Rock fabric controls on pore evolution and porosity ...

Rock fabric controls onpore evolution andporosity–permeability trendsin oolitic grainstone reservoirsand reservoir analogsHamilton M. Goodner, Eugene C. Rankey, Chi Zhang,and W. Lynn Watney

ABSTRACT

Although the general influence of rock fabric on porosity andpermeability (F–k) within carbonates is well documented, if andhow pore evolution and F–k scatter quantitatively relate to de-positional fabric remains poorly constrained. This projectempirically explores this uncertainty within oolitic grainstonesfrom a range of geologic ages and diagenetic histories to un-derstand depositional sediment–pore relationships and how theycan evolve with lithification. Integrating data from point count-ing, digital image analysis, nuclear magnetic resonance, and coreanalysis of Holocene, Pleistocene, Pennsylvanian, and Mississip-pian oolitic grainstones reveals quantitative relations among rockfabric, pores, and petrophysical parameters. Oolitic grainstones ofsimilar sedimentology taken from distinct diagenetic scenariosdisplay a unique combination of pore size, shape, spatial distribu-tion, andF–k character.Within each scenario, pore attributes and kare correlated more closely with grain size, sorting, and type thanwith cementation and compaction. Collectively, these results areinterpreted to suggest that sedimentology controls the trends orvariability within an oolitic succession but that diagenesis definesthe absolute values of pore attributes and petrophysical pa-rameters. These findings suggest that petrophysical variabilitywithin oolitic reservoirs may closely follow sedimentologictrends, whichmay be predictable within a stratigraphic framework.

AUTHORS

Hamilton M. Goodner ~ KansasInterdisciplinary Carbonates Consortium,Department of Geology, University ofKansas, Lawrence, Kansas; present address:Shell Exploration and Production Company,Houston, Texas; [email protected]

Hamilton M. Goodner, a native of Macon,Georgia, earned a B.S. degree in geology fromthe University of Georgia. He went on tocomplete his M.S. degree in geology at theUniversity of Kansas, working with GeneRankey. Currently, he is a geologist workingfor Shell Exploration and ProductionCompany in Houston, Texas.

Eugene C. Rankey ~ KansasInterdisciplinary Carbonates Consortium,Department of Geology, University ofKansas, Lawrence, Kansas; [email protected]

Eugene C. “Gene” Rankey is a professor atthe Kansas Interdisciplinary CarbonatesConsortium, Department of Geology,University of Kansas. A graduate of AugustanaCollege (Illinois) (B.S. degree), University ofTennessee (M.S. degree), and University ofKansas (Ph.D.), Gene examines carbonate andcarbonate–siliciclastic stratigraphic andreservoir systems using core, petrophysical,and seismic data, and values the insightsderived from the study of modern carbonateanalogs. He is the corresponding author ofthis paper.

Chi Zhang ~ Kansas InterdisciplinaryCarbonates Consortium, Department ofGeology, University of Kansas, Lawrence,Kansas; [email protected]

Chi Zhang is an assistant professor in theDepartment of Geology at the Universityof Kansas. Chi received her Ph.D. inenvironmental geophysics from RutgersUniversity in 2012. Chi’s research focuses onstudying complex fluid–rock interactions usinggeoelectrics, nuclear magnetic resonance, andmodeling tools.

W. Lynn Watney ~ Deceased

W. Lynn Watney received his B.S. (1970) andM.S. (1972) degrees in geology from IowaState University and Ph.D. (1985) from the

Copyright ©2020. The American Association of Petroleum Geologists. All rights reserved.

Manuscript received February 12, 2019; provisional acceptance April 24, 2019; revised manuscriptreceived July 19, 2019; final acceptance December 19, 2019.DOI:10.1306/12191919046

AAPG Bulletin, v. 104, no. 7 (July 2020), pp. 1501–1530 1501

mailto:[email protected]




http://dx.doi.org/10.1306/12191919046

INTRODUCTION

Many prolific hydrocarbon reservoirs produce from carbonatestrata, but carbonate reservoir characterization can prove challeng-ing because of complex pore networks. In seeking to understand thecontrols on these pore networks, numerous studies have docu-mented variations in porosity and permeability (F–k) and howthese relate to carbonate rock fabrics (Lucia 1983, 1995, 1999;Jennings and Lucia, 2001; Cruz et al., 2006; Lønøy, 2006), in-tegrating parameters such as particle size (Lucia, 1983; Jenningsand Lucia, 2001) or depositional texture (Jones and Xiao, 2006).These and other studies of carbonate pores commonly assumepart or all of a logical linkage: (1) rock fabric defines pore at-tributes (e.g., pore-size distribution); (2) pore attributes controlpermeability; and (3) as a result, rock fabric controls perme-ability (Enos and Sawatsky, 1981; Lucia, 1983, 1995, 1999;Melim et al., 2001; Weger et al., 2009).

As rock fabric is shaped by depositional aspects (e.g., originalmineralogy, grain size, sorting, and type) and diagenetic attributes(e.g., cement abundance and compaction porosity loss [COPL]),a question of “nature or nurture” commonly arises. Are pore net-works (and, subsequently, F–k) controlled more by their deposi-tional starting point (i.e., the attributes of sedimentologiccomponents) or by the changes they undergo (i.e., diageneticmodifications)? Original mineralogy of carbonate sediment (e.g.,aragonite vs. calcite) influences pore evolution because calciteand aragonite respond to diagenesis differently, resulting incarbonates that can include a wide variety of diagenetic over-printing. Thus, the links from textural attributes to petrophysicshave the potential to be tenuous. Perhaps as a result, efforts tosystematically and quantitatively link textural attributes of de-positional fabric (primary sedimentologic components; Choquetteand Pray, 1970) to pores, and further, to petrophysical variabil-ity, are few.

To explore these challenges, this project quantitatively teststwo linked hypotheses: (1) varied depositional fabrics correlate todistinct pore attributes and (2) pore attributes and total porositycontrol permeability. To explore these hypotheses and unravelboth rock fabric–pore attribute links and pore attribute–k links,this project examines oolitic grainstones, a class of deposits presentin carbonate accumulations of almost every geologic age. Ooliticdeposits also represent important hydrocarbon reservoirs acrossthe globe, from the United States midcontinent (Watney andFrench, 1988; Abegg, 1991) and Gulf Coast (Melas and Friedman,1992) to the Middle East (Lindsay et al., 2006; Esrafili-Dizajiand Rahimpour-Bonab, 2014; Hollis et al., 2017) and Far East (Maet al., 2011). This study statistically integrates results from petro-graphic point counting, digital image analysis (DIA), nuclearmagnetic resonance (NMR), and core analysis. In characterizing

University of Kansas. He worked as apetroleum geologist with Chevron(1972–1976) and joined the Kansas GeologicalSurvey (KGS) in 1976 where he was a seniorscientific fellow. Lynn passed away in the finalstages of revision for this paper; he is missed.

ACKNOWLEDGMENTS

This research was funded by the KansasInterdisciplinary Carbonates Consortium ofthe University of Kansas and by theGeological Society of America. We thankNikki Potter and KGS personnel for lendingtheir time and facilities during the selectionand collection of the core samples in thisstudy and Jon Smith at KGS for use of hispetrographic facilities. This is in memory ofLynn Watney.

1502 Porosity–Permeability Evolution in Oolitic Grainstones

strata from a range of ages, the ultimate goal is toresolve the degree to which relationships amongsedimentology, pores, and petrophysical responsesare maintained in oolites that have undergone a rangeof diagenetic histories (e.g., prediagenesis [Holocene],early diagenesis [Pleistocene], and prolonged dia-genesis of originally aragonitic [Pennsylvanian] andcalcitic [Mississippian] sediment). The results il-lustrate how different depositional properties caninfluence petrophysical trends and heterogeneitywithin comparable oolitic reservoirs; this infor-mation is pivotal to advancing conceptual under-standing and quantitative models of oolitic carbonatereservoirs.

BACKGROUND

This study examines four groups of samples that rep-resent distinct diagenetic settings (Figure 1; Table 1)but include similar ranges of sedimentologic char-acter (i.e., granulometry and grain-type proportions)(Figure 2). These four sample groups could be con-sidered distinct diagenetic scenarios: unlithifiedsediment, early diagenesis, and two distinct latediagenetic end members (i.e., aragonitic vs. calciticprecursor sediment). Together, these groups repre-sent snapshots along potential diagenetic pathways,facilitating understanding of original pores and howthey can be modified by diagenesis. Not everypossible diagenetic scenario is included, however,and certainly other diagenetic pathways could beconsidered.

The sediment and rock samples include a rangeof sedimentologic, stratigraphic, and diagenetic char-acter (Figures 1, 2; Table 1). Holocene samples areunlithified oolitic sediment (i.e., the starting pointfor all oolitic grainstones) from Schooner Cays,Great Bahama Bank, and Fish Cays, Crooked–AcklinsPlatform, Bahamas (Ball, 1967; Rankey and Reeder,2011, 2012; Huber, 2016; Rush and Rankey, 2017)(Figure 1A, B; Table 1). Pleistocene samples are lith-ified strata from Long Cay and Crooked Island,Crooked–Acklins Platform, Bahamas; these are unitsthat have been exposed to marine and early meteoricdiagenetic alterations (shallow burial [<10 m {<32.8ft}], low to moderate cementation [16.9% cement byvolumetric abundance]) (Table 1) (A. Goers, 2018,personal communication). These rocks were deposited

as dominantly aragonitic sediment, and their min-eralogy has stabilized only partly. Cementation hasoccluded pores incompletely, and dissolution hascreated pores within grains (e.g., dissolved ooidlaminae) and enlarged preexisting pores (Figure 1C,D). These samples display pore systems that includea mix of interparticle pores, moldic pores, and mi-croporosity. Pennsylvanian samples are from reser-voir intervals (Bethany Falls Limestone, MissourianLansing–Kansas City Group) in multiple fields inKansas (Watney and French, 1988; French andWatney, 1993; Byrnes et al., 2003) (Table 1). Theserocks likely were deposited as aragonitic sediment(e.g., Sandberg, 1983), but after extensive dissolutionand cementation, they now display well-developedmoldic pores and some relict interparticle pores.Oomolds are generally large (commonly hundredsof microns) and isolated; they may be crushed orpreserved as round to oval shapes (Figure 1E, F).Because Pennsylvanian samples represent a moldicend member oolitic reservoir, they are distinct fromMississippian samples (Abegg, 1991; Parham andSutterlin, 1993), which display well-connectedinterparticle pores. These samples were taken fromthe St. Louis Formation B interval in productivefields in southwestern Kansas (Qi and Carr, 2005) andwere deposited as dominantly calcitic sediment (e.g.,Sandberg, 1983), which is less susceptible to disso-lution, preserving grains and much of the primaryinterparticle porosity (Figure 1G, H). These rocksare broadly comparable to those of the Holocene interms of grain condition and pore type, but theyhave undergone various degrees of cementation andcompaction.

The samples from the Pennsylvanian and Mis-sissippian intervals focus on porous zones withinreservoirs and do not include tight zones. Further-more, samples from all groups were selected to avoidfractures and touching vugs (nonfabric selective, in-terconnected pores) (Lucia, 1995), which can alsoimpact permeability.

METHODS

Sample Collection and Preparation

Holocene sediment (n = 12) samples were collectedat the sediment–water interface, whereas Pleistocene

GOODNER ET AL. 1503

Figure 1. Thin-section photomicrographs illustrating sedimentologic and diagenetic variability within and among sample groups. (A)Fine, moderately sorted sand, Holocene, Bahamas. (B) Medium, well-sorted sand, Holocene, Bahamas. (C) Pleistocene sample, Bahamas,showing parts of laminae. The lower, fine-grained part includes more abundant cement; in contrast, the upper part is coarser and less wellcemented. (D) Medium sand-size, well-sorted Pleistocene sediment, Bahamas, displaying partly dissolved ooids, associated moldic pores,and patchy cement. (E) Medium sand-size, very well-sorted Pennsylvanian sample including oomoldic pores, occluded oomolds, re-crystallized ooids, and some preserved interparticle pores. Core plug taken from well API 15-167-23179 at depth 2893.2 ft (881 m). (F)Medium sand-sized, moderately sorted Pennsylvanian sediment with diverse grain types. Core plug taken from well API 15-155-20566 atdepth 3507 ft (1068 m). (G) Medium sand-size, well-sorted Mississippian sediment with patchy cement and compaction indicators such assutured grain contacts and reduced intergranular volume. Core plug taken from well API 15-055-20141 at depth 4721 ft (1439 m). (H)Medium sand-size, well-sorted Mississippian sediment with thin isopachous cement rims and few compaction features. Core plug takenfrom well API 15-055-20149 at depth 5462 ft (1665 m).


(n = 19) rocks were taken from outcrops as handsamples. Downhole cores provided Mississippian(n = 18) and Pennsylvanian (n = 17) samples. The1-in. (2.54-cm)-diameter plugs from hand samplesor cores included ends that provided billets for thinsections. Billets were impregnated with blue epoxyand subsequently cut for standard thin-sectionpreparation.

Characterization of Rock Fabric

This study uses the term rock fabric to describe thesolid constituents of a sediment or rock (Choquetteand Pray, 1970). Genetically, rock fabric includesboth depositional (sedimentologic) and diageneticcomponents. Depositional fabric refers to the char-acteristics of primary sedimentologic components (e.g.,grain size), whereas characteristics of diagenetic originare termed diagenetic attributes.

To characterize the rocks, quantitative digitalpetrography using JMicroVision captured grain-sizedistribution. Using this program, 100 grain-size mea-surements were taken at randomly generated points onthin-section images. Because grain-size measurementsextracted from thin sections are apparent sizes, theyrequire conversion to be compared to sieve distribu-tions of sediment samples (Flugel, 2010). This studyimplements the regression model of Merta (1991) totransform thin-section distributions to sieve-size dis-tributions. The cumulative frequency curves of thesedistributions facilitate the graphical extraction ofgraphic mean size (“grain size”), inclusive graphicstandard deviation (“sorting”), inclusive graphic skew-ness (“skewness”), and graphic kurtosis (“kurtosis”)(Folk and Ward, 1957; Flugel, 2010). These quan-titative measurements were confirmed qualitativelyagainst comparative grain-size and sorting charts.Grain-size data presented herein use Udden sizedivisions with the Krumbein phi scale (Udden, 1914;Krumbein, 1939).

Point counting included grain-type quantification.Using a mechanical petrographic stage programmedfor regular grid stepping, at least 300 observationsper thin section differentiated ooids, composite grains,peloids, and various skeletal grains. In addition to graintype, point counting facilitated the quantificationof diagenetic parameters such as cement abundanceand intergranular volume (IGV). To characterize

compaction, the relative abundance of grains, in-terparticle cement, and interparticle porosity weredocumented, and they were then used to calculatea compaction index (“COPL” in Lundegard, 1992;Budd 2002):

COPL = Pi - ðð100 - PiÞ · IGV Þ=ð100 - IGVÞ (1)

The COPL estimates interparticle porosity loss causedby compaction. The variable Pi represents an assumedvalue of initial interparticle porosity, herein assumedto be 43%. This value is consistent with porosity datafor sedimentologically similar oolitic samples in Enosand Sawatsky (1981) and the NMR porosity dataof Holocene sediment samples presented herein.Fractures and stylolites are also documented, butthey are generally absent or very rare.

Characterization of Pore Attributes

Pore attributes such as pore size, shape, spatial dis-tribution, and type are quantified using point counting,NMR, and DIA. Point counting differentiated theproportions of pore types. The dominant pore types(Choquette and Pray, 1970) in these strata includeinterparticle, intraparticle, and moldic.

Bulk-property, three-dimensional (3-D) estima-tions of porosity and pore-size distribution are pro-vided by NMR (Coates et al., 1999; Song, 2013).During experiments, the NMR machine repeatedlytransmits a magnetic pulse through fluid-saturatedsediment or rock samples. After each pulse, a re-ceiver records the decay of resonating hydrogen ionsin the pore fluids in the form of an echo decay (Coateset al., 1999). These echo decays provide a multitudeof information about pore networks. This study usestransverse relaxation time (T2) curves, which describethe time record of the full spectrum of decay signals(Coates et al., 1999), and T2 data are common inboth laboratory and borehole settings (NMR logs).Typically, T2 curves plot relaxation time againstamplitude so that the area under the curve equalsthe initial amplitude of the echo decay, thus pro-viding ameasure of total porosity (Coates et al., 1999).The full spectrum of relaxation times serves as acrude proxy for a pore-size distribution (T2 time »pore size) (Coates et al., 1999; Vincent et al., 2011;Song, 2013). These T2 curves (time domain) may be

GOODNER ET AL. 1505

used to calculate pore-size distributions (length do-main) quantitatively by using certain calibrationsand assumptions that may or may not hold for car-bonate strata (Brownstein and Tarr, 1979; Godefroyet al., 2001; Vincent et al., 2011). As such, thisstudy presents T2 times instead of pore-size dis-tributions. Relaxation times are plotted on a loga-rithmic scale against porosity units (cf., Westphalet al., 2005). From these T2 distributions, certainpore attributes can be extracted, including modaltime (T2 mode) (cf., Doveton and Watney, 2014),mean time (logarithmic), curve peakedness (T2

kurtosis), total porosity, and macro- and microporosity.Prior to laboratory NMR analysis, all sediment

samples and plugs from core and outcrop were driedfor at least 24 hr at 60°C. Dried samples were weighed,subsequently saturated with deionized water un-der vacuum conditions for 10 hr, and then weighedagain using a water displacement method. Bulk volumecalculated from these measurements provided inputfor each NMR experiment. Samples were wrappedin Teflon tape during experiments to preventwater loss. The NMR experiments used a Magritek2-MHz NMR rock core analyzer, and all experi-ments attained a signal-to-noise ratio of at least100:1.

Included in DIA is a suite of methods to quantifyattributes of pores, such as size, shape, and spatial

distribution (Ehrlich et al., 1984; Fortey, 1995;Anselmetti et al., 1998; Russ, 1998; Lindqvist andAkesson, 2001; Weger et al., 2009) from digital im-ages of thin sections. Herein, DIA analyses generallymimic the methodology outlined in Weger (2006)and include three broad steps: image acquisition,pore network segmentation, and pore geometrycalculations. Two-dimensional thin-section imagesof each sample were acquired under plane-polarizedlight. Pore space in these images is distinguishedreadily because samples are saturated with blueepoxy. Through image segmentation, a binary image ofthe pore network was created by designating all bluepixels as pore and nonblue pixels as rock matrix. Anyair bubbles weremapped as “pore” in the binary images.

The DIA data used for pore geometry charac-terizations include two broad categories: metrics thatrepresent the geometry of individual pores (“localparameters”) and metrics that characterize the porenetwork as a whole (“global parameters”) (Russ, 1998;Weger, 2006). ImageJ software quantifies the rawmeasurements of pore area, perimeter, axis lengths ofbounding ellipse, and the angle between axes. Thesebasic measurements facilitate the calculation of localparameters for each pore on each thin-section imageand include the equivalent diameter, gamma, aspectratio, circularity, roundness, and compactness (Weger,2006; see Table 2 for explanations). These local

Table 1. Sedimentologic, Stratigraphic, and Diagenetic Character of Sample Sets

SampleGroup Area or Stratigraphic Unit

DepositionalEnvironment Dominant Pore Type References

Holocene Fish Cays, Crooked–AcklinsPlatform, Bahamas; SchoonerCays, Great Bahama Bank,Bahamas

Ooid shoalcomplex

Interparticle Ball (1967); Rankey and Reeder(2010, 2011, 2012); Rush andRankey (2017)

Pleistocene Crooked Island and Long Cay,Crooked–Acklins Platform,Bahamas

Shoreface Interparticle and intragranularmicroporosity; minor moldic

A. Goers and E. Rankey, 2018,personal communication

Pennsylvanian Lansing–Kansas City Group fromAmes, Bell, Hall–Gurney, Silica,and Victory Fields (Kansas)

Mobile ooidshoal

Oomoldic; minor interparticle Watney and French (1988);French and Watney (1993);Byrnes et al. (2003)

Mississippian St. Louis B from Big Bow andSand Arroyo Creek Fields(Kansas)

Mobile ooidshoal

Interparticle Abegg (1991); Parham andSutterlin (1993); Qi and Carr(2005)

Each group represents ooid grainstone of a distinct diagenetic scenario, ranging from unlithified sediment (Holocene) to early diagenesis (Pleistocene) to contrasting latediagenetic end members (Pennsylvanian, Mississippian).


parameters are summarized by statistics (e.g., mean,median, area-weighted mean) of their frequencydistributions, which serve as global parameters.Additional global parameters are calculated to fur-ther describe the pore network, including the sum ofthe pore area, sum of the pore perimeters, and totalperimeter over the area (PoA). Dominant pore size(DOMSize) is a size parameter (Weger, 2006)that represents the maximum pore size required toconstitute 50% of the total pore area or the pore

size at the 50% threshold of a cumulative area curve,given in equivalent diameter. Pores smaller than 100pixels were omitted from data analysis (followingWeger, 2006) to avoid distortion of geometric databy pores whose shapes may not be reliably charac-terized. Because Holocene samples are loose sedimentdisturbed by collection and absent of compaction, DIAwas not applied to these samples.

Beyond pore size and shape, the spatial distri-bution of pores can be characterized using lacunarity

Figure 2. Quantitative metrics describing sedimentologic character and diagenetic attributes of the four sample groups. On plots,whiskers represent minimum and maximum and boxes represent 25th, 50th, and 75th percentiles. (A) Granulometry data illustratingthat samples are fine to coarse grained and moderately (Mod.) to very well sorted. Ooid abundance typically is greater than 50%. (B)Cementation is reported as the percentage of the intergranular volume (IGV) that is occupied by cement, whereas compaction isreported as interparticle porosity loss that is attributed to compaction (compaction porosity loss [COPL]; calculated as in Lundegard,1992). Note that Pleistocene samples have suffered relatively little cementation and compaction. Pennsylvanian rocks include thehighest cement abundance but low compaction, whereas Mississippian samples display moderate cement abundance and highcompaction.

GOODNER ET AL. 1507

analysis (Allain and Cloitre, 1991; Plotnick et al.,1993). Lacunarity is a scale-dependent measureof spatial heterogeneity, which was assessed usingthe FracLac plug-in for ImageJ (Karperian, 2015).Following Allain and Cloitre (1991), Plotnick et al.(1993), and Rankey (2002, 2016), binary images(pore vs. nonpore) are scanned systematically atsuccessive scales using a gliding box algorithm. Inthis method, a square box of width r starts in theupper-left corner of the thin-section image, andthe number of pixels within that box that represent

pore space is documented, referred to as the boxmass S. The box then slides one increment to theright, again documenting S. This process is re-peated until all areas of the image have been ana-lyzed. A box mass probability distribution,Q(S,r), isgenerated:

QðS; rÞ = nðS; rÞ =NðrÞ (2)

such that n(S,r) is the number of boxes with size rthat contain a box mass S, and N(r) is the totalnumber of boxes (Plotnick et al., 1993). From this

Table 2. Local and Global Digital Image Analysis Parameters Characterizing Pore Size and Shape

Parameters Definition Description

Local ParameterAspect ratio Major

Minor Ratio of axis lengths of the bounding ellipse of a pore;distinguishes elongate features from star or circleshapes but fails to distinguish stars from circles(dimensionless)

Circularity 4pAP2 Inverse of gamma squared; sensitive to edginess or

smoothness of boundaries; scale dependent(dimensionless)

Compactness Affiffiffiffiffiffiffiffiffiffiffiffiffiffi

4pðMajorÞ2

qRatio of area and length of the major ellipse axis, notsensitive to edginess (dimensionless)

Equivalent diameter 2ffiffiffiAp

qDiameter of a circle with the same area as the pore;used to compare pore sizes regardless of poreshape (mm)

Gamma P2ffiffiffiffiffipA

p Ratio of pore perimeter to pore area(“unroundness”); distinguishes elongate or starshapes from circles but fails to distinguish elongateshapes from stars (dimensionless)

Roundness 4Ap · FD Scale-independent ratio of area and FD; robust

measure sensitive to elongate features(dimensionless)

Global ParameterTotal pore area �A Sum of area of all pores (mm2)Total pore perimeter �P Sum of the perimeters of all pores (mm)

PoA �P

�ADescribes complexity of the pore network’s boundary;especially sensitive to edginess; normalized forporosity variations (1/mm)

DOMSize 50th percentile Maximum pore size needed to occupy half of thepore space; given in equivalent diameter (Weger,2006) (mm)

Based on Russ (1998) and Weger (2006). Local parameters are calculated from the raw data produced by ImageJ, indicated by pore area, pore perimeter,major axis of bounding ellipse, minor axis of bounding ellipse, and Feret’s diameter, which is the longest distance between any two points along poreboundary. In addition to these four global parameters, the mean and median of each local parameter were calculated, as well as the area-weighted averageof gamma.

Abbreviations: A = pore area; DOMSize = dominant pore size; FD = Feret’s diameter; Major = major axis of bounding ellipse; Minor = minor axis of bounding ellipse;P = pore perimeter; PoA = perimeter over area.


distribution, the first and second moments are cal-culated, representing the mean (Z1) and stan-dard deviation (Z2), respectively. Lacunarity (L)of box size r is then calculated using the followingformula:

LðrÞ = Z2� ðZ1Þ2 (3)

This entire process and generation of a single lacu-narity value is replicated for nine incrementally largerbox sizes, with the largest box size equal to 45% ofthe thin-section area. A single lacunarity value is thedimensionless ratio of variance to (mean)2 for a givenbox size but ultimately is calculated across a range ofbox sizes.

The calculated lacunarity is a function of threefactors. The first factor is the total porosity present ina thin section: at a given box size, samples of higherporosity will exhibit lower lacunarity than that oflower-porosity samples. The second factor is the boxsize: as box size increases, lacunarity will also de-crease as the standard deviation decreases relative tothe mean. The third factor is the “gappiness” of thepore network: for a given porosity, samples withclumped or isolated pores will exhibit higher lacunarity(Plotnick et al., 1996; Rankey, 2016). Conversely, rockswith homogenously distributed pore networks exhibitlower lacunarity.

Lacunarity data typically are presented by plot-ting lacunarity (in this study, 10 values for each thin-section image) against box size on a log–log scale tocapture the scale dependence of the metric. In ad-dition, to recognize lacunarity distinctions amongsample groups, lacunarity values at each box sizewere averaged for an entire sample group, providinga characteristic lacunarity distribution for eachgroup. Furthermore, to mitigate the effects of porositydifferences between samples and sample groups, la-cunarity distributions were normalized by dividingeach value by the lacunarity at the smallest box size.When correlations of linear regressions required a sin-gular lacunarity value, the value at the smallest box sizewas chosen.

Across these analysis methods, pore attributescan be categorized by what they describe about apore (Table 3). For example, modal pore size orDOMSize characterize pore size. Compactness orcircularity characterize pore shape, and lacunarityassesses the spatial distribution of pores.

Characterization of Porosity andPermeability

Routine core analysis measured helium porosity(percent), air permeability (millidarcys), and graindensity (grams per cubic centimeter) for Pleistocene(n = 13), Pennsylvanian (n = 16), and Mississippian(n = 16) rocks. Some samples were unfit for analysisbecause of laboratory restrictions or sample quality(e.g., irregular plug shape or poor lithification) andthus do not have F–k data.

These F–k measurements are supplemented byNMR and DIA data. The NMR T2 curves provideporosity data, and a T2 cutoff (Coates et al., 1999)distinguishes micro- and macroporosity contribu-tions. Microporosity has been defined using any of avariety of criteria (summarized inVincent et al., 2011),and many studies have investigated the T2 cutoffs thatdistinguish microporosity from macroporosity (Coateset al., 1999; Al-Marzouqi et al., 2010; Vincent et al.,2011). This study implemented a microporosity–macroporosity cutoff of 100 milliseconds (ms) (cf.,Coates et al., 1999), corresponding approximately toa 5-mm pore (Al-Marzouqi et al., 2010). Porosityderived from NMR is typically 3%–4% porosity lessthan that from helium analysis of samples herein,which is assumed to stem from the ability of he-lium gas to penetrate smaller pore throats thanwater. Image analysis also provides porosity es-timates, but DIA does not reliably resolve micro-porosity as defined in this study because those poresare below the resolution of the thickness of the thinsection (32 mm).

RESULTS

Sedimentologic and Diagenetic Variabilityamong Sample Groups

Petrographic point counting quantifies the sedimen-tologic and diagenetic character of the four samplegroups (Figure 2). Samples are fine to coarse grainedand moderately to very well sorted. Ooid abun-dance is typically greater than 50%. Pleistocenesamples have undergone relatively low cementation(reported as the percentage of the IGV occupied bycement) and compaction (reported as interparticle

GOODNER ET AL. 1509

porosity loss caused by compaction, COPL). Penn-sylvanian samples include the greatest cementationbut low compaction, whereas Mississippian sam-ples display relatively moderate cementation and highcompaction.

Comparison of Pores and Porosity andPermeability among Sample Groups

The T2 distributions of representative samples fromeach sample group (Figure 3) reveal the general char-acteristics of the distinct pore-size distributions amonggroups. For example, Holocene samples (n = 12) ex-hibit unimodal distributions with high-amplitude peaks(>1 porosity unit) in the macroporosity domain (aver-age modal time = 563 ms), and total porosity averages43.6%. The T2 curves of Pleistocene samples (n = 15)are more complex and commonly include bimodaldistributions with low-amplitude T2 peaks (~0.5 po-rosity units) and modal T2 times in the macroporositydomain that are slightly smaller than Holocene sedi-ment (average = 502 ms). Average total porosity is34.6%. The peaks in the microporosity domain arepronounced, andmicroporosity commonly contributesmore than 50% of the total porosity.

In contrast, Pennsylvanian samples (n = 12) exhibitunimodal T2 curves dominated by macroporosity.Curves include moderate- to high-amplitude (>0.5porosity units) peaks with large modal relaxationtimes (average = 1.4 s) and an average total porosity of20.0%. The T2 curves of Mississippian oolites (n = 17)are consistently unimodal with low-amplitude peaks(<0.5 porosity units) at large relaxation times (average =1.1 s) and an average total porosity of 14.1%.

Quantitative pore attributes calculated usingDIA reveal differences in pore size, roundness, andspatial distribution in all three rock groups (Figures 4,5). Pores of Pleistocene samples are moderate in size(average DOMSize = 131 mm) and exhibit low round-ness (average = 0.53). In contrast, Pennsylvanian samplesincluded larger (average DOMSize = 189 mm) androunder (average roundness = 0.58) pores, and Missis-sippian samples have the smallest (average DOMSize =84 mm) pores with relatively low roundness (averageroundness = 0.53) (Figure 4).

Pores are not uniformly distributed. Some sam-ples (Figure 5A) include small pores that are evenlydistributed, whereas others include larger pores thatare more clumped (Figure 5B). The metric of lacu-narity provides a means to quantify spatial hetero-geneity in pores across a range of scales. Analysis ofthe samples reveals a range of lacunarity among in-dividual samples. In samples with similar porosity,pore networks that are more evenly distributed ex-hibit lower lacunarity (Figure 5A–C).

Table 3. Data Types Used Throughout This Study

Attributes Data Collected

Rock FabricDepositional Fabric Grain size

SortingSkewnessKurtosis

Ooid content, %Skeletal content, %

Composite grain content, %Mud content, %

Diagenetic Factors Cement abundanceCompaction (F loss)

Fracture presence (Y or N)Pore Attributes

Size DOMSizeT2 mode

T2 log meanT2 kurtosis

Shape PoACircularity

CompactnessGamma

Aspect ratioRoundness

Spatial Distribution LacunarityType Intergranular porosity

Moldic porosityF–k

Porosity, % Helium porosityDIA porosityNMR porosity

NMR macroporosityNMR microporosity

Permeability Air (k), md

Rock fabric includes depositional and diagenetic components and is characterizedusing digital petrography and point counting. Pore attributes are derived fromnuclear magnetic resonance, digital image analysis, and point counting, andthey quantify pore size, shape, spatial distribution, and type. These measuresof rock and pore character are compared to porosity and permeability datafrom routine core analysis, digital image analysis, and nuclear magneticresonance.

Abbreviations: F–k = porosity and permeability; DIA = digital image analysis;DOMSize = dominant pore size; N = no; NMR = nuclear magnetic resonance;PoA = perimeter over area; T2 = transverse relaxation time; Y = yes.


Figure 3. Thin-section photomicrographs (A–D) and associated nuclear magnetic resonance transverse relaxation time (T2) curves (E)of representative, sedimentologically similar samples (well-sorted, medium sand) of each age (e.g., diagenetic scenarios). For each T2curve (E), relaxation time (a proxy for pore size) is plotted against porosity units so that the area under the curve corresponds to totalporosity (in percent). (A) Unconsolidated Holocene oolitic sand with interparticle porosity. This sample displays a high-amplitude,unimodal peak in the macroporosity domain (>100 milliseconds [ms]) (E). (B) Pleistocene grainstone. Note cementation of interparticlepores and partial dissolution of grains (bluish tint). Resultant pore-size distribution is more complex, exhibiting a bimodal distribution witha moderate-amplitude macroporosity mode and clear contributions of microporosity (E). (C) Pennsylvanian grainstone. Grains aredissolved, and original interparticle pores are largely occluded with cement, leaving large isolated oomolds within a cement matrix.The T2 curve (E) is dominantly unimodal with high-amplitude mode at relaxation times greater than 1000 ms. (D) Mississippiangrainstone. Note preserved ooids and interparticle pores; corresponding T2 curve (E) displays low-amplitude modes at relaxationtimes greater than 1000 ms.

GOODNER ET AL. 1511

However, not all samples have similar porosity.In fact, differing total porosity among sample groups(e.g., Figure 3) is just one factor that contributes toeach group displaying distinct average lacunaritydistributions (Figure 5D). To mitigate the effectsof differing porosity, normalized lacunarity distribu-tions were also compared (Figure 5E). The data revealthat pores of Pennsylvanian samples display relativelyhigh lacunarity (i.e., isolated oomolds), whereas Mis-sissippian samples include the lowest lacunarity(i.e., evenly distributed intergranular pores). Incontrast, Pleistocene samples display relatively lowlacunarity at box sizes less than 7000 mm2 (i.e., aneven distribution similar to Mississippian examples)but have relatively high lacunarity at larger scales(i.e., clumped distribution akin to Pennsylvanianexamples).

A plot of porosity versus permeability revealsthat each sample group falls in distinct regions(Figure 6), akin to the data of Byrnes et al. (2003),which are also plotted. Pleistocene rocks (n = 9) havehigh porosity (25.2%–38.3%) and generally highpermeability (70 md–12.9 d) but include scatter onF–k plots. Pennsylvanian samples (n = 15) displayvariable porosity (6.3%–30.0%) and generally low,but variable permeability (0.02–145 md). Penn-sylvanian data broadly represent an extension ofthe Pleistocene F–k trend (consistent with Cruzet al., 2006). In contrast,Mississippian samples (n = 16)display a distinct trend, with low tomoderate porosity(9.6%–21.2%) and moderate to high permeability

(37–1134 md), which is higher than Pennsylvaniansamples of comparable porosity.

Depositional Fabric: Influence on PoreAttributes

The oolitic grainstones exhibit variability in terms ofsize, shape, and spatial distribution of pores (Figures4, 5); these distinctions may be related to sedimen-tology. For example, within the simplest case (un-cemented Holocene sediment), fine-grained sampleswith low ooid abundance exhibit modal pore sizesthat are smaller than those of coarse-grained sampleswith higher ooid abundance (Figure 7A–C). A 3-Dscatterplot visually reflects how differences in grainsize and ooid abundance are accompanied by changesin modal pore size (Figure 7D).

These qualitative relationships can be quantifiedusing multivariate linear regression by modeling therelationship between several independent variables(metrics of depositional fabric) and a dependentvariable (e.g., one of the various attributes of poresor porosity). For example, in these Holocene sedi-ment samples, metrics of depositional fabric (includinggrain size, sorting, ooid abundance, and skeletalabundance) are correlated statistically (coefficient ofdetermination [R2] = 0.92) withmodal pore size (cf.,Figure 7D). These parameters also influence the rangeof pore sizes (T2 kurtosis; R2 = 0.83) and total abun-dance of macroporosity (R2 = 0.69). These relations

Figure 4. Digital image analysis data illustrating differences in pore size (dominant pore size [DOMSize]) and shape (roundness) of allthree lithified sample groups. On plots, whiskers represent minimum and maximum, whereas boxes represent 25th, 50th, and 75thpercentiles. Data show that Pleistocene pores are of moderate size and roundness; Pennsylvanian rocks display large, rounder pores; andMississippian samples contain relatively small and less round pores.


Figu

re5.

Plot

illustratingdistinctp

atternsof

pore

configurationam

ongsamples

andsamplegroups.(A,

B)Binary

images

(red

=pore)of

twoPennsylva

nian

(Penn)

oomoldic

samples

with

similarp

orosity

(~10%,fromdigitalimageanalysis),eachrepresentingan

area

ofapproximately1.5cm

inwidth.The

sampleas

show

nin(A)includesrelativelysm

all,

evenlydistributed

pores,whereas

thesampleas

show

n(B)includesrelativelyclu

mped,isolatedpores.(C)L

acunarity

distributions

fromsamples

asshow

nin(A)a

nd(B).No

tethe

sampleasshow

nin(B)disp

layshigherlacunarityateach

boxsize,w

hich

isaresultofthegappierporenetwork.Lacunarityvaluesused

forlinearregressions

weretakenatthesm

allest

boxsize.(D)Average(Avg)lacunarityfro

meach

samplegroupat

each

boxsize.(E)Lacunaritydistributions

norm

alizedto

accountforvaryingporosityam

ongsamples

and

subsequentlyaveraged

foreach

samplegroupateach

boxsize.Datarevealvariability,forexam

ple,poresof

Pennsylva

nian

samples

displayrelativelyhigh

lacunarity(i.e.,isolated

oomolds),whereas

Mississippian

(Miss)samples

inclu

delowestlacunarity

(i.e.,evenlydistributed

intergranularpores).Pleist

=Pleisto

cene.

GOODNER ET AL. 1513

quantify the qualitative observations that uncementedsamples with larger grain sizes, better sorting, and higherooid abundance exhibit higher porosity (cf., Beard andWeyl, 1973), larger pores, and peaked (i.e., high kur-tosis) pore-size distributions.

In lithified rocks, rock fabric is more complicatedbecause it represents a combination of both deposi-tional and diagenetic components. Pleistocene porenetworks reveal the effects of early diagenetic alter-ations, with pore-size distributions that are complexand commonly bimodal (e.g., Figure 3). Despite thesechanges in the pore-size distribution, the modal mac-ropore size is influenced by depositional fabric, as ispore complexity (i.e., PoA) (Figure 8A, B). Fine-grained,poorly sorted rocks exhibit complex pore networks(high PoA); samples with larger grain size and in-creased sorting include simpler pores (low PoA).Multivariate regression quantifies these relationshipsand reveals that the attributes of Pleistocene depo-sitional fabric exhibit significant (P < 0.05) quanti-tative relationships with pore size (measured as T2

mode, R2 = 0.63) and pore complexity (PoA, R2 =0.81) (Figure 8B, blue bars). To assess the combinedinfluence of sedimentology and diagenesis on pores,regressions included both depositional fabric anddiagenetic metrics of cement abundance (percentageof IGV) and COPL. Integrating depositional anddiagenetic attributes into the regressions with T2

mode, DOMSize, and PoA increases R2 values toat least 0.80 (Figure 8B, orange bars).

Pennsylvanian samples are dominated by oomol-dic pores created by the dissolution of ooids (Figures 1,3C). Thus, it is not surprising that pore size generallyincreases with grain size (Figure 8C). Metrics of de-positional fabric also appear to influence the spatialdistribution of pores in Pennsylvanian samples. Higherooid abundance is associated with higher porosity andlower lacunarity (i.e., a more evenly distributed porenetwork). Multivariate regression reveals depositionalfabric correlates with pore size, complexity, and la-cunarity (Figure 8D), each with an R2 of at least 0.55.Including cementation and COPL as inputs in the

Figure 6. Porosity and permeability scatterplot, with data colored by geologic age. Samples collected as part of this study are noted bysquare markers, whereas unpublished data points from the Kansas Geological Survey (KGS) reservoir database are marked with lightercircles. Of the samples of this study, Pleistocene samples (n = 9) generally exhibit the highest porosity and permeability. Pennsylvaniansamples (n = 15) display variable porosity and relatively low permeability. In contrast, Mississippian samples (n = 16) display lowerporosity but a higher permeability for a given porosity than Pennsylvanian samples and plot on a well-defined trend.


pore-attribute regressions boosts correlations onlymarginally to between 0.58 and 0.78.

Similar to Pennsylvanian samples, pore sizes ofMississippian samples generally increase with largergrain size. Differing pore sizes also coincide with changesin grain type: rocks with a higher ooid abundance cor-respond to larger pores (Figure 8E). Depositional fabricexhibits significant statistical relationships with not onlypore size but also pore complexity and lacunarity (R2 >0.54 for all) (Figure 8F; Appendix). Including diageneticfactors of cementation and compaction increasesthe R2 of all three correlations, ranging from 0.65to 0.91.

Pore Attribute Controls on Porosity andPermeability

TheF–k data reveal that each sample group displaysa distinct character onF–k plots (Figure 6). One wayof characterizing pores is through pore-size distribu-tions, which are approximated through NMR T2 curves.The T2 curves of Pleistocene samples indicate bimodal

distributions revealing variable but pronounced (com-monly >50% of total F) contributions from micropo-rosity (T2 < 100ms) (Figure 3). The bimodal PleistoceneT2 curves are distinct from the curves of Pennsylvanianand Mississippian samples, which generally displaysimilar unimodal distributions with large (>1 s)modalrelaxation times (Figure 3).

Additionally, an explicit comparison of Pennsyl-vanian and Mississippian samples of comparable totalporosity (Figure 9) reveals similarity among T2 curvesacross a range of permeability. This observation ofsimilar T2 curves, which suggests similar pore-sizedistributions, in samples with distinct permeabil-ity is surprising because pore-size distributions havebeen interpreted to control permeability (e.g., Lucia,1983). That rocks with visually comparable T2 curves(and, presumably, pore-size distributions) includepermeabilities spanning more than three orders ofmagnitude suggests that pore attributes other thanpore-size distribution impact permeability (cf.,Bliefnick and Kaldi, 1996; Melim et al., 2001; Wegeret al., 2009).

Figure 7. Relations among depositional fabric and nuclear magnetic resonance transverse relaxation time (T2) curves for Holocenesediment. (A) Photomicrograph of fine-grained, moderately sorted oolitic and peloidal sediment. (B) Photomicrograph of medium, well-sorted oolitic sediment. (C) The T2 curves of sediment as illustrated in (A) (gold) and (B) (blue), illustrating distinct porosity, mode times,and mode porosity contributions. (D) The three-dimensional scatterplot revealing the relationship among grain size, ooid abundance, andmodal pore size. ms = millisecond.

GOODNER ET AL. 1515

Figure 8. Comparison of depositional and diagenetic attributes with pore attribute variability for three groups. (B, D, F) Each barrepresents a coefficient of determination (R2) value of the correlation between rock fabric metrics (independent variable) and a singlepore attribute (dependent variable); the pore attributes vary among groups and are noted below. In this analysis, rock fabric is split intometrics of depositional (grain size, sorting, ooid abundance, and skeletal abundance) and diagenetic (cement abundance and compactionporosity loss) character. Regression strength (R2) using solely depositional fabric metrics is illustrated by blue bars, whereas R2 valuesusing depositional fabric and diagenetic attributes are noted by orange bars. (A) The three-dimensional scatterplot illustrates that grainsize and sorting are inversely related to pore complexity (perimeter over area [PoA]) in Pleistocene samples. (B) Correlations betweenmetrics of Pleistocene rock fabric and modal pore size (transverse relaxation time [T2]) and pore complexity. (C) Crossplot illustrating the


To assess the influence of pore attributes otherthan pore-size distribution on permeability, analysesalso explicitly related pore geometry and spa-tial distribution to permeability variations. Linearregressions reveal that pore complexity is the singleparameter correlated most closely with k for Pleis-tocene samples (R2 = 0.74), followed by intergranularporosity (R2 = 0.61) and pore size (R2 = 0.57). A 3-Dscatterplot (Figure 10A) illustrates that samples withlow pore complexity, large pore sizes, and abundantintergranular porosity have high permeability. Amultivariate linear regression including those threepore attributes to estimate permeability indicates anR2 of 0.90 in Pleistocene rocks.

Pennsylvanian samples include somewhat differ-ent trends. Total porosity (NMR) displays the strongestcorrelation with k (R2 = 0.67). Factoring in pore cir-cularity and complexity as independent variables in aregression with permeability yields an R2 of 0.84.These results demonstrate that Pennsylvanian sampleswith high porosity, circular pores, and low pore com-plexity include high permeability (Figure 10B). InMississippian samples, helium porosity exhibits thestrongest correlation of any individual parameterwith permeability (R2 = 0.64), but pore size andspatial distribution are also correlated (R2 of 0.60 and0.49, respectively). Rocks with high porosity and large,evenly distributed pores yield high permeability (re-gression among these parameters has an R2 of 0.88;Figure 10C).

Some pore attributes consistently yield a statis-tically significant relationship with permeability acrossall sample groups. For example, abundant macro-porosity and circular (high circularity) pores favorelevated permeability in all groups (Appendix). How-ever, the pore attributes that aremost closely correlatedwith k vary among ages, suggesting that certain poreattributes are more important in some sample groupsthan in others. For example, pore size shows no sta-tistically significant relationship with k in Pennsylvaniansamples (R2 = 0.02, P = 0.60), but it correlates to the

permeability of Mississippian samples (R2 = 0.60, P =0.0004) (Appendix).

Sedimentologic Controls on Porosityand Permeability

These results show the relations between deposi-tional fabric and pore attributes, as well as amongpore attributes and F–k. The question remains: isthere a direct link from depositional fabric toF–k? Inshort, the answer appears to be yes becausemetrics ofdepositional fabric correlate to the permeability inPleistocene (R2 = 0.73), Pennsylvanian (R2 = 0.50),and Mississippian (R2 = 0.68) samples (Figure 11).The details of which parameters are most relevant dovary among sample groups, however. For example, interms of individual parameters, grain size and ooidabundance are the parameters of Pleistocene deposi-tional fabric most closely correlated to permeability:coarse-grained deposits with high ooid abundancedisplay high permeability (Figure 11A). AlthoughPennsylvanian samples display more variability in per-meability than that of Pleistocene samples, their sedi-mentologic attributes also correlate with permeability.In contrast to Pleistocene samples, sorting has animpact greater than grain size on permeability, andwell-sorted samples with high ooid abundance yieldthe highest permeability (Figure 11B). Interestingly,although they include pore types distinct from Penn-sylvanian samples, Mississippian samples documentsimilar relationships, with well-sorted samples withhigh ooid abundance displaying high permeability(Figure 11C). Including the diagenetic attributes ofcement abundance and compaction strengthens cor-relations within each sample group only marginally,increasing the R2 between 0.12 and 0.15 (Figure 11).

Although the specific metrics of depositional anddiagenetic variability that aremost strongly related topore attributes and permeability are distinct amongsample groups, one link appears consistent. In each,ooid abundance and sorting are related to lacunarity

Figure 8. Continued. positive relationship between grain size and dominant pore size (DOMSize) (on log scale), Pennsylvanian samples.(D) The R2 values of correlations between rock fabric and pore size (captured as log[DOMSize]), pore complexity, and lacunarity,Pennsylvanian samples. (E) The three-dimensional scatterplot illustrating the relations among grain size, ooid abundance, and pore size(DOMSize), Mississippian samples. (F) The R2 of correlations among rock fabric and pore size (DOMSize), pore complexity, and lacunarity,Mississippian samples. Collectively, the data reveal varied depositional fabrics are associated with changes in pore attributes.

GOODNER ET AL. 1517

Figure 9. Relations between nuclear magnetic resonance (NMR) curves and petrographic character. All samples have comparableporosity (18%–20%). (A) The NMR transverse relaxation time (T2) curves of illustrative samples from Pennsylvanian (Penn.)Lansing–Kansas City Group and Mississippian (Miss.) St. Louis Formation oolitic strata. (B–E) Thin-section photomicrographs of thesamples of Pennsylvanian (B, C) and Mississippian (D, E) age. These data show that samples of very distinct pore types and connectivitycan have similar NMR characters. k = permeability.


Figu

re10

.Thethree-dimensionalscatterplotsillu

stratingsomerelations

amongporeattributes(x,y,andza

xes)andperm

eability(k)(colorscale)foreach

rocksamplegroup.(A)In

Pleisto

cene

samples,porecomplexity,poresize,andintergranularporosity

aremostcloselyrelatedtok.Multiplelinearregressionbetweenthesethreeporeattributesand

kexhibitsa

coefficientofdeterm

ination(R

2 )of0.90.(B)

InthePennsylva

nian

subset,nuclearmagnetic

resonance(NMR)

porosity,porecircularity,andporecomplexity

estim

atekmostclosely.

MultiplelinearregressionrevealsanR2

of0.84.(C)

Helium(He)porosity,poresize,andlacunarity(atm

inimum

boxsize)aremostcloselyrelatedtokinMississippian

samples;m

ultiple

linearregressio

nyields

anR2

of0.88.C

ollectively,theserelations

suggestthatthe

pore

attributes

mostcloselyrelatedto

kvary

amonggroups.D

OMSize

=dominantp

ore

size;

IG=intergranular;PoA=perim

eter

over

area.

GOODNER ET AL. 1519

Figu

re11

.Thethree-dimensio

nalscatterplotsandmultivariate

linearregressio

ncorrelations

illustratingrelations

amongrock

fabricmetrics(independentvariables)andper-

meability(k)(dependentvariable)am

ongsamplegroups.Inthetablesbeloweach

plot,the

metric

ofdepositionalfabric

mostcloselycorrelated

tokislistedinthetoprow,along

with

thecoefficientofdeterm

ination(R

2 )betweenthatvariableandk.Themetricso

fdepositionalfabric(determined

byaste

pwise

regressio

nofallpossiblecombinations)m

ostinfluential

onkpredictionareinclu

dedsuccessivelyintheregressio

n,as

notedby

the“+

(variable)”insuccessiverows.(A)G

rainsize,sorting,and

ooidabundanceexhibita

positive

correlation

with

kinPleisto

cene

samples.(B)

Sorting

andooidabundancedisplayapositive

correlationwith

kof

Pennsylva

nian

samples.(C)

Sorting

andooidabundanceinclu

deapositive

correlationwith

kinMississippian

samples.Thesedatarevealthatvarieddepositionalfabricsareassociatedwith

distinctk,although

thesedimentologicm

etricsm

ostcloselyrelatedtok

change

amonggroups.C

OPL

=compactionporosityloss.


(Figure 12A); higher ooid abundance and bettersorting result in lower lacunarity or more evenly dis-tributed pore networks. Such relations are intuitive forsamples both with interparticle pores and moldicpores. These relations can be extended to permeabilityas well. A plot of lacunarity, pore compactness, andk illustrates that samples with compact and evenlydistributed pores have high k (Figure 12B). Thesefindings indicate a linkage of depositional fabric topore attributes, as well as pore attributes to perme-ability across several diagenetic scenarios.

DISCUSSION

Oolitic grainstones have excellent reservoir potentialat the time of deposition; however, as diagenesisensues, pore structure and connectivity can vary widely(Hollis et al., 2017). To address this variability, thisstudy examines oolitic samples frommultiple geologicages that represent a range of diagenetic scenarios(e.g., deposition, early lithification, and two distinctlate diagenetic pathways related to original ooidmineralogy). In doing so, it tests the hypotheses thatvaried depositional fabrics correlate to changes inpore attributes, and those variations in pore attri-butes control differences in permeability.

Although the absolute magnitude of influence ofspecific sedimentologic attributes (e.g., grain size,sorting, or type) changes among sample groups,these measures exhibit statistically significant rela-tionships with the size, shape, spatial distribution,and abundance of pores in all groups (Figure 8). InHolocene examples, distinctions in depositional fab-ric correspond to changes in pore-size distributions,revealing that depositional fabrics control initial porenetworks. These depositional fabrics and associatedpore networks are the framework for subsequentmodification via diagenesis.

In the early stages of diagenesis, depositional fabricretains an imprint on pore attributes, but the influenceof diagenesis is also evident. For example, T2 curves ofPleistocene samples include bimodal distributions,reflecting partial ooid dissolution, but the mode ofmacropore sizes also correlates to metrics of de-positional fabric (R2 = 0.63). These data quantifythe qualitative observation that the sizes and typesof grains impact the size and shape of pores be-tween those grains (Figure 2).

Pennsylvanian samples experienced extensivediagenetic modification, in many cases resulting inan almost complete inversion of the rock matrix andpore network. Yet, depositional fabrics display sta-tistical correlations with pore size, complexity, andlacunarity, probably because many pores simply areformer grains. Perhaps surprisingly, because they arearguably the most diagenetically altered sample group,accounting for diagenesis (e.g., cement abundance andCOPL) boosts R2 values less in Pennsylvanian samplesthan in other sample groups. One possible reason whydiagenesis (asmeasured here) has a limited influence onpore attributes is that the intergranular space in most ofthe Pennsylvanian samples is filled almost entirely withcement (Figure 2B; average = 93%). As such, thesample set does not provide much variability, suchas differences that could drive statistical distinctionsin pore attributes. Alternatively, the Pennsylvaniansamples noted herein show relatively limited com-paction and only 10.4%COPL on average (Figure 2B).Thus, it is not surprising that compaction (as mea-sured here) does not have a marked statistical in-fluence on the prediction of pore attributes orpermeability. Nonetheless, other studies have docu-mented the effect of compaction and crushedmolds inmarkedly enhancing permeability (e.g., Byrnes et al.,2003; Poteet, 2007). Perhaps using different metricsor a broader range of samples would reveal moresubtle associations.

Because they are dominated by well-connectedinterparticle pores rather than isolated moldic pores,Mississippian samples represent a rock type that con-trasts markedly with Pennsylvanian oomoldic samples.Similar to Holocene examples, the sizes and shapesof grains have a direct impact on the attributes ofintergranular pores. Thus, despite considerable com-paction and cementation, metrics of depositionalfabric display statistically significant correlations topore attributes describing pore size, complexity, andlacunarity.

These results are consistent with numerous studieson siliciclastic and carbonate sediment that illustratehow depositional fabrics can control original pore net-works (Krumbein and Monk, 1942; Beard and Weyl,1973; Enos and Sawatsky, 1981; Sprunt et al., 1993).For example, Krumbein and Monk (1942) and Spruntet al. (1993) demonstrated that permeability ofunconsolidated siliciclastic sand could be estimatedreliably using grain size and sorting. Similarly, Enos

GOODNER ET AL. 1521

Figu

re12

.Illu

strative

thin-section

photom

icrographs(A–C)and

three-dimensional(3-D)scatterplots

(D–E)illu

strating

relations

among

depositionalfabric,

pores,

and

porosity–perm

eability(k)acrossthe

samplesets(age

indicatedby

color).(A)

ModeratelysortedPennsylvanian

samplewith

moderateooidabundanceinclu

desisolatedporesand

lowk

(0.72md).(B)

Well-sortedPennsylvanian

rockwith

relativelyhigh

ooidabundancecontains

lessisolatedporesand

moderatek(145

md).(C)

Well-sortedPleisto

cene

samplewith

highest

ooidabundanceinclu

desevenlydistributed

poresand

exhibitshighestk

ofallthree

samples(12.4d).(D)

The3-Dcrossplotillustratingthatwell-sortedsedimentw

ithhigh

ooidabundance

(percent)exhibits

lowlacunarity(i.e.,evenlydistributed

porenetworks).(E)The

3-Dcrossplotshowingthatsedimentw

ithlowlacunarityandcompactporesh

avehigh

k.Theseresults

illustratevarieddepositionalfabricsareassociatedwith

distinctp

oreattributes,which

areinturn

relatedto

changesink.Collectively,these

relations

suggestthatd

epositionalfabric

influences

pore

networks

andpetro

physicalparam

etersacrossdiageneticscenarios.


and Sawatsky (1981) demonstrated that depositionalporosity and permeability of carbonate sediment varywith Dunham (1962) textural classification and grain-size distribution.

Similarly, even with a complete porosity inver-sion, in which pores becomematrix and grains becomepores, sedimentary attributes can markedly influencepore attributes at a reservoir scale. For example, Byrneset al. (2003) recognized multiple shallowing-upwardcycles in a Pennsylvanian oomoldic reservoir in theHall–Gurney field of central Kansas. These cyclesinclude an upward increase in grain size, sorting, andooid abundance and are accompanied by an upwardincrease in oomold pore size and total porosity. Sim-ilarly, examining the same reservoir of the Hall–Gurney field as Byrnes et al. (2003), Watney et al.(2006) demonstrated grain-size distribution and grain-type trends paralleled by changes in pore type. Theydocumented an upward increase in grain size, sorting,and ooid abundance that corresponded to increasedabundance of oomoldic pores. Collectively, the resultsdocument that trends between depositional fabric andpore attributes can persevere across a range of diage-netic scenarios, although their absolute values do vary.

An additional goal of this study is to understandwhich pore attributes control permeability. Pore-throat–size distributions have been cited as a primary controlon permeability (H. D. Winland, unpublished results;Pittman, 1992; Sigal, 2002). Typically, pore throats arecharacterized via mercury injection–capillary pres-sure experiments, which can be expensive and arelimited to laboratory measurements of cored sam-ples. In efforts to conserve cost and time, numerousmethods more readily applied can estimate perme-ability. The NMR method, a relatively cheap andfast, noninvasive technique that can be undertakenusing downhole logs in the absence of core, has beenused to estimate permeability by several models (mostnotably, SDR of Kenyon et al., 1988; Coates of Coateset al., 1999). Previous research on carbonate porenetworks has even suggested that pore-size distribu-tion controls permeability (Lucia, 1983, 1995,1999; Coates et al., 1999; Jennings and Lucia, 2001;Weger et al., 2009; Smith and Hamilton, 2014). Inthis context, the comparison of NMR T2 curves andF–k data provides an interesting perspective. Fourillustrative T2 curves (from samples of comparableporosity) (Figure 9) are nearly identical despite per-meabilities that span almost four orders of magnitude.

These observations suggest that pore-size distributionsare not the sole control on F–k.

These data reveal that pore-size distribution alonedoes not control permeability; rather, it is but one ofseveral factors that impact permeability (Figure 10).Among sample groups, fundamental differences in thegeologic nature of pore networks (Figures 1, 4, 5;Table 1) are reflected in the variability in pore at-tributes that most directly influence k.

An example of geologic influences is provided bythe Pleistocene samples, that is, rocks impacted onlyby early diagenesis. As such, the possible effects ofdiagenesis are developed incompletely and, in somecases, are distributed unevenly. For example, cemen-tation is uneven between laminations (Figure 1C), andooid dissolution is incomplete (bluish hue of ooids)(Figure 1D). These geologic controls are reflected inthe high total porosity (average 34.6%) and the mi-croporosity that accounts for more than half of thetotal pore volume in some samples (Figure 3E). Fol-lowing Keith and Pittman (1982), Cantrell andHagerty(1999), Byrnes et al. (2003), and Cruz et al. (2006),this microporosity may be isolated or poorly connectedand thus have a negligible contribution to fluid flow. Asa result, total porosity is not a significant predictor ofpermeability. Instead, pore complexity (PoA), pore size(DOMSize), and intergranular porosity are the stron-gest permeability predictors (Figure 10A).

In contrast, diagenesis is more advanced in Penn-sylvanian samples. A considerable part of interparticleporosity is occluded by cement, and many ooids aredissolved completely (e.g., Figure 1F), although neitherprocess is universal in all samples (e.g., remnant inter-particle porosity, minor grain preservation) (Figure1E). These geologic effects result in pore networkscharacterized by (1) a volumetric contribution frommicroporosity less than that in Pleistocene samples(Figure 3) and (2) large, isolated pores representingoomolds (Figures 1E, F; 4; 5). Because microporosityis not as prevalent, the correlation between totalporosity and permeability is clearer, showing a sig-nificant, positive statistical correlation (R2 = 0.67;P = 0.0001). Qualitatively, pore size does not ap-pear to control pore-throat size (Figure 1E, F), con-trasting with Pleistocene and Mississippian samples inwhich larger pores are associated with larger throats(Figure 1C, D, G, H). Assuming pore-throat sizescontrol permeability, it is no surprise that the poresize of Pennsylvanian samples does not show a

GOODNER ET AL. 1523

significant statistical relationship with permeabil-ity (R2 = 0.03, P = 0.58). In contrast, lacunarity has asignificant correlation with permeability (R2 = 0.59,P = 0.002), suggesting that pore spatial distributionmarkedly influences permeability but just a bit lessthan total porosity in Pennsylvanian samples.

Mississippian samples have been subjected toadvanced diagenetic modifications, although theeffects are distinct from Pennsylvanian strata. Forexample, on the whole, Mississippian samples displayfewer dissolution features (e.g., moldic pores) (relatedto original calcite mineralogy) and lower cementabundance but commonly include well-developedcompaction features (Figures 1G, H; 2B). As a result,many Mississippian samples include lower porosityand pores that are smaller but more evenly distrib-uted than those of Pennsylvanian samples (Figures4–6). Despite these geologic distinctions, as in Penn-sylvanian samples, the porosity of Mississippian sam-ples displays the strongest relationshipwith permeability(R2 = 0.64). However, in contrast to trends of Penn-sylvanian samples, pore size displays a significant positiverelationship with permeability (R2 = 0.60, P = 0.0004).Similar to the trends in Pleistocene samples, qualitativeobservations suggest that Mississippian samples withlarger pores include larger pore throats (e.g., Figure1G, H).

The preceding results are consistent with hy-potheses that varied depositional fabrics correlateto changes in pore attributes, and pore attributescontrol permeability. If these concepts are valid,links between depositional fabric and permeabilityshould be evident. Although correlations betweendepositional fabric and permeability are lower thanthose linking pore attributes and k (Figures 10, 11),sedimentologic attributes display statistically significantcorrelations with permeability in all three rock samplegroups (Appendix). Furthermore, results are consistentwith the notions articulated by Lucia (1983, 1995,1999), Jennings and Lucia (2001), and Jones andXiao (2006), which suggested particle (i.e., grain)size is a primary control on F–k relationships, andthe shape and sorting of those particles is also im-portant. This general concept that F–k are related todepositional processes is broadly (albeit implicitly)applied in constructing facies-based geological modelsthat use distinct F–k distributions for each facies (e.g.,Cavallo and Smosna, 1997; Palermo et al., 2012; Rushand Rankey, 2017).

The results herein quantify how specific pa-rameters of depositional fabric combine to influencepermeability for different diagenetic scenarios. Thecorrelations between depositional fabric and per-meability for each sample group (R2 = 0.73, 0.50, and0.68 for Figure 10A–C, respectively) are stronger thanthose between diagenetic attributes (COPL, percentof cement) and permeability (R2 = 0.61, 0.31, and0.41, respectively). Collectively, these results suggestthat within each sample group, depositional fabric is amore direct control on pore attributes and perme-ability than diagenetic attributes, at least for thosemetrics considered in this study (cf., Lucia, 1983;Qiao et al., 2016; Hazard et al., 2017).

These findings do not imply that diagenesis is nota factor in determining rock fabric–permeability re-lationships. Diagenesis clearly impacted these samples,which include over-compacted and highly cementedrocks, as well as moldic pores (Figures 1, 2). Rather,the present-day pore network is a complex functionof both the initial sedimentologic character and thechanges it underwent (i.e., nature and nurture). Forexample, sedimentology, which defines the deposi-tional pore network, can influence subsequent modi-fications and, as a result, can control the trends orvariability of pores andF–kwithin a succession (Figures8, 11, 12).However, as each sample group (representingdistinct diagenetic scenarios) has a unique combinationof pore size, shape, spatial distribution, abundance,and connectivity, diagenesis may define the absolutevalues of pore attributes and petrophysical parameters(Figures 3–6). This variability in diagenesis that affectsdifferent absolute values in F–kmay also explain whycorrelations (statistically significant within groups) lacksignificant correlations across groups.

IMPLICATIONS

Many studies have illustrated how sediment char-acter varies in Holocene oolitic tidal sand shoals(Newell et al., 1960; Ball, 1967; Hine, 1977; Harris,1979; Rankey and Reeder, 2011; Sparks and Rankey,2013; Rush and Rankey, 2017). In these shoals, sys-tematic changes in sediment granulometry and graintype occur from bar crests to bar flanks and amongdifferent geomorphic bar types (e.g., linear, parabolic,and shoulder), which also include distinct internalarchitecture and sedimentologic character (Sparks


and Rankey, 2013; Rush and Rankey, 2017). Assuch, Holocene shoals appear to include system-atic stratigraphic (vertical and lateral) changes ingrain size, sorting, and type; these types of trendscan persist as sediment becomes rock (Cantrell andWalker, 1985; Evans and Ginsburg 1987; Lindsayet al., 2006; Hazard et al., 2017). These types ofsedimentological changes have the potential to influ-ence a reservoir’s pore network in at least two ways.

First, sediment character defines the depositionalpore network, which is the framework for subse-quent modifications. This concept is consistent withthe data of this study (Figures 1A, B; 7) and is welldocumented in the literature (Krumbein and Monk,1942; Beard andWeyl, 1973; Enos and Sawatsky, 1981;Sprunt et al., 1993).

Second, sedimentologic differences can influencediagenetic processes that modify depositional pores.On a shoal scale, for example, Cantrell and Walker(1985) described anOrdovician oolite fromTennesseein which each shoal subenvironment was associatedwith distinct paragenetic sequences. Mobile shoal andtidal channel facies experienced extensive early marinecementation, whereas bankward, stabilized en-vironments underwent limited early cementationand retained primary porosity into later diagenesis.

Similarly, Keith and Pittman (1982) documentedtrends within a Cretaceous shoal complex of theRodessa Limestone in eastern Texas. This study in-terpreted a skeletal-rich subfacies on the flanks of theshoal to have been exposed to active circulation ofmarinewaters, facilitating extensive cementation and porosityreduction. In contrast, the ooid-rich subfacies in the shoalcrest was exposed to stagnant, near-equilibrium porefluids and had less cement, thus preserving porosity.

At a finer scale, Halley and Evans (1983) andEvans and Ginsburg (1987) highlighted fabric-selectivediagenesis in the Pleistocene Miami Limestone. In thatunit, depositional fabrics within individual cross-bed laminae control early cementation and poredevelopment; coarser-grained laminae commonlyshow less abundant cement than finer-grained lami-nae. This dynamic was interpreted to result from finer-grained layers that preferentially held water bycapillary forces and included more possible cementnucleation sites. Their observations are consistentwith data from laminated Pleistocene samples in thisstudy, in which laminae with contrasting grain sizes

commonly show differences in cementation, withthe finer-grained lamina including more abundantcement and lower porosity (e.g., Figure 1C).Quantitatively, grain size in Pleistocene and Missis-sippian samples is inversely related to cement abun-dance (R2 = 0.40 and 0.22, respectively); these are notstrong correlations, but they are both statistically sig-nificant (P = 0.005 and 0.05, respectively). Onepossible reason these correlations are not strongerstems from the metrics used in the correlations. In thisstudy, grain size is represented by the mean of asample’s grain-size distribution; however, meangrain size does not capture the bimodal distribution ofgrain sizes in a laminated sample. If grain size andcement abundance were compared within individuallaminae, correlations likely would be stronger. Re-gardless, these examples at multiple scales dem-onstrate how depositional fabric (and hence, F–kdistribution) influences early fluid flow and cementnucleation sites, which in turn, can control diagenesis.

Because initial sediment character controls de-positional pores and influences subsequent modifi-cations, systematic stratigraphic changes in grain size,sorting, and type have the ultimate potential to influ-ence petrophysical properties within oolitic reservoirs(cf., Jennings and Lucia, 2001; Rankey et al., 2018).

For example, Cantrell and Walker (1985) docu-mented a stratigraphic succession interpreted to rep-resent mobile shoal settings of coarse to very coarse,very well-sorted sediment with high ooid abundance(e.g., high depositionalF–k), whereas strata interpretedas tidal channel deposits are poorly sorted and includediverse grain types. The channel deposits (e.g., lowerdepositionalF–k) display less earlymarine cementationand preserve interparticle porosity. These observationsare consistent with results of this study in that sedi-mentologically distinct samples display differencesin diagenetic effects, pore attributes, and petro-physical parameters.

In another example, Cavallo and Smosna (1997)demonstrated how porosity trends mimic depositionalpatterns within a Mississippian oolitic shoal system ofthe Appalachian Basin. Environments interpretedas shoal crests are coarse, well-sorted sediment withhigh ooid abundance and relatively high porosity. Incontrast, shoal flanks include less porous inter-bedded packstone and grainstone of finer grain size,poorer sorting, and lower ooid abundance, andchannels include nonporous bioturbated packstone.

GOODNER ET AL. 1525

The study documented that grain size, sorting, andooid abundance increase toward the bar center andupward within the shoal, parallel with trends inporosity. These conclusions are consistent with theobservations of this study, which suggest that increasedgrain size, sorting, and ooid abundance result in morefavorable reservoir character.

In a third example, Esrafili-Dizaji and Rahimpour-Bonab (2014) documented detailed sedimentologicpatterns and associated petrophysical responses fromthe Permian–Triassic Dalan and Kangan Formationsof Iran (Khuff equivalents). These strata include anupward increase in grain size, sorting, and ooid abun-dance within several shallowing-upward oolitic suc-cessions. These sedimentologic changes are associatedwith concomitant upward increases in F–k withineach succession. These patterns are consistent withthe results of this study: the samples that show increasedsorting and ooid abundance display favorable pore at-tributes (e.g., compact, evenly distributed pores) andresultant higher permeability (cf., Figure 12).

Certainly, there are situations in which relationsbetween depositional fabric and reservoir characterare not consistent within a reservoir interval. For ex-ample, Wagner and Matthews (1982) interpreted po-rosity distribution within the Jurassic SmackoverFormation of Arkansas to be unrelated to grain size,sorting, or type because the same depositional facies(e.g., oolitic grainstone) includes both reservoir andnonreservoir quality rock. Instead, they invoked adiagenetic control on petrophysical parameters:sediment that underwent mineral stabilization priorto burial resisted compaction and preserved deposi-tional porosity. In contrast, sediment that had notstabilized mineralogically prior to burial experiencedextensive compaction and porosity reduction. None-theless, in this field, it remains that well-connectedinterparticle porosity in well-sorted ooid grain-stone that has the highest permeability and lowerenergy packstone (shoal flank facies) includes lessfavorable F–k because of cementation and the mudmatrix (Bliefnick et al., 1991).

The impacts of diagenesis can have other man-ifestations. For example, Heydari (2003) documentsan example from the Smackover Formation of southernMississippi in which burial diagenesis destroyed grain-stone porosity (F = 0%), eliminating any potential in-fluence of depositional fabric (or early diagenesis forthat matter) on reservoir character. Alternatively, a

regional study of the Smackover by Kopaska-Merkelet al. (1994) illustrated the importance of dolomitiza-tion inmany reservoirs. Although porosity was interpretedto have not changed markedly from depositional(interparticle) porosity in many intervals, perme-ability was influenced strongly by dolomite crystalmorphology and size that controlled pore-throat size.

CONCLUSIONS

This study analyzes oolitic grainstones of four geo-logic ages that include similar ranges of grain size,sorting, and type but represent distinct diageneticscenarios (e.g., deposition, early diagenesis, distinct[aragonite vs. calcite precursor] late diageneticpathways). These diagenetic distinctions resultin each group including a unique combination of poresize, shape, spatial distribution, and connectivity.

Within each age group, changes in pore attri-butes and permeability correlate more closely tometrics of depositional fabric than to diageneticattributes. The details of correlations (i.e., the strengthof correlations and the specific parameters that aremost closely related to pore attributes) vary amongage groups, however, as do the absolute values ofF–k. At least some of these differences are relatedto initial ooid mineralogy, through its influence onpore type and pore spatial distribution, and pore-throat sizes as diagenesis proceeds (e.g., more iso-lated moldic pores vs. better connected interparticlepores). These factors can lead to variable impactsof the same diagenetic process; for example, com-paction will reduce F–k in calcitic–ooid successionswith interparticle porosity, but it can markedly enhancepermeability in aragonite–ooid (moldic) successions.Thus, distinct types of nurture and distinct diageneticpathwaysmay hold for sedimentologically distinct rocksand decrease trends across ages.

Collectively, these results are interpreted to sug-gest not only that sedimentology controls the trends orvariability within a succession but also that diagenesismay define the absolute values of pore attributes andpetrophysical parameters among successions. Theimplication of these findings is that petrophysicaltrends within oolitic reservoirs are driven largelyby differences established at the time of deposi-tion, and these are factors that may be predictablewithin a stratigraphic framework.


APPENDIX

REFERENCES CITED

Abegg, F. E., 1991, Sedimentology and lithostratigraphy ofthe Upper Mississippian Ste. Genevieve and St. Louis Lime-stones, southwestern Kansas: Lawrence, Kansas, KansasGeological Survey Open-File Report 91-52, p. 1–33.

Allain, C., and M. Cloitre, 1991, Characterizing the lacu-narity of random and deterministic fractal sets: PhysicalReview A., v. 44, no. 6, p. 3552–3558, doi:10.1103/PhysRevA.44.3552.

Al-Marzouqi, M. I., S. Budebes, E. Sultan, I. Bush, R. Griffiths,K. B. M. Gzara, R. Ramamoorthy, et al., 2010, Resolvingcarbonate complexity: Oilfield Review, v. 22, no. 2, p. 40–55.

Anselmetti, F. S., S. M. Luthi, and G. P. Eberli, 1998,Quantitative characterization of carbonate pore sys-tems by digital image analysis: AAPG Bulletin, v. 82,no. 10, p. 1815–1836.

Ball, M. M., 1967, Carbonate sand bodies of Florida and theBahamas: Journal of Sedimentary Petrology, v. 37, no. 2,p. 556–591.

Beard, D. C., and P. K. Weyl, 1973, Influence of texture onporosity and permeability of unconsolidated sand: AAPGBulletin, v. 57, no. 2, p. 349–369.

Bliefnick, D. M., and J. G. Kaldi, 1996, Pore geometry: controlon reservoir properties, Walker Creek Field, Columbia

and Lafayette Counties, Arkansas: AAPG Bulletin, v. 80,no. 7, p. 1027–1044.

Bliefnick, D. M., J. G. Kaldi, S. K. Bissmeyer, and T. T. Dang,1991, Multidisciplinary reservoir description, WalkerCreek Field, Columbia and Lafayette Counties, Ar-kansas, in R. Sneider, W. Massell, R. Mathis, D. Loren,and P. Wichmann, eds., The integration of geology,geophysics, petrophysics and petroleum engineering inreservoir delineation, description and management:AAPG Special Publication 26, p. 301–325.

Brownstein, K. R., and C. E. Tarr, 1979, Importance of clas-sical diffusion in NMR studies of water in biological cells:Physical Review A, v. 19, no. 6, p. 2446–2453, doi:10.1103/PhysRevA.19.2446.

Budd, D. A., 2002, The relative roles of compaction and earlycementation in the destruction of permeability in car-bonate grainstones: A case study from the Paleogene ofwest-central Florida, U.S.A.: Journal of Sedimentary Re-search, v. 72, no. 1, p. 116–128, doi:10.1306/061501720116.

Byrnes, A. P., E. K. Franseen,W. L.Watney, andM. K. Dubois,2003, The role of moldic porosity in Paleozoic Kansasreservoirs and the association of original deposi-tional facies and early diagenesis with reservoir prop-erties: Lawrence, Kansas, Kansas Geological SurveyOpen-File Report 2003-32, accessed February 6, 2020,

Variables

Pleistocene Pennsylvanian Mississippian

R2 with F R2 with k R2 with F R2 with k R2 with F R2 with k

Parameter of depositional fabricGrain size 0.31 0.49 0.17 0.01 0.12 0.01Sorting 0.01 0.08 0.62 0.32 0.35 0.22Ooid abundance, % 0.15 0.03 0.63 0.27 0.19 0.33Skeletal abundance, % 0.28 0.05 0.26 0.00 0.09 0.03% cement of IGV 0.04 0.61 0.11 0.24 0.10 0.30COPL 0.03 0.00 0.42 0.14 0.04 0.00

Pore attributeDOMSize 0.38 0.02 0.60PoA 0.82 0.12 0.22Gamma 0.18 0.02 0.33AR 0.03 0.01 0.03Circularity 0.31 0.53 0.30Roundness 0.01 0.00 0.04Compactness 0.58 0.32 0.30Lacunarity, m 0.00 0.59 0.39Lacunarity, minimum box size 0.02 0.50 0.49Helium porosity 0.00 0.33 0.64NMR porosity 0.00 0.67 0.50NMR macroporosity 0.44 0.64 0.46T2 mode 0.43 0.03 0.38Intergranular porosity 0.59 0.26 0.08

Statistically significant correlations (P £ 0.05) are indicated in bold.Abbreviations: F = porosity; AR = aspect ratio; COPL = compaction porosity loss; DOMSize = dominant pore size; IGV = intergranular volume; k = permeability;

NMR = nuclear magnetic resonance; PoA = perimeter over area; R2 = coefficient of determination; T2 = transverse relaxation time.

GOODNER ET AL. 1527

http://dx.doi.org/10.1103/PhysRevA.44.3552



http://dx.doi.org/10.1306/061501720116

http://www.kgs.ku.edu/PRS/publication/2003/ofr2003-32/P1-02.html.

Cantrell, D. L., and R. M. Hagerty, 1999, Microporosity inArab Formation carbonates, Saudi Arabia: AAPG Searchand Discovery article 30008, accessed February 5, 2020,http://www.searchanddiscovery.com/pdfz/documents/cantrell/images/Cantrell.pdf.html.

Cantrell, D. L., and K. R. Walker, 1985, Depositional anddiagenetic patterns, ancient oolite Middle Ordovician,eastern Tennessee: Journal of Sedimentary Petrology, v. 55,no. 4, p. 518–531.

Cavallo, L. J., and R. Smosna, 1997, Predicting porosity dis-tribution within oolitic tidal bars, in J. A. Kupecz, J. Gluyas,and S. Bloch, eds., Reservoir quality prediction in sandstonesand carbonates: AAPG Memoir 69, p. 211–229.

Choquette, P. W., and L. C. Pray, 1970, Geologic nomen-clature and classification of porosity in sedimentary car-bonates: AAPG Bulletin, v. 54, no. 2, p. 207–250.

Coates, G. R., L. Xiao, and M. G. Prammer, 1999, NMRlogging principles and applications: Houston, Texas, Halli-burton Energy Services, 234 p.

Cruz, F. E., G. P. Eberli, and A. P. Byrnes, 2006, Petrophysicalheterogeneity of a Pleistocene oolitic shoal: Lessons for an-cient reservoirs, in R. M. Slatt, N. C. Rosen, M. Bowman,J. Castagna, T. Good, R. Loucks, R. Latimer, M. Scheihing,and R. Smith, eds., Reservoir characterization: Integratingtechnology and business practices: 26th Annual GCSSEPMFoundation Bob F. Perkins Research Conference, Houston,Texas, December 3–6, 2006, p. 813–848.

Doveton, J., and W. L. Watney, 2014, Textural and pore sizeanalysis of carbonates from integrated core and nuclearmagnetic resonance logging: An Arbuckle study: Inter-pretation, v. 3, no. 1, p. SA77–SA89, doi:10.1190/INT-2014-0050.1.

Dunham, R. J., 1962, Classification of carbonate rocks ac-cording to depositional textures, in W. E. Ham, ed., Clas-sification of carbonate rocks—A symposium: AAPGMemoir1, p. 108–121.

Ehrlich, R., S. K. Kennedy, S. J. Crabtree, and R. L. Cannon,1984, Petrographic image analysis, I. Analysis of reservoirpore complexes: Journal of Sedimentary Petrology, v. 54,no. 4, p. 1365–1378.

Enos, P., and L. H. Sawatsky, 1981, Pore networks in Holo-cene carbonate sediments: Journal of Sedimentary Pe-trology, v. 51, p. 961–985.

Esrafili-Dizaji, B., and H. Rahimpour-Bonab, 2014,Generation and evolution of oolitic shoal reservoirs in thePermo-Triassic carbonates in the South Pars Field, Iran:Facies, v. 60, no. 4, p. 921–940, doi:10.1007/s10347-014-0414-4.

Evans, C. C., and R. N. Ginsburg, 1987, Fabric-selective dia-genesis in the late Pleistocene Miami Limestone: Journalof Sedimentary Petrology, v. 57, p. 311–318.

Flugel, E., 2010, Microfacies of carbonate rocks: Analysis,interpretation, and application, 2nd ed.: Berlin, Springer-Verlag, 984 p., doi:10.1007/978-3-642-03796-2.

Folk, R. L., and W. C. Ward, 1957, Brazos River bar [Texas]:A study in the significance of grain size parameters: Journal

of Sedimentary Petrology, v. 27, no. 1, p. 3–26, doi:10.1306/74D70646-2B21-11D7-8648000102C1865D.

Fortey, N. J., 1995, Image analysis in mineralogy and pe-trology:MineralogicalMagazine, v. 59, no. 395, p. 177–178,doi:10.1180/minmag.1995.059.395.01.

French, J. A., and W. L. Watney, 1993, Stratigraphy anddepositional setting of the lower Missourian (Pennsyl-vanian) Bethany Falls and Mound Valley limestones,analogues for age-equivalent ooid-grainstone reservoirs,Kansas: Lawrence, Kansas, Kansas Geological SurveyBulletin 235, p. 27–39.

Godefroy, S., M. Fleury, F. Deflandre, and J.-P. Korb, 2001,Temperature effect on NMR surface relaxation: SPEAnnual Technical Conference and Exhibition, NewOrleans, Louisiana, September 30–October 3, 2001,SPE-71700-MS, 13 p., doi:10.2118/71700-MS.

Halley, R. B., and C. C. Evans, 1983, The Miami Limestone:A guide to selected outcrops and their interpretation:Miami, Florida, Miami Geological Society, 67 p.

Harris, P. M., 1979, Facies anatomy and diagenesis of a Ba-hamian ooid shoal: Miami, Florida, University of Miami,Sedimenta 7, 163 p.

Hazard, C. S., S. M. Ritter, J. H. McBride, D. G. Tingey, andR. W. Keach III, 2017, Ground-penetrating-radar char-acterization and porosity evolution of an upper Pleisto-cene oolite-capped depositional cycle, Red Bays, northwestAndros Island, Great Bahama Bank: Journal of Sedimen-tary Research, v. 87, no. 5, p. 523–545, doi:10.2110/jsr.2017.9.

Heydari, E., 2003, Meteoric versus burial control on porosityevolution of the Smackover Formation: AAPG Bulletin,v. 87, no. 11, p. 1779–1797, doi:10.1306/07070302009.

Hine, A. C., 1977, Lily Bank, Bahamas: History of an activeoolite sand shoal: Journal of Sedimentary Petrology, v. 47,no. 4, p. 1554–1581.

Hollis, C., D. A. Lawrence, M. Deville de Periere, and F. AlDarmaki, 2017, Controls on porosity preservation withina Jurassic oolitic reservoir complex, UAE: Marine andPetroleum Geology, v. 88, p. 888–906, doi:10.1016/j.marpetgeo.2017.09.015.

Huber, M. E., 2016, Relationships between foraminifera andgeomorphology: Holocene, Crooked-Acklins Platform,southern Bahamas, Master’s thesis, University of Kan-sas, Lawrence, Kansas, 63 p.

Jennings, J. W., and F. J. Lucia, 2001, Predicting permeabilityfrom well logs in carbonates with a link to geology forinterwell permeability mapping: SPE Annual TechnicalConference and Exhibition, New Orleans, Louisiana,September 30–October 3, 2001, SPE-71336-MS, 16p., doi:10.2118/71336-MS.

Jones, G. D., and Y. Xiao, 2006, Geothermal convection inthe Tengiz carbonate platform, Kazakhstan: Reactivetransport models of diagenesis and reservoir quality: AAPGBulletin, v. 90, no. 8, p. 1251–1272,doi:10.1306/04030605194.

Karperian, A., 2015, FracLac for ImageJ, accessed April12, 2017, http://rsb.info.nih.gov/ij/plugins/fraclac/FLHelp/Introduction.htm.

Keith, B. D., and E. D. Pittman, 1982, Bimodal porosity inoolitic reservoir—Effect on productivity and log response,


http://www.kgs.ku.edu/PRS/publication/2003/ofr2003-32/P1-02.html

http://www.kgs.ku.edu/PRS/publication/2003/ofr2003-32/P1-02.html

http://www.searchanddiscovery.com/pdfz/documents/cantrell/images/Cantrell.pdf.html

http://www.searchanddiscovery.com/pdfz/documents/cantrell/images/Cantrell.pdf.html

http://dx.doi.org/10.1190/INT-2014-0050.1

http://dx.doi.org/10.1190/INT-2014-0050.1

http://dx.doi.org/10.1007/s10347-014-0414-4

http://dx.doi.org/10.1007/s10347-014-0414-4

http://dx.doi.org/10.1007/978-3-642-03796-2

http://dx.doi.org/10.1306/74D70646-2B21-11D7-8648000102C1865D

http://dx.doi.org/10.1180/minmag.1995.059.395.01

http://dx.doi.org/10.2118/71700-MS

http://dx.doi.org/10.2110/jsr.2017.9


http://dx.doi.org/10.1306/07070302009

http://dx.doi.org/10.1016/j.marpetgeo.2017.09.015


http://dx.doi.org/10.2118/71336-MS

http://dx.doi.org/10.1306/04030605194

http://rsb.info.nih.gov/ij/plugins/fraclac/FLHelp/Introduction.htm

http://rsb.info.nih.gov/ij/plugins/fraclac/FLHelp/Introduction.htm

Rodessa Limestone (Lower Cretaceous): East Texas Basin:AAPG Bulletin, v. 67, no. 9, p. 1391–1399.

Kenyon, W. E., P. I. Day, C. Straley, and J. F. Willemsen,1988, A three-part study of NMR longitudinal relaxationproperties of water-saturated sandstones: SPE FormationEvaluation, v. 3, no. 3, p. 622–636, doi:10.2118/15643-PA.

Kopaska-Merkel, D. C., S. D. Mann, and J. W. Schmoker,1994, Controls on reservoir development in a shelf car-bonate: Upper Jurassic Smackover Formation of Alaba-ma: AAPG Bulletin, v. 78, no. 6, p. 938–959.

Krumbein, W. C., 1939, Graphic presentation and statisticalanalyses of sedimentary data, in P. D. Trask, ed., Recentmarine sediments: Tulsa, Oklahoma, SEPM SpecialPublication 4, p. 558–591, doi:10.1306/SV10340C32.

Krumbein, W. C., and G. D. Monk, 1942, Permeability as afunction of size parameters of unconsolidated sands:Englewood, Colorado, Petroleum Technology, AmericanInstitute of Mining, Metallurgical, and Petroleum Engi-neers Technical Publication 1492, v. 5, p. 1–11.

Lindqvist, J. E., and U. Akesson, 2001, Image analysis appliedto engineering geology, a literature review: Bulletin ofEngineering Geology and the Environment, v. 60, no. 2,p. 117–122, doi:10.1007/s100640100106.

Lindsay, R. F., D. L. Cantrell, G. W. Hughes, T. H. Keith,H.W.Mueller III, and S. D. Russell, 2006, Ghawar Arab-D reservoir: Widespread porosity in shoaling-upwardcarbonate cycles, Saudi Arabia, in P. M. Harris andL. J. Weber, eds., Giant hydrocarbon reservoirs of theworld: From rocks to reservoir characterization andmodeling: AAPG Memoir 88, p. 97–137, doi:10.1306/1215875M88576.

Lønøy, A., 2006, Making sense of carbonate pore systems:AAPG Bulletin, v. 90, no. 9, p. 1381–1405, doi:10.1306/03130605104.

Lucia, F. J., 1983, Petrophysical parameters estimated fromvisual descriptions of carbonate rocks: A field classifica-tion of carbonate pore space: Journal of PetroleumTechnology, v. 216, p. 221–224.

Lucia, F. J., 1995, Rock-fabric/petrophysical classification ofcarbonate pore space for reservoir characterization:AAPG Bulletin, v. 79, no. 9, p. 1275–1300.

Lucia, F. J., 1999, Carbonate reservoir characterization: Berlin,Springer-Verlag, 226 p.

Lundegard, P. D., 1992, Sandstone porosity loss—A “big picture”view of the importance of compaction: Journal of Sed-imentary Petrology, v. 62, no. 2, p. 250–260, doi:10.1306/D42678D4-2B26-11D7-8648000102C1865D.

Ma, Y. S., X. Y. Cai, and P. R. Zhao, 2011, The research statusand advances in porosity evolution and diagenesis of deepcarbonate reservoir [in Chinese with English abstract]:Earth Science Frontiers, v. 18, no. 4, p. 181–192.

Melas, F. F., and G. M. Friedman, 1992, Petrophysical char-acteristics of the Jurassic Smackover Formation, Jay Field,ConecuhEmbayment,Alabama and Florida:AAPGBulletin,v. 76, no. 1, p. 81–100.

Melim, L. A., F. S. Anselmetti, and G. P. Eberli, 2001, Theimportance of pore type on permeability of Neogenecarbonates, Great Bahama Bank, in R. N. Ginsburg,ed., Subsurface geology of a prograding carbonateplatform margin, Great Bahama Bank: Results of the

Bahamas drilling project: Tulsa, Oklahoma, SEPMSpecial Publication 70, p. 217–238, doi:10.2110/pec.01.70.0217.

Merta, T., 1991, A new, universal method of thin-section – to –

sieve transformation of granulometric data: Acta GeologicaPolonica, v. 41, no. 1–2, p. 117–146.

Newell, N. D., E. G. Purdy, and J. Imbrie, 1960, Bahamianoolitic sand: Journal of Geology, v. 68, no. 5, p. 481–497,doi:10.1086/626683.

Palermo, D., T. Aigner, B. Seyfang, and S. Nardon, 2012,Reservoir properties and petrophysical modelling ofcarbonate sand bodies: Outcrop analogue study in anepicontinental basin (Triassic, Germany), in J. Garland,J. E. Neilson, S. E. Laubach, and K. J. Whidden, eds.,Advances in carbonate exploration and reservoir analysis:Geological Society, London, Special Publications 2012,v. 370, p. 111–138, doi:10.1144/SP370.6.

Parham, K. D., and P. G. Sutterlin, 1993, Ooid shoals of theMississippian St. Louis Formation, Gray County, Kansas, inC. W. Zuppann and B. Keith, eds., Mississippian oo-lites and modern analogs: AAPG Studies in Geology35, p. 185–198.

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

Plotnick, R. E., R. H. Gardner, W. Hargrove, K. Prestegaard,and M. Perlmutter, 1996, Lacunarity analysis: A generaltechnique for the analysis of spatial patterns: PhysicalReview. E, v. 53, no. 5, p. 5461–5468, doi:10.1103/PhysRevE.53.5461.

Plotnick, R. E., R. H. Gardner, and R. V. O’Neill, 1993,Lacunarity indexes as measures of landscape texture:Landscape Ecology, v. 8, no. 3, p. 201–211, doi:10.1007/BF00125351.

Poteet, J. E., 2007, Porosity and permeability evolution of theRaytown Limestone oolite, central Kansas, Master’sthesis, University of Kansas, Lawrence, Kansas, 200 p.

Qi, L. S., and T. R. Carr, 2005, Core description of the St.Louis Limestone, Big Bow and Sand Arroyo Creek fields,southwest Kansas: Lawrence, Kansas, Kansas GeologicalSurveyOpen-File Report 2005-16, accessed April 19, 2018,http://www.kgs.ku.edu/PRS/publication/2005/OFR05_16/index.html.

Qiao, Z., X. Janson, A. Shen, J. Zheng, H. Zeng, andX.Wang,2016, Lithofacies, architecture, and reservoir heteroge-neity of tidal-dominated platform marginal oolitic shoal:An analogue of oolitic reservoirs of Lower Triassic Feix-ianguan Formation, Sichuan Basin, SW China: Marineand Petroleum Geology, v. 76, p. 290–309, doi:10.1016/j.marpetgeo.2016.05.030.

Rankey, E. C., 2002, Spatial patterns of sediment accumu-lation on a Holocene carbonate tidal flat, northwest An-dros Island, Bahamas: Journal of Sedimentary Research,v. 72, no. 5, p. 591–601, doi:10.1306/020702720591.

Rankey, E. C., 2016, On facies belts and facies mosaics:Holocene isolated platforms, South China Sea: Sedimen-tology, v. 63, no. 7, p. 2190–2216, doi:10.1111/sed.12302.

GOODNER ET AL. 1529

http://dx.doi.org/10.2118/15643-PA

http://dx.doi.org/10.1306/SV10340C32

http://dx.doi.org/10.1007/s100640100106

http://dx.doi.org/10.1306/1215875M88576

http://dx.doi.org/10.1306/1215875M88576

http://dx.doi.org/10.1306/03130605104

http://dx.doi.org/10.1306/03130605104

http://dx.doi.org/10.1306/D42678D4-2B26-11D7-8648000102C1865D

http://dx.doi.org/10.1306/D42678D4-2B26-11D7-8648000102C1865D

http://dx.doi.org/10.2110/pec.01.70.0217

http://dx.doi.org/10.2110/pec.01.70.0217

http://dx.doi.org/10.1086/626683

http://dx.doi.org/10.1144/SP370.6

http://dx.doi.org/10.1103/PhysRevE.53.5461

http://dx.doi.org/10.1103/PhysRevE.53.5461

http://dx.doi.org/10.1007/BF00125351

http://dx.doi.org/10.1007/BF00125351

http://www.kgs.ku.edu/PRS/publication/2005/OFR05_16/index.html

http://www.kgs.ku.edu/PRS/publication/2005/OFR05_16/index.html



http://dx.doi.org/10.1306/020702720591

http://dx.doi.org/10.1111/sed.12302

Rankey, E. C., H. Goodner, and J. Doveton, 2018, Deposi-tional architecture and petrophysical variability of anoolitic tidal sand shoal: Pennsylvanian (Missourian),Kansas, U.S.A.: Journal of Sedimentary Research, v. 88,no. 9, p. 1114–1131, doi:10.2110/jsr.2018.57.

Rankey, E. C., and S. L. Reeder, 2010, Controls on platform-scale patterns of surface sediments, shallow Holoceneplatforms, Bahamas: Sedimentology, v. 57, no. 6, p. 1545–1565, doi:10.1111/j.1365-3091.2010.01155.x.

Rankey, E. C., and S. L. Reeder, 2011,Holocene oolitic marinesand complexes of the Bahamas: Journal of SedimentaryResearch, v. 81, no. 2, p. 97–117, doi:10.2110/jsr.2011.10.

Rankey, E. C., and S. L. Reeder, 2012, Tidal sands of the Ba-hamian archipelago, inR. A. Davis Jr. and R.W.Dalrymple,eds., Principles of tidal sedimentology: Dordrecht, theNetherlands, Springer, p. 537–565, doi:10.1007/978-94-007-0123-6_20.

Rush, J. W., and E. C. Rankey, 2017, Geostatistical faciesmodeling trends for oolitic tidal sand shoals: AAPG Bulletin,v. 101, no. 8, p. 1341–1379, doi:10.1306/09221616032.

Russ, J. C., 1998, The image processing handbook: Boca Raton,Florida, CRC Press, 771 p.

Sandberg, P. A., 1983, An oscillating trend in Phanerozoicnon-skeletal carbonate mineralogy: Nature, v. 305, no. 5929,p. 19–22, doi:10.1038/305019a0.

Sigal, R., 2002, Coates and SDR permeability: Two variationson the same theme: Petrophysics, v. 43, no. 1, p. 38–46.

Smith, C., and L. Hamilton, 2014, Carbonate reservoir per-meability from nuclear magnetic resonance logs: Interna-tional Petroleum Technology Conference, Kuala Lumpur,Malaysia, December 10–12, 2014, 14 p.

Song, Y.-Q., 2013, Magnetic resonance of porous media(MRPM): A perspective: Journal of Magnetic Resonance,v. 229, p. 12–24, doi:10.1016/j.jmr.2012.11.010.

Sparks, A. G., and E. C. Rankey, 2013, Relations betweengeomorphic form and sedimentologic-stratigraphic vari-ability: Holocene ooid sand shoal, Lily Bank, Bahamas:AAPG Bulletin, v. 97, no. 1, p. 61–85, doi:10.1306/05101211125.

Sprunt, E. S., R. E. Gilliland, and M. L. Barrett, 1993, Pre-dicting the permeability of unconsolidated sedimentsfrom grain size measurements: Gulf Coast Associationof Geological Societies Transactions, v. 43, p. 373–380.

Udden, J. A., 1914, Mechanical composition of clastic sedi-ments: Geological Society of America Bulletin, v. 25,no. 1, p. 655–744, doi:10.1130/GSAB-25-655.

Vincent, B., M. Fleury, Y. Santerre, and B. Brigaud, 2011,NMR relaxation of neritic carbonates: An integratedpetrophysical and petrographical approach: Journal ofApplied Geophysics, v. 74, no. 1, p. 38–58, doi:10.1016/j.jappgeo.2011.03.002.

Wagner, P. D., and R. K. Matthews, 1982, Porosity pres-ervation in the Upper Smackover (Jurassic) carbonategrainstone, Walker Creek Field, Arkansas: Response ofpaleophreatic lenses to burial processes: Journal of Sedimen-tary Petrology, v. 52, no. 1, p. 3–18, doi:10.2110/jsr.52.24.

Watney, W. L., E. K. Franseen, A. P. Byrnes, R. D. Miller,A. E. Raef, S. L. Reeder, and E. C. Rankey, 2006, Char-acterization of seismically imaged Pennsylvanian ooidshoal geometries and comparison with modern: AAPGSearch and Discovery article 20038, accessed February5, 2020, http://www.searchanddiscovery.com/documents/2006/06093watney/images/watney.pdf.

Watney, W. L., and J. French, 1988, Characterization of car-bonate reservoirs in the Lansing-Kansas City Groups(Upper Pennsylvanian) in Victory Field, Haskell County,Kansas, in S. M. Goolsby and M. W. Longman, eds., Oc-currence and petrophysical properties of carbonate res-ervoirs in the Rocky Mountain region: Denver, Colorado,Rocky Mountain Association of Geologists, p. 27–45.

Weger, R. J., 2006, Quantitative pore/rock type parametersin carbonates and their relationship to velocity deviations,Ph.D. dissertation, University of Miami, Miami, Florida,232 p.

Weger, R. J., G. P. Eberli, G. T. Baechle, J. L. Massaferro, andY. Sun, 2009, Quantification of pore structure and itseffect on sonic velocity and permeability in carbonates:AAPG Bulletin, v. 93, no. 10, p. 1297–1317, doi:10.1306/05270909001.

Westphal, H., I. Surholt, C. Kiesl, H. F. Thern, and T. Kruspe,2005, NMRmeasurements in carbonate rocks: Problemsand an approach to a solution: Pure and Applied Geo-physics, v. 162, no. 3, p. 549–570, doi:10.1007/s00024-004-2621-3.



http://dx.doi.org/10.1111/j.1365-3091.2010.01155.x


http://dx.doi.org/10.1007/978-94-007-0123-6_20

http://dx.doi.org/10.1007/978-94-007-0123-6_20

http://dx.doi.org/10.1306/09221616032

http://dx.doi.org/10.1038/305019a0

http://dx.doi.org/10.1016/j.jmr.2012.11.010

http://dx.doi.org/10.1306/05101211125

http://dx.doi.org/10.1306/05101211125

http://dx.doi.org/10.1130/GSAB-25-655

http://dx.doi.org/10.1016/j.jappgeo.2011.03.002

http://dx.doi.org/10.1016/j.jappgeo.2011.03.002


http://www.searchanddiscovery.com/documents/2006/06093watney/images/watney.pdf

http://www.searchanddiscovery.com/documents/2006/06093watney/images/watney.pdf

http://dx.doi.org/10.1306/05270909001

http://dx.doi.org/10.1306/05270909001

http://dx.doi.org/10.1007/s00024-004-2621-3

http://dx.doi.org/10.1007/s00024-004-2621-3

Rock fabric controls on pore evolution and porosity ...

Documents

Transcript of Rock fabric controls on pore evolution and porosity ...