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GEOPHYSICS, VOL. 71, NO. 5 �SEPTEMBER-OCTOBER 2006�; P. G261–G268, 10 FIGS., 1 TABLE.10.1190/1.2335633

etrophysical inversion of borehole array-induction logs:art II — Field data examples

arlos Torres-Verdín1, Faruk O. Alpak2, and Tarek M. Habashy3

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ABSTRACT

We describe the application of Alpak et al.’s �2006� petro-physical inversion algorithm to the interpretation of boreholearray induction logs acquired in an active North Americangas field. Layer-by-layer values of porosity and permeabilitywere estimated in two closely spaced vertical wells that pene-trated the same horizontal rock formation. The wells weredrilled with different muds and overbalance pressures, andthe corresponding electromagnetic induction logs were ac-quired with different tools. Rock-core laboratory measure-ments available in one of the two wells were used to constrainthe efficiency of gas displacement by water-based mud dur-ing the process of invasion. Estimated values of porosity andpermeability agree well with measurements performed onrock-core samples. In addition to estimating porosity and per-meability, the petrophysical inversion algorithm provided ac-curate spatial distributions of gas saturation in the invadedrock formations that were not possible to obtain with conven-tional procedures based solely on the use of density and resis-tivity logs.

INTRODUCTION

The Hugoton field straddles the states of Kansas, Texas, and Okla-oma. Undergoing exploitation since 1927, it comprises the largestas-producing area in North America �Pippin, 1970� with over0,000 wells �Sorenson, 2005�. Reservoir flow units consist of rela-ively thin �2–10 m� marine carbonates that are separated by thin2–10 m�, low-permeability nonmarine siltstones. Alternating lay-rs were deposited in a series of stacked marine-nonmarine sedimen-ary cycles �Sorenson, 2005�. In this paper, we consider well-log andock-core measurements acquired in two closely spaced wells

Manuscript received by the Editor October 19, 2005; revised manuscript re1The University of Texas at Austin, Petroleum and Geosystems Eng

ail.utexas.edu.2Formerly The University of Texas atAustin,Austin, Texas. Presently Shel3Schlumberger-Doll Research, 36 Old Quarry Road, Ridgefield, Connectic2006 Society of Exploration Geophysicists.All rights reserved.

G261

rilled by Anadarko Petroleum Corporation: Youngren J-1H �here-fter referred to as J-1H� and Youngren J-2 �hereafter referred to as-2� and focus exclusively on the Krider Formation �Chase Group,orenson, 2005� penetrated by the two wells. In general, estimatingas saturation from resistivity logs in porous and permeable forma-ions penetrated by wells in the Hugoton field is difficult to impossi-le because of deep mud filtrate invasion of freshwater mud and ex-remely salty connate water �George et al., 2004�.

The objective of this paper is to use the petrophysical inversion al-orithm developed by Alpak et al. �2006� to estimate layer-by-layerorosity and permeability across the Krider Formation in the Hugo-on field.As a by-product, the inversion algorithm estimates the spa-ial distribution of gas saturation in the invaded formation. This lastevelopment is significant in that it offers the possibility of estimat-ng in-situ gas saturation otherwise not possible in the Hugoton fieldith standard interpretation methods based on density and deep-

ensing resistivity logs.Wells J-1H and J-2 are spaced at a distance of approximately

00 m and were drilled with water-based muds of salinities in theange of 300–2000 ppm. On the other hand, the salinity of connateater is very high, on the order of 200,000 ppm. From the onset ofrilling, the permeable formation was subject to water-based mud-ltrate invasion. Lithology in the Krider Formation consists of inter-

ayered clastic carbonates along with fine-grained clastics andhales. The penetrated thickness of the formation in the two wells ispproximately 10.67 m �35 ft�; gas saturation fluctuates between0% and 85%.

In this paper, we express the geoelectrical property of interest inerms of electrical resistivity R�r� �ohm-m�, in contrast to the con-ention adopted in the numerical sensitivity study of Part I �Alpak etl., 2006�, where the same property was expressed in terms of elec-rical conductivity ��r� �mS/m� �the vector variable r is here used toefine location�.

January 21, 2006; published online September 7, 2006.g, 1 University Station, Stop C0300, Austin, Texas. E-mail: cverdin@

ational Exploration and Production.7. E-mail: thabashy@ridgefield.oilfield.slb.com.

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WELL LOGGING

Well J-2 was drilled using a heavy freshwater-based mud, causingn overbalance pressure approximately equal to 7.3 MPa. Porosity

igure 1. Plot of the basic suite of wireline logs, including dual-induccquired in well J-2. Depths are given in meters below the well’s kellron log �NPHI� is expressed in limestone porosity units.

igure 2. Plot of the basic suite of wireline logs, including array-ents, acquired in well J-1H. Depths are given in meters below the whe neutron log �NPHI� is given in limestone porosity units.

f the gas-bearing formation is low, on the order of 15%, giving riseo deep invasion.Amajor challenge faced in evaluating the gas reser-oir penetrated by well J-2 is that the deep invasion of mud filtrate

adversely affects the response of electrical resis-tivity measurements. Indeed, Dual Induction Im-ager Resistivity Tool logs �DIL, hereafter referredto as dual-induction logs� acquired in well J-2�Figure 1� exhibit a reverse resistivity profilewhere deep dual-induction �ILD, hereafter re-ferred to as deep dual-induction� readings �20–22 ohm-m� are lower than the medium dual-in-duction �ILM, hereafter referred to as mediumdual induction� readings �25–30 ohm-m�. Aver-age readings of deep and medium dual-inductionlogs are lower than the shallow readings �90–100 ohm-m� acquired with the spherically fo-cused microresistivity tool �MicroSFL� and thespherically focused resistivity tool �SFL�.

By contrast, well J-1H was drilled with a lightfoam-based mud, resulting in very shallow in-vasion. The overbalance pressure for well J-1Hwas much lower than the one enforced to drillwell J-2. Resistivity logs acquired in well J-1Hshowed a normal resistivity profile across theKrider Formation �Figure 2�. On average, arrayinduction imager tool �AIT, hereafter referredto as array induction tool� readings are 50–60 ohm-m for the 90-inch log, 40–50 ohm-m forthe 60-inch log, and 30–35 ohm-m for the 10-inch log. Well J-1H is considered a key well in thepresent study because of both shallow invasionand the availability of extensive log and rock-core measurements �rock-core measurementswere not available in well J-2�. This well providesa unique reference to quantify the reliability andaccuracy of the petrophysical inversion of induc-tion logs to estimate permeability and porosity. Inaddition, the complete suite of measurementsprovides a benchmark to quantify the effect ofmud-filtrate invasion on resistivity logs acquiredalong the Krider Formation in well J-2.

LAYER PARAMETERS

For the purpose of parametric petrophysical in-version of induction logs acquired in wells J-1Hand J-2, we constructed a 2D cylindrical forma-tion model with a vertical well at its center. Thevertical borehole penetrates the gas-bearingKrider Formation, consisting of isotropic perme-able horizontal layers. As shown in the verticalcross section of Figure 3a, the formation is shoul-dered by impermeable shale layers. Resistivitiesof the upper and lower shoulder beds are also dis-played in Figure 3a. Measurements conducted onmud-filtrate samples indicated that the salinity ofmud filtrate in wells J-2 and J-1H was approxi-mately 2000 and 340 ppm, respectively. Down-hole fluid samples taken within the formation of

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nterest revealed the salinity of connate water was approximately00,000ppm.

Based on the interpretation of rock-core data and density logs, weescribed the formation of interest with three isotropic horizontalayers of thicknesses 4.57 m, 2.44 m, and 3.66 m. Prior to invertinghe induction logs, the values of permeability and porosity for eachayer were estimated from rock-core measurements acquired in well-1H. These values are also displayed in Figure 3a. The constant coreorosity and permeability values assigned to each layer were ob-ained by arithmetic and logarithmic averaging, respectively, of thectual core measurements. Statistical dispersion of the core porositynd permeability measurements about the assigned constant layeralues is negligible for all practical purposes.

PVT AND FLUID PROPERTIES

We assumed instantaneous temperature equilibrium betweenud-filtrate and in-situ fluids. This assumption renders the mud-fil-

rate invasion phenomenon an isothermal flow of two immiscibleuid phases �namely gaseous and aqueous phases� in a permeableock formation. For the gaseous phase, we used laboratory pressure,olume, and temperature �PVT� measurements to constrain density,iscosity, formation volume factor, z-factor, andompressibility relationships as a function ofressure. Laboratory measurements of density,iscosity, formation volume factor, and com-ressibility as functions of salt concentration aresed for the aqueous phase — more specifically,ud filtrate. Table 1 describes the numerical val-

es of the PVT properties of the gaseous phase atreference pressure of 1 atm �surface conditions�long with the PVT properties of the aqueoushase.

ROCK-FLUID PROPERTIES

We used the available rock-core data in well-1H to constrain relative permeability and capil-ary pressure functions for each flow unit �layer�.

ithin the framework of our petrophysical inver-ion algorithm, laboratory measurements of rela-ive permeability �Figure 3b� performed on coresxtracted from each of the reservoir layers werenput to the near-borehole fluid-flow simulator.he highly irreducible aqueous-phase saturation

or each layer hints at a strong water-wet system.n this case, the aqueous phase is the wettinghase, and the wetting/nonwetting convention ofhe relative permeability plot should be interpret-d accordingly. Capillary pressure data �Figurec� were derived from laboratory measurementsor the drainage cycle for the above layers. Be-ause of the lack of laboratory capillary pressureor the imbibition cycle, the available drainage-ycle data were used for the numerical simula-ions of the imbibition process, namely, water-ased mud-filtrate invasion in a strongly water-et system.

Figure 3. �a� Tof borehole eKrider Formasion. PermeabJ-1H are showcapillary press“rw” and “rnwcase, aqueous

ARCHIE’S EQUATIONS ANDPARAMETERIZATION

The use of Archie’s equations in the present study is justified giv-n the clastic nature of the carbonate sequence under consideration.lso, the high salinity of connate water makes it unnecessary to cor-

ect for the presence of clay in Archie’s equations. Parameters usedn Archie’s saturation equation are listed in Table 1. For the forma-ion under consideration, laboratory measurements consistently in-icated marginal statistical variability of Archie’s parameters.herefore, we made no further attempt to quantify the impact of un-ertainty in Archie’s parameters on the inverted values of porositynd permeability.

We computed the spatial distribution of the initial aqueous-phaseaturation within the formation of interest using conventional inver-ion of array induction logs acquired in well J-1H. Specifically,ayer-by-layer spatial distributions of deep resistivity, Rt, were de-ived by inverting the deepest-sensing induction log for a more fine-y layered medium. In so doing, we considered an eight-layer para-

etric model to describe the spatial distribution of Rt. Layer thick-esses for the assumed eight layers were determined from the depthariability of the array induction logs acquired in well J-1H. The ini-

ensional axisymmetric formation model assumed for the inversionagnetic induction logs acquired in wells J-1H and J-2 across the

he three-layer formation is subject to water-based mud-filtrate inva-nd porosity values obtained from rock-core measurements in welle above cross section. �b� Water-gas relative permeability and �c�uration functions used in the simulation of fluid flow. The subscripts� are used to identify relative permeability values for wetting �in thisonwetting �in this case, gaseous� phases, respectively.

wo-dimlectromtion. Tility an in thure sat” in �b

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ial spatial distribution of the aqueous-phase saturation was derivedsingArchie’s equations in conjunction with core porosity measure-ents. We determined the spatial distribution of gaseous-phase satu-

ation using a saturation identity for two-phase flow and the spatialistribution of aqueous-phase saturation. The fluid saturation do-ain was described with a finer spatial parameterization than the

hree-layer permeability-porosity parameterization derived fromock-core measurements. Within the context of the petrophysical in-ersion algorithm, we used the estimated initial spatial distributionf aqueous- and gaseous-phase saturations �determined for theight-layer saturation domain� to derive the initial condition neces-ary to simulate mud-filtrate invasion.

INVASION CONSTRAINTS

Samples of mud and mud filtrate in well J-2 provided adequate in-ormation to constrain fundamental parameters governing the pro-ess of mud-filtrate invasion such as mud-cake growth and effectiveow rate across the mud cake. The flow rate of mud filtrate across theud cake was modeled using INVADE �Wu et al., 2005� as a func-

able 1. Summary of geometrical, petrophysical, mud cake, fln the inversion of field electromagnetic induction logs.

Variable

Mud-cake permeability �well J-2�

Mud-cake porosity �well J-2�

Mud solid fraction �well J-2�

Mud-cake maximum thickness �well J-2�

Formation rock compressibility

Aqueous-phase viscosity �mud filtrate�

Aqueous-phase density �mud filtrate�

Aqueous-phase formation volume factor �mudfiltrate�

Aqueous-phase compressibility �mud filtrate�

Gaseous-phase reference viscosity �f�p� fortemperature = const.�

Gaseous-phase reference density �f�p� fortemperature = const.�

Formation pressure at the formation top �at thereference depth = 0 m�

Mud hydrostatic pressure �well J-2�

Wellbore radius

Formation outer boundary location

Formation temperature

a — constant in Archie’s equation

m — cementation exponent in Archie’s equation

n — aqueous phase saturation exponent inArchie’s equation

Mud conductivity

Upper-shoulder bed conductivity �well J-1H�

Lower-shoulder bed conductivity �well J-1H�

Upper-shoulder bed conductivity �well J-2�

Lower-shoulder bed conductivity �well J-2�

Depth-sampling interval

ion of invasion time. Mud-cake parameters required by this compu-ation are documented in Table 1. However, for well J-1H, mud-cakearameters required to compute the rate of mud-filtrate invasionere not available. On the other hand, for both wells J-1H and J-2,

he logging record indicated that logs were acquired four days afterhe onset of invasion. For filtrate invasion in well J-2, both dynamicrowth of mud-cake thickness and dynamic decrease of mud-cakeermeability remain coupled to formation properties. This processesults in a monotonic decrease of flow rate across the borehole wall.or the purpose of computing the time-domain flow-rate response ofud cake, we used rock-core permeability and porosity values ac-

uired in well J-1H. In the present work, the layer-dependent rate ofud-filtrate invasion is assumed to be the steady-state value yielded

y the simulations of invasion. Since the mud-cake parameters inell J-1H were not available, the rate of mud-filtrate invasion in well

-1H was derived from a conventional inversion of electrical resis-ivity. Using Archie’s equations, we determined the total volume of

ud filtrate that invaded the formation in well J-1H. Subsequently,iven that the duration of invasion was known, an average mud-ltrate invasion rate was determined for well J-1H. Rates of mud-

nd sensor parameters for the rock formation model assumed

Unit Value

mD 0.030

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fraction 0.200

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kPa−1 1.450 � 10−7

Pa.s 1.087 � 10−5 @ 1.0 atm

g/cm3 9.781 � 10−4 @ 1.0 atm

MPa 0.662

MPa 7.950

m 0.100

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dimensionless 1.000

dimensionless 2.000

dimensionless 2.000

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mS/m 200.000

mS/m 327.900

mS/m 200.000

mS/m 400.000

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ltrate invasion for wells J-1H and J-2 were imposed as a sourceondition for the fluid-flow module integrated to the petrophysicalnversion algorithm.

Induction logs acquired in wells J-1H and J-2 consistently indi-ate increasing shaliness toward the bottom of the Krider Formation.he spatial location of this trend corresponds to the depth segmentomprised by the third petrophysical layer derived from rock-corenalysis. Therefore, for the petrophysical inversions, the third layeruggested by the rock-core analysis was divided into two separateayers. Inversions were then conducted using four layers. A betteray of performing the petrophysical inversion would be to parame-

erize the formation of interest using many small layers and perform1D inversion of permeability and porosity with-ut assuming the thickness of the layers. Howev-r, numerical experiments performed using suchmodel discretization proved computationally

rohibitive because of the increased number oforward simulations required for the computationf the Jacobian matrix �Alpak et al., 2006�.

We first investigated the petrophysical inver-ion of induction logs acquired in well J-2. Figureshows permeability and porosity values invert-

d from induction logs acquired with the dual-nduction configuration. Inversion results arehown for two different uniform initial-guess val-es of permeability and porosity. Inverted valuesre shown together with permeability and porosi-y values derived from core analysis of rock sam-les acquired in well J-1H �the core porosity andermeability values are used solely for compari-on purposes�. We used uniform initial-guess val-es to assess the reliability of the petrophysicalnversion algorithm. These initial-guess valuesre also shown in each panel of Figure 4 that dis-lays a particular inversion result.

Figure 5 describes the quality of the postinver-ion data fit achieved by inverting dual-inductionogs. In this plot, we compare the simulated mea-urements against the actual field measurementsor the final iteration of the inversion algorithm.ubsequent to the quantitative estimation of per-eability and porosity, we simulated the spatial

istributions of near-borehole fluid saturationsnd salt concentration. The cross section of elec-rical conductivity in the invaded Krider Forma-ion was computed from the simulated profiles ofqueous-phase saturation and salt concentrationiaArchie’s equations.

INVERSION OF ELECTRICALCONDUCTIVITY

As shown in Figure 6a, the petrophysical inver-ion algorithm can also be used to estimate thepatial distribution of near-borehole electricalonductivity in well J-2. In this figure, the crossection of electrical conductivity is displayedith a logarithmic scale, i.e., log10���r��. Figurea and b shows the postinversion reconstructions

Figure 4. Perminduction logsquired four datwo initial-guscription of thability were ac

Figure 5. Postand input appguess set 1 sho

f the near-borehole spatial distributions of gas saturation and saltoncentration, respectively.

Figure 7 shows permeability and porosity values simultaneouslynverted from induction logs acquired with the array-induction toolonfiguration in well J-1H. Inverted permeability and porosity val-es are shown for two inversion examples where we make use of ahree-layer and a four-layer parameterization of the Krider Forma-ion. Inverted values are shown together with permeability and po-osity values obtained from rock-core analysis in the same well. Inhis case, we initialized the inversion with uniform permeability andorosity values. Such initial-guess values are also shown in Figure 7,ach panel of which displays a particular inversion outcome.

ty and porosity values yielded by the inversion of electromagnetic-red with the dual induction tool in well J-2. Measurements were ac-r the onset of mud-filtrate invasion. Inversion results are shown forue of permeability and porosity for �a–b and c–d� a four-layer de-ation of interest. Rock-core measurements of porosity and perme-in well J-1H and are shown for comparison purposes only.

on data match of dual-induction logs acquired in well J-2. Simulatedsistivity logs are plotted for inversions performed using �a� initial-

Figure 4a–b, and �b� initial-guess set 2 shown in Figure 4c–d.

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Figure 8a shows the array induction logs acquired in well J-1H. Inhe remaining panels of Figure 8, the quality of the postinversionata fit achieved by inverting array-induction tool measurements isisplayed independently for each apparent resistivity log. Data-omain fit shown in Figure 8b-f corresponds to the case of the four-ayer permeable medium.

After estimating permeability and porosity, we calculated the spa-ial distributions of near-borehole saturation and salt concentrationsing the inverted permeability and porosity values. Subsequently,he spatial distribution of electrical conductivity was obtained fromhe simulated spatial distributions of aqueous-phase saturation andalt concentration using Archie’s equations. Figure 9a shows theostinversion reconstruction of the spatial distribution of near-bore-ole electrical conductivity around well J-1H.

igure 6. Postinversion simulations of spatial distributions of near-hown�, �b� gaseous-phase saturation, and �c� salt concentration in wnd plotted with a logarithmic scale, i.e., log10���r��. The spatial dith units of pore volume fraction. Values of salt concentration are g

cale.

igure 7. Permeability and porosity values yielded by the inversionnduction logs acquired with an array induction imager tool in well Jere acquired four days after the onset of mud-filtrate invasion. I

hown for two cases: �1� a three-layer description of the formationnd b�, and �2� a four-layer description of the formation of interest �pa

Postinversion reconstructions of the near-borehole spatial distri-utions of gas saturation and salt concentration are shown in Figureb and c, respectively. In the next inversion study, porosity values re-ain fixed at porosity values obtained from rock-core analysis. Fieldeasurements are inverted to yield near-borehole permeability val-

es only. Figure 10 shows permeability values inverted from induc-ion logs acquired with the array induction tool in well J-1H. Twoifferent initial-guess values of permeability were used for both dataets as shown in Figure 10a and b.

DISCUSSION

Permeability values inverted from array-induction-tool measure-ments in well J-1H are in close agreement withpermeability values measured from rock-coresamples. For the case of well J-2, there are no coremeasurements to compare the permeability val-ues inverted from dual-induction measurements.However, the inverted permeability values inwell J-2 are not in good agreement with the refer-ence core permeability values of well J-1H. Asemphasized by the results obtained in Part I �Al-pak et al., 2006� from synthetic numerical experi-ments, we would expect that permeability valuesinverted from dual-induction measurementswould be less accurate than permeability valuesinverted from array-induction-tool measure-ments. Based on these results, we can only specu-late that the relatively higher discrepancy be-tween inverted and reference core permeabilityvalues in well J-1 is partly from the use of dual-in-duction measurements.

Measurement sensitivity to permeability isembedded in electrical resistivity logs that exhib-it multiple radial lengths of investigation. Clearly,a five-array induction imaging tool configuration�array-induction tool� is more sensitive to radialvariations of electrical conductivity than a toolwith only two resistivity logs �dual-inductiontool�. Fewer electrical resistivity logs combinedwith deep invasion decreases the reliability andaccuracy of the estimated permeability values �asin the case of well J-2�.Also, we note that some of

le �a� electrical conductivity �shoulder-bed conductivities are also. Electrical conductivity values are expressed in millisiemens/metertion of gaseous phase saturation �Sg�r� = 1.0 − Sw�r�� is describedn the units of parts per million �ppm� and plotted with a logarithmic

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Petrophysical inversion, field examples G267

the discrepancies between inverted and rock-corepermeability values could be from differences inspatial length of support �vertical and radial reso-lution�. Whereas core permeability is measuredon small rock samples, induction logs are sensi-tive to a larger region of space in the invaded rockformation. The increase in length of spatial sup-port causes a natural reduction in the spatial vari-ability of the estimated values of permeabilityand, therefore, a discrepancy with the rock-corepermeability values.

Porosity values inverted from both array-induction and dual-induction measurements, onthe other hand, agree very well with the corre-sponding values measured on rock-core samples.Inversion results indicate that for cases wherelaboratory measurements of relative permeabilityand capillary pressures are available, and the pa-rameters governing the saturation equation �Ar-chie’s equations� are reliable, induction logs yieldreliable and accurate values of porosity. In addi-tion, through experience gained with several in-version exercises, we found that accurate knowl-edge of the spatial distribution of initial fluid satu-rations plays a significant role in obtaining accu-rate porosity values.

The near-borehole electrical conductivity im-age derived for well J-2 suggests a substantial ra-dial length of mud-filtrate invasion, which is aconsequence of using heavy mud. The radius ofinvasion in the upper section of the Krider Forma-tion is on the order of 1–1.5 m. However, in thelower section of the formation, the radius of inva-sion decreases to approximately 0.5–1.0 m. Con-versely, the near-borehole electrical conductivityimage derived for well J-1H suggests a relativelyshort radial length of mud-filtrate invasion, whichis consistent with the use of light mud. The radiusof invasion in the upper section of the Krider For-mation is on the order of 0.35–0.45 m. However,in the lower section of the formation, the radius of

er formation.stivity values

ole �a� electrical conductivity �shoulder-bed conductivities are also. Electrical conductivity values are expressed in the units of mS/m

ion of gaseous phase saturation �Sg�r� = 1.0 − Sw�r�� is describedthe units of parts per million �ppm� and plotted with a logarithmic

igure 8. �a� Apparent resistivity logs acquired in well J-1H across the Kridb–f� Comparison of measured �meas.� and simulated �sim.� apparent resior the five logs included in the array-induction-tool configuration.

igure 9. Postinversion simulations of the spatial distributions of near-borehhown�, �b� gaseous phase saturation, and �c� salt concentration in well J-1Hnd plotted with a logarithmic scale, i.e., log10���r��. The spatial distributith units of pore volume fraction. Values of salt concentration are given in

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nvasion decreases to less than 0.1 m. Electrical conductivity imag-s around wells J-1H and J-2 also indicate the presence of a high-onductivity �low-resistivity� annulus in the transition region be-ween the flushed and virgin zones.

We strongly recommend that the inversion of porosity and perme-bility from induction logs be preceded by a systematic sensitivitynalysis of all the petrophysical, rock physics, mud, and geometricalroperties involved. Only when induction logs remain highly sensi-ive to porosity and permeability will the inversion provide reliablend accurate estimates, especially in light of uncertainty on mudroperties and possible systematic biases in the calculation of trade-ark apparent resistivity logs from raw voltage measurements. For

he cases considered in this paper, uncertainty in parameters govern-ng the process of mud-filtrate invasion �e.g., mud properties, over-alance pressure, and time of invasion� played a marginal role in theccuracy and reliability of the estimated values of porosity and per-eability.

CONCLUSIONS

The field data examples described in this paper confirm that it isossible to reliably and accurately estimate porosity and permeabili-y values from induction logs acquired in mud-filtrate-invaded rockormations. This process requires that rock-core measurements ofapillary pressure and relative permeability be available to constrainhe efficiency of displacement of in-situ fluids by mud filtrate. Esti-

ated values of porosity were in good agreement with the corre-ponding values measured in rock-core samples. For the case of per-eability, the agreement between rock-core and inverted values was

ot good in all cases. Differences between rock-core and invertedermeability values could be caused by differences in vertical reso-ution between the two measurements involved.

Field examples described in this paper included cases of shallownd deep invasion as well as two types of induction logs acquiredcross the same rock formation. We found that induction logs thatxhibit five radial lengths of investigation are in general much betteruited for reliably estimating permeability than dual-induction elec-

igure 10. Permeability values yielded by the inversion of electroogs acquired with the array induction imager tool in well J-1H. Meauired four days after the onset of mud-filtrate invasion. Two differees of permeability were used for both data sets �a–b�. Porosity valunversion and are equal to those of rock-core measurements.

trical resistivity logs. We also found that reliableinformation about initial water saturation, rela-tive permeability, and capillary pressure are es-sential to estimate porosity and permeability ac-curately. For the cases considered in this paper,uncertainty in parameters governing the processof mud-filtrate invasion �e.g., mud properties,overbalance pressure, and time of invasion�played a marginal role in the accuracy of the esti-mated values of porosity and permeability.

One of the important outcomes from this paperis the possibility of estimating continuous spatialdistributions of fluid saturation, salt concentra-tion, and electrical resistivity as a by-product ofthe inversion of porosity and permeability. Thesethree spatial distributions not only honor theavailable induction logs but also remain consis-tent with physical constraints imposed by mass

onservation and the processes of salt mixing and immiscible fluidisplacement in porous media. Such constraints provide a naturalay to reduce nonuniqueness in the inversion process. Prior to this

tudy, it was not possible to reliably estimate in-situ gas saturation inugoton wells drilled with freshwater-based mud and subject toeep filtrate invasion. The estimated spatial distributions of gas satu-ation are one of the most significant technical contributions of thisaper.

ACKNOWLEDGMENTS

We are obliged to Anadarko Petroleum Corporation for permis-ion to publish the results of the inversions of field induction logs. Aote of special gratitude goes to Steve Arcone, Tsili Wang, and twononymous reviewers for their constructive editorial and technicalomments. Funding for the work reported in this paper was providedy U.T. Austin’s Research Consortium on Formation Evaluation,ointly sponsored byAnadarko Petroleum Corporation, BakerAtlas,P, ConocoPhillips, ENI E&P, ExxonMobil, Halliburton Energyervices, Mexican Institute for Petroleum, Occidental Oil and Gasorporation, Petrobras, Precision Energy Services, Schlumberger,hell International E&P, Statoil, and Total.

REFERENCES

lpak, F. O., C. Torres-Verdín, and T. M. Habashy, 2006, Petrophysical in-version of borehole array-induction logs, Part I: Numerical examples:Geophysics, 71, this issue.

eorge, B. K., C. Torres-Verdín, M. Delshad, M. R. Sigal, F. Zouioueche, andB. Anderson, 2004, Assessment of in-situ hydrocarbon saturation in thepresence of deep invasion and highly saline connate water: Petrophysics,45, 141–156.

ippin, L., 1970, Panhandle-Hugoton field, Texas, Oklahoma, and Kansas,the first 50 years, in M. T. Halbouty, ed., Geology of giant petroleum fields:AAPG Memoir 14, 204–222.

orenson, R. P., 2005, A dynamic model for the Permian Panhandle andHugoton fields, westernAnadarko basin: AAPG Bulletin, 89, 921–938.u, J., C. Torres-Verdín, K. Sepehrnoori, and M. A. Proett, 2005, The influ-ence of water-base mud properties and petrophysical parameters on mudcake growth, filtrate invasion, and formation pressure: Petrophysics, 46,14–32.

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