.,F: 100 CORRELAT N: BEGGS • BRILL
4
....
26
PIPELINE I.D., IN.:
WATER FRACTION: 3
24
28
374
Production Oprimi=ation Using Nada! Analysis
4
6
8
PRESSURE, 100 PSIG 10' 12 14 1618
1
24
-~~
+,
LIQUID RATE, STBL/D: WATER FRACTION:
3 4
6 7 8
.
8
9
~
.10
'" '&"111 '" 8
12 13 14 15 16 17 18 1 2
1000
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
5
o o o
26
4
PIPELINE 1-
2
20
"- + -1 +-r f
28
Pressure Traverse Curves
375
4
1 2
6
8
10
PRESSURE, 1.00 PSIG 12 14 16 18
'.
" ::t: :t:
20
22
24
PIPELINE I. D., IN.:
26
4
LIQUID RATE, STBL/D: 1000WATER FRACTIDN: O
3 4
GAS GRAVITY: 0.65OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
5 6 7 8
. E<
9
o o o
n
,10
'E"<
'"
¡;jll ,.:¡
12 13 14 15 16 17 18 1 2
++
28
Production Optimization Using Nodal Analysis
376
4
6
8
10
PRESSURE, 100 PSIG 12 14 16 18 .-.L __ "-
±PIPELINE
1 2
26
20
~_.I
-1"
,
,
I.O.,
4
LIQUIO RATE, STBL/O: 1500
-- _.>-
WATER FRACTION: 1 3 4 5 6
7
.... o o o
8 9
'""',lO
'.". el
~11
H
12 13 14 15 16 17 18 1 2
GAS GRAVITY: 0.65' OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
28
PresslIre Traverse Curves
377
4
1 2
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
20
24
26
I. D. ,
LIQUID RATE, STBL/D: 1500 WATER FRACTION: O
3 4
5 6
7
..
8
o o o
9
O<
~
."'
.10
~11
>.:l
12 13 14 15 16
17 18 1 2
GAS GRAVITY: 0.65· OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
28
Prodllction Optimiza/ion Using Noda! Analysis
378
oO
4
2
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
24
22
20
26
28
-++ ,-¡-I--
-1+il-~ -
2
n::¡-I I
...1-.
PIPELINE I.D., IN.: LIQUID RATE, STBL/D:
4 2000
1-
WATER FRACTION: 3
1
GAS GRAVITY: 0.65OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
4
5
-'-j-- -
. rT --
-
6
7 8
.. 8
o o o
9
I
~
,lO
o:
8
t!1
¡;j1l H
12
~1tM
13 14
15 16 17 18 19 2
•mi-
o:
..
,
t
i
J~
~-r
-
Pressure Traverse Curves
379
4
6
8
PRESSURE, 100 PSIG 1012 14 16 18
20
24
26
1 4
2
LIQUID RATE, STBL/D: WATER FRACTION:
3
4
6 7 8 9
o o o
.... ,lO
.."' eJ
í;jll ..., 12 13
14 15 16 17 18 1 2
O
GAS GRAVITY: 0.65· OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
5
....
2000
+-r
28
Production Optimization Using Nodal Analysis
380
oO 1 2
2
4
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
20
22
4 5
4
LIQUID RATE, STBL/D:
3000
1
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLDWING TEMP.,F: 100 CORRELATIDN: BEGGS & BRILL
++ -1+
--
~.
6 7
8
.....
9
o o o
.... •10
.r+
.'lO.." ¡;¡ 11 H
12 13 14 15 16 17
18 1 2
26
PIPELINEI.D., IN.:
WATER FRACTION: 3
24
,r
28
Pressure Traverse Curves
2
oO
381
4
6
8
10
PRESSURE. 100 PSIG 12 14 16 18
20
22
'++ ::t, +
PIPELINE LO .• IN.:
4
LIQUIO RATE.
3000
STBL/o:
WATER FRACTION: 3 ft\\1\
I
5 6 7 8
E-<
9
o o o
~
,la
'" i";'jll E-<
H
12 13 14 15 16 17 18 1 - -ro
2
28
·1~itj:j+t+Hm~l:UiftH+H-Ht¡i tltJítttul-H-I+HFI+
.. :r:l: -
2
..
26
- il-~U_-U
1
4
24
o
GAS GRAVITY: 0.65OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP •• F: 100 CORRELATION: BEGGS & BRILL
Production Optimiza/ion Using Nadal Analysis
382
4
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
1 -1~-
2
20
22
PIPELINE I.D., IN.:
4
LIQUIDRATE, STBL/D:
5DOO-
WATER FRACTION: 3
5 6 7 8 E-<
r.
9
.... •10 tI:
E-<
<él
f:lll .:l
12 13 14
15 16 17 18 1 2
28
1
GRAVITY, 0.65API GRAVITY: 35 SPECIFIC GRAVITY: 1.07 AVERA FLOWING TEMP.,F: 100 CORRELA ION: BEGGS & BRILL
4
o o o
26
24
- - --1"-
Pressure Traverse Curves
2
383
4
6
8
10
PRESSURE, 100 PSIG 18 12 14 16
1
'-1 1-
2
--i+ -'-.
,
22
20
PIPELINE l. D.
I
5 6 7 8 9
o o o
",10
.. o:
el
..,511 12 13 14 15 16 17 18 1
- - ·1
20
26
4 5000
O
GAS GRAVITY: 0.65· IL API GRAVITY: 35 W ER SPECIFIC GRAVITY: 1. 07 AVE GE FLOWING TEMP.,F: 100 CORR ATION: BEGGS & BRILL
4
.....
IN. :
LIQUID RATE, STBL/D: WATER FRACTION:
3
24
.. ._¡
1-,
28
384
Production Optimization Using Nodal Analysis
6
1
8
10
PRESSURE, 100 PSIG 12 14 16 18
20
26
PIPELINE
IN.:
LIQUID RATE, STBL/D:
2
WATER FRACTION: 3
5 6
7 8 9
o
~
.10
.,o:
:1.
lO
~11
H
12 13 14 15 16 17 18 1 - - - :j
2
8000
1
GRAVITY: 0.65API GRAVITY: 35 R SPEClfIC GRAVITY: 1.07 AVE GE FLOWING TEMP.,F: 100 CORRE TION: BEGGS & BRILL
4
., o'" o
4
-1
-
- -1
-r "
28
Pressure Traverse Curves
385
4
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
20
24
26
1 LIQUID RATE,
2
STBL/D:
WATER FRACTION: 3
5 6 7 8 9
o o o
.... ,la
.."'
-+
C9
1311 H 12 13
14 15 16 17 18 1 2
o
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 ATER SPECIFIC GRAVITY: 1.07 A RAGE FLOWING TEMP.,F: 100 CO ELATION: BEGGS & BRILL
4
.
8000
..
~ ~ ~
-j
-1- ~ ~I~
28
Production Optimization U'iing Noda! Ana~vsis
386
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
20
26
28
1 LIQUID RATE, STBL/D:
2
WATER FRACTION: 3
10000
1
GAS GRAVITY: 0.65' OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1. 07 VERAGE FLOWING TEMP.,F: 100 RELATION: BEGGS & BRILL
4 5 6 7
... o
8 9
O> O> ~
,lO
.."'
, 1
l?
&i 11 H
12 13 14 15 16 17 18
". - -
1 --j
2D
" -1-
-,
-]-
-
\ r-
Pressure Traverse Curves
387
4
2
6
8
10
PRESSURE, 100 PSIG 18 16 12 14
1
"
2 3
--- - - -
4
-
+f-
-'--
20
24
PIPELINE I.O. , IN. : LIQUID RATE, STBL/D: WATER FRACTION:
6
7 8
..
E-<
9
.... ,la
'"
,
~J.
E-<
"f;'jll >-1
12 13 14 15 16 17 18 1 2
- -:- -1-r--1-
4 10000
a
GAS GRAVITY: 0.65OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1. 07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
5
o o o
26
,r
28
388
Production Optimiza/ion Using Noda! Analysis
4
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
1
'ti
ti-' . -;-f---'-,-'--
20
22
24
PIPELINE LO., IN.:
26
5
1-
2
~I-
LIQUID RATE, STBL/D: 2000 WATER FRACTION:
3
4
1
GAS GRAVITY: 0.65OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
5 6 7 8 &<
O<
9
o o o ~
10
'&"<
"f;'jll H
12 13
14 15 16 17 18 1 2
f-
28
Pressure Traverse Curves
389
4
6
8
10
PRESSURE, 100 PSIG 12 14 16 18 I
1 2
_.1
20
22
24
26
( . +Ullittlli±±±:l±Uill±l±±J±J:±j PIPELINE 1. D., IN.:
5
LIQUID RATE, STBL/D: 2000 WATER FRACTION: O
3 4 5 6 7 8
....
9
o o o
~
..'"
,lO
'"
¡;jll
"' 12 13 14 15 16 17 18 1 2
28
.l..
GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
390
Production Optimi=atiQn Using Noda! rlna(l-'sis
4
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
22
20
24
26
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PIPELINE 1. D., IN.:
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LIQUID RATE, STBL/D: 3000 WATER FRACTION: 1
3 4
GAS GRAVITY: 0.65· DIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLDWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
5 6 7
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12 13 14 15 16 17 18 1
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Pressure Traverse Curves
391
4
6
8
10
PRESSURE, 100 P5IG 12 14 16 18
22
20
24
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PIPELINE 1. D., IN.: ¡.. ~
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LIQUIO RATE, STBL/O: 3000 WATER FRACTION: O
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GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
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Prodllction Optimi=ation U'iing Nodal AJ1ulysis
392
4
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8
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PRESSURE, 100 PSIG 12 14 16 18
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20
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LIQUID RATE, STBL/D: SOOO
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WATER FRACTION: 3
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GAS GRAVITY: 0.65OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
4
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28
Pressure Traverse Curves
393
4
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PRESSURE, 100 PSIG 12 14 16 18
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PIPELINE 1. O., IN.: . - _
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WATER FRACTION: O 3
GAS GRAVITY: 0.65· OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
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12 13 14 15 16 17 18 1 ~
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Production Optimization Using Noda! Ana(vsis
394
4
6
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PRESSURE, 100 PSIG 12 14 16 18
20
24
26
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PIPELINE 1. D., IN.:
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WATER FRACTION: 3 4 5 6 7 8
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GAS GRAVITY: 0.65' OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 ERAGE FLOWING TEMP.,F: 100 CO RELATION: BEGGS & BRILL
28
Pressure Traverse Curves
395
6
8
10
PRESSURE, 100 PSIG 12 14 16 18
20
22
24
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PIPELINE I. D., IN.:
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LIQUID' RATE, STBL/D: 8000· WATER FRACTION: O
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GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 RRELATION: BEGGS & BRILL
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396
Production Optimi:::a/ion Using Noda! AnQ!ysis
4
6
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PRESSURE, 100 PSIG 12 14 16 18
1
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20
22
24
PIPELINE I. D., IN.:
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LIQUID RATE, STBL/D: 10000 WATER FRACTION: 1
3
GAS GRAVITY: 0.65OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
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398
Production Optimization Using Noda/ Analysis
6
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PRESSURE, 100 PSIG 12 14 16 16
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LIQUID RATE, STBL/D: WATER FRACTION:
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GAS GRAVITY: 0.65 OIL API GRAVITY: 35 WATER SPECIFIC GRAVITY: 1.07 AVERAGE FLOWING TEMP.,F: 100 CORRELATION: BEGGS & BRILL
4
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Pressure Traverse Curves
2
399
4
6
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PRESSURE,
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Index
Abandonment conditions. 18 Abscissa correlating group, 110 Absolute permeability, 14, 15,26 pressure, 124 temperature, 124 Acceleration, 84,86,87,93,97,191,194
component,67, 83, 84 term, 84 Acidizing, 49, 139 Actual density, 195 downstream pressure, 125 drawdown, 26 gas velocity, 65, 66 ¡íquid holdup, 66, 85 Iiquid velocity, 65. 66 producing capacity, 139
volumetric flow rates, 76 wellhead pressure, 100 Algorithms, 68, 78 for coupling pressure and heat loss calcularians, 81 heat transfer calculation. 73 incremellting on length, 68
incrementing on pressure, 68 Altered zone penneability, 48, 52
effects of. 14 Altered radius etTects of, 14 zane, 48, 52, 53 Alves flow pattero, 108 American Gas Association, 109, 110 Analysis. 150, 152 artificiallift wells, 155 components ofsystem, 185
OST, PVT, 144 forces acting on various areas of valve,
165 gravel-packed completions, 174 laboratory, 72
multiwell systems, 151 outtlow, 155 pressure-volume-temperature, 72 single wells, 151 Angle, choke opening, 126 Angle of indination, (13 Annular, 67, l09 area, 158 flow,90 prediction capability, 90 tests, 86 mist partero, 87 Annulus, 83, 90, 180,260
AOF, 43, 44, 45, 46 API,97 equation, 127
grav;ly, 75, 78, 80, 95 Application curves, 98 total system analysis, 151 Vogel Method-Non-Zero Skin Factor (Standing Modification), 26 Vogel Method-Zero Skin factor, 23, 24 Aquifer, 18, 19 Artificiallift, 4, 7, 24, 40, 136, 137, 141, 148,
150,151,153 analysis, 155 design, 155 methods, 155, 177, 183 gas lift, 155 hydraulic pumping, 155 submersible pumping, 155 sucker rod or beam pumping, 155 weHs, 146, 155, 178 Average flowing temperature, 97, 98 Average pressure, la, 113, 143 Average reservoir pressure, 2, 9,12,20,21,
22 Average system pressure, 88 Average temperature, 113 Aziz flow regimes, 88
Aziz, Govier and Fogarasi Methoct, 87 Back Pressure equation,43 Baker flow partero map, 108, 109 Basic pressure gradient equation, 58 Beam pumping, 155, 177 unit, 178 Bean diameter, 127 Beggs and Brin correlation, 117, 118 data, lI4,lI5 flow partero map, 108
method, 88, 89, 90, 98, 108, lll, ll2, lI4, lI8, 192, 194 Bellows pressure, 166 Bemoulli equation, 123 Beta ratio, 127 BHP, flowing, static, 163 Bit size, 36 Borehole,9 size,51 Bortomhole, 136 chokes, 123 flowing pressure, 5, 9, 13, 14,98, -lOO,
lI4,177 pressure, 5, 43, 84, 140, 147, 155, 182 pressure gage. 31 temperature, 81 Brill and Beggs equation. 78 (modified by Standing), 78 Brine viscosity, 80 Bubble regime, 67 Bubble-flow partero, 86, 87 Bubble·rise velocity, 87 Bubblepoint, 75 pressure, 15, 18, 20, 24. 36, 37, 5l, 79,
148 Buildup test, 45 Calculated [iquid holdup values, [14
401
Produclion Optimiza/ion Using Noda! Ana(vsis
402 Calculator application, ll2 Carnco methad, 163 Capacitance probe, 65 devices, 83
gravel pack, 143 open hole, 143 perforated. 143 Components, 47, 48,57,86.108,11 J, 133,
Casing, 83.160,162,180
acceleration, 67.69 changes, 57 charaeteristics. 57 downstream. 2 elevation, 69 friction, 69 laminar grave! pack, 48 perforation,47 reservoir, 47 turbulel1{ gravel pack, 48 perforation, 48 reservoir, 48 upstream, 2, 3, 9 Compressible, 10 flow, 64 Compressibility, 9, 79 factor, 123 Compressor, 146, 150, 152 pressures, J46 Computer application, 86, 98, 112 calculation, 68, 150 program, MONA, 90 subroutíne, 108, 111 Condensate, 72, 97, 122 Conductive heat 105s, 71 resistance, Continuous flow gas lift, 155 system design, 155 well,60 Convection lenn. R 7l f Convective acceleracion, 63 heat !oss, 10 heal: transfer, 71 resistanee, 71 Conventional flow·afier·flow test, 31 test pressure diagrams, 32 producing rute, 32 Convergence, 72, 85, 123,125,182 Core,49 data, 38 Comish Method, 91 Correlating parameters, 66 Correlations for holdup factor, 85 forRs ' 78 for secondary correction factor. 85 for viscosity number coefficíent, 85 for pipeline flow prediction. lO8 Corrosion,61 Cricondenthenn, 20 Critical flow {sanie), 123. 124, 125, 141, 142, 153 gas saturation. [8 pressure drop, 143 pressure ratío, 124. 125 ratio of downstream to upstream pressure, 124
annulus, 177 diameler, 174 gas pressure, 160 inside diameter, [82 pressure, 163, [66, 168, 177 reduction, 163 lraverse, 162 valves, 165 size, 135, 174 tied into tlowine, 180 Casinghead flowline, 175 gas, 174, 175 Centrifugal separator, t 74 Ceramic choke disk operatían, 126 Chierici, Ciucci and Sclocchi Method, 88 Choke. 123, 126 at wellhead, capacity, 173, 176, 177 constants, 124, 126 control, 153 diameter, 124, 126, 127, 128 discharge coefficient, 126 [ocated at separator, 141, 142, 143 located at wellhead, t 41,142, L43 loeatian, 143 setting, 126 size, 123, 124. 125, 143, 163 Circular drainage, 31 area, 12, 14 Clausis inequality, 59 Clay swelling, 14 Coefficients, 123 Colcbrook equation, 61, 62 Combination drive, 19 reservoir, 19 Commingled rate, 153 well,38 Commíngling, 153 flow streams, 152 point, 153 point pressure, 153 well streams, 152 Compacted permeability, 51, 52 zone, 48, 50, 5 [,52,53, 144 permeability, 51 radius, 51, 52 thlekness, 53 Compaction,47 Comparison studies, 92 Completion, 143 configurations design, 146 effect, 143 efficieney, 45, -1:6, 47, 48 ¡ength,45 methods, 47, 143 pressure drop, 143 zonc,4S Completions,
174
regime, 124 temperature, 20 Crude oil, 66,72 viscosity, 66 Crushed zone. 50 permeability. 5) damage,48 Cul1ender and Smith method, 97 Cumulntive oil production, 150. 151 data, 150 increment, 150 recovery, 18 Damaged well, 20 Damaged-zone penneability, 51 Darey flow, 35,48 Darcy's equatíon, 30 equation for radial gas flow, 43 law,9, ID, 11, 14,21 Darcy-Wiesbach thction factor, 60 Daca banlc, 114 Dead ni1 interfaciai tension, 81 Declining production rate, 95 Deep welIs, J 60 Deganee aod Atherton f10w pattern, 108 Degree of scatter, 92 of s\ippage, 66 Deliverability, 1, 150, l63 Density, 5, 57, 64, 65, 67, 73, 75, 87, 96, 100,
176,180,182,191 air, 87 calcu1ating, 66 changes,65 definition, 65 gas/liquid mixture, 66 oil,75 tenn, 66,111 two-phase, 65 water, 15, 87 Depletion, 40, 46, 54, 55, 61,148,155 depletíon parameters gas/oil ratio, 148 gaslliquid ratio, 148 water cut, 148 type field, 93 Depth axis, 100 Design gradient, 168, 169 method, t63 liquid rate, 162 rnethods, 98 procedure, 174 safety factors, 165 surface pressure, tubing load. 169 Designing t1owtines, 1 04 long distance pipelines, 104 Determining maximum tubing size, 96 producing cap3clry, 151 Development planning, ! SO Deviated wells, 90 Dewpoint pressure. 15,20 Diameter, 51 Dimensional analysis. 61. l11
lndex Dimensionless flow rate, 21 groups, Reynolds number, 7 \ Grashof number, 71 Prandtl number, 71 IPR. 21, 22 curves, 21, 26 numbers, 66, 85, 86, 97,109,19[,192 pressure, 21 ratio, 22 slip velocity, 86 Direction of flow, 68 Directional well, 90, 93, 98, 104 Directionally drilled wel1s, 90, 97, 174 Discharge coefficiem, 123, 124, 127 pressures, 175 Dispersions, 95 Dissolved gas, 80, 175 drive, 18 drive mechanism, 18 drive performance, 18 Dissolved or solution gas calculation, 77 Dissolved solids, 80 Dividíng well into short increments, 96 Division point (node), 2 Dome pressure, 165, 166, 169 Downhill flow, lIS Downhole, 165 Downstream, 153 components, 2, 133 conditions. 125 gas density, 124 pressure, 123, 125, 126, 127, 128, 141,
142,143,153,172 Downward flow, 64, 68, 69, 89 incUnation, 109 mavement, 87 Drainage area, 19, 150 radius, 12, 14 Drawdown, 9,14,17,20,21, 24,34,54 actual, 26 effect, gas wells, 54 ideal, 26 rate, 19 test, 45 Drew, Koo and McAdams equation, 60, 61,62 OríU stem test, 36, 144 Orive mechanism, 9, J 7 Dry gas, 97 reservo ir, 21, 47 wells,82 DST analysis, 144 Oukter, et al., Method, 109, 110 Dukler correlatian, ¡ 17 frictíon factor cOrTelatíon, ! 12 liquíd holdup correlation, 112 method,111 Dukler-Eaton correlation, 1[4 method, 114 Duns and Ros method, 86, 87, 98
403 Eatan correlation, 114 for fríction factor and liquid holdup, 109,
111 Eaton, et al., Method, 109, ¡ 10 Eaton liquid holdup correlation, 1[1 Economic evaluarion, 150 Effect of compressor pressures, 146 depletion, 20, 148 on pressure profile, 21 on [PR,21 downhole separator, 176 final outlet pressure, 152 flow rate, 116 flowlines on well performance, 118 flowline sizes, 146 gas injection rote, 146, 157 gaslliquid ratio, 94, 116 gas rate, 94 gravity, on liquid, 67 injection depth, 157 injeccian rate, line diameter, 117 negative skio, 20 perforating density, 144 pipeline angle 00 flow partern, 109 positive skin, 20 stimulation, 139, 140 tubing size, 96, 135, 146 on minimum production rate, 96 on injection rate, turbulence,43 upper string size, 137 variables on pipeline performance, 116 viscosity, 95 water cut on required flowing pressure,
94,95 Effective mixture viscosity, ¡ 17 permeability, 15,47 stimulation, 140 viscosity, 65 Efficiency factor, 113, 117 Ekofisk field, North Sea, 90 Electric submersible pumps (ESP), 153, 174 Elevation change, 63, 65 component, 66, 116 component, 83, 91,98, 108, 112 Emperícal correlation, 65, 66, 68, 83, 84, 91,114,191 fluid property correlation, 73, 76 enthalpy correlation, 72 methods,73 Emulsioos, 95, 117 Energy balance, 58 equation, 59, 69 Energy loss, 60, 84 Energy of expansion or compression, 58 Engineering eguation of state for a gas, 75 English system ofunits, 123 Enthalpy, 59 change, 8Z gradient, 69 specific, 69 Entropy,59 Equation for calculacing gas in solution in Water, 79
Equation for estimating minimum gas producing rate, 97 Equivalent length concept, 128 Erosion, 61. 129 Erosional flow rate, 129 velocity, 129 velocity eguation, 129
ESP, 176 ESlimating flowing temperature, 82 Evaluatíng completion etTects, 143 correlations, 91 usiog field data, 91 pipe flow correlations, ¡ 14 EvalualÍon srudies, 93 Expansion factor, 127 Fanning equation, 60 Fetkovich equation, 34, 40 method, 30, 37, 42, 142 present and future IPRs, 42, 43 Field data, 91, 92, 93, 98, 114, 115, 116 Field producing capacity, 151 Final autlet pressure, 152 Finding optimum rubing size, 5 Fitting type, 128, 129 size, 128 Flanigan efficiency factor, 113 equation, 113 method, 111,112,118 Flow capacity, 3, 122, 135, 140 characteristics, laminar, 71 transitían, 71 turbulent, 71 coefficient e, 42 conditions, 83 conduit,67 critical, 123 direction of, 68 diversion, 122 efficiency, 26, 29, 47,140, 141
gas, two-phase, 123 geometry, 11, 60, 83 in casing, 176 in directional wells, 97 in gas wells, in pipelines, 108 inclined downward, 67 inclined upward, 67 non-steady, 71 of gases, 82 parameters, 90 panem, 65, 66, 67, 7[, 72, 83, 84, 85, 86,
87,88.90,97,108,109,114,117,192, 193,194,195 bubble regime, 66 descríptions for vertical air/water flow,
67 descriptions for horizontal air/water flow, 67 map, 84,86, 108
Produclion Optimization Using Nada/ Ana/ysis
404 mist,67
properties,9, 15,41,57,64,67,68,69,78,
existing, 67 expected, 67 horizontal tlow, predicting,
vertical f1ow, predicting, 67 period, <1-3
rate, 2,3,7,9,13,21,24,43,49,65,73, 75,82,83,84,85,88,91, IDO, [04, [16,ln,123,124,126,12~133,137,
141, 143, 144, 145, 167, 194 through choke, 124 total in-situ, 66
in-situ,76 standard, 76 regirr:e,9 resistance, ¡ 44
splitting problem, 122 steam, 64, 65 stream, 109, 152 subcritícal, 123
tests, 31 after·flow, 30, 31. 32, 33. 34, 43
Flowing bottom.hole pressure, 24, 94, 100, 102, 104, 162,163,174,183 Quid, to, 14,69,70
temperature, 165 viscosity, 66 gasllit¡uid mixture, S
density, 65 gradient, 163, 168 load fluid gradient curve, 1fi3 performance, 93 pressure, 31 pressure traverses, production wel1s, 146 temperature gradient, t 67 temperature in pipelines, 82 temperature in wells. 82 temperamre profile, 81 temperatures, 81 test, 102 tubing prcssure, 160, 163 tubing pressure traverse, 163, 173 wellbore pressure, 9, 24, 21, 31, 98, 155 weUs, 141, t55, 15R F1owline, 104, 114, 123, 136, 141, 142, t43, 156,114,178
diameter, 139 pressure drop, 137, l56 calculations, 174 requirements, 158 size, 14, 1I8, L37, 139, 146, 158 size effect, 136, 137 too large, 136, 137 too small, 136, 137 Fluctuating tlow, 65 Fluid co1urnn, 1RO density, 72, 73, 75, 83, 129 tlow equations, 58 gradient traverse, 163 [evel, [60, 179, 180 mixture, 180 operated va[ves, 165 phase, 65 superficial velocity, 65 physical properties, 81,125
84,98, 192
t:valualion, 127 oil grav\ty, 66 gas gravity, 66 dissoLved gas, 66 calculations, 72 correlalion, 81, 88,194 data, PVT properties, 75 5ample, 36, 98 analysis, 4 t ~aturation, 9 lemperature, 70, 81, 175 ve[ocity, 4, 5, 9, 64, 72, 76, 93, 100 viscosiry value, 80 Folds of inerease, 26 Force balance, 60 Formation, 162 damage,9,14,17,30,48,49,54,55,lJ5 clay swelting, 14 gas welIs, 14 pore plugging, 14 gaslliquid ratio, GLR, 156, 158, 162, 168, 172, 174
stimulation, 9 thickness, 45, 51 volurne factor, 76,79, 125, t76 brine in contact with gas, 79 Fraction of oil flowing, 125, 175 Fracüon ofwater tlowing, 125 Fmcturing, 139 Free gas, 15, 18, 37, 57, 94,175,176
flow rate, j6 saturation, 19 Friction, 59, 60. 104, 112, 116, 156, ¡58 component, 67, 83, 94,112 factor, 60,.61, 62, 64, 67, 72, 83. 84, 86. 90,91,95,108,109,110,117,191,195
comparison study, 114 correlatian, 67, 84, 85, \09,114 equation, 90 for pipe flow, 61,62,128 prediction, 114 two~phase, 67,89 loss, 5, 37, 59, 60, 63, 65, 68, 80, 83, 93, 98,113,116,128,135,156 component, 64 in annulus, t58 methods, 113
pressure drop, 95,117,139,143,180 component, [14 tenn, 84,93, 104, 117
eompression, ¡58 conCensate pipeline, 1t2 coning,37 density, SO, 81, 124, 125 deviation factor, 97 equatlOD of state, 96 to express density, 129 flow, JI, 12, D, 123. 127 equation,47,123 rate, 76, 88, l22. 12.7, t 29 fOnTI;ltion volume factor, 76, 79 calcuation, 79 gravity,78, 79. 80,82,97,98,127,129 correction cquation, 78 holdup,65 in-situ t10w rate, 65 velocity, 76 injection, 19,94,147, J56 pressure, 155 rate, 5, 6, [48, 156, l57, 158, 16S, 169 surface pressure, 160 wells, 146 ¡ift,94, 102, \ 53, 155, 158, 173 valve, 155, 160, 162, 163, 165, 167
design, 165 dome pressure, 1 71 performance, 165 well, 116, 137, 155, 156
analysis, 157 schematic, \56 Une pressure drop, 117 tiquid flow, 117, 124 mixture density, 66 viseosity, 95 ratio (GLR), 38, 83, 85, 93, 94, 96, 116, 117,122, 124, 148, 149, 152, 155, 174
mass flow rate, (24 oil eontact, 19 interfacial tension, 81 mixture, 81 viscosity,9S oiVwater viseosity, 95 ratio, 93, [48,150,158
phase, 64, 66, 86, 87, 9 t pipeline equations, 117 pressure, 160, 162. 172 productivity index, 13 properties, 65, 124
pressure 10s$ in pipelines, t08 Future gas well performance, 150 Future IPRs, 41
rate, 88,109,112.115,123.137,149,180 relative penneability. 15 reservQir, 15,46 equ3tions. 14<1-
Gagc pressures, 22,43 Gas bubble 180 velocity, 87
Reynotds number. 122 saturation, 15,20,30,37, 39,40,-l1, 47,54 separation, 174 single·phasc tlow, 57 specific gravity, \0, 75, I~J. 125 splitting, 122, 123 storage operations, 147 reservoirs. 146 superficial velocities, 87
Gas cap, 19
drive, 18 perfonnance, 18 reservoir,18
Gas compressibiliry, 127 factor, 45, 76, 77,129, 158
lndex
405
veiocity, 85, 90, lDS, 112, 113, 117 superficial, 76 viscosity, 47, 80,122,191 yoid fmetion, 65
cOrTelatían, 90 vo!ume, 157, 173 water interfacial tcosian, 81 weight, 162, 182
well, 49, 54, 81, 82, 83, 96,97,149 backpressure equatían. 146 predicting future IPRs, 43, 47 Gas·free viscosity, 80 Gas-liquid ratio, 126 wells, 129 separatían, 174 Gas-oiL relative penneability data, L7 Gas-producing rates, 76 Gas~well
testing, 31
Gas/liquid mixture, 72 Gathering
Iines, 104 system, 122 General energy eguatían, 58 General equation for flow through restnetioos, 123 General eguatían for frietían factor, 114 General inflow equations, 47 General pressure gradient equation, 96, 97,
108 General pressure traverse curves, 104 Generalized curves, 98 Generating LPR, 155 Geometry for linear flow, 11 system, la Geothermal gradient, 82, 167 Gilbert's "5" curve, 180 GLR, 84, 97, 98,100,102,104, !l8, 140,153,
163,172,176,177 curve, 100 maximum value. 98 Gradient curves, 98, 168 Graphical solution for valve spacing, 162 Grashof number, 71 Gravel pack, 9, 53, 54, 144, 145 analysis, producing capacity, 144 system pressure drop, 144 completion, 11,53,47, 143 equations, 53 resistance, 144 gravel penneability, 53,144 wells,53 Gravitational separation, 65 Gravity. effect of. 67 of stock tank oil, 81 Gray method, 97 Gregory, et aL, correlations, 114, ¡ 16 Griffith correlation, 86 Hagedom and Brown. 86 correlation, 93, 98 method, 85, 93, 98, 191 lbe study, 93 Hagen-Poiseuille equarian for laminar flow,
60
Hand calculations, 68 Handheld, prograrnmable calculators, 89 Hasan and Kabir method, 90, 98 Head gain, 176, 177 Heat balance equation, 69 energy, 58 loss, 57,81,82 conductive 71 convective, 70 gradient, 70 transfer, 65 calculation algorithm, 73 calculations, 69 coefficient, 70, 82 conductive, 71 convective, 71 due to thennal radiation, 71 steady state, 71 unsteady sta te, 71 Heat-per~unit mass, 69 Heat-transfer coefficients, High capacity wells, 163 HilIyterrain, ll2, 117, 118, 139 pipelines, 111, 112. 113, 194 Holdup correlation, 110 factor, 112, 114 Hole angle,174 size, 135 vohune,51 Horizontal curves, 104, lI8,138, 142 flow, 10,63,67, 109, !lO pattero, 88, 89, 108, l09 pattem maps, 109 panem prediction, 108 regime,88 lines, 116 pipe, 192, 193 flow.60 pressure traverse curves, ¡ 13 two-phase flow, 118 wel1s,37 Horsepower, 175 Hybrid Model, I !4. ll5 Hydrau!ic diameter, 90, 91 fluid, 183 lift system, 183 pumping, 155, 183 radíus concept, 90, 91 HydraulicaUy powered centrifuga! pumping,
n
183 Hydrocarbon gases. 77 Hydrostatic component. 63,93,94, 98,108, 112, 118 loss, 5, 108 pressure, 64, 68,113,156,160,180 drop, 112, 113 grodient in rubing, 155 loss, 136 term, 84, 93, 104 Ideal drawdown, 26 ldealized behavior, 31,32 Immiscible liquids, 65
ln-situ conctitions, 75 deIlsity, 96 flow nHe. 10. 76 gas. 65 liquid,65 oil,65 water, 65 fluid properties, 72 gas density, 87 flow ra!e, 67 liquid imerfaeial tension, 87 density, 87 flow rate, 67 mass, 72 superficial velocity, 194 oil,76 water, 76 values,75 velocity, 76, 96, 129 gas, 76 oíl,76 water, 76 volume,76 Inclination angle, 69, 88 downward flow, 67 upward flow, 67 lncompressible flow, 64 Incrementing, 191 calculating viscosity, 66 length,66 algorithms, 68 pipe length, 68 pressure algorithms, 68 pressure drop procedure, 69 production, 150 lnflow, 38, 133, 135, 140, 144, 145, 149, 153,
158,162,174,179 calculation, 138, 143, 175 conditions, 148, 155 curve, 4, 5, 6, 133, 140, 143, 147, 149,
150,156,157,158,175 equation, 21,33 for oil flow, 13 expression, 156, 179 perfonnance, 4, 9,17,19,20,28,30,36,
37,45,48,54 calculation, 147 equations, 47 gas wells, 54 methods, t 68 oil wells, 54 factors affecting, 21 plot.19 relationship (IPR), 9, 20, 38 plots, 152 to node, 146 Intlow-outflow intersection, [43 Initia! pressure, 18,30 reservoir, [5 Injected gas, 174 gas volume, 156 GLR, 156. 157, [58 rate, 168
.
406 surface temperarure, 1T!.. Injection depth. 155, 156, [57, J60, 168 gas, 5, 160 ¡iquid ratio, pressure, 156, 157, 163 rate, 147, 162, 168 vo\ume, 156. 163
GLR, 160, 16J pressure, 157,166,165 operated valves, 168 pump, 146 rate,5, 146, l47, 158 wells, 146 lnterfadal tension, 66, 81 air, 87 between gas and liquid phases, 81 water, 87 Intermediate nades, 152 lntermittent f1ow, 88 gas lift, 183 Internal el1ergy, 58 teon,59 Interploatian, 100 TPR. 15, 19,20,21,22,24,25,26,28,29,32,
33,34,36,35,37,39,42,54, 148 behavior of gas weHs, 20 construction, 36, 37 equations,39 methods,39 undersaturated reservoir, 24, 25 Irreversible losses, 123 lsochronal test, 3D, 31, 32, 34, 43 pressure diagrams, 32 producing rate, 32 (sothermal compressibility, 19, 80 for gas equation, 80 fOI water cquation, 80 Iterative, 158, 165, 180 procedure, 147 solution, 127 Jain equation, 61, 62, 64, 191 Jet pwnping, 183 Jones, Blount and Glaze Method., 35, 45 Joule-Thomson coefficient. 82 Kili fluid, 160 gradient, 160, 162, 168 Kinetic energy, 58, 60, 63, 64, 65 change, 63, 67 Laminar coefficent, 45, 47
tlow, 14,35,4;,48,60,64 perforation component, 51 reservoir component 47, 4R single·phase tlow, 67 Large diameter pipelines, 11 l Lawson study, 93 Lee gas viscosity equation, 80
LGR,97 Line size, l16, 153 Linear flow, lO, 11,37,45.53 function of pressure. 31
Production Optimization Using Nodal Analysis plot, 31, 35 temperatl.:re profile, 81 Liquid accumulation, I J 3, 117 column, 180 condensate. 83 density, 82, 94, 113, 124, 125 displacement, 162 Distributíon Coefficiem. 87 now rate, 88, 91, 93, 98,100,114, 1!6,
124, 125, 180 gas ratio, 97 grnvity. 9'7
holdup, 64, 65, 66, 67, 72, 83, 84, 85, 86, 88,89,90,97,98, 108, 109, 110, 114, 115,117,136.192,193 companson studies, 114, 115 correlalÍon, 95.109 measurements, 114 predicting, hydrostatic gradient, 18D in-situ fIow rate, 65 level, 160,177 producionrate, 5, 113, 156, 157, 160, 174 productivity index, 37 propertit:s, 65, 124 saturation, 15 single-phase flow, 57 slug frequencies, expected. 67 sizes, expected, 67 specific gravity, 75, 126. 127 splitting, 122, 123 superficial velocities, 87 to gas ratio, 113 trapped, 65 velocity, 65, &5, 90,108 actual,65 superficial, 65 viscosity, 85, 93, 95,109,117,191 Load fluid, 160 gradicnt, 162, 163, 172 Location of restrictions, 141
Logdata, 38 Log.log coordinates, 31, 43 Looped pipe!ines, 122 Loopíng, 122 flowline, 158 surface line, \52 Low gas ¡iquid ratios, 109 low productivity, 140 Low reservoir pressures, 18 Low-pressure, high·velocity segments, 69 Low-pressure wells, 104 Mandane, 1 t 4 flow pattem map, 108, 109, I[ O Mandrels, 162 spacing, 160 Mass flow rate, 10,64,81,82,84.91 gas, l25 total, 125 Mass mctioo of gas, 124 Material balance calculation, 41, 148 model, 150 Mathematical reservoir model, 21, 150
Matthews and Russell water viscosity correJatioo,80 Maximum
inflow.26 producing capacit)', 123 producian r:líe,39, 144 McLeod model, 51 Measured
deplh (MD), 91, 98,104 viscosities, 66 well nuid leve!, 179 Mechanical energy balance, 59 equivalent efheat constan!, 3, 69 Mechanistic madel, 59 Meehan water viscosity equation, 80 Methods for measuring, nuclear desitometers. 94 capacitance dcvices, 94 Minimum production rate, 39,96 velocity, 97 Mist,67 flow, pattero, Mixing rules, 64 Mixture 191 density, 65, 83, 84, 87, 88 enthalpy, 72, 74 gravity,97 velocity, 66, 72. 127 viscosity, 91
Modified flow~pattern
map, 88 isocnronal test, 3 l. 32,43,45 pressure diagrams, 32 producing rate, 32 Mole fraetion, 72 MONA, Asheim Method, 90,114
Moody diagn¡m, 61, 63, 85, 91,191,193 fiiction factor, 60, 61 Motor assemb1y, 183 MOV wellhead choke design, 126 Mukberjee study, 109 Multicomponent systems, 69 Multi.phase flow, 82. 108 correlations. 96, 98 well tlow problem, 84 two-phase friction factor, 84 Mu!tipoint (back pressure test), 43 Multistage centrifugal pump, 174 Multiwel! system, 151 Natural gas, 66. 72, 80 viscosity, 66 Narurally flowing well. 148, 155 Negative pressure gradient. M, 69 Negative S', 14 Negative skin, effect of. 20 factor. 19 Nikuradse's equation. 61
No-slip densiey, 87,91. 127, 195 holdup, 72,84,85,97, 111
Index gas, 65 l¡quid holdup, 65, 83 mixture enthalpy, 72 Nodal analysis. 2, 5, 7. 39,123,133,141, 146,151, 156, 174, 177 of injection wells, 146 Nade (division point), 2. 9,133,152 inflow,57 location, 1]7, 158, 141, 152, 155
outflow, 57 pressure, 2, 3, 4, 9, 57,137,142,143,144, 149, 152, 156, 174, 179 selection, 135, 156, 137, 155 at bottomhole, t46
Non-Darcy dfects,45 flow, lO, 35, 43, 45, 52 pressure drop, 53 Non-isothermal, 68, 69 flow, 71 Non·zera skin factor, 20, 21 Non-radial flow regime, 37 Nonnalized frietian factor, 111 Numerical reservoir madel, 37 Nusselt factor, NNU, 71
Non~steady
Odeh equatioDS, 14 Offshare
pipelines. 114 wells, 83, 141
Dil API gravity, 80, 98 compressibihty, 80 density, 35, 65, 75, 94,125,177,180
flow, 10, 11, 65 equation, 47, SI rate, 76 fonnation volume factot, calculation, gravity, 82, 98, 128, 169 in-situ flow rate, 65 superficial vetocity, ve(ocity,76 isothermal compressibility, 79 producion rate, 76, 125, 158 producing capacity, 151 rate,39, 136, 176, 158 reservoir, 17, 19,40,46 equations, 144 phase behavior, 15 phase diagram, 17 saturated with gas, 80 saturation, 41 surface tension, 66 viscosity, 93 behavior, 15, 17 equation, 80 water contact, 19 emulsion, 66 gas mixture density, 65, 180 interface. 180, 182 mixture, 95 viscosity. 66, 95, ISO well. 49. 54, 81, 82. 96,129.135,137,144. 150
407 back·pressure curves, JO predicting future ¡PRs, 40 tests. 31 zone, 18 Open ho1e completion, 4i, 48, [43 Opening pressure. 166 Operating casing pressure, 168 differential pressure, 172 valve depth, l68, [72 Optimum gas injection rate, 5, 156, 157 tubing size, 5 Orifice valves (MOV), 126 Original oil in place, 18 Orkiszewski Method, 86, 87 Otis design procedure, 167 Outflow,4, 38,133,135,137,138,140,143, 144,145,146,153,158,174,180 analysis,155 calculation, 137, ISO conditions, 148, 149, 155 curve, 3,5,6, 140, 143, 149, 150, 153, 133, 147, 156, 157, 158, 175 data, 135, 149 plat, 138 expression, 156, ]79 perforations. 136, 146, 155 performance, calculated using backpressure equation for gas wells, 146 pressure, 113, 143,145 rate, 133 restrictions, 139 Out1et elevation of pipeline, 113 pressure,2 temperature, 69, 82 Overall pressure drop, 117 Overloaded flowlines, 116 Packer, 157 Panhandle equation, 113 Paraffin bui1dup,71 Parallel pipelines, 122 Partial1y depleted field, 30 Parteros, bubble-flow, slug-flow, mist-flow, 86 Perforation, 9, 36, 37, 46, 47, 135, 143, 144, 146 completion, 43, 48 efficiency, 51 components, 51 damage,48 density. 6, 45, 49, 51,143,144. [46 effect,6 diameter, 48,51 effects, 54, 55 flow, 53 gravel·packed comp[etions, 53 improved, 49 interval length, 51 length, 51, 52, 144 mid-point, 180 number, 48, 51, 53,143 parameters. 53
pattero, 47, 51, 53 penetration depth, 48 performance, 49 pressure drop, 6, 145 radius, 51, 52 size, 44, 50 tunne[, 53 length, 53 unimproved,49 Performance vs. time, 151 Permeability, 14, 19, 2l, 30, 36, 48 alteration, [4,26,43 lo gas. 45 lo oil, 39 lo water, 39 turbulence, 14 Phase behavior in oi! reservoirs, 15 in reservoirs. 15 Phase diagram, (9 Phasing,5l Physical properties, 67 Pipe ang(e, 83, 84,97,98 inclinations, 65, 67, 68, 69, 83, 111 measured from vertical, 97 measured from horizontal, 97 Pipe area, 65, 129 configuration, 70 diameter, 65, 83, 84, 88, l17, 128 fittings, 123, 128 flow correlations, 114, 116, 117 inc1ination, 65, 67, 68, 69, 83, 111 angle, 62, 88 inside diameter, 97, 98, 122, 127 roughness, 63, 64, 83 size, 84, 88, 98, 104, 137 Pipeline, 114, 115, 192 correlations, 114 curves (horizontal), 137 design, 111, 114 flow, 108 correlations, 104 model,114 pattero, 108 inclination, 1I 1 performance, I profile, 117, ll8 system,4, 5, 38, 57. 73, 76, 136, 146 ca1culating pressure drops-, 153 performance, 95, 116, 133 pressure drop, 156 Plotting node pressure, 133 pressure drop, 144 test data, 45 Plunger lift, 185 Poettmann and Carpenter Method. 84 Point of balance, 162 Point ofinjection, 163, 165, 167, 169 Pore plugging, 14 Porous medium, 9 Port size, 168, 172, 173 for operating valve, 168 Positlve displacement pump. 178, 183 Positive skin, effect of, 20
408
Production Optimiza/ion Using Nada! Analysis
factor, [9 Potential energy, 58, 63, 65 Power fluid, ¡83 Power requirement, 175
Prandtl number, 71 Predicting tlowing temperatures, 81 future IPR 's. gas wells, 46 in-situ liquid holdup. 1\ 1 pressure draps. 109, 110 Prepared pressure traverse curves, 133,136 use of, 118 Present time production tests, 42 IPR [or gas well, 43 Primary depietion, 18 Primary performance for a gas cap drive reservoir, ! 8 Procedure for applying Nodal Analysis, 6 for calcu!ating pressure drop, 158 for determining optimum gas rate, 156 to relate reservoir and well performance to time, 150 Producing capacities, l35,136, 137, 140, 141, 142,
144,145, 146, 150, 151, 153,155, 156, 158, 174 characteristics. 152 formarían, 37
gas/liquid tates (GLR), 18,76,97,100, 124, 148 ratio, 18,76.91,100, 124, 140 interval, 150 hfc t 93 operations, 165 rate, 1,9,24,18,19,32,44,57,81,141,
152,153,163,175,177,174,183 conventional test, 32 isochronal test, 32 modified isoehronal test, 32 time, 32 water cut, 38 water fraetion, 38, 180,182 Produetion inerements, 150 logging,38 mechanism,37 pressure, 166 effect, 166 effeet factor, ! 66 operated valves, 168 valves, 165 Productivity gains, 37 index, 13. 15, 19,22.24,25,37,38,40 concept, 13 faetors affecting, 15
J,13.34.37 oil well, 54 ratio, PR, 26 Prudhoe Bay field, 37.90 Pseudo·steady state. 12 Pseudocritical pressure, 77, 78 ternperature, 77, 78 Pseudoflowing wellbead pressure, [63
Pseudoreduced pressure, 77. 78 Pseudosteady state, 37 flow, 14 Pulling tubing, ]60 Purop, 180 3nd engine assembly, l83 diseharge pressure, 174, 177 installation, 183, 185 intake pressure, 174 retrieval, I 83 schematic, 183 setting depth, 176, 177, 178 size, 175 speed, 176 suction pressure, 174, 176 Pumping cycle, 179 fluid levels, 182 sucker rod, beam, 177 weU calculation, 180
PVT analyses, 72, 78, 144, 148 properties, 68, 69, 128 Radial flow, 11, 37, 45 ratio (RFR), 49 system,11 Radioactive tracers, 86 Radius, 12, 19 altercd, 14 Ramey equation for temperature in a well, 82 Rate dependent component, 35 Ratio of absolute pressures, 43 of flow efficiencies, 26 of productívity indices, 26 ofspecific heats, 123 specific rate for gas, 124 Reflections of sound waves, 180 Relating perfonnance to time, 150 Relative advantages of artificial1ift sySlems,
procedures, 174 penneability, 31. 48, 49 horizontal, 5 t vertical, 51 pressure, 4. 9,18,20,36,43, ,¡6, 47, 48, 148,150.151,152,155 drop, 155 component. 143 protite, 12, 13, 19 producing capacity, 150 retrograde condensute, 47 rack, 15 system performance, 95 temperature, 15,82 wet gas, 47 Resistance coefficient, 128 Resistivity probe, 65 Restriction, 124, 141 opening, 124 length, 124 location of, 14/ subsurface safety valves (SSSV), 123 surface and bottomhole chokes, 123 valves aod fittings, [23 Retrograde condensate, 15 gas reservoir, 20 reservoir, 47, 54 gas reservoir behavior, 20 Reynolds number, 60, 61, 62, 64, 65, 66, 67,
71,80,85,90,91,95,111, 117, 122, 124, 191, 193 two-phase, 91 Rock properties, 9 Rod purnps, 178 Rod~pumped well, 178, [79, 183 schematic, 178 Ros coefficients, 143 Rossland evaluation study, 98 Rough wall pipe, 61 Route selectivity, 122
177 Relative in~situ volume, gas, 65 liquid,65 Relative penneability, 15,39,40 behavior, 15 togas,15 Relaxation distanee, 82 Required bottomhole flowing pressure, 160 Required horsepower, 175 Reservoir, 9,20,21, 39,123,146 capacity, 139 characteristics, 47, 135 component, 9, 5! data, 1J5 deve10pment 40 drive, 19 dry g"-', 47 engineering calculations, 73 flow, 37 gas cap drive, 18 gas volumes, 18 intlow capacity, 148 inflow perfonnance, 7, 155 mode1, 21, 41 perfonnance, 1,4,40,57,150
Sachdeva, et aL, equations, 124, 1.25 Safety factors, 162, 163, 165 in design calculations, 163 Sand filters, 10 Sandface pressure, 9 Saturated oH, 18 Saturated reservoirs, 21,24,30 Scale buildup, 71 Secondary recovery, 155 Segregated tlow, 88 Semi-Iog plot ofpressure vs. radius, t3 Separation facilities, 108 Separator, 1, 76, 104, 108, liS, 141, 174,
175, 185 pressure, 2, 3, 57, [18, 135, 137, 139, 142.
158 Shearing stresses, 95 Shell curves, 98 Shell Method, 86 Shiu and Beggs empirical method, 82 Shut in, 39 condition,43 fluíd levels, 182 period, 43, 45 time, 31,32
!ndex we!!, 182 wel] calculation, 182 SI Metric system of units, 123 Side pocket mandrels, 160, 165 Similarity analysis, 111 Single-phase, compressible transient flow, 64 flow, 57, 62, 63, 64, 67, 91, 96,122,124, 128 fluid, 65, 108
gas, 123 flow, 65, 117 liquid, 126 flow, 65, 126 parameters,71 Sizing lines, ¡08
Skin,15 effect, 14, 15,45
factor, 17, 19,29,30,47,48,51,54 negative, ! 9 non-zero,20 positive. 19 Slip velocity, 65, 86 Slippage, 65, 95 Slug, 67,87, 109 catchers, 108
flow, 65, 88, 108 pattem, 86,8 7 Small diameter pipelines, 111 Smooth wall pipe. 61 Solution gas, 37, 75. 76, 79 oil ratio, 37, 76,80,125 Sanie velocity, 124 Specifications
for Carneo pressure operated gas lift valves, 169 for ütis spreadmaster pressure operated gas lift valves, 170 Specified opening pressure, 166 SSSV, 128 Stabilized flow, 12, 37 conditions, 83 production tests, 39 test, 32, 43, 44 Standard fIow rates, 76 Standing and Katz correlation, 77 Standing's graph, 26,28 method, 4D, 48 modification, 21, 26, 29 Static BHP, 163 fluid [evels, 182 gradient, 160 liquid level, 172 pressure, 39, 43 reservoir pressure, 37, 39,45, 147, 150, l;8,160 wellbore pressure, 32 Steady state energy balance, 58 flow, 63, 64 heat transfer, 71 laminar flow, 12 Stimulation, 17,20,26,27,28,36,48,54,55, 135, 139, 140
409 gas wells, 55 Stratification, 67 Stratified flow, 67, 109 formations, 37,38 reservo ir, ]8 Subcritical (subsonic) fIow, 123, 124, 125, l26, l27, 141, 143 Submersible pumps, 174 assembly, 178 installation, [78 schematic, [78 se[ection, t 79 Submersible pumping, 155, 174 Subsurface hydralic motor, 183 safety valves (SSSV), 123,127, 141, 143 Sucker rod pumping, 153, \ 55. [77, 183 Suction conditions, 176 Suction pressures, 175 Superficial gas velocity, 65, 76, 109, 113 liquid velocity, 65,76, 109 ve1ocities, 65, 90 of liquid phases, 86 of gas phases, 86 Surface casing pressure, 162, 178, 180 choke, 123, 137, 141 conditions, 141, 169 equipment, 36 flowing temperature, 81, 97 flowHne calculations, 81 ftow rutes, 76 gas injection pressure, 156, 163 lines, 122 Une sizes, 152 operating pressure, [57 pipelines, 90 pressure, 84, 114, 157 producing gas/oH ratio, 18 temperature, 81 tension, 64, 66 tubing pressure, 162 Surging fluid, 49,50 System analysis, 2, 57,140,143,176,183 for wells with restrictions, 141 plot,143 procedures, 133 capacities, 153 components, 133, 151 design,57 nodal analysis, 156 pressure, 109
sensitive vaives, 163 Tension, interfacial, 66 oil surface, 66 water surface, 66 Test rack, 166, l67, 168 opening pressure, 166, 167, 169 Thermal conductivity, 71 radiation [oss, 71 radiation transfer, 70 Tight wells, 31 Time, 150 dependent function, 71 increment, 150 Transient f1ow, 64,71 test, 30, 43, 47, 48 weU tests, 36 Trnnsition zone, 86, 88 Traverse curves, 98, I ¡8, 138 application, 98 True vertical depth (TVD), 97, 98, 157 Tubing, 83, 97,117,123,143,144,1;;,160, 162, l74, 178, 183 design, 111 diameter, 95, 140 on mínimum rate, 96 Elfec! (TBl, 166 Effect Factor (rEP), 166 flowing pressure traverse, 162 flowing wellhead pressure, (62 gradient, 163 increments, 147 inside diameter, lOO, 128 lengtb, 104 outside diameter, 182 pressure, 160, 163, 165, 166, 168 at gas lift valve, 157 drop, 136 drop calculations, 174 traverse, 162 requirements, 158 size, 3, 4,5,36,85,93,95,100, 141, 146, l47, 149, 1;0, 1;6, 1;8, 167 flow capacities, 135 optimum, 135 selection,5, 135 velocity, 95 Tubing string, 94, 97, 98, 135 Tubing-conveyed method,48 perforating techniques, 49, 50 Tunnellength, 5] Turbulence,9, lO, 14, 15, 17.20,21. 37, 43,
4;, ;3 Tapered tubing string, 136 Temperature, ID, 59, 68, 69, 73, 75, 77, 78, 79,80,82,96,97,129,16;, m change.57,65 effects,72 Correction Factors, 17 [ distribution, 69 inclination, 68 los5, 57 profile, 82 in pipeline, 82
coefficient, 14,45,47 effects, 35, 43, 45, 55 flow, 20, 52, 60, 61, 64, 71 calculations, 64 fluid flow, 60 pressure drop. 45. 46 term, 35 Tumer, et al., equation, 97 TVD,I04 Twenty percent design gradient method, 163, l67
410
Production Optimiza/ion Using Nodal Analysis
Two-phase density, 65.90, 193 design calculations. 71 discharge coefficient, t26 flow, 51, 57, 58, 63, 64, 65, 91,112,123, 124,125,127,128 acceleration component, 67 calcuations, 80. 90 correlations, 65, 97
elevation change component, 66 empirical equation, 124 heat tnmsfer calcuations, 69 methods, 180 models,90
pattems,67 pipelines, variables, 64 flowing pressure gradient, 67, 75, 83, 93 tlowing pressure traverse, 67, 68
fluid densicy, 7S friction factor, 67, 83, 84, 85, 88, 111
methods,66 predicting, 67 gaslliquid viscosity, 66 mixture, 64, 72 gradient curves, 168 horizontal flow, 108 parteros, 69 mixture, 108, 124 pipeline, 108, 112 pressure gradient calculations, 81
Reynolds number, 111 velocity, 66 vertical flow parteros, 68 viscosity, 66 Unaltered reservoir permeability, 51 Unbalanced pressure charged valve, 165 Unconsolidated formation, 144 Underbalance, optimum degree, 49 pressure, 49, 50 perforating, 48, 49, 50 methods of, 48 Undersaturated reservoir, 24, 25, 29, 30, 31, 34 Units for Darcy's Law, 10 Unloading operations, 165 process, 160 producing rate, 163 sequence, 161 valve design process, 162 valves, 160, 168 Unsteady state heat transfer, 71 Uphill flow, 115 Upward inclination, lO9 Vpward two-phase flow, 86 Valve, 83, 123, 128, 143, 165 bellows, 165 closing pressure, 165, 167, 171 dosure, ¡ 66 depth, 160, 162, 163, 165, 166. 169, 172 designo l55, 165 dome pressures, 166. 169
location. 155 nonrelrievable, 165 opening. 160. 162, 165 pressure, 163, 166, 167, 169 operating temperature, 163 port. 166 pressure setting, 162 retrievable, 172 seat, 166 spacing. 160, 162, 165. 169 problems, 160, ¡62. 165 temperature. 166, 169 Vapor-liquid equilibrium flash calculations, 72 Variable gradient design, 164 Vasquez and Beggs correlations. 78, 79 equation, 80 method,79 Velocity, 11,20,37,57,64,65,73,75,83, 87,96, 117, 126, 129, 139, 180 actual gas, 65 actualliquid, 65 change,64 coefficient, 35,48, 52 correlation, 35 increase, 64 in-situ superficial water, 76 mixture. 66 profile, 60 slip, 66 superficial. 65, 66 gas, 65, 109 liquid, 65, 76, 109 mixture, 76 two-phase, 66 Vertical correlations, 140 curves, 100, 102. 104, 118, 140 flow pattem, 87 map, 87 flowing pressure loss, 61 traverses. 99 permeability, 51 pressure traverse curve, 137, 145, 149, 176,177 rises, 113 two-phase flow, 86 Viseosity, 64, 66, 72, 80, 85, 117 ealculating, 66 erude oil, 66 flowing fluid, 66 gas/oil mixture, 95 gasJoiVwater mixture, 95 natural gas, 66 of oil equation, 80 oiVwater mixture, 66, 95 two-phase, 66 two-phase, gas/liquid, 66 water, 66 Viseous oil,117 shear, 60 shear 10ss, 80 Vogel equation, 26, 28, 34, 31, 39, 40, 42, 43,
138,149 dimensionless lPR, 23 method, 21, 23, 24, 26, 29. 34. 36. 37, 39. 100,102.135,137,172 method-Zero skin factor, application oC 23,24 Vogel-Slanding equalions, 30 Vohra, et al., study. 114 Void fraction. 65 VoJume.57 actual, 79 e1ement. 65 fraetion, 65 in-situ, 79 standard, 79 Volumetric tlow rate, 10 actual, 76 gas, 123
Wall shear stress, 60 Water coning,37 cut, 39, 84, 93, 94, 95. lOO, 104, 116. 117, 136, 148, 149, ISO, 158 density, 65, 15, 95, 125 drive, 18, 148 performance, 19 flow, 65 forrnation, 15 volume factor, 125, 116 fraetion, 98, 100, lI1, 152, 153, 169 gas ratio, 97 gravity,98 in-situ flow rate, 65 veloeity,16 injeetion, 18, 19,38,72, 146 oil ratio (WOR), 93, 94 production, 39 rate, 176 salinity, 79, 80 saturation,37 surface tension, 66 viscosity, 66, 80 WateNirive gas reservoir behavior, 20 reservoir, 18, 38,149 Waterflood, 37, 38 projects, 31 theory,38 we1ls, 37 Wave flow, 109 Weighting factors, 66 Well capacity, 139 eompletion design, 135 effects, 46. 47 effieieney, 35. 46 sehemes, 143 condítions, 86 deplh,96,97 design problems, 98 tlow, Si. 92 calculations. 108 correlations. 83, 90,91,92,93,98, 1I ( methods, 91. 97
Index pressure gradient methods, 84
increment of length, 97 perforated in brine, 53
performance, 35, 116, 136, 153. 156 etTects ofvariables, 93 equations, 9 gas/liquid ratio GLR, 153 water/oil ratio WüR, wel1 mtes, 153 spacing,36 stimulation, 14
4[[ Wellbore, 12, 14, 15, 19,20,37,38,45,47, 70,144,155, l85 damage, 26, 27
tlowing pressure, 22 pressure, 31, 38. 48 radius. 36, 48. 51 Wellhead. 141 choke, 125. 136, 137
flowing pressure. 97 pressure, 2, 4, 96, 97.100,104,116, Il7, 118, 123, 129, 135, 136. 137, 138, 140,
system, 123
1~1~1~1~1~ID,I~15'
test, 29, 41
163
tubing, 83 unloaded, 172
temperature, 129 Wet gas reservoir, 20, 47
Winkler method, 163 Working liquid level, t 78 Workovers, t 50
Z-factor, 47, SO, 97
gas compressibility factor, 77 Zera depth, 100 drawdown productivity index, 40 pressure, 98 gradient, 68, 69 radius skin effect, 20 skin factor, 19 well depth, 98
