GEOHORIZONS AUTHORS - Cockrell School Faculty … Gandhi, Carlos Torres-Verdín, Ben Voss, ... 380...

AUTHORS

Ankur Gandhi � University of Texas at Austin,Austin, Texas; present address: Anadarko Petro-leum Corporation, Room #7067, 1201 LakeRobbins Dr., The Woodlands, Texas;[email protected]

Ankur Gandhi has been a petrophysicist at AnadarkoPetroleum Corporation in The Woodlands, Texassince 2010. Previously, he worked for two yearsas logging engineer, followed by serving as a res-ervoir engineer for a year. Gandhi has workedon various onshore and deep-water offshore proj-ects. He holds a bachelor’s degree in petroleumengineering from the Indian School of Mines, andan M.S. degree in petroleum engineering from theUniversity of Texas at Austin. He is the author ofthree technical papers. Ankur’s interests includeformation evaluation, well testing, application offorward and inverse modeling techniques in the oiland gas industry, and reservoir engineering.

GEOHORIZONS

Correction of invasion effectson well logs in Camisea gasreservoirs, Peru, with theconstruction of static anddynamic multilayerpetrophysical modelsAnkur Gandhi, Carlos Torres-Verdín, Ben Voss,Federico Seminario Gros, and Johnny Gabulle

Carlos Torres-Verdín � University of Texasat Austin, Austin, Texas; [email protected]

Carlos Torres-Verdín received a Ph.D. in engineeringgeoscience from the University of California atBerkeley in 1991. From 1991 to 1997, he held theposition of research scientist at Schlumberger-DollResearch. From 1997 to 1999, he was reservoirspecialist and technology champion at YacimientosPetroliferos Fiscales (YPF) (Buenos Aires, Argenti-na). Since 1999, he has been affiliated with theDepartment of Petroleum and Geosystems Engi-neering of the University of Texas at Austin, wherehe is currently a full professor; holds the ZarrowCentennial Professorship in Petroleum Engineering;and conducts research on borehole geophysics,formation evaluation, well logging, and integratedreservoir characterization. Dr. Torres-Verdín is thefounder and director of the Research Consortiumon Formation Evaluation at the University of Texasat Austin. He has served as guest editor for RadioScience, the Journal of Electromagnetic Waves andApplications, and the Society of Petroleum Engi-neers (SPE) Journal, and is an associate editor forpetrophysics (Society of Petrophysicists and WellLog Analysts [SPWLA]) and geophysics. Dr. Torres-Verdín is recipient of the 2006 Distinguished Tech-nical Achievement Award from SPWLA; the 2008Formation Evaluation Award from SPE; the 2003,2004, 2006, and 2007 Best Paper Awards in Petro-physics by SPWLA; and the 2006 Best Presentation

ABSTRACT

The concept of common stratigraphic framework was pre-viously introduced to construct and cross-validate multilayerstatic and dynamic petrophysical models by invoking the in-teractive numerical simulation of well logs both before andafter invasion. This article documents the successful imple-mentation of the common stratigraphic framework conceptto examine and quantify the effects of mud-filtrate invasion onapparent resistivity, nuclear, and magnetic resonance logs ac-quired in the San Martin, Cashiriari, and Pagoreni gas fieldsin Camisea, Peru. Conventional petrophysical interpretationmethods yield abnormally high estimates of water saturationin some of the reservoir units that produce gas with null waterinflux. Such an anomalous behavior is caused by relatively lowvalues of deep apparent electrical resistivity and has otherwisebeen attributed to the presence of clay-coating grains and/orelectrically conductive grain minerals coupled with fresh con-nate water. Concomitantly, electrical resistivity logs exhibitsubstantial invasion effects as evidenced by the variable sep-aration of apparent resistivity curves (both logging-while-drillingand wireline) with multiple radial lengths of investigation. Inextreme cases, apparent resistivity logs stack because of very

Award and the 2007 Best Poster Award by SPWLA.

Ben Voss � University of Texas at Austin, Austin,Texas; [email protected]

Benjamin C. Voss graduated from the CaliforniaInstitute of Technology (Caltech) in 2003 with a

Copyright ©2013. The American Association of Petroleum Geologists. All rights reserved.

Manuscript received January 26, 2011; provisional acceptance August 24, 2011; revised manuscriptreceived May 11, 2012; final acceptance July 3, 2012.DOI:10.1306/07031211017

AAPG Bulletin, v. 97, no. 3 (March 2013), pp. 379–412 379

B.S. degree in engineering and applied scienceand earned his M.S. degree in electrical engi-neering, also from Caltech, in 2004. He has beenwith the Center for Petroleum and GeosystemsEngineering at the University of Texas at Austinsince 2006, developing graphical user-interfacesoftware and algorithms for well-log modeling andinterpretation, under the auspices of the FormationEvaluation Joint Industry Research Consortium.

Federico Seminario Gros � Pluspetrol PeruCorporation SA, Lima, Peru;[email protected]

Federico Seminario received a B.S. degree fromUniversidad Nacional Mayor de SanMarcos in Lima,Peru, and later received his graduate degree inengineering geology from Universidad NacionalMayor de San Marcos, Lima, Peru, in 1996. He hasmore than 22 years of experience in the industry.His interests include reservoir geology character-ization, well-log interpretation, and project man-agement. He is currently the geosciences manager(exploration and development) for Pluspetrol PeruCorporation He has held different positions atOxy Peru and Pluspetrol Argentina. He is also thechairman of the XVI Congreso Peruano de Geologiaand SEG 2012 Conference.

Johnny Gabulle � Pluspetrol Peru CorporationSA, Lima, Peru; [email protected]

Johnny Gabulle is a senior geologist at PluspetrolPerú Corporation S.A., where he is the developmentteam leader in the Camisea project, Ucayali Basin.He has 15 years of experience in the oil and gasindustry. In 1998, he received his B.S. degree ingeology engineering from Universidad NacionalMayor de San Marcos in Lima, Peru. He workedas a geologist for Pluspetrol Norte for 6 years,where he was responsible for the exploration anddevelopment of the fields in the Marañon Basin.He started as a trainee geologist at the OccidentalPetroleum Company in 1997 and was employedthere until joining the Perez Companc Company in1999 and Pluspetrol Norte later in 2000.

ACKNOWLEDGEMENTS

We thank Pluspetrol, Hunt Oil Company, SK En-ergy Corporation, Ltd., Tecpetrol, and SonatrachOil and Gas Group for their permission to publishthe field data. The work reported in this articlewas partially funded by the research consortium onformation evaluation of the University of Texasat Austin.The AAPG Editor thanks the following reviewersfor their work on this paper: Terrilyn M. Olsen,David A. Pivnik, and Raymond P. Jorensen.

380 Geohorizons

deep invasion. We diagnose and quantify invasion effects onresistivity and nuclear logs with interactive numerical model-ing before and after invasion. The assimilation of such effects inthe interpretation consistently decreases previous estimates ofwater saturation to those of irreducible water saturation in-ferred from core data. We show that capillary pressure effectsare responsible for the difference in separation of apparent re-sistivity curves in some of the reservoir units. This unique fieldstudy confirms that well logs should be corrected for mud-filtrate invasion effects before implementing arbitrary shalysand models and parameters thereof in the calculation ofconnate-water saturation.

INTRODUCTION

Conventional well-log interpretation uses general-purposerock-physics models to calculate petrophysical propertiesfrom borehole measurements. These interpretation modelsseldom consider the physics governing the process of mud-filtrate invasion and the corresponding effects on well logs.

In a previous publication (Voss et al., 2009), we in-troduced and successfully implemented the concept of com-mon stratigraphic framework (CSF) to construct reliable andverifiable multilayer static and dynamic reservoir models. TheCSF explicitly and quantitatively honors the available welllogs and core data as well as the process of mud-filtrate in-vasion to estimate layer-by-layer static and dynamic petrophy-sical properties. Moreover, the CSF permits cross-validation ofrock-physics models via numerical simulation of well logs.The method enforces petrophysical consistency among therock-physics model, the available borehole and/or core mea-surements, and the process of mud-filtrate invasion.

This article describes a unique example of petrophysicalinterpretation where the concept of CSF is invoked to obtainreliable estimates of water saturation in gas-bearing sand-stone reservoir units. Conventional petrophysical interpre-tation of well logs yields abnormally large values of watersaturation in some of the gas-bearing reservoir units that un-dergo production with null water influx. This behavior iscaused by abnormally low values of apparent resistivity. Oneinformal explanation for such a behavior is the presence ofelectrically conductive minerals in the matrix and/or the pre-sence of grain-coating clay coupled with fresh connate water.Despite the relatively low values of rock volumetric con-centration of clay (lower than 5%), the argument insists on

mineral and/or clay effects on electrical resistivitybecause of their peculiar spatial distribution in thematrix of the rock and because of relatively lowvalues of water saturation and connate-watersalinity. Available core measurements do notsystematically confirm that hypothesis. The sameargument suggests that decreasing Archie’s sa-turation exponent, n, is an adequate strategy toaccount for the abnormally low values of apparentelectrical resistivity caused by conductive mineralsand/or grain-coating clay in the calculation of gassaturation. However, the effect of mud-filtrate in-vasion on apparent resistivity logs is ubiquitous andmanifested by the variable and prominent separa-tion of resistivity logs with multiple radial lengthsof investigation. This latter observation suggeststhat, although conductive-matrix effects on elec-trical resistivitymeasurements could be significant,it is imperative that a possible correction for thoseeffects be implemented only after correcting resis-tivity logs for invasion effects. Specifically, Archie’sporosity and saturation exponents cannot be arbi-trarily modified to obtain estimates of water satu-ration consistent with core data without previouslycorrecting resistivity logs from invasion and shoulder-bed effects.

In the sections below, we first introduce thegeographical location and geologic backgroundof the gas fields under consideration. We describegeneric suits of well logs and core measurementsto define the petrophysical assessment problem.Subsequently, we quantify mud-filtrate invasioneffects on apparent resistivity logs using a rockclassification method that explicitly considers thestatic and dynamic petrophysical properties of in-vaded rock formations via the CSF concept. Weshow that invasion effects on resistivity and nuclearlogs are primarily governed by the dynamic pet-rophysical properties of the invaded formations.More importantly, we show that the explicit in-tegration of the process of mud-filtrate invasioninto the petrophysical interpretation of well logsyields estimates of water saturation that are con-sistent with both core and fluid-production mea-surementswithout arbitrarymanipulation ofArchie’sporosity and saturation exponents. The systematicintegration of dynamic petrophysical properties in

the interpretation of well logs is an effective methodto articulate borehole petrophysical assessmentswith reservoir engineering studies and practices.

Reservoir Description and Location

The study reported in this article focuses on gas-bearing siliciclastic reservoirs located in Camisea,Peru. We examine Cretaceous and Permian res-ervoir units within the San Martin, Cashiriari, andPagoreni fields. Facies primarily originate from ma-rine and eolian depositional environments (Díaz daJornada, 2008). Rock formations consist of mod-erately to highly cross-bedded sandstones and in-clude a wide range of variations in grain, pore, andthroat sizes. Sixmajor gas-bearing formations exist:Vivian,Chonta,Nia, Shinai,Noi, andEne.TheupperVivian consists of fine-grained quartzose sandstonewith thin clay interbeddings and siliceous cement;porosity ranges between 7 and 19%, and perme-ability ranges between 0.03 and 338md.The lowerVivian is a medium to very coarse-grained sand-stone; porosity ranges between 4 and 20%, and per-meability ranges between 1 and 2700md. The upperNia is a fine-grained to conglomeratic sandstonewith moderate cement content; porosity rangesbetween 16 and 21%, and permeability rangesbetween 50 and 1000 md. The middle Nia For-mation is composed of conglomeratic channel de-posits and fine to coarse-grained sandstone; po-rosity ranges between 14 and 16%, with an averagepermeability of 140 md. The lower Nia is a fine tomedium-grained sandstone; porosity ranges be-tween 12 and 18%, and permeability ranges be-tween 50 and 800 md. The Noi and Ene forma-tions consist of alternating fine-grained sandstoneand siltstone deposits; porosity ranges between 9and 17%, and permeability ranges between 1 and600 md. All formations were drilled with water-base mud whose salinity varied across the variousfields.

Figure 1 shows the geographical location of theSan Martin, Cashiriari, and Pagoreni fields in thesouthern Ucayali Basin, 431 km (268 mi) east ofLima and 230 km (143 mi) north of Cusco, Peru.The San Martin and Cashiriari fields are located in

Gandhi et al. 381

Camisea Block 88, whereas the Pagoreni field islocated in Camisea Block 56. Both blocks comprisean area of approximately 2895 km2 (1118 mi2) andare located in the fold and thrust belt of the south-ern Ucayali Basin; their hydrocarbon reserves areestimated at 15 tcf of gas and 600 million bbl ofcondensate (Carrillo Barandiarán, 2000).

Figure 2 describes the stratigraphic columnand generic lithofacies of the southern Ucayali Ba-sin (Seminario et al., 2002). The figure also showsgeneric gamma-ray and resistivity logs across gas-bearing reservoirs encountered in the San Martin,Cashiriari, and Pagoreni fields. The upper Vivian,lower Nia, and lower Noi Formations pose petro-

382 Geohorizons

physical interpretation challenges that are explainedin the following section.

Problem Statement

Conventional petrophysical interpretation of welllogs across formations other than the upper Vivian,lower Nia, and lower Noi yields water saturationvalues consistent with core and production data.Figure 3 shows results obtained from the con-ventional petrophysical interpretation of welllogs across the middle and upper Nia Formationin well SM 1002D. Low values of water saturation(approximately 20%) are in agreement with

Figure 1. Map showing the location of the San Martin, Cashiriari, and Pagoreni fields (shown in red) in the southern Ucayali Basin(blocks 88 and 56) of Camisea, located 431 km (268 mi) east of Lima and 230 km (143 mi) north of Cusco, Peru. The red line denotes thegas transport line from the Camisea field to the coast of Lima (modified from Díaz da Jornada, 2008). O and GIP = oil and gas in place;TCF = trillion cubic feet.

production measurements, indicating the ab-sence of mobile water. Shallow mud-filtrate in-vasion in these formations gives rise to the separa-tion of apparent resistivity logs with differentradial lengths of investigation.

Conversely, conventional petrophysical inter-pretation of well logs across the upper Vivian, lowerNia, and lower Noi Formations yields values ofwater saturation higher than 60%. Such relativelylarge values of water saturation are higher than

Figure 2. Stratigraphic column, generic gamma-ray and resistivity logs, and lithofacies of the southern Ucayali Basin in Camisea, Peru(modified from Díaz da Jornada, 2008). See Appendix 1 for a list of acronyms and abbreviations for expanded terms. Upp = upper; Mid =middle; Low = lower.

Gandhi et al. 383

irreducible water saturation inferred from coremeasurements (approximately 20%). Productiondata from these formations indicate null waterinflux, and hence, no mobile water pore volume.Figure 4 shows the results obtained from the con-ventional petrophysical interpretation of well logsacross the lower Nia Formation in well SM 1002D.Calculated porosity is in agreement with core mea-surements. However, the calculated water satura-tion is more than 60%, which is substantially higher

384 Geohorizons

than values of irreducible water saturation mea-sured on core samples. Core measurements of wa-ter saturation were acquired using a centrifugetechnique and were assumed equal to irreduciblewater saturation in view that the formation didnot produce water. Similar abnormally high valuesof calculated water saturation are encountered inall existing wells within the San Martin, Cashiriari,and Pagoreni fields, which are inconsistent withproduction measurements. The following are two

Figure 3. Conventional petrophysical interpretation of well logs across the upper and middle Nia Formation in well San Martin–1002D(SM-1002D). Track 1: depth. Track 2: gamma-ray log. Track 3: logging-while-drilling apparent resistivity logs acquired with different radiallengths of investigation. Track 4: wireline apparent resistivities acquired with different radial lengths of investigation. Track 5: neutron anddensity logs. Track 6: computed apparent matrix density and measured core grain density. Track 7: total water saturation and measuredcore water saturation. Track 8: computed pore-fluid fraction. Track 9: NMR T2 distribution. Track 10: P factor rock-quality index (refer tothe section titled Rock Typing). Track 11: estimated lithology with measured core porosity. See list of acronyms and abbreviations forexpanded terms.

salient features of gas-bearing formations exhib-iting abnormally high values of water saturationwhen calculated with conventional well-log inter-pretation procedures:

1. Stacking (overlapping) of apparent resistivitylogs with different radial lengths of investigationwhen the salinity of mud-filtrate (Cmf) is com-parable to the salinity of connate water (Cw)

2. Relatively low values of deep-sensing apparentresistivity, giving rise to abnormally high valuesof calculated water saturation

Calculation of water saturation via conven-tional well-log interpretation was performed usingeither Archie’s or dual water saturation–porosity–resistivity models and included average valuesof Winsauer’s factor, a, equal to 1; saturation

Figure 4. Conventional petrophysical interpretation of well logs across the lower Nia Formation in well San Martin–1002D (SM-1002D).Track 1: depth. Track 2: gamma-ray log. Track 3: logging-while-drilling apparent resistivity logs with different radial lengths of in-vestigation. Track 4: wireline apparent resistivities with different radial lengths of investigation. Track 5: neutron and density logs. Track 6:computed apparent matrix density and measured core grain density. Track 7: total water saturation and measured core water saturation.Track 8: computed pore-fluid fraction. Track 9: NMR T2 distribution. Track 10: P factor rock-quality index (refer to the section titiled RockTyping). Track 11: estimated lithology with measured core porosity. See Appendix 1 for a list of acronyms and abbreviations for expandedterms.

Gandhi et al. 385

exponent, n, equal to 1.68; and porosity exponent,m, equal to 1.78. These parameters were deter-mined from laboratory experiments performed oncore samples. See Appendix 2 for explanations ofsymbols.

Figure 5 shows scanning electron microscopyimages of lower Nia core samples. These imagesindicate that grains can be completely coated withchlorite and/or illite and/or smectite. In addition,mineral analyses of core samples from the sameformation yielded volumetric concentrations ofapproximately 1 to 2% of iron-bearing minerals ingrains, such as hematite and chalcopyrite. Althoughhematite has negligible electrical conductivity, it is

386 Geohorizons

ferromagnetic and exhibits abnormally high mag-netic susceptibility that can affect magnetic res-onance and high-frequency electromagnetic in-duction measurements. Because of this, it has beensuggested that the abnormally low values of ap-parent resistivity could be caused by the presenceof electrically conductive minerals and/or grain-coating clay with relatively high values of cationexchange capacity per unit pore volume. The samehypothesis postulates that the effect of the twomaterials (grain-coating clay and electrically con-ductive minerals) on the electrical conductivity ofthe rock is exacerbated because of their spatialdistribution almost exclusively on grain surfaces

Figure 5. Scanning electron microscopyphotograph of a core sample indicating awell-sorted arenite quartz with laminaeof fine and medium sand. The images in-dicate grain coatings of illite and smectiteas well as impregnations of hematite,which develop euhedral crystals over clastsurfaces.

despite their relatively low values of volumetricconcentration measured on core samples. Finally,the argument that attempts to explain relativelylow values of electrical resistivity in these for-mations in terms of mineral and/or clay spatialdistribution invokes the corresponding effect ofrelatively low salinity of connate water (approxi-mately 15,000 ppm ofNaCl equivalent). Indeed, itis well known (Winsauer and McCardell, 1953;Hill and Milburn, 1956) that the effect of clay onthe electrical conductivity of the rock increaseswithdecreasing values of salt concentration and de-creasing values of water saturation. Both situations(low salinity of connate water and low water sat-uration) are encountered in these formations and,therefore, should be properly assimilated in thepetrophysical interpretation of well logs.

Following the previous argument, it has beensuggested that decreasing the value of Archie’s sat-uration exponent, n, counteracts the abnormal de-crease of electrical resistivity caused by the com-bined effects of (1) the presence of clay-coatinggrains and/or electrically conductive grain minerals,(2) the low values of connate-water salinity, and(3) the low values of water saturation, on the cal-culation of in-situ water saturation in these for-mations (Worthington, 2011).

The objective of this article is to explore andquantify the alternate possibility of downward-biased deep-reading apparent resistivity logs causedby water-base mud-filtrate invasion. We empha-size that possible enhancements of electrical con-ductivity caused by electrically conductive miner-als and/or clay-coated grains can only be accountedfor in a petrophysically consistent manner onceapparent resistivity logs have been corrected forinvasion effects. The signature of invasion on ap-parent resistivity logs acquired in these reservoirs ismanifested in multiple ways:

1. Progressive separation of apparent resistivitylogs withmultiple radial lengths of investigation(in some instances, the separation from theshallowest- to the deepest-sensing resistivitylogs being as large as one order of magnitude)

2. Separation of apparent resistivity logs acquiredwith logging-while-drilling (LWD) induction

measurements indicates invasion effects that oc-cur almost immediately after drilling

3. Abnormal reversal of apparent resistivity logs(both LWDandwireline) because of salt mixingduring invasion in wells where an measurabledifference between the salinities of mud filtrateand connate water exists

4. Stacking (overlapping) of apparent resistivity logsacross low-permeability formations, possibly be-cause of large radial length of invasion (in thiscase, the stacking of resistivity logs occuring atrelatively low values of electrical resistivity, whichagrees with a hypothesis of abnormally high val-ues of water saturation caused by deep water-base mud-filtrate invasion displacing in-situ gas)

5. Decrease in the separation of apparent resistiv-ity logs when a difference between the salt con-centration of mud filtrate and connate waterexists (the separation between apparent resis-tivity logs significantly increasing when the saltconcentrations of mud filtrate and connate wa-ter are approximately the same)

6. Crossover between neutron and density logs evenin cases of deeply invaded formations, therebyindicating the presence of substantial residualgas saturation

7. Magnetic resonance T2 distribution curves thatexhibit negligible clay-bound water and are al-most exclusively associated with invading mudfiltrate in formations where resistivity logs stack

Apparent resistivity logs provided by well-logging companies are routinely corrected for bore-hole and skin (in the case of induction logs) effects.Occasionally, corrections are performed to reducemud-filtrate invasion effects via one-dimensionalradial inversion techniques. In the case of laterologmeasurements, such invasion-correction techniquesare reliable for the case of steep ramp-up radial re-sistivity profiles (i.e., electrical resistivity increaseswith radial distance into the invaded formation).More general corrections for invasion, such as thoseof ramp-down or annulus radial profiles requireadditional knowledge about the invasion processand can give rise to nonunique results if not in-terpreted properly. Depending on both radiallength of invasion and shape of the invading radial

Gandhi et al. 387

water-saturation front, invasion corrections for ap-parent resistivity logs can be significant.

The following sections describe the proceduresthat we developed to incorporate the process ofmud-filtrate invasion into the calculation of in-situwater saturation.

METHOD OF INTERPRETATION

The method implemented in this article for thepetrophysical interpretation of well logs and coredata consists of the following sequential steps: (1)rock typing, (2) construction of multilayer staticreservoir models, and (3) construction of multi-layer dynamic reservoir models.

Rock Typing

We implemented bothWinland’s method (Pittman,1992) and a well log–based technique to performrock classification. In Winland’s method, forma-tions were classified on the basis of their storageand flow capacities inferred from core measure-ments. Figure 6 shows the results obtained fromWinland’s rock classification method, emphasizingfour distinct flow units.

388 Geohorizons

Another technique applied for rock classifica-tion was based entirely on well-log responses. Eachflow unit possesses a unique set of petrophysicalproperties, that is, capillary pressure, relative per-meability, absolute permeability, andporosity,whichgives rise to a specific radial invasion profile that,in turn, determines the corresponding well-log re-sponse. Well-log responses are different for differ-ent rock types, whereby rock typing based on welllogs should yield equivalent rock classes to thoseinferred withWinland’s method. Figure 7 describesthe proposed rock classification based on well-logresponses. The plot includes the following threeindependent variables derived from combinationsof well logs:

K ¼ ðfCD � fCNÞft

ð1Þ

where fCD is shale-corrected density porosity, fCN isshale-corrected neutron porosity, ft is total poros-ity, andK is a qualitative relativemeasure of residualhydrocarbon pore volume. Residual hydrocarbon

Figure 6. Graphical description of Winland’s method for rockclassification based on storage and flow capacities, indicatingfour distinct rock types. k = absolute permeability; FF= porosity.

Figure 7. Rock classification based on well logs. Rock typesidentified based on Winland’s method are recognizable in therock classification performed with well logs. Rock types A and B,C, D1, and D2 are inferred as separate clusters on the rockclassification plot constructed with well logs. Refer to the text foran explanation of both K (a measure of pore volume) and re-sistivity index.

pore volume is in turn determined by the underly-ing pore-size distribution.

RI ¼ RDapp

RSapp

ð2Þ

whereRDapp is deep apparent resistivity, RS

app is shal-low apparent resistivity, and RI is the resistivityindex that quantifies the separation between ap-parent resistivity logs; RI is considered for rock clas-sification purposes because the separation betweenapparent resistivity logs is determined by the radialprofile of mud-filtrate invasion (in turn governedby the pore-size distribution).

RDapp ð3Þ

(deep apparent resistivity) is a direct qualitativemeasure of in-situ water saturationmeasureable withresistivity logs. Deep-sensing apparent resistivity isconsidered for rock classification because it is affectedby the radial length of mud-filtrate invasion.

The four rock types identified with Winland’smethod were confirmed in the well log–based clas-sification as separate clusters of data points. Specif-ically, types A and B rocks cluster together in thewell log–based rock classification, thereby support-ing the observation that the radial invasion profile issimilar for these two rock types. Rock type C ap-pears as a separate cluster of data points, whereasrock type D appears as two different data clustersdefined as typesD1 andD2.TypesD1 andD2 rocksare sandstones and conglomerates, respectively,and give rise to different well-log responses. Theseclusters exhibit different pore-size distributionsand/or pore structures,whereby they are associatedwith different radial profiles ofmud-filtrate invasion.

We quantified the log-based rock classificationby introducing aP factor log, which was synthesizedfrom various log responses. The P factor primarilyconsiders the effect of salinity contrast (betweenmud-filtrate and formationwater) on the separationof apparent resistivity logs for different rock types.It also considers the effect of salinity contrast on thedeepest sensing apparent resistivity log. Moreover,the P factor gives rise to a histogram that was inturn used to determine the likelihood of a given

depth point to be associated with a specific rocktype, referred to as the P factor rock-quality index.Rocks within different formations were classifiedas good, better, or best depending on their P factorrock-quality index. The P factor indicates that rocktype A/B is petrophysically better than rock types Cand D. It also concurs with nuclear magnetic res-onance (NMR) T2 distributions showing a decreasein rock quality with a decrease of pore size. The Pfactor is given by

P factor ¼1

Rmf+ 1

Rw

2Rw

" #×RD

app × ðftÞm ×RI ð4Þ

where Rmf is mud-filtrate resistivity, Rw is connate-water resistivity, RD

app is deep-sensing apparent re-sistivity, m is Archie’s porosity exponent, and RI isthe resistivity index.

Construction of Static and Dynamic MultilayerReservoir Models

Static and dynamic multilayer models were con-structed to explicitly incorporate the process ofmud-filtrate invasion in the calculation of in-situgas saturation. Accordingly, we constructed a CSFwith the software UTAPWeLS (developed by theUniversity of Texas at Austin’s Research Consor-tium on Formation Evaluation) and included differ-ent radial invasion profiles for different rock types.Numerical simulation of the process of mud-filtrateinvasion was performed to describe the radial dis-tributions of water saturation and salt concentra-tion into the invaded formations. This simulationincluded drilling variables such as type of mud,time of invasion, formation pore pressure, and over-balance pressure. It also included layer-by-layervalues of porosity, permeability, capillary pressure,and relative permeability, which were defined basedon available core data. Finally, the simulation in-cluded fluid properties such as density, viscosity,salt concentration of mud filtrate, salt concentrationof connate water, and temperature. Subsequently,the numerically simulated radial distributions ofwater saturation were transformed into radial dis-tributions of electrical resistivity (using Archie’s

Gandhi et al. 389

equation with nominal values of the variables a, m,and n), bulk density, and migration length to nu-merically simulate the corresponding apparent re-sistivity, density, and neutron logs.

Figure 8 describes the CSF method used toconstruct multilayer reservoir models. It is an iter-ative optimization process intended to decreasethe mismatch betweenmeasured and numericallysimulated resistivity and nuclear logs. Initial res-ervoir properties, that is, absolute permeability,porosity, relative permeability, water saturation,and capillary pressure, are inferred from the con-ventional petrophysical interpretation of well logsand available core measurements. For formationswhere core data were not available, an initial guessfor petrophysical properties was made using pre-viously defined rock types whose core measure-mentswere available in someother formation.Mud-filtrate invasion was numerically simulated usingthose formation properties as well as the corre-

390 Geohorizons

sponding apparent resistivity and nuclear logs.Numerically simulated logs were then comparedto measured logs. Depending on the degree of

Figure 8. Flow chart describing theiterative optimization method adopted inthis article to decrease the mismatch be-tween numerically simulated and mea-sured resistivity and nuclear logs. Thisprocess yields static and dynamic multi-layer reservoir models that honor all theavailable measurements and the physics ofmud-filtrate invasion.

Figure 9. Radial profile of water saturation after 20 days ofmud-filtrate invasion for rock types A/B, C, D1, and D2.

mismatch between numerically simulated andmeasured logs, progressive adjustments were madeto estimate layer-by-layer petrophysical propertiesuntil an acceptable agreement was reached. In sodoing, all the petrophysical parameters were ad-justed in a manner that was consistent with thestatic and dynamic petrophysical properties of thepreviously defined rock types.

PETROPHYSICAL PROPERTIES AND RADIALINVASION PROFILES ASSOCIATED WITHDIFFERENT ROCK TYPES

Differences in the pore-size distribution for the var-ious rock types resulted in different radial invasionprofiles. This observation indicates that the finalmatch between numerically simulated andmeasuredresistivity and nuclear logs was petrophysically con-sistent with the static and dynamic petrophysicalproperties of previously defined rock types.

Figure 9 shows the radial profile of mud-filtrateinvasion simulated after 20 days of invasion for rocktypes A/B, C, D1, and D2. Figure 10 shows thecorresponding radial resistivity profile for the dif-ferent rock types. Table 1 summarizes the rock andfluid properties assumed in the parametric descrip-tion of saturation-dependent relative permeabilityand capillary pressure using the Brooks-Corey for-mulation (Brooks and Corey, 1964). Figure 11 de-scribes the corresponding saturation-dependentrelative permeability and capillary pressure curvesused to simulate the process of mud-filtrate inva-sion for the four different rock types considered inthis article. Table 2 describes the mudcake, fluid,and formation properties assumed in the simula-tion of the process of mud-filtrate invasion.

The radial saturation profile for formations ofrock type A/B shows significant mud-filtrate inva-sion of approximately 2.5m (8.2 ft) with irreduciblewater saturation as low as 10%. Modern commer-cial resistivity tools have a maximum radial lengthof investigation of approximately 3 m (10 ft), thatis, longer than the radial length of invasion for rocktypes A and B. Therefore, the radial saturationprofile for rock types A and B is closely reflected inthe apparent resistivities measured across the re-spective formations. Typical characteristics of rocktypes A and B containing gas include high deep-sensing apparent resistivity and significant separa-tion between apparent resistivity logs with differentradial lengths of investigation when Cmf is com-parable to Cw.

The radial water saturation profile for forma-tions of rock type C evidences considerable mud-filtrate invasion of more than 3.5 m (11.5 ft). Ir-reducible water saturation is approximately 27%,whereas residual gas saturation is approximately

Figure 10. Radial profile of electrical resistivity after 20 days ofmud-filtrate invasion for rock types A/B, C, D1, and D2.

Table 1. Rock-Fluid Properties Assumed for the Simulation of Mud-Filtrate Invasion to Construct Generic Type Well Logs*

Rock Type
Sor ft (%) k (md) P0c (psi d1/2) ep k0rnw enw
G

k0rw

andhi et al

ew

.

Swr

A/B
0.2 20 500 120 10 1 2 0.2 8 0.08 C 0.22 12 30 90 5 0.7 2 0.4 4 0.3 D1 0.25 13 5 40 5 0.7 2.25 0.47 10 0.2 D2 0.25 9 10 40 5 0.7 2.25 0.47 10 0.2
*See Appendix 2 for explanations of symbols.

391

20%. Because the radial length of mud-filtrate in-vasion is longer than the typical radial length ofinvestigation of deep-sensing resistivity measure-ments, the virgin (noninvaded) saturation responseis not adequately reflected in the apparent resis-tivity log. Therefore, water saturation calculatedfrom deep-sensing apparent resistivity yields ab-normally high values. This undesirable situationcauses a reduction of hydrocarbon reserves when

392 Geohorizons

calculated with conventional well-log interpreta-tion methods. Major characteristics of such forma-tions are very low deep-sensing apparent resistiv-ities and small separation between resistivity logswith different radial lengths of investigation whenCmf is comparable to Cw.

The radial saturation profile for formations ofrock type D1 evidences significant mud-filtrateinvasion deeper than 3.5 m (11.5 ft). Irreduciblewater saturation and residual gas saturation are bothapproximately equal to 20%. Analogous to rocktype C, apparent resistivity logs for rock type D1do not reflect virgin (noninvaded) values of satu-ration. This behavior causes a reduction of hydro-carbon reserves in the calculation of water satura-tion from deep-sensing apparent resistivity logs.Mud-filtrate invasion in formations of rock typeD1results in both low apparent resistivities and neg-ligible separation between resistivity logs with dif-ferent radial lengths of investigation when Cmf iscomparable to Cw.

Rock type D2 has a similar radial invasion pro-file to that of rock type D1. The radial saturationprofile shows considerable mud-filtrate invasiondeeper than 3.7 m (12.1 ft). Irreducible water sat-uration and residual gas saturation are approxi-mately equal to 20%. Apparent resistivity logs donot reflect the virgin (noninvaded) water satura-tion profile, and consequently, conventional well-log interpretation yields abnormally low values ofgas saturation. Rock type D2 mainly consists of

Figure 11. Water-gas relative permeability and capillary pressure curves assumed in the simulation of the process of mud-filtrateinvasion for the four rock types.

Table 2. Summary of Mudcake, Fluid, and Formation Properties
Assumed in the Simulation of the Process of Mud-Filtrate Invasion
Variable
Units Value
Wellbore radius
m 0.1026 Maximum invasion time days 20 Formation outer boundary m 610 Reservoir temperature °F 167 Initial reservoir pressure psi 3132 Gas viscosity (reservoir conditions) cp 0.0221 Overbalance pressure psi 670 Mud-filtrate density (at STP*) g/cm3 1.00 Mud-filtrate viscosity (at STP) cp 1.00 Mud-filtrate compressibility (at STP) psi–1 3.6 × 10–6
Formation compressibility
psi–1 4 × 10–7
Mudcake reference permeability
md 0.03 Mudcake reference porosity fraction 0.30 Mud solid fraction fraction 0.06 Mudcake maximum thickness m 0.0102 Mudcake compressibility exponent fraction 0.40 Mudcake exponent multiplier fraction 0.10
*STP = standard temperature and pressure.

conglomerates with presence of dolomite in theform of cement and grains. The saturation profileis similar to that of rock type D1. Different rockfacies with respect to those of rock type D1 are themajor reason for the discrepancy in well-log re-sponses between the two rock types. Importantcharacteristics of rock type D2 formations are highapparent resistivities and a relatively low porosity(approximately 8%).

Figure 9 compares the radial profiles of mud-filtrate invasion simulated after 20 days of invasionfor the different rock types. Rock types A and Bexhibit relatively shallow and sharp radial profiles ofmud-filtrate invasion. Rock types C and D are as-sociated with deeper and smoother radial profilesof mud-filtrate invasion than rock types A and B.The smoothness of the radial profile of invasion is

primarily controlled by capillary forces. Indepen-dent confirmation of the differences in the radialprofiles of mud-filtrate invasion for the variousrock types comes from the trends of formation porepressure documented in Appendix 3.

Figure 10 compares the radial resistivity pro-files for the different rock types (calculated from thecorresponding radial profiles of water saturationshown in Figure 9). For the case of rock types A/B,significant differences between deep- and shallow-sensing resistivities lead to uniform separation fromshallow- to deep-sensing apparent resistivities.Although the deep-sensing apparent resistivitylogs for these rock types are affected by invasion,the calculation of water saturation directly fromthem is only slightly affected by invasion. How-ever, for the case of rock types C andD, relatively

Figure 12. Generic-type well logs corresponding to rock type A/B for the base case. Track 1: apparent resistivity logs with differentradial lengths of investigation. Track 2: neutron and density logs. Track 3: radial cross section of total water saturation. Track 4: NMR T2distribution. Track 5: lithology with core photograph of the rock type. See Appendix 1 for a list of acronyms and abbreviations forexpanded terms.

Gandhi et al. 393

small differences between the deep- and shallow-sensing resistivities lead to the stacking of shallow-to deep-sensing apparent resistivity logs. Longerradial lengths of invasion in rock types C and Dcompared to rock types A and B cause a significantdecrease in deep-sensing apparent resistivities, there-by giving rise to abnormally large estimations ofwater saturation with conventional well-log inter-pretation procedures.

Generic Type Logs

We calculated generic-type logs assuming com-parable salt concentration between mud filtrateand connate water. Figure 12 shows the generic-type logs for rock types A/B. A significant sep-aration between apparent resistivity logs exists,

394 Geohorizons

whereas the NMR T2 distribution indicates thepresence of macropores (the mud-filtrate T2 peakoverlaps with the T2 peak because ofmacropores).The neutron-density crossover indicates high po-rosity (approximately 20%), and core data indi-cate good grain sorting with larger grain size thanfor other rock types. Likewise, the radial cross sec-tion of total water saturation indicates that mud-filtrate invasion is relatively shallow (shorter than1 m [3 ft]), whereby the deep-sensing apparentresistivity log properly resolves the true formationresistivity in the noninvaded (virgin) zone.

Figure 13 shows the generic type logs for rocktype C. The separation between apparent resis-tivity logs is small. Resistivity logs indicate lowerformation resistivity compared to other rock types.Both the neutron-density crossover and the NMR

Figure 13. Generic type well logs corresponding to rock type C for the base case. Track 1: apparent resistivity logs with different radiallengths of investigation. Track 2: neutron and density logs. Track 3: radial cross section of total water saturation. Track 4: NMR T2distribution. Track 5: lithology with core photograph of the rock type. See Appendix 1 for a list of acronyms and abbreviations forexpanded terms.

T2distribution indicate thepresence of residual gassaturation. Core descriptions indicate finer grainsthan those for rock type A/B. The radial cross sec-tion of total water saturation indicates that mud-filtrate invasion is relatively deep (approximately4 m [13 ft]), whereby the deep-sensing apparentresistivity log does not adequately resolve the trueformation resistivity in the noninvaded (virgin) zone.

Figure 14 shows the generic type logs for rocktype D1. A negligible separation between apparentresistivity logs exists. Resistivity logs indicate higherformation resistivity compared to that of rock typeC. The NMR T2 distribution indicates the presenceof micropores. Both the neutron-density crossoverand the T2 distribution confirm the presence of re-sidual gas saturation.Core descriptions indicate finergrains than those for rock type A/B but are com-parable to those of rock type C. The radial dis-tribution of total water saturation indicates that

mud-filtrate invasion is relatively deep (approxi-mately 3.5 m [11.5 ft]), whereby the deep-sensingapparent resistivity log does not adequately resolvethe true formation resistivity in the noninvaded (vir-gin) zone. Differences in the distribution of pore-throat radii give rise to differences in the radialprofile of mud-filtrate invasion between rock typesC and D1. This difference is clearly reflected in theradial distribution of total water saturation for thetwo rock types.

Figure 15 shows the generic type logs for rocktype D2. A small separation between apparentresistivity logs exists. Likewise, resistivity logs in-dicate a formation resistivity higher than those forrock types C andD1 but smaller than those for rocktype A/B. The NMR T2 distribution indicates avariable pore-size distribution, with the increase ofgrain density resulting in marginal neutron-densitycrossover. Core descriptions indicate poor grain

Figure 14. Generic type well logs corresponding to rock type D1 for the base case. Track 1: apparent resistivity logs with different radiallengths of investigation. Track 2: neutron and density logs. Track 3: radial cross section of total water saturation. Track 4: NMR T2distribution. Track 5: lithology with core photograph of the rock type. See Appendix 1 for a list of acronyms and abbreviations forexpanded terms.

Gandhi et al. 395

sorting and the presence of conglomerates. Theradial distribution of total water saturation indi-cates that mud-filtrate invasion is relatively deep(approximately 4 m [13 ft]), whereby the deep-sensing apparent resistivity log does not adequatelyresolve the true formation resistivity in the non-invaded (virgin) zone.

FIELD CASE NO. 1: WELL SANMARTIN–1002D

This field case examines a siliciclastic sequence en-countered in well SanMartin–1002D (SM-1002D),with mud-filtrate salinity (approximately 14,350ppm of NaCl equivalent) comparable to that offormation water (approximately 14,450 ppm of

396 Geohorizons

NaCl equivalent). It constitutes the base case forrock classification of formations encountered inthe San Martin reservoir. Figure 6 describes theresults obtained fromWinland’s rock classification

Figure 15. Generic type well logs corresponding to rock type D2 for the base case. Track 1: apparent resistivity logs with different radiallengths of investigation. Track 2: neutron and density logs. Track 3: radial cross section of total water saturation. Track 4: NMR T2distribution. Track 5: lithology with core photograph of the rock type. See Appendix 1 for a list of acronyms and abbreviations forexpanded terms.

Figure 16. Photograph of core samples retrieved from themiddle Nia sandstones in well San Martin–1002D (SM-1002D).

method based on flow units, whereas Figure 7shows the rock classification constructed with welllogs. Gas present in rock formations penetrated bythe well is mainly composed of methane and somelighter fractions.

Middle Nia Formation

This formation contains rock types A/B and D2.Segments of rock type D2 are present as a singlelayer of conglomerate in a thick sandstone layer ofrock type A/B. Figure 16 shows a photograph ofcore samples retrieved from the sand layer in themiddle Nia Formation; grains are well sorted withthe presence of cross-bedding. Figure 17 shows aphotograph of core samples retrieved from theconglomerate in the middle Nia Formation; grainsare poorly sorted with the presence of calcite ce-ment. Figure 3 shows the results obtained fromthe conventional petrophysical interpretation ofwell logs together with available core measure-ments. A prominent separation between resistiv-ity logs with different radial lengths of investi-gation exists. Deep-sensing resistivity logs readapproximately 30 ohm m. Calculated porosityand grain density are in good agreement with coremeasurements. The estimated water saturation is

lower than 15% in rock type A/B, which is close toirreducible water saturation. However, the inter-pretation indicates water saturation of approxi-mately 30%, whereas that of core measurements isapproximately 20% for rock type D2. The primaryreason for the difference in water saturation betweencore measurements and conventional well-log inter-pretation for rock typeD2 is that apparent resistivitylogs are affected by mud-filtrate invasion. Radiallydeep mud-filtrate invasion causes a decrease inthe separation between apparent resistivity logs.The deep-sensing resistivity log reads approximately50 ohm m for reservoir units of rock type D2.

Figure 18 describes the multilayer reservoirmodel constructed for the middle Nia Formationof rock type A/B. The multilayer model indicatesmud-filtrate invasion of 1 to 1.5 m (3–4.9 ft) sim-ulated for 20 days. In this particular case, the staticmultilayer model was sufficient to match numeri-cally simulated andmeasuredwell logs. In addition,water saturation estimated with the multilayermodel is in agreement with water saturation calcu-lated with conventional well-log interpretation.This result indicates that the deep-sensing resistivitylog is adequately sensing the virgin (noninvaded)formation resistivity.

Figure 19 describes the multilayer reservoirmodel constructed for the middle Nia Formationof rock type D2, indicating mud-filtrate invasionof approximately 3 m (10 ft) and simulated after20 days of invasion. The dynamic multilayer res-ervoir model was constructed to match numeri-cally simulated and measured well logs. Water sat-uration estimated with the constructed multilayerreservoir model is approximately 20%, which is inclose agreement with core data. This behavior im-plies that, because of relatively deep radial lengthof invasion, the deep-sensing resistivity log does nothave the necessary radial length of investigation toprobe the noninvaded formation resistivity.

Lower Nia Formation

Figure 4 shows the results obtained from conven-tional well-log interpretation across the lower NiaFormation, together with available core measure-ments. The formation includes depth sections with

Figure 17. Photograph of core samples retrieved from themiddle Nia conglomerates in well San Martin–1002D (SM-1002D).

Gandhi et al. 397

reservoir units of rock types C and D1. Water sat-uration in rock type C is approximately 80%, whichis higher than irreducible water saturation and con-tradicts measurements of water-free gas produc-tion. Water saturation calculated with conventionalwell-log interpretation in rock type D1 in the lowerNia Formation ranges between 40 and 80% de-pending on porosity. Core measurements indi-

398 Geohorizons

cate low water saturation, of approximately 20%.At the same time, porosity and grain density are ingood agreement with core measurements. The dis-crepancy in water saturation is mainly caused bythe effect of mud-filtrate invasion on apparent re-sistivity logs. Relatively low values of deep-sensingapparent resistivity (approximately 7 and 15 ohmm in rock types C and D1, respectively) together

Figure 18.Multilayer reservoir model constructed for the middle Nia Formation in well San Martin–1002D (SM-1002D). Track 1: depth.Track 2: measured (solid lines) and numerically simulated (dashed lines) apparent resistivities for different radial lengths of investigation.Track 3: measured (solid lines) and numerically simulated (dashed lines) neutron and density logs; the yellow and red crossovercorresponds to that of measured and simulated logs, respectively. Track 4: spatial distribution of water saturation obtained from thenumerical simulation of mud-filtrate invasion. Track 5: CSF-derived water saturation (blue), conventional-interpretation water saturation(red), and measured core water saturation (black dots). Track 6: CSF-derived nonshale porosity and measured core porosity (black dots).See Appendix 1 for a list of acronyms and abbreviations for expanded terms.

with stacking of resistivity logs indicate relativelylong radial length of invasion. Figure 20 shows aphotograph of core samples retrieved from thelower Nia Formation. The rock is sandstone com-posed of abundant very fine grains and commonmedium-size grains, most likely responsible for adecrease in permeability. Sand units include high-angle planar cross-bedding consisting of avalanche,ripple, and grain fall deposits. Calcareous cementthat can be observed as white spots on the slabbedcore surface is present.

The constructed multilayer reservoir modelshown in Figure 21 indicates mud-filtrate inva-sion of approximately 6 m (20 ft) simulated for20 days for rock typeC in the lowerNia Formation.Figure 22 describes the constructed multilayer res-ervoir model for rock type D1 in the lower NiaFormation; it indicates a radial invasion length ofapproximately 3.3 m (10.8 ft). Construction of adynamic multilayer reservoir model was necessaryfor both rock types to match numerically simu-lated and measured well logs. Water saturation

Figure 19. Multilayer reservoir model constructed for the middle Nia Formation (conglomerate) in well San Martin–1002D (SM-1002D). Track 1: depth. Track 2: measured (solid lines) and numerically simulated (dashed lines) apparent resistivities for differentradial lengths of investigation. Track 3: measured and numerically simulated neutron and density logs. Track 4: spatial distribution ofwater saturation obtained from the numerical simulation of mud-filtrate invasion. Track 5: CSF-derived water saturation (red) andconventional-interpretation water saturation (blue). See Appendix 1 for a list of acronyms and abbreviations for expanded terms.

Gandhi et al. 399

estimated from the constructed multilayer reser-voir model is approximately 30% for the lower NiaFormation; this value is in better agreement withproduction and core measurements than the onecalculated via conventional well-log interpretation.

FIELD CASE NO. 2: WELL CASHIRIARI-3 ST2

Well Cashiriari-3 ST2 (CR-3 ST2) penetratedsiliciclastic formations using mud-filtrate salinity(approximately 4500 ppm of NaCl equivalent)comparable to connate-water salinity (approximate-ly 2500 ppm of NaCl equivalent). We describe in-terpretation results for formations of rock type Cwhere triaxial induction resistivity measurementswere available. Themaximumwell deviation angleis approximately 10°.

Effect of the Spatial Distribution of WaterSaturation on Resistivity Anisotropy in theVivian Formation

The estimation of resistivity anisotropy can be af-fected by the spatial distribution of water saturationin the near-wellbore region. This phenomenon hasbeen documented in the past (Walsgrove et al.,

400 Geohorizons

1999; Faivre et al., 2002), suggesting that it is im-perative to correct induction resistivity measure-ments for the presence of mud-filtrate invasion be-fore estimating resistivity anisotropy.

Triaxial induction resistivity measurementswere acquired in well CR-3 ST2with the objectiveof detecting and quantifying resistivity anisotropyin gas-bearing formations. Figure 23 shows thecorresponding well logs (vertical, Rv, and hori-zontal,Rh, electrical resistivities) together with theconventional petrophysical analysis of well logsacross the Vivian Formation. Resistivity anisot-ropy (Rv/Rh) approximately equal to 3 is observedacross the lower and middle Vivian Formation,which subsequently decreases in the upper VivianFormation. Finally, resistivity anisotropy is negli-gible in the upper Vivian Formation, suggesting thatthe formation is electrically isotropic. The pres-ence of resistivity anisotropy in the absence of mud-filtrate invasion could not explain this phenome-non. Furthermore, the effect of resistivity anisotropyon apparent resistivity logs is contradictory to theobserved resistivity log response, that is, higher re-sistivity anisotropy resulting in the separation ofapparent resistivity logs and vice versa. However,differences in radial profiles of mud-filtrate invasionbetween the upper Vivian and the lower and mid-dleVivian could explain the observed resistivity logresponse. The P factor rock-quality index showsthat the upper Vivian has inferior petrophysicalquality, hence is prone to deeper mud-filtrate inva-sion than the lower and middle Vivian Formation.Because the estimated resistivity anisotropy was notcorrected for mud-filtrate invasion effects, we con-clude that the variations of resistivity anisotropy inwell CR-3 ST2 are most likely caused by the dif-ferences in the radial profile ofmud-filtrate invasion.

Upper Vivian

Figure 23 shows the results obtained from theconventional petrophysical interpretation of welllogs across the upper Vivian Formation, whichcomprises reservoir units of rock type C. Watersaturation obtained from conventional petrophys-ical interpretation ranges between 100 and 20%,

Figure 20. Photograph of core samples retrieved from thelower Nia sandstones in well San Martin–1002D (SM-1002D).

representing a decreasing trend with depth. How-ever, the formation produces water-free gas. Valuesof water saturation calculated with the constructedmultilayer reservoir model are approximately 28%for the upper Vivian Formation, which are in betteragreement with production data than those ob-tained with conventional well-log interpretation.The model indicates radial mud-filtrate invasionof approximately 6 m (20 ft). Figure 24 shows aphotograph of core samples retrieved from theupper Vivian Formation. The formation consists offine-grain sandstone, very likely resulting in lowerpermeability than the lower Vivian.

Figure 23 also shows the NMR T2 distributionacross the Vivian Formation, indicating a gradualincrease of pore size with increasing depth. Thevariation of pore sizes gives rise to differences inrock type. Rock type C, encountered in the uppersection, is composed of smaller pore sizes, therebyresulting in deep mud-filtrate invasion.

FIELD CASE NO. 3: WELL PAGORENI-1004D

Siliciclastic formations penetrated by well Pagoreni-1004D (PAG-1004D) are characterized by values

Figure 21. Multilayer reservoir model constructed for the lower Nia Formation in well San Martin–1002D (SM-1002D). Track 1: depth.Track 2: measured (solid lines) and numerically simulated (dashed lines) apparent resistivities for different radial lengths of investigation.Track 3: measured and numerically simulated neutron and density logs. Track 4: spatial distribution of water saturation obtained from thenumerical simulation of mud-filtrate invasion. Track 5: CSF-derived water saturation (blue) and conventional-interpretation water sat-uration (red). See Appendix 1 for a list of acronyms and abbreviations for expanded terms.

Gandhi et al. 401

of mud-filtrate salinity (approximately 4000 ppmof NaCl equivalent) lower than those of forma-tion water salinity (approximately 14,450 ppm ofNaCl equivalent). Salt mixing and dispersion ef-fects give rise to a radial gradient of salt concentra-tion, which has a measurable effect on apparentresistivity logs. Consequently, it is necessary to inferthe corresponding radial profile of salt concentra-tion to accurately estimate gas saturation.

402 Geohorizons

Comparison of Resistivity Logs Acquiredacross Different Rock Types in thePagoreni Reservoir

Figure 25 compares LWD and wireline logs ac-quired in formations of rock types A/B and D1 inwell PAG-1004D. In the set of LWD logs, we ob-serve that the deep-sensing apparent resistivity ishigher than both shallow- and intermediate-sensing

Figure 22. Multilayer reservoir model constructed for the lower Nia Formation in well San Martin–1002D (SM-1002D). Track 1: depth.Track 2: measured (solid lines) and numerically simulated (dashed lines) apparent resistivities for different radial lengths of investigation.Track 3: measured and numerically simulated neutron and density logs. Track 4: spatial distribution of water saturation obtained from thenumerical simulation of mud-filtrate invasion. Track 5: CSF-derived water saturation (blue) and conventional-interpretation water sat-uration (red). See Appendix 1 for a list of acronyms and abbreviations for expanded terms.

resistivity logs; we also observe a monotonic sep-aration between apparent resistivity logs. This be-havior indicates a high propensity of reservoirformations toward invasion. Wireline logs were ac-quired after approximately 14 days of mud-filtrateinvasion; they indicate a reversal in the resistivitytrend from shallow to deep sensing when com-pared to LWD resistivity logs, with shallow-sensingresistivity higher than deep-sensing resistivity. Such

an abnormal behavior of resistivity logs is a directconsequence of the process ofmud-filtrate invasion,which is governed by the interplay among gasmobility, salt mixing, and dispersion effects. Theseparation between deep- and shallow-sensingwireline apparent resistivity logs is approximately2% across the upper and middle Nia formations(which include reservoir units of rock type A/B),whereas it is higher than 10% across the lower Nia

Figure 23. Conventional petrophysical interpretation of well logs across the Vivian Formation in well Cashiriari-3 ST2 (CR-3 ST2). Track 1:depth. Track 2: gamma-ray log. Track 3: laterolog apparent resistivities acquired with different radial lengths of investigation. Track 4: 2-ft(1-m)–resolution induction apparent resistivities acquired with different radial lengths of investigation. Track 5: vertical (red) and hor-izontal (black) deep-sensing resistivities. Track 6: neutron and density logs. Track 7: computed apparent matrix density and measured coregrain density. Track 8: computed total water saturation and measured core water saturation. The computed total water saturation is morethan one decimal unit above 6873 ft (2095 m). Track 9: computed pore-fluid fraction. Track 10: NMR T2 distribution. Track 11: P factorrock-quality index (refer to the section titled Rock Typing). Track 12: estimated lithology with measured core porosity. See Appendix 1 fora list of acronyms and abbreviations for expanded terms.

Gandhi et al. 403

Formation (which comprises reservoir units ofrock type D1). This behavior indicates significantcapillary pressure effects giving rise to a radiallydeep but tapered invasion profile in formations ofrock type D1, which is consistent with the radialprofiles of mud-filtrate invasion previously de-scribed for field cases 1 and 2.

Figure 26 shows the LWD and wireline re-sistivity logs acquired in well PAG-1004D acrossformations of rock type C. The trend of the deep-and shallow-sensing apparent resistivities is similarto that observed across the lower Nia Formation,except that the shallow-sensing apparent resistiv-ity is approximately 30% higher than the deep-sensing apparent resistivity compared to 10% acrossthe lower Nia Formation. This behavior indicatesdominant capillary pressure effects giving rise to awide radial resistivity annulus. We therefore con-clude that capillary pressure effects on the radialinvasion front are more dominant in formations ofrock type C than in formations of rock type D1.

Effect of Salt Concentration Contrastbetween Mud Filtrate and Connate Wateron Apparent Resistivity Logs

The salt concentration contrast between mud fil-trate and connate water has a marked effect on

404 Geohorizons

apparent resistivity logs. Figure 27 shows mea-sured and synthetic apparent resistivity logs acrossformations of rock type A/B. Measured logs in-clude the effect of salt concentration differencebetween mud filtrate and connate water, whereassynthetic logs were calculated under the assump-tion of null salt concentration difference. The sep-aration between apparent resistivity logs increasessignificantly (more than two-fold) when no dif-ference in the salt concentrations of mud filtrateand connate water exists. In addition, the plotemphasizes significant mud-filtrate invasion ef-fects on apparent resistivity logs. This observa-tion confirms that apparent resistivity logs needto be corrected for mud-filtrate invasion effectsbefore using them for petrophysical analysis andinterpretation.

Lower Noi Formation

Figure 28 shows the results obtained from theconventional interpretation of well logs across for-mations of rock type C. Water-free gas productionis inconsistent with the relatively high values ofwater saturation yielded by conventional well-loginterpretation. Water saturation ranges between30 and 50%. Radially deep mud-filtrate invasionand the presence of awide resistivity annulus causedby the interplay between high capillary pressureand substantial salt concentration differences be-tween mud filtrate and connate water have a sig-nificant impact on deep-sensing resistivity logs. Thisobservation confirms the need of a multilayer CSFto estimate in-situ water saturation.

Static properties for each layer of theCSFweredefined with values obtained from conventionalwell-log interpretation. Likewise, dynamic proper-ties obtained for equivalent formations in the SanMartin and Cashiriari fields were used to simulatethe process of mud-filtrate invasion. Radial salinitygradients are primarily governed by salt mixingand dispersion effects. We calculated the radialsalinity profile using an iterative optimization meth-od that progressively reduced the mismatch be-tween numerically simulated and measured re-sistivity and nuclear logs. In so doing,we assumed a

Figure 24. Photograph of core samples retrieved from theupper Vivian sandstone in well Cashiriari-3 ST2 (CR-3 ST2).

radial profile of water saturation equivalent to thatof the lower Noi Formation in the San Martin andCashiriari fields. Depending on the mismatch be-tween numerically simulated and measured re-sistivity and nuclear logs, we adjusted the radialsalinity profile. Every progressive adjustment wasfollowed by resimulation of resistivity and nuclearlogs. Matrix and shale compositions calculated inthe Pagoreni field were consistent with those ofthe San Martin and Cashiriari fields. Likewise, theestimated radial salinity profile was consistent withthe salt concentrations of both mud filtrate andconnate water.

Figure 29 shows the multilayer reservoir modelconstructed after securing a good match betweennumerically simulated andmeasured resistivity logs.Water saturation was estimated at approximately18%, which is consistent with available productionmeasurements.

CONCLUSIONS

We systematically showed that the construction ofmultilayer reservoir models with the CSF methodyielded static and dynamic petrophysical propertiesthat were in very good agreement with core mea-surements and production data. Numerical simu-lation and matching of well logs confirmed thatmud-filtrate invasion is a dominant cause of abnor-mally low apparent resistivities measured in someof the gas-producing reservoir units in the SanMartin, Cashiriari, and Pagoreni fields. Thus, cor-rection of apparent resistivity logs for the effect ofmud-filtrate invasion was necessary to obtain reli-able estimates of in-situ gas saturation.

The construction of a multilayer CSF enabledus to explicitly calculate the effect of mud-filtrateinvasion on apparent resistivity logs, thereby allow-ing reliable calculations of in-situ gas saturation. It

Figure 25. Comparison ofwireline and LWD apparent re-sistivity logs in well Pagoreni-1004D (PAG-1004D). Track 1:depth. Track 2: gamma-ray log.Track 3: wireline apparent re-sistivities acquired with differentradial lengths of investigation.Track 4: LWD apparent resistiv-ities acquired with different ra-dial lengths of investigation. Thefirst and second sets are for rocktypes A/B and D1, respectively.See Appendix 1 for a list ofacronyms and abbreviations forexpanded terms.

Gandhi et al. 405

was shown that apparent resistivity logs acquiredin formations associated with shallow and sharpradial profiles of mud-filtrate invasion (giving riseto uniform separation of resistivity logs) can bereliably corrected for invasion effects using a staticreservoirmodel. However, when the radial profile ofwater saturation resulting frommud-filtrate invasionis radially deep and smooth, apparent resistivitylogs exhibit negligible to null separation and thedeep-sensing resistivity log exhibits abnormally lowvalues. Apparent resistivity logs for such forma-tions can only be corrected with a dynamic reser-voir model that explicitly accounts for the processof mud-filtrate invasion on well logs.

406 Geohorizons

Our analysis showed that magnetic resonancelogs (T2 distributions) acquired across the fourgeneric rock types were consistent with the radialinvasion profiles associated with them. In addi-tion, we showed that the length of the crossoverobserved between density and neutron logs in thevarious rock types was consistent with both theradial profile of invasion and the pore volume ofresidual gas left behind in the flushed zone by theinvading water-based mud filtrate. Furthermore,observed variations of rock mobility were found to

Figure 26. Comparison of wireline and LWD apparent re-sistivity logs for the formation of rock type C in well Pagoreni-1004D (PAG-1004D). Track 1: depth. Track 2: gamma-ray log.Track 3: wireline apparent resistivities acquired with differentradial lengths of investigation. Track 4: LWD apparent resistivitiesacquired with different radial lengths of investigation. See Ap-pendix 1 for a list of acronyms and abbreviations for expandedterms.

Figure 27. Measured (solid) and numerically simulated (dashed)apparent resistivity logs across a formation of rock type A/B.Measured and numerically simulated logs are with and withoutsalinity contrast between mud filtrate and connate water, re-spectively. See Appendix 1 for a list of acronyms and abbrevia-tions for expanded terms.

be consistent with the petrophysical properties ofthe various rock types. An additional confirmationof this behavior was provided by the depth trendsof pore pressure documented in Appendix 3.

We obtained gas saturations that were con-sistent with production and core measurements inthe three fields of study. Gas saturations calcu-lated from invasion-corrected apparent resistivitylogs systematically and conclusively yielded an in-crease in gas reserves compared to conventional in-terpretation methods applied to resistivity logs

uncorrected for invasion effects. Although our in-terpretation method does not rule out the possibleinfluence of conductive minerals on apparent re-sistivity logs, it does confirm that invasion effectsare significant and need to be accounted for beforecorrecting for the presence of conductive mineralsin the calculation ofwater saturation. Also, althoughthe presence of electrically conductive minerals inthe rock matrix could explain a part of the observedreduction of apparent resistivity, they cannot ex-plain the prominent variations in the separation

Figure 28. Conventional petrophysical interpretation of well logs across the lower Noi Formation in well Pagoreni-1004D (PAG-1004D).Track 1: depth. Track 2: gamma-ray log. Track 3: apparent resistivities, acquired with different radial lengths of investigation. Track 4:neutron and density logs. Track 5: computed apparent matrix density. Track 6: total water saturation. Track 7: computed pore-fluidfraction. Track 8: NMR T2 distribution. Track 9: P factor rock-quality index (refer to the section titled Rock Typing). Track 10: estimatedlithology with measured core porosity. See Appendix 1 for a list of acronyms and abbreviations for expanded terms.

Gandhi et al. 407

between apparent resistivity logs observed acrossthe various reservoir units. The extreme case ofabnormally low and stacked apparent resistivitylogs with different radial lengths of investigationcannot be explained without invoking the conceptof mud-filtrate invasion.

Last, we emphasize that multilayer modelsconstructed with the CSF concept are intimatelyrelated to reservoir engineering models and henceprovide useful information for primary and/or en-hanced recovery practices.

408 Geohorizons

APPENDIX 1: ACRONYMS AND ABBREVIATIONS

Pc = Capillary PressureHRLA® = Schlumberger’s High-Resolution Latero-

log Array ToolLWD = logging-while-drilling1-D = one-dimensionalSGR® = spectral gamma rayCMR® = Schlumberger’s Combinable Magnetic

Resonance ToolRTSc® = Schlumberger’s RT Scanner Tool

Figure 29. Multilayer reservoir model constructed for the lower Noi Formation in well Pagoreni-1004D (PAG-1004D). Track 1: depth.Track 2: measured (solid lines) and numerically simulated (dashed lines) apparent resistivities for different radial lengths of investigation.Track 3: neutron and density field logs. Track 4: spatial distribution of water saturation obtained from the numerical simulation of mud-filtrate invasion. Track 5: CSF-derived water saturation (blue) and conventional-interpretation water saturation (red). See Appendix 1 fora list of acronyms and abbreviations for expanded terms.

NMR = nuclear magnetic resonanceT2 NMR = transverse relaxation timeSTP = standard temperature and pressureCSF = common stratigraphic frameworkUTAPWeLS =University ofTexas atAustin’s Petro-

physical and Well-Log Simulatorppm = parts per millionCEC = cation exchange capacitytcf = trillion cubic feetWL = wirelineMMB = million metric barrelCR = CashiriariSM = San MartinPAG = PagoreniMIP = Mipayam = meterTc = lower middle EoceneTr-Ju = Triassic–JurassicP16Hds = LWD phase high-frequency 16-in.

(41-cm) apparent resistivityP22Hds = LWD phase high-frequency 22-in.




(102-cm) apparent resistivityRLA1 = wireline laterolog shallowest apparent

resistivityRLA2 = wireline laterolog shallow apparent resistivityRLA3 = wireline laterolog deep apparent resistivityRLA4 = wireline laterolog deeper apparent resistivityRLA5 = wireline laterologdeepest apparent resistivityNPOR = sandstone neutron porosityRHOZ = bulk densityRHOMA = apparent matrix densityRealDensity = measured matrix density from coreSW = total water saturation calculated with con-

ventional interpretationIrreducible = irreducible water saturationPHIE = nonshale porosityPHIT = total porosityAMP_DIST = CMR T2 amplitude distributionT2LM = logarithmic mean of T2 amplitudems = millisecondsT2CUTOFF = CMR T2 free fluid cutoff

VWCL = volume fraction of wet shaleVSILT = volume fraction of siltYRA1 = simulated wireline laterolog shallowest

apparent resistivityYRA2 = simulated wireline laterolog shallow ap-

parent resistivityYRA3 = simulated wireline laterolog deep ap-

parent resistivityYRA4 = simulated wireline laterolog deeper ap-

parent resistivityYRA5 = simulated wireline laterolog deepest ap-

parent resistivityNPHI (simul.) = simulated alpha-processed sand-

stone neutron porosityNPHI = alpha-processed sandstoneneutronporositySW_Conventional = water saturation calculated

with conventional interpretationAT10 = wireline induction 10-in. (25-cm) ap-

parent resistivityAT20 = wireline induction 20-in. (51-cm) ap-




parent resistivityRH72_NEW = 72-in. (183-cm) horizontal ap-

parent resistivityRV72_NEW = 72-in. (183-cm) vertical apparent

resistivityCore:Real = measured matrix density from coreBPHI LWD = sandstone neutron porosityROBB LWD = bottom-sector bulk densitydec = decimalO and GIP = oil and gas in placeSS = sandstoneSim = simulatedres = resistivity

APPENDIX 2: NOMENCLATURE

a = Winsauer’s factor in Archie's equationk = Permeability (md)m = Archie’s porosity exponentn = Archie’s saturation exponent

Gandhi et al. 409

fCD = Shale-corrected density porosity (fraction)fCN = Shale-corrected neutron porosity (fraction)ft = Total porosity (fraction)fns = nonshale porosity (fraction)Sor = residual non–wetting phase saturation (fraction)Cw = connate water salinity (ppm)Cmf = mud-filtrate salinity (ppm)Rw = connate water resistivity (ohm m)Rmf = mud-filtrate resistivity (ohm m)Swt = total connate-water saturation (fraction)ep = pore-size distribution exponentenw = experimental exponent (non–wetting phase)

for Brooks-Corey equationew = experimental exponent (wetting phase) for

Brooks-Corey equationSwr = residual wetting-phase saturation (fraction)P0c = coefficient for Pc equation (psi d1/2)

k0rnw = krnw end point

410 Geohorizons

k0rw = krw end pointRDapp = deep apparent resistivity (ohm m)

RSapp = shallow apparent resistivity (ohm m)

Rv = vertical resistivity (ohm m)Rh = horizontal resistivity (ohm m)RI = resistivity index (fraction)rta = simulated alpha-processed bulk density (g/cc)Sw,t = common stratigraphic framework–derived

total water saturation (fraction)Swirr = measured irreducible core water saturation

(fraction)Pc = Capillary Pressure

APPENDIX 3: PORE-PRESSURE INTERPRETATION

This appendix describes the results obtained from the anal-ysis of available formation pore-pressure data and their

Figure 30. Pressure gradient plot con-structed with pore-pressure data acquiredacross the Nia and Basal Chonta Forma-tions in wells Cashiriari (CR)-01, CR-02,CR-03, and CR-1005D. TVDss = true verticaldepth.

interpretation with respect to the petrophysical propertiesof previously defined rock types.

Figure 30 shows the pressure gradient plot obtained byanalyzing pore-pressure data acquired in the Nia and basalChonta Formations in wells CR-01, CR-02, CR-03, and CR-1005D. All the pressure data points are located along fluidpressure gradients. Pressure data acquired after pumping for-mation fluids (during fluid sampling) and pretest pressure datalie on the same fluid-gradient trend. This behavior indicatesshallow to negligible mud-filtrate invasion in the upper NiaFormation.However, pore-pressure data acquired in the lowerNia Formation suggest supercharging because measured pres-sures are higher than those expected from the correspondingfluid-gradient trend. Supercharging indicates the presence ofdeep invasion, whereby this condition confirms that the petro-physical quality of rock formations in the lower Nia is inferiorto that of the upper Nia.

Figure 31 shows the qualitative pretest permeability pa-rameter obtained at different depths from formations of rocktypes A/B, C, D1, andD2 in wells CR-01, CR-02, CR-03, andCR-1005D. The pretest permeability parameter increases with

a decrease in rock mobility; it is lower for formations of rocktype A/B compared to the pretest permeability parameter forformations of rock types C, D1, and D2. Such a behavior in-dicates that rock types C, D1, and D2 exhibit lower mobilitythan rock type A/B, thereby confirming that the petrophysicalquality of rock type A/B is inferior to that of rock types C,D1, and D2. This conclusion validates the diagnosis and def-inition of rock types implemented throughout our interpre-tation study.

REFERENCES CITED

Brooks, R. H., and A. J. Corey, 1964, Hydraulic properties ofporous media: Fort Collins, Colorado, Colorado StateUniversity, Hydrology paper 3, 27 p.

Carrillo Barandiarán, L., 2000, Yacimientos de Camisea: Es-timado de las reservas para reservorios naturalmentefracturados de gas condensado retrógrado: Proceedingsof the 2nd Congreso Latinamericano y Del Caribe De

Figure 31. Qualitative pretest perme-ability parameter obtained at differentdepths across formations of rock types A/B,C, D1, and D2 in the Cashiriari (CR)-01, CR-02, CR-03, and CR-1005D wells, respectively.

Gandhi et al. 411

Gas y Electricided, Punta del Este, Uruguay, March 27–29, 2000.

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Faivre, O., T. Barber, L. Jammes, and D. Vuhoang, 2002,Using array induction and array laterolog data to charac-terize resistivity anisotropy in vertical wells: Proceedingsof the Society of Petrophysicists and Well Log Analysts43rd Annual Logging Symposium, Oiso, Japan, June2–5, 2002, p. 3–4.

Hill, H. J., and J. D. Milburn, 1956, Effect of clay and watersalinity on electrochemical behavior of reservoir rocks:American Institute of Mining Metallurgical and Petro-leumEngineers PetroleumTransactions, v. 207, p. 65–72.

Pittman, E. D., 1992, Relationship of porosity and perme-ability to various parameters derived from mercury in-jection capillary pressure curves for sandstones: AAPGBulletin, v. 76, no. 2, p. 191–198.

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Voss, B., C. Torres-Verdín, A. Gandhi, G. Alabi, and M.Lemkecher, 2009, Common stratigraphic frameworkto simulate well logs and to cross-validate static and dy-namic petrophysical interpretations: Proceedings of theSociety of Petrophysicists and Well Log Analysts 50thAnnual Logging Symposium, The Woodlands, Texas,June 21–24, 2009, p. 15–16.

Walsgrove, T., B. Anderson, and T. Barber, 1999, Case studyof an anisotropic cross-bedded reservoir: Improving pre-dictions of reservoir properties through modeling the re-sistivity: Proceedings of the Society of Petrophysicistsand Well Log Analysts 40th Annual Logging Sympo-sium, Oslo, Norway, May 30–June 3, 1999, p. 1–3.

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http://dx.doi.org/10.2118/144688-MS

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