Investigating the influence of mineralogy and pore shape on the velocityof carbonate rocks: Insights from extant global data sets

Mark G. Kittridge1

Abstract

Using a variety of recent public-domain data sets comprising porosity, velocity (P- and S-waves), and, in mostcases, mineralogy and petrographic data, I created an extensive global data set and evaluated the importance ofmineralogy and pore type on the elastic properties behavior of carbonate core plugs. Results from this inves-tigation clearly illuminated the potential for overinterpreting elastic properties behavior as a function of poretype(s) when mineralogy was not explicitly included in the analysis. Rock-physics analysis using a combinationof heuristic and theoretical models illustrated that mineralogy exerted a significant additional variation onvelocity at a given porosity. Failure to account for mineralogy exacerbated inferences about the effect of poretype(s) made using a comparison of P-wave velocity to an inappropriate empirical model (Wyllie) that did notaccount for pore shape(s). In this analysis, extreme variability in carbonate velocity was observed in onlyportions of two data sets, when mineralogy was explicitly considered and robust models that accounted forinclusion (pore) shape were used. Results from this analysis resulted in a recommended workflow, includinga rock-physics template and dry-rock modulus diagnostics, for the evaluation of lab-based carbonate rock-physics data. The workflow was amenable to further integration with well-based data and other core-basedpetrophysical measurements (e.g., electrical properties).

IntroductionMethods for seismic-based reservoir characteriza-

tion require rock-physics relationships to relate petro-physical properties (lithology, porosity, saturation) togeophysical variables (bulk density and P- and S-wavevelocities), which are responsible for the recorded seis-mic behavior. Exploration and prospect appraisal com-monly rely on amplitude variation with offset (AVO)techniques, which emphasize the importance of S-wavevelocity to enhance fluid and reservoir detection. Simi-larly, seismic inversion using multiple seismic offset vol-umes uses reservoir-specific rock-physics relationshipsto infer reservoir properties (porosity, net-to-gross,hydrocarbon saturation) using a combination of twoderived seismic property volumes (e.g., P-impedance,VP∕VS ratio). Finally, time-lapse (4D) seismic interpreta-tion requires the ability tomodel dynamic changes in res-ervoir stress, saturation, and fluid properties, as well aspotential changes in the reservoir overburden. Tremen-dous effort has been made in recent decades in seismicrock physics, as noted in classic review articles (Yale,1985; Wang, 2001), in a ubiquitous handbook (Mavkoet al., 2009), and in a practical interpretation textbook(Avseth et al., 2005).

To date, considerably more attention has been de-voted to the development of rock-physics relationships

for siliciclastic rocks, whereas efforts focused onunderstanding carbonate rock properties have gener-ally lagged behind and received comparatively lessresearch attention. Several factors likely explain thehistorical emphasis on clastic (reservoir) rocks. First,early success with the direct detection of hydrocarbonusing seismic (e.g., “bright spots,” AVO) found readyapplication (and economic success) in high-porosity,acoustically “soft” unconsolidated sands and sand-stones common in deltaic and turbidite environments(see the excellent summary by Forrest, 2010). Second,carbonate reservoirs (exclusive of chalk) are generallyof lower porosity and acoustically “stiff,” reducing orrendering, nearly nonexistent, any seismic fluid signal.Fournier and Borgomano (2007) present a compellingexample from the Philippines of the use of seismicto image reservoir architecture in a carbonate buildup.Here, porosity and pore type, largely the result ofdiagenetic processes, control variations in (reservoirscale) acoustic impedance. Clearly, the pervasive diage-netic overprint frequently observed in carbonate reser-voir rocks, resulting in complex mineralogy (calcite,dolomite, sulfate) and variable pore type(s), requires anapproach to rock-physics model development that isunique from the significant experience compiled fromsiliciclastic reservoirs.

1HESS Corporation, Houston, Texas, USA. E-mail: mkittridge@hess.com.Manuscript received by the Editor 19 March 2014; revised manuscript received 5 May 2014; published online 24 November 2014. This paper

appears in Interpretation, Vol. 3, No. 1 (February 2015); p. SA15–SA31, 18 FIGS., 3 TABLES.http://dx.doi.org/10.1190/INT-2014-0054.1. © 2014 Society of Exploration Geophysicists and American Association of Petroleum Geologists. All rights reserved.

t

Special section: Geologic, geophysical, and petrophysical interpretation of core data and well logs

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Recent carbonate rock-physics resultsRecent work in carbonate reservoirs has focused on

the effect of pore type(s): shape, concerns about rock-fluid interaction(s) and the possible impact on fluidreplacement, and the impact of texture (chalks, micriticcarbonates) on elastic properties behavior. Additionalstudies have shown the importance of lab protocolin the measurement of velocity on carbonate samplesand the role of frequency when integrating lab- andwell-based data with seismic (reflection, VSP) infor-mation. The following review is provided for clarityand will help frame the subsequent data analysis andinterpretation.

Carbonate pore type(s)Observations that the nature (type) of carbonate

pore(s) present in a sample exert a significant influenceon velocity date to at least 1997 (Anselmetti and Eberli,1997; Marion and Jizba, 1997; Wang, 1997). Large,equant (high-aspect ratio) pores (e.g., vugs) are seen toincrease velocity, whereas thin, crack-like (low-aspectratio) pores reduce velocity. Works by Brie (2001), Xuet al. (2006), and Sayers (2008), using two different(theoretical) models incorporating relevant pore-shapeterms (aspect ratio), suggest similar effects from varia-ble aspect ratio pores, based on a variety of lab- andwell-based data sets. It should be noted that Wang(1997), and references cited therein, uses a theoreticalrock-physics model (closely related to the model usedby Xu et al., 2006) to describe velocity response in car-bonates as a function of high- and low-aspect-ratiopores (vugs, fractures). Note that several authors (An-selmetti and Eberli, 1997; Baechle et al., 2008; Verweret al., 2008; Weger et al., 2009) base the observation ofvelocity deviation (particularly to higher velocity) usinga comparison of measured (lab) data to the Wyllie timeaverage (WTA) model (Wyllie et al., 1956). In earlierworks, Brie et al. (1985) also use the WTA model inan interpretation method that infers spherical porosityfrom well log data in which the “primary medium” ispresumed to follow the Wyllie model. The suitabilityof that particular model for comparison with carbonatevelocity data, in particular the case of P-wave velocityonly, will be discussed further in a subsequent section.

Fluid replacementConcerns about the effect of varying pore fluid type

and more importantly the potential violation of one ormore necessary conditions in the use of the Gassmannfluid substitution algorithm were recently highlighted inlab studies by Baechle et al. (2005) and Adam et al.(2006). Earlier works by Wang (1997) and referencescited therein also make note of velocity differences be-tween measured and Gassmann-predicted values, withthe largest differences observed in P-wave velocity atlow differential (effective) pressure. Baechle et al.(2005) use lab-measured (ultrasonic) data from 30 lime-stone (calcite) samples from Cretaceous and Miocenereservoirs, under dry and saturated conditions (typi-

cally the same sample). While many of the samplesrespond as per Gassmann expectation (saturated VP >dry VP, saturated VS < dry VS), several samples do notexhibit this behavior. A comparison of the dry and sa-turated shear modulus, which is a function only of mea-sured VS and bulk density, and predicted to be aninvariant as a consequence of the Gassmann model,also showed anomalous behavior in some samples. Thisvariability is described as either “shear weakening” or“shear strengthening.” The study by Adam et al. (2006)uses nine samples (calcite and dolomite) from a singlereservoir and included low-frequency and ultrasonicdata. At low (seismic) frequency (100 Hz), all samplesshow shear modulus weakening at low (3.5 MPa) differ-ential pressure, but significantly less at high (reservoir)differential pressure (31 MPa). Using the ultrasonicvelocity data, the samples show no shear moduluseffect with the data uncertainty at low and reservoirdifferential pressures.

Importance of lab protocolPetrophysicists working on carbonate reservoir

rocks have long understood the challenges that sam-ple-based heterogeneity (properties) and inhomogene-ity (sample condition) impose on the measurement ofroutine formation properties. For geophysical applica-tions, Wang (1997) observes that sample size (plug,whole core) and the size of geologic heterogeneity (e.g.,vug, mold) play an important role in geophysical mea-surements, particularly when making ultrasonic (i.e.,0.8–1 MHz) pulse transmission measurements. More re-cently, Rasolofosaon et al. (2008) made a cogent set ofrecommendations specific to the petroacoustic charac-terization of carbonate samples. Sample-specific het-erogeneity that may induce acoustic scattering (“pathdispersion”) must be avoided by using a combinationof sample selection and an alternate velocity measure-ment procedure. Samples with visible plug-scale hetero-geneity should be discarded. Pore-scale heterogeneitythat may prevent the uniform spatial saturation of asample must also be recognized. Finally, the use ofphase velocity is recommended as the best way to min-imize the effect of sample heterogeneity on the acousticvelocity measurements. By following this guidance, Ra-solofosaon et al. (2008) present a compelling examplein which lab data demonstrate experimental verifica-tion of the Gassmann equation in (calcite) carbonatesamples. Adam and Batzle (2008) further emphasize theimportance of frequency and differential pressure dur-ing lab testing and suggest that bulk modulus (as shownin Rasolofosaon et al., 2008) should be preferred (overvelocity) when evaluating the applicability of the Gass-mann equation.

Organization of the paperBuilding from the introduction, this paper next de-

scribes the data and the rock-physics models consid-ered in the subsequent analysis. Using the global dataset and a variety of rock-physics models, I critically

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evaluate the importance of mineralogy and pore type onthe elastic properties behavior. From this analysis, anintegrated rock-physics workflow, utilizing a rock-physics template and dry-rock modulus diagnostics(Kittridge, 2006), emerges as a suggested minimumstandard for the evaluation of carbonate rock-physicsdata. Finally, I review and comment on specific chal-lenges in seismic petrophysics for carbonate reservoirs,particularly in the area of lab- and well-based data in-tegration. The integrated global data set, suggestedworkflow, and conclusions drawn from the deliberateapplication of heuristic and theoretical rock-physicsmodels should be of interest to petrophysicists and geo-physicists using core, well log, and seismic data forappraisal and seismic-based reservoir characterizationin carbonate reservoirs.

Data and methodsAll of the data analyzed in this study are taken from

published, public-domain sources. The measured dataare reported in tabular form in the original source(s)and were manually transcribed from the original source.(Data from Verwer et al. [2008] were available as a digitaldownload directly from http://www.seg.org with the full-text reference). No data were obtained indirectly fromscanned data plots. When available, additional geologicinformation (age, mineralogy), sample analyses, and tex-tural information (dominant pore type, digital imageanalyses) are noted from the original reference. Table 1provides a summary of the core data sets considered.

Rock-physics dataFour data sets are reviewed in this study, all from

geologically diverse global locations and a variety oforiginal sample sources (well, outcrop). With the excep-tion of one data set (Weger et al., 2009), all data setsinclude P- and S-wave velocities, frequently for dryand wet conditions, porosity, and grain density. Thevelocity measurements were made in various labs, withvariables but generally comparable (isostatic) confiningstress, stress path, and ultrasonic (0.7–1 MHz) frequen-cies. When available, dry and wet velocity data enabledthe estimation of velocity differences attributable tofluid replacement and the potential issue of shearmodulus variability discussed previously. Specific chal-lenges in analysis of the Weger et al. (2009) data set,which were missing S-wave velocity and grain density,will be discussed in a subsequent section. The work re-ported by Weger et al. (2009) is known to have includedlaboratory measurements of S-wave velocity (see p.1299 in original citation), although no data are reportedand no use or evaluation of VS data is included in thisparticular reference. In fact, in 2011, a direct inquiryto the lead author seeking access to those data (andmeasured grain density) was declined.

Data 1 — Miocene outcrop, MallorcaThe data are from outcrop and surface-drilled bore-

holes (3) of a Miocene outcrop in Mallorca. Data are notidentified in any manner that enables determinationof the outcrop or (surface) borehole source for the

Table 1. Summary of core data sets analyzed.

Source Location(s) Type #Spl VP VS ρg Lab velocity GeologyAdditional

descriptor(s)

Verweret al. (2008)

Cap Blancof the

LlucmajorPlatform,Mallorca

Outcropand

surfaceborehole

(3)

250 (131) Yes Yes Yes Wet (deairedbrine 35% NaCl)and dry; Peff 10MPa; Ppore

0.1 MPa; 1MHz

Miocene; low- andhigh-Mg calcite,

dolomite,aragonite.

Mostly dolomitic.

XRD,petrography,

texture(granular,crystalline)

Wegeret al. (2009)

Middle East(Shu”aiba);

southeast Asia(Miocene);

Marion Plateau(Miocene)

Wells 120 Yes No No Wet (distilledH20); Pconf

20 MPa; Ppore 2MPa; 1 MHz

Limestoneor Dolomite

(<2%noncarbonate)

Dunham texture;pore type(dominant,minor);

Digital imageanalysis

Bakhorji(2010)

Arab-Dreservoir(Saudi

Arabia) fromseven wells

Wells 37 Yes Yes Yes Wet and dry;Pconf

5-25 MPa(increasing,decreasing

stress); ∼1 MHz

Limestoneor Dolomite

(<1%noncarbonate)

Samplescharacterized

as macro, micro,dual porosity.Petrography,SEM, mercuryporosimetry

Fournieret al. (2011)

Four outcroplocations,southeastFrance

Outcrop 80 Yes Yes Yes Dry; Pconf 2.5, 5,10, 20,

and 40 MPa; Ppore0.1 MPa; 1 MHz

Lower Cretaceousplatform;

microporouslimestone

All grainstonetexture,

absence ofintergranular,

intercrystal-line,or moldicporosity

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individual sample. Very few permeability data are re-ported and are not further considered in this analysis.The original data set was edited to include only sampleswith wet and dry velocities and measured mineralogyand in which mineral-based grain density agreed with

the reported grain density. Subsequent rock-physicsanalysis on the edited data set (Figure 1) is based oncalcite (n ¼ 16) and dolomite (n ¼ 115) end-members(>0.9 v∕v), with average grain densities of 2.72 and2.857 g∕cm3, respectively.

Data 2 — Global cored wellsThe data are from cored wells at

three different sites (Middle East, South-east Asia, Australia), and all samples areeither limestone or dolomite, with lessthan 2% noncarbonate minerals. Dataare identified in a manner that enablesdiscrimination into one of three datagroups (B, L, and M) that reflect location(Figure 2). One of the locations is doc-umented as the Marion Plateau (Aus-tralia) with data acquired during ODPleg 194 (Ehrenberg et al., 2003). Furtheranalysis and evaluation of specific datafrom the three locations is describedbelow as part of the rock-physics analy-sis. Minimum reported permeability is0.1 mD, and entries with zero permeabil-ity (n ¼ 2, Location L) were assigned apermeability of 0.01 mD. No further ed-iting of the original data set was made.Two pore shape parameters from digitalimage analysis are reported and usedin the rock-physics analysis: perimeterover area (PoA) and dominant pore size(DomSize). The interested reader is re-ferred to the original publication for fur-ther details on these parameters.

Data 3 — Arab-D reservoir, Saudi ArabiaThe data are from seven cored wells

in the Arab-D from a reservoir in SaudiArabia. Data are identified in a mannerthat enables discrimination by well.Using reported mineralogy data, sam-ples are grouped based on mineralogy(Figure 3). Subsequent rock-physicsanalysis is based on calcite (n ¼ 26)and dolomite (n ¼ 6) end-members(>0.9 v∕v), with average grain densitiesof 2.714 and 2.839 g∕cm3, respectively.Velocity data (dry and wet) are at20 MPa and are taken from the increas-ing confining stress cycle. Minimumreported permeability is 0.01 mD, withindividual samples reported as 0.1 and0.01 mD.

Data 4 — Outcrop grainstone, FranceThe data are microporous limestone

samples from four different outcroplocations in southeast France. Dataare identified in a manner that enables

0 0.2 0.4 0.60

5

10

15

20

25

30

35

40

Porosity (frac.BV)

Num

ber

sam

ples

Data: Verwer (2008)

0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

(frac.BV)

Num

ber

sam

ples

Dolomite content

2.75 2.8 2.850

20

40

60

80

100

120

(g/cm3)

Num

ber

sam

ples

Grain density

Figure 1. Basic petrophysical properties for data compiled by Verwer et al.(2008). Mineralogy (dolomite, calcite) based on reported XRD data.

0 0.1 0.2 0.3 0.410

−1

100

101

102

103

104

Porosity (frac.BV)

Per

mea

bilit

y (m

D)

Data: Weger (2009)

Locn: BLocn: MLocn: L

0 100 200 3000

10

20

30

40

(mm−1)

Num

ber

sam

ples

PoA

0 500 10000

10

20

30

40

(µ)

Num

ber

sam

ples

Domsize

Figure 2. Basic petrophysical properties for data compiled by Weger et al.(2009). Digital image analysis was used to generate DomSize and PoA data.

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discrimination by (outcrop) locale. All the samples aregrainstones and are well-sorted and medium- to verycoarse-grained. The intergranular and intraskeletalspace is almost completely filled with calcite cements.The average micrite content is 0.656 v∕v (σ ¼ 0.11), andthe average grain density is 2.705 g∕cm3

(Figure 4). Velocity data (dry) are at20 MPa (using VS1for shear velocity).No permeability data are reported.

A variety of additional carbonatevelocity data sets are reported andknown from the public domains, whichare not included here. Sayers (2008) an-alyzes a single published data set, and Idid not repeat that analysis in this study.Several other data sets are omittedbecause of mineralogical complexity(varying carbonate and sulfate fraction,admixtures with quartz), no reportedS-wave velocity, and/or concerns aboutmeasurement protocol and sample via-bility. The data considered here enablea detailed evaluation of generally mono-mineralic samples for carbonate (calciteand dolomite) reservoir end-members.

Rock-physics modelsNumerous rock-physics models exist

for a wide variety of lithologies that arerelevant to subsurface petroleum explo-ration and production (e.g., Mavko et al.,2009). Model details and formulas maybe found in Mavko et al. (2009) and theoriginal references cited therein. Thediscussion that follows will use the gen-eral classification of rock-physics mod-els described in Avseth et al. (2010).Of paramount importance in the analy-sis of the carbonate data sets reportedhere is the distinction between modelsthat explicitly include factor(s) relatedto pore shape(s) and those (often fre-quently used) models that actually haveno pore-shape (or texture) parameter(s)at all in the (often empirical) model. Fur-thermore, the rock-physics analysis thatfollows incorporates three novel fea-tures: (1) deliberate evaluation of theinfluence of mineralogy (calcite anddolomite) on the interpretation of mea-sured velocity data; (2) application of avariety of (heuristic, theoretical) modelsto the measured data (including dry-rock modulus diagnostics [Kittridge,2006]), often applying one or more mod-els not used by the original authors; and(3) integration between data sets, seek-ing insights into mineralogically and/or

textural behavior consistent across multiple (global)data sets.

Mineral-specific rock properties and rock-physicsparameters are summarized in Table 2. Average calciteand dolomite mineral-based end-member grain density

0 0.1 0.2 0.3 0.4 0.510

−2

10−1

100

101

102

103

104

Porosity (frac.BV)

Per

mea

bilit

y (m

D)

Data: Bakhorji (2010)

CalciteMixedDolomite

2.7 2.75 2.8 2.85 2.90

5

10

15

20

25

(g/cm3)

Num

ber

sam

ples

Grain density

0 0.1 0.2 0.3 0.40

2

4

6

8

(frac.BV)

Num

ber

sam

ples

Porosity

Figure 3. Basic petrophysical properties for data compiled by Bakhorji (2010).

0 0.1 0.2 0.30

2

4

6

8

10

12

14

16

Porosity (frac.BV)

Num

ber

sam

ples

Data: Fournier (2011)

0.4 0.5 0.6 0.7 0.80

5

10

15

20

(frac.BV)

Num

ber

sam

ples

Micrite content

2.66 2.68 2.7 2.72 2.740

5

10

15

20

25

30

(g/cm3)

Num

ber

sam

ples

Grain density

Figure 4. Basic petrophysical properties for data compiled by Fournier et al.(2011).

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values from the data of Verwer et al. (2008), Bakhorji(2010), and Fournier et al. (2011) agree with values re-ported in Table 2. Note that other sample-based (e.g.,Sayers, 2008; Verwer et al., 2008) and computationalrock-physics studies (Dvorkin et al., 2012; Andraet al., 2013) use mineral values that are consistent withindividual mineral (e.g., calcite) values given in Mavkoet al. (2009). The rock-physics models described in thefollowing section use the average properties (graindensity, moduli, velocity) for calcite and dolomite(Table 2) determined from data reported in Mavko et al.(2009).

Empirical modelsA variety of mineral-specific (calcite and dolomite)

empirical transforms are known (Mavko et al., 2009)and commonly applied in carbonate rocks. In general,these relationships are direct (regression) fits to data,using functional forms relating velocities (VP and VS)to porosity and VS to VP (Figure 5). The models maynot agree with the data, are often inconsistent with puremineral end-point VP and VS (Table 2), and generallyhave very limited predictive capability (or possibly nopredictive capability). It should be readily apparent thatnone of these empirical models will be able to modelthe effect of varying carbonate pore(s) on velocity

(Brie [2001] reports an empirical modelfor calcite that includes a “sphericalpore” fraction as a variable in the rela-tionship).

As noted previously, several authorsmake use of the empirical Wyllie rela-tionship (Table 3), in which departurefrom the behavior expected by the WTAmodel is cited as evidence for pore-shapeeffects on carbonate velocity. Two im-portant observations on theWyllie modelare evident (Figure 5): (1) Calcite anddolomite show very little VP differencesat a given porosity and (2) the model cal-cite data (φ < 0.3) are faster (higher VP)than WTA model predictions for calcite(and also dolomite). Mavko et al. (2009)provide a useful reminder about the inad-equacies of the WTA as a credible rock-physics relationship.

Theoretical modelsA variety of theoretical models rel-

evant to carbonate rock physics areused, including bounds, inclusion mod-els, and computational models. Boundmodels (e.g., Voigt, Reuss) are rigorouslycorrect, are generally free from (geologi-cally) idealized behavior, and find greatutility in placing limits on realistic behav-ior, which often facilitates measurementquality control (QC). Although a varietyof inclusion models are available, I re-strict my use to the self-consistentapproximation (SCA), in which poresand grains are considered to be (ideal-ized) ellipsoidal inclusions in the com-posite (Table 3). Additionally, I utilizethe model of Xu et al. (2006) (XuP) asit handles variable mineral-specific poreshapes and has been applied (Xu et al.,2009; Xu and Payne, 2009) to reservoirand lab data comparable to those dataanalyzed in this study. Although Avsethet al. (2010) would likely describe theXu et al. (2006) model as an “empirical

Table 2. Reported mineral-specific properties and rock-physicsparameters.

Mineral ρg Kg μg VP VS φc Source

Calcite 2.708 70.8 30.3 6.41 3.35 0.4 Mavko et al. (2009).Avg. value (five samples)

Calcite 2.71 73.3* 32 6.41 3.44 Bakhorji (2010).* value unique from

Mavko et al. (2009). VP andVS computed.

Dolomite 2.873 80.2 48.8 7.11 4.12 0.6 Mavko et al. (2009).Avg. value (three samples)

Dolomite 2.84 94.9 45.7* 7.41 4.01 Bakhorji (2010).* value unique from

Mavko et al. (2009). VP andVS computed.

0 0.1 0.2 0.3 0.4 0.52

3

4

5

6

7

Porosity (frac.BV)

VP (

km/s

)

Empirical models

CalcDoloWyllie (calc)Wyllie (dolo)

0 0.1 0.2 0.3 0.4 0.51

1.5

2

2.5

3

3.5

4

Porosity (frac.BV)

VS (

km/s

)

ChalkDoloCalc

2 3 4 5 6 71

1.5

2

2.5

3

3.5

4

VP (km/s)

VS (

km/s

)

Data: Finney pack (DRP)

DoloCalc

0 0.1 0.2 0.3 0.4 0.51.5

1.6

1.7

1.8

1.9

2

2.1

2.2

Porosity (frac.BV)

VP

/VS (

−)

Finney Pk (fluid sub.)

Figure 5. Empirical relationships for calcite, dolomite, and chalk as reported inMavko et al. (2009). All models are for brine-filled conditions. Data are for cal-cite, using computational results reported in Dvorkin et al. (2012).

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relationship sometimes disguised as theoretical,” I in-clude it here given that it relies on an inclusion model(Kuster-Toksoz) to describe the effect of variable poreshape(s) on moduli and velocity. XuP model properties(calcite, dolomite) were calculated using commercialsoftware. The Kuster-Toksoz inclusion model has beenavoided, given the constraint on dilute (noninteracting)inclusions (see Wang, 1997). With the emergence ofcomputational (digital rock physics) approaches torock physics (Xu et al., 2006; Dvorkin et al., 2012),3D image-based computed rock-physics properties(moduli, velocity) extend and improve our understand-ing of the elastic behavior, particularly in which lab-based methods are difficult or prone to measurementirregularities.

Bound-filling modelsOf several bound-filling models, two are used in the

subsequent analysis: Modified Voigt and the modifiedupper Hashin-Shtrikman (HSM) models (Table 3). Bothof these models use the critical porosity (φc) concept tomodify original Voigt and upper HSM bounds. Thebound-filling models do not explicitly use any pore-shape parameters; rather, the critical porosity is seento be the adjustable model parameter, perhaps with aconnection to geology (perhaps the texture?).

The theoretical and bound-filling models for calciteare shown in Figure 6 using a graphically robust rock-physics template, which I will use in my subsequentanalysis. The models describe bulk (Kd) and shear(Gd) modulus as a function of porosity and mineralogy.From the dry-rock moduli, fluid-filled VP and VS are cal-culated using Gassmann’s relationship. Fluid replace-ment (Gassmann) and dry-rock moduli determinationfollow the procedures described in Wang (1997) andSmith et al. (2003). The free parameter in the boundmodels (Voigt, HSM) is critical porosity (no pore-shapeinformation), whereas the theoretical models (XuP,SCA) use one (or more) pore shape(s) to be modeledusing variable aspect ratio(s). For reference, I usedthe computational results on the Finney Pack, with

matrix properties for calcite, as reported by Dvorkinet al. (2012). The Finney Pack is a reference (computa-tional) media in which all pore spaces are found be-tween uniform-sized spheres; porosity is varied in thePack by changing the sphere size. As such, all porosityis interparticle, and this (numerical) configuration in-cludes no anomalous pore shape(s) as may be foundin natural carbonate core material. The computed prop-erties are comparable with the “reference” interparticlepore (α ¼ 0.15) of, for example, Xu and Payne (2009).The models and computational results (Figure 6) enablethe following observations: Computed moduli are be-tween the bound-filling models and generally consistentwith all models; pore-shape models, using similar as-pect ratios, yield very similar results and are close tothe (HSM) bound model; bound and theoretical modelperformance varies when compared to data in bulk andshear modulus space; and both models and data yieldhigher VP than Wyllie model predictions at a givenporosity.

Results: Analysis of carbonate rock-physics dataIn this section, I analyze each of the individual

core-based velocity data sets previously described. Theanalysis necessarily treats calcite and dolomite asdistinct, given the differences in matrix moduli, and Irely on a combination of heuristic and theoretical mod-els, some (XuP, SCA) including variable pore-shapeparameters.

The theoretical and bound-filling models used in thesubsequent analysis share three important advantages:(1) Dry-rock modulus behavior (bulk and shear) is pre-dicted as a function of porosity and mineralogy, (2) themodels are assured to honor mineral-based moduli andvelocity at the matrix (zero porosity) point, and (3) theyreadily facilitate evaluation of dry and saturated labora-tory-measured velocity data. None of the models areregressed to the data; the only adjustments are formineralogy (grain moduli at zero porosity, Table 2),critical porosity (bound-filling models), and pore aspectratio (SCA model). The models and the associated

Table 3. Summary of rock-physics models and input parameters.

Model typeModel name

(figure legend)Critical

porosity, φc

Pore aspectratio Comment

Empirical WTA N/A None Matrix VP for calcite and dolomitefrom Table 2 (Mavko et al., 2009).

Bound-filling Modified Voigt (Voigt) 0.42, 0.44, 0.5 None Matrix Kg and μg for calcite and dolomitefrom Table 2 (Mavko et al., 2009).

Bound-filling Modified upper Hashin-Shtrikman (HSM)

0.42, 0.44, 0.5 None Matrix Kg and μg for calcite and dolomitefrom Table 2 (Mavko et al., 2009).

Theoretical Xu-Payne (XuP) N/A 0.15 Constant “reference” pore aspect ratiofor calcite and dolomite.

Theoretical Self-consistentapproximation (SCA)

N/A Variable Reference aspect ratio 0.2. Varied aspect ratiocases with single (0.1, 0.175, 0.25, 0.3, 0.45, 0.8),

and dual (0.3, 0.8) aspect ratio pores.

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(graphical) rock-physics template pro-vide a sound heuristic basis from whichobservations about mineralogy and pore-shape-based variability may be crediblyevaluated from lab-measured velocitydata.

Single mineralogy (calcite)First, I examine the monomineralic

data reported by Fournier et al. (2011).All of the samples are calcite, and theresults are shown in Figure 7. The dryvelocity-derived moduli are consistentwith bounds, computational results onthe Finney Pack, and the zero porositymatrix point for calcite. Moduli are gen-erally well described by the HSM boundand pore-shape models (XuP, SCA),with both using a single pore aspectratio (0.15, 0.2, respectively). In fact,all data are generally within a very nar-row SCA aspect ratio range of 0.1–0.2,implying very little pore-shape variabil-ity across the data set. As such, optimalmatching to the total data set wouldinvolve empirical adjustments to φc(HSM) and sample-specific variationsin pore aspect ratio (XuP, SCA), pos-sibly using a distribution of more thanone aspect ratio. The fitting with varia-ble pore aspect ratio(s) leads to a non-unique result. Fluid-replaced VP data areall generally faster than the WTA modelprediction, but they are compatible withresults from the Finney Pack.

Mixed mineralogy (reservoirsamples)

To extend the analysis for a singlemineral, I next examine the Saudi Ara-bian oilfield data reported by Bakhorji(2010). Measured sample grain density,supported by petrographic evidence, en-ables a clear distinction between calciteand dolomite samples. Dry-rock moduliinferred from the (dry) measured veloc-ities are consistent with bounds forcalcite and dolomite (Figure 8). Notethat the large separation in shear modulimakes the distinction between carbon-ate minerals more diagnostic. Thecomputed moduli for the (assumed cal-cite) Finney Pack are also compatiblewith bounds for calcite, particularlyfor the narrowly separated shearmoduli. The Voigt bound also suggeststhe potential for sample QC, particularlyfor the single high-porosity calcite sam-ple (φ ¼ 0.381 v∕v). Modeling with SCA

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VoigtHSMXu−PayneSCA

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VP: Water saturated

WTA−calcData (fluid sub.)

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Porosity (frac.BV)

VS (

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)

VS: Water saturated

Finney Pk (fluid sub.)SCA (fluid sub.)

Figure 7. Theoretical and bound-filling relationships for calcite. Data are calcitesamples reported in Fournier et al. (2011). SCA single pore aspect ratio α ¼ 0.1(φ ¼ 0.15) model (magenta symbol). See the caption in Figure 6 for additionaldetails.

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CalcFinney pack

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Data: Finney pack (LM)

VoigtHSMXuPSCA

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Porosity (frac.BV)

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WTA−calc

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3.5VS: Water saturated

Porosity (frac.BV)

VS [

km/s

]Finney Pk (fluid sub.)

Figure 6. Theoretical and bound-filling relationships for calcite. Critical poros-ity (φc) is 0.44 and single pore aspect ratio is 0.15 (XuP) and 0.2 (SCA). Data arefor calcite, using computational results reported in Dvorkin et al. (2012).

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at φ ¼ 0.375 v∕v and a significant frac-tion (φ ¼ 0.15 v∕v) of large aspect ratio(α ¼ 0.8) pore space does not ade-quately describe the measured datapoint.

Brine-saturated velocity data, mea-sured wet and the dry data (fluid) sub-stituted to wet, are shown for calciteand dolomite samples in Figure 9. Sepa-ration between values for a given sam-ple might be a suggestive of Gassmannfluid replacement issues and/or originalsample measurement QC. In general,the data are consistent with bound (con-stant φc) and theoretical models (singleaspect ratio), particularly when mineral-ogy is accounted for. Velocity deviation(s) is generally small and can be seen tobe faster and slower than a given modelacross the sample suite. In particular,dolomite samples are generally consis-tent with bound and theoretical models,but they are faster than Wyllie (WTA)model prediction and would be consis-tently faster (most notably in shearvelocity) than any of the calcite models,at a given porosity.

Mixed mineralogy (outcropsamples)

I further our evaluation of the role ofmineralogy and pore shape(s) nowevaluating the outcrop data reported byVerwer et al. (2008). In contrast to thereservoir data reported by Bakhorji(2010), the outcrop data set is domi-nated by dolomite samples, and the do-lomite samples extend to significantlyhigher porosity (φ > 0.5 v∕v). Dry-rockmoduli inferred from the (dry) measuredvelocities are compared with bounds,and XuP (Figure 10) and SCA models(Figure 11) for calcite and dolomite.Calcite sample data are consistent withbounds and computational model re-sults; theoretical model performance isvariable, with XuP (single pore) calciteperformance in better agreement thandolomite, whereas the SCA model, using(single) variable aspect ratios, is in muchbetter agreement with data, particularlyfor calcite (Finney Pack and outcropdata). The high-porosity (φ > 0.46 v∕v)dolomite data exceed relevant boundsand are stiffer than SCA model predic-tion using a large (α ¼ 0.8) single aspectratio pore. Properties of these samplesmay be unique and a result of the (out-crop) nature of the original sample.

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Bound and heuristic model

CalcDoloFinneyData: CalcData: Dolo

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Voigt: calcHSM: calcXuP: calcVoigt: doloHSM: doloSCA: calc

Figure 8. Dry-rock moduli inferred from (dry) measured velocities for datacompiled by Bakhorji (2010). Critical porosity (φc) is 0.42, SCA single pore as-pect ratio is 0.175 (φ ¼ 0.25), and two pore aspect ratios α ¼ 0.3 (φ ¼ 0.225) andα ¼ 0.8 (φ ¼ 0.15) for the high-porosity (φ ¼ 0.375) model (magenta symbols).See caption in Figure 6 for additional details.

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DolomiteWTA−doloData (DM): SubData: Wet

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VS (

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Bakhorji (2010) DM

HSMXuPSCA

Figure 9. Theoretical relationships for calcite and dolomite. Data are calcite(top) and dolomite (bottom) samples reported in Bakhorji (2010). Critical poros-ity (φc) is 0.42; see the caption in Figure 6 for additional details.

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Computational results on the invertedFinney Pack (Dvorkin et al., 2012) struc-ture at comparable porosity (using calcitematrix moduli) are higher than the high-porosity (outcrop) dolomite samples.

Brine-saturated velocity data, bothmeasured wet and the dry data (fluid)substituted to wet, are shown for calciteand dolomite samples in Figure 12. Ingeneral, sample velocities are fasterthan the WTA model for calcite anddolomite, but deviations from a theoreti-cal (SCA) single pore model, accountingfor matrix mineralogy, are much reduced(100 sm∕s). Samples with notable devia-tion from SCA model velocity (moreprevalent in dolomite samples thancalcite) also frequently show the largestdifference between wet- and fluid-re-placed velocity, which may be indicativeof Gassmann fluid replacement issues,original sample measurement QC, orpore-type variability. Velocity variabilityin the low (φ < 0.4 v∕v) ratio is con-sistent with a larger (e.g., α ¼ 0.45)single pore aspect ratio (SCA model);in contrast, all of the high-porosity (φ >0.46 v∕v) dolomite samples are signifi-cantly faster than SCA model predictionswith a single, large aspect ratio pore(α ¼ 0.8), as expected from dry-rockmoduli (Figure 11) behavior.

Finally, note that the need to invokea larger (single) aspect ratio pore toexplain dolomite sample velocities is afunction of (high) porosity and is a non-unique (and sample-specific) determina-tion. For dolomite samples with φ <∼0.38 v∕v, a single larger aspect ratiocan explain the measured data. Dolo-mite samples with a larger porosity arenot well described by an inclusionmodel using a single large aspect ra-tio pore.

Mixed mineralogy(no shear velocity)

The preceding analyses clearly illus-trate the importance of mineralogy andthe utility of dry-rock modulus diagnos-tics in the evaluation of carbonate veloc-ity data. Challenges arise in the analysisof data reported by Weger et al. (2009),as I have only P-wave velocity data(wet) and no direct sample-specific min-eralogy information.

One of the three data sets (MarionPlateau) is specifically identified, andreferences therein further identify that

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Bound, heuristic and XuP model

CalcDoloFinneyData: CalcData: Dolo

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Voigt: calcHSM: calcVoigt: doloHSM: doloXuP: calcXuP: dolo

Figure 10. Dry-rock moduli inferred from (dry) measured velocities for datacompiled by Verwer et al. (2008). Critical porosity (φc) is 0.42 for calcite and0.5 for dolomite. XuP single reference pore aspect ratio is 0.15 for calciteand dolomite. See the caption in Figure 6 for additional details.

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CalcDoloFinneyFinney (inv)Data: CalcData: DoloSCA: dolo

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Voigt: calcHSM: calcVoigt: doloHSM: doloSCA: calc 0.25SCA: dolo 0.3

Figure 11. Dry-rock moduli inferred from (dry) measured velocities for datacompiled by Verwer et al. (2008). SCA single pore aspect ratio is 0.25 for calciteand 0.3 for dolomite. SCA single pore aspect ratio α ¼ 0.45 (φ ¼ 0.36) and α ¼ 0.8for the high-porosity (φ ¼ 0.46) model (green symbols). See the captions inFigures 6 and 10 for additional details.

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the data are from ODP Leg 194. Originalsample data, including porosity, per-meability, and mineralogy (calcite anddolomite), are available in an earlierreference (Ehrenberg et al., 2003). Usingthose data, in particular the reportedpermeability (detailed to as many as fivesignificant digits), I can uniquely identify(38 of 52) well “L” samples as the ODPdata (Figure 2). All but five of the well“L” samples are dolomite. The per-meability data tabulated in Weger et al.(2009) at or below 2 mD cannot beuniquely matched with data reportedin the original ODP-194 compilation(original with three significant digits).Although I can match permeability data“exactly,” I also note that porosity val-ues reported in Weger et al. (2009) varyfrom those given in the original ODP-194data compilation.

The remaining data sets (referencedas wells “B” and “M,” Figure 2) are fromthe Middle East and Southeast Asia.Middle East samples are from theShu’aiba Formation and are Aptian inage. A general search in the open liter-ature indicates that this formation islimestone (calcite) in, for example, theBu Hasa field. Data from the SoutheastAsia source are from an isolated plat-form of the Miocene age. The Malam-paya field (Fournier and Borgomano,2007) may be such an example of theSoutheast Asia data set. Core-based re-sults in Fournier and Borgomano (2007)and additional references cited thereinindicate that the Malampaya reservoiris limestone (calcite). In the followinganalysis, all data identified as wells “B”and “M” are treated as calcite.

The measured (wet) P-wave velocitydata are shown in Figure 13 (calcite)and Figure 14 (dolomite). As in previousexamples, nearly all the samples arefaster (significant departure in dolomitesamples) than the WTA model predic-tion for calcite and dolomite. Data aregenerally well described by modelsusing a single pore aspect ratio (XuP,SCA), with deviations to lower andhigher velocities on the order of the100 sm∕s. The dolomite samples are invery good agreement with the (singlepore) SCA model, with a few notabledepartures at higher porosity (φ >0.3 v∕v). Samples with larger (positive)velocity deviations tend to have largerpores (DomSize), but there are samples

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Porosity (frac.BV)

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Verwer (2008) DM

HSMXuP 0.15SCA 0.3SCA: dolo

Figure 12. Theoretical relationships for calcite and dolomite. Data are calcite(top) and dolomite (bottom) samples reported in Verwer et al. (2008). Seecaptions in Figures 6, 10, and 11 for additional details.

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HSM Phi−crit .42XuP 0.15SCA .25Finney Pk (fluid sub.)

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Figure 13. Measured P-wave velocities for calcite sample data compiled byWeger et al. (2009). Color scale is DomSize (image analysis) in the upper figureand dominant pore type (1 ¼ interparticle, intercrystalline and 2 ¼ moldic,vuggy, intraframe, and micromoldic) in the lower figure. See caption in Figure 6for additional details.

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that deviate with small pores and samples with largerpores that show minimal velocity deviation. Similarly,the nature of the dominant pore type (interparticle ver-sus “vuggy”) does not consistently explain velocity de-viations nor is it a useful discriminator for samples thatare in good agreement with a single aspect ratio “refer-ence” model (XuP, SCA). Notable positive velocity de-viations in several dolomite samples (Figure 14) areconsistent with a dual-pore aspect ratio SCA model,in which a large fraction (>50%) of the total porosityis a large aspect ratio (α ¼ 0.8) pore. In this instance,the nature of the dominant pore type is not always con-sistent with this (nonunique) modeling choice; twohigh-porosity dolomite samples with positive velocitydeviation are dominated by interparticle porosity. Itis likely that this is an indication of the need for aquantitative description of carbonate texture (poreshape(s), rock fabric) that is consistent with the effec-tive media model(s) that includes a term to describepore shape(s).

Discussion on the application of seismicpetrophysics workflows to carbonatereservoir rocksSeismic petrophysics

Seismic petrophysics is an integrated workflow to in-tegrate lab- and well-derived rock-physics data. Although

the analyses described here focus exclusively on lab-based measurements, I include comments that are par-ticularly relevant for the application in well-based stud-ies of carbonate reservoirs. For workflow details, theinterested reader will find (siliciclastic) examples in Kit-tridge et al. (2008) and Smith (2011). Comments thatfollow reference, the two-part workflow of Kittridgeet al. (2008), and emphasize work elements in whichchallenges and aspects unique to carbonate reservoirsare likely.

Reservoir petrophysicsThis segment of the seismic petrophysics workflow

includes data QC; evaluation of local pressure, temper-ature, and (effective) stress; fluid acoustic propertiesdetermination; and quantitative reservoir petrophysics.Given the importance of carbonate mineralogy in theunderstanding of velocity, it is imperative that the res-ervoir petrophysical evaluation include a quantitativedetermination of mineral volumes. Water saturationdetermination is often problematic in carbonates, thecombined result of reservoir heterogeneity (variablecementation exponent, “m”), temporal changes in for-mation of water salinity (waterflood), and complexsaturation distribution (transition zone, residual hydro-carbon saturation). The use of NMR data in carbonates,particularly for porosity partitioning, may provideunique in situ information that would enhance the

evaluation of pore type(s) and theirpotential impact on measured velocity.

Rock physicsThis segment of the seismic petrophy-

sics workflow includes shear log QC andestimation, fluid replacement modeling,and the development of end-memberrock-physics relationships. Although thegeneral approach to shear log QC andestimation would not be different, thechoiceof appropriatemodel(s) is critical.The results developed in the precedingsection suggest a workflow that is ame-nable to velocity log QC and estimationincarbonatesusingporosityandmineral-ogy, forward model VP and VS using oneormore theoreticalmodels, andcompareto measured well data. This is similar tothe view advocated by Xu et al. (2009).Challenges for fluid replacement model-ing in carbonates with Gassmann werediscussed briefly in the Introduction.When working with well data, additionalissues may include invasion effects (seethe example suggested in Xu et al.,2009) and the choice of a fluid-mixingmodel. A complex in situ fluid distribu-tionmay require an alternative fluid-mix-ing model to correctly infer dry-rockmoduli from hydrocarbon-saturated log

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DolomiteWTA−doloODP−194: [DM]

Domsize

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Data: Weger (2009) min: DM

HSM Phi−crit .5XuP 0.15SCA 0.3SCA: dolo

1

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1.8

2

Figure 14. Measured P-wave velocities for dolomite sample data compiled byWeger et al. (2009). Color scale is DomSize (image analysis) in the upper figureand dominant pore type (1 ¼ interparticle, intercrystalline and 2 ¼ moldic,vuggy, intraframe, and micromoldic) in the lower figure. SCA pore aspect ratioα ¼ 0.3 (yyφ ¼ 0.125) and α ¼ 0.8 (φ ¼ 0.19, φ ¼ 0.25) for the two porous(φ ¼ 0.315, φ ¼ 0.375) model cases (green symbols). See caption in Figure. 6for additional details.

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data. Rock-physics model development should neces-sarily integrate lab- and well-based data, using appro-priate (heuristic, theoretical) model(s) and the rock-physics template approach employed in the precedingdata analyses. Additional comments on a proposedwork-flow for carbonate rock-physics model development fol-low in a subsequent section. Finally, the integration ofwell-based data will necessarily require the (vertical) up-scalingofwell logdata.Theuseofmineral-andpore-basedclassification scheme(s) would naturally facilitate therock-physics analysis. For example, averaging by petro-physically determined reservoir rock types particularlythosebasedoncapillarypressureorotherpore-type-based(NMR) methods would obviously enable and enhanceelastic properties modeling as described in the previousexamples.

A workflow for carbonate rock-physics model development

The data analyses and results presented for the fourpublic-domain data sets naturally suggest a preferredworkflow (Figure 15) for the development of a carbon-ate rock-physics model. As a minimum standard, the fol-lowing analytical elements are required:

1) Using analytical (e.g., XRD) and/or descriptive(petrographical) methods, characterize sample min-eralogy. Validate sample mineralogy with mea-sured grain density, using published mineral values(Table 2).

2) Core-based measurements should include VP andVS, and preferably measurements of dry and satu-rated velocities.

3) QC sample-based velocity measurements usingdry-rock modulus diagnostics (Kittridge, 2006) andrelevant mineral-specific theoretical and heuristicbounds on dry-rock moduli.

4) Use a rock-physics template in the analysis ofcarbonate velocity behavior. Samples should beevaluated using relevant, mineral-based heuristic,and theoretical models. Moduli and velocity behav-ior are linked, and additional interpretive insight isrealized from the analysis of corendered moduli andvelocity data and models.

5) Wet and dry data should be compared, and sampleswith large velocity deviation should be examinedfurther.

6) Sample(s) with anomalous behavior can be testedusing theoretical model(s) and varying pore aspectratio values in an iterative attempt to reproducemeasured behavior. Digital rock-physics results area natural addition to this evaluation.

The suggested workflow is amenable to integrationof lab- and well-based data and computational (digital)results. Additional value is derived from the iterativeapplication of the workflow, particularly with dry-rockmoduli, rock-physics template(s), and the testing ofvariable (single, multiple) aspect ratio pores.

Limitation of empirical modelsAs noted previously, several authors (Anselmeti and

Eberli, 1997; Verwer et al., 2008; Weger et al., 2009) haveused sample-based (P-wave) velocity deviations fromthe WTA model as an indication of the presence ofanomalous carbonate pore type(s). The WTA modelhas no theoretical justification and includes no informa-tion about pore shape(s). Further, several authors (An-selmeti and Eberli, 1997; Weger et al., 2009) use theWTA model to make the fatuous claim that mineralogydoes not matter, as the model predicts very similar VPfor calcite and dolomite at a given porosity. Though theargument is numerically correct, the use of an inappro-priate model leads to an erroneous conclusion aboutthe role of mineralogy.

Returning to the data of Weger et al. (2009) to exam-ine and deconstruct this misleading interpretation,results are presented in Figure 16. The upper figure re-produces what was shown by the original authors (theirFigure 3). The lower figure captures the results of themineral-based interpretation, using a credible theoreti-cal rock-physics model (including pore-shape param-eter). In their analysis, Weger et al. (2009) attribute allof the (positive) P-wave velocity deviation, when com-pared to WTA model, as evidence of pore-shape effects.Results after application of the preferred workflowdescribed in the previous section are substantially dif-ferent: (1) Mineralogy (calcite, dolomite) exerts a sig-nificant control on carbonate velocity and (2) for agiven mineral, velocity variation at a given porosity ismuch reduced, with significant portions of the dataset (particularly the dolomite samples) well describedby a theoretical model using a single (“reference”) poreshape. Note that much of the velocity departure in thecalcite samples is to lower VP at a given porosity, sug-gesting a lower aspect ratio than the reference(α ¼ 0.25) used in the SCA model.

A second example of an empirical carbonate modelis the one presented by Brie (2001). Using computed

Figure 15. An iterative workflow for the evaluation anddevelopment of carbonate rock-physics model(s).

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results from an effective media (Kuster-Toksoz) model,Brie (2001) fits an empirical (linear) relationship to themodel (dry) VP∕VS ratio, including a “spherical porefactor” term. As used, this term represents the fractionof the porosity that is “spherical” porosity, presumablythe equant larger aspect ratio pores. In Figure 17, I

compare this empirical approximation to the measured(dry) rock sample data and the theoretical results usingthe SCA model. In this instance, the empirical fit is invery good agreement with the theoretical model andcomputed results (to φ ∼ 0.31v∕v). Measured sampledata (none were available to the original author) are

also in reasonable agreement with theempirical fit. One potential use of suchan empirical model would be as aconstraint or external input to the Gass-mann-fluid-replacement modeling, par-ticularly for the case of log-based fluidsubstitution in the absence of a mea-sured shear log.

Linking pore-shape effects onelectric and elastic properties

Petrophysicists working in carbonatereservoir formation evaluation have longunderstood the challenges for resistivitylog interpretation. Variable carbonatepore types particularly vuggy and moldic(large aspect ratio) pores are known toresult in higher formation resistivityfactor (FRF) and implied (Archie)m ex-ponents. Herrick and Kennedy (1995)describe a model and present data froma MidEast oomoldic carbonate reser-voir. Ragland (2002) presents a compre-hensive globally distributed data set andstatistical analysis, suggesting an aver-age m exponent of 1.93 and 2.46 forintercrystalline and moldic-dominatedsamples, respectively. More recently,computational methods have been usedto determine FRF for carbonate sam-

ples. Knackstedt et al. (2007) present directional (x,y, and z) results for four sucrosic dolomite samples. An-dra et al. (2013) give computational results for Gros-mont carbonate, using a variety of numerical solutionalgorithms. Digital rock physics provides a uniqueand complementary data source for the joint evaluationof electrical and elastic properties in carbonate samples(e.g., Knackstedt et al., 2008).

As an example of the combined evaluation of electri-cal and elastic properties, I utilized the data of Verweret al. (2011). Data and interpretive results are shown inFigure 18. Using specific data from digital image analy-ses (DomSize and PoA) and reported permeability, Iwas able to uniquely identify 19 samples in Verwer et al.(2011) that have velocity (VP only) results given inWeger et al. (2009). The well L samples are all knownto be dolomite, whereas the well B samples are all as-sumed to be calcite (see the Discussion in the precedingsection).

Well B samples show variability in FRF with impliedm between average intercrystalline (m ¼ 1.93) andaverage moldic (m ¼ 2.46) bounds. All of the samples

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SCA: calcSCA: doloFinney Pk (fluid sub.)

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Figure 16. Carbonate P-wave velocity versus porosity. Data are from Wegeret al. (2009). Upper figure shows a completely empirical approach, with no dis-tinction made for sample mineralogy. Lower figure shows samples by mineralogy(circles: calcite and squares: dolomite) and with pore information (color scale isDomSize from image analysis). See the captions in Figures 13 and 14 for addi-tional details.

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CalcDoloFinney PkFournier (2011)Bakhorji (2010)Verwer (2008)Brie (spf=0.3)SCA calc (.25)

Figure 17. VP∕VS ratio versus porosity, dry calcite sampledata. The empirical model of Brie (2001) with a spherical porefactor of 0.3 is shown (green) and compared with the theoreti-cal results from the SCA model (α ¼ 0.25).

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are small DomSize, with a large range in PoA. Velocitydata are very consistent with XuP and SCA calcite mod-els for a single reference pore type, suggesting littleelastic impact from anomalous (large aspect ratio)pores. In fact, velocity data for these samples are moreconsistent with a smaller pore aspect ratio (lower veloc-ity than the model), which is in agreement with imageanalysis results. The range in FRF and implied variabil-ity in m seem greater than indications that may be in-ferred from elastic behavior alone.

Well L samples show significant variability in FRFwith nearly all samples that are at or higher than theaverage moldic reference trend. In fact, at least threesamples have reported FRF values that seem substan-tially out of range, based on the analog core measure-ments and DRP results, suggesting a measurement QCissue. It is important to note that the porosity value re-ported in Verwer et al. (2011) for well L data differsfrom the value given in Weger et al. (2009) and in theoriginal ODP-194 data table (Ehrenberg et al., 2003).Choice of porosity value does not change the observa-tion about anomalous (high) FRF values. All of the sam-ples are large DomSize, with a small (limited) range inPoA. Velocity data are very consistent with the SCAdolomite model for a single reference pore type, sug-gesting little elastic impact from anomalous (largeaspect ratio) pores. As such, this makes the disconnectbetween electrical and elastic behaviors more pro-nounced for the (well L) dolomite samples than forthe (well B) calcite samples. Even though there isnothing that would require the electrical and elastic

properties to behave similarly, it is instructive to notethe variations demonstrated in this relatively small,but well characterized, sample set. Further work, par-ticularly with computational rock physics and perhapsalternate methods to characterize pore space morphol-ogy, seems necessary to provide a causal explanationfor this particular data set.

ConclusionsUsing a variety of recent public-domain data sets

comprised of porosity, velocity (P- and S-waves) and, inmost cases, mineralogy and petrographic data, I createan extensive global data set and evaluate the impor-tance of mineralogy and texture (pore type) on the elas-tic properties behavior. Results from this investigationclearly illuminate the potential for overinterpretingelastic properties behavior as a function of pore type(s) when mineralogy is not explicitly included in theanalysis. Inferences of this type are exacerbated bythe application of an inappropriate (WTA) model thathas neither theoretical justification nor the ability tomodel variable pore type(s). With a diverse set of lab-based rock-physics data and a combination of heuristicand theoretical rock-physics recipes, I developed thefollowing results:

1) Mineralogy (calcite and dolomite) exerts a signifi-cant, first-order control on elastic properties. Fail-ure to account for the differences in mineralogycould lead to erroneously attributing velocity varia-tion, at a given porosity, to pore shape(s).

2) For a known monomineralic sample,several theoretical models (XuP,SCA) describe the measured velocitydata using (total) porosity and a single(“reference”) pore aspect ratio. Theheuristic models used here (Voigt,HSM) do not include an explicit pore--shape variable. These models mayoften describe the measured velocitydata with comparable accuracy as thecommonly applied theoretical (effec-tive) media models that use a variablepore-shape factor.

3) The effective media model(s) com-monly used in carbonates is nonuni-que and is frequently applied usingpore-shape parameters (aspect ratio)as “fitting parameters.” With sucha technique, some data are shownto be consistent with a dual-poresystem, in which large aspect ratiopores form a large portion of the (to-tal) porosity. Even though the physicsunderlying the model(s) certainlyhas appeal, inappropriate applicationmay create a false sense of geologicsecurity in the (inferred) aspect ratiodata.

10−1

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F (−

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FRF: Meas. Core data and DRP

Ragland (2004)SPWLA−95Finney PackKnackstedt (2007)Andra (2012)Verwer (2011):L Verwer (2011):B Ref m = 1.97m=1.5

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SCA: calcSCA: dolo

Figure 18. Joint evaluation of carbonate resistivity and elastic properties data.FRF data include measured data and digital rock-physics results. Velocity sam-ples are those uniquely identified as also having FRF measurements (Verweret al., 2011). See text for additional comments.

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I also examine the role of seismic petrophysics in in-tegrated studies of lab- and well-based carbonate rock-physics data. I describe a minimum standard (iterative)workflow for those modeling elastic properties datafrom carbonate reservoirs. Although the specific inter-pretation of the four data sets described here seemsconclusive, I advocate continued studies that bringtogether quantitative petrology, sound analytical data,and complementary digital rock-physics results thatseek a causal explanation for rock the physics behaviorin these important reservoir rocks.

AcknowledgmentsI thank the HESS Corporation for supporting the

release and preparation of this paper. This paper wasoriginally presented as Paper A at the SPWLA 55thAnnual Logging Symposium (Abu Dhabi); SPWLA isrecognized for permitting publication. The manuscriptbenefited from the technical editing and organizationprovided by R. Thompson (Shea Writing Solutions)and reviews from T. Lane (BP) and two anonymous re-viewers that improved the final manuscript. I gratefullyrecognize ongoing technical dialog and exchange withthe following individuals: R. Hofmann (Shell), M. Sen-gupta (Hess), M. Prasad and M. Batzle (ColoradoSchool of Mines), and C. Torres-Verdín (The Universityof Texas at Austin). The opinions expressed in this pub-lication remain solely of the author.

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Mark G. Kittridge is a petroleumengineer with more than 25 years ofexperience in petrophysics, includingwell operations, integrated reservoirstudies, enhanced oil recovery, androck physics. He received a B.S.(1986) and professional degrees ingeological engineering from The Colo-

rado School of Mines and received an M.S. (1988) in petro-leum engineering from The University of Texas at Austin.He is currently a geophysics manager — physics of rocksfor HESS Corporation. Previously, he was a regional dis-cipline lead (petrophysics) and global principal technicalexpert (QI petrophysics) at Shell International EP, Inc. Ad-ditional roles included manager — petrophysics and rockphysics (ConocoPhillips) and vice president of technology(Ikon Science). He is also the coinventor of one U.S. patentfor the characterization of logging tool performance.

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