digiovanni castlegate

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s@/vi9200(3 - 050/cMicromechanics of compaction in an analogue reservoir sandstoneA. A. DiGiovanni, J. T. Fredrich, D. J. Holcomb, W. A. OlssonSandia National Laboratories, Albuquerque, New Mexico

ABSTRACT: Energy production, deformation, and fluid transport in reservoirs are linked closely. Recentfield, laboratory, and theoretical studies suggest that, under certain stress conditions, compaction of porousrocks may be accommodated by narrow zones of localized compressive deformation oriented perpendicular tothe maximum compressive stress. Triaxial compression experiments were performed on Castlegate, an ana-logue reservoir sandstone, that included acoustic emission detection and location. Initially, acoustic emissionswere focused in horizontal bands that initiated at the sample ends (perpendicular to the maximum compres-sive stress), but with continued loading progressed axially towards the center. This paper describes micros-copy studies that were performed to elucidate the micromechanics of compaction during the experiments. Themicroscopy revealed that compaction of this weakly-cemented sandstone proceeded in two phases: an initialstage of porosity decrease accomplished by breakage of grain contacts and grain rotation, and,a second stageof firther reduction accommodated by intense grain breakage and rotation.

1 INTRODUCTIONEnergy production, deformation, and fluid transportin reservoirs are linked strongly. Hydrocarbon ex-traction reduces pore pressure and causes an in-crease in the effective stress (e.g. Teufel et al. 1991).For very porous or wezikly consolidated formations,the increase in effective stress may be sufficient tocause inelastic deformation of the reservoir rock(e.g. Jones & Leddra 1989, Goldsmith 1989, Rhett1988, Schutjens et al. 1988, Fossum & Fredrich1998). The consequences of reservoir compactioncan be severe and can include surface subsidence,casing damage, and other production problems (e.g.Smits et al. 1988, de Waal & Smits 1988, Ruddy etal. 1989, Elf Aquitaine 1991, Myer et al. 1996,Fredrich et al. 1996, 1998, Patillo et al. 1998). Theinelastic deformation of the producing formation canalso, in turn, affect fluid flow patterns within thereservoir.Recent field (Mollema & Antonelli 1996), labo-ratory and theoretical (Olsson 1999, Issen & Rud-nicki 1999) studies suggest that, under certain stressconditions, compaction may be accommodated bynarrow zones of localized compressive deformationthat are oriented perpendicular to the maximumcompressive stress. In this paper, we describe recentlaboratory tests that resulted in formation of com-paction bands and microscopy studies that were

conducted on a sample deformed triaxially underconditions conducive to compaction band foimation.

2 LABORATORY EXPERIMENTSThe rock used in our study was from the CastlegateFormation, and is a weak high porosity sandstonethat is used commonly as an analogue reservokrock. The Castlegate is a fine to medium-grained (-0.2 mm grain size) sublitharenite with quartz beingthe dominant phase (70-80%) and a clay contentthat ranges from 510% (TerraTek, Inc.). Other mi-nor phases include feldspar, siderite, and lithics in-cluding chert. The bulk porosity is 2870and intrinsicpermeability measured under a few thousand psi (i.e.tens of MPa) effective confining pressure is 0.2-0.4.x 10-12m2 (Fredrich, unpublished data). The micro-structure of the pristine material, and its relation tothe mechanical behavior, is described subsequentlyin more detail.2.1 Experimental proceduresConventional triaxial compression experiments wereconducted on cylindrical test specimens preparedparallel to bedding with a diameter to length dimen-sion of 50.8 x 127 mm. Specimens were firstwrapped in a thin foil of copper and twelve piezo-

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DISCLAIMERThis report was prepared as an account of work sponsoredby an agency of the United States Government. Neither theUnited States Government nor any agency thereof, nor any of their employees, make any warranty, express or implied,or assumes any legal liability or responsibility for theaccuracy, completeness, or usefulness of any information,apparatus, product, or process disclosed, or represents thatits use would not infringe privately owned rights. Referenceherein to any specific commercial product, process, orservice by trade name, trademark, manufacturer, orotherwise does not necessarily constitute or imply itsendorsement, recommendation, or favoring by the UnitedStates Government or any agency thereof. The views andopinions of authors expressed herein do not necessarilystate or reflect those of the United States Government orany agency thereof.


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Portions of this document may be illegiblein electronic image products. Images areproduced from the best available originaldocument.


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2.2 Stress-strain behaviorThe material behavior during the hydrostatic loadingwas essentially elastic, with no significant anisot-ropy indicated by the radial and axial strains (Fig.la). There was no pronounced inflection in the pres-sure-volume behavior during the hydrostat to 80MPa, and the initial yield surface associated with theonset of inelastic compaction (e.g. see Fossum &Fredrich this volume) was intersected during the tri-axial segment (Fig. lb). After reaching a peak stressof -150 MPa, the sample experienced a small stressdrop, and then deformed at an approximately con-stant differential stress of 135 MPa before beingunloaded at a (total) axial strain close to 5%. Notethat the deformation measured during the triaxialsegment by the radial strain transducer that was lo-cated at the sample mid-point tracks almost identi-cally for loading versus unloading. That is, the de-formation in the radial direction at that location upto the point of unloading was dominantly elastic.

H //1 2.3 Acoustic emission data() [-m I-.-J I I I d . ., 1 J0.00 0,01 0.02 0.03 0.04 0.05 0.06

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Figure1. Stress-strain behaviorobservedin experimentCG6during (a) hydrostatic and (b) triaxial compression loading.Note that load-unload loops were performed at several stagesfor measurement of incremental elastic moduli.

electric transducers were then mounted onto thecopper jacket. The sample was then coated with athick film of polyurethane to prevent the confiningfluid from penetrating the specimens, and after cur-ing, loaded in conventional triaxial compression us-ing a servo-controlled triaxial system with the porepressure system drained to atmosphere. Confiningpressure, was measured with a conventional straingauge transducer, and measurements of force on anexternal load cell were used to calculate axial stress.Axial and radial strains were measured using twolinear variable displacement transducers that weremounted axially and radially. Olsson & Holcomb(2000) describe the larger test program; this paperfocuses on a single experiment.The sample of interest was loaded hydrostaticallyto a confining pressure of 80 M.Pa, and then loadedtriaxially under displacement control to yield a strainrate of 10-5S-l.The relative arrival times of acousticemission (@) events were recorded by the twelvePZT transducers and used later to locate AE events.

The AE data were analyzed in time and space (Fig.2). Forty thousand of 10 million total events werelocatable. The criteria for location included that theevent was recorded by at least four of the twelvetransducers. The location error was -*2 mm.A small number of AE were recorded during thehydrostatic loading (Fig. 2, left). The events weredistributed throughout the sample volume, with aslight concentration at the sample ends. The initialpart of the triaxial segment was relatively quiet; butwhen the total axial stress increased to -50 MPa, anescalation in AE rate was associated with the devel-opment of two distinct bands of AE that were lo-cated initially at the sample ends (Fig. 2, secondfrom left). Olsson & Holcomb (2000) discuss thestress conditions at the sample ends and this aspectis not discussed here. As the stress approached thepeak value, the AE bands moved away from thesample ends, and propagated towards the samplecenter throughout the portion of the triaxial segmentduring which the stress maintained a roughly con-stant value (Fig. 2, center, right and far right). Notethat the presence and subsequent movement of thebands of intense AE are superimposed on a back-ground of diffuse AE events that were distributedthroughout the sample during the course of the tri-axial loading.2.4 Macroscopic observationsVisual observations of the sample made after re-moval of the jacketing material suggested the exis-


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Figure 2. Three-dimensional volume renderings of AE events in the sample during the (left) hydrostatic segment, and during thetriaxial loading segment to (second from left) just prior to peak stress, (center) through peak stress and over the duration of thesmall stress drop, and (second ffom right and far right) during the extended period of approximately constant stress difference).For clarity, the extent of the five timesegmentsareindicatedn Fiwre 3. The diameter to length dimension of the sample is 5Q8 x127 mm,_andthe linear voxel dimensions 1 mm.

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Figure 3. Total axial stress versus axial strain during the hy-drostat and triaxial loading. The intervals marked correspondto the time increments for the AE volume renderings shown inFigure 2. Note that load-unload loops were performed at sev-eral stages for measurement of incremental elastic moduli.

formation. Both the upper and lower thirds of thesample exhibited macroscopic signs of deformation,including multiple inclined diffuse shear bands and apervasive lightening in color. The color change wasassociated presumably with grain crushing andgranulation in the upper and lower portions as theseregions were very fragile, and prone to surficialdisintegration during even gentle handling. In con-trast, the center portion maintained its color, retainedits integrity, and appeared largely unchanged.Post-test measurements of compressional (P)wave velocity corroborated the visual observationsand again suggested the existence of different de-formation regimes within the sample. The P-wavevelocity measured diametrically in the upper andlower regions of the sample was reduced to 1.6-1.8rndps, and the velocity gradually increased to nearits pristine value (- 2.8 3.0 mrdps) as the samplecenter was approached.

3 MICROSCOPYTo substantiate the occurrence of compaction bandsand to elucidate the micromechanics of compactionwe conducted microscopy studies on the deformedsamples using light optical and scanning electronmicroscopy. The deformed sample was vacuum im-pregnated with a low-viscosity epoxy that wasdoped with rhodamine-B. Following curing of theepoxy, several 25.4 mm diameter cylindrical sub-cores were diamond-cored from different locationswithin the large sample and used subsequently toprepare polished (to 0.05 ~m) thin sections for opti-cal and thick sections for scanning electron micros-copy. The cores were taken horizontally from loca-tions in the upper, central, and lower thirds of thesample, and orientation was maintained throughoutthe preparation of the polished microscopy sections.Observations made on sections prepared from theupper and lower portions of the sample were similarso that we do not discriminate between them hereand these samples are denoted simply as CG6-SD.Samples sub-cored from the central region of thesample are referred to as CG6-UD. A pristine sam-ple was similarly impregnated, sub-cored, and sec-tioned for direct comparison with the deformedsample. This sample is referred to as CGO.3.1 ObservationsAs noted above, both optical and scanning electronmicroscopy was performed. Optical microscopy re-veals the gross features of the deformation but theresolution is insufficient to resolve the details of thegrain scale cracking and fragmentation. Scanningelectron microscopy was performed on carboncoated polished thick sections using a Hitachi S-4500 SEM operated at 25 kV using the backscat-


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Figure 4, Backscatteredcanningelectronmicrographof pris-tineCastlegatesandstoneCGO(theimageis 0.80mmacross).Quartzis thedominantphase,andthe lightcoloredgrainontheupperedgeis potassiumfeldspar.Thedarkphasepartiallycoatingsomequartzgrains,and occasionallypartiallyfillingpores,isclay(dominantlylliteandkaolhdte).tered imaging mode and only those results areshown here.A micrograph of the undeformed Castlegate(sample CGO) is shown in Figure 4. The dominantmineral is quartz, and lithic fragments and potassiumfeldspar are minor framework phases. Clay phasesinclude kaolinite, illite, and possibly m6nt-morillinite. Clays are present occasionally as pore-lining, sometimes as pore-filling, and frequently ce-menting minimally the framework grains. Also ofnote is the high number of point and tangential con-tacts between grains; that is, the original texture ofthe sand has not been affected significantly by sub-sequent diagenesis and a pre-compaction texture hasbeen largely maintained. The small amount of pore-filling clays in combination with the occasional localenhancement of porosity by dissolution results in apore network that is extremely well connected withpore sizes that occasionally exceed the size of thelargest grains by a factor of 2 or more.The microstructural evolution during the triaxialcompression experiment is revealed in Figure 5 ofthe deformed sample CG6. As discussed previously,the central region of the sample was associated withonly diffuse AE activity during the hydrostatic andtriaxial loading (Fig. 2) and showed no pronouncedoutward signs of deformation. The microscopy,

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Figure 5. BackScattered images (0.80 mm across) from (Top)the central region of sample CG6 (CG6-UD) which appearedlargely undeformed to the naked eye, and (Bottom) the lowerregion of CG6 (CG6-SD) which efilbited obvious signs of de-formation and through which the band of high AB activitypropagated. In CG6-UD, grains are intact but closer togetherthan in the CGO (see Fig. 4), and edge (tangential) grain con-tacts have increased (decreased). In CG6-SD, porosity is fur-ther reduced and grains are intensely comminuted. The maxi-mum compressive stress was vertical.


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Figure 6, High magnification backscattered images (0.20 mmacross) showing intense grain scale microcracking in CG6-SD(see Fig. 5, bottom, for detail area). (Top) The grain on the leftis quartz and is only lightly damaged. The lighter grain on theright is feldspar and is intensely comminuted. Fine mi-crocracking parallel to the strong cleavage in the feldspar isapparent, as is subsequent rotation of the cleaved grain frag-ments, (Bottom) Intense microcracking developed in twoquartz grains that may have originally had a point contact. Themaximum compressive stress was vertical.

however, reveals a microstructure that is alteresubtly (Fig. 5, top). The matrix grains have retainetheir integrity and are utiactured, however, thgrain structure appears more compact in that grainare closer together as a result of the pore space beinreduced between neighboring grains. In additionthere are few point or tangential contacts betweegrains; the dominant contacts are line or edge. Thporosity reduction is also revealed dramatically witoptical microscopy due to the presence of the redye epoxy, but those rnicrographs are not showhere.The microstructure is dramatically different in thupper and lower regions of the sample (Fig. 5, botom). As described previously, these parts of thsample showed obvious deformation to the nakeeye, and they were the regions of the sample througwhich bands of intense AE activity had migrateduring the triaxial loading portion of the experimenThe original fabric of the sandstone has been completely destroyed. The porosity is reduced markedlboth in terms of its bulk amount and the size of thremaining pores. Grain fragmentation is profoundfew grains show no sign of damage, and mangrains are fractured heavily and crushed (Fig. 6The less rigid clay phases sometimes filling thoriginal pore space have in some instances deformedmarkedly. The large reduction in bulk volume habeen accommodated through both fragmentation ansubsequent rotation of the crushed grains.3.2 Quantitative stereologyStereological techniques (Underwood 1970) werapplied to quantify the microstructural evolutionduring the initial phase of compaction that is accomplished with rare or no grain fragmentation. Thmean phase intercept length, L3, and the number ointerceptions of objects per unit line length, NL,wermeasured for the CGO and CG6-UD samplesMeasurements were not made on sample CG6-SDbecause of the inherent complexity of the microtructure (see Fig. 5, bottom) associated with thesecond stage of compaction (i.e. accommodated bypronounced grain fragmentation and crushing andassociated with the intense AE activity that propagated as a band).The method was implemented as follows. Original grayscale digital images at (1024 x 816) weredivided into four (513 x 409) images and overlainwith a regular amay of 13 evenly spaced test linesthat were the length of the image and with a secondarray of 34 randomly distributed line segments olength 1.The quarter image fields were 398.4pm inheight and 499.7 ~m in width. The short line segments were 75 pm in length. Three (1024 x 816images (yielding 3 x 4 = 12 quarter images) were


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used for each sample, such that an area equal to 2.4rnm2was covered for both CGOand CG6-UD.The array of regularly spaced lines was used tomeasure the number of intercepts of the object ofinterest per unit test line length, PL, here defined asboundaries separating individual grains (Pti) andboundaries separating the pore and grain phases(Pm~). Tangential intercepts were counted as %.Theclay solid phase contains a significant amount of mi-croporosity, and this was not measured in our analy-sis. That is, the measurements reported here wereintended to characterize exclusively changes in themacroporosity with deformation. From the numberof intercept points per line, the number of particlesper unit length, NUa), for the grain phase is given byNUa)= ?4(2Pka + Pm~). (1)Because a boundary cannot exist between porephases, NUa)for the pore phase is equal toNUa)= ?4PUP. (2)The array of random line segments was used to

determine the mean phase intercept length L3. Eachline segment has two end points, and the number ofend points falling in the phase of interest, p, and thenumber of intersections of line segments with thephase boundary, P, were counted. The mean phaseintercept length is given byL3=lp/P (3)and can be related to a mean grain diameter for aparticular assumed grain shape as detailed in Un-derwood (1970).Finally, the calculations of NL and L3 were usedto calculate the volume fraction for the phase of in-terest, VV,by the relationVv(a)= NU.) L3 (4)and the mean free path, A,between grains usingk =(1 - VV(a))/ N4a). (5)

The results for the grain and pore phase areshown in Tables 1 and 2. The data support clearlythe qualitative microscopy observations discussedpreviously. Specifically, (1) the particle size in thecentral region of the test specimen (sample CG6-UD) has not been reduced in comparison to the pris-tine material CGO (identical L3), and (2) there was a40% reduction in the inter-grain spacing for sampleCG6-UD versus the pristine sample CGO. This cor-responds to a 27% reduction in the macroporosity,or, equivalently, a net reduction in the volume frac-tion of macroporosity from 22 to 16%. Note alsothat the data for CGO imply that the clay rnicropo-rosity accounts for -6% of the total bulk porosity of28%.

Table 1.Stereological data for the grain phase.Sample lua$) Pure) NL(.) L3 A/mm /mm Am-n pm J.lmCGO 10.7M.5 1.8KL7 7.1*1.2 76.4+14.7 68.&!22.7CG6-TJD 11.9+1.8 3.M1.4 8.9ti.l 76.5fi2.6 41.4*14.5

Table 2. Stereological data for the pore phase (note that claymicroporosity was not included).Sample P~*) NL L3 Vv

/mm hnm Urn %CGO 11.2*1.6 5.6M.8 37.8k8.9 21.0+525.5CG6-UD 10.1H.2 5.M1.1 32.M1O.7 15.4f3.o

4 DISCUSSIONThe microstructural observations confirm the exis-tence of fundamentally distinct zones of deformationwithin the test specimen. In conjunction with themacroscopic stress-strain (Fig. 1) and acousticemission (Fig. 2) data, the microscopy analyses sug-gest that compaction of this weakly cemented sand-stone under the triaxial load path followed duringthe test was accommodated in two distinct stages.The first stage of compaction was associated withbreakage of the minimal cement bonding the frame-work grains and subsequent rotation of the intactframework grains to yield a more compact grainpacking. This stage reduced the macroporosity by anestimated 27%. The second stage of compaction wasassociated with intense grain cornminution and sub-sequent rotation of the grain fragments and resultedin substantial additional reduction in porosity andbulk volume.The acoustic emission data reveal that the secondstage of compaction propagated as a localized bandof deformation through the test specimen. The me-chanical data indicate that the sample deformed at anapproximately constant deviatoric stress during thisstage as the localized compaction band propagatedthrough the sample. Olsson (1999) and Issen andRudnicki (1999) proposed that the occurrence of lo-calized compaction bands can be understood withinthe fiarnework of the bifurcation theory of localiza-tion proposed originally by Rudnicki and Rice(1975). In particular, Issen and Rudnicki (1999) pre-sent a modification to the theory that incorporatesthe possibility of cap plasticity. Olsson & Holcomb(2000) discuss this aspect of our experiments infurther detail.Our microscopy observations have significant


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and failure of porous rock. In particular, the obser-vations suggest that the processes involved in thefirst stage of compaction are reasonably inefficientgenerators of acoustic emissions. As discussedabove, the first stage of compaction was associatedwith breakage of grain bonds and subsequent rota-tion, but was marked by only limited diffuse AE ac-tivity. In contrast, the second stage of compactionthat was accommodated by intense grain-scale mi-crocracking was associated with intense AE activity.Lockner (1993) has discussed previously the com-plexities related to the interpretation of microme-chanical sources of AE during the failure of low po-rosity rock. Our work suggests a similarlycomplicated scenario for the deformation of porousrock, and we hope to resolve further this issue bydetailed analysis of the waveform data in conjunc-tion with microstructural analysis.The micromechanical compaction behavior thatwe observed for the Castlegate sandstone is inmarked contrast to previous observations for Bereasandstone (Men~ndez et al. 1996). Those workersperformed a suite of compaction tests under differ-ent load paths including hydrostatic compressionand triaxial compression. They observed, however,that the initiation of inelastic yield (compaction) un-der both hydrostatic and triaxial loading conditionswas associated with the onset of brittle microcrack-ing at grain contacts (see Figure 5 of Men6ndez etal.). In contrast, our study of Castldgate showsclearly an initial stage of compaction accommodatedby breakage of grain contacts and subsequent rota-tion of intact grains with no grain fragmentation.The primary differences between the two sandstonesare their fabric and cementation. The Berea has un-dergone a diagenesis that has resulted in a more in-durated fabric with well-developed grain boundariesand significantly more cementation. In contrast, asdiscussed previously, the Castlegate has maintaineda pre-compacted fabric throughout its diagenesis, thegrain contacts are often point or tangential, and thecementation is minimal. Thus, the Castlegate fabricis sufficiently weak such that a large amount of vol-ume reduction can be accomplished through grainre-arrangement alone in the absence of significantgrain breakage and fragmentation.The different rnicromechanical behaviors ob-served for the Castlegate versus that observed for theBerea (Men6ndez et al. 1996) have significant im-plications for the evolution of fluid transport prop-erties during deformation. Specifically, the pro-nounced grain crushing that is associated with theonset of inelastic compaction in the Berea reducespermeability dramatically by both reducing the localhydraulic conductance of the pores and by increas-ing the tortuosity of the flow paths (Zhu and Wong1997). Our rnicrostructural analyses suggest that thepermeability evolution during the initial stage of

compaction in the Castlegate may differ, in that thedominant microstructural change relates to grain re-arrangement as opposed to grain fragmentation.Therefore we expect the tortuosity of the flow pathsto be approximately maintained during the initialstage of compaction. Furthermore, the second stageof compaction that occured as a localized band ofdeformation that propagated through the samples isexpected to result in significant spatial anisotropy ofthe fluid transport properties.

5 CONCLUSIONThis paper describes microscopy studies that wereperformed to elucidate the micromechanics of com-paction during triaxial compression experiments per-formed on Castlegate sandstone. The microscopyrevealed that compaction of this weakly-cementedsandstone proceeded in two phases: an initial stageof porosity decrease that is accomplished by break-age of grain contacts and subsequent grain rotation,and a second stage of further volume reduction thatis accommodated by intense grain breakage and ro-tation. Furthermore, the second stage of compactionwas revealed through acoustic emission location tohave occurred as a localized compaction band thatpropagated though the sample in a direction perpen-dicular to the maximum compressive stress. Recentwork by Olsson (1999) and Issen and Rudnicki(1999) suggests a theoretical framework for pre-dicting this behavior.To complement the optical and scanning electronmicroscopy that is presented here, we have also per-formed recently three dimensional imaging on boththe pristine and deformed samples using synchrotronscomputed microtomography in collaboration withM. L. Rivers and others at the Advanced PhotonSource at Argome National Laboratory. That work,which includes quantitative analysis of the three-dimensional microgeometry and numerical simula-tion of fluid flow (e.g. Fredrich 1999, OConnor andFredrich 1999), will be reported elsewhere.Depending upon the generality of the deformationbehavior observed here (i.e. in terms of the micro-structural characteristics, stress states, and load pathsthat favor such behavior) researchers may need toconsider whether this deformation mode of localizedcompaction needs to be considered in numericalsimulations of complex geosystems. Applicationsinvolving compacting materials such as basin evolu-tion or coupled reservoir-geomechanics may need toinclude a more complex constitutive model that al-lows for bifurcating compaction behavior (i.e. Issen& Rudnicki 1999) rather than the uniform deforma-tion that is predicted by traditional cap plasticitymodels (e.g. see Fossum & Fredrich, this volume).Barnichon & Charlier (1999) described recently the


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incorporation of the classic Rudnidci Rice (1975)constitutive theory for shear bifurcation into finiteelement models of sedimentary basin evolution.

Acknowledgement. We gratefully acknowledge sup-port from the U.S. Department of Energy (DOE) Of-fice of Basic Energy Sciences, Chemical Sciences,Geosciences and Biosciences Division. The labora-tory rock mechanics tests were also partially sup-ported by the OffIce of Fossil Energy, National Pe-troleum Technology Oi%ce. This work wasperformed at Sandia National Laboratories fundedby the U.S. DOE under Contract No. DE-AC04-AL85000. Sandia is a multiprogram laboratory op-erated by Sandia Corporation, a Lockheed MartinCompany, for the United States Department of En-ergy.

REFERENCESBarnichon, J.-D. &R. Charlier 1999. Finite element modelingof shear banding in sedimentary basins undergoing tectoniccompression, paper presented at 2nd Euroconference onRock Physics and Rock Mechanics, 14-18 November 1999Edinburgh, Scotland.de Waal, J. A. &R. M. M. Smits 1988. Prediction of reservoircompaction and surface subsidence: Field application of anew model, SPE Form. Eval. p. 347-356.Elf Aquitaine 1991. The role of rock mechanics in oil and gasexploration, Supplement to Nature. 350:8-10.Fossum, A, F. &J. T. Fredrich 1998. Estimation of constitutiveparameters for the Behidge Diatomite, South Belridge Di-atornite field, SAND98-1407: 32 pp. Albuquerque, NewMexico: Sandia National Laboratories.Fossum, A, F. & J. T. Fredrich 2000. Cap plasticity models andcompactive and dilatant pre-failure deformation, Proc. 4North Am. Rock A4ech. Symp. (this volume). Rotterdam:A,A, Balkema.Fredrich, J. T,, J, G, Arguello, B. J. Theme, W. R. Wawersik,G, L. Deitrick, E. P. de Rouffignac, L. R. Myer, &M. S.Bruno 1996. Three-dimensional geomechanical simulationof reservoir compaction and implications for well failuresin the Belridge diatomite, SPE 36698, Proc. 71st ATCE.Houston, Texas: Society of Petroleum Engineers.Fredrich, J. T., G. L. Deitrick, J. G. Arguello &E. P. deRouf-fignac 1997. Reservoir compaction, surface subsidence, andcasing damage A geomechanics approach to mitigationand reservoir management in EurockRock Mechanics in

Petroleum Engineering. v. 1: p. 403-412, SPEIISRM47284. Houston, Texas: Society of Petroleum Engineers.Fredrich, J. T. 1999. 3D imaging of porous media using laserscanning confocal microscopy with application to micro-scale transport processes, Phys. Chem. Earth. 24:551-561.Goldsmith, A. S. 1989, Permeability decline and compressibil-ity in sandstone reservoir rocks, in Rock at Great Depth, p.923-928. Rotterdarn A. A. Balkema.Issen, K.A. & J.W. Rudnicki 1999. Submitted to J. Geophys.Res,Jones, M. E. & M. J. Leddra 1989. Compaction and flow of po-rous rocks at depth, in Rock at Great Depth, p. 891-898.Rotterdarn. A. A. Balkema.

Lockner, D. A. 1993. The role of acoustic emission in the studyof rock fracture, Int. J. Rock Mech. Min. Sci. Geomech.Abstr. 30:883-899.Men6ndez, B., W. Zhu & T.-f. Wong1996.Micromechanicsfbrittlefaultingandcataclasticflowin Bereasandstone,.

Struct. Geol. 18:1-16.Mollema, P.N. & M.A. Antonelli, 1996. Tectonophys. 267:209-228.Myer, L., J. Jacobsen, J. Horsman, J. T. Fredrich, W. R. Waw-ersik, J. G. Arguello, M. Bruno & H. Qian 1996. Use ofvisualization techniques in analysis of well failures in di-atomite reservoirs, The Leading Edge. March 185-189.OConnor, R. M. & J. T. Fredrich 1999. Microscrde flow mod-eling in geologic materirds, Phys. Chem. Earth. 24 611-616.Olsson, W. A. & D. J. Holcomb 2000. Submitted.Olsson, W. A. 1999. Theoretical and experimental investiga-tion of compaction bands in porous rocks, J. Geophys. Res.1047219-7228.Patillo, P.D., T.G. Kristiansen, G.V. Sund & R.M. Kjelstadii,Reservoir compaction and seafloor subsidence at Valhall, inEurockRock Mechanics in Petroleum Engineering. 1: p.377-386, SPEIISRM 47274. Houston, Texas: Society ofPetroleum Engineers.Rhett, D. W., Ekofisk revisited: A new model of Ekofisk Res-ervoir Geomechanical Behavior, in Eurock-Rock Mechan-

ics in Petroleum Engineenng. 1: p. 367-376, SPEIISRM47273. Houston, Texas: Society of Petroleum Engineers.Rudnicki, J. W. &J. R. Rice 1975. Conditions for the localiza-tion of deformation in pressure sensitive dilatant materials,J. Mech. Phys. Solids. 23:371-394.Schutjens, P. M. T. M., T. L. Blanton, J. W. Martin, B. C. Lehr& M. N. Baaijens, Depletion induced compaciton of anoverpressured reservoir sandstone, in Eurock-Rock Me-chanics in Petroleum Engineenng. 2 p. 53-62, SPEIISRM47277. Houston, Texas: Society of Petroleum Engineers.Smits, R. M. M, J. A. de Wad, &J. F. C. van Kooten 1988.Prediction of abrupt reservoir compaction and surface sub-sidence caused by pore collapse in carbonates, SPE Form.Eval., p. 340-346.Teufel, L. W., D. W. Rhett & H. E. Farrell 1991. Effect of res-ervoir depletion and pore pressure drawdown on in sitmstress and deformation in the Ekofisk Field, North Sea, inProc. 32nd U. S. Symp. Rock Mech: pp. 63-72. RotterdrmxA. A. Brdkema.Underwood, E. E. 1970. Quantitative Stereology, 274 pp.Reading, Massachusetts: Addison Wesley.Zhu,W.&T.-f.Wong1997.The transitionfrombrittlefault-ingto cataclasticflow:Permeabilityevolution.1.Geophy.s.Res. 102:3027-3041.

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