AUTHORS

Jennie E. Cook � Department of Geoscience,University of Wisconsin, Madison, Wisconsin;jcook@geology.wisc.edu

Jennie Cook completed her Ph.D. in 2010 at theUniversity of Wisconsin-Madison on the struc-tural and mechanical effects of diagenesis insandstone. She presently works for BP as ageologist.

Systematic diagenetic changes inthe grain-scale morphology andpermeability of a quartz-cementedquartz areniteJennie E. Cook, Laurel B. Goodwin, and David F. Boutt

Laurel B. Goodwin � Department ofGeoscience, University of Wisconsin, Madison,Wisconsin; laurel@geology.wisc.edu

Laurel Goodwin has been a professor at theUniversity of Wisconsin–Madison since 2004,after working at New Mexico Tech. Herresearch interests include the mechanics offracture and faulting and fluid-fault interactionsin granular porous media. She received a B.A.degree from the University of Maine-Orono andan M.A. degree and Ph.D. from the Universityof California-Berkeley.

David F. Boutt � Department of Geo-sciences, University of Massachusetts, Amherst,Massachusetts; dboutt@geo.umass.edu

David F. Boutt is an assistant professor ofgeosciences at the University of Massachusetts–Amherst. He received his Ph.D. from NewMexico Tech in 2004 with a specialization inhydrology. His research is focused on under-standing the coupling between fluid flow anddeformation in permeable media, with the goalof improving the characterization and concep-tualization of hydrogeologic systems.

ACKNOWLEDGEMENTS

This work was supported by funds provided byDOE grant DE-FG02-05ER. This support doesnot constitute an endorsement by DOE of theviews expressed in the article. J. Cook thanksM. French for assistance in sample collection.

ABSTRACT

Thematerial properties of sedimentary rocks are controlled bya range of parameters, including grain size, sorting, and modi-fication of the original sediment through the diagenetic pro-cesses of compaction and cementation. To isolate the effects ofdiagenesis and explore how they modify permeability, wequantified changes in grain and pore morphology accompany-ing progressive diagenesis of a simple system: a well-sorted,variably quartz-cemented quartz arenite of relatively uniformgrain size. The most common type of authigenic cement insandstones, quartz overgrowths, is responsible for significantporosity and permeability reduction. The distribution of over-growths is controlled by available pore space and the crystal-lographic orientations of individual quartz grains.

We show that progressive quartz cementation modifiesthe grain framework in consistent, predictable ways. Detailedmicrostructural characterization and multiple regression anal-yses demonstrate that both the number and length of graincontacts increase as the number of pores increases and thenumber of large well-connected pores decreases with progres-sive diagenesis. The aforementioned changes progressively alterpore shape and reduce pore-size variability and bulk perme-ability. These systematic variations in the pore network corre-late with changes in permeability, such that we can use our datato calibrate the Kozeny-Carmen relation, demonstrating thatit is possible to refine predictions of permeability based onknowledge of the sedimentary system.

Constructive reviews by S. N. Ehrenberg, G. M.Gillis, N. B. Harris, B. Tikoff, and R. H. Wordensignificantly improved the article. The AAPGEditor thanks the following reviewers for theirwork on this paper: Stephen N. Ehrenberg,Nicholas B. Harris, and Richard H. Worden.

Copyright ©2011. The American Association of Petroleum Geologists. All rights reserved.

Manuscript received January 20, 2010; provisional acceptance May 10, 2010; revised manuscriptreceived September 14, 2010; final acceptance November 15, 2010.DOI:10.1306/11151010009

AAPG Bulletin, v. 95, no. 6 (June 2011), pp. 1067– 1088 1067

INTRODUCTION

Diagenesis results in systematic grain-scale changesin sandstone, as both compaction and chemicalprocesses, such as cementation, fundamentally al-ter rock structure. These changes are known to af-fect both the mechanical properties and perme-ability of the resulting lithifiedmaterial (Beard andWeyl, 1973; Houseknecht, 1987; Dvorkin and Yin,1995; Ehrenberg et al., 2008). However, quanti-tative correlation of diagenetic processes with re-sulting physical properties remains elusive, in partbecause of the wide variation in mineralogical andtextural characteristics exhibited by sandstones.To address this gap in understanding, we inves-tigated samples of a supermature quartz arenitecollected from a part of the Tonti Member of theSt. Peter Sandstone that experienced shallow burialand a simple diagenetic history. Although the sam-ples come from a single lithostratigraphic unit anddisplay little variation in mineralogy, grain size,and sorting, they experienced variable amounts ofcompaction and quartz cementation. Thus, changesin the physical characteristics of the sandstone canbe directly related to variations in the degree ofcompaction and cementation, allowing us to quan-titatively explore the effects of each of these dia-genetic processes on physical properties. We focuson the grain-scale effects of these diagenetic pro-cesses on hydrologic properties and address theirimpact on mechanical properties in a separatearticle.

Using detailed sample characterization, imageanalysis, and multiple regression analysis, we quan-tified the effects of compaction and cementation onthe grain framework and pore network of eachsample and subsequently explored the relationshipbetween measured characteristics and permeabil-ity. The results of this study show that physicalcompaction and quartz cementation result in pre-dictable changes in the physical characteristics ofthe grain framework and pore network (which werefer to as micromorphology) of the St. Peter Sand-stone. These systematic changes correlate withchanges in permeability, such that we can invertour data to calibrate an empirical constant in theKozeny-Carmen equation, a mathematical model

1068 Systematic Diagenetic Changes in a Quartz-Cemented Q

commonly used to estimate permeability based oncharacteristics of the pore network. By calibratingthe Kozeny constant, we demonstrate that it ispossible to refine predictions of permeability basedon knowledge of the sedimentary system.

SANDSTONE DIAGENESIS

Numerous studies have identified porosity as aprimary control on the hydrologic characteristicsof sandstone (Nelson, 2004). Final intragranularporosity is the result of multiple diagenetic pro-cesses that can influence the grain-pore frame-work in different ways. In clean quartzose sand-stones, porosity reduction occurs through bothphysical and chemical compaction and precipita-tion of cements, thus, final porosity is a functionof the relative contributions of these two pro-cesses. Compaction results in a more efficientpacking with an increased number of grain-graincontacts and smaller pores. Precipitation of ce-ment in quartz-cemented sandstones alters thegrain-pore system by the addition of material atgrain contacts and grain boundaries. Both pro-cesses are expected to alter grain and pore contactproperties and grain and pore shapes, but in dif-ferent ways and with different efficiency.

Natural sandstones have grain-cement-poregeometries that are mostly dictated by grain andcement mineralogy. For example, calcite cementin quartz arenites is commonly poikilotopic, withlarge calcite crystals engulfing detrital quartz grainsand filling porosity (Scholle, 1979). Quartz cement,in contrast, is typically precipitated as overgrowthson quartz grains where space is available, with ageometry that is crystallographically controlled. Thegeometry of these quartz overgrowths is distinctfrom that of calcite or other cement types, and thisdistinction should have hydrologic effects. In otherwords, progressive cementation should result insystematic and predictable changes in micromor-phology. These changes are controlled by cementand sandstone mineralogy and result in systematicand predictable changes in hydrologic properties.

Syntaxial quartz overgrowths are the most com-mon formof authigenic cement in quartz sandstones

uartz Arenite

(McBride, 1989; Worden and Morad, 2000). Theymay form at several stages in sandstone diagenesis(Vagle et al., 1994) and are thought to develop in acontinuous three-stage process: (1) formation ofsmall rhombohedral and prismatic projections that(2) coalesce into large crystal faces and (3) ulti-mately form polyhedral quartz crystals (Ernst andBlatt, 1964;Waugh, 1970; Pittman, 1972). At earlystages of quartz cementation, the cement is likely toprecipitate at narrow constrictions, particularly atgrain contacts, but at later stages, cement growth iscrystallographically and space controlled (McBride,1989; Lander et al., 2008). Examples of variableamounts of cementation of quartz arenite samplesare shown in Figure 1. Grains in low-cement (<5%)samples exhibit thin encrusting layers of quartzwith isolated crystal facets and interconnected porespaces. In contrast, high-cement (>10%) sampleshave an interconnected network of cement withwell-defined facets and diminished pore connec-tivity (Figure 1).

Sedimentologists, hydrologists, and petroleumgeologists are commonly interested in predictingtype, occurrence, and distribution of cements andthe associated porosity and permeability loss; rockmechanicians are interested in predicting mechan-

ical behavior, such as strength, cohesion, sandingpotential, and so on; and structural geologists arecommonly interested in predicting style, distribu-tion, and abundance of deformation-related fea-tures. For example,Dunn et al. (1973) documentedan important mechanical transition in sandstonesthat corresponded to approximately 12% porosity.Sandstoneswith porosity below this threshold failedthrough the formation of fractures, whereas sand-stones with higher porosities failed through the for-mation of deformation bands. Thus, understandinghow the micromorphology of a sandstone changeswith progressive diagenesis is of interest to a widerange of earth scientists. In particular, it will allowbetter predictive capabilities through better param-eterization of hydrologic, mechanical, and poro-elasticmodels.Grain contact parameters determinedfrom real rocks can, for example, be used as modelinputs to explore howmicroscale changes producedby diagenesis impact the macroscale response of asandstone to pumping stresses (Plourde, 2009).

In previous work, cementation has been in-corporated into models only in idealized form. Forexample, cements have been modeled as bridgesbetween grains (Wong andWu, 1995), concentricrings around circular grains (Dvorkin and Yin,

Figure 1. Comparison of ce-ment micromorphology and dis-tribution in areas of low (3.5%)versus relatively high (15.6%) ce-ment abundance. Both samplesare from the Ordovician St. PeterSandstone in Wisconsin. (A)Cathodoluminescence images inwhich grains (g) are distinguishedfrom cement (c) by differencesin luminescence. (B) False-colorimages of the same areas. Ce-ment is light gray, grains are darkgray, and pores are white. Theintergranular area of the twoimages is roughly the same, butporosity in the high-cement ex-

ample is less than half that of thelow-cement location. (C) Imagesshowing only areas of cementwithin each sample.

Cook et al. 1069

1995; Dillon et al., 2004), or as pore fill (Pandaand Lake, 1995). The grain-bridging geometry is asimple easy-to-model approximation, but hema-tite is the only cement in quartz arenites we haveseen exhibit such a morphology. The concentriccement model is a better approximation of quartzovergrowths; however, it neglects important as-pects of quartz cementation such as preferentialearly cementation of grain contacts and asymmetricprecipitation and distribution of cements (McBride,1989). Weak pore-filling cements, such as clays,would likely have minimal mechanical impact butcan greatly impact permeability. In addition, manyconceptual models neglect the effect of compac-tion, commonly the greatest cause of porosity re-duction (Lundegard, 1992). Importantly, the evo-lution of pore shape during diagenesis also likelyimpacts both permeability and mechanical behav-ior, as it influences both compressibility and theresponse of the system to changing pore pressure(Storvoll and Bjorlykke, 2004). Pores may be mod-eled as cracks, circles, cylinders, and so on, all ofwhich have distinct mechanical and hydrologicproperties. All of these cementation and poremodels

1070 Systematic Diagenetic Changes in a Quartz-Cemented Q

can be useful; none provide a complete descriptionof mechanical and hydrologic behavior. This arti-cle reports a distinctly different approach to ad-dressing this problem. We begin with a thoroughquantitative description of the micromorphologiccharacteristics of a sandstone, explore relationshipsbetween measured parameters, then address theimpact of these characteristics on permeability.

ST. PETER SANDSTONE

Geologic Setting

The Middle Ordovician St. Peter Sandstone is acratonic supermature quartz arenite (Odom et al.,1979; Mai and Dott, 1985). The unit is laterallyextensive, blanketing a region from Michigan, Wis-consin, and Minnesota to Illinois, Missouri, and Ar-kansas. We collected samples from outcrops of theSt. Peter Sandstone exposed along the flanks of theWisconsin arch in southern and central Wisconsin(Figure 2). Although the sandstone was buried to

Figure 2. Map of sample locations in central and southern Wisconsin.

uartz Arenite

significant depths in the Michigan and Illinois ba-sins, burial inWisconsin was shallow, likely less than1000m (3281 ft). Kelly et al. (2007) provided twoarguments supporting this burial estimate: (1) pre-servedoverlying Silurian throughMississippianunitshave a thickness of only approximately 500 m(∼1640 ft), andWisconsin has been above sea level,thus not receiving sediment, since theMississipian;and (2) Paleozoic stratigraphy thins onto the Wis-consin arch, indicating that it has been a structuralhigh since deposition of the St. Peter Sandstone.

The St. Peter overlies a basal unconformity,thus, its thickness is variable but is generally be-tween 25 and 75 m (82–246 ft) thick. The St.Peter Sandstone consists of three members: Reads-town, Tonti, and Glenwood. Samples collected forthis study come from the Tonti Member. Theenvironment of deposition of the St. Peter Sand-stone remains controversial, but the Tonti Mem-ber is generally considered to have both fluvial andeolian components that have experienced marinereworking (Mai and Dott, 1985). The St. PeterSandstone typically consists of greater than 97%quartz grains (Mai and Dott, 1985). In samplesselected for this study, quartz is the only primarygrain type present. Grains consist of fine to me-dium size, very well sorted, and rounded sand.

Kelly et al. (2007) suggested that the homo-geneity of d180 values of quartz overgrowths inthe St. Peter Sandstone precluded a systematic re-gional temperature variation and concluded thatquartz cements in the St. Peter Sandstone aresilcretes, with d180 values consistent with precipi-tation at shallow depths and low temperatures. Incontrast to most quartz cements, which form be-tween 80 and 120°C, where more sources of silicaare present, silcretes typically develop in the nearsurface at weathering profiles or stable water ta-bles (McBride, 1989). Silcretes can have the sametextures as sandstones cemented at much greaterdepths under different diagenetic conditions.

Summary of Diagenesis Reactions and/orEvents in St. Peter Sandstone

Five stages of diagenesis were previously identifiedwithin the St. Peter Sandstone: (1) local precipi-

tation of potassium feldspar and encrusting quartzcements; (2) precipitation of local illite, smectite,kaolinite, calcite, and dolomite; (3) the develop-ment of euhedral quartz overgrowths; (4) pre-cipitation of pyrite; and (5) precipitation of kao-linite (Odom et al., 1979). Samples investigated forthis study record some of these diagenetic events;however, none of the samples studiedhave evidenceof carbonate cements, and very little evidence ofauthigenic clay precipitation exists. In addition, thetiming of diagenetic events within the St. Petersamples we have studied differs from that reportedby Odom et al. (1979).

In the following paragraphs, we discuss evi-dence of diagenetic events in our samples in orderfrom earliest to latest. In the samples we studied,pyrite and iron oxide abundance is typically lessthan 0.5% of the rock volume, but these phasesappear to have precipitated early in the diagenetichistory. Small pyrite crystals precipitated on grainsurfaces are typically surrounded by quartz over-growths and pores occluded by iron oxides typi-cally lack quartz overgrowths, whereas quartzovergrowths may be common in adjacent pores(Figure 3A, B). In zones with significant potassiumfeldspar, grain contacts show no evidence of dis-solution, indicating that precipitation of diageneticpotassium feldspar predates significant pressuresolution (Figure 3C).

The relationship between quartz cement andpressure solution is unclear. However, quartzprecipitation appears to have postdated potassiumfeldspar precipitation based on the following ob-servations: (1) potassium feldspar precipitated di-rectly on grain surfaces; (2) no evidence of feldsparprecipitated on existing quartz overgrowths exists,and pores with significant potassium feldsparprecipitation generally lack quartz cement; and(3)where quartz and feldspar overgrowths are bothpresent, quartz appears to have grown aroundfeldspar overgrowths (Figure 3D).

Just one sample contains local evidence forprecipitation of clay coatings with meniscus geom-etries following major phases of quartz cementa-tion (Figure 3E), suggesting formation in the va-dose zone. In addition, some feldspar overgrowthshave evidence of local dissolution, but no relative

Cook et al. 1071

Figure 4. Inferred sequence ofdiagenetic events in samplesof the St. Peter Sandstone in-vestigated for this study. Not allevents are recorded in all sam-ples; only physical compactionand quartz cementation aredocumented in all samples.

Figure 3. Backscattered elec-tron images of diagenetic phaseswithin the St. Peter Sandstone. Inthese images, black is open porespace, dark gray grains arequartz, light gray cements arepotassium feldspar, and whitecements are pyrite or iron oxide.(A) Small pyrite crystals pre-cipitated on detrital grain sur-faces (arrows), later envelopedby quartz overgrowths. (B) Poreoccluded by iron oxide (arrow)with no evidence of quartzovergrowths. (C) Localized areaof feldspar cement (f) with noevidence of pressure solution,adjacent to areas without feld-spar cements with abundant su-tured contacts (sc). (D) Feldsparcements precipitating directly ongrain surfaces and abuttingquartz overgrowths. (E) Rare claygrain coatings and cements withmeniscus geometries.

1072 Systematic Diagenetic Changes in a Quartz-Cemented Quartz Arenite

timing could be determined. The nature and rel-ative timing of diagenetic events determined fromthe samples studied are summarized in Figure 4.

SAMPLE CHARACTERIZATION

Methods

To evaluate the effects of progressive compactionand quartz cementation on sandstone grain andpore morphology, a suite of samples was chosen toencompass a range of initial porosity and cementabundance. For this exercise, a TinyPerm air mini-permeameter was used as an outcrop-screening tool,under the assumption that samples with a range ofpermeabilities would exhibit a range of porosities.

Nine sampleswere selected for a detailed study(Figure 2). Although the total sample number issmall, the samples were chosen to encompass awide range in porosity and cement percentage. Allcame from exposed surface outcrops. Six samplesconsisted of uniform sandstone, with no evidenceof bedding at the sample scale, and three samplescontained centimeter-scale bedding heterogeneity.

Using a Hitachi S-3400 variable-pressure scan-ning electron microscope with Gatan PanaCL/Fcathodoluminescence detector operated at 15 kVat the University of Wisconsin–Madison, a seriesof backscattered electron (BSE), cathodolumi-nescence (CL), and secondary electron imageswastaken for each sample.Mosaics of images collectedat 150× magnification were constructed to eval-uate porosity, cement percentage, grain size, andgrain contact properties. Mosaics represent areasof the samples that range in size from approxi-mately 4.4 × 3.3 mm to 3.7 × 2.7 mm, consistingof 36 or 25 images, respectively.

To evaluate sample porosity using image anal-ysis, BSE image mosaics were used. In BSE images,epoxy in open pore spaces appears black, thus, thearea fraction occupied by black pixels can be usedto approximate the two-dimensional porosity of theimages. In addition to image analysis, bulk porosityof most samples was also evaluated at the core scaleusing a helium pycnometer on 1-in. diameter cores.

Comparison of two-dimensional (2-D) calculatedand three-dimensional (3-D) measured porositiesallows us to assess whether images accurately repre-sent rock characteristics. For consistency with other2-D analyses, we use the porosity results obtainedthrough image analysis in our statistical analysis.

Cathodoluminescence images were used toevaluate cement percentage and grain-grain rela-tionships. Because quartz cements grow in opticalcontinuity with primary grains, such features aredifficult to distinguish in either standard BSE orplane-light images. However, because cements typi-cally differ in luminescent properties from originalgrains, they can generally be distinguished in CLimages (Sprunt and Nur, 1979; Blenkinsop andRutter, 1986; Onasch, 1990; Laubach, 2003). Inthe CL mosaics of the St. Peter Sandstone samples,later stage quartz cements commonly appear darkerthan primary grains. Because of color variabilityfrom grain to grain, detrital grains cannot be reliablydistinguished from quartz cements using imageanalysis alone. Thus, two estimates of cement per-centage weremade for each sample: the first throughimage analysis of cement tracings and the secondby point counting (300 points) of image mosaics.The average cement value of these two measure-ments was used in subsequent statistical analyses.

Sample Characteristics

Sample characteristics are summarized in Table 1.Sample porosity ranges from 8% to approximately25%. Remarkably good agreement is present be-tween porosities estimated from 2-D images andthose measured using a pycnometer. We thereforeassume that the 2-D images provide an adequaterepresentation of the core-scale properties. Quartzcement abundance is generally inversely propor-tional to porosity, with quartz cement percentageranging from 0.1 to 14%. Diagenetic potassiumfeldspar cements are present in 8 of 9 samples atabundances of 1% or less of the entire rock vol-ume. Unlike quartz cements, which precipitatedthroughout the sample volume, potassium feld-spar cements were only precipitated locally, inisolated pores or groups of pores (Figure 3D). As

Cook et al. 1073

previously mentioned, iron oxide cements andrare pyrite and clay grain coatings are present inlocalized pore spaces of several samples. Becausethey represent such a small volume of the solidframework, these cements are not included in ouranalyses. Original porosity or intergranular volume(IGV) of all samples, calculated by adding porositypercentage and cement percentage, ranges from21 to 31%. Sample 14_1 had the lowest IGV of20.9% and contained extensive sutured and in-terpenetrating contacts, indicating that chemicalcompaction was active. Other samples containedno evidence of chemical compaction.

Average grain size was calculated throughimage analysis from the average diameter of par-ticles, where diameter was chosen as the maxi-mum width of a grain (including cement), a rea-sonable estimate of well-rounded relatively equant

1074 Systematic Diagenetic Changes in a Quartz-Cemented Q

grains. Because a 2-D slice through a 3-D packingof spherical grains does not represent the actualparticle-size distribution and because no correc-tions were applied to the resulting data, the grain-size values reported are smaller than the actual 3-Dgrain sizes. The focus of this study, however, is acomparison of samples within the data set, andthese values are internally consistent. Samplesconsisted dominantly of fine sand, with an averagegrain size between 0.15 and 0.20 mm.

EFFECTS OF DIAGENESIS ONMICROMORPHOLOGY AND PERMEABILITY

In each of the following sections, we first address themethodofmeasurement of a givenmicromorphologic

Table 1. Sample Characteristics Listed from Highest to Lowest Porosity

Sample

Mean Porosity (%)(Image Analysis)

Porosity (%)(Pycnometer)

Mean QuartzCement (%)

Potassium FeldsparCement (%)

uartz Arenite

Mean IntergranularVolume (%)

Average GrainSize (mm)

OtherPhases*

1_2

24.6 5.9 0.2 30.9 0.20 5_2 24.4 25.3 0.9 0.9 26.4 0.17 IC 13_1 20.7 21.0 9.4 0.0 30.2 0.19 P, CC 14_1 19.5 0.6 0.7 20.9 0.17 IC 4_1 19.0 8.1 0.6 28.0 0.20 3_2 16.6 14.9 11.5 0.6 28.7 0.17 IC 3_1 15.3 15.3 13.4 0.5 28.9 0.15 IC 11_2 12.4 12.4 11.4 1.0 24.3 0.15 IC 12_1 8.7 8.1 16.6 0.1 25.3 0.17 IC, CC

*CC = clay coatings; P = pyrite; IC = iron oxide cement.

Figure 5. Procedure for mea-suring contact length (A) andbond-to-grain ratio (BGR) (B).For cases where the contact wasdiscontinuous, the total contactlength (LT) was calculated as thecombined length of the sep-arate segments (La, Lb), so thatLT = La + Lb.

parameter of interest. Each brief methods section isfollowed by details of the results.

Grain-Grain Relationships

To investigate changes in grain contact parametersassociated with progressive diagenesis, a combina-tion of BSE and CL images was used. Two primaryparameters, grain contact length and bond-to-grainratio (BGR), were measured from photomosaics.For each sample, the grain contact length was mea-sured as the shortest width of a given contact be-tween adjacent grains (Figure 5A). The BGR wasapproximated as the total number of grain-grain orgrain-cement-grain contacts divided by the numberof grains completely contained within each mosaicand associated with each contact (Figure 5B).

The results of these analyses are presented inTable 2. The BGR generally increases with de-creasing porosity and increasing cement percent-age (cf. Table 1; Figure 6). Sample 14_1, however,with evidence of significant pressure solution, hasa lower BGR than would be expected for sampleswith similar porosity and a higher BGR than sam-ples with a similar cement percentage. Averagecontact length generally decreases with grain sizeand increases with cement percentage. Again,sample 14_1 is anomalous with longer averageand normalized contact lengths compared withsamples with similar cement percentages.

Pore Shape

Images of pores, like images of grains, are 2-Dslices through a 3-D geometric network. Becausepores vary in both size and shape, 2-D images arelimited approximations of 3-D geometry (Ehrlichet al., 1991). Nevertheless, progressive changes in2-D pore geometries will result from the changesin pore architecture that accompany diagenesis.These variations in 2-D pore geometry can becharacterized and compared within the data set.Because the tools needed for thin section analysisare more broadly available than those required for3-D analysis of equivalent resolution, this ap-proach is also more generally useful.

For pore analysis, images of pore spaces wereextracted from BSE images using National In-stitutes of Health ImageJ (Rasband, 2009). Theseraw images were then processed using a combi-nation of median filters to minimize noise andemphasize the basic pore geometries. Only poresthat were fully contained within the entire mo-saic were analyzed. Because higher porosity sam-ples generally contain larger pores that are morelikely to be truncated by the image edge, the per-centage of total pore space analyzed decreasedwith increasing porosity. For low-porosity sam-ples, 85 to 90% of the total porosity imaged wassampled, whereas only 45% of the imaged poros-ity was sampled from the highest porosity sam-ple. In general, the smaller size fraction of pores

Table 2. Summary of Grain Contact Parameters Presented from Highest to Lowest Porosity Samples

Sample

No. Bondsper Image

No. Grainsper Image

Bond-to-GrainRatio

Total Contact Lengthper Image (mm)

Cook et al

Average ContactLength (mm)

1_2

12.97 9.25 1.40 0.72 5.55 × 10−2

5_2

20.16 14.52 1.39 0.74 3.67 × 10−2

13_1

15.92 10.16 1.57 1.04 6.51 × 10−2

14_1

18.22 11.97 1.52 1.23 6.80 × 10−2

4_1

17.36 10.08 1.72 1.27 7.30 × 10−2

3_2

25.97 14.86 1.75 1.64 6.30 × 10−2

3_1

36.32 18.88 1.92 2.25 6.18 × 10−2

11_2

35.44 18.16 1.95 2.19 6.20 × 10−2

12_1

31.92 14.28 2.24 2.69 8.42 × 10−2

. 1075

had a higher probability of being sampled in allcases, but this effect is most significant at higherporosities.

Several pore space descriptors were char-acterized for each sample: (1) total number ofpores; (2) total and average pore area; (3) varia-

1076 Systematic Diagenetic Changes in a Quartz-Cemented Q

tion in average pore area, reported as standarddeviation; (4) total and average pore perimeter;and (5) a geometric pore shape factor (SF):

SF ¼ pCpP

Figure 6. Results of multiple regression analyses. Bond-to-grain ratio (BGR) (A), specific surface area (B), and pore-size variability (C)are plotted with respect to porosity. (D)-(F) appear on following page. Average pore size (D) and normalized number of pores (E) areplotted with respect to both porosity and grain size. (F) Pore shape is plotted as a function of both intergranular volume (IGV) andcement percentage. Note that the plots shown in panels D, E, and F have been rotated so that the planes illustrating relationshipsbetween the three variables shown are viewed on edge. The rotations are evidenced by the orientations of the x and y axes.

uartz Arenite

Figure 6. Continued.

where pC is the perimeter of a circle of the samearea as the pore, and pP is the perimeter of thepore; and (6) specific surface area (SSA):

SSA ¼ 4×PPð Þp ×PAð Þ

where PP is the summed perimeter of all poreswithin a mosaic, and PA is the summed area of allpores. The SSA is a parameter used in the Kozeny-Carman relationship to predict permeability fromrock porosity and micromorphology.

Results of pore analyses are given in Table 3.The number of pores generally decreases with in-creasing porosity, decreasing cement, and increas-ing IGV. Bothmean pore size and variation inmeanpore size decrease with decreasing porosity, in-creasing cement, and decreasing IGV. More circu-lar pores have shape factor (SF) values approach-ing 1, whereas more complexly shaped pores havelower values. Pores generally become more cir-cular with increasing cementation and decreasingIGV. Sample 14_1 is again an exception, withmorecircular pores than samples with similar cementpercentages or porosities.

Effects of Diagenesis on Measured andPredicted Permeability

Permeability measurements were conducted atNew England Research, at a confining pressure of14.5 MPa (2103 psi). The confining pressure waschosen based on estimated maximum burial condi-tions assuming 1 km (3281 ft) of burial and hydro-static fluid pressure. For samples with anticipatedpermeabilities greater than 500 md, a gravity flowtechnique was used. For low-porosity samples, atransient pressure technique was used (cf. Fetter,2001). Both methods were used to measure thepermeability of an intermediate porosity sampleto facilitate comparison. Sample permeabilitiesare presented in Table 4. As expected, permeabil-ity generally decreases with decreasing porosityand increasing cement percentage; sample 14_1 is,once more, a prominent exception to these gen-eral trends.

INFLUENCE OF DIAGENETIC PATH

For quartz-cemented quartz arenites, primary sedi-mentary characteristics such as grain size, sorting,

Cook et al. 1077

shape, and composition are independent of dia-genesis. Secondary characteristics, such as the na-ture and types of grain contacts, cement percentage,and cement distribution, are controlled by post-depositional diagenetic processes. Other character-istics such as IGV, pore shape, and pore-size vari-ability are a function of both primary and secondaryprocesses. The limited variability in sorting, grainsize, and grain composition and shape in the St. PeterSandstone (Table 1) (Mai and Dott, 1985) meansthat variations in IGV, pore size, and pore shapeare primarily a function of diagenetic modifications.

Final porosity is a function of the relativecontributions of compaction and cement precipi-

Lo

1078 Systematic Diagenetic Changes in a Quartz-Cemented Q

tation. For this reason, micromorphologic param-eters (i.e., BGR, contact length, mean pore size,etc.) are evaluated based on the relative contri-butions of these two primary processes.We assumethat all samples had an initial porosity of approxi-mately 40%—a typical initial porosity for quartzarenites (Beard and Weyl, 1973; Houseknecht,1987). Lower IGV values indicate a greater de-parture from this original porosity and thus agreater magnitude of compaction. Given this as-sumption, IGV can be used as a direct proxy forcompaction (Lander and Walderhaug, 1999).

To evaluate how well micromorphologic pa-rameters such as BGR or contact length are pre-dicted by variables such as porosity or cementpercentage and IGV, data were analyzed usingmultiple regression.We considered the dependentvariables BGR, average grain contact length,average pore size, pore-size variability, SSA, poreshape, number of pores, and permeability in ouranalysis. For each dependent parameter, two pri-mary linear regressions were computed: (1) thedependent parameter with respect to porosity and(2) the dependent parameter with respect to IGVand quartz cement percentage.We also consideredwhether the addition of mean grain size as an in-dependent parameter improved the model fit.Sorting was not considered in multiple regressionanalyses because it varies little in this select sampleset. Other measures of the grain-size distributionmaybe important formore heterogeneous suites ofsamples.

Table 3. Summary of Pore Parameters with Samples Listed in Order of Decreasing Porosity

Sample

No. Poresper Image

Percent of TotalPorosity Sampled

Average PoreSize (mm2)

Average PorePerimeter (mm)

uartz Arenit

Pore Shape

e

Pore Size StandardDeviation (mm2)

Specific SurfaceArea (mm−1)

1_2

6.94 45.22 8.16 × 10−3 0.45 0.71 3.50 × 10−2 70.01 5_2 10.04 71.84 8.24 × 10−3 0.51 0.63 2.03 × 10−2 78.31 13_1 8.96 64.54 7.50 × 10−3 0.42 0.73 1.90 × 10−2 71.38 14_1 9.31 73.78 7.42 × 10−3 0.40 0.77 2.05 × 10−2 67.98 4_1 9.42 73.08 6.62 × 10−3 0.40 0.72 1.36 × 10−2 76.81 3_2 14.42 87.03 4.32 × 10−3 0.28 0.82 1.08 × 10−2 83.70 3_1 19.48 83.55 2.96 × 10−3 0.23 0.83 6.46 × 10−2 100.53 11_2 20.20 90.93 2.48 × 10−3 0.21 0.83 5.17 × 10−2 109.21 12_1 19.80 84.04 1.47 × 10−3 0.14 0.97 3.18 × 10−2 121.24

Table 4. Measured Permeability*

Sample

Permeability

(md)

g Permeability

(md)

AnalyticalMethod

1_2

2860 3.46 S 5_2 3370 3.53 S 13_1 1294 3.11 S 14_1 2633 3.42 S 4_1 1240 3.09 S 3_2 NM NM S 3_1 357 2.55 S 11_2 58 1.76 S 11_2 11.2 1.05 T 12_1 5.9 0.77 T

*S = steady state flux technique; T = transient pressure technique; NM = notmeasured.

Table 5. Results of Multiple Regression Analysis

Dependent R2 StandardPartial Regression Coefficients**

Parameter* R2 Adj. n Error Intercept Porosity IGV CMT GS Regression Equation

BGR 0.98 0.97 8 4.80 × 10−2 2.65 −5.12 × 10−2 BGR = 2.65 + (−5.12 × 10−2) PORCL 0.99 0.99 8 1.55 × 10−3 −6.20 × 10−3 −1.44 × 10−3 2.95 × 10−3 4.57 × 10−1 CL = −6.20 × 10−3 + (−1.44 × 10−3) IGV +

(2.95 × 10−3) CMT + (4.57 × 10−1) GSAverage PA 0.98 0.97 8 4.65 × 10−4 −7.77 × 10−3 4.10 × 10−4 3.26 × 10−2 PA = −7.77 × 10−3 + (4.10 × 10−4) IGV +

(3.26 × 10−2) GSPore-Size Variability(LogStD) 0.95 0.94 8 8.28 × 10−2 −3.03 6.03 × 10−2 LogStD = −3.03 + (6.03 × 10−2) POR

SSA 0.85 0.83 8 7.86 144.47 −3.14 SSA = 144.47 + (−3.14) PORPore Shape Factor(SF) 0.94 0.92 8 2.91 × 10−2 8.52 × 10−1 −9.22 × 10−3 1.92 × 10−2

SF = 8.52 × 10−1 + (−9.22 × 10−3) IGV +(1.92 × 10−2) CMT

No. Pores (nP) 0.98 0.97 8 0.90 48.32 −6.28 × 10−1 −133.89 nP = 48.32 + (−6.28 × 10−1) POR + (−133.89)GS

Partial Regression Coefficient

R2 nStandardError Intercept Ln (porosity) Regression Equation

Log permeability 0.99 7 1.45 × 10−1 −4.77 2.61 LogPERM = −4.77 + (2.61) Lnf

*BGR = bond-to grain ratio; CL = contact length; PA = pore area; LogStD = log standard deviation; SSA = specific surface area.**IGV = intergranular volume; CMT = cement; GS = grain size.

Cooketal.

1079

To evaluate the quality of fit of each linearregression to the data, both the R2 value and anadjusted R2 (described below) were used. The ad-dition of independent parameters (e.g., IGV pluscement compared with porosity or porosity plusaverage grain size compared with porosity alone)generally increased both the R2 value and the ad-justed R2. Because the R2 will generally increasewith the inclusion of additional predictors in theregression, the adjusted R2 is a regression statisticthat accounts for additional predictors and increasesonly when the R2 increases more than would beexpected by chance. Thus, the adjusted R2 will beless than or equal to R2.

To select which linear regression model bestfit the data, for example, (1) porosity ± grain sizeor (2) IGV and cement percentage ± grain size, anF test was used. The F test determines the sig-nificance of the increased R2 value for each re-gression with an added predictor variable. An Fstatistic was calculated for each pair of regressions,and if the value of that statistic was less than thecritical F value for the 90% confidence level, thenthe more complex regression model was rejectedin favor of the simpler regression model withfewer predictors.

Using the above procedure, if a regression of aparticular characteristic with respect to porosityalone was selected as the best model, then weconcluded that the diagenetic path could be ne-glected, and porosity loss through diagenesis wasthe most important predictor of that characteristicregardless of whether it was achieved throughcompaction or cementation. If regression withrespect to IGV and cement percentage was se-lected as the best model, then we concluded thatthe diagenetic path should be considered. Re-gardless of which primary model was chosen, grainsize was a significant additional parameter in severalanalyses. However, it should be noted that thevariation in grain size within the St. Peter Sandstoneis small; larger grain-size variations in otherwisesimilar systems might have a more significant ef-fect on resulting parameters.

As mentioned previously, sample 14_1 hassignificant evidence of pressure solution, and datapresented in Tables 1 to 4 indicated that pressure

1080 Systematic Diagenetic Changes in a Quartz-Cemented Q

solution alters the grain framework differentlyfrom physical compaction and cementation. There-fore, each regression was performed both with andwithout sample 14_1. For every model, adjustedR2 improved with the exclusion of sample 14_1from the regression. We also conducted a sensi-tivity analysis, where each regression was com-puted iteratively, leaving out one sample for eachiteration for each dependent parameter. Sample14_1 was the only sample whose exclusion re-sulted in an increase in R2 for every dependentparameter. Thus, the final regression analyses forall parameters exclude sample 14_1.

Results of multiple regression analyses formicromorphologic parameters and permeabilityare included in Table 5. Additional informationfor all regressions considered is included in theAppendix. For each analysis, partial regressioncoefficients are reported, including statistical es-timates of model fit. Regression results suggestthat BGR, SSA, and pore-size variability can beapproximated as a function of porosity alone, andthus the method of pore occlusion is unimportant(Figure 6A–C). For a 5% decrease in porosity,BGR increases by approximately 0.26. The SSAhas the most unexplained variability in the data.Average pore size and number of pores are bestapproximated as a function of porosity and grainsize (Figure 6D, E). Thus, the method of porosityreduction is unimportant for these parameters aswell, but grain size should be considered.

Two parameters were found to be sensitive todiagenetic path: grain contact length and poreshape (Figure 6F). Pore shape is a function of IGVand cement percentage, whereas average graincontact length is a function of IGV, cement per-centage, and grain size. Cementation results inmorecircular pores than physical compaction alone. Themagnitude of regression coefficients suggests thatcementation is at least twice as important as changesin IGV to resulting contact length.

The correlation between porosity and per-meability is a property of granular porous mediathat reflects the change from interconnectedmacroporosity at high porosity to more isolatedsmaller pores at lower porosities (Ehrenberg et al.,2008). It is therefore not surprising that regression

uartz Arenite

analyses show that permeability is primarily afunction of porosity. However, the specific re-lationship between porosity and permeability canvary markedly between different depositional anddiagenetic systems (Nelson, 2004). Thus, it is alsounsurprising that sample 14_1, excluded fromregression analyses as previously indicated, ex-hibits permeability that is distinctly different from(approximately double that of) samples of similarporosity.

Although porosity was commonly selected asthe better fit for the data based on statistical tests,inmany cases, the data weremodeledwith a higherR2 and adjusted R2 when IGV and cement wereused as predictors instead of porosity. However,because of the small sample size, these improve-ments were typically not significant. Further in-vestigation with a larger more varied data set mayindicate that more parameters are sensitive to dia-genetic path than those identified in this study.

DISCUSSION

A shortcoming of statistical approaches like theone outlined in this study is that the predictions areonly useful for sandstone compositions, textures,and geologic settings similar to the initial calibra-tion data sets (Bloch, 1991; Gal et al., 1998; Landerand Walderhaug, 1999). We therefore do not sug-gest that the reported regression coefficients aredirectly applicable to other sandstones; instead,these results indicate that predictable variations inmicromorphology of the grain-pore system aredirectly related to diagenetic processes. Under-

standing these relationships for a given sandstonetype and diagenetic history can provide insightinto the mechanical and hydrologic effects of sand-stone diagenesis, with the ultimate hope of betterpredictive capabilities.

The evolution of grain and pore morphol-ogy reported here is therefore specific to quartz-cemented quartz arenite. Precipitation of othertypes of cement will result in different morpholo-gies, distinct from quartz cements, which are ex-pected to result in a different set of predictablevariations in the grain-pore system.

Diagenetic Changes in Grain-Pore Frameworksof the St. Peter Sandstone

During diagenesis of quartz arenites, both the num-ber and length of grain contacts increase. The num-ber of pores increases, whereas the total porositydecreases, resulting in decreased connectivity ofpores and increasing homogeneity in pore size.Table 6 demonstrates how these data can be usedto anticipate variations in dependent parameterswith degree of diagenesis by illustrating how mi-cromorphological parameters would vary with a5% increase in the independent parameters po-rosity, IGV, and cement percentage or a 0.01-mmincrease in grain size.

Statistical analyses demonstrate that porosityreduction, instead of physical compaction or ce-mentation alone, is the best predictor of BGR, apoint illustrated by the strong correlation shown inFigure 6A. Thus, either compaction or cementa-tion can effectively increase the number of graincontacts in a quartz-cemented quartz arenite. We

Table 6. Change in Dependent Parameters for a 5% Increase in Porosity, IGV, and Cement or a 0.01-mm Increase in Grain Size

DependentParameter

BGR

ContactLength (mm)

Pore-Size Variability (mm)(Log Standard Deviation)

Average PoreSize (mm2)

SSA (mm2)

Pore ShapeFactor

Cook et al.

No. Pores

Porosity

−2.56 × 10−1 3.01 × 10−1 2.05 × 10−3 −1.57 × 101 −3.14E × 100

IGV

−7.18 × 10−3 −4.61 × 10−2

Cement

1.48 × 10−2 9.62 × 10−2

Grain Size

4.57 × 10−3 3.26 × 10−4 −1.34E × 100

1081

infer that physical compaction increases the num-ber of grain contacts because pore spaces collapseand are reorganized, whereas cementation increasesthe number of bridges between grains. If grainswere perfectly spherical, physical compactionalone would not increase grain contact length.However, because grains are irregularly shaped,physical compaction should result in more effi-cient grain packing, thereby increasing contactlength, along with BGR. The addition of cementlengthens grain contacts, and the preferential pre-cipitation of cements at narrow grain contactsamplifies this effect.

Average pore size decreases, as expected, withporosity; however, this reduction is achieved pri-marily through destruction of the largest pores,producing multiple smaller pores. These largestwell-connected pores primarily control permeability.As they are preferentially destroyed, permeabilityand pore-size variation exponentially decrease(Figure 7). The SSA also decreases with decreas-ing porosity and destruction of the largest pores.

The number of pores does not stay the samewith continued diagenesis (Gal et al., 1998). Ourdata show that the number of pores increases,regardless of whether porosity reduction is domi-nated by compaction or cementation (Figure 6E),

1082 Systematic Diagenetic Changes in a Quartz-Cemented Q

and pores become progressively more sphericalwith increasing diagenesis (Figure 6F).

Timing of Diagenetic Events

Physical compaction and cementation were prob-ably not coeval in the St. Peter Sandstone becausephysical compaction appears to shut down afterprecipitation of relatively small amounts of graincontact cement (Hiatt et al., 2007; Melzer andBudd, 2008). Precipitation of even small amountsof cements at grain contacts can significantly stiffenthe grain framework, increasing strength and pre-venting grain sliding and rotation (Spinelli et al.,2007). Thus, diagenesis in mature quartz arenites

Figure 7. Plot of permeability versus pore-size variation. De-struction of the largest pores results in an exponential decreasein both permeability and pore-size variation.

Figure 8. Schematic illustration of three possible diageneticpathways, showing how compaction can be shut down by ce-mentation at different stages in a quartz arenite’s burial history. Theinitial porosity of a quartz arenite is typically approximately 40%.Early cementation, represented by path A, preserves a relativelyhigh intergranular volume (IGV) because cementation shuts downcompaction before it accomplishes significant porosity loss. Thecement strengthens the grain framework, so most porosity lossoccurs subsequently through cementation. The sandstone in path Bexperiences cementation only after significant compaction, re-cording an IGV of approximately 32%. Path C illustrates the max-imum possible porosity reduction through compaction, resulting inan IGV of 26%, with subsequent porosity loss occurring entirelythrough cementation.

uartz Arenite

Figure 9. Schematic diagrams for prediction of grain contact and pore properties of variably quartz-cemented quartz arenites based onregressions in Table 5. The gray line in each figure illustrates a possible grain-pore evolution with diagenesis for sample 3_1. Solid anddashed lines are contours of predicted grain-pore parameters of interest. Regression analyses (Table 5) are used to show predictedchanges in dependent parameters with variations in intergranular volume (IGV) and cement percentage. For all predictions, the onlyporosity-reducing processes are assumed to be compaction and precipitation of cement. For cases where the dependent parameter is afunction of porosity, the dependent parameter changes equally for a reduction in IGV or an equal increase in cement percentage. Thecorresponding IGV and cement percentage for a given porosity can be calculated through the relationship: Porosity = IGV-%Cement. (A)Bond-to-grain ratio (BGR) (solid lines) and contact length (millimeters) (dashed lines) are predicted for sandstones with a mean grain sizeof 0.15 mm. This can be adapted for other grain sizes by adding 0.023 mm to the contour values for contact length for every 0.05 mmincrease in grain size (cf. Table 6). (B) Log permeability (millidarcys) (solid lines) and pore shape (dashed lines) are predicted for a varietyof IGV and cement percentages. The area shown in gray is outside of the calibration data set for permeability, thus no predictions are made.

Cook et al. 1083

in the absence of chemical compaction may beimagined as the result of two distinct phases, anearly phase dominated by physical compaction,followed by a second phase dominated by quartzcementation (Figure 8). The length of time withineach “window” and the relative magnitude of eachprocess determine the final micromorphology ofthe sandstone.

PanelsA andBof Figure 9 illustrate the potentialeffects of diagenesis involving physical compac-tion and precipitation of cements on grain andpore properties. These diagrams are contour plotsshowing changes in predicted BGR and contactlength (Figure 9A) and log permeability and poreshape (Figure 9b), with changes in IGV and ce-ment percentage. Only the diagenetic processes ofcompaction and cementation are considered. Afterdeposition, initial compaction increases the numberof grain contacts, with only small increases in con-tact length. Permeability decreases as pore throatsare closed by pore collapse and cement precipita-tion. Once significant quartz cementation initiates,the number of contacts continues to increase, con-tact length and pore circularity increase rapidly, andpermeability reduction slows as diagenesis prog-resses. Permeability decreases equally with poros-ity loss through cementation and physical com-paction within the St. Peter Sandstone. However,without grain breakage, the final porosity achievedthrough physical compaction in clean quartz arenitesis limited to approximately 26% (Beard andWeyl,1973; Paxton et al., 2002). Because permeabilitychanges vary with porosity changes in these rocks,permeability reduction through physical compac-tion alone is therefore also limited.

Predicting Permeability in Quartz-CementedQuartz Arenites

When permeability measurements are not avail-able, the permeability of a granular porous me-dium is commonly estimated based on empirical ortheoretical models. A commonly usedmodel is theKozeny-Carman relationship. The Kozeny-Carmanrelationship relates two easily acquired parametersfrom an image of a grain-pore network-specific

1084 Systematic Diagenetic Changes in a Quartz-Cemented Q

surface area and porosity (Panda and Lake, 1995;Mowers and Budd, 1996) to permeability as follows:

k ¼ f3

K0ðL0LEÞ2ð1� fÞ2SSA2

where k is permeability, f is porosity, K0 is an em-pirical Kozeny constant related to the cross sec-tional area of the pore, L0/LE is the tortuosity,and SSA is the specific surface area. A proportion-ality constant, c, is typically substituted for the K0

(L0/LE) parameter (Mowers and Budd, 1996). Formany calculations, a constant value of 5 is used forparameter c, but this constant of proportionalityshould vary with the pore system (Carman, 1956;Mowers and Budd, 1996).

Diagenesis alters the amount and distributionof pore space, creating smaller more disconnectedpores, therefore a uniform constant of proportion-ality should not be sufficient to encompass differ-ences in permeability related to physical compactionand cementation. Therefore, we use permeabilitiesdetermined from the regression equation in Table 5to calculate variations in the proportionality constantusing the equation previously given.We use values ofpermeability from the regression analyses insteadof the individual measured values to minimize the

Figure 10. Plot of calibrated constants of proportionality versusporosity.

uartz Arenite

effect of natural sample variability. Table 7 liststhe measured permeability, predicted permeabilitybased on regression analysis (cf. Table 5), and anestimate of a calibrated constant of proportionalityfor each sample. The calculations indicate that foraccurate predictions of permeability within thisdata set, the constant of proportionality for the poresystems decreases exponentially with increasingporosity (i.e., decreasing diagenetic alteration)(Figure 10). Because the constant of proportionalityis dependent on both K0 and (L0/LE), it is difficultto estimate either parameter without more data.Nevertheless, our analysis suggests that diageneticalteration has a strong effect on the cross sectionalarea of the pores (expressed throughK0 and/or thetortuosity, which is represented by [L0/LE]). Fur-thermore, the trend shown in Figure 10 suggeststhat consideration of samples with a wider range ofporosities would result in a variation of approxi-mately an order of magnitude in the constant ofproportionality, resulting in a significantly greatervariation in calculated permeability than is evidentwith the constant fixed at 5.

Effect of Pressure Solution on theGrain-Pore Framework

Sample 14_1had an anomalously low IGV(Table 1)and contained significant evidence of sutured andinterpenetrating grain contacts—an indication ofpressure solution despite its shallow burial. Othersamples had higher IGV and contained little evi-dence of grain suturing. Thus, we conclude that

modification of the grain framework from chemi-cal compaction was minor in samples other than14_1. Compared with samples that contained littleor no evidence of pressure solution, sample 14_1was an outlier in evaluation of diagenetic trends inmicromorphologic parameters andwas not includedin any regression. For example, sample 14_1 had arelatively low average pore perimeter, more circularpores, and lower SSA than would be anticipatedbased on trends defined by other samples.

Although only one sample exhibited theseanomalous features, these observations suggestthat pressure solution may affect the evolution ofsandstone micromorphology differently than phys-ical compaction and cementation alone. In thissample that has undergone moderate pressuresolution, grain contacts are significantly lengthened,mimicking the effect of cement on contact length.In this way, pressure solution can effectively de-crease the pore perimeter by destroying elongatespaces between touching grains, thus increasingpore circularity and decreasing SSA. For a givenporosity, a lower SSA results in a higher perme-ability calculated from the Kozeny-Carmen rela-tionship. Interestingly, the permeability measuredfrom sample 14_1 is approximately 1000 mdhigher than that predicted from the characteristicsof samples with no evidence of pressure solution(Table 7). Thus, our very limited data suggest thatfor a given porosity, a sample with significant ce-mentation would likely have lower permeabilitythan a sample whose final porosity was achieveddominantly through pressure solution.

Table 7. Permeability Prediction Parameters

Sample

Log Measured

Permeability (md)

Log Predicted

Permeability (md)

Cook e

Calibrated Constantof Proportionality

1_2

3.46 3.59 0.9 5_2 3.53 3.57 0.6 14_1 3.42 Not included in analysis 13_1 3.11 3.14 1.3 4_1 3.09 2.91 1.5 3_2 Not measured 2.56 1.8 3_1 2.55 2.35 1.6 11_2 1.76 1.80 2.7 12_1 0.77 0.86 5.5

t al. 1085

CONCLUSIONS

Grain-scale properties of rocks control macro-scopic behavior. Therefore, understanding howrock characteristics and material properties evolveat the grain-pore scale provides insight into hy-drologic and mechanical behavior at the core scaleand above. In this study, we considered the effectof diagenetic processes on changes in the grainframeworks and pore networks of quartz-cementedsandstones and found that these processes resultin predictable changes: the number and length ofgrain-grain contacts increase, the number of poresincreases, whereas average pore size decreases,pore-size variability decreases, and pore spacesbecome progressively more circular with progres-sive diagenesis.

Diagenesis in the clean quartz-cemented sand-stones we studied likely occurred in two separatephases: the first, dominated by physical compac-tion, and the second, by quartz cementation.Changes in morphology reflect this history withsignificant changes in grain contact length andpore shape initiating only after the onset of sig-nificant quartz cementation. Cementation increasescontact length and pore circularity approximatelytwice as much as an equivalent reduction in IGV.

1086 Systematic Diagenetic Changes in a Quartz-Cemented Q

In samples that have undergone physical com-paction and precipitation of quartz cements, reduc-tion in permeability correlates well with reductionin porosity. The largest well-connected pores con-trol permeability. As these pores are preferentiallymodified through compaction and cement precip-itation, pore-size variability and permeability de-crease. This reduction in permeability is expressedas a dramatic increase in constant of proportion-ality in the Kozeny-Carman relation (Figure 10).Different sandstones should show similar trendsof increasing constant of proportionality with de-creasing permeability; however, the specific rela-tionships between diagenesis and permeability, andtherefore between porosity and the constant of pro-portionality, are expected to varywith the sandstonesystem. For example, the patchy development thatis typical of carbonate cements in quartz arenitesmight result in the local preservation of large con-nected pores that could serve as high-permeabilitypathways at lower bulk porosity than would beseen in a quartz-cemented quartz arenite. Depend-ing on the spatial distribution of carbonate patches,the calibrated constant of proportionality could belower (i.e., the permeability would be higher) for agiven porosity than the constant for the quartz-cemented quartz arenite we describe here.

APPENDIX:. ESTIMATED MODEL FIT FOR ALL LINEAR REGRESSIONS CONSIDERED

Porosity

IGV and Cement

u

Porosity + Mean Grain Size

artz Arenite

IGV and Cement + MeanGrain Size

Regression Model:Dependent Parameter*

R2 R2 Adj. R2 R2 Adj. Fs** Fc

†

R2 R2 Adj. Fs Fc R2 R2 Adj. Fs Fc

BGR

0.98†† 0.97†† 0.98 0.97 Contact length 0.54 0.46 0.70 0.58 0.94 0.91 32.49‡ 4.06 0.99†† 0.99†† 29.43††,‡ 4.54††

Average pore area

0.94 0.93 0.93 0.91 0.98†† 0.97†† 9.91††,‡ 4.06†† 0.98 0.97 Pore-size variability(Logstandarddeviation) 0.95†† 0.94†† 0.97 0.95 2.12 4.06‡

SSA

0.85†† 0.83†† 0.91 0.87 3.05 4.06‡

Pore shape factor

0.89 0.87 0.94†† 0.92†† 4.77††,‡ 4.06††

No. pores

0.81 0.78 0.83 0.76 0.98†† 0.97†† 46.88††,‡ 4.06†† 0.98 0.97 Log permeability (md)‡‡ 0.93 0.92 0.94 0.92 1.01 4.54‡

*Regressions for intergranular volume (IGV) and cement are compared with regressions of porosity. Regressions of porosity and mean grain size are compared withporosity. Regressions of IGV and cement and mean grain size are compared with regressions for porosity and mean grain size.

**Fs = value of F statistic for model pair (fewer, more predictors).†Fc = critical F value for significance testing.††Model selected.‡Values in bold indicate the higher of Fs and Fc for each model pair.‡‡n = 8 for all regressions is 8, except permeability regression with n = 7.

REFERENCES CITED

Beard, D. C., and P. K. Weyl, 1973, Influence of texture onporosity and permeability of unconsolidated sand: AAPGBulletin, v. 57, p. 349–369, doi:10.1306/819A4272-16C5-11D7-8645000102C1865D.

Blenkinsop, T. G., and E. H. Rutter, 1986, Cataclastic deforma-tionofquartzite in theMoine thrustzone: JournalofStructuralGeology,v.8,p.669–681,doi:10.1016/0191-8141(86)90072-6.

Bloch, S., 1991, Empirical prediction of porosity and perme-ability in sandstones: AAPG Bulletin, v. 75, p. 1145–1160 , do i : 10 . 1306 /20B23C73 -170D-11D7-8645000102C1865D.

Carman, P. C., 1956, Flow of gases through porous media:New York, Academic Press, 182 p.

Dillon, C. G., R. H. Worden, and S. A. Barclay, 2004, Simu-lations of the effects of diagenesis on the evolution ofsandstone porosity: Journal of Sedimentary Research,v. 74, p. 877–888, doi:10.1306/040404740877.

Dunn, D., L. LaFountain, and R. Jackson, 1973, Porosity de-pendence and mechanism of brittle fracture in sand-stones: Journal of Geophysical Research, v. 78, p. 2403–2417, doi:10.1029/JB078i014p02403.

Dvorkin, J., and H. Yin, 1995, Contact laws for cementedgrains: Implications for grain and cement failure: Interna-tional Journal of Solids and Structures, v. 32, p. 2497–2510, doi:10.1016/0020-7683(94)00279-6.

Ehrenberg, S., P. Nadeau, and O. Steen, 2008, A megascaleview of reservoir quality in producing sandstones fromthe offshore Gulf of Mexico: AAPG Bulletin, v. 92, p. 145–164, doi:10.1306/09280707062.

Ehrlich, R., S. J. Crabtree, K.O.Horkowitz, and J. P. Horkowitz,1991, Petrography and reservoir physics: I. Objectiveclassifiction of reservoir porosity: AAPG Bulletin, v. 75,p. 1547–1562.

Ernst, W. G., and H. Blatt, 1964, Experimental study ofquartz overgrowths and synthetic quartzites: Journal ofGeology, v. 72, p. 461–470.

Fetter, C.W., 2001,Applied hydrogeology:New Jersey, Pren-tice Hall, 598 p.

Gal, D., J. Dvorkin, and A. Nur, 1998, A physical model forporosity reduction in sandstones: Geophysics, v. 63,p. 454–459, doi:10.1190/1.1444346.

Hiatt, E. E., T. K. Kyser, M. Fayek, P. Polito, G. J. Holk, andL. R. Riciputi, 2007, Early quartz cements and evolutionof paleohydraulic properties of basal sandstones in threePaleoproterozoic continental basins: Evidence from insitu delta (super 18) O analysis of quartz cements: Chem-ical Geology, v. 238, p. 19–37, doi:10.1016/j.chemgeo.2006.10.012.

Houseknecht, D. W., 1987, Assessing the relative importanceof compaction processes and cementation to reduction ofporosity in sandstones: AAPGBulletin, v. 71, p. 633–642.

Kelly, J. L., B. Fu, N. T. Kita, and J. W. Valley, 2007, Opti-cally continuous silcrete quartz cements of the St. PeterSandstone: High-precision oxygen isotope analysis byion microprobe: Geochimica et Cosmochimica Acta,v. 71, p. 3812–3832, doi:10.1016/j.gca.2007.05.014.

Lander, R. H., and O.Walderhaug, 1999, Predicting porosity

through simulating sandstone compaction and quartzcementation: AAPG Bulletin, v. 83, p. 433–449, doi:10.1306/00AA9BC4-1730-11D7-8645000102C1865D.

Lander, R. H., R. E. Larese, and L. H. Bonnell, 2008, Towardmore accurate quartz cementmodels: The importance ofeuhedral versus noneuhedral growth rates: AAPG Bulle-tin, v. 92, p. 1537–1563, doi:10.1306/07160808037.

Laubach, S. E., 2003, Practical approaches to identifyingsealed and open fractures: AAPG Bulletin, v. 87, p. 561–579, doi:10.1306/11060201106.

Lundegard, P. D., 1992, Sandstone porosity loss: A “big pic-ture” view of the importance of compaction: Journal ofSedimentary Petrology, v. 62, p. 250–260.

Mai, H., and R. H. Dott, 1985, A subsurface study of theSt. Peter Sandstone in southern and eastern Wisconsin,U.S.A., University of Wisconsin-Extension, Geologicaland Natural History Survey, Madison, Wisconsin, U.S.A.,Information Circular 47, 26 p.

McBride, E. F., 1989, Quartz cement in sandstones: A re-view: Earth-Science Reviews, v. 26, p. 69–112, doi:10.1016/0012-8252(89)90019-6.

Melzer, S. E., and D. A. Budd, 2008, Retention of high per-meability during shallow burial (300 to 500 m) of car-bonate grainstones: Journal of Sedimentary Research,v. 78, p. 548–561, doi:10.2110/jsr.2008.060.

Mowers, T. T., and D. A. Budd, 1996, Quantification of po-rosity and permeability reduction due to calcite cementa-tion using computer-assisted petrographic image analysistechniques: AAPG Bulletin, v. 80, p. 309–322, doi:10.1306/64ED87C8-1724-11D7-8645000102C1865D.

Nelson,P.H., 2004,Permeability-porositydata sets for sandstones:Leading Edge, v. 23, p. 1143–1144, doi:10.1190/1.1813360.

Odom, I. E., T. N. Willand, and R. J. Lassin, 1979, Paragen-esis of diagenetic minerals in the St. Peter Sandstone(Ordovician), Wisconsin and Illinois, in P. A. Scholleand P. R. Schluger, eds., Aspects of diagenesis: SEPMSpecial Publication 26, p. 425–443.

Onasch, C. M., 1990, Microfractures and their role in defor-mation of a quartz arenite from the central Appalachianforeland: Journal of Structural Geology, v. 12, p. 883–894, doi:10.1016/0191-8141(90)90061-3.

Panda, M. N., and L. W. Lake, 1995, A physical model of ce-mentation and its effects on single-phase permeability:AAPG Bulletin, v. 79, p. 431–443, doi:10.1306/8D2B1552-171E-11D7-8645000102C1865D.

Paxton, S. T., J. O. Szabo, J. M. Ajdukiewicz, and R. E.Klimentidis, 2002, Construction of an intergranular vol-ume compaction curve for evaluating and predictingcompaction and porosity loss in rigid-grain sandstone res-ervoirs: AAPG Bulletin, v. 86, p. 2047–2067.

Pittman, E. D., 1972, Diagenesis of quartz in sandstones asrevealed by scanning electron microscopy: Journal ofSedimentary Petrology, v. 42, p. 507–519, doi:10.1306/74D725A4-2B21-11D7-8648000102C1865D.

Plourde, K. E., 2009, Quantifying the effects of cementationon the hydromechanical properties of granular porousmedia using discrete element and poroelastic models:Master’s thesis, University of Massachusetts, Amherst,Massachusetts, 75 p.

Rasband,W. S., 2009, ImageJ, version 1.42q,Maryland, U.S.A.:

Cook et al. 1087

U. S. National Institutes of Health, Bethesda, Maryland:http://rsb.info.nih.gov/ij/ (accessed March 2010).

Scholle, P. A., 1979, A color illustrated guide to constituents,textures, cements, an porosities of sandstones and asso-ciated rocks: AAPG Memoir 28, 201 p.

Spinelli, G. A., P. S. Mozley, H. J. Tobin, M. B. Underwood,N. W. Hoffman, and G. M. Bellew, 2007, Diagenesis,sediment strength, and pore collapse in sediment ap-proaching the Nankai Trough subduction zone: Geolog-ical Society of America Bulletin, v. 119, p. 377–390,doi:10.1130/B25920.1.

Sprunt, E. S., and A. Nur, 1979, Microcracking and healingin granites: New evidence from cathodoluminescence:Science, v. 205, p. 495–497, doi:10.1126/science.205.4405.495.

Storvoll, V., and K. Bjorlykke, 2004, Sonic velocity and graincontact properties in reservoir sandstones: PetroleumGeoscience, v. 10, p. 215–226, doi:10.1144/1354-079303-598.

1088 Systematic Diagenetic Changes in a Quartz-Cemented Q

Vagle, G. B., A. Hurst, and H. Dypvik, 1994, Origin ofquartz cements in some sandstones from the Jurassicof the Inner Moray Firth (UK): Sedimentology, v. 41,p. 363–377, doi:10.1111/j.1365-3091.1994.tb01411.x.

Waugh, B., 1970, Formation of quartz overgrowths in thePenrith sandstone (lower Permian) of northwest Englandas revealed by scanning electron microscopy: Sedimen-tology, v. 14, p. 309–320, doi:10.1111/j.1365-3091.1970.tb00197.x.

Wong, T., and L. Wu, 1995, Tensile stress concentration andcompressive failure in cemented granular material: Geo-physical Research Letters, v. 22, p. 1649–1652, doi:10.1029/95GL01596.

Worden, R. H., and S. Morad, 2000, Quartz cementation inoil field sandstones: A review of the key controversies, inR. H. Worden and S. Morad, eds., Quartz cementationin sandstones: International Association of Sedimentolo-gists Special Publication 29, p. 1–20.

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