ABSTRACT The focus of this study is an active gas -producing field. Lithology consists of inter-layered carbonates along with fine-grained clastics and shales. Recent wells have been drilled with water-base muds of salinities close to 2,000 ppm. On the other hand, the salinity of the connate water is very high, of the order of 200,000 ppm. Two major challenges faced in the petrophysical evaluation of these reservoirs are: (1) deep mud filtrate invasion beyond the depth of investigation of the induction logging tools, and (2) low deep resistivity readings which cause biased estimates of in-place gas reserves. The low deep resistivity readings have been attributed to the presence of a low resistivity annulus around the borehole. However, the origin and extent of the annulus have never been explained from basic petrophysical principles. A consistent exp lanation of this phenomenon is presented in this paper based on the physics of mud-filtrate invasion. A 30 ft -thick carbonate formation in a key well was selected as a representative zone. Gas saturation of this formation is about 80-85%. The process of mud-filtrate invasion was modeled with a two-dimensional chemical flood simulator that included the effect of salt mixing between mud filtrate and connate water. Extensive core and well-log data were used to constrain petrophysical parameters such as porosity, absolute permeability, relative permeability, and capillary pressure during the simulations. In addition, samples of mud and mud filtrate provided adequate information to constrain fundamental parameters governing the process of invasion such as mud cake growth and effective flow rate across the mud cake. Radial resistivity profiles were obtained from the simulated profiles of water saturation and salt concentration using Archie’s law. These profiles clearly showed the presence of a low-resistivity annulus in the transition region between the flushed and virgin zones. Numerical simulation of induction logs was performed to validate the agreement between the mud-filtrate invasion model and the available wireline induction

logs. These log simulations provided a way to further constrain the parameters governing the process of mud-filtrate invasion, especially time of invasion. An extensive sensitivity analysis was performed to quantify the effect of additional petrophysical parameters, such as capillary pressure and relative permeability, on the radial profiles of water saturation and salt concentration. Results from this study show that standard induction tools are extremely sensitive to a low-resistivity annulus, which effectively reduces their depth of penetration and hence cannot accurately determine gas saturation in the virgin zone. It was also found that the pre-annulus and annulus segments of the resistivity profile remained insensitive to initial water saturation, thereby impeding an indirect estimation of in-situ gas saturation. By contrast, laterolog measurements remain only slightly affected by the presence of a low-resistivity annulus. The sensitivity analysis described in this paper provides a rigorous quantitative method to assess chemical effects of different types of muds on the invaded zone prior to drilling. It also provides a means to design and time borehole logging operations and interpretation procedures that can yield accurate estimates of in-situ petrophysical variables in the presence of deep invasion. INTRODUCTION The drilling of wells with heavy mud causes large overbalance pressures, resulting in deep invasion of mud filtrate into porous and permeable layers. In the past, the effect of mud filtrate invasion on induction logs has been studied using simplified models of radial invasion. The simplest invasion model is the step invasion profile, which assumes a completely flushed zone of resistivity Rxo and diameter Di, beyond which lies the undisturbed (virgin) formation of resistivity, Rt. Such a model embodies three unknowns (Rt, Rxo, and Di) that, in theory, can be resolved using three resistivity logs exhibiting complementary depths of investigation. This is a useful but idealistic approach because a sharp boundary seldom exists between the

A CASE STUDY INTEGRATING THE PHYSICS OF MUD-FILTRATE INVASION WITH THE PHYSICS OF INDUCTION LOGGING: ASSESSMENT OF IN-SITU HYDROCARBON SATURATION IN THE PRESENCE OF DEEP

INVASION AND HIGHLY SALINE CONNATE WATER

Bovan K George, Carlos Torres-Verdín, and Mojdeh Delshad, The University of Texas at Austin Richard Sigal and Farid Zouioueche, Anadarko Petroleum Corporation

Barbara Anderson, Schlumberger-Doll Research

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completely flushed zone of resistivity Rxo and the undisturbed formation of resistivity Rt. Actual radial invasion and resistivity profiles can be quite complex and largely depend on specific petrophysical properties of the rock as well as on the static and dynamic properties of the fluids involved. The study presented in this paper is focused on a gas -bearing carbonate formation in well X-2 that was drilled using a heavy fresh water base mud (Table 1), causing an overbalance pressure in excess of 1000 psi. Lithology in the gas-bearing zone consists of inter-layered carbonates along with fine-grained clastics and shales. Porosities of gas -bearing formations are low, usually less than 15%, hence contributing to deep invasion. A major challenge faced in the evaluation of this reservoir is the deep invasion of mud filtrate adversely affecting the response of resistivity measurements. Gas saturation of the formation is about 80-85% with the remaining pore space occupied by the irreducible connate water. Salinity of the mud filtrate is about 2,000 ppm whereas the salinity of connate water is about 200,000 ppm. Dual Induction Logs (DIL∗ ) acquired in this well X-2 (Figure 1) exhibit a reverse resistivity profile where deep dual-induction (ILD) readings (20-22 ohm-m) are lower than the medium dual-induction readings (ILM, 25-30 ohm-m). Both ILD and ILM readings are lower than the shallow, Rxo, readings (90-100 ohm-m) indicated by MSFL and SFL. A nearby well, here referred to as X-1, was drilled a few hundred feet away from well X-2. This well was drilled with a light mud (Table 2) resulting in very shallow invasion. Resistivity logs acquired in well X-1 showed a normally ordered resistivity profile across the same formation (Figure 2) with the following array induction (AIT∗ ) readings: AIT90=50-60 ohm-m, AIT60=40-50 ohm-m and AIT10=30-35 ohm-m. In addition to Array Induction data, Dual Laterolog (DLL∗ ) data were acquired in well X-1 (Figure 3). Well X-1 is considered a key well in the present study due to both negligible invasion and the availability of extensive log and core data. Core and well-log data acquired in well X-1 are used as a benchmark in the present work. This well provides a unique reference to quantify the effect of mud filtrate invasion on the resistivity logs acquired along the same formation in well X-2. Lower-than-normal deep resistivity readings cause overestimation of connate-water saturation, which results in underestimated hydrocarbon reserves. The study reported in this paper was undertaken to quantify the effect of mud filtrate invasion on resistivity logs. It ∗ Mark of Schlumberger.

was hoped that proper modeling of the mud-filtrate invasion profile would help correct deep resistivity readings and hence improve estimates of in-situ water saturation using existing well-log data. Preliminary studies performed prior to the work reported in this paper had suggested the presence of low resistivity annulus as the cause for the low resistivity readings in well X-2. Presence of a low resistivity annulus was discussed in the past by several authors, including Dumanoir et al., 1957, Gondouin et al., 1964, Ramakrishnan and Wilkinson, 1996, and Zhang et al., 1999. However, a petrophysical explanation for the origin and properties of such an annulus has not been presented before, especially in light of field data. In this paper, a consistent explanation is developed for the presence of a low resistivity annulus based on the physics of mud-filtrate invasion and salt mixing between mud filtrate and irreducible connate water. Invasion of mud filtrate into the formation is modeled as a two-dimensional (2D) axisymmetric chemical flood process. Filtrate invasion is simulated to obtain water saturation profiles as a function of radial distance away from the borehole wall. A radial salinity profile is also obtained by modeling the mixing of salt between the invading fresh mud filtrate and the highly saline connate water. This simulation approach yields an advancing water saturation front whose salinity increases radially into the formation. Radial variation of salinity within the invasion front is responsible for the presence of a low resistivity annulus around the borehole. NUMERICAL SIMULATION OF MUD-FILTRATE INVASION Mud filtrate invasion is treated as a water injection process into a gas reservoir wherein two-phase immiscible fluid flow is assumed in the simulations (Dewan and Chenevert, 2001, and Semmelbeck et al., 1995). Rate of invasion of mud filtrate is calculated as a flow rate function resulting from the mud cake buildup (Wu et al., 2001). The flow of mud filtrate through mud cake can be described by Darcy’s law, i.e.

fQ = µkA

mchP∆ , (1)

where fQ is the flow rate of mud filtrate across the borehole wall, k is the mud cake permeability, A is the cross-sectional area through which the filtrate flows, µ is the viscosity of filtrate, mch is the thickness of mud cake, and P∆ is the pressure drop across the mud cake. In this paper, flow of mud-filtrate across the mud cake is modeled using an axisymmetric version of the 3D multi-phase, multi-component comp ositional simulator UTCHEM, developed by The University of Texas at

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Austin (Saad, 1989, and Delshad et al., 1996). Both dynamic growth of mud-cake thickness and dynamic decrease of mud-cake permeability are coupled to formation properties (Wu et al., 2001). This process results in a dynamic monotonic decrease of flow rate across the borehole wall. After a short initial spurt of mud filtrate invasion, the rate of flow is found to reach a steady state value specific to a particular layer. The simulation of mu d filtrate invasion can also take into account several cycles of mud-cake rub-off and buildup. In the present work, the layer-dependent rate of mud-filtrate invasion is assumed to be the steady-state value yielded by the simulations of invasion. The assumptions made by the model are: (a) local thermodynamic equilibrium, (b) slightly compressible fluids, (c) Fickian dispersion, and (d) Darcy’s law. The general form of the mass balance equation for the k-th component can be written as

( ) k

n

lkllklkkk RDuCC

t

p

=

−⋅∇+

∂∂ ∑

=1

~ρρφ , (2)

where φ is porosity, kC is the overall concentration of

component k per unit pore volume, klC is the

concentration of component k in phase l , kρ is

density, lu is the Darcy flux for phase l , Rk is the total

source/sink term for component k and klD~ the

dispersive flux, defined as

klkllkl CKSD ∇⋅= φ~ , (3)

where lS is the saturation for phase l , and

klK is a

dispersion tensor. In the present work, the assumption of a slightly compressible fluid is justified for a gas-water mixture by the relatively low in-situ reservoir pressure (96 psi). At this value of pressure, the compressibility of gas becomes negligible for all practical purposes. Salt mixing between mud filtrate and connate water is modeled as part of the fluid-flow simulations performed with UTCHEM. As the invading mud filtrate moves radially away from the borehole wall, it mixes salt with connate water through convection and dispersion. The dispersive mixing on a pore scale is the outcome of uneven fluid flow through pores, local velocity gradients, mechanical mixing, and molecular diffusion. The dispersion tensor

klK , which includes molecular diffusion, can be written as (for the i and j directions):

( )l

ljli

l

TlLll

l

Tlklklij u

uu

Siju

Sij

DK

φ

ααδ

φ

αδ

τ

−++≡ , (4)

where klD is the molecular diffusion coefficient, τ is a

tortuosity factor, Lα and Tα are the longitudinal and transverse dispersivities,

ijδ is the Kronecker delta

function and liu and lju are the component of Darcy

velocity of the phase l in the i and j directions, respectively. The first term in equation (4) is due to diffusive transport and the second term in the same equation represents dispersion due to convective transport. For very small flow rates of mud filtration, the convective term becomes negligible and the total mixing is caused mainly by diffusion. For higher flow rates where the interstitial velocity is greater than about 3 cm/day (Lake, 1989), convective mixing dominates diffusive mixing. This is because for large fluid velocities in the pores, time available for diffusion will not be sufficient for complete mixing. In the present work, the flow rate of mud filtration taking place across a layer of thickness 2 ft is about 8 ft3/day. This corresponds to an interstitial velocity of about 320 cm/day near the borehole wall assuming a porosity of 0.14. At such large interstitial fluid velocities, mixing is predominantly due to convective transport. Cylindrical flow is assumed for the numerical simulation of mud-filtrate invasion near the borehole. Variable grids with smaller grid sizes near the borehole are used to capture the finer variations in water saturation and salinity. The radial profiles for water saturation and salt concentration are obtained directly from the simulation results. In turn, salt concentrations are converted into equivalent values of connate water resistivity, Rw, using the conversion formula (Dresser Atlas Inc., 1982):

WR =

+

955.0

5.36470123.0

WC 398.182

+T, (5)

where T is temperature measured in degrees Centigrade, and Cw is salt concentration measured in ppm. WATER SATURATION AND ELECTRICAL RESISTIVITY IN THE INVADED ZONE As described in the preceding section, radial profiles of water saturation and salt concentration are obtained as the output of the numerical simulation of mud-filtrate invasion. In turn, values of water salinity and salt concentration are converted into an equivalent value of water resistivity using equation (5). The final step is to compute the corresponding value of electrical resistivity. This is accomplished using Archie’s equation, namely,

mt

wnw

aRR

Sφ

= , (6)

where Sw is water saturation, a is the tortuosity/cementation factor, n is the saturation exponent, φ is porosity, and m is the cementation exponent. The use of Archie’s law in the present study is justified given the clastic nature of the carbonate sequence under consideration. Also, the high salinity of

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connate water makes it unnecessary to apply corrections for the presence of clay to Archie’s equation. Tables 3a and 3b contains a summary of specific values used in this study for the various parameters included in equation (6). Simulation of mud-filtrate invasion was performed on a 5-layer synthetic model reconstructed from the depth interval X493-X551 ft of Well X-2 shown in Figure 1. Two of these 5 layers were placed on the upper and lower boundaries of the model and consisted of impermeable shale barriers (Figure 4). The remaining 3 layers in the interval X506-X536 ft, corresponded to separate flow units within the actual formation. Additional numerical layers were included within the 3 permeable layers to secure accurate results rendered by the numerical simulation of mud-filtrate invasion. Capillary pressure data (Figure 5) from laboratory measurements for the drainage cycle is available for the above layers. Because of the lack of laboratory capillary pressure for the imbibition cycle, the available drainage-cycle data were used in the numerical simulations for both imbibition and drainage cycles of capillary pressure. The relative permeability data used for the simulations is shown in Figure 6. Figure 7 shows the calculated radial profiles of water saturation and water resistivity along the middle of the 5-layer model described in the previous paragraph. Petrophysical properties of this layer are given in Tables 3a and 3b. The invasion profile shows a depth of invasion of about 7 feet, whereas the salinity profile, represented as Rw, shows that salinity near the borehole is very low, equal to that of mud filtrate. Salinity begins to increase at a radial distance of about 4 feet from the borehole wall and it attains a maximum value (equal to that of the salinity of connate water) at a radial distance of about 6 feet from the borehole wall. It becomes evident from Figure 7 that the salinity front trails the saturation front as the invasion progresses. This behavior results in a high-salinity, high water saturation region, at the front face of the advancing mud-filtrate column, thereby originating a low-resistivity annulus. The electrical resistivity profile (Rt) calculated with the use of equation (6) shows a low resistivity annulus at a distance of about 5 feet from the borehole wall (Figure 8). This annulus is formed in the overlapping region of the radial profiles of water saturation and water resistivity. The deep resistivity log, with a depth of investigation of about 5-6 feet, for the most part is sensing the annulus region of low resistivity. On the other hand, the shallow resistivity log senses the higher resistivity of about 110 ohm-m closer to the borehole. This model agrees with the observed deep (ILD=20-22 ohm-m), medium (ILM=25-30 ohm-m) and shallow (MSFL=90-100 ohm-m) resistivity readings reported by the field log and shown in Figure

1. The true resistivity of the formation is about 90 ohm-m, a value that is much higher than the measured deep induction resistivity (20-22 ohm-m). Water saturation calculated using the true formation resistivity is about 15% whereas that calculated using the deep induction measurement is about 28-30%. Therefore, reservoir evaluation performed with the deep induction measurements in the presence of a low resistivity annulus, results in underestimation of in-place hydrocarbon reserves. SENSITIVITY OF THE RADIAL INVASION PROFILE TO VARIOUS PETROPHYSICAL PARAMETERS A detailed sensitivity analysis was performed to assess the effects of various rock and fluid parameters on the simulated radial profile of electrical resistivity. Reference formation and fluid properties used in the simulations are summarized in Tables 3a and 3b. The sensitivity analysis described below consisted of making slight changes to the benchmark parameters and assessing the influence of such changes on the simulated profile of electrical resistivity. Results from this sensitivity analysis are summarized in Table 4. Figure 9 illustrates the sensitivity of the resistivity profile to invasion time. The low resistivity annulus is located at a distance of 2.5 feet after 1 day of invasion. As the invasion progresses, the annulus moves radially away from the borehole. Width of the annulus also increases with time of invasion. Hence, the resistivity measured by induction logging tools will vary depending on the time of logging. The acquired resistivity readings will be erroneously low when the depth of investigation of a particular measurement falls within the annulus region. An unbiased resistivity measurement can only be obtained if the logs are acquired a short time after the onset of invasion. Sensitivity of the resistivity profile to formation porosity is described in Figure 10. Porosities of 0.07, 0.14 and 0.28 were considered for the analysis. When the porosity is reduced to half (0.07) of its reference value, the annulus moves farther from the borehole and its width increases. For higher porosities, the annulus remains closer to the borehole wall and its width becomes smaller. As suggested by equation (6), the overall resistivity increases as porosity decreases from 0.28 to 0.07. Resistivity profiles simulated for different values of connate water salinity are shown in Figure 11. Connate water salinity affects the resistivity of the annulus as well as the resistivity of the virgin formation. By contrast, the flushed zone resistivity remains unaffected by the presence of an annulus as it is almost entirely saturated with mud filtrate. Figures 12 and 13 describe the sensitivity of the resistivity profile to the saturation

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exponent n and to the cementation exponent m, respectively. A variation of n affects only the undisturbed formation resistivity, whereas changes in m affect the resistivities of the flushed zone, of the annulus, and of the virgin formation. Figure 14 describes the effect of changing the mud filtrate salinity on the simulated radial profile of electrical resistivity. The flushed zone profile varies for different values of mud filtrate resistivity. However, both the resistivity of the annulus and the resistivity of the undisturbed formation remain unchanged. Resistivity profiles simulated for different values of initial water saturation (Swi) are shown in Figure 15. Capillary pressure and relative permeability curves were adjusted to conform to the various values of initial water saturation considered in the sensitivity analysis. The initial water saturation affects both the undisturbed formation resistivity and the width of the annulus, but has no effect on either the annulus resistivity or the flushed-zone resistivity. This is a significant (although unfortunate) result for the present work. It means that the pre-annulus and annulus segments of the resistivity profile remain highly insensitive to initial water saturation, thereby impeding an indirect estimation of in-situ gas saturation solely with resistivity measurements originating from these two regions of the invasion profile. The convective and dispersive term for the salt species contained in equation (2) can be further multiplied by a coefficient to control the efficiency of salt mixing. A value of one corresponds to complete mixing while a value of zero for the same coefficient corresponds to null mixing. Efficiency of salt mixing was of interest here as there was some preliminary indication that, to some extent, it was conditioned by the dual pore size distribution exhibited by reservoir rocks (micro and macro porosity). The effect of salt mixing efficiency between mud filtrate and connate water is graphically illustrated in Figure 16. Mixing efficiency affects the width of the annulus as well as the resistivity of the flushed zone. However, it has no significant effect on the resistivity of the annulus itself. The reference (Type A) two -phase gas -water relative permeability curves used in this study are shown in Figure 6. Sensitivity analysis was performed to assess the role played by relative permeability using the Type-B relative permeability curves shown in Figure 17. Simulation results for Sw and Rw, as well as for the computed resistivity profile, Rt, are shown in Figures 18 and 19, respectively. The water saturation front is less sharp compared to that of the reference model (shown in Figure 7). Radia l resistivities monotonically increase in the flushed zone region, rising to a maximum of 155 ohm-m, then steeply falling into the

annulus region to finally reach the true formation resistivity. Resistivity logs acquired in such an environment will yield medium resistivity values (ILM) and Rxo resistivity values higher than the deep resistivity reading (ILD). NUMERICAL SIMULATION OF BOREHOLE RESISTIVITY MEASUREMENTS Readings of various borehole resistivity tools were simulated numerically using as input the computed radial profiles of electrical resistivity. Figure 22 shows apparent resistivity values simulated for dual induction, array induction, and dual laterolog tools as a function of the time of invasion, from 2 to 6 days. The shallow array induction reading, AIT10, provides a good indication of Rxo as it is not affected by the presence of the annulus. This is because after 2 days of invasion the annulus has moved away into the formation, beyond the depth of investigation of the AIT10 reading. Measurements performed with shallow laterolog (LLS) and other shallow resistivity (SFL) tools yield apparent resistivity values slightly lower than Rxo, although gradually approach to the latter value as the annulus recedes away from the borehole wall. The deep laterolog reading, LLD, provides resistivity values closer to Rt since it is only slightly affected by the presence of the annulus. This behavior is due to basic operating principles of resistivity logging tools, which indicate that laterolog tools respond to resistive anomalies whereas induction tools respond to conductive anomalies. Induction tool readings AIT20, AIT30-ILM are close to 34 ohm-m and 26 ohm-m, respectively, after 2 days of invasion; the same values monotonically increase as invasion progresses . Induction resistivity readings, AIT60-ILD increase very slowly, from about 24 ohm-m, whereas the deep array induction reading, AIT90, first decreases below the AIT60-ILD value and then gradually increases from 4 days onward. Figure 20 shows the simulated dual-induction (DIL-SFL) tool readings assuming a radial resistivity profile corresponding to an invasion time of 4 days (Figure 8). Values of Rt and Rxo used in the simulation are varied slightly as a function of depth based on the field logs. The simulated log readings for ILD are about 18-25 ohm-m, for ILM are about 28-35 ohm-m, and those for SFL are about 70-80 ohm-m. As shown in Figure 20, these simulation results are in close agreement with those of the measured log data. Resistivity values falls steeply at the lower part of the formation mainly due to increased shale content. Simulated log responses for various sensitivity studies are summarized in Table 5. For completeness, Figure 21 shows the dual laterolog response simulated in the presence of an annulus resistivity profile equal to that shown in Figure 8. Simulated LLD and LLS readings yield resistivity

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values of 70-80 ohm-m and 55-65 ohm-m, respectively. Such values are much closer to the actual virgin-zone resistivity values (80-90 ohm-m) than those yielded by the deep induction measurements. This exercise clearly suggests that laterolog measurements remain much less affected by the presence of a low resistivity annulus than induction tools.

CONCLUSIONS Differences in salt concentration between mud filtrate and connate water can result in convective salt mixing within porous formations. Because of this, the electrical resistivity of connate water will experience rapid spatial variations radially away from the borehole wall. Estimation of in-situ water saturation from resistivity measurements via, for instance, Archie’s law, require that the resistivity of formation water be known as a function of radial distance away from the borehole wall. Large differences in salinity between mud filtrate and connate water can cause the presence of a prominent low resistivity annulus some distance away from the borehole wall. This phenomenon has been diagnosed in a number of previous publications dealing with the interpretation of wireline resistivity logs. The formation and geometrical characteristics of such an annulus are governed by the particular combination of parameters such as time of invasion, porosity, absolute permeability, relative permeability curves, capillary pressure, initial water saturation, connate water salinity, mud salinity, and cementation factor, among others. In turn, the presence of a low-resistivity annulus seriously compromises the radial length of penetration of borehole induction tools thereby impairing the accurate estimation of in-situ hydrocarbon saturation. The above phenomena were successfully recognized and described from well-log data acquired in active gas producing field. In this particular case, a low resistivity annulus was formed because of both the usage of fresh water mud and the presence of extremely salty connate water. Simulations of mud-filtrate invasion and salt mixing provided radial profiles of electrical resistivity consistent with actual borehole induction data. Further sensitivity analysis provided valuable insight to the role played by formation and fluid properties to the presence and characteristics of the low-resistivity annulus. Simulation results presented in this paper indicate that previously acquired borehole induction measurements cannot be corrected for the presence of a low-resistivity annulus to yield unbiased estimates of in-situ water saturation. Such a correction would require a reliable extrapolation of the profile of electrical resistivity beyond the annulus region. Given (a) the lack of sensitivity of the pre-annulus and annulus regions of the resistivity profile to the value of initial water saturation, and (b) the large variability of the resistivity annulus

properties, namely, width, height, and distance from the borehole wall, an extrapolation of resistivity beyond the annulus region becomes extremely non-unique. However, it was also found that laterolog measurements could provide a practical technical alternative to overcoming the limited depth of investigation experienced by induction tools in the presence of a low-resistivity annulus. Finally, the simulation results described in this paper indicate that numerical simulation of mud-filtrate invasion can be used to assess the influence of a given type of mud on the response of induction and laterolog resistivity measurements. It is also possible to make use of such a simulator to design chemical properties of muds in order to minimize potential formation damage. Chemical properties of muds could also be controlled to optimize the operation of borehole logging tools and therefore to improve the accuracy of log interpretation techniques used to estimate in-situ rock formation properties. ACKNOWLEDGEMENTS We are obliged to Anadarko Petroleum Corporation for permission to publish these results. Partial funding for the work reported in this paper was provided by UT Austin’s Research Consortium on Formation Evaluation, jointly sponsored by Baker Atlas, Halliburton, Schlumberger, and Anadarko Petroleum Corporation.

REFERENCES 1. Delshad M., Pope G.A. and Sepehrnoori K., “A

Compositional Simulator for Modeling Surfactant Enhanced Aquifer Remediation,” Journal of Contaminant Hydrology, 23, 1996, pp 303-327.

2. Dewan J.T. and Chenevert M.E., “A Model for Filtration of Water-Base Mud During Drilling,” Petrophysics, May-June 2001, pp 237-250.

3. Dresser Atlas Inc., Well logging and interpretation techniques, Dresser Industries, USA, 1982.

4. Dumanoir J.L, Tixier M.P. and Martin M., “Interpretation of the Induction-Electrical Log in Fresh Mud,” Petroleum Transactions AIME, 1957, pp 202-217.

5. Gondouin M. and Heim A., “Experimentally Determined Resistivity Profiles in Invaded Water and Oil Sands for Linear Flows,” JPT, March 1964, pp 337-348.

6. Lake L.W., “Enhanced Oil Recovery,” Prentice Hall, 1989.

7. Ramakrishnan T.S. and Wilkinson D.J., “Water Cut and Fractional Flow Logs from Array Induction Measurements”, SPE 36503, SPE Annual Technical Conference and Exhibition, 1996.

8. Saad N., “Field Scale Simulation of Chemical Flooding,” PhD Dissertation, The University of

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Texas at Austin, 1989. 9. Semmelbeck M.E., Dewan J.T. and Holditch S.A.,

“Invasion-Based Method of Estimating Permeability from Logs,” SPE 30581, SPE Annual Technical Conference and Exhibition, 1995.

10. Wu J., Torres-Verdin C., Sepehrnoori K. and Delshad M., “Numerical Simulation of Mud Filtrate Invasion in Deviated Wells,” SPE 71739, SPE Annual Technical Conference and Exhibition, 2001.

11. Zhang J., Hu Q. and Liu Z., “Estimation of True Formation Resistivity and Water Saturation with a Time -Lapse Induction Logging Method,” The Log Analyst, March-April 1999, pp. 138-148.

ABOUT THE AUTHORS Bovan K George is Graduate Research Assistant, pursuing Masters in Petroleum Engineering at The University of Texas at Austin. He works as a Log Analyst with Oil and Natural Gas Corporation (ONGC), India. Bovan received a Master of Science in Physics from the University of Kerala and a Master of Technology in Industrial Physics from IIT Kharagpur, India. He is currently working on modeling mud filtrate invasion into the formation and studying its effects on the response of resistivity logging tools. Carlos Torres-Verdín received a Ph.D. in Engineering Geoscience from the University of California, Berkeley, in 1991. During 1991-1997, he held the position of Research Scientist with Schlumb erger-Doll Research. From 1997-1999, he was Reservoir Specialist and Technology Champion with YPF (Buenos Aires, Argentina). Since 1999, he is an Assistant Professor with the Department of Petroleum and Geosystems Engineering of The University of Texas at Austin, where he conducts research in formation evaluation and integrated reservoir characterization. He has served as Guest Editor for Radio Science, and is currently a member of the Editorial Board of the Journal of Electromagnetic Waves and Applications, and an associate editor for Petrophysics (SPWLA) and the SPE Journal. Mojdeh Delshad is a research engineer with the Center for Petroleum and Geosystems Engineering at The University of Texas at Austin. She holds M.Sc. and Ph.D. degrees in Petroleum Engineering from The University of Texas at Austin. Her research interests are in petrophysical property modeling, enhanced oil recovery, reservoir engineering, simulation, and groundwater modeling and remediation. She is a member of the SPE Editorial Review Committee. Richard Sigal joined Anadarko as part of a new engineering technology group in May of 2001. Before joining Anadarko he spent 21 years with Amoco mostly in their Tulsa Technology Center. After retiring from

Amoco, he worked for two years at Halliburton in Houston. At Anadarko, his primary responsibilities are in the technologies used in reservoir description. During the last 15 years much of his time has been spent on understanding permeability and the technologies used to characterize and estimate it. He worked in Petrophysics and core measurements at Amoco and supervised the development of Petrophysical applications at Halliburton. Among his areas of special expertise are NMR and Hg capillary pressure measurements. Richard was trained in mathematics and physics. His Ph.D. thesis from Yeshiva University was in general relativity. Farid R. Zouioueche is a reservoir engineer formerly of Anadarko Petroleum Corporation. He graduated with a Master's Degree in Petroleum Engineering from The University of Texas in Austin in 2000. His research interests cover near wellbore remediation processes, capillary flow theory and phase behavior. Barbara Anderson is a principal research scientist at Schlumberger-Doll Research in Ridgefield, CT. She joined SDR in 1966, and since that time she has worked on developing computer codes for modeling resistivity tool response. Her ongoing goal is to minimize uncertainty in log interpretation by integrating forward modeling directly into the interpretation process. She is presently working in the areas of anisotropy interpretation and inversion. Barbara is a past-president of SPWLA, and in 1996 she received the SPWLA Distinguished Technical Achievement Award. She received a Ph.D. from Delft University in 2001.

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Depth(ft) Mud Weight (ppg)

Viscosity (cp)

Loss Control Material (lb/gal)

Ph Chloride (ppm)

W/L (cc/30 min.)

Solids (%)

X215 Native X920 8.8 35 6 8.5 X500 9 33 6 8 X080 8.9 36 6 8 1200 X540 9 38 6 8.8 1000 14 5.2 X015 9 38 8 8 900 13 5 X375 9.1 38 8 8.5 900 11 X730 9.1 37 8 8.5 900 11 Bit Trip X200 9.1 50 8 9.9 800 9.2 X300 9.1 50 8 10 950 9.6 5.7

Table 1. Summary of mud properties for Well X-2 (deep invasion).

Depth (ft) Mud Weight (ppg) Viscosity (cp) Ph Chloride

(ppm) X444 1.2 81 8.1 1250 X497 1.1 81 8 400 X552 0.96 82 8.1 280 X559 1.1 82 8.02 260 X592 1.2 82 8.02 240 X608 1.2 82 8 230 X608 9 82 8.03 320

Table 2. Summary of mud properties for Well X-1 (negligible invasion).

Porosity Horiz.

Perm (md)

Vertical Perm (md)

Tortuosity-Cementation

Factor, a

Cementation Exponent

m

Saturation Exponent

n 0.14 6.83 0.93 1 2 2

Table 3a. Summary of rock properties for well X-2.

Invasion Time

(Days)

Initial Water

Sat. (Swi)

Formation Temp (deg F)

Formation Pressure

(psi)

Salinity of Mud Filtrate

(ppm)

Salinity of Connate Water

(ppm) 4 0.14 98 96 2,000 200, 000

Table 3b. Summary of formation and fluid properties for well X-2.

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Sensitivity Parameter

Value of Parameter

Rxo, ohm-m

Rann, ohm-m

Rt, ohm-m

Distance of Annulus, ft

Width of Annulus, ft

6 Hrs 105 5 90 1 1 1 Day 105 5 90 2 2Days of 2 Days 105 5 90 3 2.5Invasion 4 Days 105 5 90 4.5 3.25 6 Days 105 5 90 5.5 3.5 Porosity/2 435 20 370 6 3Porosity Porosity 105 5 90 4 2.5 2*Porosity 25 3 22 3 1.5 Swi/2 105 5 360 4.5 2.5Initial Water Swi 105 5 90 4.5 2.5Saturation, Swi 2*Swi 105 5 23 4.5 3.5 Salinity 105 5 90 4.5 2.5Salinity of Mud Filtrate 2*Salinity 54 5 90 4.5 2.5 5*Salinity 23 5 90 4.5 2.5 10*Salinity 12 5 90 4.5 2.5 Salinity 105 5 90 4.5 2.5Salinity of Connate Water Salinity/4 105 22 270 5 2.5 Salinity/8 105 32 490 5.5 2.5 1.5 105 5 35 4.5 2.5Saturation 2 105 5 90 4.5 2.5Exponent, n 2.5 105 5 240 4.5 2.5 1.5 40 2 37 4.5 2.5Cementation 2 105 5 90 4.5 2.5Exponent, m 2.5 280 12 240 4.5 2.5 100% 105 5 90 4.5 2.5Mixing Efficiency 50% 55 5 90 3.5 3.5 25% 28 7 90 2.5 4.5

Table 4. Summary of the sensitivity of resistivity to various petrophysical and fluid parameters.

SFL (ohm-m)

ILM (ohm-m)

ILD (ohm-m)

Petrophysical/Fluid Parameter

83.0 27.0 23.6 2 days of invasion 90.5 36.1 25.0 4 days of invasion 94.0 45.0 27.5 6 days of invasion 21.7 20.2 20.1 Mud filtrate salinity = 10,000 ppm 94.1 51.4 37.1 Connate water salinity = 50,000 ppm

124.6 31.4 19.8 Type B relative permeability 85.9 19.4 13.5 Initial water saturation = 0.28 92.1 34.8 23.9 Capillary Pressure is Half 34.4 19.5 14.7 Cementation Exponent m = 1.5 91.6 28.7 18.8 Saturation Exponent n = 1.5 49.6 27.9 23.0 Mixing Efficiency is Half 96.7 55.9 40.1 Mud Cake Permeability is 0.15 µ d

392.7 222.7 155.1 Porosity is Half (0.07)

Table 5. Simulated Dual Induction-SFL (DIL-SFL) log readings for various sensitivity studies.

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Fig.1. Plot of the basic suite of measured wireline logs including dual induction logs along Well X-2.

Fig. 2. Plot of the basic suite of measured wireline logs including array induction logs along Well X-1.

Fig. 3. Plot of basic suite of wireline logs along Well X-1 including dual laterologs (compare to Fig. 2).

X510

X550

X500

X550

X500

X550

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Fig. 4. Description of the geometrical and petrophysical properties of the reservoir flow unit considered in this study.

Fig. 6. Plot of the original (TYPE A) water-gas relative permeability curves.

Fig. 8. Plot of resistivity as a function of radial distance away from the borehole wall.

Fig. 5. Plot of the measured capillary pressure as a function of water saturation.

Fig. 7. Plot of water resistivity (Rw) and water saturation (Sw) as a function of radial distance away from the borehole wall. Fig. 9. Plot of resistivity as a function of radial distance away from the borehole wall for different invasion times.

0

2000

4000

6000

8000

10000

12000

14000

0 0.2 0.4 0.6 0.8 1

Sw

Cap

. Pre

ssu

re, p

si

PCGW

SHALE

LAYER3, Kh=14.33 md,

LAYER2, Kh=40.97 md,

LAYER1, Kh=6.83 md,

SHALE 13 ft

15 ft

6 ft

9 ft

15 ft

14.0=φ

14.0=φ14.0=φ

SHALE

LAYER3, Kh=14.33 md,

LAYER2, Kh=40.97 md,

LAYER1, Kh=6.83 md,

SHALE 13 ft

15 ft

6 ft

9 ft

15 ft

14.0=φ

14.0=φ14.0=φ

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Fig. 10. Plot of resistivity as a function of radial distance away from the borehole wall for different values of formation porosity.

Fig. 12. Plot of resistivity as a function of radial distance from the borehole wall for different values of saturation exponent, “n.”

Fig. 14. Plot of resistivity as a function of radial distance from the borehole wall for different values of mud-filtrate salinity.

Fig. 11. Plot of resistivity as a function of radial distance from the borehole wall for different values of salinity of connate water. Fig. 13 Plot of resistivity profile as a function of radial distance away from the borehole wall for different values of cementation exponent, “m.” Fig. 15. Plot of resistivity as a function of radial distance from the borehole wall for different values of initial water saturation.

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Fig. 16. Plot of resistivity as a function of radial distance from the borehole wall for different values of salt mixing efficiency.

Fig. 18. Plot of water saturation (Sw) and water resistivity (Rw) assuming TYPE B relative permeability.

Fig. 20. Numerically simulated wireline logs of dual induction (ILD and ILM), and shallow resistivity (SFL) as a function of depth across the formation of interest. The corresponding field logs are shown in red for comparison.

Fig. 17. Plot of the TYPE B relative permeability curves.

Fig. 19. Plot of resistivity as a function of radial distance from the borehole assuming TYPE B relative permeability curves.

Fig. 21. Numerically simulated wireline logs of dual laterologs (LLS and LLD) as a function of depth across the formation of interest.

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Fig. 22. Numerically simulated apparent resistivity readings of dual induction (ILM and ILD), shallow resistivity (SFL), dual laterologs (LLS and LLD), and array induction (AIT10, AIT20, AIT30, AIT60, and AIT90) measurements. The figure shows simulated apparent resistivity readings as a function of time of invasion. For comparison, the figure also shows the corresponding values of flushed-zone resistivity (Rxo), annulus-zone resistivity (Rann), and virgin -zone resistivity (Rt).