Calcite cement distribution and its effect on ﬂuid …AAPG Bulletin, v. 86, no. 12 (December...

AAPG Bulletin, v. 86, no. 12 (December 2002), pp. 2007–2021 2007

Calcite cement distribution andits effect on fluid flow in adeltaic sandstone, FrontierFormation, WyomingShirley P. Dutton, Christopher D. White, Brian J. Willis,and Djuro Novakovic

ABSTRACT

Precipitation of extensive calcite cement during burial diagenesiscan strongly modify the depositional permeability of a sandstonereservoir and affect fluid flow during production. To predict sub-surface flow through cemented reservoirs, permeability distribu-tions used in fluid-flow models must reflect this diagenetic over-print. Calcite cements in sandstones commonly occur as irregularlydistributed concretions, which makes it difficult to predict diage-netic permeability modifications in the subsurface from typicallyspaced wells. Outcrops can provide a continuous image of hetero-geneity produced by concretionary calcite cements.

The size and distribution of calcite concretions were mappedin outcrops of the Frewens sandstone, Frontier Formation, in centralWyoming. Large, tabular calcite concretions in this deltaic sand-stone generally follow basinward-inclined bedding. Median thick-ness of the concretions is 0.6 m, length is 4.2 m, and width is 5.3m. The highest cement fraction is in the high-permeability facies atthe top of the sandstone body. Concretion centers are approxi-mately Poisson distributed within the sandstone. The upward-in-creasing cement fraction is caused by upward-increasing concretionsize. Lateral variation in the fraction of the sandstone cemented bycalcite has a normal distribution, with a mean of 12% (r � 5%).

Spatial distribution of calcite cement in the Frewens sandstonewas modeled using indicator geostatistics. Variograms were inferredfrom outcrop maps of cement. Indicator semivariograms of cementhave a range of 30 m horizontally and 2.5 m vertically, dimensionsthat correspond approximately to the size of the largest concretions.Stochastic images of cement were created using indicator simula-tion with vertically varying cement proportion.

Flow models indicate that concretions make flow paths moretortuous and retard flow in the coarser facies near the top of thesandstone. The fastest path through the sandstone is in the lightly

Copyright �2002. The American Association of Petroleum Geologists. All rights reserved.

Manuscript received July 9, 2001; revised manuscript received May 15, 2002; final acceptance May 28,2002.

AUTHORS

Shirley P. Dutton � Bureau of EconomicGeology, John A. and Katherine G. JacksonSchool of Geosciences, University of Texas atAustin, Austin, Texas, 78713;[email protected]

Shirley P. Dutton received a B.A. degree fromthe University of Rochester and an M.A. degreeand Ph.D. from the University of Texas at Austin,all in geology. She is a senior research scientistat the Bureau of Economic Geology. Herresearch focuses mainly on sedimentology,sedimentary petrology, and clastic diagenesis,particularly the effect of diagenesis on reservoirquality.

Christopher D. White � The Craft andHawkins Department of Petroleum Engineering,CEBA Building Room 3516, Louisiana StateUniversity, Baton Rouge, Louisiana, 70803;[email protected]

Christopher White is a petroleum engineer withresearch interests in reservoir engineering andstatistics. He earned his Ph.D. from StanfordUniversity in 1987. White is an assistantprofessor of petroleum engineering at LouisianaState University and formerly worked at theBureau of Economic Geology and at ShellDevelopment Company.

Brian J. Willis � Texas A&M University,Department of Geology and Geophysics, CollegeStation, Texas, 77843; [email protected]

Brian Willis is an assistant professor in geologyat Texas A&M University. His research interestsinclude understanding sequence stratigraphiccontrols on clastic deposition and quantifyingsedimentologic variations to predict reservoirheterogeneity. He received a B.S. degree fromthe University of Minnesota and an M.S. degreeand Ph.D. from Binghamton University (NewYork). He has been a research fellow at theSmithsonian’s Nature History Museum, aresearch scientist at the Bureau of EconomicGeology, a visiting professor at SUNY-Oswego,and a geologist with BP Canada EnergyCompany.

Djuro Novakovic � The Craft and HawkinsDepartment of Petroleum Engineering, CEBABuilding Room 3516, Louisiana State University,Baton Rouge, Louisiana, 70803;[email protected]

Djuro Novakovic is a petroleum engineer withprofessional interest in reservoir engineering. He

2008 Calcite Cement Distribution and Fluid Flow in a Deltaic Sandstone

cemented, high net-to-gross center of the sandstone body. Be-cause the cement mainly occurs within the highest permeabilityfacies in the sandstone body, a model based on depositional faciesalone would overestimate upscaled permeability of the Frewenssandstone.

INTRODUCTION

Permeability distribution in most sandstone reservoirs is influencednot only by depositional processes, which control grain size, sorting,and shale-bed distribution, but also by postdepositional diagenesis.Precipitation of cements during burial adds a diagenetic overprintto permeability distribution that must be included in reservoir mod-els to simulate fluid flow accurately. Carbonate cement may havea strong influence on fluid flow (for example, Kantorowicz et al.,1987; Saigal and Bjørlykke, 1987; Bjørkum and Walderhaug,1990a; McBride et al., 1995; Morad, 1998) because it is commonlyconcentrated in layers or concretions rather than being uniformlydistributed. The influence of concretionary carbonate cement onfluid flow in reservoirs is not easy to quantify, however, because itis difficult to determine the distribution of this diagenetic hetero-geneity from subsurface data.

Outcrops provide a continuous image of interwell-scale cementdistribution in reservoir analogs. In our study, calcite concretionswere mapped in a well-exposed outcrop of a deltaic sandstone, andthe effects of the concretions on fluid flow were quantified by flowmodeling. The outcrop exposes the Upper Cretaceous Frewenssandstone, the deposit of a tide-influenced delta in the Frontier For-mation of central Wyoming. Our goals were to (1) quantify the sizeand spatial distribution of calcite concretions, (2) model the effectof the cement on fluid flow, and (3) provide geostatistical data thatcan be used to condition models of concretionary calcite-cementdistribution in the subsurface.

Our study demonstrates the importance of including diagene-sis-modified permeability distribution in reservoir models of ce-mented sandstones. Although concretion dimensions and distribu-tion may be different in analog reservoirs, few geostatistical datasets for such diagenetic features are available in the literature. Inthe absence of reservoir-specific information, the Frewens data canbe used to stochastically estimate cement distribution in analogousdeltaic sandstones.

GEOLOGIC SETT ING

Deposition of the Frewens Sandstone

The Frewens sandstone (Figure 1) is interpreted to be deposits of atide-influenced delta that prograded into the Cretaceous Interiorseaway (Willis et al., 1999; Bhattacharya and Willis, 2001). The

ACKNOWLEDGEMENTS

This research is a product of the Clastic Reser-voirs Group at the Bureau of Economic Geology,University of Texas at Austin, sponsored byAmoco Production Company; BP Exploration Op-erating Company Limited; Chevron Oil Field Re-search Company; Conoco, Inc.; Elf ExplorationProduction; Exxon Production Research Com-pany; Intevep S.A.; Japan National Oil Company;Maxus Energy Corporation; Occidental Interna-tional Exploration and Production, Inc., and OXYUSA, Inc.; Oryx Energy Company; Saga Petro-leum; Statoil; and Union Oil Company of Califor-nia. Parts of this research were supported by theCraft and Hawkins Department of Petroleum En-gineering at Louisiana State University. Partialsupport of publication costs was provided by theOwen-Coates Fund of the Geology Foundation,University of Texas at Austin. Janok P. Bhatta-charya interpreted the regional stratigraphic set-ting of the Frewens and other Frontier sand-stones in the outcrop and adjacent subsurfacearea. James Jennings provided guidance and in-sight into geostatistical procedures. Sharon Ga-bel, Charl Broquet, and Christopher Swezey didfieldwork, mapped, and helped interpret the ge-ology. Yugong Gao prepared the digitized out-crop diagrams. Isotopic analyses were done atthe Stable Isotope Laboratory, directed by PeterSwart, at the University of Miami’s RosenstielSchool of Marine and Atmospheric Science. Res-ervoir simulation software was provided byComputer Modeling Group, Ltd., and Schlumber-ger Technology Company. Illustrations were pre-pared by the graphics staff of the Bureau ofEconomic Geology under the direction of JoelLardon, graphics manager. Thomas L. Dunn,Earle F. McBride, an anonymous reviewer, andBulletin editor John C. Lorenz provided construc-tive reviews that improved this article. Publishedby permission of the director, Bureau of Eco-nomic Geology, University of Texas at Austin.

holds an M.S. degree in petroleum engineeringand is a doctoral candidate at Louisiana StateUniversity.

Dutton et al. 2009

Powder RiverPowder RiverPowder River

Big HornBig HornBig Horn

Study areaStudy areaStudy area

CasperCasperCasper

SevierSevierSevierOrogenicOrogenicOrogenic

BeltBeltBelt

WYOMINGWYOMINGWYOMING

Wind RiverWind RiverWind River

GreaterGreaterGreaterGreenGreenGreenRiverRiverRiver

0 100 mi

0 100 km

N

Laramide basins

Figure 1. Location of the study area on the west margin ofthe Powder River basin and the position of other Laramide ba-sins in Wyoming (modified from Dutton et al., 2000).

sandstone is elongate into the basin (southeast) andcontains two upward-coarsening internal sandstonebodies, each as much as 30 m thick, 3–4 km wide, andabout 20 km long (Willis et al., 1999). The bodies eachrecord delta-lobe progradation into a narrow troughbetween an older wave-dominated delta lobe to thesouth and a basin-floor ridge created by subtle struc-tural uplift to the north (Bhattacharya and Willis,2001). Both sandstone bodies have gradational basesand sharp upper contacts with overlying shales. Thesandstone bodies are composed of meters-thick, sea-ward-inclined beds that tend to be sandier updip andmore heterolithic downdip. Beds record deposition ofsands during rapid delta-front progradation, followedby the more gradual aggradation of shales and tidalreworking.

Frewens sandstones are composed of five faciesthat generally occur in the following upward-coarsen-ing succession: (1) thinly interbedded, rippled sand-stones and mudstones; (2) decimeter-thick sandstonebeds isolated within facies 1; (3) meter-thick beds ofheterolithic cross sets; (4) meter-thick beds of rela-tively homogeneous, cross-stratified sandstones; and(5) meters-thick cross sets of homogeneous sandstone(Willis et al., 1999). The abrupt top of the sandstonebodies records transgressive ravinement during flood-ing of the delta (Willis et al., 1999). The transgressive

unconformity above the Frewens sandstone juxtaposesshell-bearing marine shales close to the top of the up-per Frewens sandstone (Cobbin et al., 1994; Bhatta-charya and Willis, 2001).

Origin of Frewens Concretions

Iron-bearing calcite is the most abundant cement in theFrewens sandstone, ranging in volume from 0 to 36%(average 2.6%) (Dutton et al., 2000). Most of the cal-cite cement is localized in concretions. These large,tabular concretions generally follow bedding but mayterminate within a bed or cut across facies. Many con-cretions are adjacent to shale drapes, either at the topof sandstone beds below a shale or at the base of sand-stone beds above a shale. Calcite in many concretionshas partly dissolved, probably since being exposed inoutcrop, and hematite has precipitated in the resultingpores. The hematite gives the concretions a reddishcolor, easily distinguished from uncemented sand-stones. The Frewens sandstone outcrops consequentlyprovide an excellent opportunity to map cement dis-tribution at the interwell scale.

In a previous study, petrographic and isotopic datawere used to interpret the origin of the calcite cementin the Frewens sandstone and the timing of its pre-cipitation (Dutton et al., 2000). The d18O compositionof the calcite ranges from �9.3 to �12.4‰ (Peedeebelemnite [PDB]), and the d13C composition rangesfrom �0.1 to �14.2‰ (PDB). The calcite cement isinterpreted as having precipitated near maximum bur-ial depth (1.5 km), from evolved meteoric water ormixed meteoric-marine pore water (Dutton et al.,2000).

The d13C composition indicates that the source ofcarbon was mostly biogenic carbonate, with a contri-bution of 13C-depleted carbon derived from oxidationor decarboxylation of organic matter. No fossil frag-ments or molds of dissolved fossils, and very few tracefossils of burrowing organisms, have been observed inFrewens sandstone, suggesting that little internal bio-genic carbonate existed. Instead, shell-bearing marineshales above the upper Frewens sandstone are inter-preted to be the source of the biogenic carbonate (Dut-ton et al., 2000).

The lack of an internal source of calcite cementimplies that the Frewens concretions formed by fluidadvection. At the relatively shallow maximum burialdepth of 1.5 km, the hydrologic regime in whichthe concretions formed was probably dominated bymeteoric flow, although shallow compactional flow


continued as well (Dutton et al., 2000). Compactionof the overlying marine shale appears to have expelledfluids containing calcium and biogenic carbonate intothe Frewens sandstone, where it mixed with meteoricwater in the regional groundwater flow system. Be-cause permeability in the sandstone was greatest in theplane of bedding, flow followed bedding and concre-tions grew most rapidly in that direction, resulting intheir tabular shape (McBride et al., 1994, 1995; Moz-ley and Davis, 1996).

DIMENSIONS AND DISTRIBUTION OFCALCITE CONCRETIONS

Cement distribution was quantified in a 362 m–longdip-parallel outcrop wall (Figure 2) and an adjacent216 m–long strike-parallel wall of the upper Frewenssandstone. Photomosaics of the two outcrop walls wereproduced by digitally splicing together a succession ofphotographs taken on medium-format film from a hel-icopter. Digital maps of bedding, facies, shale beds, andcements were made from the photomosaics (Willis andWhite, 2000).

The size and spatial distribution of concretions inthe upper Frewens sandstone were measured from theoutcrop maps. Apparent length and thickness of 110concretions were measured in the dip-parallel outcropwall, and apparent widths of 43 different concretionswere measured in the adjacent strike-parallel wall.Concretions as thin as about 15 cm were mapped; thin-ner concretions were not resolved. Concretion thick-ness was not measured in the strike wall because thedip of the beds and the backstepping of the outcropface made it difficult to determine thickness accurately.

Limits of data collection were the edges of the ex-posed outcrop, but irregular outcrop boundaries cancause significant artifacts in fluid-flow simulation (Wil-lis and White, 2000). To maximize the size of a rec-tangular flow-model interval, facies and bedding wereextrapolated short distances beyond the outcrop limits,but cement bodies were not extrapolated. Thus, someareas at the top of the flow model show no concretionsbecause that area of the outcrop was not exposed.

Calcite concretions occur in both the upper andlower Frewens sandstone bodies, but they are consid-erably more abundant in the upper body, particularlyin the high-permeability, cross-stratified facies in theupper part of the sandstone. In the dip-parallel wall,66% of the concretions occur in facies 5 and 23% infacies 4 (Figure 2).

Median dimensions of the concretions are 0.6 m inthickness (T), 4.2 m in length (L), and 5.3 m in width(W) (Figure 3A–C). The median aspect ratio (T/L) ofthe concretions exposed in the dip section is 0.11 (Fig-ure 3D). McBride et al. (1995) described concretionswith aspect ratios less than 1.5:1 (T/L � 0.67) asequant and concretions with aspect ratios greater than2.5:1 (T/L � 0.4) as elongate. Concretions of inter-mediate dimensions are considered subequant. By thatdefinition, most Frewens concretions are elongate(96%), and a few are subequant (4%). The volumes ofthe concretions exposed in the dip wall were calculatedby assuming that the concretions are ellipsoids inwhich relations between thickness and length andthickness and width were the same (Dutton et al.,2000). Most concretions are small (�40 m3), but a fewhave volumes greater than 500 m3 (Dutton et al.,2000). The median volume is 4.4 m3.

Concretions make up 12% of the area exposed inthe dip-parallel outcrop wall. The percentage of thesandstone cemented by calcite ranged laterally be-tween 0 and 27% (Figure 4); this proportion was nor-mally distributed with a standard deviation of 5%. Arandomly drilled vertical well through the sandstonewould be cemented over 2–22% of its length in 95 outof 100 cases (two standard deviations).

Cement abundance increases toward the top ofthe outcrop (Figure 5), but this vertical trend is irreg-ular with a standard deviation from mean values of11%. In the lower 10 m of the sandstone only 2% ofthe deposits are cemented on average, whereas in theupper 11 m of the sandstone 21% of the deposits arecemented on average. Although evidence for de-creased cements in the upper 3 m of the outcrop (Fig-ure 5) is probably an artifact of sampling across theirregular upper outcrop edge, others have reported ex-amples where shale-derived calcite did not precipitatedirectly at the shale-sandstone contact (Sullivan andMcBride, 1991; McBride et al., 1995; Taylor et al.,2000).

The distribution of concretions can be quantifiedby plotting their centers (Figures 6, 7). Concretion cen-ters appear to be randomly distributed across the out-crop and are spaced on average at about one per 70m2. A statistical test to determine if concretion centersare randomly distributed compared variability in thenumber of concretion centers exposed in specific sub-sampled regions of the outcrop to variability predictedassuming concretions centers are a univariate Poisson-distributed random variable. The observed concretioncounts were compared with those predicted using a

Duttonet

al.2011

West

East

0

0 20 m

80 ft

Facies 5Facies 4Facies 3Facies 2 Concretion

Mat

ch li

ne

Mat

ch li

ne

Ver

tical

pos

ition

(m

)

10

0

Ver

tical

pos

ition

(m

)

10

0

200 300Horizontal position (m)

100

Facies 1

Figure 2. Dip-oriented outcrop wall of the Frewens sandstone that was used to quantify concretion size and distribution (modified from Willis and White, 2000). Concretionsare the darker areas on the photomosaic within the light-colored sandstone. A graphic overlay made from the photomosaic shows distribution of facies and concretions.


0 0.5 1 1.5 2 2.5

99.99

99.9

99

9590807050302010

5

1

.1

.010 10 20 30 40 50

99.99

99.9

99

9590807050302010

5

1

.1

.01

99.99

99.9

99

9590807050302010

5

1

.1

.010 20 40 60 80 100

2.5

2

1.5

1

0.5

00 10 20 30 40 50

Cum

ulat

ive

perc

ent

Cum

ulat

ive

perc

ent

Cum

ulat

ive

perc

ent

Thi

ckne

ss (

m)

1:1 2.5:1

(A) (B)

(C) (D)

Thickness (m) Length (m)

Width (m) Length (m)

Mean = 0.6Median = 0.6St. Dev. = 0.4



Figure 3. Plots of (A) concretion thickness, (B) length, and (C) width vs. cumulative percent and (D) crossplot of length and thickness.McBride et al. (1995) described concretions with aspect ratios greater than 2.5:1 (T/L � 0.4) as elongate. According to that definition,most Frewens concretions are elongate.

Figure 4. Horizontal variationin cemented fraction of the up-per Frewens sandstone body.This plot is equivalent to takinga series of vertical wellsthrough the outcrop and mea-suring the fraction of the sand-stone thickness that is ce-mented. The cemented fractionhas a normal distributionaround a mean of 0.12 (r �0.05).

Cem

ente

d fr

actio

n

Horizontal profile

Running average

Horizontal position (m)

0

0.05

0.1

0.15

0.2

0.25

0.3

0 50 100 150 200 250 300 350 400

Dutton et al. 2013

Ver

tical

pos

ition

(m

)

Cemented fraction0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

0

5

10

15

20

Figure 5. Vertical variation in cemented fraction of the upperFrewens sandstone body. This plot is equivalent to taking aseries of horizontal wells through the outcrop and measuringthe fraction of the sandstone thickness that is cemented. Ce-mented fraction increases toward the top of the outcrop. Thelower 10 m of the outcrop has an average cemented fractionof 0.02, whereas the upper 11 m has an average of 0.21. Thecemented fraction has a bimodal distribution, with a mean of0.12 (r � 0.11).

Out

crop

hei

ght (

m)

Outcrop length (m)

0

10

20

0 100 200 300

Figure 6. Plot showing thecenters of all concretions. Thecentroid positions approximatea univariate Poisson-distributedrandom variable in both x andz. The concretion centers tendto be aligned along the dippingforesets.

outcrop) have an average area of 1.6 m2, whereas thosein the upper part of the outcrop average 7.7 m2. Thelarger concretions at the top of the sandstone may havebeen formed by the aggregation of multiple originalnucleation centers. As the individual concretions grew,many of those at the top of the sandstone may havegrown together. The shapes of many of the largest con-cretions (Figure 2) suggest that they formed by aggre-gation of one or more concretions.

COVARIANCE MODELS FOR CEMENTDISTRIBUTION

Geostatistics based on covariance is used widely tomodel both continuous and categorical variables.Compared with object models, covariance models aresimpler to condition to observations and are sometimessimpler to infer. Methods of inferring variograms andcreating stochastic images (or simulations) for contin-uous and categorical (or indicator) variables are welldocumented (e.g., Deutsch and Journel, 1998).

Computing the Indicator Semivariograms

Indicator semivariograms were calculated to show ver-tical and horizontal anisotropy in the cement distri-bution within the Frewens sandstone. In this calcula-tion, cement was transformed to an indicator variableassigned a value of 1 if cement were present at a givenlocation and 0 if absent. The horizontal semivariogramhas a range of about 30 m, and the vertical semivari-ogram has a range of about 2.5 m (Figure 10). Thesedimensions correspond approximately to the size ofthe largest concretions in the Frewens sandstone.

The variance of the indicator variable is 0.104 [�fc(1 � fc), where fc is the cement fraction]. The hori-zontal semivariogram never reaches the total variancebecause of the vertical trend in cement fraction. Thevertical semivariogram is remarkably well behaved. Itis linear at small distances, and there is a suggestion of

Poisson model, where k � 0.014 m�2 (0.014 m�2 �

1 concretion/70 m2 of outcrop) and testing against thev2 statistic at the 90% significance level (Figure 8). Thetest confirmed that concretion centers were approxi-mately Poisson distributed. The concretion locationsare only weakly correlated spatially (C. D. White,2001, unpublished data).

The lack of correlation in concretion centroid lo-cations indicates that the upward increase in cement(Figure 5) does not reflect a vertical increase in thenumber of concretions. Instead, the observed trend iscaused by an upward increase in the size of the con-cretions (Figure 9). Concretions in the lower part ofthe Frewens sandstone (lower 10 m of the dip-parallel


cyclicity (or a so-called hole effect) with a wavelengthof approximately 3.3 m. This cyclicity is seen in thedecrease of the semivariogram at approximately 6.6 mand the excursion above the semivariogram sill at ap-proximately 10 m (Figure 10).

Cement distribution is clearly anisotropic; that is,its pattern of spatial variability changes with direction.The direction of greatest continuity is inclined 2.5�downward to the right, following depositional dip. Thedirection of least continuity is nearly vertical. Theanisotropy factor for the cement, defined as the ratioof the range in the greatest and least continuity direc-tions (Kupfersberger and Deutsch, 1999), is approxi-mately 12. Because the horizontal and vertical semi-variogram sills are not equal, the anisotropy is zonalrather than geometric (Deutsch and Journel, 1998, p.27–30). This feature can be modeled by using nestedstructures; the horizontal range of the additional vari-ance component (needed to model the zonal aniso-tropy) is set to a very large value.

Distributing Cement in Reservoir Models

Many deltaic sandstone reservoirs have evidence fromcores or geophysical logs (particularly density and neu-tron logs [Walderhaug et al., 1989; Worden and Ma-tray, 1998]) that calcite concretions are present (forexample, Ambrose et al., 1995). To be realistic, a res-ervoir simulation should attempt to capture the dia-genetic permeability overprint, as well as facies-con-trolled permeability trends. Reservoir-specific datafrom logs and core could be used to condition the mod-

0

10

20

30

40

50

0 1 2 3 4

Number of concretions in bin

Cou

nt F

requ

ency

Observations -- Vertical Bins

Observations -- Horizontal Bins

Poisson Model, λ = 0.014/m2

Figure 8. The frequency of concretions observed on the out-crops is matched adequately by a Poisson model with k �0.014 m�2. In the vertical and horizontal directions, the Poissonmodels cannot be rejected at the 90% confidence level usingv2 tests.

Figure 7. (A) Horizontal and(B) vertical frequency distribu-tion of concretion centers.

0

5

10

15

20

0 50 100 150 200 250 300 350 400

Fre

quen

cy

Outcrop length (m)

0

5

10

15

20

0 5 10 15

Frequency

Out

crop

hei

ght (

m)

(A) (B)

0

5

10

15

20

0 10 20 30 40 50 60 70

Out

crop

hei

ght (

m)

Area in dip wall (m2)

Figure 9. Plot of concretion area vs. height in the outcrop wallshows an upward increase in the size of concretions. This up-ward increase in concretion size, not an increase in the numberof concretions, is the reason that cemented fraction increasesvertically (Figure 5).

Dutton et al. 2015

els that predict the size and spatial distribution ofconcretions.

The outcrop data described in a preceding sectionsuggest that two different types of models could beconsidered to predict the distribution of calcite con-cretions in the subsurface: (1) a method that assumesa Poisson distribution for concretion centers and con-ditions concretion abundance, size, and shape fromvertical well logs, analog outcrop data, or both; or (2)a geostatistical approach based on variography. ThePoisson approach would be similar to the way shale-length data are used in object modeling (Begg andKing, 1985; MacDonald and Halland, 1993; Robinsonand McCabe, 1997). However, the relatively low r2

values (Figure 9) for the dimensional correlations sug-gest that it would be difficult to reproduce the ob-served trends in cement using this Poisson process, andobject models may be more difficult to condition. Anindicator variogram approach may be more useful forsubsurface prediction of concretions using the Frewenssandstone data set.

An indicator variogram model to predict subsur-face cement distribution is developed in White et al.(C. D. White, 2001, unpublished data) and is brieflydiscussed here to demonstrate one possible use of thetype of outcrop analog data presented here. An indi-cator variogram (for example, Figure 10) of cementoccurrence is converted to equivalent variograms for atruncated Gaussian variable (Matheron et al., 1987).

Once cement distribution is described in terms of aGaussian variable, it is relatively easy to include ob-served trends in cement abundance. Images of cementconcretions are created by imposing a vertically varyingtruncation probability (a proportion curve) on a geo-statistically simulated Gaussian variable. The trunca-tion process transforms the Gaussian simulations to ce-mented vs. noncemented indicator maps. These mapsare refined using a simulated annealing algorithm(Deutsch and Journel, 1998) to improve conformancebetween specified and simulated semivariograms. Onlythe variogram is used in the annealing procedure, sothat the annealing could be applied in three dimen-sions. Multipoint statistics (Caers et al., 2000) con-densed the diffuse zones of cement predicted by Gaus-sian simulation to compact concretions observed inoutcrop. The multipoint probabilities are more diffi-cult to translate to three dimensions. An example im-age is shown in Figure 11. The concretions mapped inoutcrop (Figure 11A) and those predicted by this geo-statistical simulation (Figure 11B) share many features:the overall proportion of cement is the same, the ver-tical trend is the same, and the angle of inclination ofthe cemented regions appears to be approximately cor-rect. Similar images could be constructed for subsur-face reservoirs using core-defined proportion curvesand the variograms defined from this outcrop study.

FLUID-FLOW SIMULATION

The influence that concretions would have on fluidflow in a reservoir was demonstrated using reservoirsimulation. Flow through the dip-parallel Frewens out-crop wall was modeled in two dimensions; develop-ment of this reservoir-simulation model from quanti-tative outcrop data was described in Willis and White(2000), and methods to quantify effects of geologicvariability on reservoir-simulation predictions are de-scribed in White et al. (2001). For the simulationsshown here, depositional permeability variations weredefined by a mean permeability for each facies type anda decrease in transmissibility between beds with drap-ing shales (White and Barton, 1999) (Figure 2). Per-meability, determined from more than 2900 measure-ments on the outcrop using a probe-style, steady-statepermeameter, ranged from 460 md in facies 1 to 3100md in facies 5. Areas within calcite concretions wereassigned a permeability of 0.1 md. The flow models(Computer Modeling Group, 1997; SchlumbergerTechnology Company, 1997) simulated a waterflood

Indi

cato

r S

emiv

ario

gram

Vertical Lag (m)

Horizontal Lag (m)

0 5 10 15

0

0.04

0.08

0.12

0 20 40 60 80 100

ModelVertical dataSill: s2 = 0.1037

Model Horizontal data

Figure 10. Indicator semivariograms summarize the spatialcorrelation of calcite cement. The vertical separation distance isplotted on the axis at the top of the figure. Cement fraction iscorrelated horizontally for at least 30 m, and the vertical rangeis approximately 2.5 m. The oscillation in the vertical semivari-ogram may be due to cyclicity in cement occurrence. The os-cillation in the horizontal semivariogram may not be significant.


Figure 11. (A) The referenceimage and (B) a geostatisticalimage of cement appear to besimilar. The geostatistical imagereproduces the reference imagesemivariograms and thesmoothed vertical trend in ce-ment proportion. The geostatisti-cal image was prepared usingtruncated Gaussian simulation,simulated annealing, and multi-point statistics. The geostatisti-cal image is conditioned at thetwo ends of the outcrop panel;note that the two images(A and B) match at the extremeleft and right ends.

10

50 mVertical exaggeration = 5x

0

m

150 ft

ft

30

0

Cement No cement

(B)

(A)

displacing oil. The water is injected into the left sideof the simulation models, and oil and water are pro-duced from the right side. The distribution of oil andwater are shown after one-half of the pore volume ofthe model has been injected (Figure 12).

The effect of concretions on flow can be seen bycomparing reservoir models with and without concre-tions. Concretions make flow paths more tortuous andcause breakthrough to occur lower in the section.Without concretions, breakthrough occurs first in thecoarse facies 5 interval at the top of the section (Figure12B). With concretions, breakthrough occurs lower inthe section (in facies 3 and 4) because flow is retardedby the abundance of cement near the top of the sand-stone body (Figure 12C). By preferentially reducingpermeability of the coarsest grained facies, concretionsmay actually improve the vertical sweep efficiency ofdisplacements.

Concretions significantly reduce upscaled perme-ability compared with uncemented sandstones. Theupscaled permeability of this two-dimensional panel ofFrewens sandstone was calculated by solving the

steady-state flow equation for the permeability distri-bution with and without concretions. The presence ofthe concretions decreases the upscaled permeability ofthe modeled area by about 45% compared with a sand-stone having the same shale-bed and facies distributionbut no concretions (from 1220 to 667 md). Concre-tions have a large impact on upscaled permeability be-cause the cement occurs within the most permeablepart of the sandstone body. A model based on depo-sitional facies alone would significantly overestimateupscaled permeability, thus demonstrating the impor-tance of including diagenetic permeability modifica-tion in detailed reservoir models.

The upscaled permeability derived from thesteady-state flow solution was compared to the geo-metric and arithmetic mean permeabilities. The geo-metric mean is kg � , where kg is the overallf 1�f¯c ck kc ss

geometric mean, kc is the concretion permeability, andkss is the upscaled permeability of the unaltered sand-stone. The concretion fraction is fc. The heterogeneoussandstone permeability was upscaled using a steady-state flow solution to estimate kss. The geometric mean

Dutton et al. 2017

0Water saturation (fraction)

1

Permeability (md)0 2500

Vertical exaggeration 3

200 ft0

50 m0

(A)

(B)

(C)

Cemented zone Shale

Inle

tIn

let

Out

let

Out

let

x

Figure 12. Reservoir simulation was used to examine the influence that concretions would have on fluid flow in a reservoir. Willisand White (2000) described preparation of the outcrop data for flow simulation. (A) Distribution of shale beds and concretions inthe dip-parallel outcrop wall that was modeled in two dimensions. (B) Simulation including shales but not concretions (modified fromWillis and White, 2000). Low-permeability, inclined shales have a pronounced effect, shunting flow along the dip of the clinoformbeds. (C) Simulation including both shales and concretions (modified from Willis and White, 2000). Cemented regions make the flowpath more tortuous and reduce effective permeability by about one-half. Concretions cause breakthrough to occur earlier and lowerin the section because they retard flow most in high-permeability facies near the top of the sandstone body.


Figure 13. The water satura-tions for (A) the reference caseand (B) a geostatistical cementimage are similar. Correspond-ing cement images are shownin Figure 11. Breakthrough oc-curs somewhat earlier in thereference case than in the geo-statistical image (note the largerlight area in the right center ofthe reference saturation image),but the overall front shapesmatch reasonably well.

10

50 mVertical exaggeration = 5x

0

m

150 ft

ft

30

0

(B)

(A)

Wat

er in

ject

ed o

n th

is s

ide

of m

odel

Wat

er a

nd o

il pr

oduc

ed fr

om th

is s

ide

of m

odel

Water saturation

0 1

underestimates upscaled permeability (kg � 550 mdvs. ktrue � 667 md from the steady-state flow model).The arithmetic mean, ka � fckc � (1 � fc)kss, over-estimates the upscaled permeability (ka � 1070 md).The arithmetic and geometric mean bound the up-scaled horizontal permeability, kg � ktrue � ka (Card-well and Parsons, 1945; Li et al., 1999). For this case,the bounds are wide, 550 md � ktrue � 1070 md.

Reservoir behavior was also simulated for theFrewens sandstone with calcite concretions modeledby the geostatistical methods of White et al. (C. D.White, 2001, unpublished data). The flow effects ofthe outcrop-mapped concretions (Figure 13A) werecompared to those of the geostatistical calcite concre-tions (Figure 13B). To clarify comparison of concretioneffects on flow, facies permeability variations were theonly depositional heterogeneity included in these res-ervoir simulations (shales were not included). Al-though details of these flow models differ, the visualsimilarity of displacement predicted by these two mod-els is compelling. First breakthrough occurs in the cen-ter and a secondary breakthrough occurs in the top ofboth models. A statistical analysis of flow effects pro-duced by stochastic concretions has been performed onthe basis of many models and multiple realizations

(C. D. White, 2001, unpublished data). This analysisshowed that predictions of breakthrough time, averagepermeability, and sweep efficiency are similar for mod-els based on concretions mapped in the outcrop andthose with geostatistical concretions. The differencebetween the mean responses of models with geosta-tistical concretions and the model with outcrop con-cretions is less than 5%, and the range of the stochastic-model responses includes those predicted by theoutcrop model for most responses. Unlike upscaledpermeability, there are no analytic formulae to predictthe effects of permeability heterogeneity on break-through time or sweep efficiency.

DISCUSSION

In the past 15 years, considerable work has been donemeasuring horizontal permeability variation caused bydepositional processes (see articles summarized inKupfersberger and Deutsch [1999]), but similar stud-ies of diagenetic heterogeneity lag behind. Little quan-titative information is available in the literature on thedistribution of calcite concretions in deltaic sandstones,so it is difficult to know whether the Frewens cement

Dutton et al. 2019

distribution is characteristic or how widely this modelcan be applied to other sandstones. Many excellent in-vestigations of calcite concretions have been publishedrecently (for example, Bjørkum and Walderhaug,1990a, b; Wilkinson, 1991; McBride et al., 1995; Tay-lor et al., 1995, 2000; Milliken et al., 1998; Walder-haug and Bjørkum, 1998; Klein et al., 1999), but mostresearchers focused on the origin of the calcite cementrather than on quantitative data that can be used topredict low-permeability cement bodies in reservoirmodels. In addition, most of these studies have beenof shallow-marine and shoreface deposits or turbidites,in which the concretions grew by diffusion from aninternal source of biogenetic carbonate.

Most of the Frewens concretions occur in thecoarsest, most permeable sandstones high in the sand-stone body, above the position where shale-bed drapesare abundant (Figure 12A). It appears that the fluidscarrying calcium and biogenic carbonate into the Frew-ens sandstone from the overlying fossiliferous shaleprecipitated calcite where fluid flow was greatest. Theflow simulation that includes only facies and shale beds(Figure 12B) can be considered a model of fluid flowin the Frewens sandstone before cementation began; ina sense, the simulation provides a forward model of theregional flow system in which we think the concretionsprecipitated.

A greater concentration of cement in the most po-rous and permeable sandstones was observed on alarger scale as well. The Frewens sandstone bodiesshow systematic trends across successive beds overhundreds of meters, defined by an alternation ofthicker, sandier, more steeply inclined beds with thin-ner, finer grained, more gently inclined beds (Willis etal., 1999). Although not quantified, cement is mostabundant in the sandier beds. Similarly, cement ap-pears to be more abundant in the sand-rich deposits atthe axes of the sandstone bodies than in the finergrained deposits along the margins. The outcrop doc-umented in our study was a relatively sand-rich part ofthe Frewens interval, along the axis of the progradingdelta. More work is needed to demonstrate whetherthe distribution of concretions observed here is alsocharacteristic of the more heterolithic delta-margindeposits.

The Frewens concretion model would be most ap-propriately applied to analogous reservoirs in upward-coarsening, deltaic sandstones lacking internal shellmaterial and overlain by marine shales. The Frewenssandstones are interpreted to have derived their sedi-ment primarily from a tide-reworked fluvial influx on

rapidly prograding tidal-channel-mouth bars. Shellswere sparse in this brackish setting, and most of thecalcite cement was derived from overlying fossiliferousshales. It is probably not appropriate to apply the Frew-ens concretion model to sandstones containing abun-dant internal biogenic carbonate. Unlike the Frewenssandstone, the location of concretions in these sand-stones generally reflects diffusional redistribution ofbiogenic carbonate whose location was controlled bydepositional environment (Bjørkum and Walderhaug,1990a, b; Walderhaug and Bjørkum, 1998). Clearly,more studies like that presented in this article are re-quired before a general model for calcite-concretiondistribution in sandstones can be advanced.

CONCLUSIONS

Frewens sandstones have been variably overprinted bydiagenesis, most significantly by precipitation of calciteconcretions whose permeability contrasts markedlywith the surrounding uncemented or poorly cementedhost sandstones. The concretions are tabular, with theirshort dimension perpendicular to bedding. The calciteoccurs mainly in the coarser grained facies at the topof the upper Frewens sandstone body. Concretion cen-ters are randomly distributed. On average 12% of thesandstone is cemented, but this value ranges between2 and 22% laterally along the outcrop. Cements in-crease upward because concretions are larger towardthe top of the sandstone. Fossiliferous intervals in theoverlying transgressive marine shale are inferred to bethe source of calcium carbonate.

Data on the spatial distribution of cement deter-mined from the Frewens sandstone can be used to pop-ulate permeability models of deltaic sandstones havingsimilar diagenetic histories if reservoir-specific data arenot available. The spatial distribution of cement in theFrewens sandstone can be modeled using indicatorsemivariograms. The presence and vertical distributionof cement in a reservoir can generally be determinedfrom log and core data. This information can be usedto condition the simulation and estimate vertical trendsin cement proportion, while using the Frewens data tomodel the spatial correlation of cement.

Flow models of the Frewens sandstone indicatethat modeling permeability from depositional faciesalone will overestimate upscaled permeability and in-correctly predict flow paths. Upscaled permeability ofthe upper Frewens sandstone body is reduced by abouthalf compared with that of an uncemented sandstone,


and concretions cause fluid breakthrough to occurlower in the section because they retard flow in thecoarser facies near the top of the sandstone body.

REFERENCES CITED

Ambrose, W. A., E. R. Ferrer, S. P. Dutton, F. P. Wang, A. Padron,W. Carrasquel, J. S. Yeh, and N. Tyler, 1995, Production op-timization of tide-dominated deltaic reservoirs of the LowerMisoa Formation (lower Eocene), LL-652 area, Lagunillas field,Lake Maracaibo, Venezuela: University of Texas at Austin, Bu-reau of Economic Geology Report of Investigations 226, 46 p.

Begg, S. H., and P. R. King, 1985, Modelling the effects of shales onreservoir performance: calculation of effective vertical perme-ability: Society of Petroleum Engineers Reservoir SimulationSymposium, SPE Paper 13529, p. 331–344.

Bhattacharya, J. P., and B. J. Willis, 2001, Lowstand deltas in theFrontier Formation, Powder River basin, Wyoming: implica-tions for sequence stratigraphic models: AAPG Bulletin, v. 85,p. 261–294.

Bjørkum, P. A., and O. Walderhaug, 1990a, Geometrical arrange-ment of calcite cementation within shallow marine sandstones:Earth-Science Reviews, v. 29, p. 145–161.

Bjørkum, P. A., and O. Walderhaug, 1990b, Lateral extent of calcite-cemented zones in shallow marine sandstones, in A. T. Buller,E. Berg, and O. Hjelmeland, eds., North Sea oil and gas reser-voirs–II: London, Graham and Trotman, p. 331–336.

Caers, J. K., S. Srinivasan, and A. G. Journel, 2000, Geostatisticalquantification of geological information for a fluvial-type NorthSea reservoir: Society of Petroleum Engineers Reservoir Eval-uation and Engineering, v. 3, no. 5, p. 457–467.

Cardwell, W. T., and R. L. Parsons, 1945, Average permeability ofheterogeneous oil sands: Transactions of the American Instituteof Mining and Metallurgical Engineers, Petroleum Division,v. 160, p. 34–42.

Cobbin, W. A., E. A. Merewether, T. D. Fouch, and J. D. Obrado-vich, 1994, Some Cretaceous shorelines in the Western Interiorof the United States, in M. V. Caputo, J. A. Peterson, and K. J.Franczyk, eds., Mesozoic systems of the Rocky Mountain re-gion, U.S.A.: Rocky Mountain Section SEPM, p. 393–413.

Computer Modeling Group, 1997, IMEX Version 97 advanced oil/gas reservoir simulator’s guide: Calgary, Alberta, Canada, Com-puter Modeling Group, 593 p.

Deutsch, C. V., and A. G. Journel, 1998, GSLIB: geostatistical soft-ware library and user’s guide: New York, Oxford UniversityPress, 369 p.

Dutton, S. P., B. J. Willis, C. D. White, and J. P. Bhattacharya, 2000,Outcrop characterization of reservoir quality and interwell-scale cement distribution in a tide-influenced delta, FrontierFormation, Wyoming, USA: Clay Minerals, v. 35, p. 95–105.

Kantorowicz, J. D., I. D. Bryant, and J. M. Dawans, 1987, Controlson the permeability and distribution of carbonate cements inJurassic sandstones: Bridport Sands, southern England, and Vi-king Group, Troll field, Norway, in J. D. Marshall, ed., Diagen-esis of sedimentary sequences: Oxford, Blackwell, p. 103–118.

Klein, J. S., P. Mozley, A. Campbell, and R. Cole, 1999, Spatialdistribution of carbon and oxygen isotopes in laterally extensivecarbonate-cemented layers: implications for mode of growthand subsurface identification: Journal of Sedimentary Research,v. 69, p. 184–191.

Kupfersberger, H., and C. V. Deutsch, 1999, Methodology for in-tegrating analog geologic data in 3-D variogram modeling:AAPG Bulletin, v. 83, p. 1262–1278.

Li, D., B. Beckner, and A. Kumar, 1999, A new efficient averagingtechnique for scaleup of multimillion-cell geologic models: So-ciety of Petroleum Engineers Annual Technical ConferenceandExhibition, SPE Paper 56554, 15 p.

MacDonald, A. C., and E. K. Halland, 1993, Sedimentology andshale modeling of a sandstone-rich fluvial reservoir: upper Stat-fjord Formation, Statfjord field, northern North Sea: AAPGBulletin, v. 77, p. 1016–1040.

Matheron, G., H. Beucher, C. de Fouquet, and A. Galli, 1987, Con-ditional simulation of the geometry of fluvio-deltaic reservoirs:Society of Petroleum Engineers Annual Technical Conferenceand Exhibition, SPE Paper 16753, v. X/�, p. 591–599.

McBride, E. F., M. D. Picard, and R. L. Folk, 1994, Oriented con-cretions, Ionian Coast, Italy: evidence of groundwater flow di-rection: Journal of Sedimentary Research, v. A64, p. 535–540.

McBride, E. F., K. L. Milliken, W. Cavazza, U. Cibin, D. Fontana,M. D. Picard, and G. G. Zuffa, 1995, Heterogeneous distri-bution of calcite cement at the outcrop scale in Tertiary sand-stones, northern Apennines, Italy: AAPG Bulletin, v. 79,p. 1044–1063.

Milliken, K. L., E. F. McBride, W. Cavazza, U. Cibin, D. Fontana,M. D. Picard, and G. G. Zuffa, 1998, Geochemical history ofcalcite precipitation in Tertiary sandstones, northern Apen-nines, Italy, in S. Morad, ed., Carbonate cementation in sand-stones: International Association of Sedimentologists SpecialPublication 26, p. 213–239.

Morad, S., 1998, Carbonate cementation in sandstones: distributionpatterns and geochemical evolution, in S. Morad, ed., Carbon-ate cementation in sandstones: International Association of Sed-imentologists Special Publication 26, p. 1–26.

Mozley, P. S., and J. M. Davis, 1996, Relationship between orientedcalcite concretions and permeability correlation structure in analluvial aquifer, Sierra Ladrones Formation, New Mexico: Jour-nal of Sedimentary Research, v. 66, p. 11–16.

Robinson, J. W., and P. J. McCabe, 1997, Sandstone-body and shale-body dimensions in a braided fluvial system: Salt Wash Sand-stone Member (Morrison Formation), Garfield County, Utah:AAPG Bulletin, v. 81, p. 1267–1291.

Saigal, G. C., and K. Bjørlykke, 1987, Carbonate cements in clasticreservoir rocks from offshore Norway—relationships betweenisotopic composition, textural development and burial depth,in J. D. Marshall, ed., Diagenesis of sedimentary sequences:Ox-ford, Blackwell, p. 313–324.

Schlumberger Technology Company, 1997, Eclipse 100 referencemanual: Abingdon, United Kingdom, Schlumberger Technol-ogy Company, variously paginated.

Sullivan, K. B., and E. F. McBride, 1991, Diagenesis of sandstones atshale contacts and diagenetic heterogeneity, Frio Formation:AAPG Bulletin, v. 75, p. 121–138.

Taylor, K., R. L. Gawthorpe, and J. C. Van Wagoner, 1995, Strati-graphic control on laterally persistent cementation, Book Cliffs,Utah: Journal of the Geological Society, v. 152, p. 225–228.

Taylor, K. G., R. L. Gawthorpe, C. D. Curtis, J. D. Marshall, andD. N. Awwiller, 2000, Carbonate cementation in a sequence-stratigraphic framework: Upper Cretaceous sandstones, BookCliffs, Utah–Colorado: Journal of Sedimentary Research, v. 70,p. 360–372.

Walderhaug, O., and P. A. Bjørkum, 1998, Calcite growth in shallowmarine sandstones: growth mechanisms and geometry, in S.Morad, ed., Carbonate cementation in sandstones: InternationalAssociation of Sedimentologists Special Publication 26, p. 179–192.

Walderhaug, O., P. A. Bjørkum, and H. M. Nordgard Bolas, 1989,Correlation of calcite-cemented layers in shallow-marine sand-stones of the Fensfjord Formation in the Brage field, in J. D.Collinson, ed., Correlation in hydrocarbon exploration: Lon-don, Graham and Trotman, p. 367–375.

Dutton et al. 2021

White, C. D., and M. D. Barton, 1999, Translating outcrop data toflow models, with applications to the Ferron Sandstone: Societyof Petroleum Engineers Reservoir Evaluation and Engineering,v. 2, p. 341–350.

White, C. D., B. J. Willis, S. P. Dutton, and K. Narayanan, 2001,Identifying and estimating significant geologic parameters withexperimental design: Society of Petroleum Engineers Journal,v. 6 no. 3, p. 311–324.

Wilkinson, M., 1991, The concretions of the Bearreraig SandstoneFormation: geometry and geochemistry: Sedimentology, v. 38,p. 899–912.

Willis, B. J., and C. D. White, 2000, Quantitative outcrop data forflow simulation: Journal of Sedimentary Research, v. 70,p. 788–802.

Willis B. J., J. P. Bhattacharya, S. L. Gabel, and C. D. White, 1999,Architecture of a tide-influenced delta in the Frontier Forma-tion of central Wyoming: Sedimentology, v. 46, p. 667–688.

Worden, R. H., and J. M. Matray, 1998, Carbonate cement in theTriassic Chaunoy Formation of the Paris basin: distribution andeffect on flow properties, in S. Morad, ed., Carbonate cemen-tation in sandstones: International Association of Sedimentol-ogists Special Publication 26, p. 163–177.

Calcite cement distribution and its effect on ﬂuid …AAPG Bulletin, v. 86, no. 12 (December...

Documents

Transcript of Calcite cement distribution and its effect on ﬂuid …AAPG Bulletin, v. 86, no. 12 (December...