-
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;
[email protected]
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;
[email protected]
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,
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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 (
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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
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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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Appendix. Cont.
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
*DomSize = dominant pore size; PoA = perimeter over area; AR =
aspect ratio; VPpressure of 20 MPa at a frequency of 1 kHz); Phi =
porosity; K = permeabili
**G = grainstone; P = packstone; W = wackestone; M = mudstone;
FL = floatstonhyphen; rDol = completely recrystallized rocks.
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vuggy; WPO = intrapain the table is estimated to contain more than
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