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1. INTRODUCTION

The continuity of fracture-porosity is fundamentalto how fractures conduct fluids. One approach to

predicting the spatial arrangement of opening modefracture networks is through geomechanicalmodeling. We utilize a model based on subcriticalcrack growth to generate fracture trace patterns andmechanical opening distributions for various

boundary conditions and material properties [1,2].An important capability of such modeling is theability to predict the presence or absence of fractureclustering, as well as the shape of the fracture lengthdistribution. Another aspect of the problem is howdiagenesis modifies fracture porosity and effectivelength distribution and may affect the dynamics offracture propagation. Cements may also alter thecompliance of fractures and host rock, tending to

preserve fracture pore space under changing loadconditions. Although most recent literatureemphasizes Earth stress orientation [3,4],cementation in fractures and host rock is likely acritically important control on porosity, fluid flow

attributes, and even sensitivity to effective stress

changes [5-7].Little is known of the evolution of fracture networksin the context of the diagenetic pathway followed

by the host rock or of the influence on fracturegrowth of diagenetic processes within fractures. Yetthe high temperatures and reactive fluids insedimentary basins suggest that interplay andfeedback between mechanical and geochemical

processes could have significant influence onevolving rock and fracture properties. In this paperwe show how coupling fracture mechanics and

diagenesis considerations can lead to improved predictions of flow performance in fracturedreservoirs.

2. CEMENT IN SANDSTONE FRACTURES

Here we focus on the effects of quartz cement because diagenetic modeling can be used to predictthe distribution and abundance of this phase [8,9].Quartz is the most abundant and widespread cementin sandstones exposed to temperatures in excess of

ARMA/NARMS 04-563

Improving fracture permeability prediction bycombining geomechanics and diagenesis

Olson, J. E. and Laubach, S. E.

The University of Texas, Austin, TX USA

Lander, R. H.Geocosm, Austin, TX USA

Copyright 2004, ARMA, American Rock Mechanics Association

This paper was prepared for presentation at Gulf Rocks 2004, the 6 th North America Rock Mechanics Symposium (NARMS): Rock Mechanics Across Borders and Disciplines, held inHouston, Texas, June 5 – 9, 2004.

This paper was selected for presentation by a NARMS Program Committee following review of information contained in an abstract submitted earlier by the author(s). Contents of the paper,as presented, have not been reviewed by ARMA/NARMS and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of NARMS,

ARMA, CARMA, SMMR, their officers, or members. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of ARMA isprohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgementof where and by whom the paper was presented.

ABSTRACT: High temperatures and reactive fluids in sedimentary basins dictate that interplay and feedback between mechanical

and geochemical processes could significantly influence evolving rock and fracture properties. In this paper, we propose anintegrated methodology of fractured reservoir characterization and show how it can be incorporated into fluid flow simulation. Inrecent years, there have been a number of important discoveries regarding fundamental properties of fractures, in particular relatedto the prevalence of kinematically significant structures (crack-seal texture) within otherwise porous, opening-mode fractures, andthe presence of an aperture size threshold below which fractures are completely filled and above which porosity is preserved.Significant progress has been made as well in theoretical fracture mechanics and geomechanical modeling, allowing prediction ofspatial distributions of fractures that mimic patterns observed in nature. Geomechanical modeling shows the spatial arrangementof opening mode fractures (joints and veins) is controlled by the subcritical fracture index of the material. Fluid flow simulation ofrepresentative fracture pattern realizations shows how integrated modeling can give new insight into permeability assessment inthe subsurface. Using realistic, geomechanically generated fracture patterns, we propose a methodology for permeabilityestimation in non-percolating networks.

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~90 ºC for geologically significant periods [10,11].It is therefore not surprising that virtually alltransgranular fractures in such sandstones show atleast some degree of porosity loss due to quartzcementation. However, not all fractures areoccluded by quartz cement. In a wide range ofsandstones, there is a threshold kinematic fractureopening (separation between two previouslyadjacent points across the fracture regardless oflater mineral filling) above which fracture porosityis preserved and below which fractures arecompletely filled. This fracture aperture size is theemergent threshold [12].

0

5

10

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20

25

0 5 10 15 20 25

Measured Quartz Cement, %

C a l c u

l a t e d Q u a r

t z

C e m e n

t , %

Ashland #1 SFOT

Sun #2 D. O. Caudle

Fig. 1. Correspondence between measured andcalculated quartz cement abundances for unfracturedmatrix of Travis Peak Formation sandstones,demonstrating effectiveness of quartz cementationmodeling [18].

Quartz cement in sandstones generally occurs asovergrowths that nucleate on detrital quartz grains.The concept that the kinetics of quartz crystal

precipitation is the rate limiting process for theoverall growth rate in many types of sandstone [13-17] represents an important milestone in

understanding the controls on quartz cementabundances. Using this concept, quartz cementationrates are a function of temperature and nucleationsurface area. Computer simulators incorporatingthis concept accurately reproduce measured quartzcement abundances in sandstones from diversegeologic settings (Fig. 1)[18] and have been used to(1) reconstruct the diagenetic evolution ofsandstones and to predict reservoir quality whencoupled with compaction models (e.g., 18-20), (2)

constrain thermal histories [21], and (3) evaluatehow the magnitudes and rates of pore volume lossassociated with quartz diagenesis influence fluidoverpressure development [22-25].

High-resolution cathodoluminescence imaging offracture zones in sandstones reveals that fracturekinematic apertures represent the cumulativeexpression of hundreds or thousands of micronscale fracturing events [26]. In some cases quartzcement may bridge across the fracture zone betweenmicrofracturing events. Thus the nucleation surfacearea for quartz cement within fracture zones mayvary significantly through time as cementationreduces surface area by partial or complete sealingof fractures and micro fracturing events increasesurface area by crystal breakage.

0

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50

60

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100

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Fracture Opening Rate / Maximum Quartz Precipitation Rate

P o r o s

i t y o

f F r a c

t u r e

Z o n e ,

%

Poorly Sorted

Well Sorted

0

10

20

30

40

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60

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0.0 0.5 1.0 1.5 2.0 2.5 3.0

Fracture Opening Rate / Maximum Quartz Precipitation Rate

P o r o s

i t y o

f F r a c

t u r e

Z o n e ,

%

Poorly Sorted

Well Sorted

Poorly Sorted

Well Sorted

Fig. 2. Simulated dependency in fracture zone porosityon the ratio of net rate of fracture opening to quartz

precipitation rate. From [9].

Recently the approach toward simulation of quartzcementation in unfractured sandstones has beenextended to consider quartz cementation instructurally deformed sandstones [8,9]. Factors of

particular importance for such sandstones that areconsidered in this model include the effects ofcementation and fracturing on nucleation surfacearea as well as the control of crystallographicorientation and nucleation surface type on crystalgrowth anisotropy. Simulations of quartzcementation within the fracture zone by Lander etal. [8,9] indicate that fracture porosity is a functionof the ratio of the net rate of fracture opening to therate of quartz precipitation. The quartz precipitationrate, in turn, is a strong function of temperature and

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is also influenced by compositional and texturalcharacteristics of the host sandstone.

Lander et al. [9] simulated the controls on fracture porosity in fine-grained litharenite sandstonesassuming constant rates of fracture opening at aconstant temperature. Simulations indicate thatfracture porosity increases with the ratio of fractureopening rate to quartz precipitation rate because

progressively fewer crystals are able to grow acrossfracture apertures between fracturing events. Whenthe ratio value is less than 0.5, most quartzovergrowths will seal the fracture aperture betweenfracturing events thereby pervasively sealing thefracture zone (Fig. 2). By contrast, when the ratioexceeds a value of two, no crystal will bridge acrossthe fracture aperture and overgrowths will thereforeoccur exclusively as rims of euhedral crystallitesalong an otherwise open fracture. At intermediateratios the cement morphology will be a mixture ofeuhedral crystal linings and bridge crystals that are

pillar-like structures that span the fracture.

Fracture walldominated bycomparativelysmall euhedral

crystals

Fracture walldominated bylarge quartz

bridges

5 mm

Fig. 3. Cretaceous Travis Peak Formation core samplenear tip of a vertical fracture (core photograph). Quartzcement is more abundant toward tip of fracture (bottom

part of image) than where aperture widens (top part ofimage).Sample depth is ~9,800 ft. See [27] forbackground information.

Based on these model results we expect a transitiontoward greater fracture porosity in the centers oflarger aperture fractures due to the faster netfracture opening rates compared to the tips. Such

transitions occur in nature as illustrated for a samplefrom East Texas sandstone in Fig. 3.

In addition to the important role that quartzcementation plays in controlling fracture porosity, italso is likely to greatly reduce the compliance offractures. During the development of fracturesystems quartz cementation occurs not only withinthe fracture zone itself but also within theunfractured matrix of the host sandstone. Thus themechanical strength of the host rock will tend toincrease with time. Furthermore, quartz cement thatlines or bridges fractures also will decrease fracturecompliance, even for fractures that havecomparatively high porosities. Euhedral quartzcrystals within otherwise open fractures have highspatial anisotropy and will not permit fracture

porosity to go to zero even with large changes instress orientations, and quartz bridges are likely tohave an even larger strengthening effect on thefracture zone.

Precipitation of cement as a part of rock diagenesiscan be divided into three stages – prekinematic,synkinematic and postkinematic, where thekinematic event referred to in the timing is theformation of natural, opening-mode fractures [27,12]. Because quartz precipitates over a widetemperature range, it is commonly pre-, syn- and

postkinematic. Post-kinematic cements, includingcarbonate minerals, are commonly responsible for

sealing large fractures [12]. However, owing to thecontrols on quartz precipitation alluded to previously, syn- and postkinematic quartz tends toseal only small fractures, and in sandstones the

phases that commonly seal large fractures are postkinematic carbonate and sulfate minerals.

Why is quartz cement so common in sandstonefractures? Quartz cementation contemporaneouswith fracture may merely reflect prevalence of rock-dominated chemistry through much of a rock’s

burial history, including times when conditions areamenable for fracture growth. In sandstone,synkinematic quartz (and in dolostone,synkinematic dolomite), could simply be the mostlikely phase to precipitate through a protractedloading history [12].

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3. GEOMECHANICAL FRACTURE PATTERNMODELING

Modeling studies and comparisons to field datademonstrate that subcritical crack growth can beused to explain the presence or absence of fractureclustering and the shape of fracture length andspacing distributions [1, 2, 29, 34]. The fracture

pattern variability illustrated in Fig. 4 is causedsolely by the variation of the subcritical index, amaterial property that is postulated to depend ongrain size, porosity, and mineralogy [35-37]. Asexpected, for a given rock layer, increasing strainapplied to a body increases the total amount offracture trace length created (or cumulative fracturelength).

However, for the case of similar layers (samemechanical thickness, elastic moduli and fracturetoughness) all experiencing the same amount ofstrain, Olson et al. [2] showed that the subcriticalindex controls the shape of the length distributionmaking up the fracture population and thecumulative length created (Fig. 5). High subcriticalindices ( n>40) cause fractures to grow as clusterswhere the median fracture segment length is verylow (point at which cumulative frequency is 0.5)and overall fracture intensity is low. Intermediatevalues (20< n

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As mentioned in the previous section, cumulativefracture length created and mean fracture segmentlengths for a given imposed strain can be related tothe subcritical index. Variations in cumulativefracture trace length, holding other conditions and

properties the same, can also be related to themechanical layer thickness. The layer thicknesseffect is related to the oft observed outcroprelationship that fracture spacing is roughly

proportional to layer thickness [38, 39]. Thus, for agiven strain, thinner beds generate more cumulativefracture trace length, which implies greater fracture

permeability according to the results in Fig. 6.

At first glance, this conclusion may seem consistentwith the parallel plate law of equation (1), wheredecreasing fracture spacing, S , causes an increase infracture permeability. However, the mechanicalanalysis of bed-bounded fractures also shows thatfracture aperture is expected to be less in thin bedsthan in thick beds, all other things equal [40]. Sincefracture permeability has a stronger dependence onaperture than spacing in equation (1), it seems thatthicker beds might have higher permeability eventhough their fracture intensity is less. Interestingly,this is a point where the inadequacy of the parallel

plate law for large scale permeability estimation ismost pronounced. If the assumption of through-going fractures is not true (fracture flow paths aresegmented and non-percolating), Philip et al. [30]showed that a doubling of fracture aperture foridentical fracture trace networks, which should haveresulted in nearly an order of magnitude equivalent

permeability increase according to the parallel platelaw, had virtually no effect on equivalent

permeability.

5. DIAGENESIS EFFECTS ON APERTUREAND PERMEABILITY

Although Philip et al. [30] showed that fractureaperture did not affect permeability as implied in

the parallel plate law, they did show that imposingthe effects of an emergent threshold on the fracture pattern influenced permeability. Thegeomechanical simulations were performed using a

boundary element program [41], where eachindividual fracture is made up of multiple short

patches or elements. Fracture aperture for a givenfracture can vary from element to element, wherethe narrowest apertures are typically at and near thefracture tips. A dimensionless emergent thresholdwas defined as a multiple of the mean kinematic

aperture of the fracture patches for a given networkgenerated by the geomechanical model. The resultsof Fig. 6 were made assuming an emergentthreshold of zero, where all of the kinematicallyopen fracture patches were open to flow(geologically speaking, no mineral precipitation hadoccurred in the fractures). Increasing the emergentthreshold resulted in some of the fracture patches

being closed to flow, starting with those that had thesmallest kinematic aperture.

Fig. 7: The effect of synkinematic cement on equivalent permeability for a simulated fracture pattern. From [30].

Since these are typically at the tips of the fractures,filling the fractures with cement not only reducedhydraulic aperture of the fractures but decreasedtheir lengths. It is the diminution of length that will

be most important for non-percolating networks,and Philip et al. [30] showed how equivalentfracture permeability decreases dramatically withincreasing emergent threshold (Fig. 7).

Finally, we analyzed the emergent threshold effectson fracture continuity for more complex fracture

patterns than the single parallel fracture set case ofPhilip et al. [30]. The simulations of Olson et al. [2]and Philip et al. [30] assume strong in situ stressanisotropy at the beginning of fracture propagation

that forces fractures to propagate in planar, non-interacting paths. However, it is common thatnatural fractures interact and form curving ororthogonal, ladder-like patterns [42-44] as shown inFig. 8. Such a pattern was generatedgeomechanically (Fig. 9) by applying a constantstrain rate extension in the y direction and holdingthe strain in the x-direction constant (zero normaldisplacement). Early propagation is dominated byfractures propagating in the x-direction, relieving

0

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0 0.5 1 1.5 2 2.5Emergent threshold ratio (dimensionless)

P e r m e a

b i l t y M u l

t i p l i e r

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fracture promoting stresses acting in y until the principal stresses flip to favor fracture propagationin the y-direction (in response to the fracture

promoting stresses caused by the Poisson effect)[45].

Fig. 8. Bedding plane exposure of natural fracture pattern with good trace pattern connectivity (6 inch scalein middle of photo).

Fig. 9a shows the resultant fracture trace pattern,showing strong connectivity in both the x and y

directions in what would be a percolating fracturenetwork. Fig. 9b, however, shows how aperturevaries throughout the network, where the thicknessof the fracture segments is proportional to kinematicaperture (widths exaggerated for clarity). Thewider, gray-filled fractures represent fractureapertures of 1 to 3 mm. The thinner black lineshave apertures ranging from 0.1 to 1 mm. Based onthe parallel plate law, the flow resistance of a singlefracture by itself (not accounting for surroundingmatrix rock) can be characterized as the

permeability k f as

12

2bk f =

. (2)

Local permeability variations caused by an order ofmagnitude aperture reduction at the fracture tipsfrom 1 to 0.1 mm would represent a 100 timesreduction in fracture permeability.

Finally, if the emergent threshold for this particularfracture pattern were 1 mm, only the fatter gray

fracture segments would be left open, and the blackconnecting fracture segments would be completelymineralized and closed. Thus, based on thisqualitative assessment of permeability, analogous tothe more quantitative work described in the

previous section for parallel fracture sets, it isevident that the interaction of diagenetic andkinematic effects play a pivotal role in determiningthe flow properties of a given fracture network.

6. CONCLUSIONS

Natural fractures are complex structures formed bymechanical breaking of rock and the diageneticalteration of those broken surfaces. Numericalmodeling of diagenesis occurring simultaneouslywith fracture opening shows how some fracturescan be completely filled with cement while othersmay only be partially filled (bridged) or largelyopen. Analysis of cement patterns in fracturenetworks shows that fracture aperture variabilitycan have a strong influence on flow continuity andultimately permeability. Diagenetic effects can beimprinted during development of these morecomplex fracture patterns or after the fact.Permeability estimation through modeling showsthat systematic changes can be expected wherefracture length distributions are modified byvariable thermal aging histories experienced by thefracture network, in other words varying emergentthreshold values (minimum kinematic aperture thisis hydraulically open). Both the rock properties thatgovern fracture pattern development and thecementation process that modify effective fracture

porosity are amenable to accurate prediction usingdiagenetic modeling. Based on the concepts

presented in this paper, future progress on permeability modeling of fractured reservoirs willrequire a coupling of geomechanically-basedfracture network generation and diagenetic

processes in both the fracture and matrix porespace.

7. ACKNOWLEDGMENTS

Supported by the Chemical Sciences, Geosciencesand Biosciences Division, Office of Basic EnergySciences, Office of Sciences, U.S. Department ofEnergy, and by industry sponsors of fracture anddiagenesis research at The University of Texas atAustin and Geocosm.

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a)-25

-15

-5

5

15

25

-25 -15 -5 5 15 25 b) -25

-15

-5

5

15

25

-25 -15 -5 5 15 25

Fig. 9. Fracture network generated by uniaxial strain in the y-direction (zero strain in x) and starting with an isotropic insitu stress. The body is 50x50 m in map view and the mechanical layer thickness is 8m. The subcritical indexused was n=20. a) Fracture tracemap with no aperture information. b) Kinematic aperture map whereapertures are exaggerated but appropriately scaled (maximum aperture is 3x10 -3 m).

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