GEOHORIZONS

Quantification of pore structure

acoustic velocity at a given porosity than samples with small,

AUTHORS

Ralf J. Weger University of Miami,Rosenstiel School of Marine and AtmosphericScience, Division of Marine Geology and Geo-physics, 4600 Rickenbacker Causeway, Miami,Florida 33129; rweger@rsmas.miami.edu

Ralf J. Weger was a postdoctoral researcher withthe Comparative Sedimentology Laboratory atthe University of Miami when the article waswritten. He received his B.S. degree in systemsanalysis (2000) and his Ph.D. in marine geologyand geophysics (2006) from the University ofMiami. His dissertation focuses on quantitativepore- and rock-type parameters in carbonatesand their relationship to velocity deviations. Hismain interests range from processing and visu-alization of geophysical data to petrophysicalcharacterization of carbonate rocks.

Gregor P. Eberli University of Miami, Ro-senstiel School of Marine and AtmosphericScience, Division of Marine Geology and Geophys-ics, 4600 Rickenbacker Causeway, Miami, Florida33129; geberli@rsmas.miami.edu

Gregor P. Eberli is a professor in the Division ofMarine Geology and Geophysics at the Universityof Miami and the Director of the ComparativeSedimentology Laboratory. He received his Ph.D.from the Swiss Institute of Technology (ETH) inZrich, Switzerland. His research integrates thesedimentology, stratigraphy, and petrophysicsof carbonates. With laboratory experiments andseismic modeling, his group tries to understandthe physical expression of carbonates on log and inseismic data. He was a distinguished lecturer forAAPG (1996/97), Joint Oceanographic Institutions(1997/1998), and the European Association ofGeoscientists and Engineers (2005/2006).

Gregor T. Baechle University of Miami,Rosenstiel School of Marine and AtmosphericScience, Division of Marine Geology and Geo-physics, 4600 Rickenbacker Causeway, Miami,Florida 33129

Gregor T. Bchle graduated from the Universityof Tbingen in 1999 with a Diploma (equivalent toM.Sc. degree) in geology. In 2001, he joined theComparative Sedimentology Laboratory (CSL)with a Scholarship of the German Academic Ex-change Service to obtain a Ph.D. from the Univer-sity of Tbingen. From 2004 to 2008, he was aresearch associate in the CSL, managing the rockphysics laboratory. He is currently working forExxonMobil Upstream Research Company, Quan-titative Interpretation, Houston, Texas.complicated pores. Estimates of permeability from porosityalone are very ineffective (R2 = 0.143) but can be improvedwhen pore geometry information PoA (R2 = 0.415) and Dom-Size (R2 = 0.383) are incorporated.

Furthermore, results from the correlation ofDIAparametersto acoustic data reveal that (1) intergrain and/or intercrystalline

Copyright 2009. The American Association of Petroleum Geologists. All rights reserved.

Manuscript received January 7, 2009; provisional acceptance March 27, 2009; revised manuscriptreceived May 2, 2009; final acceptance May 27, 2009.DOI:10.1306/05270909001and its effect on sonic velocityand permeability in carbonatesRalf J. Weger, Gregor P. Eberli, Gregor T. Baechle,Jose L. Massaferro, and Yue-Feng Sun

ABSTRACT

Carbonate rocks commonly contain a variety of pore typesthat can vary in size over several orders of magnitude. Tradi-tional pore-type classifications describe these pore structuresbut are inadequate for correlations to the rocks physical prop-erties. We introduce a digital image analysis (DIA) methodthat produces quantitative pore-space parameters, which canbe linked to physical properties in carbonates, in particularsonic velocity and permeability.

The DIA parameters, derived from thin sections, capturetwo-dimensional pore size (DomSize), roundness (g), aspectratio (AR), and pore network complexity (PoA). Comparingthese DIA parameters to porosity, permeability, and P-wavevelocity shows that, in addition to porosity, the combined ef-fect of microporosity, the pore network complexity, and poresize of the macropores is most influential for the acoustic be-havior. Combining these parameters with porosity improvesthe coefficient of determination (R2) velocity estimates from0.542 to 0.840. The analysis shows that samples with large sim-ple pores and a small amount of microporosity display higherAAPG Bulletin, v. 93, no. 10 (October 2009), pp. 1297 1317 1297

1999). This modeling was based on (1) Wyllies time-averageequation (Wyllie et al., 1956) and (2) the assumption that

Jose L. Massaferro Gerencia Geologa yEstudios Integrados, Direccin Exploracin y De-sarrollo de Negocio, Macacha Gemes 515,(C1106BKK), Puerto Madero, Buenos Aires,Argentina

Jose Luis Massaferro is a geology manager inRepsol YPFs exploration office in Argentina. Hereceived his Ph.D. from the University of Miami in1997. He was a Fulbright Fellow while pursuinghis studies in Miami. Prior to his Ph.D. studies, heworked for Texaco as a geologist. In 1998, he joinedShell E&P and was involved in different projects,including 3-D seismic volume interpretation, high-resolution sequence stratigraphy, and kinematicmodeling of compressional structures. In 2005,he joined Repsol in Madrid.

Yue-Feng Sun Department of Geologyand Geophysics, Texas A&M University, CollegeStation, Texas 77843

Yue-Feng Sun is an associate professor at TexasA&M University. He received his Ph.D. (1994)from Columbia University. He has 25 years ofexperience as a geoscientist in the industry andacademia. His professional interests includecarbonate rock physics, poroelasticity, poroelectro-dynamics, reservoir geophysics, and petroleumgeology. He is a member of AAPG, the AmericanGeophysical Union, American Physical Society,and the Society of Exploration Geophysicists.

ACKNOWLEDGEMENTS

The methodology presented in this paper wasdeveloped in collaboration with Shells carbon-ate development team in Rijswijk, Holland, andthe Comparative Sedimentology Laboratoryof the University of Miami. We acknowledge fi-nancial support from Shell and the IndustrialAssociates of the Comparative SedimentologyLaboratory. Discussions with Guido BraccoGartner, Gene Rankey, and Peter Swart wereessential to the technical development of theequipment and methodology. Comments andreviews on several versions of the manuscriptsby Wayne Ahr, Stephen Ehrenberg, Jerry Lucia,Mark Longman, David Kopaska-Merkel, andJeroen Kenter greatly improved the manuscript.The AAPG Editors thanks the following reviewersfor their work on this paper: Jeroen Kenter,David C. Kopaska-Merkel, and Mark W.Longman.

1298 Geohorizonsseparate-vug porosity has a minor influence on the acousticlog (Schlumberger, 1972, 1974; Lucia, 1987; Doveton, 1994).Lucia and Conti (1987) and Lucia (1991) calibrated the influ-ence of separate-vug porosity on acoustic logs by point countingseparate-vug porosity on thin sections of oomoldic rocks, andand separate-vug porosity cannot always be separated usingsonic logs, (2) P-wave velocity is not solely controlled by thepercentage of spherical porosity, and (3) quantitative pore ge-ometry characteristics can be estimated from acoustic data andused to improve permeability estimates.

INTRODUCTION

Several attempts have been made to find a rock or pore-typeclassification that would capture rock texture, pore type, andpetrophysical characteristics (Archie, 1952; Choquette andPray, 1970; Lucia, 1983, 1995; Lny, 2006). In this article,we describe a digital image analysis (DIA) method for mea-suring quantitative pore-structure parameters derived fromthin sections and introduce four parameters that are most re-liable for capturing the geometrical character of pore struc-ture in carbonates.

Many studies have recognized that acoustic velocity in car-bonates is dependent upon pore geometry (Anselmetti andEberli, 1993, 1997, 1999; Kenter et al., 1995; Wang, 1997; Sunet al., 2001; Eberli et al., 2003; Baechle et al., 2004; Wegeret al., 2004; Weger, 2006). In many theoretical studies, thepore aspect ratio is assumed to be the main geometric variableinfluencing acoustic velocity (Assefa et al., 2003; Saleh andCastagna, 2004; Agersborg et al., 2005; Kumar and Han,2005; Rosseb et al., 2005). The theoretical concept is thathigh-aspect-ratio pores, such as molds and vugs, provide moregrain-to-grain contact than interparticle and intercrystallinepores, thus decreasing the pore compressibility and provid-ing more stiffness to the rock at equal porosity (Mavko andMukerji, 1995; Saleh and Castagna, 2004). Consequently, asequence of rocks with mostly moldic and/or vuggy porositywill have a higher acoustic velocity than a formation with pre-dominantly intercrystalline and/or interparticle porosity withthe same amount of total porosity. Many scientists exploitedthis fact to quantitatively estimate the amount of secondaryporosity (Schlumberger, 1972, 1974) and separate-vug po-rosity by modeling porosity from acoustic logs (e.g., Nurmi,1984; Lucia and Conti, 1987; Wang and Lucia, 1993; Lucia,

are Aptian in age, the Southeast Asian samples are

sional and two independent orthogonally polarizedproposed empirical equations to calculate separate-vug porosity from acoustic transit time. Anselmettiand Eberli (1993, 1997, 1999), however, showedhow in carbonates a variety of pore types producevariable velocities in rocks with similar porosity.Other experiments documented that oomoldic car-bonate sampleswithnear-spherical pores show largescatter in velocitieswith up to 2500m/s (8202 ft/s)difference at a given porosity (Baechle et al., 2007,2008a; Knackstedt et al., 2008).

In an attempt to quantify the influence of porestructure on permeability, Anselmetti et al. (1998)defined the DIA parameter g that describes theroundness of pores and compared it with mea-sured permeability values of plugs with character-istic pore types. The parameter showed a strongcorrelation to permeability. Anselmetti and Eberli(1999) also quantified the pore-structure-inducedscatter of velocities at any given porosity with thevelocity deviation, which is defined as the differ-ence between measured velocities and velocitiesestimated using Wyllies time-average equation.Intervals from MiocenePliocene cores from theGreat Bahama Bank with high positive velocitydeviation and oomoldic porosity show low perme-ability. This finding corroborated the general no-tion that rocks with a high amount of separate-vugporosity have a high velocity and low permeabil-ity. The application of the deviation log provedless successful in Cretaceous carbonates wherethe separation between the medium and deep in-duction curves better detected the high flow zones(Smith et al., 2003), indicating that the separationbetween interparticle or intercrystalline and intra-grain or vuggy porosity is insufficient to captureall pore type-velocity-permeability relationships.These complications were the motivation behindthe study presented in this article. The goal was tofind a repeatable, independent measure of the porestructure that is needed to quantitatively evaluatethe influence of pore geometry on acoustic velocityand other petrophysical properties.

The here-described methodology of DIA pro-duces parameters that quantify the relationshipbetweenpore geometry, acoustic velocities, andper-meability. The high correlation between the DIAparameters and the petrophysical values illustratesshear waves simultaneously using a pulse trans-mission technique developedbyBirch (1960). Bothtransducers (compressional and shear) generatefrom an isolated platform of Miocene age, and theAustralian samples are from two drowned cool-subtropical platforms on the Marion Plateau andare also Miocene in age (Ehrenberg et al., 2006).Vertical plugs were drilled from reservoir and non-reservoir intervals to capture a wide range of totalporosity, rock types, and pore types. The set of se-lected samples includes textures ranging fromcoarse-grained packstones with interparticle tovuggy porosity to fine-grained wackestone domi-nated by interparticle to micromoldic porosity(mG). All samples are either limestone or dolomitewith less than 2% noncarbonate minerals.

The samples have high-quality measurementsof velocity, porosity, and permeability. Thin sec-tions are impregnated with blue epoxy and cutfrom the end of the plug sample on which thesemeasurements were performed. Petrophysical mea-surements, geological description, and DIA param-eter values are listed in the Appendix.

METHODS

Petrophysical Measurements

Sonic velocity was measured using an ultrasonictransmitter-receiver pair with piezoelectric trans-ducers forming the core of the equipment. Thetransducer arrangement measures one compres-the advantages of quantitative geometrical param-eters over qualitative pore-type classifications.

DATA SET

One hundred twenty carbonate core-plug samples(1-in. [25.4-mm] diameter by 1- to 2 in. [25.450.8 mm] long) were selected from cored wells atseveral locations in theMiddle East, SoutheastAsia,and Australia (Baechle et al., 2004). The MiddleEast samples are from the Shuaiba Formation andWeger et al. 1299

measured at a confining pressure of 20 bar. All val-

tion under XPL to image and segment pore andues are reported as Klinkenberg-corrected perme-abilities in units of millidarcies.

Descriptive Thin-Section Analysis

Thin sectionswere qualitatively described and clas-sified using traditional carbonate rock and pore-type classifications according to Dunham (1962),the extended Dunham terminology (Embry andKlovan, 1971), Choquette and Pray (1970), andLucia (1995, 1999). Rocks altered by recrystalliza-tion that obliterated the original texture are referredto as recrystallized rocks.

Pore space was described using a limited Cho-quette and Pray (1970) terminology. In our sam-ples, we determined interparticle, intercrystalline,moldic, vuggy, and intraparticle porosity, and in-cluded intraframe porosity to describe the porespace within boundstone and rudstone. In addi-tion,weuse the termmicromoldic (mG) to describemicroscopic molds (

This difference is then combined with color valuesfor image segmentation into pore space and rock(Weger, 2006).

Pore-Shape Parameters from DigitalImage Analysis

Two different types of parameters exist for poreshape calculation (Russ, 1998): global parametersthat describe the entire pore systemon a photographor thin section and local parameters that are ob-tained from individual pores. All shape param-eters used here are derived from two-dimensional(2-D) images. We are aware of the limitation of2-D-derived geometrical properties for correlationto the physical property of the three-dimensionalsample volume. However, any kind of thin-sectionanalysis, quantitative or not, suffers from this limi-tation. In addition, we performed a variety of tests

on computed tomography (CT) scans of core plugsat a resolution comparable to that of our OLMimages that suggested that directionality has littleinfluence on geometrical parameter values.

In our DIA, 37 parameters are measured oneach thin section. A principal component analysiswas performed to identify the most important anddistinguishable parameters (Weger, 2006). FourDIA parameters proved to best describe severalaspects of the pore system. Definitions and shortdescriptions of the parameters characteristics aregiven below.More specific explanations on the deri-vation and characteristics of these parameters aregiven by Weger (2006).

Perimeter Over AreaPerimeter over area (PoA) is the ratio between thetotal pore-space area on a thin section and the totalperimeter that encloses the pore space. The PoA

Figure 1. (a) Image acquired using plane-polarized light shows a thin-section photomicrograph of a carbonate impregnated with blueepoxy resin. Minerals and grains are beige, whereas pore space is blue except for an air bubble with color identical to the matrix. (b) Theintensity image of absolute cross-polarized-light (XPL) variation covers the same area and is derived using XPL images at different angles.(c, d) The close ups and the distributions illustrated in panel (e) show that the red-green-blue (RGB) color bands of the subsection are notcapable of separating air bubbles from the matrix mineral, but the XPL variation of intensity is clearly different in those regions.Weger et al. 1301

can be regarded as a 2-D equivalent to a specificsurface, the ratio between pore volume and poresurface. Generally, a small number indicates a sim-ple geometry. ThePoAvalues in our data range fromless than 40 mm1 to more than 250 mm1. Be-cause of the almost log-normal distribution ofthese parameter values, some figures are plottedin log10(PoA) instead of PoA.

Dominant Pore SizeDominant pore size (DomSize) is determined as theupper boundary of pore sizes of which 50% of theporosity on a thin section is composed. This param-eter provides an indication of the pore-size rangethat dominates the sample. In our data, DomSizeranges from less than 100 mm to more than 1 mm(0.039 in.) (units given in length as equivalent diam-eter). As in the case of PoA, some figures show val-ues of log10(DomSize) instead of DomSize.

GammaGamma (g) was defined byAnselmetti et al., (1998)as the perimeter over an area of an individual porenormalized to a circle; i.e., a perfect round circlewould have a g of 1. The g describes the roundnessof the pore. In our data, the area-weighted meanof g for the entire thin section ranges from 1.5to 4.5.

Aspect RatioAspect ratio (AR) is defined here as the ratio be-tween the major and the minor axis of an ellipsethat encloses the pore. The AR describes the elon-gation of the pore-bounding ellipsoid. The arith-metic means of AR values for the entire thin sec-tion range from 1 to 2.5. In acoustic modeling,pores are commonly assumed to be ideal ellipsoidalinclusions with a variable AR (Kuster and Toksz,1974; Norris, 1985). This ideal ellipsoid does notconsider the edginess, complexity, or surface rough-ness of the pore.

Amount of MicroporosityIn our methodology, macropores are defined bypores, which are vertically connected through thethin section, resulting in aminimumpore diameterof approximately 30 mm (the thickness of a thin1302 Geohorizonssection). The amount of microporosity is calcu-lated as the difference between the observedporos-ity inDIA and themeasured porosity from the coreplug. The geometry of the micropores is not as-sessed in this study, but the percentage of micro-porosity is included in the analysis.

In Figure 2, several digital photographs of differ-ent thin sections are placed next to a PoA-DomSizecrossplot to demonstrate that these parametersvaguely recognize and separate traditional carbon-ate pore classifications. These parameters are, how-ever, not limited to the grouping of samples, as tra-ditional carbonate pore-type classifications are, butprovide a continuous ordered scale of pore geome-try. Coarse grainstones with large pores and rela-tively simple pore systems tend to show large Dom-Size and small PoA. In contrast, packstones tomudstones with large amounts of microporositycommonly show high PoA and low DomSize.

Mutivariate Regressions

Multivariate linear regression is used to quantifytrends among velocity, porosity, and four differentgeometrical parameters. We use the coefficient ofdetermination (R2) between the measured and theestimated velocity to quantify how well the modelexplains the measured data. In addition to directlinear regression, a semilinear approach is used,which combines linear regression andWyllies time-average equation. Some rearrangement of the time-average equation leads to an explicit formulationof Wyllies velocity estimate (VpW).

VpW 1 fVpS f

VpF

11

where VpS and VpF are the compressional velocityof the solid and the fluid, respectively, and f is po-rosity. This formulation was used by Anselmettiand Eberli (1999) to define the velocity deviation as

DVp Vp VpW 2

where Vp is the measured compressional velocityof the sample.

Figure 2. Crossplot of perimeter over area (PoA) versus dominant pore size (DomSize) where the measured acoustic velocity is super-imposed in color. (ad) Thin-section images are shown to illustrate carbonate pore types corresponding to certain combinations of digitalimage analysis (DIA) parameters and velocity. The samples shown as images are represented by enlarged dots, and exact parametervalues are listed below each thin-section photograph.Weger et al. 1303

This formulation can be used to incorporatethe velocity deviation into a regression model de-fined as

Vp VpW c0 c1x e y^ e 3

Figure 3. Velocity-porosity crossplot of water-saturated carbon-ate samples measured at 20-MPa confining pressure. A first-orderinverse proportional relationship between velocity and porositycan be observed, but individual samples deviate from this trendin excess of 2000 m/s (6562 ft/s).1304 Geohorizonsample, samples with vuggy or moldic porosity tendto fall into the high-velocity area, but several moldicsamples display a low velocity and overlap withsamples containing interparticle porosity. Samplescontaining either micromoldic porosity or poros-ity within particles occupy the lower part of thevelocity-porosity data cloud. In contrast, sampleswith interparticle porosity cover the entire velocity-porosity space. Sampleswith high amounts ofmicro-porosity (10070%) tend to cluster around theWyllie time-average equation (Figure 4b), and atany given porosity, a trend of increasing velocitywithdecreasing microporosity is observed (Figure 4b).

The digital image parameters of the macro-pores also define trends with similar orientationin the velocity-porosity space. The PoA shows aamounts of dolomite, and variations in grain veloc-ity (e.g., calcite to dolomite) could not producesuch large velocity variations. In addition, all sam-ples were measured saturated with distilled waterso that fluid velocities are constant. Anselmetti andEberli (1993) demonstrated that such variation ofvelocity at a given porosity is typical in carbonatesand relates to the pore structure. To test this con-clusion and to quantify the effect of pore structure,we relate the four digital image parameters, PoA,DomSize, AR, and g, to sonic velocity and poros-ity. Because each of the parameters captures a dif-ferent characteristic of the pore system, this corre-lation also assesses the relative importance of eachgeometric characteristic for Vp.

Geometry and Trends inVelocity-Porosity Space

Crossplots of velocity porosity with the digital im-age parameters PoA, DomSize, AR, g, percentageof microporosity (% microporosity), and traditionalpore types using the Choquette and Pray (1970)classification superimposed in color are shown inFigure 4. Figure 4a displays the samples color codedwith the dominant pore type, which is visually esti-mated on the thin section. Most samples, however,contain more than one pore type, and these addi-tional pore geometries (the Appendix lists the mi-nor pore types) might explain some of the scatter.Nevertheless, some slight trends are visible. For ex-where Vp is the measured compressional velocity,x represents any measured geometrical parameter(e.g., PoAorDomSize), c0 and c1 are constants to bedetermined during the regression, y^ represents thenew velocity estimate, and e is the error term thatin this case would contain bothmeasurement errorand any other influences on velocity that were notaccounted for.

RELATIONSHIP OF PORE STRUCTURE TOSONIC VELOCITY

The velocity-porosity data of all core-plug samplesshow a characteristic first-order trend of increasingacoustic velocity with decreasing porosity. At anygiven porosity, a spread of velocity in excess of1500 m/s (4921 ft/s) can be observed (Figure 3).This large scatter cannot be explained by mineral-ogy because most samples contain only minor

Figure 4. Comparison between (a) Choquette and Pray (1970) pore types, (b) microporosity fraction, and four digital-image-analysisparameters: (c) dominant pore size, (d) gamma (g), (e) perimeter over area, and (f) aspect ratio. All parameters are superimposed incolor onto velocity-porosity crossplots. All show a gradient that differentiates samples with high velocity from samples with low velocity atany given porosity.Weger et al. 1305

Figure 5. Illustration of the importanceof pore structure as a factor controllingacoustic velocity using pore-shape charac-teristics as the third dimension. Three-dimensional crossplot between sonic ve-locity (Vp), porosity (f), and perimeterover area (top) and dominant pore size(bottom) with simple linear regressionsurfaces.1306 Geohorizonsclear trend in which at any given porosity, sampleswith a low value of PoA (simple pore geometry)have relatively high velocities, whereas sampleswith high values of PoA (more complex pore ge-ometry) have low velocities (Figure 4e). In otherwords, samples with simple pore geometries arefaster than samples with a complicated pore struc-ture if porosities are the same. The DomSize alsoshows a clear trend of increasing velocity with in-creasing values of DomSize at a given porosity.This trend indicates that samples with larger poresare faster than those with smaller pores at equalporosities (Figure 4c). The roundness of individ-

ual pores is captured by g, which shows generallylow values in samples with relatively low velocitiesat a given porosity and vice versa (Figure 4d). Thistrend is similar as for the DomSize but not as welldeveloped (Figure 4c, d). The AR only displays avery weak trend in velocity-porosity space wheresamples with low velocity for their given porosityare generally those with high ARs (Figure 4f). Theparameters PoA and AR form trends with similarorientation. Low values of PoA and AR correspondto high velocities, and high values of PoA and ARcorrespond to low velocities for a given porosity(Figure 4e, f). The parameters DomSize and g form

anelaelo(Rorommpedityco84IA

Porosity and PoA and % microporosity and g 0.832Porosity and PoA and % microporosity and DomSize 0.840

0.845

significantlytricalnt propotrates that what appears as a 2-D scatter (Figure 3)is mostly caused by the projection of this surfaceinto a 2-D crossplot.

A crossplot of PoA and DomSize with acousticvelocity superimposed in color (Figure 2) illustratesthe link between the parameters PoA, DomSize,and acoustic velocity and rock texture. Four thin-section images are shown to illustrate the differ-ence in pore structure detected by high, medium,and low parameter values. Low-velocity samples arecharacterized by DomSize below 200300 mm andPoA above 50mm1. The corresponding thin-sectionimages are dominated by small pores, a significantamount of small particles, and/or abundant micro-porosity (Figure 2c, d). In contrast, high-velocity sam-ples are characterized by DomSize above 300 mmand PoA below 50mm1. The corresponding thin-section images show larger pores, larger particles,and little to no mud (Figure 2a, b). In general, highvelocities correspond to samples with simple andlarge pores with smooth pore surfaces, low specificsurface, and a small amount of microporosity.

Quantitative Assessment of DifferentGeometric Characteristics

To explore the link between velocity, porosity, andpore-space geometry quantitatively, velocity is es-timated using multivariate linear regression fromcombinations of porosity and theDIA parameters.The geometrical parameters g, PoA, DomSize,and AR, and the percentage of microporosity wereused for multivariate linear regression. The correla-tion coefficients between measured and estimatedvelocity are listed in Table 1.trends in the opposite direction (Figure 4c, d), wherelow values correspond to low velocities and highparameter values correspond to high velocities atany given porosity.

The trends formed by PoA and DomSize(Figure 4c, e) are very strong (Figure 5), indicatingthat pore structure is a second independent param-eter influencing velocity. In Figure 5, these quanti-tative DIA parameters are displayed together withvelocity and porosity in three dimensions. Manysamples align closely with a simple linear best-fitsurface that is displayed for reference. This illus-Table 1. Coefficients of Determination from the Correlationbetween Measured Velocity and Estimated Velocity fromRegressions with the Following Digital Image Analysis Parametersas Input Variables: Dominant Pore Size, Gamma, Perimeterover Area, Aspect Ratio, and Percentage of Microporosity*

Estimators Used for Velocity Prediction R2

Porosity 0.542Porosity and AR 0.549Porosity and g 0.639Porosity and DomSize 0.768Porosity and % microporosity 0.769Porosity and PoA 0.786Porosity and PoA and AR 0.788Porosity and PoA and DomSize 0.800Porosity and PoA and g 0.810Porosity and PoA and % microporosity 0.820Porosity and PoA and % microporosity and AR 0.822porosity (R2 = 0.840).rameters (g, AR, PoA, DomSize, and % micro-porosity), but this correlation coefficient is onlyslightly better than the estimate from a combina-tion of porosity with PoA, DomSize, and %micro-lation coefficient of all estimates (R = 0.obtained by combining porosity with all DWeger et al.5) ispa-mate (R2 = 0.549, Table 1). The highest2rre-

porosity produces the least effective veloc esti-

sional velocity. The parameter AR combin with

% microporosity) is used to estimate co res-

and a single DIA parameter (g, AR, PoA, Do Size,

0.542. Second, a linear combination of p sity

resulted in a coefficient of determination ) of2

between the measured and the estimated v city

mator of compressional velocity. The corr tionAs a first step, porosity alone is used as esti-eters does not produce significant improvement. DomSize = dominag = gamma; PoA = perimeter over area; AR = aspect ratio; % micpercentage of microporosity.rosity =*The geometric parameters PoA and DomSize in addition to porosityimprove the correlation, whereas the combination of several geome param-

ore size;Porosity and PoA and % microporosity andDomSize and AR and gPorosity and PoA and % microporosity andDomSize and AR

0.841

Porosity and PoA and % microporosity andDomSize and g

0.8441307

Crossplots between the velocity deviation andthe log10 of DIA parameters PoA and DomSize(Figure 6) result in an R2 of 0.65 and an R2 of0.62, respectively. This means that these two quan-titative geometric parameters are able to explain6265% of the deviation of acoustic velocity (DVp)from Wyllies time-average equation at a givenporosity.1308 GeohorizonsPERMEABILITY AND PORE SHAPE

Pore size and specific surface influence permeabil-ity. In our data, pore size and pore network com-plexity (PoA), which is the 2-D equivalent of aspecific surface, have a strong influence on perme-ability (Figure 7). Samples with low permeabilityfor their given porosity have high values of PoAFigure 7. Permeability-porosity (K-f) crossplots with perimeter over area (PoA) and dominant pore size (DomSize) superimposed ingray scale. Both parameters exhibit trends in porosity-permeability space. Samples with low permeability despite relatively high porosityhave high values of PoA and low values of DomSize. Samples with high permeability have low values of PoA and high values of DomSize,representing samples with a large and simple pore structure.Figure 6. Crossplots between velocity deviation and digital image parameters. Both parameters, perimeter over area (PoA) and domi-nant pore size (DomSize), are capable of explaining more than 60% of the variability in velocity deviation.

2tive (R = 0.143, black dots in Figure 8). These es-timates can be improved using pore geometryinformation from PoA and DomSize (R2 = 0.415and R2 = 0.383, green and blue dots in Figure 8).The good relationship between sonic velocity, po-rosity, and PoA allows for the substitution of PoAby a geometry estimate derived from sonic veloc-ity. Using this geometry estimate, we obtain an R2and low values of DomSize. In turn, samples withhigh permeability for their given porosity show lowvalues of PoAandhighvalues ofDomSize. Lowval-ues of PoA represent a simple pore structure andlow specific surface, whereas high values of PoAstem from amore complex pore structure and highspecific surface (Figures 2, 7).

Quantitative Permeability Estimation

Bear (1972) refined Kozenys (1927) equation toexpress permeability as a function of porosity, spe-cific surface, and tortuosity. Here we estimate per-meability using pore geometry parameters and in-corporate them into Kozenys equation.

k cf3=S2 4

where k is permeability, f is porosity, c is Ko-zenys factor, which can be estimated from poros-ity (Fabricius et al., 2007), and S is the specificsurface with respect to bulk volume. The PoA isthe 2-Dequivalent of the specific surface, and thus,we estimate S from measured 2-D geometricalparameters (PoA and DomSize).

We compare four different approaches to esti-mate permeability. First, estimates of permeabil-ity are derived from porosity alone. For compari-son, Kozenys S is expressed as a function of PoAand DomSize and used for permeability estima-tion. Finally, the relationship between acoustic ve-locity and pore geometry is used to calculate S di-rectly from acoustic data. This estimate of S is thencombined with porosity to estimate permeabilitydirectly from a combination of measured porosityand acoustic velocity.

Figure 8 shows a comparison of measured andestimated permeabilities. Estimation of perme-ability using porosity alone is extremely ineffec-correlation between a measured and estimatedpermeability of 0.419 (red dots in Figure 8).

Microporosity and pore-throat diameter are im-portant to properly predict flow properties. Thin-section-based pore-structure analyses like the pre-sentedmethod here do not capture pore geometriesbelow the 30-mm threshold, but the macro- andmesopore system represents a large part of the flowcapacity. This is reflected in the improvement ofthe permeability estimates from R2 = 0.143 to R2 =0.415 gained by incorporating themacroscale DIAparameters into the Kozceny equation (Figure 8).Further improvements of permeability estimateswill be possible using micro-CT scans (Knackstedtet al., 2008) or by combiningDIA analysis andmer-cury injection capillary pressure.

DISCUSSION

Anselmetti and Eberli (1999) demonstrated howacoustic velocities in carbonates are influenced byporosity and a variety of pore structures using tradi-tional carbonate pore-type classification (Choquetteand Pray, 1970). In our data, the separation of sam-ples grouped according to Choquette and Prayspore-type classification is poor in velocity-porosityspace (Figure 4a), indicating that the classificationof Choquette and Pray is not capable of uniquelydefining ranges of specific acoustic properties. Incomparison, quantitative characterization of pore-space geometry using DIA parameters such as PoA(Figure 4e) has the advantage of providing a con-tinuous numerical parameter that can be used di-rectly in a mathematical formulation used to esti-mate velocity.

TheAR is the geometrical parametermost com-monly used in theoretical models to explain varia-tions in rock stiffness and acoustic velocities (Assefaet al., 2003; Saleh and Castagna, 2004; Agersborget al., 2005; Kumar and Han, 2005; Rosseb et al.,2005), although Rafavich et al. (1984) concludedthat AR does not significantly influence velocity.The weak correlation for velocity estimates usingporosity and the DIA parameter for roundness(g) and AR, respectively, questions this assump-tion. Our results indicate that (1) the amountWeger et al. 1309

1310 Geohorizonsof microporosity and (2) the size and complexityof the macropore system are muchmore importantfactors for determining the stiffness and, thus, theacoustic behavior of carbonates (Table 1). A recentstudy of oomoldic rocks by Baechle et al. (2007)also documented that the percentage of sphericalpore shape is not the dominant factor in producingpositive deviations from the Wyllie time-averageequation. They attribute the variable acoustic re-sponse of up to 2000m/s (6562 ft/s) at a given po-rosity to variations in intercrystalline porosity inthe rock frame; a conclusion that is corroboratedby ultra-high-resolution CT tomography and scan-ning electron microscope (SEM) analysis on thesame samples (Knackstedt et al., 2008).

Baechle et al. (2008b) proposed that the frac-tion of stiff macropores versus soft micropores isresponsible for the variation of velocity at any givenporosity and develop a rock physicsmodel that cap-tures thepresence of bothmacro- andmicroporosityto better estimate velocity and permeability. Thepercentage of microporosity for this dual porosityDEMmodel is derived with the DIA methodologydescribed here (Baechle et al., 2008b).

The assumption that rocks withmostlymoldicand/or vuggy porositywill have a faster acoustic ve-locity than a formation with predominantly inter-crystalline and/or interparticle porosity has beenused for quantitative estimates of separate-vug po-rosity from acoustic logs (e.g., Nurmi, 1984; Lucia

Figure 8. Comparison betweenmeasured and estimated permeability (k). Estimates are derived using four different models with differentinput parameters. Green dots are estimates derived from porosity alone. Both blue and black dots are derived using measured porosityand the measured geometric parameters perimeter over area (PoA) and dominant pore size (DomSize). Red dots represent permeabilityestimates derived using measured porosity (f), measured acoustic velocity (Vp), and assumed grain and fluid velocities (VpS and VpF).

overlap exists between thesetwo groups, indicating that rocksand Conti, 1987;Wang and Lucia, 1993; AnselmettiandEberli,1999). To test this assumption,wedistrib-ute the samples into two groups. The vuggy group1996). In carbonates, cementation at grain contactsaremeniscus cements derived frommeteoricwaters(Harris, 1978; Longman, 1980) ormicritic bridging

with interparticle and/or inter-crystalline porosity can in somecases have a stiff frameworkand high velocity.Figure 9. Velocity-porositycrossplot of samples measuredat 20 MPa with annotation ofporosity types separated into twogroups. Open circles are sam-ples with vuggy, moldic, intra-frame, and intragrain porosity,black and gray dots representsamples with interparticle andintercrystalline porosity. A largeconsists of samples whose primary pore types arevuggy, moldic, intraframe, and intraparticle poros-ity. The interparticle group consists of sampleswithinterparticle and intercrystalline porosity as theprimary pore type. Plotting the two groups in thevelocity-porosity space reveals a considerable over-lap (Figure 9). The samples of the vuggy group gen-erally plot above the Wyllie time-average equa-tion, and a cluster of interparticle samples in thelow velocity area is observed. However, nearly anequal amount of samples from each group displayan exceptionally high velocity at a given porosity(Figure 9).

High velocity at a given, sometimes high poros-ity is possible if pore compressibility is low andconsequently if the stiffness of the rock is not sig-nificantly decreased (Mavko and Mukerji, 1995).Such a stiff frame is well known to occur in rockswith vugs or molds, but it also occurs in rocks withinterparticle and intercrystalline porosity. A pro-cess that can produce frame stiffening in these latterrocks is contact cementation (Dvorkin and Nur,

cements in the marine realm (Hillgrtner et al.,2001). In a Holocene grainstone, small amountsof bridging cement (15% of the total rock) producea Vp of 4500 m/s (14,764 ft/s) at 20 MPa (Eberliet al., 2003). Some of the samples displayed inFigure 9 are dolomites; in this case, the extremestiffening of the frame is not caused by early cementbut more likely by interlocking crystals. Anselmettiet al. (1997) documented this process on Neogenecarbonates, in which the velocity of sucrosic dolo-mite increases dramatically as isolated rhombohe-dra grow together to form a stiff framework.

CONCLUSIONS AND IMPLICATIONS

The DIA quantifies the influence of pore types onvelocity and permeability. A combination of porosityand (image-derived) microporosity is capable ofestimating velocity with R2 = 0.77; a combina-tion of porosity and digital image parameters isable to explain more than 85% of the variationWeger et al. 1311

of acoustic velocity (R2 = 0.85). The geometricalcharacteristics most influential for acoustic velocityare the complexity of pore space (PoA) and the sizesof the pores (DomSize). These parameters com-bined with porosity estimate velocity with R2 =0.79 and 0.77, respectively. In short, carbonates witha large amount of microporosity, a complex porestructure (high specific surface), and small poresgenerally show low acoustic velocity at a given po-rosity. Samples with a simple pore structure (lowspecific surface) and large pores show high acousticvelocity for their porosity.

Knowledge of roundness (g) and the aspect ra-tio of pores (AR) does not significantly enhancethe ability to estimate sonic velocity in carbonates.Thus, incorporating parameters that capture bothsize and complexity (e.g., DomSize and PoA) po-tentially improves acoustic velocity models.

The finding that samples with interparticle

rosity (oomoldic), these estimatesworkwell (LuciaandConti, 1987;Wang andLucia, 1993;Anselmettiand Eberli, 1999). The nonunique acoustic re-sponse of separate-vug porosity might explain whyestimates based on these models do not alwaysyield the expected results. Given the relationshipbetween permeability and the DIA parametersPoA and DomSize, in theory, it should be possi-ble to discriminate high and low permeability at agiven porosity directly fromwell-log data. For ex-ample, rocks with high acoustic velocity for theirgiven porosity generally show low specific surface(PoA) and large pore sizes (DomSize, Figures 4, 5).Rocks with low specific surface and large poresizes also have high permeability for their given po-rosity (Figure 7, Appendix). These relationshipsimply two things: (1) not all fast intervals in car-bonates that produce a positive acoustic impedanceare necessarily tight, low-porosity sequences, and(2) a quantitative assessment of the pore types byDIA and their acoustic response is beneficial foran accurate interpretation of log-based pore-typeestimates.

e A

mSizmm)

394873

18818887

1062026378

11320820852

108and intercrystalline porosity can display high ve-locity similarly to samples with separate-vug poros-ity is an unwelcomed finding because its nonuniqueacoustic response adds uncertainty to quantitativeestimates of separate-vug porosity from velocitylogs. It is well documented that separate-vug po-rosity is mostly ineffective with regard to velocity,and in reservoirs that are dominated by such po-

Appendix. Texture, Pore Type, DIM (Digital ImagMeasurements*

SampleDunhamIndex**

DominantPore Type

MinorPore Type Gamma

Do(

C5-B1 G IP 2.15C5-B100 G MO 2.37C5-B101 G IP WG 2.25C5-B102 G IP MO 2.61C5-B103 G IP MO 2.61C5-B104 G IP 2.17C5-B105 G IP FR, MO 1.78C5-B106 G IP MO 2.55C5-B107 P-G IP 2.05C5-B108 G IP 1.98C5-B109 P-G MO 2.03C5-B110 G WF 2.38C5-B111 G WF 2.38C5-B112 G mG 1.85C5-B113 G IP 2.781312 Geohorizonsnalysis) Parameter Values, and Petrophysical

e PoA(mm1) AR VP (m/s) Phi (%)

MicroPhi (%) K (md)

167 0.52 3177 28.0 26.8 6.7151 0.59 3185 27.6 25.3 11.3103 0.55 3262 30.4 25.3 35.669 0.54 3738 25.8 21.8 26.169 0.54 3866 26.3 22.3 26.189 0.54 3458 29.0 24.4 37.883 0.59 3853 23.7 21.7 4.558 0.54 4050 29.9 21.4 184.0

117 0.58 3406 27.4 25.3 13.899 0.52 4893 12.8 9.8 9.879 0.57 3435 26.2 22.9 7.752 0.53 4259 22.5 17.3 4.252 0.53 4177 22.1 16.9 4.2

137 0.61 3466 26.7 25.7 3.990 0.56 3403 27.4 19.3 25.8

APPENDIX: DATA TABLE

Appendix. Cont.

SampleDunhamIndex**

DominantPore Type

MinorPore Type Gamma

DomSize(mm)

PoA(mm1) AR VP (m/s) Phi (%)

MicroPhi (%) K (md)

C5-B114 G IP WG 2.87 97 92 0.54 3377 28.0 22.6 23.5C5-B115 G WF IP 2.96 262 55 0.54 3867 29.8 23.0 63.8C5-B116 G IP 2.10 90 84 0.53 3520 26.8 18.4 36.7C5-B117 G-P IP MO 2.43 170 66 0.55 3974 25.4 15.1 64.7C5-B118 G IP 3.74 178 73 0.57 3714 29.4 24.4 55.3C5-B119 G IP MO 2.23 151 71 0.55 4782 17.9 14.8 2.9C5-B120 G IP WG 2.44 143 70 0.54 3513 28.3 24.4 71.5C5-B58 FR VUG IP 2.88 560 34 0.54 4703 21.8 15.5 2195.0C5-B60 RD IP WP, MO 2.58 680 30 0.53 4555 25.7 15.9 1321.1C5-B61 P VUG IP 1.95 421 45 0.59 4564 18.7 17.1 12.7C5-B72 RD-FR IP VUG, WF 2.89 519 42 0.49 4628 15.9 10.5 9.0C5-B74 G WF IP 2.51 1200 18 0.54 4362 23.6 10.6 646.0C5-B75 P-G mG MO 1.84 50 150 0.60 3466 29.4 28.2 13.2C5-B79 G IP IP 2.61 31 196 0.50 3179 26.4 25.1 2.1C5-B80 P mG MO 1.97 39 157 0.56 2898 30.8 30.2 4.1C5-B81 G-RD IP MO, WP 2.19 224 42 0.54 3856 26.7 14.8 113.5C5-B82 W-P MO VUG 1.82 129 63 0.57 3936 28.8 25.8 20.8C5-B84 P-G IP MO 1.61 102 71 0.57 4171 20.1 17.5 4.1C5-B85 G IP MO 2.31 106 96 0.57 3768 27.1 26.3 14.0C5-B86 W mG 2.09 50 167 0.59 4413 15.9 15.5 0.1C5-B87 RD-FL MO IP 2.32 143 78 0.57 3374 30.0 28.5 19.9C5-B88 FL-RD WP IP, MO, FR 2.15 294 49 0.54 4102 23.9 21.5 1.5C5-B89 P IP MO 2.14 92 115 0.56 4084 21.9 10.9 4.7C5-B90 G IP 2.57 87 109 0.51 4023 21.4 18.0 221.5C5-B91 FL MO IP, FR 2.50 154 95 0.52 5156 12.1 10.1 5.0C5-B92 G-RD IP WP 1.86 135 62 0.58 3974 24.3 18.5 99.8C5-B93 G-P MO MO 3.74 215 81 0.54 3786 29.7 26.6 24.4C5-B94 G-P IP VUG 4.22 43 164 0.51 3266 26.2 24.8 1.6C5-B95 G IP 2.89 68 109 0.48 3481 29.8 27.5 18.3C5-B96 G-P IP 2.25 53 169 0.46 3535 28.4 13.4 2.4C5-B97 P-G IP 2.70 27 215 0.59 3324 22.3 22.1 1.7C5-B98 G-P IP 3.48 20 244 0.44 3692 21.8 21.5 2.3C5-B99 G MO FR 1.70 109 74 0.64 3156 28.0 26.2 4.5C5-L10 P WP MO 2.17 157 139 0.60 4753 13.4 8.4 0.1C5-L11 rDol VUG IX 2.85 345 48 0.57 5791 14.2 4.3 2.0C5-L12 G-P WP IP 2.36 118 147 0.52 4011 26.3 25.1 0.6C5-L13 rDol VUG IX 3.05 368 47 0.55 5747 20.0 12.7 562.0C5-L14 rDol MO IX 2.15 440 36 0.55 5797 19.5 9.1 2.9C5-L15 rDol IX VUG 3.53 451 40 0.55 5180 26.0 8.2 2340.0C5-L16 rDol VUG IX 3.74 790 28 0.56 4737 33.6 12.4 15,049.0C5-L17 G IP 3.64 310 71 0.55 5333 17.8 15.3 91.9C5-L19 rDol VUG IX 3.23 452 43 0.55 4658 31.9 12.4 5564.0C5-L2 G IP MO 3.77 447 41 0.54 3894 41.6 18.3 15,966.0C5-L20 rDol VUG IX 2.57 466 36 0.55 5991 11.2 1.2 123.0C5-L21 rDol VUG IX 2.73 297 51 0.55 5949 13.0 5.5 28.7C5-L22 rDol IX VUG 2.29 205 77 0.56 5890 13.3 5.2 92.2C5-L23 rDol IX MO 3.15 372 49 0.55 3274 44.7 32.0 525.0C5-L24 P IP MO 2.61 115 111 0.56 3961 25.2 15.2 1.0C5-L25 rDol VUG IX 2.45 370 38 0.55 5430 21.0 10.8 131.0C5-L26 G MO 2.09 121 112 0.52 5361 10.8 10.1 0.0

Weger et al. 1313

Appendix. Cont.

SampleDunhamIndex**

DominantPore Type

MinorPore Type Gamma

DomSize(mm)

PoA(mm1) AR VP (m/s) Phi (%)

MicroPhi (%) K (md)

C5-L27 B WF IX 3.27 357 51 0.54 6148 14.7 7.0 8.1C5-L28 P IP MO 3.07 453 53 0.55 4249 27.2 21.3 895.0C5-L29 G-B IP WF 2.22 413 38 0.56 5662 17.5 10.0 535.0C5-L3 rDol IX VUG 2.30 254 55 0.56 6080 10.1 2.9 12.2C5-L30 rDol VUG IX 2.90 702 31 0.56 5918 14.2 4.2 240.0C5-L31 rDol IX VUG 2.95 602 29 0.56 4650 32.1 12.9 29,369.0C5-L32 G IP 2.20 355 41 0.55 5908 16.4 10.5 698.0C5-L33 FL IP VUG 2.92 643 32 0.56 5356 24.2 8.9 12.7C5-L34 rDol MO IX 2.71 290 55 0.56 4951 24.8 12.7 209.0C5-L35 G MO WP 2.46 488 304 0.45 5297 11.8 11.7 2.0C5-L36 rDol IX VUG 3.28 652 35 0.54 4791 36.1 17.5 11,940.0C5-L37 P WP IP 3.50 852 41 0.55 3956 29.7 23.5 25.2C5-L38 P MO 2.55 440 51 0.56 4381 20.8 15.3 1.5C5-L39 P mG IP 2.50 325 61 0.55 4246 25.0 23.7 4.3C5-L4 rDol VUG IX 3.13 439 42 0.56 5303 20.3 3.8 29.1C5-L40 rDol MO IX 2.66 412 53 0.53 5640 13.0 7.5 0.4C5-L41 G IP 2.49 425 40 0.54 5604 18.9 10.4 2550.0C5-L42 G MO WP 2.39 132 87 0.54 4520 21.1 18.2 0.1C5-L43 rDol IX VUG 2.43 362 44 0.56 5132 24.1 14.2 167.0C5-L44 rDol MO IX 3.49 874 26 0.53 5407 21.8 0.0 0.7C5-L45 rDol VUG IX 2.62 14 35 0.56 6325 9.7 0.9 0.7C5-L46 G WP MO 1.97 134 79 0.55 4615 17.2 5.2 0.1C5-L47 P-G IP MO 3.01 471 49 0.57 4784 18.2 12.8 1575.0C5-L48 rDol VUG IX 2.62 514 38 0.55 5271 26.5 16.8 25,775.0C5-L49 P-G IP MO 2.78 352 42 0.55 4860 26.2 13.9 2032.0C5-L5 rDol IX VUG 3.05 344 45 0.55 5871 13.4 3.1 122.0C5-L50 rDol VUG IX 2.78 247 67 0.54 5335 21.0 15.5 16.1C5-L51 rDol IX MO 3.27 318 53 0.53 4259 32.7 16.7 2423.0C5-L52 P IP 2.00 93 137 0.56 5442 8.9 8.5 0.0C5-L53 G MO IX 2.67 347 54 0.56 5082 25.2 11.2 331.0C5-L54 G-B IP WF 2.86 595 38 0.57 6183 11.6 6.3 271.0C5-L55 G-B WF IP 2.24 388 46 0.56 5910 17.2 11.7 401.0C5-L6 G IP MO 2.68 279 54 0.53 4093 29.5 24.3 1410.0C5-L7 P WP MO 2.61 353 108 0.52 4977 14.2 13.8 0.7C5-L8 rDol VUG IX 3.71 1031 25 0.55 6325 10.5 0.5 94.2C5-L9 rDol VUG IX 2.44 331 48 0.56 5850 12.4 6.0 54.3C5-M18 G-P IP MO 2.90 112 105 0.54 4038 26.6 20.0 15.0C5-M56 P-G VUG MO, IP 2.56 393 35 0.58 3725 33.5 15.5 390.0C5-M57 G-P IP VUG, WP 2.98 233 65 0.55 3612 28.9 19.3 22.0C5-M59 G-P IP MO 2.27 81 125 0.59 3671 26.0 22.4 14.0C5-M62 P-G IP MO 2.18 76 140 0.57 3978 23.6 19.3 13.0C5-M63 P IP IP 3.73 230 56 0.53 4346 32.0 24.1 300.0C5-M64 P IP mG 2.04 49 149 0.58 3524 29.4 25.0 21.0C5-M65 G-P MO IX 1.91 521 36 0.57 4357 20.8 15.5 3.7C5-M66 rDol VUG IX 2.56 521 36 0.54 5604 13.0 7.9 150.0C5-M67 P VUG IP 2.56 685 43 0.53 4285 22.5 16.5 36.0C5-M68 P VUG 1.86 113 78 0.55 4105 26.7 22.8 26.0C5-M69 G IX VUG 2.38 267 51 0.54 4477 20.8 16.2 120.0C5-M70 P-G MO IP 2.18 98 97 0.57 3829 31.9 27.6 26.0C5-M71 rDol IX VUG, MO 2.46 341 43 0.56 5531 11.4 4.2 150.0

1314 Geohorizons

sections of reservoir rocks: Computer Vision, Graphics

Sizem)

1189617414846

= comty.e; FR

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SampleDunhamIndex**

DominantPore Type

MinorPore Type Gamma

Dom(m

C5-M73 G-P MO IP 2.05C5-M76 W-P IP MO 2.81C5-M77 P IP MO 2.05C5-M78 P MO VUG, IP 1.91C5-M83 P MO 2.20

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163 0.59 4117 24.1 21.6 5.5

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