VIKIZ Method for Logging Oil and Gas Boreholes

RUSSIAN ACADEMY OF SCIENCES, SIBERIAN BRANCH INSTITUTE OF GEOPHYSICS SCIENTIFIC-INDUSTRIAL ENTERPRISE OF GEOPHYSICAL EQUIPMENT «LOOCH»

VIKIZ METHOD FOR LOGGING OIL AND GAS BOREHOLES

Novosbirsk 2002

Translation of: Tekhnologiya issledovaniya neftegazovykh skvazhin na osnove VIKIZ, Novosibisk: Scientific Publishing Center of the United Institute of Geology, Geophysics and Mineralogy, SB RAS; Publishing Hourse of the SB RAS, 2000. VIKIZ Method for logging Oil and Gas Boreholes / Novosibirsk: Branch “Geo” of the Publishing House of the SB RAS, 2002, 112 ð. ISBN 5-7692-0510-5 The book represents the fundamentals of High Frequency Induction Logging Isoparametric Soundings in oil and gas boreholes. This method is known in Russia as the VIKIZ method. There have been considered a wide range of methodical problems for applying the VIKIZ method along with an interpretation of logs obtained for terrigenous sections. The experience for more than ten years of practical application of this technique in different regions has been analyzed and generalized. The multifunctional computer system of log inversion has been described and the ways for using this system have been recommended. The book is intended for geophysicists and geologists specialized in the field of production geophysics. The book will be also useful for students, post-graduate students, and researchers interested in geophysical investigations in boreholes.

Compiled by: M.I. Epov, Yu.N. Antonov, I.N. Yeltsov, S.S. Zhmaev, A.N. Petrov, V.N. Ulyanov, V.N. Glinskikh, V.N. Eremin, K.N. Kayurov, V.V. Kiselev, V.T. Lavrukhov, S.V. Martakov, M.N. Nikitenko, M.Yu. Revva, A.Yu. Sobolev, K.V. Sukhorukova, and A.B. Cheryauka Translated by: T.A. Korneva English version edited by: Yu.A. Dashevsky

ISBN 5-7692-0510-5

Ó Institute of Geophysics SB RAS, 2002 Ó SIEGE “Looch”, 2002

1

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K E Y G E O LO G I C A L A N D G E O P H YS I C A L P R O B L E M S S O LV E D B Y T H E V I K I Z M E T H O D

The method of High-Frequency Induction Logging Isoparametric Sounding has been developed for evaluation of spatial distribution of the resistivity in rocks penetrated by oil and gas boreholes. This method is widely used in geophysical investigations and it is known in Russia as the VIKIZ method. In this connection, hereafter we shall use the term “VIKIZ method” to mean High-Frequency Induction Logging Isoparametric Sounding one. Using the VIKIZ method allows solution of the following problems on geophysical investigation in boreholes: · subdivision of a section with evaluation of a thinly bedded profile with the high spatial resolution; · location of oil-water and gas-water contacts; · determination of the resistivity of undisturbed formation as well as that of an invaded zone with estimating radial depths of displacement of formation fluids; · setting and estimation of the radial heterogeneity parameters in zones of invasion including evaluation of salt formation water accumulations (“bordering zones”) as a direct qualitative indicator of the presence of moveable hydrocarbons in reservoir rocks. The VIKIZ method based on measurement of the relative phase characteristics can be used for investigation in boreholes filled with highly conductive drilling mud (resistivity is less than 0.5 ohm × m) as opposed to three-coil probes of Induction Logging by which the absolute values of signals are measured on the background of the compensated source field. The results of quantitative VIKIZ log interpretation after integrating with data on other geophysical methods and petrophysical information allow evaluation of the hydrocarbon saturation and lithology of a terrigenous section. Estimation of a heterogeneity of reservoir properties within intervals of porous permeable formations and distinguishing tight sandstone with carbonaceous or silica cement, etc. can be obtained from the interpretation results as well.

2

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PETROPHYSICAL DESCRIPTION OF THE TARGETS U N D E R I N V E S T I G AT I O N . G E O LO G I C A L AND GEOPHYSICAL MODELS

2.1. Geological Models of Terrigenous Reservoirs The sedimentary complex of West Siberia region is represented by Mesozoic-Cenozoic sandy-siltstones and shaly rocks. Their total thickness increases to the center and north of the region where it is as much as 4–5 km. The hydrocarbon-bearing floor thickness is about 2–3 km. The commercial oil-gas accumulations are stratigrafically confined to Cretaceous and Jurassic deposits. The greatest oil accumulations are concentrated in the Lower Cretaceous and Upper Jurassic deposits; gas and condensate-gaseous accumulations are found in the Upper Cretaceous (Cenomanian) deposits and Upper Jurassic. Geological processes of accumulation and formation of deposits caused the great variety of reservoir rocks by their granulometric and mineral composition as well as by geochemical features of cementation and, as a result, stipulated the complicated structure of the space with poraperm propertics. The distinctive features of these accumulations are: the low oil viscosity, low permeability of productive formations, high initial water saturation, and increased formation temperature. Paleozoic, Jurassic, and even Cretaceous deposits in many West Siberia regions were subjected to the deep fluid treatment. Because of this treatment, productive deposits are represented by both porous and fractured reservoirs. Most of oil and gas reservoirs belong to the complicated type since their frame is made up of minerals of multicomponent composition with the complicated structure of porous channels. Low-permeable shaly reservoir rocks interbedded with impermeable deposits present particular difficulties for investigation. At the beginning of production, hydrocarbons are taken from cracks and then, with increasing the differential pressure after the cracks are “shut off”, the porous reservoir structure provides drainage. In the view of many investigators, the cracked porosity determined by the real content of hydrocarbons in the exhausted fields is about 0.2 %. The maximum cracked porosity may be as much as 1.0 %. The hydrocarbon composition of oil has essential effect on electrical parameters. Thus, the presence of surface-active naphthenic and oleic acids in oil leads to change in the values of surface tension at the interfaces of hydrocarbons/water and hydrocarbons/mineral

Petrophysical Description of the Targets under Investigation

5

components. These factors essentially decrease the thickness of the bound water film and increase the resistivity. In the invaded zone of productive formations, complicated spatial resistivity distributions can occur. Thus, for instance, if a borehole penetrates a hydrophilic stratum, two ways of invasion are possible. If formation water is tightly bound with the rock frame, so oil is displaced from pores by water filtrate invading from a borehole. As this takes place, in most cases, a resistivity increases in the near borehole space. The decreasing invasion is observed only in some accumulations. The possible explanation is as follows. It has been shown that high-molecular naphthene acids presented in oil in very small amounts (0.1 %) are capable of producing rather stable emulsions when interacting with water base mud filtrate which contains ions of alkali additives (for instance, sodium bicarbonate). These processes lead to isolation of filtrate by oil films (“water-in-oil”) and to increase in the resistivity of an invaded zone in spite of displacement of non-conductive oil by conductive solution. These circumstances impede the evaluation of the formation porosity from the data on parameters of the invaded zone obtained from direct current measurements. The problem is compounded by the fact that emulsifiability of oil with identical density and viscosity varies in the wide ranges. The high values of water saturation can not be accounted for hydrophobization of rocks, but may be caused by emulsification. Emulsification in an invaded zone, especially in its “flushed” part, is responsible for the distinctions between estimations of its resistivity by DC methods and inductive ones. Along with the mentioned above features of forming electrical heterogeneity, other situations can occur in an invaded zone. In particular, the presence of microfracture in terrigenous deposits, which is of considerable importance for the phase permeability, can not be ruled out. This fracturing can affect the distribution of electrical properties in the invaded zone. Distinctions as in the content of different viscosity fluids so in degree of mixing oil and water are possible in thin-bedded sedimentary deposits with reservoir features. Displacement of fluids from beds with the high water content is likely to be more intense than that from less oil-saturated beds. Apparent resistivities in such rock masses can differ greatly from corresponding transformations in isotropic formations. If loosely bound water presents in sandstone, the water can be displaced after oil. This leads to accumulation of loosely bound water in the disturbance zone of formation fluid. A bordering zone is formed which resistivity is lower than that in the surrounding formation. The radial depth of the bordering zone is typically about 5–20 % of the total invaded zone radial depth. The models with a bordering zone are often found in accumulations of the Ob River oil zone. A bordering zone does not have to be formed if the productive formation is thinly bedded since boundaries with different fluid saturation would be at different distances from the borehole wall because individual beds possess varying permeability.

2.2. Petrophysical Features of Oil and Gas Reservoirs of West Siberia Petrophysics serves as a link connected geological targets and geophysical methods. Petrophysics of sedimentary rocks focuses on investigation of porosity with its various man-

6 ifestations, fluid saturation characteristics of rocks, capability of rocks to pass fluids through a porous space, as well as mineralogical and granulometric composition of rocks. These petrophysical characteristics as individually so in combination are associated with particular physical parameters. The conductivity or resistivity as well as the adsorptivity, density, water content, and natural radioactivity are assigned to these characteristics. The conductivity of basic types of sedementary rocks does not depend on their mineralogical composition since the resistivity of rock-forming minerals is exceedingly high (108– 1014 ohm × m). Anthracite coals and sulfide minerals, which resistivity is less by one order, provide the exception. The increased conductivity may be due to water in which salts of various metals are solved. Chlorides (NaCl, CaCl2, MgCl2, and others) are of primary importance, their molecules being dissociated in a water medium. Depending on the composition of magnitude of dissolved salts and solution temperature, the resistivity of solution changes by three orders roughly: from 0.01 to 10 ohm × m. Because of complexity of describing the real structure of a porous rock space provided by winding pores and irregular distribution of mineral particles interacting with formation fluids, the connection between petrophysical parameters (porosity, water-, oil-, and gassaturation) and resistivity of reservoir rocks is expressed by empirical dependencies of various types: r

IZRJ

=3 r V

IZ

=3 3 r . V

S

Z

Here rfwog is the resistivity of water-, oil-, and gas-saturated formation; rfw is the resistivity of the same formation when 100 % saturated with water; rw is the resistivity of formation water; Ðs and Ðp are parameters of saturation and porosity, respectively. The saturation parameter Ðs or hydrocarbon resistivity index shows how much times the resistivity of a rock increases when the rock is partially or completely saturated with oil and (or) gas. The dependence of the hydrocarbon resistivity index on the water saturation Êw can be expressed by the empirical relation: Ðs = a[Êw]–n. Here a and n are empirical values depending on the type of coating of a pore surface with formation fluids (hydrophilic or hydrophobic). The formation resistivity factor (Ðp or relative resistivity) depends on the porosity coefficient Êp and structure of the porous space. For example, in the case of shale-free rock: Ðp = a[Êp]–m. Here a and m are empirical values characterizing the structure of pores depending on compaction of rocks. At the low conductivity, an influence of polarization properties of a medium on generation of an electromagnetic field is possible. Polarizability of a medium is stipulated above all by dipole moments of water molecules being in free and loosely bound states. The

Petrophysical Description of the Targets under Investigation

7

polarizability is described quantitatively by the permittivity. In some cases, polarization effects caused by the secondary pyritization of terrigenous deposits are possible. Petrophysical models of the rock resistivity are widely used in practice for the quantitative estimation of poroperm parameters of porous-permeability rocks. The resistivities of multi-component porous-permeability media are determined by variety of parameters: quantity, form, location, mineral properties of solid and liquid phases, and their interaction.

2.3. Basic Geoelectrical Models and Their Typical Characteristics The presence of water of various salinity in porous-permeability sedimentary rocks can change their resistivities in the wide range. In this case, the most part of a porous space is occupied with water (bound, loosely bound, or free water, or all the three types of water in different ratios), the lesser is the rock resistivity. Formation water, that is saline water as a rule, may be in two main states: bound water and free one. In the course of drilling and after its completion, mud filtrate invades into formation. In the formations when 100 % saturated with formation water, a geoelectrical heterogeneity occurs due to filling the porous volume with more fresh mud filtrate. Resistivity in this heterogeneity is higher than that in the undisturbed formation (Fig. 2.1). The heterogeneity around a borehole can be described in the coordinates “resistivity – radial dimension of the invaded zone” (Fig. 2.2). The radial depth of invasion and the rate of resistivity change at the interfaces of different salinity fluids depend on the porosity and permeability of formation (Fig. 2.3). In formations with the high porosity and good filtration properties, boundaries formed between fluids in the transition zone are more clearly defined than those in reservoir rocks with increased content of clay minerals subjected to hydration. The depth of filtrate invasion from a borehole is usually larger in water-saturated formations than that in oil-saturated reservoirs. Entering pores, filtrate displaces a moveable formation fluid. The greatest displacement is observed when rock is fractured by a percussive chisel in the course of drilling. As this takes place, the advanced filtrate invasion occurs. Further, the intervals of previously penetrated permeable formations are under hydrostatic pressure of drilling mud. Filtration of water from drilling filtrate is impeded at the expense of a mud cake deposited within the porous permeable intervals. The filtrate invasion is accompanied by occurrence of the zone with electrochemical composition of the water solution other than that in the formation. If formation pores are filled with oil (gas) along with loosely bound water, the filtrate entering pores of the hydrophilic reservoir first displaces oil and then formation water. In Figs. 2.4–2.6 there are shown the schemes of forming geoelectrical heterogeneity when oil and saline water is displaced by filtrate of the decreased salinity. As it can be seen from Fig 2.4, such a heterogeneity adjoins the borehole. It occurs at the expense of pores filled with water-base drilling mud filtrate containing residual for-

Fig. 2.1. One-dimensional model: borehole – invaded zone – formation.

8 mation water and oil (the filtrate salinity is less than formation water one). Another heterogeneity is formed at the expense of accumulation of formation water being displaced after moveable oil (gas). Next to the zone of mixed fluids, the “undisturbed” formation with the unaltered composition is retained. Fig. 2.2. Radial resistivity distribution in a model: zone of increasing invasion formation.

Fig. 2.3. Forming increasing invasion zone.

Fig. 2.4. One-dimensional model: borehole – bordering zone – formation.

In reservoirs containing moveable oil and formation water, two areas with different fluid properties occur around a borehole. The near borehole area contains water filtrate from the borehole and remains of non-displaced oil and formation water. At the some distance from the borehole wall, pores from which oil was displaced, are filled with the mixture of residual formation water and water from the borehole, the latter being of increased salinity due to the contact with residual formation water. Thus, the area of anomalous saline water occurs. It is clear, that these two zones with solutions of variable concentration will be distinguished by their resistivities and both zones will be differentiated from the undisturbed formation. The formation part adjacent to the borehole can be characterized by higher resistivity than the undisturbed formation. It will be observed in the case if the pore volume filled with fresh filtrate turns to be less conductive than the formation. However in practice, the zone nearest to a borehole is not sufficiently contrast to be revealed. The reason is that the mean conductivity of displaced hydrocarbons (of high resistivity) and formation water (of high conductivity) is close to the filtrate conductivity. In such cases, the small volume of displaced formation water together with oil is found to be comparable by the column conductance with significantly larger volume of fresh water from the borehole. The radial dimensions of invaded zones depend on the formation permeability (clay cement), rheological properties of drilling mud as well as drilling conditions and time of logging. In Fig. 2.7 there are given the plots of radial resistivity profiles (rf =

Petrophysical Description of the Targets under Investigation

9

= 1–100 ohm × m) for oil reservoirs of complicated polymictic composition depending on the resistivity of formation water rw and that of drilling mud rm. Three groups with the same type of resistivity profiles can be selected: · in the models 1–3, the near borehole part includes two zones with lower resistivity values that are lower than resistivity values in the undisturbed formation, the salinity of drilling mud being higher or close to that of formation water;

Fig. 2.5. Fluid distribution when forming a bordering zone.

· in the models 4 and 5, the drilling mud filtrate resistivity is less or equal to that of formation water; the pore space is filled with filtrate after oil is displaced that leads to decrease in resistivity of the invaded zone; · in the models 8 and 9, accumulation of saline formation water displaced after oil occurs in the forefront of fresh filtrate. The last models represent the development stages of zones with decreasing invasion. Transient stages of invasion can be revealed when analyzing time-lapse measurements. The investigations performed by means of the VIKIZ method in many boreholes of the Surgut Arch confirm the occurrence of such processes.

Fig. 2.6. Radial resistivity distribution in the presence of a bordering zone.

It is obvious that development of invaded zones by stages depends not only on water resistivities, but on many other conditions: the structure of porous-permeability space, porosity (in its various manifestations), fluid composition, properties of electrical double-layers, etc. The crucial role of time when forming a heterogeneity especially during intermediate round-trip actions in boreholes can be outlined once again. In many cases, development of invasion depends strongly on the relationship between intra-formation pressure, hydrostatic one, and overpressure. By the action of these factors, the micro-fractured porosity is formed and additional flow conditions for formation fluids occur.

Fig. 2.7. Radial resistivity distribution for oil-saturated formations.

10

Fig. 2.8. Estimates of both resistivity (a–c) and invasion depth (d ) at different fluid saturation of reservoir: O stands for oil; O+W stand for oil with water.

Summary results of analysis of log data on the Middle Ob fields are listed in Fig. 2.8. In the Fig. there are given the ranges of resistivities characterizing invaded zones and rocks of water- and oil-saturated formations. Here the estimations of invasion depths and shoulder bed resistivities are given as well. Note that these data are given for mud with the resistivity of rb=1–2 ohm × m. For analysis of the spatial resolution of the method, the radial and vertical characteristics are used. The possibilities for resistivity determination in the undisturbed formation in the presence of a borehole and an invaded zone are assessed through the radial characteristics. In this case, a cylindrically layered model (borehole – invaded zone – bordering zone – formation, Fig. 2.9) is a basic model for analysis of radial characteristics, and a horizontally layered model (overlying rocks – formation – underlying rocks, Fig. 2.10) is a basic model for analysis of vertical characteristics. Moreover, there are many cases (thin beds, highly permeable shoulder beds, deep invaded zones) when it is necessary to take into account as the finite formation thickness so the resistivity distribution from a borehole to undisturbed formation. In this context, twodimensional models (a borehole crosses the formation of the finite thickness and the invaded zone is present, Fig. 2.11) should be used. At last, there exist the most complicated tree-dimensional models when the formation of the finite thickness is crossed by a dipping borehole and invaded zones are present (Fig. 2.12). Let us consider the set of geoelectrical models that are typical for West Siberia. The following basic situations can be selected by the type of the radial resistivity distribution. Low permeability (tight) formation. The simplest model is a two-layer one. Unchanged borehole diameter (practically, it always corresponds to the nominal diameter) and the high resistivity are characteristic properties of the model: the drilling mud resistivity is 0.01–5.0 ohm ×m; the borehole radius is 0.108–0.125 m; the formation resistivity is 50–200 ohm × m. Shaly formation. Shaly formation with fairly complicated structure is usually represented by thinly interbedded siltstones, argillites, and shaly sandstones. The borehole profile

Petrophysical Description of the Targets under Investigation

11

is complicated and cavernous in nature. The simplest model is a two-layer (borehole – formation) one that reflects its structure adequately. A three-layer model can be considered as additional one when a shallow invaded zone stipulated by filtration of drilling mud into the sandiest varieties is present: the drilling mud resistivity is 0.01–5.0 ohm × m; the borehole radius is 0.108–0.2 m; the formation resistivity is 2.0–6.0 ohm × m. Water-saturated formation. The type of formations is common in terrigenous sections of West Siberia. The distinctive feature of the formation is increasing invasion. The radius of the invaded formation part may be up to 2.0 m (riz /rb = 2–20). The resistivity of an invaded zone ranges from 10 to 50 ohm ×m; that of formation is from 2 to 6 ohm ×m. In some cases, neutral invasion can be observed, then the model is degenerated to two-layer one: the resistivity is 0.01–5.0 ohm × m, 10– 50 ohm × m, and 2.0–6.0 ohm × m for drilling mud, invaded zone, and formation, respectively; the borehole radius is 0.108–0.125 m; the invaded zone radius is 0.2–2.0 m.

Fig. 2.9. Cylindrically-layered model: borehole – invaded zone – bordering zone – formation.

Oil-saturated reservoir. That is the main type of formations for which quantitative interpretation is executed. The distinc- Fig. 2.10. Horizontally-layered model: overlying tive feature of the reservoir is increasing or rocks – formation – underlying rocks. neutral invasion. Here the formation resistivity ranges from 4.0 to 50 ohm × m. The resistivity of an invaded zone is higher than that of water-saturated formation due to residual water-saturation and it varies in the range from 10 to 100 ohm × m. As an additional model, a four-layer one may be used in which a bordering zone exists aside from the invaded zone. The presence of a bordering zone in hydrophilic terrigenous oil-saturated reservoirs has been proved by the analysis of field logs. The bordering zone is a ring layer of insignificant thickness (about 0.1–0.2 m) with the high content of mineral water. The resistivity of this zone is nearly the same as that of water-saturated formation (riz >rf >rbz ). An invaded zone that is thin or low contrast by resistivity may occur in thinly bedded sand-shale reservoir rocks. This zone does not practically affect signals being measured. In these cases, the model includes two-layers: the resistivity is 0.01–5.0 ohm × m, 10–50 ohm ×m, 2–6 ohm × m, and 4.0–50.0 ohm × m for drilling mud, invaded zone, bordering zone, and formation, respectively; the borehole radius is 0.108–0.2 m; the invaded zone radius is 0.2–2.0 m; the bordering zone thickness is 0.05–0.2 m. Gas-saturated reservoir. As increasing so decreasing invasion can be revealed in a gassaturated reservoir: the resistivity is 0.01–5.0 ohm × m, 10–150 ohm × m, 0.2–2.0 m; 30–200 ohm × m for drilling mud, bordering zone, invaded zone, and formation, respectively; the borehole radius is 0.108–0.2 m.

12 When using the cylindrically layered model, the thickness of formation being investigated is assumed to be sufficient for neglecting shoulder bed effects. Further, the geological situations are described when the thickness of formations under investigation is such that shoulder beds affect the probe signals. Next in order of complexity model is that when as a formation so shoulder beds have an invaded zone. Low-permeability, tight formation, shoulder beds are shaly rocks. The resistivity of shoulder beds is 2–4 ohm × m, that of formation is 100–200 ohm × m.

Fig. 2.11. Two-dimensional model: vertical borehole – invaded zone – formation.

Water-saturated formation, shoulder beds are shaly rocks. The resistivity of shoulder beds is 2–4 ohm × m, that of formation is 2–6 ohm × m. Oil-saturated reservoir, shoulder beds are shaly rocks. The resistivity of shoulder beds is 2–4 ohm × m, that of formation is 4–30 ohm × m. Gas-saturated reservoir, shoulder beds are shaly rocks. The situation is consequently being worse as compared with water- and oil-saturated formations since the contrast of electrical resistivities increases as in the invaded zone so in undisturbed formation. Formation resistivity ranges from 30 to 200 ohm × m. The other combinations are also possible.

Fig. 2.12. Three-dimensional model: inclined borehole – invaded zone – formation.

Oil-saturated reservoir, the top is shaly bed, the bottom is a water-saturated stratum. The distribution of resistivity is observed in the downward direction: 2–4 ohm × m; 4–30 ohm × m; 2–6 ohm × m.

Gas-saturated reservoir, the top is shaly bed, the bottom is water-saturated stratum. The distribution of electrical resistivity is observed in the downward direction: 2–4 ohm × m; 20–300 ohm × m; 2–6 ohm × m. Gas-saturated reservoir, the top is shaly bed, the bottom is oil-saturated reservoir. The distribution of electrical resistivity is observed in the downward direction: 2–4 ohm × m; 30– 200 ohm × m; 4–30 ohm × m.

3

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THEORETICAL FUNDAMENTALS OF THE METHOD. V I K I Z TO O L R E S P O N SE I N H E T E R O G E N O U S M E D I A

3.1. Focusing Systems in Electromagnetic Logging The main purpose of electromagnetic logging is to make estimates of formation resistivities as correctly as possible. To aid this, the multi-coil probes are employed. The parameters are so chosen that resistivity of the undisturbed formation would determine the signal being measured and as the borehole effect so invaded zone effect would be relatively insignificant. It is common practice in logging to designate probes of this type as focusing ones. In the induction logging (frequencies up to 250 kHz), the principles of frequency and geometric focusing based on the theory of generalized geometrical factor are used for designing probes. When geometric focusing, moments of coils and distances between them are so fitted that contributions (geometrical factors) from a borehole and an invaded zone would be significantly diminished. The another, less common approach to focusing systems, is measuring the inphase component of the secondary field or dual-frequency difference of the quadrature component. Improving the radial characteristics of focusing probes leads to increase of shoulder bed effect on a measured signal. This comes into particular prominence when the formation thickness is comparable with the probe spacing. The another peculiarity of focusing systems is essential decrease in the signal level being measured. Thus, when probes are designed, the compromise between two alternative conditions is required. For improving radial characteristics, it is necessary to reduce the frequency or elongate the probe spacing. For improving vertical characteristics and increasing a signal being measured, it is necessary to increase the frequency and to shorten the probe spacing. All the probes that common used in induction logging have been designed with regard to these contradictory requirements. The principle of focusing an electromagnetic field in the high-frequency range is radically different. It has been established that the relative difference between amplitudes and phases measured in two closely spaced coils depends very weakly on the borehole parameters even at very high (up to 15 MHz) frequencies. Thus, the phase difference measurement allows one to satisfy the two requirements at once: to eliminate a borehole effect without loosing a good vertical resolution. When high frequencies are used, the signal levels become high even in a relatively low conductive (up to 120 ohm × m) medium that extends the range of resistivities being measured.

14

3.2. Phase Difference and Its Relation to the Resistivity of an Uniform Space. Apparent Resistivities High frequency methods use three-coil probes when measuring relative characteristics. Such a probe consists of one transmitter coil (T) and two receiver coils (R1 and R2). All the coils are coaxial. Receivers are arranged on one side from the transmitter. The transmitter coil is supplied with an alternating current: J = J0 H

- LwW

.

Here w =2p f is a circular frequency; f is a frequency, J0 is a current amplitude. The transmitter coil moment Mt is defined by a current J, the area enclosed by one turn of a coil S, and the number of turns in the coil nt : Mt = Jnt S. Moments of receiver coils Mr are defined by the area S and the number of turns n: Mr = nr S. The distance between centers of a transmitter coil and long-distance receiver coil M1 is a probe spacing L1. The relative distance between centers of receiver coils DL/L1 will be referred to as a probe base. An alternating current in a transmitter coil generates a varying electromagnetic field in a homogenous conductive medium. If spacing between transmitter coil and receiver ones significantly exceed their sizes ( / ? 6 ), all the coils can be considered as magnetic dipoles. In this case, the magnetic field at centers of receiver coils is described by the expression: + = M

0 H p / W

LN/M

 - LN/   M M

 .

M

Here k is the wave number related to medium parameters in the following way:

N = Lwms + emw  , s = 1/r is conductivity, r is resistivity; m = m0 m*, m0 = 4p  × 10–7 H/m, m* is the relative magnetic permeability; e  = e0 e *, e0 = 8.85 × 10–12 F/m, and e * is the relative permittivity. In receiver coil of number j, e.m.f. is induced:

H =M

 W

M

,

where Fj = m Mrj Hj is the magnetic flux. The phase of a magnetic field jt is described by the expression

j M = DUFWJ

,P + M 5H + M

= -DUFWJ

5H H M ,P H M

.

Theoretical Fundamentals of the Method. VIKIZ Tool Response in Heterogenous Media

15

When quasistationary conditions in a nonmagnetic medium (wer < 0.1; r £ 150 ohm × m,  m * = 1) are satisfied, the wave number k is transformed to the following form:

e* £ 5–10,

N = p  + L  IP  r , here fm is the frequency in MHz. In this case, the phase difference Dj between e.m.f. in two coils is

j = S d / - DUFWJ

here S =

Sd / ,  + S  - d / +  S  - d /

p Im / , DL=L1–L2, dL1=DL/L1. r 

From the expression represented above, one can see that the phase difference in a homogenous medium will be the same and depend only on the medium resistivity if two conditions are valid: I / = FRQVW 

D/ = FRQVW . /

Three-coil probe for which these conditions are realized is given the title isoparametric probe. The following parameter values have been chosen for the VIKIZ tool: I / =  µ    

D/ =  , /

where f is the frequency, in Hz. The dependence of the phase difference Dj on resistivity of a homogenous medium for these isoparameter values is shown in Fig. 3.1. As it can be seen, there exists the simple relation between Dj and r values that is used for introducing the apparent resistivity ra. It should be emphasized that readings of all VIKIZ probes correspond to the apparent resistivity value that is equal to the resistivity of a medium (ra = r). As real measurements have some errors, let us analyze the influence of signal error on the apparent resistivity uncertainty. As it is known, the relative error of apparent resistivity determination dra is connected with the relative measurement error dDj by the following approximate expression: dra » kr Dj,

hr =

 OQ _ Dj _  N r =  .  OQ r hr

The kr value is called the propagation coefficient of a relative measurement error and hr is the sensitivity of measured signal Dj relative to the medium resistivity r. In Fig. 3.2 there are given curves of both the sensitivity hr to resistivity of a homogenous medium and the propagation coefficient of error when transforming measured signal into apparent resistivity. As it can be seen from these curves, the least values of kr (1.3–1.5) are observed for a high conductive medium ( r » 1–10 ohm × m). The greatest increase in

16 relative error (1.9–2.0) takes place when transforming the phase difference into apparent resistivity in low conductive media ( r > 100 ohm × m). When the resistivities of a medium are high, the dependence of a measured signal on dielectric permittivity occurs at high frequencies. For long VIKIZ probes, quasistationary conditions (the weak influence of e) are satisfied with high accuracy when terrigenous deposits and drilling mud have common values of resistivities. However, for the shortest probe located in high resistive rocks, a signal is affected by the dielectric permittivity. Fig. 3.1. Dependence of phase difference on resistivity of a homogenous medium.

In Figs. 3.3 and 3.4 dependencies of Dje and Dj0 values on the resistivity of a homogenous medium are given for different dielectric permittivity values, e * (Dje e is the phase difference that takes account for e * and Dj0 is the phase difference in quasistationary approximation). The relative contribution of wave processes into a signal of the short probe is less than 5–7 % for typical clays with the resistivity less than 4 ohm × m even at e * = 40. In reservoir rocks, a signal of the shortest probe is defined by the parameters of an invaded zone. At the typical increasing invasion (riz » 20 ohm × m), the relative influence of e * = 20 is less than 10 % at the frequency of 14 MHz.

The dependence of signals from five three-coil probes at the same depth Fig. 3.2. Curves of both phase difference sensitivity to on a spacing of the basic two-coil pair, resistivity of a medium (blue line) and propagation cowe will designate as a VIKIZ sounding efficient of error (red line). curve. Two types of curves will be considered: dependencies of phase difference and those of apparent resistivity on the probe spacing. The combination of sounding curves at different depths is a VIKIZ log. The logs can also be represented in the form of phase difference and apparent resistivities. In a homogenous medium, signals of all probes are equal within the limits of measurement errors. If the signals are not equal (i.e., the sounding curve is not a straight line), this points to the spatial heterogeneity of resistivities. As far as all probes have the different spacing and those operate at various frequencies, currents that flow in variable medium

17

Theoretical Fundamentals of the Method. VIKIZ Tool Response in Heterogenous Media

Fig. 3.3. Dependence of phase difference on dielectric permittivity of a homogenous medium (0.5 m probe).

Fig. 3.4. Dependence of phase difference on dielectric permittivity of a homogenous medium (0.7 m probe).

spaces contribute to a signal being measured. Here, the lower is the frequency and the more is the spacing, the farther apart the probe there is the space that influences probe signals. Particularly, if formations being investigated are rather thick (their thickness exceeds the probe spacing), the sounding curve reflects the resistivity change from a borehole toward an undisturbed formation. In this case, measurement of the differential characteristic, i.e., phase difference, allows the influence of the near the probe area (in particular, the borehole) to be suppressed.

3.3. The Uncertainty of Model Parameter Prediction as a Function of Measurement Errors The five phase differences are measured in the VIKIZ probes: Dji (i = 1,..., 5) from the shortest probe to the longest one. The model of a medium is characterized by the r parameter vector, S = ^ S S SP ` , where m is the number of model parameters. For instance, there are five model parameters in such a model as borehole – invaded zone – formation: the drilling mud resistivity, borehole radius, invaded zone resistivity, external radius of the invaded zone, and formation resistivity. As it is known, the sensitivity hij of the phase difference Dji measured in i-probe relative to the j-parameter pj is determined by the following expression:

h = LM

 OQ _ Dj _ .  OQ S L

(3.1)

M

‰

‰

The relation between relative changes of model parameters d S and signals d D j when the parameter variations are small can be written as: ‰

·

‰

d D j  'd S ,

(3.2)

18 ‰

where d Dj = {dDj1, dDj2, ... , dDj5} is the vector of relative errors of measured phase

‰

differences, d S = {dp1, dp2, ..., dpm} is the vector of relative errors of model parameter ·

determination. The matrix ' of dimensionality (5´m) is called a sensitivity matrix: · Ê  OQ Dj Ú '=Ë Û , i = 1, ..., 5; j = 1, ..., m . Ì  OQ S Ü

(3.3)

L

M

‰

The relative determination errors of model parameters d S can be estimated from the

‰

relation (3,2) if the relative measurement errors of phase differences d Dj are known:

‰

·7·

·7

d S =  ' ' - ' ·7

‰

d Dj .

(3.4)

·

Here ' stands for a transposed matrix ' . The relation (3.4) is a basic one for analysis of radial and vertical characteristics as well for evaluation of the inversion quality of both logs and sounding curves.

3.4. Typical Sounding Curves One of the main VIKIZ problems is estimation of the radial distribution of the resistivity from a borehole toward the undisturbed formation. This problem is solved on the basis of interpretation of sounding curves. As it has been pointed, the principle of radial sounding is based on increase in radial depth of investigation with lengthening a probe spacing and lowering a frequency as well as on measuring phase difference, which depends weakly on the borehole parameters. Strictly speaking, the radial soundings are possible only if the formation is thick enough. In this case, overlying and underlying deposits weakly affect signals linked with formation. Just such situations are considered here, and therefore, the cylindrically layered models are used to calculate synthetic logs. Shaly low resistive formation penetrated by borehole (Fig. 3.5). There is either a shallow invaded zone or no invaded zone. When calculating curves, it is taken into account that clays are characterized by the high dielectric permittivity (e * » 40) that can influence signals of two shortest probes. Apparent resistivities for all probes except the shortest one coincide with the true formation resistivity. A borehole influences signals of the shortest probe. But this influence is less than 10 % even for high conductive mud. Note that the influence of high conductive mud increases the apparent resistivity as compared with true one. This is explained by the fact that the signal transformation into ra in a homogenous medium is not adequate for high-resistivity contrast medium. Tight low permeable highly resistive formation penetrated by borehole (Fig. 3.6). There is either a shallow invaded zone or no invaded zone. In this case, the borehole effect manifests itself in signals of practically all probes, the conductive borehole lowering (up to 25 %) apparent resistivities as compared with the true resistivity. Lowering in apparent resistivities of long probes is either due to dielectric permittivity effect in high resistive formations or because of transformation for a homogenous medium is used in a highresistivity contrast section.

Theoretical Fundamentals of the Method. VIKIZ Tool Response in Heterogenous Media

Fig. 3.5. Sounding curves for shales without invasion (rf = 4 ohm × m, rb = 0.108 m), rb=2.0 (1 ), 0.5 ohm × m (2).

Fig. 3.7. Sounding curves for water-saturated formation with increasing invasion (riz= 20 ohm × m, riz = 0.6 m, rf = 4 ohm × m).

19

Fig. 3.6. Sounding curve for tight highly resistive formation without invasion (rf = 200 ohm × m).

Fig. 3.8. Sounding curves for oil-saturated reservoir with increasing invasion (riz= 30 ohm × m, riz= 0.5 m, rf = 6 ohm × m).

See the rest designations for Fig. 3.5.

Water saturated formation with increasing invasion (Fig. 3.7). The sounding curve reflects the radial resistivity distribution. Apparent resistivities for two short probes are mainly defined by the resistivity of an invaded zone. Signals of four long probes are not practically affected by the drilling mud resistivity. High conductive mud (up to 0.02 ohm × m) is responsible for lowering the apparent resistivity for the shortest probe by about 7 %. As for signals of long probes, those are close to the true formation resistivity. Such sounding curves allow reliable qualitative evaluation of the formation saturation nature. Oil saturated reservoir with increasing invasion (Fig. 3.8). Sounding curves, just as in the previous case, reflect the true resistivity distribution. Apparent resistivities of two short probes result mainly from the resistivities of an invaded zone. The high conductive mud effect (up to 0.02 ohm × m) manifests itself in lowering in an apparent resistivity for two short probes by about 12 %. Signals of two long probes are closely related as to each other so to

20

Fig. 3.9. Sounding curves for gas-saturated reservoir with decreasing invasion (riz= 30 ohm × m, r iz = 0.7 m, r f = 60 ohm × m). r b = 2.0 (1 ), 0.5 ohm × m (2 ).

Fig. 3.11. Sounding curves depending on bordering zone location (riz= 30 ohm × m, rbz= 3.1 m rf = 6.2 ohm × m). Radius of invasion zone and bordering zone, respectively, m: 1 – 0.42, 0.54; 2 – 0.52, 0.68; 3 – 0.62, 0.68.

Fig. 3.10. Sounding curve for oil-saturated reservoir with increasing invasion and bordering zone (r iz =30 ohm × m, r iz = 0.5 m, r bz =3 ohm × m, rbz = 0.5 m, rf = 6 ohm × m).

Fig. 3.12. Sounding curves depending on bordering zone location (riz=12 ohm × m, rbz= 3.7 m, rf = 5.2 ohm × m). See the rest designations for Fig. 3.11.

the resistivity of the undisturbed formation. In this situation, reliable qualitative evaluation is possible as well. Gas saturated reservoir with decreasing invasion (Fig. 3.9). Sounding curves exhibit increase in the resistivity from a borehole to the undisturbed formation. Signals from two short probes are close to the resistivity of an invaded zone, whereas apparent resistivities of two long probes are near-completely defined by the formation resistivity. As it has been noted, one of a possible feature of an oil-saturated reservoir is the presence of a narrow high conductive bordering zone. Oil-saturated reservoir with increasing invasion and bordering zone (Fig. 3.10). In the presence of a bordering zone, the type of a sounding curve can be changed from a monotype to a curve with the extremum. In this case, the apparent resistivities for short probes are essentially lower than the resistivities of an invaded zone, but the former significantly exceed the resistivities of a bordering zone. Apparent resistivity of the long probe coincides with the formation resistivity. Changes in sounding curves at different locations of a bordering zone are shown in Fig. 3.11. Farther from the bordering zone, the minimum of sounding curve is shifted to the

Theoretical Fundamentals of the Method. VIKIZ Tool Response in Heterogenous Media

21

range of successively longer probes. Simultaneously, gradual increase in apparent resistivities is observed for short probes, which gradually approach the resistivities of an invaded zone. A bordering zone is determined by the minimum on a sounding curve. Note that this feature is observed only when there is the sharp contrast between resistivities of an invaded zone and a bordering zone. That is, a bordering zone can be selected on sounding curves if drilling mud and formation water differ greatly in resistivities. In Fig. 3.12 there are given sounding curves when riz is not in marked contrast to rbz. In this case, the curves become monotonically decreasing without the minimum caused by a bordering zone.

3.5. Typical Logs One of the main problems solved through VIKIZ method is subdivision of a section. Let us consider fragments of logs as reflecting typical geoelectrical situations so related to distinguishing specific elements of the section. Synthetic records have been calculated for the two-dimensional model (Fig. 2.11). Two cases when formation thickness H = 0.8 m and H = 2.4 m are considered.  Tight low permeable formation in shaly deposits (Fig. 3.13, r VKE = 3.5 ohm × m,  r = 6 ohm × m, U  = 0.2 m, r =100.0 ohm × m, r =3.5 ohm × m, r  = 6.0 ohm × m, VKE f U  = 0.2 m). The logs reflect the true resistivity distribution depending on depth. In the thin formation, apparent resistivities are lowered, so ra is less than the formation resistivity for any probe. In the central part of the thick formation, short probe signals have the constant value that exceeds the formation resistivity by about 20 %. The distinctions are observed between logs for the thin and thick formations within the interval when passing through the 

L]

L]

L]

L]

Fig. 3.13. Logs for a model: shale – tight formation – shale. Color codes for probe spacing (m) are: red for 0.5 m, green for 0.7 m, brown for 1.0 m, blue for 1.4 m and black for 2.0 m, respectively.

22

Fig. 3.14. Logs for a model: oil saturated formation – tight layer – water saturated formation. See designations for Fig. 3.13.

formation top. These distinctions are associated with the fact that the first model has log points at which transmitter coils and receiving ones are located in overlying and underlying rocks, respectively. The asymmetry of logs relative to the center of the formation is caused by the asymmetry of three-coil probes. The asymmetry degree of logs increases for longer probes. Note that if formation is thin, maximum signals are measured at nearly the same depth, so the difference between depths of these signals in the thick formation is about 0.5 m. The apparent resistivity for the long probe is significantly lowered mainly due to effect of well conductive shoulder beds. Tight low permeable formation overlain by shale and underlain by water satura ted formation (Fig. 3.14, r VKE = 3.5 ohm × m, r  = 6 ohm × m, U  = 0.2 m, rf =100.0 ohm × m,   r VKE=4.5 ohm × m, r =30 ohm × m, U  = 0.6 m). As opposed to the previous model, shoulder beds are distinguished by resistivities. The logs for long probes are similar to those shown in Fig. 3.13, but the former have some peculiarities because their apparent resistivities under the formation come close to the water saturated formation resistivity. As compared with the previous model, increase of the shoulder bed effect leads to increasing ra for short probes. L]

L]

L]

L]

 Water saturated formation in shaly deposits (Fig. 3.15, r VKE= 3.5 ohm × m,    r = 6 ohm× m, U = 0.2 m, rf = 4.5 ohm× m, r  =30 ohm×m, U = 0.6 m, r  =3.5 ohm × m, VKE r  = 6 ohm × m, U  = 0.2 m). The logs reflect the true resistivity distribution over the section, but at the same time, these logs are asymmetric relative to the formation center. Apparent resistivities of the long probe are close to the true resistivity even in a thin formation. The values of ra closest to the formation resistivity are observed in the interval above the formation bottom. It can be explained by the fact that in such situations, the most part of formation or the entire formation under investigation turnes out to be inside  the probe. Note that when leaving the thin formation, the intermediate asymptote r VKE »3.6 ohm × m 

L]

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Theoretical Fundamentals of the Method. VIKIZ Tool Response in Heterogenous Media

Fig. 3.15. Logs for a model: shale – water saturated formation – shale. See designations for Fig. 3.13.

Fig. 3.16. Logs for a model: shale – water saturated formation – tight formation. See designations for Fig. 3.13.

23

24

Fig. 3.17. Logs for a model: shale – oil saturated formation – shale. See designations for Fig. 3.13.

Fig. 3.18. Logs for a model: shale – oil saturated formation – water saturated formation. See designations for Fig. 3.13.

Theoretical Fundamentals of the Method. VIKIZ Tool Response in Heterogenous Media

25

Fig. 3.19. Logs for a model: gas saturated formation – oil saturated formation – water saturated formation. See designations for Fig. 3.13.

Fig. 3.20. Logs for a model: shale – gas saturated formation – shale. See designations for Fig. 3.13.

26 is observed within the interval that is practically the same as the probe spacing. The effect of formation in the overlying medium begins to be noticeable at the distance approximately equal to the probe base. Logs of short probes reflect the resistivity distribution in the top area. The position of formation tops is estimated well at the intersection of logs of all probes. Water saturated formation overlain by shale and underlain by tight low permeable rocks     (Fig. 3.16, r VKE = 3.5 ohm × m, r VKE = 6 ohm × m, U = 0.2 m, rf = 4.5 ohm × m, r = 30 ohm × m,  U   = 0.6 m, r VKE = 100.0 ohm × m). The logs reflect well the resistivity distribution over the section. Apparent resistivities for two long probes are close to the formation resistivities even for the thin formation. The position of a formation top is coincident with the intersection of profiling curves. The effect of the high conductive upper part is extended in an insulating medium for the distance close to the probe spacing. Signals for the short probe in the formation are close to the resistivities of the invaded zone L]

L]

L]

  Oil-saturated reservoir in shaly deposits (Fig. 3.17, r VKE = 3.5 ohm × m, r = 6 ohm × m,  U = 0.2 m, rf = 8 ohm × m, r = 20  ohm × m, U   = 0.5 m, r VK E = 3.5 ohm × m, r  = 6 ohm × m, U  = 0.2 m). The logs are asymmetric relative to the formation center and, as a whole, these logs correctly reflect the resistivity distribution over the section. The interval where apparent resistivities are coincident with formation resistivities is shifted to its bottom. In the thin formation, signals of the long probe differ from rf value by about 25 %. The formation top coincides with the intersection point of profiling curves for tree-coil probes. When going under the bottom, the reservoir markedly affects a signal over the interval that is nearly equal to the probe spacing. The explicit reservoir effect on probe signals in the top is observed within approximately the same interval that the probe base is. Signals of the shortest probe are close to the resistivity values of the invaded zone. L]



L]

L]

L]

L]

L]

 Floating oil-saturated reservoir overlain by shale (Fig. 3.18, r VKE = 3.5 ohm × m,     r = 6 ohm × m, U = 0.2 m, rf = 8 ohm × m, r  = 20 ohm × m, U = 0.5 m, r VK = 4.5 ohm × m, E    r = 30 ohm × m, U = 0.6 m). The logs are strongly asymmetric relative to the formation center. As a whole, logs for long probes correctly reflect the true resistivity distribution over the section. Logs for short probes reflect the resistivity distribution in the near a borehole zone. The interval of coincidence of apparent resistivities with formation ones is adjacent to the bottom. The apparent resistivity for the longest probe in the thin formation differs by no more than 25 % from the rf value. Location of the formation top coincides with intersection points of profiling curves for three-coil probes. 

L]

L]

L]

L]

L]

L]

Floating oil-saturated reservoir overlain by gas-saturated deposits (Fig. 3.19,    r VK = 50 ohm × m, r = 20 ohm × m, U  = 0.4 m, rf = 8 ohm × m, r = 20 ohm × m, U   = E      = 0.5 m, r VKE = 4.5 ohm × m, r =30 ohm × m, U = 0.6 m). Logs for long probes correctly reflect the true resistivity distribution throughout the section. Logs for two short probes demonstrate the resistivity distribution in the invaded zone. The thin formation is not practically distinguished through the signals of three long probes that form “the transition zone”, but this formation can be distinguished on logs for short probes only by distinctions in the invaded zone. The effect of both well conducting reservoir rocks and bottom layer is observed in gas-saturated formation at the distance that is approximately equal to one and half probe spacing. L]

L]

L]

L]

L]

L]

Gas-saturated reservoir in shaly deposits (Fig. 3.20, r VKE = 3.5 ohm × m, r = 6 ohm × m, U = 0.2 m, r f = 50 ohm × m, r   = 20 ohm × m, U   = 0.4 m, r VK E = 3.5 ohm × m, r  = 6 ohm × m, U  = 0.2 m). The logs are asymmetric relative to the formation center and those correctly reflect the true resistivity distribution in the vertical direction. Apparent resis

L]

L]

L]



L]



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L]

Theoretical Fundamentals of the Method. VIKIZ Tool Response in Heterogenous Media

27

Fig. 3.21. Logs for a model: shale – gas saturated formation – oil saturated formation. See designations for Fig. 3.13.

tivities of all probes in the thin formation differ greatly from the formation resistivity. At the same time, signals of the 1.4 m long probe in the thick formation differ by no more than 10 % from the true formation value. Location of the formation top coincides with the intersection point of profiling curve for three-coil probes. When the measure point comes to the bottom, apparent resistivities of all probes become practically close to the underlying rock resistivity. Gas-saturated reservoir overlain by shale and underlain by oil-saturated reservoir      (Fig. 3.21, r VKE = 3.5 ohm × m, r = 6 ohm × m, U = 0.2 m, rf = 50 ohm × m, r = 20 ohm × m, U   = 0.4 m, r VK E = 8 ohm × m, r  = 20 ohm × m, U  = 0.5 m). Logs for the section with the thin gas formation do not take the values close to the formation resistivity. Apparent resistivity for the short probe differs from true one by about 20 %. The profiling curve for the long probe in the thin formation is the most complicated and that has two maxima within the reservoir depth. In this case, the difference between the minimum and maximum values is about 1.5 ohm × m. L]

L]

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3.6. General Limitations on Electromagnetic Sounding Methods Application of inductive methods should be preceded by assessment of their possibilities in particular geoelectrics situations. Discrepancy of models with the realistic structure and physical characteristics of a geological medium along with the presence of errors when measurements are performed is the basic reason for all limitations. When using induction excitation of electromagnetic fields, the investigation of low conductive geological deposits presents some difficulties. The presence of high resistive rocks leads to reducing a signal being measured corresponding to an increase in both the signal-to-noise ratio and relative

28 measurement error. When inversion of such data is executed, relative errors of parameter determination increases to an extent that the result becomes uncertain. Let us consider a simple example. At the present time, the new technique provides absolute determination accuracy of about 0.5° in phase difference measurements. A signal in a homogenous medium at the resistivity equal to 300 ohm × m is 0.77° (i.e., the relative error is about 0.65). In this case, the propagation coefficient of error when transforming into apparent resistivity is 1.11. Thus, a homogenous medium resistivity is determined with the relative error equal to 0.72 and confidence interval equal to 300 ± 216 ohm × m. The combination of high conductive drilling mud (less than 10–3 ohm × m) and a deep invaded zone of low resistivity with high resistive formation is disadvantageous for applying VIKIZ method. For instance, let us asses a possibility for determination of the gas formation resistivity (rf = 50 ohm × m) in the presence of decreasing invasion (riz = 0.2 ohm × m, riz = 0.7 m) and when mud resistivity rb = 5 × 10–3 ohm × m. We assume the relative measurement errors to be equal to 0.03. The mean propagation coefficient of error for inversion is 22.1. Thus, the relative determination error of a formation resistivity will be about 0.66 that corresponds to the confidence interval 17–83 ohm × m. When invaded zones with lowered resistivity are deep (comparable with the probe spacing), one faces with analogous problems on reliable determination of a formation resistivity.

4

.

E Q U I P M E N T. CE R T I F I C AT I O N A N D M E T R O LO G I C A L V E R I F I C AT I O N

The VIKIZ tool provides measurement of phase differences between e.m.f. induced in receiver coils of five three-coil isoparametric probes and the spontaneous potential, SP. The dimensions of the borehole tool are as follows: diameter is 0.073 m and length is 4.0 m. The tool consists of the probe array, unit of electronics, and surface panel.

4.1. Spatial Layout of the Probe Array Elements The array of five three-coil probes is used in the VIKIZ tool. The probe array is assembled on the same rod and all the coils are arranged in line. Geometrical characteristics of probes are listed in Table 4.1. Table 4.1

Geometrical characteristics of probes 3UREHVFKHPH 557 557 557 557 557 63

6SDFLQJP

%DVHP

0HDVXUHSRLQWP

    

    

     

Fig. 4.1 shows the coil configuration of the probe array. The following designations are taken: T1, T2, T3, T4, and T5 stand for transmitter coils; R1, R2, R3, R4, R5, and R6 stand for receiver coils. All transmitter and receiver coils of probes with less spacing are arranged between coils of 2 m long probe.

Fig. 4.1. Five probe array. See explanations in the text.

30

4.2. Scheme of the Tool The schematic representation of the borehole instrument is shown in Fig. 4.2. The unit of electronics provides alternate work of probes. First, the T1 transmitter coil is switched on and phase difference between e.m.f. induced in R1 and R2 receiver coils is measured. Then, the T2 coil is switched on and e.m.f. induced in R2 and R3 receiver coils is measured. Further, the transmitter coils of other probes are switched on alternatively. The electronic circuit involves: output (power) amplifiers – 1, 2, 3, 4, 5; mixers – 6, 7, 8, 9, 10, 11 ; analog switchboard – 12 ; tunable heterodyne – 13 ; control panel of a borehole tool – 14 ; intermediate frequency amplifiers – 15, 16; supporting quartz transmitter – 17 ; wide-band phase meter – 18 ; telesystem transmitter – 19 ; output unit – 20 ; power pack – 21. Mixers are arranged in the probe array alongside with receiver coils. The analog switchboard is arranged in the same place. The rest elements of the circuit are arranged in the unit of electronics. The borehole tool is linked up to a surface panel by three-core cable. When signals are recorded by a logging unit, the specially designed software can execute functions of the surface panel. The surface panel is an autonomous microprocessor system that performs the following basic functions: · provides borehole tool with power supply; · receives digital signals from a downhole tool; · reads and states “zero level” (phase shifts in a non-conductive medium); · transforms signals being received into values of the normalized phase difference; · transforms processing data into analogue signals (if analog recorders are used); · transmits processing data thorough the standard sequential RS-232 interface; · displays status codes and measurement results. The surface panel involves the following blocks of (Fig. 4.3): · microcontroller; · input signal conditioner; · 5 channel digital-to-analogue converter; · RS-232 interface; · RAM (random access memory); · light-emitting diode indicator; · control block; · filter of SP signal; Fig. 4.2. Scheme of the borehole tool. See explanations in the text.

· line-operated power supply; · power supply for a borehole tool.

Equipment. Certification and Metrological Verification

31

Fig. 4.3. Block diagram of the surface panel.

Microcontroller provides general control of the panel. A signal conditioner distinguishes an information signal from voltage of probe power supply (they both are transmitted through the same cable conductor) as well as the conditioner transforms a signal into the square pulse train. For analog data recorder, the 5 channel digital-to-analogue converter produces voltages of direct current proportional to measured values of a phase difference. The RS-232 interface is intended for transmitting measured values as the digital code. Random access memory provides storing “zero level” values of the downhole tool which are allowed for in each measurement. The light-emitting diode indicator displays measurement results as well as status codes. The SP signal filter performs low frequency filtering. The line-operated power supply transforms line voltage into a series of steady level voltages +5 V, +24 V and –12 V which are used for supplying panel elements. The power supply of the downhole tool transforms output voltage of a line-operated power supply (+24 V) into direct current supply (+140 V).

32

4.3. Borehole Tool and Surface Panel Functioning The borehole tool operates as follows (see Fig. 4.2). A signal stabilized in frequency incomes to the control panel 14 of the borehole tool from the supporting transmitter 17 in which signals controlling transmitter frequencies are generated. At the command, working frequency is conveyed from the same panel 14 through the power amplifier 1 to the coil T1 of the first probe. At the command of the panel 14, a frequency of the heterodyne 20 is tuned, this frequency being drifted out of a transmitter frequency by the value of the intermediate frequency Df. Alternating current in a transmitter coil generates an electromagnetic field in the adjacent medium. The field induces e.m.f. in receiver coils depending on electrophysical properties of rocks. These e.m.f. are conveyed to inputs of mixers 6 –11 and the secondary inputs of the mixers receive signals with heterodyne frequency. At the output of mixers, signals of intermediate frequency occur with the same phases that are peculiar to high-frequency signals. Measurement is conducted in two stages. In the first stage, at the command of the panel 14, the analog switchboard 12 transmits a signal from the mixer 6 to the intermediate frequency amplifier 15 and the switchboard transmits à signal from the mixer 7 to the intermediate frequency amplifier 16. Amplified and formed signals are transmitted to input of the phase meter 18. At the command of the panel 14, upon finishing transient processes in transmitter, heterodyne circuits, and amplifiers 15, 16, the phase meter 18 starts the first measurement, the measuring data being stored. Then the second stage starts. By command from the panel 14, the analog switchboard 12 transmits a signal from the mixer 6 to the intermediate frequency amplifier 16, and the switchboard transmits a signal from the mixer 7 to the intermediate frequency amplifier 15. Amplified and formed signals are transmitted to inputs of the phase meter 18. At the command of the panel 14 upon finishing transient processes, the phase meter 18 starts the second measurement. The measured data are summed with the results of the first measurement. In doing so, the efficient value of phase difference is doubled and spurious value of phase difference is subtracted, the latter being due to influence of destabilizing factors on amplification channels. Thus, the cross commutation allows the measurement accuracy to be improved. In the phase meter, there is taken measurement of phase difference Dj between input signals and their period T averaged over two readings. By means of the transmitter, the connection line transmits the values of Dj and T through the output unit 20 to be recorded. The output unit separates the information being transmitted against the background of a current supplying the power pack 21 over a cable. The power pack 21 transfers direct current to apply power to some tool units. Then, at the new command of the panel 14, the first transmitter coil T1 ceases to operate and the second one T2 is brought into operating at another frequency. Simultaneously, at the output of the heterodyne 13, a signal with a new heterodyne frequency occurs, this frequency is different from the new transmitter frequency by the same Df value. The analog switchboard 12 adopts the new pair of receiver coils R2 and R3 and measurement process is repeated. Further, all the rest transmitter coils T3, T4, T5 start to operate, each operating at its own frequency. Appropriate hookups are accomplished in the heterodyne 13 and switchboard 12. After the whole cycle is completed, the first transmitter coil starts to operate and the whole cycle is repeated.

Equipment. Certification and Metrological Verification

33

The control block (the “test–work” tumbler and buttons “scrolling up” and “scrolling down”) dictates working regimes for the panel. The “test–work” tumbler controls the two main menus: the tests for the panel itself and those for the panel to operate with a borehole tool. “Scrolling up” and “scrolling down” buttons choose the submenu in each menu.

The “test” menu In this menu, the following submenus can be chosen: test 1

– at all analog outputs, the voltage is set at +2.50 V that corresponds to zero phase shift;

test 2

– at all analog outputs, the voltage is set at +3.19 V that corresponds to the phase shift of 25 degrees;

tests 3–7

– indication for each channel of “zero level” values stored when calibrating the tool;

tests 8–12

– testing separate channels by feeding the saw-tooth voltage of 0–5 V;

test 13

– the general test when saw-tooth voltage is applied to all channels.

Types of menus and corresponding indications are displayed on the indicator module.

The “operating” menu In this regime, the panel receives signals from five probes of a borehole tool, the signals being proportional to the phase shift and measurement period. Then the panel transforms the signals into the phase shift normalized by the measurement period. Then the values obtained are modified by the “zero level” value taken when calibrating. At the end of operation, scaling the results in degrees is performed and data are output to the indicator panel. In the course of operating, adjustment of the receiver to the level of a signal being taken from a cable goes on automatically. The adjustment is carried out when the borehole tool hooks up the panel. To regulate the adjustment level, one of the digital-to-analogue converter channels is used. The following submenus may be used in the “operate” menu using “scrolling up” and “scrolling down” buttons: 1

– the main submenu with subsequent displaying numbers of signals being received on the indicator panel. In the case of erroneous receiving when the relative number of transmission errors exceeds 2–3 %, the pulsed ERROR inscription is displayed on the panel;

2–6 – the current values of a phase shift of appropriate channel are displayed on indicators; 7

– the calibration submenu. The values of gauge constants are loaded to the RAM (random access memory) and then used to modify the received signals.

34

4.4. Metrological Verification Measurement in a homogenous medium with given resistivities is a basic method for monitoring metrological characteristics. A tank with mineralized water can substitute a homogenous medium. To attain admissible errors caused by finite basin dimensions, the depth, length, and width of the tank should be more than 6 m. In addition, it is necessary to obtain the same resistivity values over the entire solution volume with error less than 1 %. Because of the dependence of the phase difference Dj on the resistivity value is nonlinear, it is necessary to perform measurements at five points of working measurement range at least. It may be realized by changing water mineralization. Using a physical model imitating signals as if they were in a homogenous medium is another way of metrological monitoring. Two basic requirements are imposed on such a model: parameters have to be measurable with sufficient accuracy; the mathematical model that describes physical one should ensure the required estimation accuracy. To aid this, the wire ring that is coaxial with probe coils has been chosen. The ring constitutes a closed onering contour that involves the inductance L, resistance R, and capacitance C. The ring circuit scheme is given in Fig. 4.4. Here L1 and L2 are distances from receiver coils R1 and R2 to the transmitter coil T, respectively, b is the ring radius, and z is the distance from the ring plane to the receiver coil w R1. The change of a current J in a transmitter coil follows the law - = -  µ H . The working frequency of a probe f = w/2p. The impedance of the ring circuit is R + iX. The ohmic resistance R is a combination of losses both in a high resistive wire and capacitor, the latter being interposed into the circuit. The reactance X = 1/w іw L. In this case, e.m.f. induced in j-receiver coil is equal to L

e

Ç  - LN/ H = È p / ÈÉ

LN/ M

M

M

M

+

L w m E   - LN5   - LN5 H M

5 5  5 + L; M

L N 5

+5

M



W

× Ø L w m  Mj N, ØÙ

(4.1)

here N = J × S × n is transmitter coil moment; S and n are the area of the transmitter coil and the number of rings, respectively; k is the wave number; and m0 = 4p × 10–7 H/m is the magnetic permeability of a free space. The rest geometrical designations are given in Fig. 4.4. Calculation of e.m.f. for multi-ring transmitter and receiver coils is performed on the basis of the superposition principle. The phase difference Dj between e1 and e2 induced in receiver coils R1 and R2 is calculated according the expression (3.1).

Fig. 4.4. The ring circuit location. See explanations in the text.

The procedure of metrological certification is based on the dependence of the Dj value on electrical parameters R and X of a thin ring, its radius b, and the position of z relative to coils. When changing z from 0 to L1, the value Dj has two

Equipment. Certification and Metrological Verification

35

maxima and one minimum. If the requirement b < L1L2/(L1+L2) is satisfied, the Dj value at the minimum point is negative and, consequently, two points with zero phase difference occur. If one of these points (the nearest to the R1 coil) is chosen for the arbitrary origin, the sequence of Dj values increasing from zero to maximum can be obtained by moving the ring toward the R1 coil. The value of reactance X that depends on the ring radius b is so chosen that the Dj values would be maximal. To obtain the Dj value to be equal to the upper limit of a measurement range, the value of active resistance R is Fig. 4.5. Scheme of the imitator. fitted. Taking into account that the R See explanations in the text. value is mainly defined by losses in the ring, the wire diameter is so chosen that the wire resistance at working frequency would be somewhat less than the R value. Then the ring inductance at the working frequency is estimated. By the values of both the ring inductance and reactance X, the necessary capacitance is estimated. On this basis, the rock resistivity imitator has been developed. The scheme of imitator is shown in Fig. 4.5. The imitator proper involves the ring 7 made of manganine wire fastened on the insulating disk 4. The capacitor 8 and coaxial connector 6 are interposed in the ring circuit. Under operating conditions, the connector is short-circuited by the disk contactor switch having negligible residual inductance (less than 10–10 H). The disk with the ring can be grappled with the flange 3 by bolts 5, the flange being fixed on the sleeve 2 by mobile fastening thread. The sleeve 2 is grappled by bolts 5 on the tool body 1. The disk 4 has to be rotated for precision mounting the imitator along the probe axis. When rotating, the flange 3 and disk 4 with the fastened ring 7 will move on the thread along the sleeve 2 grappled on the tool body. To diminish distortion of an electromagnetic field, all imitator components, except the ring wire and connector, are made of insulating materials. To estimate e.m.f. of probe receiver coils in the presence of imitator, it is necessary to know parameters of the imitator and its position with reasonable accuracy. The imitator construction provides its positioning with uncertainty less than 0.05 mm. The initial position z0 at which Dj = 0 is also fixed within the same limits. The determination error of the ring radius is specified by technology of manufacturing the imitator and that is less than 0.1 mm. Resistance values R and X are determined by the MCR-1372 calibration device (Siberian Scientific Investigation Institute of Metrology, Novosibisk) according to the following procedure. The imitator is hooked up to the device by its connector from which the contactor switch is first taken away. In addition, the fairly long coaxial line is interposed between connectors of the imitator and those of the tool to eliminate interaction of an electromagnetic field generated by the imitator ring with metal part of the tool. Prior to calibration, all electrically conducting items would be locate far away from the imitator. The possible influence of these items should be estimated experimentally. The limits of admissible measurement errors of resistances R and X is 0.7–0.8 % depending on the working frequency and electrical parameters of the imitator.

5

.

SPATIAL R E S O L U T I O N C H A R AC T E R I S T I C S

The possibility of high resolution when estimating the spatial resistivity distribution in the geological medium surrounding a borehole is the most important characteristic of any probe array system. Since the complete analysis of spatial resolution is complicated due to the great number of model parameters and time-consuming codes for modeling synthetic logs for realistic models, the spatial resolution problem is usually divided into two parts: studying as radial characteristics so vertical ones. That is, dependencies of measured signals on the radial inhomogeneity of a medium (from the borehole to the undisturbed formation) and those on the vertical one (along the borehole) are investigated separately. Such an approach is possible if influence of both cylindrical boundaries around a borehole and planar boundaries between formations on a signal can be separated. This problem can be solved most simply if a section involves fairly thick (more than probe spacing) formations and this section does not contain very deep (comparable with the formation thickness) invaded zones or the resistivity contrast between underlying or overlying layers is not very sharp. In other cases, it is necessary to account completely for the spatial heterogeneity of a medium using 2D and 3D geometry.

5.1. Radial Characteristics The conventional determination of radial characteristics is based on the analysis of synthetic records and establishing the ranges of model parameters at which apparent resistivities are slightly differ from the true formation resistivities. Thus, in low frequency induction logging, the geometric factor theory is used for analysis of radial characteristics. The theory is based on the fact that a signal being measured is the sum of responses with the same sign from different parts of a medium (for instance, borehole – invaded zone – formation). It is considered that the closer to the unit is the value of the formation geometrical factor, the better is the radial characteristic (that is, the contribution of currents flowing in a borehole and invaded zone to the signal is insignificant). In the high frequency band there is no analog to the geometric factor theory as far as currents that flow in different parts of a medium interact. In this case, such a concept as “contribution of the part of a medium” can not be introduced since signals of currents that flow in separate areas of the medium can be mutually compensated in part. Because of this fact, a signal that is caused by currents in the whole space can be less than a signal from currents in the part of this space.

Spatial Resolution Characteristics

37

When sounding, radial characteristics are estimated through two criteria: possibility for accurate determination as of the undisturbed formation resistivity so of the characteristic of the resistivity distribution in an invaded zone. Radial characteristics were analyzed previously with the understanding that apparent resistivities for long probes would be coincident as well as possible with the true formation resistivity. Further we will title such characteristics as radial characteristics of the first type. These characteristics are estimated quantitatively by the relation of a signal Dj measured in a radially non-homogenous medium to a signal Dj in a homogenous medium with the formation resistivity r : L

r = L

Dj Dj , i = 1, … , 5 (i – the probe number).

Note that this characteristic describes properties of each individual probe and by no means takes into consideration that the inversion is performed for the whole sounding curve. With availability of the computer codes for solving the inverse problem, it is not necessarily that apparent resistivities for long probes and the formation resistivity are to be close to each other to execute the successful inversion. In many cases apparent resistivities differ by many times from the true resistivity, nevertheless, the latter can be estimated with relatively fair accuracy. In these cases, radial characteristics of the second type have to be used, these characteristics being described by the dependence of the relative error of resistivity determination on the outer radius of the invaded zone. Further, when calculating radial characteristics, calibration data on relative measurement errors averaged for the great number of manufactured tools will be used:

‰

d Dj = {0.03, 0.04, 0.02, 0.02, 0.02}. This implies that the relative measurement error for the shortest probe is 3 %, that for the 0.7 m probe is 4 %, and that for the rest probes is 2 %. Let us consider radial characteristics of the VIKIZ probes for different models. Two-layer medium model “borehole – formation” The two-layer model describes situations when a borehole penetrates tight low-permeable rocks with high resistivity or some relative high-conductive shaly deposits. The radial characteristics of the first type for standard drilling conditions of West Siberia are shown in Fig. 5.1. The relative borehole effect on signals of the short probe is less than 10 % when formation resistivities are up to 100 ohm × m. The borehole effect on signals of the rest probes is less than measurement errors. The presence of a borehole increases a signal being measured and, consequently, decreases an apparent resistivity as compared with the true formation resistivity The different situation is observed when mineralized low resistive drilling mud (rb = 0.15 ohm × m) is used. In Fig. 5.2 the radial characteristics of the first type are shown. Note that the borehole effect is exhibited by diminishing signals measured by long probes. Thus, the presence of a conducting borehole increases apparent resistivities as compared with the true formation resistivity. The behavior of a signal of the short probe is more complicated. At relatively low formation resistivities (rf £ 15–20 ohm × m), the conducting borehole decreases an apparent resistivity. In high conductive formations (rf > 20 ohm × m), an apparent resistiv-

38

Fig. 5.1. Radial characteristics of the first type (rb = 2 ohm × m, rb = 0.108 m). See designations for Fig. 3.13.

Fig. 5.2. Radial characteristics of the first type (rb = 0.15 ohm × m, rb = 0.108 m). See designations for Fig. 3.13.

ity increases due to the conducting borehole. Moreover, as it is seen from the given radial characteristic, the formation resistivity up to 200 ohm × m can be estimated with the relative error of 5–7 % from signals of the long probe. In Fig. 5.3 there are given the radial characteristics of the second type for different resistivity values of drilling mud. Note that determination errors rf are practically unchanged at rb ³ 0.5 ohm × m. Their values increase significantly with subsequent decreasing rb values. Moreover, the greatest determination errors rf (about 3–5 ohm × m) are observed when the high resistive formation is under investigation and a borehole is filled with well conductive mud.

Spatial Resolution Characteristics

39

As a whole, the given information testifies that the formation resistivity can be determined with good accuracy within the wide resistivity range (from 0.5 to 200 ohm × m). Three-layer medium model “borehole – invaded zone – formation” Analysis of sounding curves in a medium with two cylindrical boundaries (“borehole– invaded zone”, “invaded zone–formation”) leads to the conclusions: · apparent resistivities for short probes are close to resistivities of an invaded zone if its radius is about twice as long as the probe spacing; · apparent resistivities for long probes differ slightly from formation resistivities even at riz /rb ~ 10 if the invasion zone resistivity is twice as high as the formation resistivity;

Fig. 5.3. Radial characteristics of the second type for a two-layer medium. Drilling mud resistivity, ohm × m: 0.05 (1 ), 0.5 (2 ), 1.0 (3 ), 2.0 (4 ), and 4.0 (5 ), respectively.

· responses of the short probes have a low sensitivity to the presence of an invaded zone if the zone is shallow (riz /rb <2); at decreasing invasion, apparent resistivities for short probes are close to the invasion zone resistivities. Moreover, in many cases (deep invaded zones, high formation resistivities), apparent resistivities even for long probes can differ greatly (by hundreds per cents) from true ones. To judge the possibility for reliable estimation of formation resistivities, radial characteristics of the second type can be used. The dependencies of the absolute determination errors of formation resistivities upon both resistivities of an invaded zone and its radius are given in Figs. 5.4–5.6. The greatest determination errors rf are observed when invaded zones with decreasing invasion are deep and the formation is high resistive (Fig. 5.4). Thus, for riz = 2.0 m and rf = 200 ohm × m, the absolute error Drf » 95 ohm × m (that is, the relative determination error drf »50 %). At the same time, for shallower invaded zones (riz = 0.6 m), Drf £ 9.5 ohm × m and drf £ 5 %. When an increase in resistivities of an invaded zone is observed, the determination accuracy of the formation resistivity increases. Thus, in the most unfavorable situations at riz = 2.0 m, riz = 30 ohm × m, rf = 200 ohm × m, Drf » 52 ohm × m and drf » 25 %. For the typical water saturated formation (rf = 4–6 ohm × m) at any type of invasion (up to 2 m in the radial depth), the relative determination error drf £ 10 %. In oil saturated formations with increasing invasion (rf = 6–20 ohm × m, invasion depth is up to 1.4 m), the relative error drf £ 15 %. And only in gas saturated formations (rf » 80–140 ohm × m) at decreasing invasion up to 1 m in depth, drf £ 20 %. Thus, analysis of radial characteristics of the second type shows that the fairly accurate estimation of formation resistivity is possible with the help of computer inversion in the wide class of realistic situations. As it was repeatedly shown, one of distinguished features of the VIKIZ method is the possibility to reveal a bordering zone in oil saturated formations. In Figs. 5.7 and 5.8, there

40

Fig. 5.4. Radial characteristics of the second type (riz=10 ohm × m). Here and in Figs. 5.5 and 5.6 codes for radius of invaded zone are: 0.6 (1 ), 0.8 (2 ), 1.0 (3 ), 1.45 (4 ), and 2.0 (5 ), respectively.

Fig. 5.5. Radial characteristics of the second type (riz= 30).

Fig. 5.6. Radial characteristics of the second type (riz= 60).

are given dependencies of both relative errors of resistivity determination and the bordering zone thickness on the invaded zone radius in the typical geoelectrical model of oil-saturated formation (riz = 30 ohm × m, rbz = 2.5 ohm × m, rbz= riz + 0.15 m and rf = 8.0 ohm × m). The relative determination error for rbz evaluation increases monotonically as a bordering zone is far away from a borehole and this error is as large as 50 % when the radial depth of the zone is 1.1 m. The relative determination error of the bordering zone depth is minimal (about 25 %) when the invaded zone radius is about 0.7 m. The relative error quickly increases up to 50 %

41

Spatial Resolution Characteristics

Fig. 5.7. Relative determination error of a bordering zone resistivity.

Fig. 5.8. Relative determination error of a bordering zone thickness.

(riz » 0.4 and 1.05 m) when measurement is performed near a borehole or essentially far away from that. Note that the column conductance of a bordering zone Sbz = (rbz–riz)/rbz can be determined essentially better.

5.2. Radial Investigation Depth of Sounding The problem on estimation of radial investigation depth of sounding is close to analysis of radial characteristics. For determining this value in thick formations, let us turn to Figs. 5.9–5.11 in which the dependencies of absolute error of the formation resistivity on the invaded zone radius at different rf are given. For the radial investigation depth Rid , we take the maximum radius of an invaded zone at which rf is determined with the error less than 10 % (or 20 %).

Fig. 5.9. Radial characteristics of the second type (riz= 10 ohm × m). Here and in Figs. 5.10 and 5.11, codes for formation resistivity, ohm × m, are 20 (1 ), 50 (2 ), 100 (3 ), and 200 (4 ).

Fig. 5.10. Radial characteristics of the second type (riz = 30 ohm × m).

42

‰

‰ ‰

5 = U PD[  D j  d D j  S

‰

‰

LG

L]

LI dr —     , I

r here D j  d D j are vectors of measurements and their relative errors, respectively, and S  is the vector of model parameters.

The comparison of radial characteristics of the second type for different riz values demonstrates that radial investigation depths increase as an invaded zone resistivity increases. The least radial investigation depth of 1.0–1.3 m is observed in gas saturated low conductive (rf ³ 80 ohm × m) formations with decreasing invasion (riz /rf < 0.2). In water saturated formations with increasing invasion, radial depth of investigation exceeds 2.0 m at riz =30 ohm × m and that is as long as 3.0 m at riz= 60 ohm × m. In oil-saturated reservoirs with increasing invasion, the radial investigation depth decreases by about 10–15 % as compared with water saturated formations. Note that when the determination error rf increases up to 20 %, the radial investigation depth increases by 30–40 % on average. Another way for increase in radial investigation depth is an increase in measurement precision. As pointed out above, estimates of the spatial resolution through radial characteristics are most reliable for formations with significant thickness. If layers are relatively thin or those are in low conductive shoulder beds, as well as these layers include a deep invaded zone, two-layer models have to be used for estimation of radial depths of investigation. It is obvious that the Rid value has to decrease with diminishing the formation thickness because of the increase of the shoulder bed effect. In Figs. 5.12–5.14 the dependencies of radial investigation depth on formation resistivity are shown for different formation thickness (0.6, 1.2, and 2.4 m). In all cases it is assumed that riz= 30 ohm × m, and shoulder beds are characterized by the following resistivity  =3.5 ohm × m, r VK =4.5 ohm × m. Each Figure shows two curves of radial investivalues: r  E ] gation depth corresponding to different relative determination errors drf (10 and 20 %, respectively). L

For all formations of relative insignificant thickness (that is less or much the same as the probe spacing), monotonic decrease in radial investigation depth is observed as the

Fig. 5.11. Radial characteristics of the second type (riz = 60 ohm × m).

Fig. 5.12. Dependence of radial investigation depth on formation resistivity at the thickness of 0.6 m. Here and in Figs. 5.13 and 5.14, codes for relative determination error of formation resistivity, %, are 10.1 (1 ) and 20 (2 ), respectively.

Spatial Resolution Characteristics

formation resistivity increases. On the other hand, increase in radial investigation depth is observed as a formation thickness increases due to reduced shoulder bed effect on a signal. It can be seen from Fig. 5.12 that the lowest radial investigation depth (~0.4– 0.6 m) is observed in thin low conductive formations, moreover, the depth increases if requirements on a relative determination error of resistivities are loosen 5 G : dr I L

43

Fig. 5.13. Dependence of radial investigation depth on formation resistivity at the thickness of 1.2 m.

.

That is, radial investigation depth increases nearly proportional to the square root of the relative error drf. The same regularities can be revealed in Figs. 5.13 and 5.14. In the range of relative high resistivities (rf >20 ohm × m), the radial investigation depth decreases practically linearly as resistivities grow. In more conducive formations, the Rid value increases with the high rate. It Fig. 5.14. Dependence of radial investigation depth on formation resistivity at the thickness of 2.4 m. becomes especially more prominent when rf approaches shoulder bed resistivities and the shoulder bed effect sharply decreases. In this case, radial investigation depth becomes close to the limiting one that is estimated by thick formations (for example, Figs. 5.5 and 5.10). In this respect, it can be generally stated that increase in the vertical resolution leads to decrease in the radial depth. It should be always kept in mind especially when comparing radial depths of different probes (for example, VIKIZ probes and induction ones).

5.3. Vertical Characteristics One of the main geophysical problems solved with VIKIZ method is a detail subdivision of the section penetrated by a borehole. In this connection there exist some questions which are to be answered for reliable estimation of the vertical resolution. Selection of Measure Point The basis for log visualizing is the correct selection of the measure point position that is especially important for asymmetric VIKIZ probes. Determination of the measure point for asymmetric probes would usually not be difficult. The midpoint just as for Laterolog tools so for Symmetric Induction Logging probes coincides with the measure point. For asymmetric probes this problem can be solved by different ways. Thus, the midpoint between potential-measuring electrodes is taken for the measure point of lateral tools. Selection of a measure point for the VIKIZ probes is based on analysis of logs when crossing thin beds as insulating so conducting (Figs. 5.15 and 5.16). As it can be seen from the Figures, the extreme probe signals are best coincident with the center of a thin layer if the coordinate of the most distant R1 coil is chosen as a measure point. If invaded zones of neighboring formations differ greatly in thickness, measure points for short probes will not be coincident

44

Fig. 5.15. Logs for a model: water saturated formation – tight formation – water saturated formation. See designations for Fig. 3.13.

Fig. 5.16. Logs for a model: oil saturated formation – shale – oil saturated formation. See designations for Fig. 3.13.

Fig. 5.17. Logs for a model: water saturated formation – shale – water saturated formation. See designations for Fig. 3.13.

45

Spatial Resolution Characteristics

with extreme values corresponding to the center of a thin layer (Fig. 5.17). When computer inversion is performed, a point at which the sensitivity of signals to formation resistivities is highest should be chosen for the measure point. Types of Vertical Characteristics The problems on detail subdivision of a section can be solved in several levels that are conditioned by the possibility of determination of both formation thickness and formation resistivity. At the first (lowest) level it is possible to determine formation thickness without quantitative estimation of formation resistivity. In these cases, as a rule, the contrast between formation resistivity and shoulder bed one can be determined correctly (“the formation is more conductive than shoulder beds”, “the formation is less conductive than shoulder beds”). Such situations are typical when qualitative interpretation is performed and as thin, weakly permeable, compacted beds so shaly ones can be resolved inside fluid-saturated formations. The effective thickness of formations can be estimated more accurately if such beds are taken into account reliably. Note that in so doing, logs for short high-frequency probes having the highest vertical resolution (comparable with the step of measurement along a borehole) are used first of all. At the second (intermediate) level it is possible to determine the thickness of formation whereas its resistivity is estimated through the computer inversion after correction is made for the effect of a borehole, an invaded zone, and shoulder beds. In these cases, apparent resistivities for all probes differ greatly from the true formation resistivity. Such situations are most typical when estimating parameters of relatively thin (less than 1.5 m) oil-gas-saturated reservoir rocks in well conductive shoulder beds (shales, water-saturated sands). Another situation is associated with the presence of deep invasion when the invasion radius is comparable with the thickness of formation being investigated. At the third (highest) level it is possible to determine not only the formation thickness, but also formation resistivity from apparent resistivity logs. This is most typical for thick formations (thicker than 2.5 m) with shallow invaded zones and when the contrast between resistivities of formation and shoulder beds is insignificant. For analyzing possibilities of VIKIZ method with respect to subdivision of a section, vertical characteristics of three types are used, each characteristic corresponding to one of the three levels described above. The vertical characteristic of the third type coincides with traditionally considered “vertical characteristics of probes”. That represents the dependence of relative discrepancy between both the apparent resistivity and true formation resistivity on its thickness. Through this characteristic it is easy to determine the minimum formation thickness Hmin of the formation v3 at which extreme values of apparent resistivities rD are close to the true formation resistivity at least for one probe (as example, the values differ by no more than tripled relative error of determination of apparent resistivity dra; usually dra »3.5 %):

‰

‰

‰

Y = +PLQ Dj  d Dj  S D] 

‰

LI

rD - r I < drD , rI

‰

here Dj is the vector of measured phase difference values, d Dj is the vector of relative r errors of phase difference measurements, S is the vector of model parameters, and Dz is the step of measurements along a borehole. In permeable formations (an invaded zone is present),

46 extreme rD values are chosen from signals of two long probes which are the least affected by the near borehole inhomogeneity. The vertical characteristic of the second type is represented by the dependence of the relative error of formation resistivity determination on the formation thickness. Through this characteristic it is easy to determine the minimum formation thickness v2 at which formation resistivity can be estimated with the specified relative error d (usually d = 5–10 %)

‰

‰

Y = +PLQ  D j  d Dj 

‰

S D] 

LI dr < d . I

The dependence of the relative error of formation thickness determination on the formation thickness itself is called a vertical characteristic of the first type. Through this characteristic it easy to determine minimum formation thickness v1 with prescribed accuracy d (usually d » 5–7 %). In doing so, the formation resistivity is not estimated or the relative determination error is too serious:

‰

‰

Y = +PLQ  Dj  d D j 

‰

S D] 

LI d + — d 

dr >  -  d . I

The minimum thickness of singled out formation should be more than the doubled measurement step: v1 > 2Dz. Note that the following relation between values of vertical characteristics is most common: v1 £ v2 £ v3. This relation can fail for low-contrast media when shoulder bed resistivities differ from formation resistivities by less than 20–30 %. And lastly, layer-by-layer setting boundaries through VIKIZ logs is of exceptional importance. As analysis shows, boundaries are mainly located at points where the relative change in signals of three medium-length probes becomes maximal with depth. Fig. 5.18 exemplifies determination of boundaries through synthetic logs for three long probes for which the vertical resolution function is estimated 

 OQ _ Dj _ . ] L=

h] = Ã

L

Locations of boundaries correspond to maximum values of hz. Estimation and Analysis of Vertical Characteristics Let us estimate and analyze the vertical characteristics under typical geoelectrical conditions. Here and next, all the synthetic logs are calculated with the step of Dz = 0.1 m along a borehole. In Fig. 5.19 there are given the relative determination errors rf depending on thickness of water saturated reservoir rocks in shaly deposits. The drf values decrease monotonically as the formation is thickened and these values are practically unchanged from H = 1.8 m. Hence, if the formation thickness is somewhat less than the total probe spacing, the shoulder

Spatial Resolution Characteristics

Fig. 5.18. Determination of layers from logs.

Fig. 5.19. Vertical characteristic of the second type for water saturated reservoir rocks in shales.

47

48

Fig. 5.20. Vertical characteristic of the first type for water saturated reservoir rocks in shales.

bed effect becomes insignificant. If the formation thickness is less than 0.5 m, drf is more than 10 %, so that the vertical characteristic v2 » 0.4 m. Thus, from the VIKIZ data, resistivities can be determined with strict accuracy even for very thin (~0.4 m) water saturated reservoir rocks. In this situation, such a high vertical resolution is caused, to a large extent, by the low contrast between formation resistivities and those of shoulder beds (rf /riz » 1.4). At the same time, this circumstance causes an increase in relative errors when determining the reservoir rock thickness. Fig. 5.20 shows the estimates of dH depending on the formation thickness. Thus the relative error of 20 % will be observed at H = 0.3 m, hence, v1 » 0.3 m. Thus, water saturated beds from 0.3 to 0.4 m in thickness can be singled out on logs, however, their resistivities can not be determined with a reliable accuracy. Note that the least error of thickness determination is observed in the case if transmitter and receiver coils are placed close to the top of formation and to the its bottom (H = 2 m), respectively. When further thickening the formation, dH value increases and at H » 3.2 m becomes very great.

Fig. 5.21. Vertical characteristic of the first type for floating oil saturated reservoir overlain by shales.

Fig. 5.22. Vertical characteristic of the second type for floating oil saturated reservoir overlain by shales.

In Figs. 5.21–5.23 there are given the vertical characteristics of all the types for the model of floating oil-saturated formation overlain by shales. As it can be seen from Fig. 5.22, the minimum thickness of oil-saturated formation can be determined with the relative error of 10 % if the minimum thickness of the formation is 0.4 m, i.e., v2 = 0.4 m. The plot in Fig. 5.23 shows that ra for the long probe differs by 20 % from the true formation resistivity if the formation thickness exceeds 1.8 m, i.e., v3 = 1.8 m. It is seen from Fig. 5.21 that thin beds 0.2–0.4 m in thickness can be singled out without faithful determination of their resistivities. Let us evaluate vertical characteristics for one of the most unfavorable models as water-saturated formation overlain by shales and underlain by water saturated de-

Spatial Resolution Characteristics

posits. In this case, relative determination errors rf range up to the level of 10 per cents at H = 1.8 m (Fig. 5.24), hence, v2 = 2.8 m. As it is seen from Fig. 5.25, the formation resistivity can be determined through the apparent resistivity with the error of 20 % if the formation thickness H = 4.2 m, i.e., v3 = 4.2 m. Thus, when inversion of logs is executed for ranges of high resistive gas-saturated formations which thickness is less than 1.8 m, it is necessary to take special steps to determine the true resistivity of the formations. The basic way to improve the vertical resolution for correct determining resistivities of low conductive formations is using a priory information about shoulder beds. Fig. 5.26 demonstrates the drf (H) dependence when shoulder bed resistivities are known. In this case, it is possible to determine the formation resistivity with the relative errors of 20 % and 10 % at H =1.4 m and H =1.7 m, respectively. In this manner it is possible to improve significantly (by about the factor of 1.5) the vertical characteristic of the second type v2 »1.4–1.7 m as compared to the situation when shoulder bed resistivities are unknown (v2=2.4 m). It follows from the above estimations that when inversion of logs is executed within intervals of highly resistive reservoir rocks, it is advantageous to operate in two steps. Firstly, through the logs obtained within intervals of both overlying and underlying rocks, it is necessary to determine resistivi-

Fig. 5.25. Vertical characteristic of the third type for floating gas saturated reservoir overlain by shales.

49

Fig. 5.23. Vertical characteristic of the third type for floating oil saturated reservoir overlain by shales.

Fig. 5.24. Vertical characteristic of the second type for floating gas saturated reservoir overlain by shales.

Fig. 5.26. Vertical characteristic of the second type for gas saturated reservoir overlain by shales when shoulder bed parameters are known.

50

Fig. 5.27. The eccentricity effect (rb= 2 ohm × m, rb = 0.108 m). See designations for Fig. 3.13.

ties of these rocks as accurate as possible. Secondly, after fixing the values of shoulder bed resistivities, those of formation should be determined.

5.4. Effect of Probe Shift from the Borehole Axis on Measured Signals When logging is run, a borehole tool without centric guides is located at the borehole wall. The most common nominal borehole radius is 0.108 m and the diameter of the tool case is 0.073 m. Hence, the tool axis can be shifted from the borehole axis by about 0.07 m. The eccentricity effect is estimated by the relation d H = DjH Dj ,

here Dje and Dj0 are phase differences for probes located at the borehole wall and at the borehole axis, respectively. In Fig. 5.27 there are given dependencies of the de value on formation resistivities for all probes. It is seen from the data above that eccentricity effect makes itself evident most clearly in signals of two short probes and the effect increases with decrease in formation conductivity. In this case, measured signals are overread and, hence, the eccentricity effect for short probes is manifested itself in decrease of the apparent resistivity. Note, that eccentricity effect is less than the determination error within the practically important range rf = 2–20 ohm × m. The eccentricity effect on probe readings becomes noticeable (more than 10 %) at rf >50 ohm × m and at rf >65 ohm × m for the shortest probe and the 0.7 m long probe, respectively. The eccentricity affects most strongly the probe signals in boreholes filled with mineralized drilling fluid (rb » 0.2 ohm × m). In this case, when estimating the eccentricity effect, it is necessary to allow for the borehole case that displaces the part of well conducting drilling

Spatial Resolution Characteristics

51

Fig. 5.28. The eccentricity effect of a borehole tool with (a) / without regard (b) for the tool case effect. 1–4 – probe position (1 – at the axis, 2–4 at out of axis position: 2 – 0.03 m, 3 – 0.05 m, and 4 – 0.06 m, respectively).

fluid. In Fig. 5.28 there are given apparent resistivity curves for the formation with resistivity of 20 ohm × m as at the coaxial position of a tool so if the tool is shifted to the borehole wall. As it can be seen, the eccentricity affects signals of three short probes: the apparent resistivity decreases significantly (up two times for the short probe). Note that in the system of computer inversion, correction of signals corrupted due to the probe eccentricity is executed automatically.

6

.

LOG QUALITY CONTROL

The performance of logging company is based on its ability to minimize failures and reduce the time period when the rig is involved in logging operations. Besides the service efficiency, the total quality includes data quality (intrinsic quality of data) and relevant data (ability of data to describe the formation).

6.1. The General Requirements General and additional requirements conditioned by the specific features of the VIKIZ method are given below. The list of the required information: · the name of logging company; · the name of drilling facility; · the name of field and the borehole number; · data on a borehole (the bottomhole depth and the diameter and depth of a casing shoe); · the number of the VIKIZ borehole tool; · the date of measurements; · repeated control records that are to be more than 50 m in the range of depths under investigations; · when signals are received by the recorder with analog inputs, it is necessary to record values of “zero-signal” corresponding to Dj = 0° and “standard-signal” corresponding to Dj = 25° in the basic file. Conditions for logging: · the rate of recording is less than 2000 m/h; · the quantization step in depth is less than 0.2 m. Requirements on data quality: · deviation of both “zero-signal“ and “standard-signal” from nominal values should be less than 0.2 °; · deviation of both primary and repeated records from their arithmetic means Dj should be less than ± (0.2° + 0.03 × Dj ).

Log Quality Control

53

To evaluate quality and perform data interpretation, the following elements are to be present on a logging diagram: · calibrating levels for 0 and 25 degrees; · repeated measurement within the interval overlapping a primary record.

6.2. Calibrating Levels For recorders with an analog interface, the presence of calibrating levels in a primary record is dictated by the record technology, but as a rule, these levels are not retained after primary processing. For this purpose, when logging (in the beginning or end of recording) it is necessary to set up the calibration mode on a surface panel. In the result of this operation, the appropriate levels would be present in the basic record. For recorders with the digital interface, the program should provide appropriate levels of records. The deviation of ± 0.2° from nominal values is acceptable. Fig. 6.1 shows the log fragment with calibrating levels of 0° è 25°.

6.3. Repeated Measurements Repeated measurements within overlapping intervals are widely used in logging for log quality control. In this case, the quality of borehole tool operating is controlled rather than that of recording device. The VIKIZ tools provide the high precision of measurement. Therefore, logs of corresponding probes at repeated measurements are to have insignificant relative deviations less than 3 % for two long probes and less than 5 % for three short probes. Differences between signals at repeated records exceeding these values may be due to either a tool defect or imperfect record. It should be noted that for evaluation of data quality, the data recorded during the same logging can be taken into account, i.e., the time interval should be minimal. It is stipulated by both the high resolution of VIKIZ tools in the radial direction and sensibility of the tools to insignificant changes in geoelectrical parameters of an invaded zone. In Fig. 6.2 repeated records of logs (dotted line) within 40-m interval are given. It can be seen that differences between records are less than measurement errors.

6.4. Initial Phase Shifts of Probes All the modifications of VIKIZ tools have non-zero initial phase shifts except for the last model that uses a microprocessor. That is, when measurements are performed on the air, the VIKIZ probes give non-zero values that depend on peculiarities of each tool. The values are permanent for the entire range of signals being measured and these values can be changed only with changing either constructive probe parameters or the electronic circuit. To compensate initial phase shifts, the surface panel (calibration) provides the mode for accounting these shifts. In doing so, tool signals measured on the air are stored in a

54

Fig. 6.1. Calibrating levels of 0° and 25° on the log.

Log Quality Control

Fig. 6.2. Repeated log record.

55

56 random access memory (RAM) and then those are compensated automatically while logging. In order to operate properly in this mode, it is necessary to comply rigorously with the following measurement conditions: “zero” values are placed into memory at positive temperature if the tool mounted upon a support is far away from massive metallic items. In this case, borehole investigations can be performed only with the particular surface panel that has been used for calibration of the tools. For the recorder with a digital interface, i.e., when recording without using a surface panel, such a function is performed by the recording program. Recording VIKIZ logs without compensation of initial phase shifts is acceptable. In this case, the necessary corrections are introduced either manually or automatically when using the MFS VIKIZ inversion program (version 1.3 and next). Upon correction of initial phase shifts, it is necessary to check diagrams against ranges of admissible values of phase differences. The highest value of phase difference being measured, as a rule, should be less than 90° (that corresponds to an apparent resistivity of ra = 0.22 ohm × m): Djmax » 90°. The measured phase difference should be a positive value exceeding tool noises: Djmin » 0.2°.

7

.

Q UA L I TAT I V E E VA L UAT I O N OF A GEOLOGICAL SECTION

There are restrictions on both qualitative and quantitative interpretations of log data. Possibilities of one or another interpretation approach become more certain and unambiguous in the presence of reliable information on the section. In many instances, the proper conclusions concerning geological targets are based on the reliable data obtained. The previous chapter is devoted to the problems on both assessment of the reliability of initial data and control of these data. This allows one to consider with confidence the quality of data given below. Some problems on qualitative interpretation can be solved using the visual analysis of data obtained by VIKIZ, SP, and other methods. As a result of this analysis, it is possible to distinguish reservoirs and evaluate their vertical heterogeneity. Favorable conditions make it possible the qualitative evaluation of the of fluid saturation nature. In this case, data on boundary values of productive formation resistivities minimize the uncertainty of a qualitative conclusion. Reservoirs in a terrigenous section are most often singled out by the radial resistivity gradient. It is common if an invasion zone occurs and its resistivity differs from that of the undisturbed part of formation. Changes in apparent resistivities from probe to probe may be a direct indicator of thick formation permeability. The efficiency of qualitative interpretation and reliability of conclusion are based on: · weak dependence of measurements on parameters of both a borehole and the area immediately adjacent to the borehole; · high resolution as in the radial direction so along a borehole; · good precision and consistence of measurements. Estimation of resistivity values of reservoir rocks and invaded zones is performed using the MFS VIKIZ software tool. At the same time, field logs can give fairly vast amount of information without quantitative estimation. Thus, when invasion is relatively shallow, the correlation between apparent resistivities and true resistivity values can be obtained very easy. Analysis of data obtained by the complex of methods increases the reliability of geological conclusions. The subsequent data are discussed in details just in this context. As has already been noted, some problems on geological data interpretation can be solved on the base of visual analysis of both VIKIZ and SP logs. The reliability of conclusions increases when these data are used in combination with those of nuclear methods. If a small amount of information on drilling technology is available, reservoir can be revealed

58 with high certainty. Thus, the presence of a bordering zone is reflected by appearance of the maximum on sounding curves. It should be noted that the relation between the phase difference and resistivity is nonlinear. From different considerations, the scale of data can be represented either in phase difference values (linear scale) or in apparent resistivity values (logarithmic or linear scale). Given below is the description of distinguished features of VIKIZ logs depending on scale type. Phase differences (linear scale). In this case, the logs reflect measured responses. The higher is the conductivity of a medium, the more pronounced are changes in logs. Thus, low resistive deposits (clays, reservoir rocks saturated with saline water and etc.) are easily recognized at the expense of high values of phase differences corresponding to intervals of these deposits. Apparent resistivity (logarithmic scale). The logarithmic scale “shrinks” apparent resistivity logs in the range of low values (up to 10 ohm × m) and “stretches out” these logs in the range of high resistivities. It allows the good visual distinction of high resistive formations. Apparent resistivities (linear scale). Such a transformation leads to great changes in logs: the curves are shrunk in the low resistive range that is the most informative for induction logging methods. Such a way for data presentation decreases the visual resolution of rocks with low resistivities (sandy clays, siltstones, and etc.). At the same time, high resistive rocks are differentiated well with respect to resistivity.

7.1. Lithological Subdivision of a Section. Selection of Tight Beds Taking into account geoelectrical characteristics of Mesozoic-Cenozoic deposits in West Siberia as well as the high spatial resolution of investigation by VIKIZ tools, it is possible to obtain rather convincing and reliable information on a geological section even at a qualitative level. Let us consider some problems with respect to both qualitative analysis and quantitative interpretation. Fig. 7.1 exemplifies fragments of logs obtained in one of the boreholes of Surgut Arch by different methods of electrical and electromagnetic logging at measured depths from 1955 to 2000 m. Data for tools of the high vertical resolution, i.e., for Microlaterolog, VIKIZ-0.5 m, and Normal (0.5 m) are given in Fig. 7.1, a. It should be noted that VIKIZ logs in the ranges of low resistivities (less than 4–5 ohm × m) are well differentiated. Thin beds are resolved in sufficient details by the short probe that is second only to the Microlaterolog. In this case, apparent resistivities of these probes are different since the short probe eliminates a borehole effect more markedly than the Microlaterolog does. Fig. 7.1, b shows obvious correlation between logs of the all three tool types, namely, the VIKIZ-0.7 m, Laterolog, and Normal when subdividing the section. The good vertical resolution within ranges with relatively low resistivities is a distinctive property of the 0.7 m long probe. Note the higher resolution of electromagnetic probes as compared with that of the Normal when distinguishing formations with both low and mean resistivity values. Formation boundaries singled out through VIKIZ logs are in complete agreement with Laterolog data. A comparison between data of the conventional induction log and those of the long VIKIZ probe is shown in Fig. 7.1, c. The more detailed subdivision of a section is peculiar for the VIKIZ probe. Apparent resistivity values for these probes are different, but ra values

à – 1 – VIKIZ (0.5 m), upper scale; 2 – Microlaterolog; 3 – Normal Device (ÀÌ = 0.5 m), lower scale. b – 1 – VIKIZ (0.7 m), upper scale; 2 – Microlaterolog; 3 – Normal Device (ÀÌ = 0.5 m), lower scale. c – 1 – VIKIZ (2.0 m), upper scale; 2 – Induction Logging Tool, lower scale. d – 1, 2, 3, 4, 5 – VIKIZ probes (0.5, 0.7, 1.0, 1.4, 2.0 m); 6 – SP.

Fig. 7.1. Comparison of electrical and electromagnetic logging methods:

Qualitative Evaluation of a Geological Section

59

60 for the VIKIZ probe are closer to the true formation resistivities. Inversion results confirm this fact. As the VIKIZ so SP logs are given in Fig. 7.1, d. Depth intervals where inversion of sounding curves takes place are also singled out that points to the presence of a bordering zone. Within the intervals, oil-saturated reservoirs are revealed. Lithological subdivision of terrigenous sections on a qualitative level becomes more certain if as VIKIZ so SP logs are supplemented by such nuclear methods as Thermal Neutron Log and Gamma-Ray Log. The procedure of using these methods in combination is a matter of common knowledge. When subsequent discussing inversion results of both VIKIZ and SP logs, the data of Gamma-Ray logs will be invoked. In the series of Alym shales, tight impermeable beds are selected that are likely to be composed of sandstones characterized by high resistivity values, the low hydrogen content (from Thermal Neutron Log data), and low values of natural radioactivity (from GammaRay Log), as well as by the negative SP anomaly. Such beds can be seen on logs in Fig. 7.2. Taking into account the low hydrogen content in these beds through Thermal Neutron data, it may be established that the sandstones are cemented up. The similar synthetic logs are shown in Fig. 3.13. In a similar manner, tight beds within productive and water-bearing sandstones are selected. Thus, in the borehole 48, the cemented bed (Fig. 7.2, the 2115 m mark) separating the productive part of ÀÑ7–8 formation is singled out. This bed is characterized by high apparent resistivity values, exceedingly low porosity values (from Thermal Neutron), and the low level of pelite content of the mineral composition (from Gamma-Ray Logging and SP). The similar bed is found in water-saturated sandstone in the borehole 98 (Fig. 7.7, at 2134 m). The reliability of the lithological subdivision through the VIKIZ logs is verified by the high degree of correlation between data of different methods.

7.2. Selection of Reservoir Rocks and Evaluation of Saturation Type VIKIZ logs give in combination (Fig. 7.4) an illustrative example of possibility to distinguish reservoir rocks by the radial change in resistivities. In doing so, SP log is thought to be a source of supplement information for qualitative interpretation of a section. Essential consecutive decrease in ra values from the short probe to long one is a peculiar feature of water-saturated reservoir rocks (salinity of formation water exceeds that of filtrate). Waterbearing formation (the upper part of logs, above 1960 m) is distinguished by significant discrepancy between apparent resistivities for probes from 15 to 30 ohm × m. In this case, resistivities of shaly inhomogeneous deposits at its bottom vary from 2.2 to 4.4 ohm × m. Oil-bearing reservoirs (the middle part of logs) are characterized as by less discrepancy between curves so by enhanced ra values. In the top part of the upper oil formation (1968–1973 m), the bordering zone is selected which position in depth is determined by inverting sounding curves. Below the depth 1970.8 m, the extremum value of ra = 4.8 ohm × m points to the increased water amount in the formation. This formation with great amount of water is characterized by the vertical lithological heterogeneity through the data of both the short probe and SP curve. In Table 7.1 there are listed apparent resistivities of reservoirs through the sounding data for the logs presented in Fig. 7.1. Resistivity of drilling mud is 2 ohm × m and the borehole radius is 0.108 m.

Qualitative Evaluation of a Geological Section à

Fig. 7.2. Logs of VIKIZ, SP, Gamma-Ray, and Thermal Neutron in Cretaceous deposits with productive formations (a and b – boreholes 48 and 98, respectively).

61

62 b

Continuation of Fig. 7.2.

Qualitative Evaluation of a Geological Section c

Continuation of Fig. 7.2.

63

64 Table 7.1 Apparent resistivities in reservoirs

)OXLGW\SH

PSUREH

PSUREH

PSUREH

PSUREH

PSUREH

:DWHU











2LO











2LO











The results of qualitative interpretation are given below. For the water-bearing formation: resistivities of the formation and invaded zone are 3.1 ohm × m and 29.0 ohm × m, respectively. The invaded zone thickness is 0.56 m, i.e. that is about four borehole radii. For the oil bearing ÀÑ7 formation: resistivities of the formation, bordering zone, and invaded zone are 15.0 ohm × m, 1.9 ohm × m, and 24.0 ohm × m, respectively. The invaded zone thickness is 0.48 m. For the oil-bearing ÀÑ8 formation: resistivities of the formation and invaded zone are 6.3 ohm × m and 22.0 ohm × m, respectively. The invaded zone thickness is 0.54 m. The presence of a gradient of the radial resistivity on VIKIZ logs is one of the basic reservoir features. The gradient is most reliable for permeable formations containing either only formation water, or movable hydrocarbons and formation water, the last being more saline than drilling filtrate. Different radial gradients can be obtained if time-lapse technique is used: each VIKIZ log is compared with that run earlier. Sometimes these measurements are carried out when a radial heterogeneity is already dissipated. Consequently, single measurements of electrical properties in invaded zones of productive formations can not reflect the variety of interaction between filtrate and formation fluids. The visual analysis of all VIKIZ curves obtained soon after fresh rocks were drilled allows permeable rocks saturated with saline formation water (if drilling filtrate is weakly acid) to be indicated with certainty. In this case, discrepancy in probe signals depends on the radial depth of filtrate invasion and the extent of formation water displacement from a porous space. For qualitative evaluation of nature of reservoir saturation, information about critical values of resistivities is of basic importance. These values obtained, as a rule, on the base of multiple statistical information that include as log data so petrophysical measurements together with results of field tests and development of reservoirs permit their reliable evaluation. In Fig. 7.2 there are given logs of VIKIZ, SP, Gamma-Ray, and Thermal Neutron. The logging was run in the vertical part of the borehole penetrating Cretaceous sandstones and siltstone-shaly deposits. Productive sandstones of ÀÑ4–8 formations are differentiated from other reservoir rocks by enhanced resistivity values that can easily be recognized by correlation of apparent resistivities with SP logs within appropriate ranges of apparent resistivities. Series of Alym shales overlaying the productive sandstones are singled out on VIKIZ logs with respect to as traces of decreasing invasion so true resistivity values that are less than 4 ohm × m. If oil-saturated ÀÑ4 and ÀÑ5–6 formations are characterized by decreasing invasion according to VIKIZ data, the more complicated picture of invasion is observed for oilcontaining ÀÑ7–8 formations. The bottom part of ÀÑ7–8 formations contains formation water. It can be determined uniquely by great gradients of sounding curves and low values of apparent resistivities (less than critical ones) for long probes. Thus, significant change in apparent resistivity with decreasing invaded zone is observed in the borehole 48 (Fig. 7.2, a) over the 2142–2148 m interval. All the intervals of sandstones are differentiated by negative SP anomalies. In doing so, the formation resistivity from signals of the long probe is less than

Qualitative Evaluation of a Geological Section

65

2.5 ohm × m. The similar picture is observed as in borehole 49 from 2152 m to 2166 m (Fig. 7.2, b, excepting the tight bed from 2155 m to 2157 m), so in the borehole 98 from 2124 m to 2130 m (Fig. 7.2, c). Decreasing invasion is peculiar for both gas saturated ÀÑ4 and ÀÑ5–6 formations with higher electrical resistivity values according to the VIKIZ data. In Fig. 7.3, a, data on the borehole 49 is shown. Both ÀÑ5–6 (2118–2132 m) and ÀÑ7–8 (2140–2166 m) reservoirs are prominent as having nearly equal negative SP anomalies. According the VIKIZ data, decreasing invasion with the same signals of two long probes is observed that allows the correct determination of the true resistivity of this formation (about 30 ohm × m). Enhanced values of the parameter are obtained by Thermal Neutron Logging for entire interval of this formation that can characterize in total the reservoir as being gas-saturated. The second reservoir that lies below is selected by enhanced apparent resistivity values within oil-saturated intervals as compared with gas-saturated ones. In this case, insignificant changes in resistivities are observed because of lithological heterogeneity. Within the oil-saturated interval from 2140 m to 2148 m, signals of long probes are nearly consistent that makes possible estimating values of true resistivities as being 7–8 ohm × m. Note that these values exceed the critical level markedly. Resistivities decrease simultaneously in the depth interval from 2148 m to 2152 m as it can be seen from signals of both 1.4 m and 2 m long probes. This interval is interpreted as containing increased amount of formation water as compared with the interval above the 2148 m. The near-bottom formation part below 2152 m is interpreted as water-saturated. This interval is characterized by the obvious discrepancy between apparent resistivities: from 5.5 ohm × m for the 0.5 m long probe to 2.5 ohm × m and less for the 2 m long probe. The problem on resistivity estimation of relative thin productive formations, especially on the qualitative level, should be based on both experience and comparison of field logs, which often are fairly complicated, with data of two-dimensional mathematical modeling. Logs of VIKIZ SP, Gamma-Ray, and Thermal Neutron are given in Fig. 7.3, b. The presence of a bordering zone in the productive ÀÑ7–8 reservoir is a peculiarity of this section. Evidence of the bordering zone is observed from 2086 m where apparent resistivities for the 0.5 m probe become higher than those for other probes. This can be explained by an increase in the volume of displaced formation water as depth increases. If within the interval from 2086 m to 2090 m signals of the 0.7 m long probe only are less than those of the 0.5 m long probe, then, beginning with 2094 m, apparent resistivity values of both 1.0 m and 1.4 m probes become relatively less than those of the 0.7 m probe. In this case, traces of decreasing invasion are observed in signals of three long probes. Thus, one can see consecutive shift of probe signals relative to each other: from monotonically decreasing sounding curves in the upper part of a reservoir to those with the minimum in the bottom part of the formation. Below the closely packed, cemented sandstone, in which sharp increase in ra is observed at 2099 m, there is also the interval with inverting of 2.0 m long probe signals. Thus, this part of the reservoir can be considered as productive as well but with the higher content of formation water. Below 2102 m where increased content of both shale and formation water is observed, the apparent resistivity of three long probes is 3.7 ohm × m. Deeper formations are represented by interbedded siltstones and shales that change to water-saturated sandstone with resistivity less than 2 ohm × m (2124 to 2130 m). A tight bed with the high resistivity is singled out in the central part of this reservoir. The bed is characterized as by the low level of Gamma-Ray signal so by the rather low water content. Caution should be required in the interpretation of curves with evidence of a conductive bordering zone (when sounding curve for one of the medium-length probes has the

Fig. 7.3. Logs of VIKIZ, SP, Gamma-Ray, and Thermal Neutron in terrigenous section with gas-, oil-water, and water saturated formations. Inversion of sounding curves for the transition zone of ÀÑ7–8 formations (a) and the same logs in Cretaceous deposits with productive ÀÑ7–8 formations (b).

66 à

Qualitative Evaluation of a Geological Section b

Continuation of Fig. 7.3.

67

68 maximum). Since in this case, the number of measurements coincides with that of model parameters being estimated, geophysically justified restrictions on characteristics of a bordering zone should be introduced. Calculation shows that a bordering zone can be represented by the additional cylindrical layer in an invaded zone. It is difficult to estimate uniquely the range in which the layer thickness varies. From theoretical assumptions, a layer with the thickness that is 15–20 percent of the invaded zone thickness is considered to be ample for constructing the reliable model. In this case, the resistivity of a bordering zone may be some higher than that of water-saturated formations at the same porosity and salinity of formation water. Such an additional information allows the correct estimation of all parameters of an invaded zone by minimizing the equivalence principle effect. Experience shows that the true resistivity of oil-bearing formation is determined with strict accuracy regardless of information on a bordering zone.

7.3. Evolution of Invaded Zone Results of time-lapse measurements carried out within the same section confirm not only the presence of a bordering zone in the productive part of formation but allow dynamics of processes building up this zone to be studied. As an example, measurements made at different times within the productive reservoir are given in Fig. 7.4. These measurements were obtained from four logs that were run for eight days at one to four day time intervals. It is seen that the reservoir (from 2224 m to 2255 m in depth) was within tight and low permeable shaly deposits in which an invaded zone was nearly absent. Over the total depth of the reservoir, values of the negative SP anomaly were as high as 60 mV that corresponded to the relative parameter a sp = 0.9. The visual analysis shows that time-lapse logs for the long probe were slightly changed. This allows one to conclude that an invaded zone could only be detected by short probes. Changes in apparent resistivities for the short probe on sounding curves (Fig. 7.5) within the reservoir were less than 10–15 %. Therewith, the most changes (up to 4 ohm × m) were observed in the upper, more resistive part of the productive reservoir. In the lower part, signals for the short probe changed drastically and those for the long probe changed essentially less (up to 2 ohm × m) mainly due to general increase in resistivity (at 2250 m). Sounding curves in Fig. 7.5 gave an insight about dynamics of resistivity change in the invaded zone. Earlier measurements that were performed immediately after the reservoir was penetrated by a borehole showed the decreasing invaded zone. At that time, the flushed formation part with the enhanced resistivity that was adjoined to borehole walls was slightly distinguished even by short probe signals. On subsequent measurements when fresh filtrate displaced formation water away from the borehole, the zone resistivity increased as oil and saline water both were displaced far away from the borehole. Following the displacement of oil, saline formation water was displaced and its part was accumulated in a bordering zone. It is important to know that as formation water was displaced, fragments of the sounding curves with minimum resistivity values caused by the bordering zone “were smoothed” and progressive increase in resistivity was observed in this zone as well (Fig. 7.5, a, b). In the lower reservoir part with the high water content, a bordering zone with pure formation water occurred. In this case, apparent resistivities for the both 1.0 m and 1.4 m long probe decreased (Fig. 7.5, c).

Fig. 7.4. Time-lapse VIKIZ logs. Evolution of formation fluid displacement by drilling mud filtrate in oil saturated reservoir.

Qualitative Evaluation of a Geological Section

69

70

Fig. 7.5. Time-lapse sounding curves for oil saturated reservoir. Logging date: August, 9 (blue), August, 10 (green), August, 12 (brown), and August, 16 (red); a – at 2235 m, b – at 2245 m, c – at 2250 m.

The picture obtained from log data on gas-saturated reservoirs seems to be somewhat different. In Fig 7.6 there are given the VIKIZ logs as well as SP and Gamma-Ray ones that were run at different times in the gas-saturated part of sandy reservoir (from 2180 m to 2215 m). The logging was run immediately after the borehole was drilled and flushed. When comparing the sounding curves, it can be noted that signals for the longest probe were changed insignificantly, i.e., the invasion was shallow. It could be due to the rather high formation pressure that compensated the pressure of drilling mud. From signals of short probes, different radial depths of decreasing drilling mud invasion were caused by lithological and mineralogical peculiarities of individual intervals. It could be seen from time-lapse measurements that signals for short probes progressively changed relative consistent signals for two long probes. In this case, decrease in apparent resistivities for the 1.4 m long probe was observed to a greater extent in the upper part of the reservoir, for instance, within 2180– 2202 m. Sounding curves obtained for gas formation after the first logging was run pointed to the evidence of decreasing invasion over the entire interval except the thin impermeable bed (from 2210 to 2212 m). At one-day interval (August, 10) when the second logging was run, a decrease in apparent resistivities occurred due to as gas displacement so enhanced effect of saline formation water that was observed through the signals of both 1.0 m and 1.4 m long probes. Therewith, the signals for the long probe were unaffected. These signals remained to be nearly unaffected at the all subsequent measurements (just as after two days so after four

Fig. 7.6. Time-lapse VIKIZ logs. Evolution of formation fluid displacement by drilling mud filtrate in gas saturated reservoir.

Qualitative Evaluation of a Geological Section

71

72

Fig. 7.7. Time-lapse sounding curves for gas saturated reservoir. a – at 2186 m, b – at 2190 m, c – at 2205 m. See designations for Fig. 7.5.

days). At the same time, apparent resistivities for short probes progressively increased at the expense of fresh filtrate invasion into the formation. It is notably from signals of the shortest probe. The recent measurement (after 7 days) within the depth interval from 2190 m to 2115 m showed that signals for all short probes were close to those for two long probes. An increase in apparent resistivity for the short probe was still observed only in the near top zone. In Fig. 7.7 there are given sounding curves obtained at 2186 m, 2190 m, and 2205 m for different logging time. Time-lapse measurements showed dynamics of a bordering zone against the background of weakly changed reservoir resistivities. The curves obtained at the all three depths showed how the formation water accumulation was displaced from the borehole outwards into formation, then this water was gradually mixed with fresh drilling filtrate followed by an increase in resistivities. Three successive VIKIZ logs as well as the SP and Gamma-Ray ones are shown in Fig. 7.8 (July, 8, the second; July, 11, the third; July, 14, the fourth). A granular reservoir from 2393 m to 2413 m was composed of sandstone. From the Gamma-Ray Log data, the sandstone was characterized by the high shale content, which gradually decreased from the top downward. The reservoir was saturated with oil and water. This was confirmed by the apparent resistivity values resulting from sounding curves. Certain peculiarities of a bordering zone were also observed on these curves. Let us analyze the logs obtained over interval of water-saturated reservoir rocks (from 2406 m to 2413 m). We consider the logs obtained on July, 8. In the bottom part of the formation, resistivities for two long probes showed the good

Fig. 7.8. Time-lapse VIKIZ logs. Evolution of formation fluid displacement by drilling mud filtrate in gas saturated reservoir.

Qualitative Evaluation of a Geological Section

73

74

Fig. 7.9. Time-lapse sounding curves for oil saturated reservoir. Logging date: July, 3 (blue), July, 11 (green), and July, 14 (red); a – at 2394 m, b – at 2407 m, c – at 2410 m.

fit (4.2 ohm × m) and, hence, these were close to the true formation resistivity. With allowance of the critical value for this accumulation type (4.7 ohm × m), the interval could be considered as water bearing. However, the presence of residual oil was not ruled out in this formation. Above 2407 m, the minimum corresponding to signals for the 1.0 m long probe appeared on the sounding curves. Above 2402 m, ra values for two long probes increased significantly indicating that the transition to reservoir area with the higher oil content was completed. In this upper reservoir part, resistivities for two long probes exceeded the critical resistivity values for oil-saturated formations. At more recent logs, the progressive increase in apparent resistivities for short probes could be observed that corresponded to an increase in the invaded zone. Therewith, as it can be seen from the log obtained on July, 14, signals for two short probes were nearly the same. Hence, the volumes of porous space, which contribute to the measured probe signal were the same. These volumes were filled with mud filtrate

Fig. 7.10. Time-lapse VIKIZ logs. Dynamics of formation fluid displacement in water saturated formation.

Qualitative Evaluation of a Geological Section

75

76 and then formation fluid was no longer displaced from pores. In the nearest zone, the relations between filtrate and formation water were unchanged because formation water was no longer displaced from pores at steady-state pressure balance. At the same time, apparent resistivities for the long probe increased insignificantly indicating that formation water was displaced from a borehole outward into the formation. The curve at 2394.6 m (Fig. 7.9) was obtained soon afterwards the reservoir had been drilled (July, 8). Apparent resistivities for short probes changed from 13 ohm × m (the 0.5 m probe) to 6 ohm × m (the 1.0 m long probe). For 1.4 m and 2.0 m long probes, an increase in apparent resistivities up to 8.3 ohm × m was observed. It Fig. 7.11. Time-lapse sounding curves for water satu- was associated with an increase in resistivity outside the zone of formation water rated formation at 2426 m. accumulation. Thus, minimum apparent See designations for Fig. 7.9. resistivity values corresponding to the bordering zone effect was observed for the 1.0 m long probe. When repeated measurements were made, the minimum on sounding curves shifted to the area of longer probes. It can be attributed to the fact that the bordering zone was away from the borehole. Thus, if the resistivity minimum on sounding curves obtained on July, 11 was between the 1.0 m and 1.4 m long probes, the minimum on sounding curves obtained on July, 14 shifted to the 1.4 m probe. As the front of formation water was displaced into the area part sensitive for the long probe, the probe signals decreased due to the bordering zone effect. The last measurement that was made in six days after the first one showed that the resistivity decreased from 8.3 to 7.6 ohm × m. It can be emphasized that apparent resistivities in the bordering zone gradually increased in time. This might be associated with extension of the invaded zone and spreading displaced water. Analysis of sounding curves obtained at other depths (Fig. 7.9, b, c) showed gradual increase in apparent resistivities as in the bordering zone so in formations. At the 2407 m, near the maximum water-saturated reservoir part, a bordering zone was yet to be revealed at the first logging and that was not detected at successive measurements. At 2410 m (three m deeper), sounding curves had no traces of a bordering zone. As it can be seen from the presented logs, signals of the longest probe in all repeated measurements remained to be unchanged for entire range of the formation being investigated. This was because the process of filtrate invasion into reservoir was limited, on the one hand, by clayey caking, and on the other hand, by significant expansion of a porous space as the radius of an invaded zone was increased. Thus, the depth of invasion that is estimated by the invasion radius as well as changes in resistivities due to the invasion can become functions of the water volume inflowing into formation from the borehole. Therefore, under these conditions, development of an invaded zone is slowed down that can be observed on right branches of time-lapse curves.

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Thus, increased content of formation water in productive formation leads to more active displacement not only of oil, but of water itself. Appearance of a circular bordering zone is the diagnostic feature of oil-saturation. Measurements in transition zones give more accurate information on vertical changes in the nature of reservoir saturation. Let us consider an example of occurrence of an invaded zone in water-saturated formation through the data on measurements made at different times. In Fig. 7.10 there are given just as the time-lapse VIKIZ logs so the common SP log in water-saturated formation from 2422 m to 2430 m, and in Fig. 7.11 there are given sounding curves obtained at 2426 m. Apparent resistivities for the all probes increase in time. Therewith, the most remarkable growth of apparent resistivities is observed for the 1.0 m and 1.4 m long probes. The rate of resistivity increase for the 0.7 m long probe is less than that for the 1.0 m long probe but significantly more than the rate for the shortest probe. As it is seen from the sounding curves in Fig. 7.11, the range of enhanced apparent resistivity values shifts in time from the zone which affects the short probe into the region that is more distant from the borehole. This effect is seen on sounding curves that have been made in more recent dates. Such a behavior of sounding curves cannot be attributed to displacement of fluids, filtrate and formation water above all, in the zone adjacent to the borehole being investigated by short probes. Summing up the above discussion, it can be concluded that the realistic form of sounding curves obtained in reservoirs with movable oil and formation water both significantly differ from that of sounding curves for water-saturated formations due to occurrence of a bordering zone in the reservoirs. This allows qualitative interpretation of the formation saturation nature to be made.

8

.

FUNDAMENTALS OF QUANTITATIVE I N T E R P R E TAT I O N

Quantitative interpretation of VIKIZ logs is based on the concept of a medium as horizontally layered earth. As a result of quantitative interpretation (inversion) is a geoelectrical section involving sequential layers penetrated by a borehole. The depths of both the top and bottom of a layer define the position of each layer along the borehole. An individual layer is characterized by resistivities as in the near borehole invaded zone (with a possible bordering zone) so in the undisturbed part of the layer. The layer is characterized also by the location of cylindrical boundaries between these zones that are coaxial with the borehole. The quantitative interpretation comprises the steps of: · layer-by-layer selection (location of layer boundaries); · averaging logs within the layer (choosing layer values); · correction that reduces the shoulder bed effect, eccentricity of both a probe and its case, deviation of borehole from vertical, and etc.; · building up a sounding curve for each layer; · construction of a starting model (express-inversion); · inversion of sounding curves using different methods of optimization of model parameters to obtain the best fit to observed data; · building up confidence intervals for each parameter being estimated; · evaluation of interpretation quality by calculation of synthetic logs for the whole section and by comparison of the logs with field data. Inversion results are considered to be satisfactory if the discrepancy between synthetic experimental logs within one or another layer is less than the measurement error. The entire scheme given above provides the basis for the MFS VIKIZ computer inversion system (see Appendix). The most of its functions is performed automatically; however, there is a capability to correct intermediate results. The principle of the radial (from a borehole to an undisturbed formation) sounding is known to form the VIKIZ theoretical basis. Because of the probes are isoparametric, their signals in a homogenous medium are consistent (with allowance of the measurement error). Discrepancy in signals for different probes in fairly thick formations penetrated by boreholes that are filled with common drilling mud (resistivity is more than 0.5 ohm × m) points to the presence of a near borehole heterogeneity due to invasion of drilling mud into formation. In

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thin layers (thinner than 1.5 m), discrepancy between signals of different probes can be caused not only by the invaded zone effect (radial heterogeneity), but by the shoulder bed effect as well (vertical heterogeneity of a section). It should be noted that the signals of two short VIKIZ probes can be affected by drilling mud with very low resistivity (rb < 0.05 ohm × m).

8.1. Typical Examples of Inversion Hereafter except of special cases, we shall take the drilling mud resistivity to be rb = 2.0 ohm × m and the borehole radius to be rb = 0.108 m. The simplest for inversion are two-layer sounding curves for individual low permeable shales and tight beds. Shaly beds. The shaly bed (Fig. 8.1) with the resistivity of 3.85 ± 0.32 ohm × m is observed from 2588.7 to 2591.2 m. The sounding curves show no changes in apparent resistivities that exceed measurement errors. This suggests either the shallow invaded zone or no invaded zone, drilling mud effect being insignificant. The synthetic sounding curve agrees with experimental data within the limits of measurement errors. It should be noted that not any particular shaly layer could be described by the twolayer model. In many cases, distinctions between signals of different probes are certain. The model with the near borehole heterogeneity is used to interpret curves of such types (i.e., the model “borehole – invaded zone – formation”, Fig. 8.2). In some cases, occurrence of the near borehole zone can be, actually, at the expense of drilling mud filtrate invasion into the most sandy beds. The same effect is observed in the presence of large cavities. The short probe sounding curve shows that the inhomogeneous shaly formation involves highly resistive beds. Just this fact provides an explanation for both occurrence of drilling mud filtrate invasion and enhanced formation resistivities as compared with those of common shales. Note that in this case decreasing invasion is observed that is not peculiar for water saturated formations. Tight shaly beds composed of mudstones and siltstones are usually characterized by monotonically increasing sounding curves (Figs. 8.3–8.4). In this case, the shallow decreasing invasion is observed as opposed to reservoir rocks. The presence of the invaded zone is likely to be due to artificial fractures created by drilling. Although examples are taken from different regions, the curves are closely similar. To differentiate these beds from oil-saturated reservoir more accurately, data of both SP and Gamma-Ray logs should be invoked. Tight low permeable formations. The tight bed without invasion is from 1143.6 to 1145.8 m in depth, its resistivity is equal to (90.7 ± 38.2) ohm × m (Fig. 8.5). The sounding curve for the short probe shows decreasing apparent resistivity caused by the borehole effect. Decrease in apparent resistivity for the long probe from the bed top downward (from 110 to 80 ohm × m) is due to effect of conductive underlying deposits. Water-saturated formation with increasing invasion. Fig. 8.6 demonstrates data for the thick water saturated formation from 2678.6 to 2692.4 m. As it can be seen from the sounding result, the curve of apparent resistivity monotonically decreases as the probe spacing increases. Signals even for long probes are different from each other indicating the existence of the contrasted and rather deep invaded zone. The inversion results are as follows: riz = (15.51 ± 0.56) ohm × m, riz = (0.62 ± 0.03) m, and rf = (2.77 ± 0.07) ohm × m. This is an example of typical water-saturated formations with increasing invasion.

80

Fig. 8.1. Log fragment, sounding curve, and inversion result for shaly formation (Ob region).

Fig. 8.2. Log fragment, sounding curve, and inversion result for shaly inhomogeneous formation (West Siberia).

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Fig. 8.3. Log fragment, sounding curve, and inversion result for siltstone formation (China).

Fig. 8.4. Log fragment, sounding curve, and inversion result for siltstone formation (North of West Siberia).

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Fig. 8.5. Log fragment, sounding curve, and inversion result for tight carbonate formation (Tatarstan).

Fig. 8.6. Log fragment, sounding curve, and inversion result for water saturated formation (Ob region).

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Fig. 8.7. Log fragment, sounding curve, and inversion result for water saturated formation (Tatarstan).

Fig. 8.8. Log fragment, sounding curve, and inversion result for oil saturated reservoir (Ob region).

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Fig. 8.9. Log fragment, sounding curve, and inversion result for oil saturated reservoir in the presence of a bordering zone (Ob region).

Fig. 8.10. Log fragment, sounding curve, and inversion result for oil saturated reservoir in the presence of a bordering zone (Ob region).

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Fig. 8.11. Log fragment, sounding curve, and inversion result for gas saturated reservoir (North of West Siberia).

The sounding curve for the thin (from 1771.8 to 1773.8 m; Fig 8.7) saline water saturated formation is typical for formations with increasing invasion. The signals for two long probes that are nearly the same provide an indication of relative shallow invasion. The sounding curve approaches that for the formation resistivity. The inversion results are as follows: riz = (13.04 ± 0.39) ohm × m, riz = (0.33 ± 0.03) m, and rf = (1.04 ± 0.07) ohm × m. Oil-saturated reservoir with increasing invasion. The data obtained for the oil-saturated reservoir from 2411.6 to 2614.2 m (Fig. 8.8) confirm that any oil-saturated formation is far from to be characterized by the existence of a bordering zone. The sounding curve is representative for formations with increasing invasion. Signals for short probes are close to invaded zone resistivities, and apparent resistivity values for the long probe are overstated as compared to formation resistivities. The inversion results are as follows: riz = (29.4 ± ± 1.47) ohm × m, riz = (1.09 ± 0.13) m, rf = (8.43 ± 0.51) ohm × m. Oil-saturated reservoir with increasing invasion and a bordering zone. In the presence of a bordering zone, sounding curve can change in type: from monotone curve to that with the minimum. The sounding curve for the thick oil-saturated reservoir that is from 2731.6 to 2737.6 m (Fig. 8.9) has the pronounced minimum which locates between signals for 1.0 m and 1.4 m long probes. The inversion results are as follows: riz = (42.1 ± 1.81) ohm × m, riz = (0.68 ± 0.08) m, rbz = 4.5 ohm × m, rbz=0.81 m, rf = (22.5 ± 1.03) ohm × m. Note that a bordering zone provides the most consistent determinations of longitudinal conductance S = (rbz–riz)/rbz = 0.278. Sep-

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Fig. 8.12. Log fragment, sounding curve, and inversion result for thin gas saturated reservoir (North of West Siberia).

arate determination of both resistivity of a bordering zone and its thickness is not entirely correct operation owing to S principle of equivalence. Assuming a bordering zone to be an accumulation of formation water which resistivity is known, the bordering zone thickness may be estimated more accurately. Fig. 8.10 demonstrates a sounding curve for oil-saturated formation from 2467.6 to 2475.8 m underlain by shales. The formation has pronounced traces of a bordering zone. The sounding curve has the minimum that corresponds to a signal of the 1 m long probe. The inversion results are as follows: riz=(18.2 ± 0.60) ohm × m, riz=(0.59 ± 0.04) m, rbz = 3.70 ohm × m, rbz = 0.72 m, rf = (17.35 ± 1.24) ohm × m. Gas-saturated reservoir with decreasing invasion. Logs for short probes for the thick gas-saturated reservoir from 2732.6 to 2736.2 m (Fig. 8.11) represent invaded zone resistivity and these logs are practically unchanged within the entire reservoir interval. Whereas, logs of long probes demonstrate an increase in apparent resistivity caused by more conductive (the resistivity is approximately more than 20 ohm × m) overlying series. The sounding curve reflects an increase in resistivity from the borehole outwards. The inversion results are as follows: riz = (18.4 ± 0.64) ohm × m, riz=(0.62 ± 0.04) m, rf = (77.5 ± 1.7) ohm × m. The peculiarity of the sounding curve for the thin gas-saturated reservoir from 2752.2 m to 2753.8 m (Fig. 8.12) is an increase in apparent resistivity for the long probe. As it has repeatedly been mentioned in analyzing vertical characteristics, shoulder bed effect on the short probe signals in high resistive thin beds (less than 2 m) is very strong and cannot be corrected. Therefore, the short probe signals should not be taken into account for interpretation or the relative measurement error has to be essentially increased. The inversion results for four probes are as follows: riz = (28.5 ± 3.1) ohm × m, riz = (0.57 ± 0.08) m, rf = (117.3 ± ± 18.4) ohm × m.

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8.2. Log Interpretation in the Case of Highly Conductive Drilling Mud Last years, high conductive drilling mud (up to parts per hundred of ohm × m) with high salt content (up to 270 g/l) or specific biopolymer additives have found expanding application when drilling boreholes, especially lateral holes. The same situation is observed if a borehole penetrates through overlying salt-bearing series. As it can be seen from analysis of synthetic logs and field tests, in this case the following effects are observed: borehole effect and probe eccentricity increase, an increasing invaded zone occurs, and measurement errors increase because of electromagnetic response amplitude is markedly attenuated. When difference between resistivity of drilling mud and that of formation being investigated is the most distinctive (more than 500 times), effects caused by insignificant reasons can be observed on field logs. It may be effect of irregularity of the borehole wall or interference from change in the tool position when moving along the borehole. Deviation of a borehole from the vertical can essentially change the field logs. By these reasons, inversion of logs obtained in boreholes with high conductive drilling mud has peculiarities. To obtain the reasonable accuracy of formation resistivity determination, inclinometry data are certain to be invoked in parallel with caliper logs if the latter are available and the instrument diameter has to be pointed as well (at present it is 0.073 m and 0.102 m). Fig. 8.13 gives the data for the relative thin (1925.7–1929.1 m) shaly bed (rb = 0.2 ohm × m, rb = 0.119 m). Underestimated for the expense of drilling mud effect is the apparent resistivity for the short probe only. According to the inversion results, rf =(2.93 ± 0.32) ohm × m. The similar picture is observed also in boreholes filled with much more conductive drilling mud (rb » 0.05 ohm × m). Fig. 8.14 represents the data of inversion in the following conditions (from 2257.4 to 2260.8 m in depth). The sounding curve pattern is “two-layer” curve with lowered values of apparent resistivities for two short probes at the expense of high conductive mud effect. Three long probes show nearly the same ra values that are close to the resistivity of shales rf = (3.19 ± 0.14) ohm × m.

Fig. 8.13. Log fragment, sounding curve, and inversion result for shaly formation (Baltic region).

88

Fig. 8.14. Log fragment, sounding curve, and inversion result for shaly formation drilled with highly conductive drilling mud (Ob region).

Fig. 8.15. Log fragment, sounding curve, and inversion result for tight formation drilled with low resistive drilling mud (Ob region).

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Fig. 8.16. Log fragment, sounding curve, and inversion result for water saturated reservoir rocks (Baltic region).

Fig. 8.17. Log fragment, sounding curve, and inversion result for water saturated reservoir rocks drilled with highly conductive drilling mud (Ob region).

90

Fig. 8.18. Log fragment, sounding curve, and inversion result for oil saturated reservoir (Baltic region).

Fig. 8.19. Log fragment, sounding curve, and inversion result for oil saturated reservoir (Ob region).

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The most complicated problem on resistivity determination of tight, low permeable bed can be solved if the bed thickness is more than the probe spacing by the factor of 1.5. However, high resistive beds have in common a less thickness. It is obvious that in these cases, signals of probes which spacing is comparable with the bed thickness will be very strongly affected by shoulder beds. The shoulder bed effect cannot be corrected accurately. The bed resistivity can be estimated by the result of inversion for readings of three short probes. An appropriate example is given in Fig. 8.15 (from 2316.0 to 2317.6 m in depth). Fig. 8.16 demonstrates the data for the thin formation (from 1925.7 to 1929.1 m) saturated with saline water and drilled with moderately conductive drilling mud (rb = 0.2 ohm × m). The sounding curve monotonically decreases. This provides evidence for the formation with increasing permeability caused by drilling mud filtrate, which is fresher than formation water in spite of the filtrate is high conductive. When water-saturated formations are drilled with high conductive drilling mud (r b £ 0.05 ohm × m), an invaded zone with lowered resistivity occurs. Fig. 8.17 exemplifies such a situation (from 2307.0 m to 2315.2 m in depth). The zone resistivity is less than one ohm × m at the expense of invasion of highly mineralized filtrate. Nevertheless, the formation resistivity has the common value rf = (4.38 ± 0.19) ohm × m. Decreasing invaded zone occurs when high resistive oil-saturated reservoirs are penetrated by boreholes even with moderately conductive (rb » 0.2 ohm × m) drilling mud. Fig. 8.18 demonstrates the data for one of such situations (from 2053.8 m to 2055.8 m in depth). The sounding curve increases monotonically from 7.7 to 30.2 ohm × m. The inversion results are as follows: riz = (8.15 ± 0.98) ohm × m, riz = (0.66 ± 0.08) m, rf = (50.6 ± 6.8) ohm × m. Increase in measurement errors when determining formation resistivities can be related to the drilling mud effect. When highly mineralized mud is used (rb » 0.07 ohm × m), it is possible to estimate exactly resistivities of oil-saturated formations. The data for the interval from 2243.0 m to 2250.4 m are given in Fig. 8.19. The relative error of formation resistivity determination is less than 4.1 %.

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APPENDIX MFS VIKIZ SOFTWARE TOOL FOR PROCESSING A N D I N V E R S I O N O F V I K I Z LOGS Processing, visualization, and inversion of VIKIZ logs are performed on the basis of the multifunctional MFS VIKIZ system. That is the software in which the high speed of inversion processing is achieved by using fast and effective algorithms of neural network modeling. The software allows passing from individual processing of single intervals to automatic inversion of data on group intervals obtained over the total depth under investigation. The achieved resource characteristics approach the MFS VIKIS inversion system to real-time processing. Software tool features relive an operator of having to fit the model parameters manually and the primary attention can be given to assessment of the reliability and quality of interpretation being executed. For this purpose, the special options for evaluation of results are realized in the system. Mean square root deviations that reflect fitting quality of inversion are calculated alongside with confidence intervals of determination of both the formation resistivity and invaded zone resistivity as well as the radius of the invaded zone. The VIKIZ method aimed to determination of resistivities of both the formation and invaded zone becomes more informative when used in integration with other methods. The system provides options to visualize any log contained in the initial LAS file.

1. The General Description The MFS VIKIZ system for processing, visualization, and inversion of VIKIZ data is an advanced software tool. In comparison with earlier versions, MFS VIKIZ can operate under Windows-95 and Windows NT, its modulus run faster and the capability of data analysis has been increased. The package is real-time operating system. Raw data are contained in LAS files. The MFS VIKIZ supports LAS 2.0 data standard. In the system, the approach based on layer-by-layer processing and inversion has been kept. Layers are selected on the log. Then weighed averaging of measurements made with each particular probe within the selected layer takes place. This average value will be referred to an average layer value. The necessary corrections and compensations are introduced, starting model (initial guess for the model) is constructed, and inversion is executed. The inversion results are attended with estimation of confidence intervals. Their range depends as on a geoelectrical model so on measurement errors.

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To specify the position of layer boundaries, the algorithm for automatic layer-by-layer selection is used. The provision is made for manual correction, deleting and addition of boundaries. After defining boundaries, it is necessary to select layers for which inversion will be executed. When a layer is selected, average layer values are chosen automatically. The system provides the manual correction of these values. Further, inversion is processed under one of the following conditions: · express-inversion; · automatic fitting; · fitting within a selected interval of depths. When inversion is completed, estimation of the accuracy of parameter determination is executed automatically. When manual fitting, there is a possibility to operate separately with a sounding curve and estimate the inversion quality for each layer in details.

2. Hardware and Software To operate with the MFS VIKIZ system, the Pentium processor is required. Pentium-166 or later computer generation is recommended. The operating systems as Windows 95, 98, or Windows NT4 are needed. Windows NT is best. The minimum memory capacity to operate in the Windows 95 is 16 Ìb, the recommended one is 32 Ìb; the minimum memory capacity for Windows NT and Windows 98 is 32 Ìb, the recommended one is 64 Ìb. The system requires 30 Ìb of hard disk. Fast graphic adapter (2 Ìb memory) and SVGA monitor are also needed. When using print options, the availability of a printer supported by the operating system is needed. For the optimal realization of the functions, it is recommended to work with the display resolution more than 800´600 pixels using the 16 bit color palette.

3. The Main Program Window Description The program has the standard graphic interface. At the top of the main program window, the menu bar and control icons on a tool bar for basic operation functions are located. The scale of log values is immediately below the tool bar. At the right side of the main window, the scroll bar appears, and at the bottom of the window, the status bar is placed. The latter displays current coordinates of a cursor, the status of execution of long-term operations, and other data (Fig. A.1). The main window is divided into four basic areas. The left area displays the panel of additional methods and initial logs, the middle area displays inversion results (a geoelectrical section), and the right one contains estimations of the inversion results. The sizes of each area can be changed using a mouse. Any panel can be closed. The provision is made for simultaneous operation with logs for two depth intervals. For this goal, it is necessary to fix required dimensions of the viewport with a mouse by dragging the horizontal boundary at the top of the main program window.

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Fig. A.1. The main window of the system.

Every probe in the system has the definite name, the log of corresponding probe in the initial file being identified by this name. The names of VIKIZ probes are: IK1, IK2, IK3, IK4, and IK5 are probes with spacing of 0.5, 0.7, 1.0, 1.4, and 2.0, respectively. The upper ruler for every area of the main window is individual. The ruler for the log area displays phase differences in degrees and apparent resistivities in ohm × m. The scale of distances of cylindrical boundaries from the borehole axis in meters is drawn on the ruler in the middle window area in which a geoelectrical section is displayed. The ruler on the panel of estimations contains the percentage scale if mean square root deviations are displayed. This ruler contains the scale of resistivities (ohm× m) if confidence intervals are displayed for the resistivity of formation and that of an invaded zone. The ruler also contains the scale of radii (m) if confidence intervals for invaded zone radii are displayed. The readings from logs of additional methods can be obtained with the mouse pointer by clicking the status bar. The scale ruler of additional methods is displayed for the log under processing. The content of the “Value” box on status bar depends on the area in which the mouse pointer is positioned. For the area of logs, values of apparent resistivities (ohm × m) or the phase differences (degrees) are displayed. For the area of a geoelectrical section, resistivity values (ohm ×m) are displayed. For the area of estimations, the same values that are on the upper ruler are displayed.

95

Appendix

Apart from displaying resistivities in the area of inversion results, the system permits constructing and displaying a lithological column. This made be done by clicking on the appropriate area with the right mouse button. From the context menu that appears, the following lithological types can be selected: Sand, Shale, and Tight. The function is used only for a single layer. The lithological types are displayed on a screen and recorded into the exported files.

4. The Basic Service Functions of the System The menu bar contains the following menus (Fig. A.2): · File · View · Layers · Inversion · Estimations · ? File menu has the following commands: · Import. This command is used for data input. The system operates with data files in the LAS, VKZ, SII, NBK, DAN, and LST formats. · Export. When executing this option, downhole data and inversion results are saved. The system provides export of inversion results into the text file in the RES format and other file types: LAS, VKZ, SII, NBK, DAN, LST, ROK, and XLS. · Print. The system provides printout of VIKIZ logs, logs of additional methods, and results of inversion by means of standard print devices. · Preview. The command is used for viewing log copy before output. · Settings. The command is used for changing parameters of the system operating and allows one to modify parameters of copy output as well as parameters of processing and graphic representation of logs. · Exit. Completion of operating the program.

Fig. A.2. The File menu.

96 View menu includes the following commands (Fig. A.3): · Scale. The command allows changing the vertical scale of all the windows. · Layer boundaries. The command shows layer boundaries in the main window. · Legend. The command represents color codes for VIKIZ probes. · Apparent resistivity. The command represents logs as the apparent resistivity values (ohm × m). · Phase difference. The command represents logs as the phase difference values (degrees). · Filtering. The command is used for removing pulse noises. · Trajectory. Displaying the borehole trajectory and position of a current interval of depth. Layers menu contains the following commands: · Add or delete boundaries. Definition of layer boundary locations with provision for manual correction. · Add/delete boundaries. The command permits boundaries to be added or deleted within the selected interval. · Select layers. The command permits selecting layers with given resistivity range. The reading of layer values is executed automatically. The provision is made for manual correction of values. · Select all layers. When inversion is executed for the whole log, the function permits selecting all intervals between fixed boundaries. · Delete all layers. Deleting data on selected layers and chosen readings. · Activate all layers. Activating all layers, for example, for repeated inversion of the log. · Inactivate layers. Inactivating layers without deleting data on layers, taken readings, and lithological features. · Take all readings again. Recovery of taken readings.

Fig. A.3. The View menu.

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Appendix

Fig. A.4. The Inversion menu.

Inversion menu contains the following commands (Fig. A.4): · Express. It is the fast approximate solution of the inverse problem within intervals of selected layers with constructing a geoelectrical section. The command is used for groups of layers for the fast estimation of parameters of the space immediately adjacent to a borehole. The inversion results are considered as a starting model for automatic and manual fitting. · Fitting. The command is used to start inversion for groups of layers. It is the basic function of the system that is peculiar for constructing a geoelectrical section. The following parameters are determined: resistivities of formations, invaded zones, and bordering zones, as well as the radii of cylindrical boundaries. · Interval. It is the function for layer-by-layer inversion for an individual interval. The function is used as for groups of layers so for individual layers. It is accompanied by estimating the accuracy of determination of geoelectrical parameters and calculation of confidence intervals for the resistivity of formation and that of an invaded zone, as well as the invaded zone radius. The fitting quality is characterized by the relative deviation of the experimental values of phase differences for all probes from the theoretical ones in mean square root sense. · Stop. The command interrupts group operations (Express and Fitting). Estimations menu contains the following commands (Fig. A.5): · Mean deviation. Determining the relative mean square root deviation for evaluation of fitting quality. · Confidence intervals. Estimating the confidence intervals for three model parameters: the formation resistivity, resistivity and radius of an invaded zone. · Radial depth. Estimating the radial depth of investigation. Import of Files The command is used for data input. To execute this command, Import command from File menu or the appropriate icon on a tool bar is used. The standard window for selecting data appears on the screen.

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Fig. A.5. The Estimations menu.

The further steps are: · Open the directory with data files, select the data file and click Open button. · To cancel the data input, click Cancel button. The system can distinguish the following types of files. LAS VKZ DAN and LST

— file contains all logs. — file of the system that contains the whole information about current state of the system. — files contain inclinometry data.

Export of Data When executing this command, the initial data and inversion results are saved. The function is executed by Export command from File menu or by clicking appropriate button on a tool bar. The standard window for saving Export of files file appears on the screen queering the filename. The further steps are: · Open the directory in which data should be saved, input the new filename, and click Save button. · To cancel the function, click Cancel button. The system permits the following types of files to be saved: VKZ

—

inner format of VIKIZ and additional methods.

LAS

—

inversion results are added to the file during export.

ROK

—

file is created according to the rules of LAS file standard. Apart from initial logs of phase differences, the file contains their transformations into apparent resistivities.

XLS

—

file in the Excel 97 format. The file is used for passing data into the Excel.

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Appendix

RES

—

file of inversion results containing depths, reading values, and model parameters obtained (resistivities of cylindrical zones and radii of their boundaries), mean square-root deviation values of the model curves from experimental curves.

Printing Log Copies For printout of logs and results of formation resistivity determination, the following steps should be done: · Perform print settings (see Settings command, Print bookmark). · Choose Print command from File menu or click the appropriate button on a toolbar. Point the range of page output to a printer and the number of copies. · Set up the printer, if necessary. · To execute the command, click OK button. · To cancel the command, click Cancel button. The provision is made for the control of hard copy output and preview of logs by Preview command from File menu. Settings System Parameters The system allows one to setup and change parameters that control the work of some system functions: · Print out of hard copies (Print bookmark). · Processing (Parameters bookmark). · Additional methods (Reference book bookmark). · Visualization of VIKIZ logs (VIKIZ probes bookmark). For changing parameters, the following actions are required: · Choose Settings command from File menu or click the appropriate button on a toolbar. · Select the necessary bookmark. For changing printout parameters, the following actions are required: · Choose Settings command from File menu, select Print bookmark or click the appropriate button on a toolbar. · Point the print type: color or black-white. · In Upper boundary or Lower boundary fields, point the upper and lower boundaries of the log fragment to be printed. The right and left boundaries are fixed. · In Output box, point the paper type: pages or long paper depending on either a printer or plotter is used. · In Range box, in fields From and To, point the range of the log fragment to be printed. For printing the whole log, tick off All range. · To execute the function, click OK button. · To cancel the function, click Cancel button.

100

Fig. A.6. Processing parameters.

To change processing parameters (Fig. A.6), the following actions should be performed: · Choose Settings command from File menu, select Parameters bookmark and point the corresponding data in fields: Borehole radius, Measurement error, Minimum layer thickness, Mud resistivity, and Resistivity range. · To execute the function, click OK button. · To cancel the function, click Cancel button. Reference book contains the list of logs with their indexes and visualization parameters needed for their correct displaying (Fig. A.7). For changing parameters of additional methods, it is necessary to select Reference book bookmark from Settings command of File menu. Along with the log index (Name) of an additional method, Reference book provides Aliases by which identification is also executed. Reference book contains also Measure units, i.e., information about measurement units for each log and Description, i.e., the brief description of this method. Two parameters are used when visualizing: the visualization coefficient Visual Coeff. and the value on zero line X0.

Notice: the list of additional methods can be corrected and extended. To execute this operation, click either Apply or Cancel buttons and perform the appropriate settings. To change display parameters of VIKIZ logs, choose Settings command from File menu, select VIKIZ probes bookmark, point the appropriate probe and perform the following settings: · Point the VIKIZ probe which log is set up. · Put the flag in the non-active field if the probe data will not be used in the inversion. · The provision is made for masking one or two probes, but in this case, the inversion accuracy may be significantly decreased.

101

Appendix

Fig. A.7. The reference book.

· In Color field, display color codes for logs can be chosen. By default, the following codes are settled: red, green, brown, blue and black for the probes with the spacing of 0.5 m, 0.7 m, 1.0 m, 1.4 m, and 2.0 m, respectively. · Visualization parameters for each probe are set individually by introducing the parameters in X0 and Visual coeff. fields: the initial value and visualization coefficient, respectively. By clicking Apply to all, visualization parameters of the current probe are set for all probes. · In Measurement error field, it is necessary to define the relative measurement error of the selected probe readings. Scale The independent change in horizontal and vertical scales is a peculiarity of visualization in the main window. The horizontal scale is set up by the visualization parameters of logs (Settings command from File menu, VIKIZ probes and Reference book bookmarks). To change the vertical scale, Scale command from View menu should be executed and then the required scale values should be indicated. The scale used by default is 1:200. The acceptable values of the vertical scale are 1:100; 1:200; 1:500; 1:1000. Boundaries The function is used for visualization of layer boundaries in the main window. The visualization mode is chosen by Layer boundaries command from View menu.

102 Legend This function displays the probe color codes and color palette for the apparent resistivity. The legend visualization mode is chosen by Legend command from View menu by clicking the appropriate button on a toolbar. Transformation of Logs The system provides displaying logs in two forms: · phase difference units (degrees); · apparent resistivity units (ohm × m). An interpreter can use both forms depending on the problems being solved. For viewing data in the values being measured (phase differences) or their transformations (apparent resistivities), choose Phase difference command or Apparent resistivity one from View menu or click the appropriate button on a toolbar. The system provides the linear scale for phase differences and logarithmic one for apparent resistivities. By default, logs are displayed in phase difference form. Filtering Filtering is intended for elimination of pulse (short period) noises and smoothing out logs. Filtering is based on algorithms of median smoothing and filtering. For applying the filter, choose Filtering command from View menu or click the appropriate button on a toolbar. Filtering command is executed during the whole session of the system operating until the command is cancelled. Locate Boundaries The key to the analysis and inversion of log data is defining the location of layer boundaries. The correctness of performing this procedure stipulates in considerable measure the quality of results obtained. In the system there is realized procedure of defining layer boundaries based on vertical resolution that takes into account behavior of three probes of medium length when passing the horizontal boundary. In the case if the layer thickness is less than value that has been set in parameters, it is impossible to execute inversion for this interval. To define coordinates of boundaries, it is necessary to choose Add boundaries command from Boundaries menu or to click the appropriate button on a toolbar The provision is made for manual correction of the boundary position that supports the automatic procedure of layer definition. In this case, it is possible to add, delete, or drag a boundary. To accomplish this procedure, it is necessary to click the log area by pressing the right mouse button. Then the context menu that appears permits the following functions to de chosen: Add boundary and Delete boundary. To change the boundary depth, it is necessary to drag the boundary using a mouse.

103

Appendix

Add/Delete Boundaries When operating with the log fragment, there is possible to add or delete boundaries within the indicated interval: · Chose pears).

Add/Delete Boundaries command (Add/Delete Boundaries window ap-

· In fields From and To, point the starting and final depths of the interval. · Click Add button to add boundaries in the indicated interval. · To delete boundaries within the indicated interval, click Delete button. · To cancel the function, click Cancel button. Select Layers Inversion procedures can be applied as to a single interval so to the group of intervals. The system allows selection of layers within the resistivity range of interest, as an example, water-saturated, oil-saturated, and gas-saturated formations. Criterion for selection of layers in this case is based on mean values of apparent resistivities for the long probe within the interval under consideration. To select layers with the defined resistivity, Select layers command from Layers menu should be chosen. Select layers window appears. The following actions are: · In Minimum and Maximum fields, point the minimum and maximum resistivity values (the possible resistivity values are in the range from 1 to 200 ohm × m). · To select layer boundaries of the indicated interval, press Enter key. · To cancel the function, click Cancel button. Layers can be selected by another way. When clicking with a mouse on the left area of a log, the current layer becomes selected. Using Shift and Ctrl keys, a group of layers can be selected. When a layer or group of layers is selected, average layer values of probe readings are taken automatically (Fig. A.8). The special algorithm that is used in the most cases allows the

Fig. A.8. Taking average layer values.

104 shoulder bed effect, probe eccentricity, and other factors to be taken into account. The chosen values are displayed on logs in the form of vertical lines which color is the same as that of corresponding probe log. Provision is made for manual correction of taken values. To do it, drag with a mouse the needed value to the left or right. It should be noted that manual correction of chosen values is impossible if logs are displayed in the apparent resistivities. The system provides Select layer and Unselect layer functions. To do it, click on the log area by pressing the right mouse button, then the context menu that appears allows Unselect layer function to be chosen. Inversion is executed only for selected layers. To unselect a layer, click the selected layer part by pressing the right mouse button. In doing so, color of the layer part becomes darker. The layer is selected through the reverse sequence of actions. To select or unselect all layers, Select all layers function or Unselect all layers function from Layers menu is used. Add and Delete Layers For inversion of the whole log, all intervals should be selected. To do it, choose All layers command from Layers menu. In this case, all intervals between extreme boundaries are selected. The layers which thickness is less than the value preset in settings parameters can not be resolved. To delete data on selected layers and taken values, execute Delete all layers command from Layers menu. Inversion The concept of interactive processing is realized in the system. Inversion can be executed automatically, semi-automatically, or manually. In automatic mode, the fast approximate solution of the inverse problem with construction of a geological section is envisaged. The results are considered as an initial guess for automatic inversion. If an interpreter executes automatic fitting without a starting model, the system itself performs this operation without visualizing intermediate results. For operating with individual layers, the system provides the special graph containing elements of both automatic and manual inversion The functions listed above are realized by the following commands from Inversion menu: Express, Auto, Interval (Fig. A.4). The choice of conditions is determined by the problem being solved. The standard processing graph turns on the automatic mode either all intervals are processed with subsequent correction for complex fragments of logs or in the case of significant deviations of experimental data from theoretical ones. Inversion is always accompanied by estimation of fitting quality and values of confidence intervals. With this aim, the system provides the special functions. The residual function is a proximity criterion of experimental and theoretical data r )  S =

Ä Dj - Dj à ÅÅ Dj dDj = Æ 

W

H

L

L

H

L

L

L



Ô ÕÕ , Ö

here D j , D jLH are model and measured phase difference values, respectively, d D j is the relative measurement error which value is determined from the metrological characteristics W

L

L

105

Appendix

of a tool (the mean d D j values for commercially available tools are as follows; d D j = 0.03, d D j  = 0.04, d D j  = 0.02, d D j  = r0.02, d D j  = 0.02). Data inversion is a procedure of r minimization of the functional )  S by fitting model parameters S . In the system, the minimization method (Nelder-Mead) is applied for minimization along with the method of singular decomposition of sensitivity matrix. L

Express To obtain the fast approximate solution of the inverse problem for selected intervals with constructing a geoelectrical section, it is necessary to choose Express command from Inversion menu in the window of results or to click the appropriate button on a toolbar. The procedure is used when inversion is executed for groups of layers for fast estimating the near borehole space structure. The results of express-inversion are used as a starting model for subsequent manual or automatic fitting. The express-inversion is based on the heuristic algorithms. Thus, investigation of field data and mathematical modeling of tool responses in cylindrically layered one-dimensional media show that the class of models often can be uniquely predicted by behavior of sounding curves. Taking into account weak borehole effect on signals, it is also possible to fit approximately the model parameters using the set of two-layer charts. Such an approximate approach operates very fast and that is sometimes sufficient to obtain required inversion quality. As a result of fast solution is an approximate geoelectrical section, which is displayed in the right part of the main window (Fig. A.9). The interval shown in the Figure includes the shaly layer with the resistivity about 3 ohm × m.

Fig. A.9. Express-inversion.

106

Fig. A.10. Automatic fitting.

Automatic fitting The automatic fitting procedure is applied for inversion of logs corresponding to groups of layers. It is the basic function of the system that is used for construction of a geoelectrical section The parameters being determined are resistivity of formations and those of both an invaded zone and a bordering zone, as well as the radii of cylindrical boundaries. To execute automatic layer-by-layer inversion within interval of selected layers, choose Auto command from Inversion menu or click the appropriate icon on a toolbar. On finishing the automatic fitting, a geoelectrical section is displayed in the right of the main window and the values of mean deviations of field logs from synthetic ones are displayed in the window of estimations of results. An example of inversion of the oil-saturated interval with the shallow zone of increasing invasion (riz =27–40 ohm×m, the invaded zone thickness is 0.45–0.65 m) is shown in Fig. A.10. The resistivity of formation without invasion varies from 5 up to 11 ohm ×m. After automatic fitting is completed, it is recommended to repeat inversion for intervals where the mean square root deviation exceeds the preset limit. The value of the permissible error is determined from specifications of the tools and the geological problem being solved. As a rule, the mean square root deviation less than 2 % is considered as satisfactory. The fitting quality is conditioned by the value of relative mean square root deviation of experimental sounding curves from theoretical ones, and the inversion accuracy is conditioned by the range

107

Appendix

of confidence intervals. The procedures provided for visualization and analysis of these characteristics are combined in Estimations menu. Interval The system allows layer-by-layer inversion within every separate interval. To do it, choose Interval command from Inversion menu or click the appropriate icon on a toolbar. The window of inversion for a single interval appears. Fig. A.11 shows an example of inversion for water-saturated formation. The formation is characterized by the developed zone of increasing invasion. The zone radius is 0.58 m and its resistivity is 33.9 ohm × m, the formation resistivity is 4.0 ohm × m. Further we shall describe in details the working inversion window. On the left of the window there are the following elements. Sounding curve. A sounding curve represents results of five measurements, which are disposed in the order of successively greater probe spacing. Measured phase differences have been transformed into apparent resistivities. That reflects the resistivity distribution from a borehole to the formation part without invasion. There are vertical bars on an experimental curve, the length of the bars reflecting measurement errors. Below the sounding curve, Mean deviation (mean square root deviation) is displayed by which the proximity degree between field and synthetic sounding curves is characterized. At the bottom of the window there are program control buttons.

Fig. A.11. Inversion for a single interval.

108 Start: executes Fitting command. Stop: stops Fitting command. Close: returns into the main program window. On the right of the window there are additional functions for the control of inversion parameters. Window of model parameters. Values of thickness of cylindrical zones and their resistivities are displayed. Fields: Invaded zone and Bordering zone. With a help of these fields, a model class (two-layer, three-layer, or four-layer) can be determined. Fixed/varied. This command permits the part of model parameters to be fixed. In this case, when fitting, non-fixed parameters only are changed. Geoelectrical model. In the right window, a geoelectrical model characterizing the spatial resistivity distribution is displayed. An example of operating within the interval of the productive formation is shown in Fig. A.12. The sounding curve corresponds to the model with increasing invasion and the formation resistivity of 22.2 ohm × m. The mean square root deviation that is 0.0 % shows the best fitting quality. Here the possibility to fit model parameters is shown by an example of the productive formation with a bordering zone. Borehole parameters and the bordering zone resistivity do not change when fitting. The bordering zone resistivity is 8.0 ohm × m (the shaded cell in the table) is fixed.

Fig. A.12. An example of inversion for a single interval.

Appendix

109

Fig. A.13. Estimation of confidence intervals.

Estimations of Results The system realizes the functions for estimating the fitting quality (by the value of the relative mean square root deviation) and confidence intervals for three model parameters: the formation resistivity, the resistivity and radius of an invaded zone. For displaying the mean square deviation and confidence intervals, Estimations menu should be selected. · For displaying the relative mean square root deviation, choose Mean deviation (mean square root deviation) command from Estimations menu. · For displaying the confidence intervals for one or another parameters, choose Confidence interval command from Estimations menu. Both the mean deviation and confidence interval commands can be executed by another way. To do so, click the window of estimations by pressing the right mouse button, then a context menu appears. The menu allows the following functions to be chosen: Mean deviation, Confidence intervals, Layer resistivity, and Zone radius. Estimation of confidence intervals permits the data on correctness of inversion results to be obtained based on the statistical representations of experimental data. The procedure calculates the allowable range of model parameters (Fig. A.13). The parameter values are shown by solid lines and the confidence intervals are shown by dotted lines. The confidence interval value is determined as by measurement errors so by model properties.

110

R E C O M M E N D E D L I T E R AT U R E 1. Antonov Yu.N. High-frequency induction log isoparametric sounding // Soviet Geology and Geophysics, 1980, vol. 21, no. 6, p. 71–78. 2. Antonov Yu.N. Vertical characteristics of isoparametric well logging // Soviet Geology and Geophysics, 1981, vol. 22, no. 5, p. 106–111. 3. Antonov Yu.N. and Zhmaev S.S. Geophysical study of oil wells by electromagnetic sounding // Soviet Geology and Geophysics, 1986, vol. 27, no. 1, p. 111–119. 4. Antonov Yu.N. and Zhmaev S.S. First results if induction logging by isoparametric sounding // Soviet Geology and Geophysics, 1982, vol. 23, no. 5, p. 43–49. 5. Antonov Yu.N., Zhmaev S.S., and Rastorguev V.N. The first appempt at electromagnetic core sounding in Western Siberia // Soviet Geology and Geophysics, 1983, vol. 24, no. 9, p. 55–59. 6. Antonov Yu.N. and Krivoputsky V.S. Modeling of probes of isoparametric sounding // Soviet Geology and Geophysics, 1981, vol.22, no.10, p.114–117. 7. High-Frequency Unduction Logging Isoparametric Sounding (methodical recommendation) [in Russian], Novosibirsk, IGG SB AS USSR, 1979. 8. Yeltsov I.N., Sobolev A.Yu., and Nedel’ko V.M. Development of LAS-Standard and the LASMAKER Program [in Russian] // Karotazhnik, 1999, no. 54, p. 75–83. 9. Patent of Russian Federation No. 20663053 of 22 Sept. 1994. The equipment for Electromagnetic Induction Sounding [in Russian]. The Patentee is Institute of Geophysics, SB RAS (by Yu.N. Antonov). 10. The State and Ways for Development of Electromagnetic Logging. Materials of Conference [in Russian]. Novosibirsk, SPC of the UIGGM SB RAS, 1998, 98 p. 11. Taborovsky L.A., Epov M.I., and Sosunov O.G. Estimation of Resolution of Electromagnetic Methods and Suppression of Noise in Systems of Repeated Observations (Theory, Algorithms, and Programs) [in Russian]. Novosibirsk, IGG SB AS USSR, 1985, no. 27, 48 p. 12. Electrical and Electromagnetic Methods of Investigation in Oil and Gas Boreholes. Proceedings of Conference: Development and Efficiency Improvement of Electrical and Electromagnetic Methods of Investigation in Oil and Gas boreholes [in Russian]. Novosibirsk, UIGGM SB RAS, 1999, 334 p. 13. Epov M.I., Yeltsov I.N., and Sobolev A.Yu. Location of Formations in Terrigenous Section by VIKIZ Data [in Russian] // Karotazhnik, 1999, no. 57, p. 58–69. 14. Epov M.I. and Martakov S.V. Forward two-dimensional Problems of Electromagnetic Logging // Russian Geology and Geophysics, 1999, vol. 40, no. 2, p. 250–255. 15. Epov M.I. and Nikitenko M.N. System of 1D interpretation of HF induction log data // Russian Geology and Geophysics, 1993, vol. 34, no. 2, p. 119–125.

CONTENTS 1. KEY GEOLOGICAL AND GEOPHYSICAL PROBLEMS SOLVED BY THE VIKIZ METHOD .......................................................................................................... 2. PETROPHYSICAL DESCRIPTION OF THE TARGETS UNDER INVESTIGATION GEOLOGICAL AND GEOPHYSICAL MODELS .......................................................................... 2.1. Geological Models of Terrigenous Reservoirs ........................................................................... 2.2. Petrophysical Features of Oil and Gas Reservoirs of West Siberia ............................................... 2.3. Basic Geoelectrical Models and Their Typical Characteristics ................................................... 3. THEORETICAL FUNDAMENTALS OF THE METHOD. VIKIZ RESPONSES IN HETEROGENEOUS MEDIA ................................................................................................. 3.1. Focusing Systems in Electromagnetic Logging ......................................................................... 3.2. Phase Difference and Its Relation to the Resistivity of an Uniform Space. Apparent Resistivities ........................................................................................................... 3.3. The Uncertainty of Model Parameter Prediction as a Function of Measurement Errors 3.4. Typical Sounding Curves ....................................................................................................... 3.5. Typical Logs ......................................................................................................................... 3.6. General Limitations on Electromagnetic Sounding Methods .................................................... 4. EQUIPMENT. CERTIFICATION AND METROLOGICAL VERIFICATION .................................. 4.1. Spatial Layout of the Probe Array Elements ............................................................................. 4.2. Scheme of the Tool ............................................................................................................... 4.3. Borehole Tool and Surface Panel Functioning ........................................................................ 4.4. Metrological Verification ....................................................................................................... 5. SPATIAL RESOLUTION CHARACTERISTICS ............................................................................ 5.1. Radial Characteristics ............................................................................................................ 5.2. Radial Investigation Depth of Sounding .................................................................................. 5.3. Vertical Characteristics .......................................................................................................... 5.4. Effect of Probe Shift from the Borehole Axis on Measured Signals ............................................ 6. LOG QUALITY CONTROL .......................................................................................................... 6.1. The General Requirements .................................................................................................... 6.2. Calibrating Levels ................................................................................................................. 6.3. Repeated Measurements ........................................................................................................ 6.4. Initial Phase Shifts of Probes .................................................................................................. 7. QUALITATIVE EVALUATION OF A GEOLOGICAL SECTION ..................................................... 7.1. Lithological Subdivision of a Section. Selection of Tight Beds ................................................... 7.2. Selection of Reservoir Rocks and Evaluation of Saturation Type ................................................ 7.3. Dynamics of Invaded Zone Occurrence .................................................................................. 8. FUNDAMENTALS OF QUANTITATIVE INTERPRETATION ....................................................... 8.1. Typical Examples of Interpretation ......................................................................................... 8.2. Log Interpretation in the Case of Highly Conductive Drilling Mud ...........................................

14 17 18 21 27 29 – 30 32 34 36 – 41 43 50 52 – 53 53 – 57 58 60 68 78 79 87

APPENDIX MFS VIKIZ SOFTWARE TOOL FOR PROCESSING AND INTERPRETATION OF VIKIZ LOGS ............................................................................................................................ 1. The General Description .......................................................................................................... 2. Hardware and Software ............................................................................................................ 3. The Main Program Window Description ................................................................................... 4. The Basic Service Function of the System .................................................................................. RECOMMENDED LITERATURE ..................................................................................................

92 – 93 – 95 110

3 4 – 5 7 13 –