CSUG/SPE 146580

A New Classification Plot for Naturally Fractured ReservoirsJames R. Gilman, Huabing Wang, Sepehr Fadaei, Michael J. Uland, iReservoir.com, Inc.

Copyright 2011, Society of Petroleum Engineers

This paper was prepared for presentation at the Canadian Unconventional Resources Conference held in Calgary, Alberta, Canada, 1517 November 2011.

This paper was selected for presentation by a CSUG/SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have notbeen reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers,its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission toreproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

AbstractThe classic Nelson plot (Nelson, 2001) has been widely used to illustrate the geologic characteristics of various NFR typesranging from matrix dominated flow with some fracture enhancement to purely fracture dominated systems (e.g. basementreservoirs). However, for many reservoirs, there is significant overlap in model types and different parts of the reservoirs mayfit into different classifications. In fact, the choice of characterization and modeling approaches depends on otherconsiderations such as the fluid system, matrix geologic characteristics, and recovery processes. For example, for gas-oilgravity drainage processes, the rate of vertical oil drainage in the matrix may dominate oil recovery and dual-permeabilitymay be the desired modeling approach even in a highly fractured reservoir. Alternatively in pure depletion processes, wemight be able to model a highly fractured system with an effective single-porosity representation because of rapid matrix-fracture pressure equilibration. However, in all fractured reservoirs, of special concern is the rate of matrix-fracture fluidtransfer which is directly related to the fracture intensity of the open connected fractures.

In this paper we present a new classification plot that highlights the importance of fracture-matrix fluid transfer. Thisconsideration is not directly incorporated in the Nelson plot. Our new classification concept can be used to understanddifferences in dynamic performance of NFR for purposes of analogue selection or screening of potential recovery processes.In this paper, several characterized NFR reservoirs (including unconventional systems) are compared via the newclassification plot and their differences and performance are discussed. Additionally we provide some discussion of naturallyfractured reservoir (NFR) characteristics for the purpose of illustrating the controls on matrix-fracture fluid transfer.

IntroductionCharacterization and simulation of naturally fractured reservoirs (NFR) is a difficult process. We must apply concepts learnedfrom analogue fields as well as petrophysical and seismic methods to define the 3D distribution of fracture networkcharacteristics (permeability, connectivity, intensity, etc). Many of the concepts discussed in the next few sections aresummaries of details provided by Gilman (2003) and those concepts were a result of collaborative efforts with Dr. H.Kazemi, Colorado School of Mines (unpublished). These first sections are intended to provide the background forestablishing the importance of matrix-fracture transfer as a concept for comparing performance of NFR.

A common idealization for fractured reservoirs relies on the assumption that in the macroscopic sense, the inter-connectedopen fractures are assumed to form a continuum. Thus, both fracture and matrix components of the reservoir are consideredseparate continua in the macroscopic sense. This continuum view is analogous to that in conventional reservoirs where themicroscopic pores are very tortuous and the channel dimensions and flow properties vary drastically from point to point. Inthis case, the continuum definition of the porous medium flow equations cannot be applied on the pore level scale (Lake,1989) but must be averaged over some representative pore volume (REV). One of the most important aspects of thesesystems is the fracture-matrix transfer. This transfer is a function of the amount of matrix-fracture surface area. Its relation tofracture intensity has been frequently described and therefore will only be reviewed briefly.

Important flow characteristics of fractured reservoirs are well represented by the dual-continuum idealization such as: High apparent permeability compared to core measurements High initial productivity and rapid decline for limited matrix contribution Early breakthrough of injection fluids or early gas/water coning Highly directional flow behavior

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Large variability in well productivities and recoveries Potential loss of productivity with time Flow from a very small portion of the open interval High recoveries even for low quality matrix (e.g. as seen in unconventional reservoirs)

There are a number of issues in regard to the nature of fractures that have significant implications on reservoircharacterization and fluid-flow modeling. For example, whether fractures are a result of shear, extension, or tension, the factis that the open fractures generally exist in vertical or sub-vertical forms. However, this does not mean that effective verticalpermeability over the height of the reservoir will be high. The mechanical properties of rocks can vary significantly invarious stratigraphic layers of the reservoir possibly leading to limited vertical connectivity. The variation of properties, suchas Poisson ratio and shear modulus, results in different horizontal stress in reservoir layers, and thus different fracture lengthsand apertures if fracturing occurs. In many cases, fractures may cluster (Gale, 2002).

Additionally, the morphology (form and structure of fractures) is very important (Nelson, 2001). Fractures may be open withattendant large permeability, gouge filled with low permeability along and perpendicular to fracture, slickensided with highpermeability along the fracture and low perpendicular to it, mineral-filled leading to partial or total fracture closure as well asreduced permeability, and vuggy where vugs are imbedded in the fractures. Knowledge of morphology is a very importantpiece of information in fluid flow modeling because models require estimates of fracture spacing, effective permeability,porosity distribution, and permeability anisotropy. Diagenesis can alter the permeability and porosity of open fractures andfully mineralized fractures could, potentially, become baffles or barriers to flow.

Dual-Continuum ModelingFor dual-media simulation, the fracture network is described as a continuum with independent properties (e.g., permeabilityand porosity) defined in a manner similar to the matrix rock. For example, porosity and permeability are defined with respectto the bulk volume of the core, not with respect to individual fractures. Most approaches for quantifying the flow propertieson the fracture networks are based on a qualitative assessment of the 3D distribution of fracture network characteristics, suchas relative fracture intensity, directional aspects, and whether the fractures are generally open or closed. These qualitativeassessments are then calibrated to historical well performance via direct approaches often referred to as continuum flowmodels (CFM) or upscaled from discrete fracture models (DFM). Both methods require very similar workflows.

The characterization approaches use information such as structural data, seismic attributes, image logs, and field productionperformance to estimate the fracture network properties (e.g., Gauthier et al., 2002). Deterministic and/or stochastic modelsare built with these data and validated by comparing to the field performance (e.g., water and gas breakthrough). Non-standard dynamic field tests such as tracer tests (Kazemi and Shinta, 1993) can be useful for quantifying the fractureheterogeneity. Interference or pulse testing (Araujo et al. 1998) can also provide important information such as directionalinformation to compare to image logs, stress relations for calibrating with laboratory and fracture volume from rapid pressureresponse between wells.

Traditional methods of estimating fracture parameters have also included single-well pressure transient testing to estimatefracture network conductivity, and cores and image logs to estimate fracture network intensity. The theoretical dual-porositysignature of the pressure build-up curve (Warren and Root, 1963) is often missing because of the presence of well borestorage effects or non-uniform fracture distribution. However, comparing the pressure transient permeability to that estimatedfrom matrix permeability can give an indication of the connectivity of the fracture network.

Fracture PermeabilityIn an ideal setting, we could estimate fracture network effective permeability from aperture and porosity estimates usingparallel plate idealizations (Kazemi and Gilman, 1993) and for non-uniform fracture orientations through DFN models(Dershowitz, et. al. 2000). However, in our experience, the effective fracture permeability for a network of fractures willlikely be much smaller than calculated from such relations because fractures have rough and touching surfaces, are tortuous,may be constricted by mineral deposition, and may terminate abruptly. Furthermore, the vertical permeability of anindividual fracture could be quite high; however, if the fractures terminate in shale lenses or are of limited height for someother reason, the effective vertical permeability of the network could be quite low. Therefore, permeability is best determinedfrom field tests and not from core/log-measured fracture widths and spacing. The static data however can be used to derivescaling relations to distribute permeability in 3D.

Permeability in NFR can be highly directional. Considering this highly directional nature, the need for permeability tensorshas been widely discussed but not widely applied in field-scale fluid-flow modeling. Whether such a tensor approach isrequired is still debated because the actual data required to uniquely define the tensors are not available. Also, the extracomputation required means that additional upscaling would be required, reducing other details in the model. Aligning the

CSUG/SPE 146580 3

grid system with the directional trends and applying the main tensor diagonals (principal permeabilities) has proven to beadequate for many field scale systems.

Single-well flow tests, such as a pressure build-up test, cannot decipher permeability anisotropy. The most direct method tocalculate permeability tensor is from the interpretation of pressure interference tests conducted in various parts of a field.Haws and Hurley (1992) summarized interference test results from a number of Big Horn Basin fractured reservoirs, wherethey reported that the maximum to minimum permeability ratio varied from 10 to 1000. Tracer tests, compared tointerference tests, are more time consuming and expensive and can best be run only in displacement (e.g. injectionprocesses). However, tracer tests conducted in a naturally fractured reservoir can provide additional insight on permeabilityanisotropy (Kazemi and Shinta, 1993). Finally, the most common method used to assess the directional flow tendencies isbased on fracture orientation studies of borehole image logs, oriented cores, outcrops and water or gas breakthroughtendencies. Seismic methods can also provide a means to infer anisotropy which may be related to open natural fractures (Ataand Michelena, 1995). These seismic methods must be calibrated to dynamic data.

Effective fracture permeability tensor can be calculated for a REV cube or a grid cell using discrete fracture network (DFN)models based on measured fracture aperture, surface area and the inclination angle normal to the fracture surface. Only theopen fractures that contribute to fracture flow should be included (Oda, 1985). This approach is a common method forscaling DFN models, image logs and outcrops to equivalent dual-porosity medium (Dershowitz, et. al., 2000).

If fractures close as reservoir pressure declines, then effective permeability could decrease. A number of researchers havederived the expressions for permeability, aperture, compressibility, and porosity of smooth open fractures as functions ofpore pressure and stress state in an elastic porous media. However, fracture closure is very difficult to estimate because of thepresence of filler material, or complex stress states of the reservoir. Also at large flow rates, the onset of turbulent flow cancreate additional pressure drop causing an apparent reduction in permeability. Step rate tests can indicate if turbulent flow isimportant (Pereira, et. al. 2004).

One common method of assessment of fracture importance is a term called excess permeability. This is the permeabilityabove that expected from matrix flow. The Nelson plot incorporates this as one of the axes. As flow through the fracturesdominates, then the excess permeability ratio can be quite high (> 1000). Excess permeability can be estimated by comparingwell productivity or well-test permeability to that estimated for matrix only flow. However, such assessment alone may notbe sufficient to determine if natural fractures are important. Consider the ideal picture in Figure 1 for a theoretical case wherethe effective fracture network permeability is such that the total effective permeability (ke) is two times larger than a matrixonly system. From Eq. 1 this means that kff (what we will call kfe) is equal to km.

mffe kkk (1)

Such a factor would be within the uncertainty of matrix permeability and thus such a reservoir could easily be interpreted tobe non-fractured. If fluid is injected into the system then one-half of the fluid will flow through the fracture; however, theratio of matrix fluid velocity to fracture velocity would be m/f. Because the fracture porosity is generally one to two ordersof magnitude lower than matrix porosity, the velocity in the fracture could be more than 10 times that of the matrix. Thus, inthe absence of matrix-fracture transfer, one-half of the fluid will move at a velocity more than 10 times greater than thatexpected for matrix only flow resulting in very rapid breakthrough. This illustrates the importance of fractures to fluidmovement even when apparent permeability is not significantly greater than that of the matrix. What becomes of majorimportance is the matrix-fracture fluid transfer which can significantly affect the behavior of the system.

Fracture PorosityFracture porosity calculations require an estimate of fracture spacing (intensity) and width, which is often estimated fromcores, image logs and outcrops. The local porosity calculated for an individual fracture would essentially be 1.0; however,when calculated with respect to the bulk rock volume, fracture bulk porosity is quite small (

4 CSUG/SPE 146580

When calculated from cores, images logs or DFN models, fracture porosities are often very small (

CSUG/SPE 146580 5

I

iiAV

P1

132 (4)

In practice, shape factor is often considered a history matching parameter, but modern workflows start with the aboveequations as the best estimate of the fracture intensity (which can be converted to shape factor). The shape factor can varyover the computational grid and is only considered a constant over the REV (grid volume). Note that the numerical modelsdo not actually require any discrete representation of matrix sugar cubes. The idealization of sugar cubes is just aconvenience for illustration similar to the bundle of capillary tubes used for discussion of a single-porosity media. The dual-porosity models are simply two overlying porous media with a transfer term directly proportional to shape factor (i.e.fracture-matrix surface area). The shape factor can be calculated for any geometry (Heinemann and Mittermeir, 2006; Sarma,and Aziz, 2003).

Theoretically the shape factor can be calculated from pressure build-up curves on individual wells. Ideally, such curvesdevelop two parallel straight-line segments, indicative of dual-porosity behavior (Warren and Root, 1963). The build-up timeat the inflection point, on the transition segment between the early and late straight line build-up segments, is related to shapefactor and depends on two dimensionless parameters, the storativity and the inter-porosity flow, and , which are definedas follows:

( )( ) ( )

cc c

t f

t f t m

(5)

e

wm

krk 2

(6)

These relations are important for the classification plot presented in this paper. The inflection point on the transition betweenearly and late straight-line flow periods depends on the shape factor according to the following relation (time is given inhours):

e

wft

krnc

t

0002637.0)()( 2*

(7)

In the above equations, ke, is the effective permeability of the fractured system as calculated from the slope of the build-upcurve. The vertical pressure separation (p) between the two parallel lines is related to . Often the customary two straight-line segments do not appear on the pressure build-up curve because of well bore storage or boundary effects. The timeequation (Eq. 7) shows that the time frame for transition to occur in systems with moderate compressibility can be very short(and thus is often masked by wellbore storage effects). Also non-uniform fracturing (variable ) complicates the transitionperiod. If the dual-porosity response is not seen, shape factor will need to be inferred from other information (e.g. image logs)and calibrated via DFN modeling.

In practice, the effective fracture intensity and degree of connection is difficult to predict. This may be because fractures areoften well connected on a large scale, but a few primary pathways may dominate flow and thus many of the fractures seen inlogs and cores do not inter-connect on a large scale. Also, the apparent connectivity can depend on the well placement andthe recovery process. Thus, coarse-grid, dual-porosity models for multi-phase flow have historically been too well connected.Secondly, the fracture network appears much more heterogeneous than first estimated and in fact the effective fracturespacing can appear to be different for depletion versus waterflood. Under depletion, a near-by producer can deplete many ofthe fractures, causing matrix fluid to expand through a large fracture-matrix surface area. However, under waterflood, watercan imbibe only through the matrix surface that is contacted by water. Fractures that are not continuous along the water flowpath will not be flooded by injection water even if they are open and permeable. Recent industry activity has been directed atusing discrete stochastic distributions of fractures based on statistical and deterministic information gathered from logs, coresand outcrops to improve understanding of the fracture connectivity. These stochastic realizations can provide a means toestimate effective fracture network properties for upscaling into conventional dual-porosity models.

Fluid Flow BehaviorIn three-phase systems, consisting of gas, oil, and water, different portions of a given reservoir can undergo different

6 CSUG/SPE 146580

displacement processes leading to complex flow behavior. This usually happens because of the differences in field operationsschemes (i.e., water-flooding vs. gas injection) and rock characteristics such as wettability, fracture intensity, permeabilityvariations, layering, structural effects, capillary pressure and relative permeability hysteresis. The oil recovery mechanismsassociated with the field characteristics as well as the production schemes in the field are best studied by laboratoryexperiments and fine-grid numerical simulation. The approximations made by the simulators for coarse-grid full-field modelsmust be verified by these fine-grid studies. In the following discussion, we present some of the basic ideas for flow behaviorunder various recovery mechanisms. The idea is to illustrate the importance of various parameters on fracture-matrix transfer.

DepletionIn purely single-phase depletion, the dominant recovery mechanism is fluid expansion. In practice, this occurs normally asthe first stage of reservoir operations, and fluid recoveries are typically quite low (except for gas systems). In single-phasedepletion, oil or gas recovery rate can be much greater in NFR compared to non-fractured reservoirs because the highpermeability fracture network undergoes rapid depletion and provides large surface area for reservoir fluid in the low-permeability matrix to expand into the fractures. This has been a means to obtain significant recovery from low-permeabilityunconventional reservoirs. In multi-phase depletion, fracture flow can lead to free gas flow in the fractures, which, in turn,can invoke gravity drainage of oil from the matrix. Efficient gravity drainage can lead to high oil recoveries if the gas-oilgravity drainage process is managed properly. The important parameters that affect the rate of matrix-fracture fluid transferduring depletion can be shown to be shape factor, , matrix fluid mobility, (km/), and fracture-matrix pressure difference,(pm-pf) as can be seen from the equation for single-phase flow in the fractures. The second term in Eq. 8 represents thematrix-fracture transfer.

t

pcqppkp

k ftfffmf

mf

f

(8)

Solution of the single-phase equations for low compressibility flow shows that a double exponential flow rate decline candevelop for a closed radial reservoir, producing under constant bottom-hole pressure depletion,. Chen, et. al., (1986) showedthe exponential decline characteristics of a number of Austin Chalk wells.

Satman (1985) derived equations for the initial flow rate and for the slope of the exponential recovery lines as a function ofthe inter-porosity parameter, . Because of the small volume of fluid in the fractures, the initial period may be very short andtherefore difficult to measure. For large (> 16 rw2/re2) only a single straight line will develop because of the rapid pressureequalization between the fracture and matrix. The reservoir then responds like an non-fractured reservoir with permeabilityequal to ke and porosity-compressibility equal to that of the total system. For highly fractured systems with moderate to goodmatrix permeability and close fracture spacing (e.g. km > 0.1 md-ft-2), only one straight line will develop.

In theory, Satmans equations could be used with decline curve analysis to determine reservoir properties for the fracture-matrix system (Chen, et al. 1986). In practice this is very difficult because of variations in bottom-hole pressures, multiphase-flow, offset well interference effects, complex well geometries/completions and the long production times required to obtainboth exponential decline periods. Also, numerical simulation has shown that the first line is very short lived and the slope isaffected by matrix-fracture flow. Therefore, fracture properties are very difficult to determine from decline curve analysis.However, long-term rate and pressure decline can be used with conventional reservoir depletion analysis to determine theeffective permeability and total pore-volume of the system (fracture and matrix). The magnitude of effective permeabilitycompared to only the matrix (core) permeability gives an indication of the relative importance of fractures. This discussionshows how high fracture intensity (large ) can lead to efficient depletion of fractured systems with low matrix permeability.

Water ImbibitionWater imbibition has proven to be an effective recovery mechanism in some NFR. Imbibition in reservoir rock is the processin which water is drawn into the rock by the action of capillary forces. Mattax and Kyte (1962), through experimentalinvestigations, found that recovery in such systems could be scaled through the following dimensionless time:

tL

ktm

mD

2

(9)

This equation shows that recovery is inversely proportional to the matrix block size squared, L2. Capillary pressure isindirectly incorporated in the above equation through the interfacial tension, , permeability and porosity terms. The aboveequation can be rewritten in terms of shape factor, , by replacing the 1/L2 term as shown in Kazemi, et. al. (1992) and

CSUG/SPE 146580 7

Zhang, et al. (1996). The experimental data generated by Mattax and Kyte can be described by an exponential time function.Kazemi, Gilman and El-Sharkawy (1992) provide an analytical solution for one-dimensional flow in a fractured systemsusing such exponential relations.

The important parameters affecting oil recovery from water imbibition are shape factor, capillary pressure and oil mobility,kmkro/o. Oil rate is greater as permeability increases and matrix block size decreases (fracture intensity or shape factorincreases). Recovery rate also increases as oil relative permeability increases making it easier for water to imbibe anddisplace oil from the matrix. Higher capillary pressure increases rate of oil recovery through increased imbibition force. NFRthat have undergone waterflood or strong aquifer drive include the Fahud Field (ONeill, 1988), Ekofisk Field (Hallenbeck etal., 1991), Midale Field (Beliveau, et al., 1993) Ezzaouia Field (Gilman et. al., 1996), and Ghawar Field (Phelps and Strauss,2002). The more than 30% recovery from the Ezzaouia Field is a case that illustrates the effectiveness of water imbibitiondominated recovery in some NFR.

From a large-scale simulation perspective, some of the issues regarding recovery prediction uncertainty include incompletecoverage of the matrix block as a result of non-uniform sweep through the fractures, variations in recovery as a result of non-uniform block size in a grid block and uncertainty in laboratory measurements.

Gas-Oil Gravity DrainageIn some highly fractured reservoirs, gravity drainage can be a very effective recovery mechanism. If matrix drainage is thelimiting factor, then oil drainage can be approximated as a one-dimensional solution. In one-dimensional gas-oil gravitydrainage in a porous media, the time rate of change in elevation of a constant saturation oil shock front (that is, the gas-oilfrontal velocity, ft/d) is given by the following equation (Dykstra, 1978; Richardson, 1989):

zt

x k kSS

v og

o

ro

o So o

7 83 10 6. (10)

Assuming power-law oil relative permeability function with an exponent of n and coefficient of krom, Eq. 10 can be solvedanalytically for the initial oil rate as given by Eq. 11. This initial rate (qoi, STB/D) is sustained for a period of tqmax days:

0

5

6146.5104.4

Akkxq romvoi (11)

romv

pq nkkx

ht

50

max 104.4(12)

For times greater than tqmax, analytical solution gives Eq. 13. This defines a hyperbolic decline equation given by the secondtwo equations. The hyperbolic b factor is equal to (n-1)/n. The subscript p on porosity refers to the effective oil porosity(1-Swir-Sgc-Sorw).

)1/()1/(15

)1/()1/(10

)104.4(6146.5

nnn

romv

nnnpp

o tnkkxnhA

q

(13)

tAhnq

bD

p

oi 16146.51

(14)

b

oio bDtqq/11 (15)

The important parameters affecting gravity drainage rate are vertical permeability, density difference, and oil mobility.Fractured systems in which gas filled vertical fractures surround a vertically continuous matrix can be represented by thisequation. The above equation ignores capillary pressure. Capillary pressure has minimal effect on early rates, but can causehold-up of oil above barriers or horizontal fractures. For lab centrifuge data in which the core is spun at a rate scaled to the

8 CSUG/SPE 146580

field oil column height, the resulting relative permeability will include the capillary holdup and can be used directly in theabove equations for scale-up. Centrifuge experiments (Kyte, 1970) are a common method of assessing effectiveness ofgravity drainage which can be directly upscaled to field behavior.

Permeability variations can affect early drainage rate, but a harmonic average permeability can give a reasonableapproximation to the drainage behavior over a limited permeability range. Simulation shows that for matrix block radii of10s of ft or less, there is no difference in recovery, showing the insensitivity of this system to areal fracture spacing. Becausethe flow is controlled by matrix vertical permeability, the areal spacing of the fractures has minimal impact for relative closefracture spacing ( 50 m).However, for smaller fractures it has been demonstrated (Maloney, et al., 1997) that relative permeability in fractures is non-linear and depends on the fracture flow velocity, direction of flow, and density difference. Other fracture relativepermeability concepts have also been presented by a number of authors (e.g. MacDonald, et al., 1991; Kazemi and Gilman,1993). There have also been a number of different methods proposed to handle the effect of relative permeability for matrix-fracture flow, although the most general method is to use conventional upstream weighting. Historical performance also

CSUG/SPE 146580 9

suggests that relative permeability in the fractures is not a linear function of phase saturations. This is because the relativepermeability for a fracture network is an average of a number of discrete fractures.

Previous discussions referred to depletion. water imbibition and gravity drainage, as the most common methods forenhancing recovery in NFR; however, tertiary recovery, or enhanced oil recovery (EOR), are processes that produce furtheradditional oil economically over that which can be produced from primary and secondary recovery methods. In NFR, EORcan be viewed as the methods that accelerate oil recovery by altering reservoir fluid and rock properties to better utilize thereservoirs natural energy. The most promising EOR techniques in NFR (Christiansen, et al., 1989) include CO2 (Beliveauand Payne, 1993; Malik and Islam, 2000), heat (Reis and Miller, 1995), surfactants (Chen, et al., 2001), and polymers(Sydansk and Moore, 1992). For some of these processes we must also be concerned about diffusion rates and /or heattransfer rates between matrix and fractures. The effectiveness of these two transport phenomena is also strongly dependent onfracture-matrix surface area (shape factor).

A New Classification PlotIn this section we present our new classification plot (referred to here as the Gilman Plot) to highlight the relativeimportance of fracture-matrix transfer. This consideration is not directly incorporated in the Nelson plot (Figure 2). Effectivematrix-fracture transfer provides a means for micro-darcy rock to provide economic recovery of oil in unconventional plays.This new classification concept is intended to be used to understand and illustrate differences in dynamic performance ofNFR for purposes such as analogue selection for decline forecasts, screening of potential recovery processes or makingdecisions on modeling methodology. In this paper, several characterized NFR reservoirs (including unconventional systems)are compared via the new classification plot and their differences and performance are discussed. This plot is certainly not allencompassing with regard to fractured reservoir performance but it highlights the fact that matrix-fracture surface area is amajor aspect of understanding performance of NFR.

The first ratio we will use in the plot is the storativity ratio; as defined by Warren and Root (1963). However because weoften dont know the fracture compressibility, we will remove compressibility (ct) from this equation.

mf

f

(18)

The second ratio is the ratio of effective fracture permeability to matrix permeability; often referred to as excess permeabilityratio. However, as discussed earlier, the ratio does not need to be greater than one. For fracture permeability we generally usea geometric average of the horizontal permeability diagonal tensor terms.

m

feexr k

kk (19)

These two parameters are the basis of the Nelson plot and will remain the primary axes in our plot. These are relative easy tocomprehend in terms of magnitude as permeability and porosity are terms that we are all familiar with.

The previous discussion of depletion systems showed how Satman (1985) illustrated that the product of re2/rw2 is acontrolling factor in the long-term behavior of a radial, closed, single-phase, dual-porosity system. He showed, for example,that if this term is greater than 16, the system (under pseudo-steady state single-phase depletion) will behave like a single-porosity system with permeability ke and porosity f+m. Therefore, for use in our classification plot, a third ratio is aredefined inter-porosity flow term, A, which indicates the relative contribution of fracture-matrix flow compared to flowthrough the fractures within the well drainage area, A (Eq. 20). The term is dimensionless as long as consistent units areused. In this equation, there are different possible ways to define the well drainage area (which will change with time andwith well density). Also the drainage area is complicated for horizontal wells; however, a consistent method from field-to-field is adequate for classification purposes. In our examples we use a uniform well spacing.

(20)

The magnitude of this inter-porosity flow term is not intuitive, but in a simple sense, it is a measure of the ability of thematrix to transfer fluids to the fractures, relative to the ability of the fractures to transport fluids to the well over a drainagevolume. If we consider Satmans analysis, a value of A > 50 would suggest that matrix-fracture transfer is rapid enough to

fe

mA k

Ak

10 CSUG/SPE 146580

keep up with depletion in the fractures throughout the drainage area. This is true only for single-phase depletion after pseudo-steady state is reached, but it does give a magnitude for relative comparison. Larger values mean that the matrix-fracturetransfer can more likely keep up with fracture depletion. If we have competing mass transfer processes (e.g. pressuredepletion in fractures and diffusion from matrix to fractures), then the ratio may need to include other dimensionlessparameters such as a capillary or bond number to better estimate the effectiveness of matrix-fracture transfer relative tofracture transport.

We now present a few examples of the new plot. In the plot examples here, we suggest that the inter-porosity parameters databe broken down into a number of equalized bins (e.g. ranges of inter-porosity flow ratio). For our examples we used 10%probability ranges. This is similar to the idea for carbonate classification (Lucia, 1999), where the phi-k data is divided intodifferent flow indicator types. All of the examples presented here are from actual NFR with 1) rigorously defined matrixreservoir characterization, 2) fractures networks defined via DFN and/or CFM methods calibrated to seismic, logs and/ormatrix characteristics, and 3) calibrated to dynamic performance. The comparisons are all made assuming a 160-acre wellspacing to provide consistent inter-porosity flow ratio. The results shown are only for a limited subset of the main reservoiraround some of the most highly fractured areas. Figure 3 compares the first four examples.

Example 1: Carbonate, Light Oil, Pressure Depletion via Horizontal and Vertical Wells, Moderate Aquifer InfluxThis reservoir has moderate matrix permeability (

CSUG/SPE 146580 11

inter-porosity flow values are quite high, because of the large matrix-fracture surface area. Dual-porosity or dual-permeabilitymodels are required to match early pressure depletion in the near-well shattered rock volume, but later time declines areindicative of a total system response with effective permeability one to two orders of magnitude greater than matrixpermeability. Of course, this is for one specific example only and is not a general rule.

Example 6: Unconventional Light Oil/Condensate with Free Gas Phase, Pressure Depletion via HydraulicallyFractured Horizontal Wells (single-well characterization)A recent single-well calibration in a different unconventional play is also shown in Figure 4(B). At first glance it looks tohave similar characteristics to the previous plot. However, here productivities are quite low. This is the difficulty in simplyusing dimensionless parameters for comparison. There are many other factors besides excess permeability which dictate thewell performance. Other concerns include PVT characteristics, initial pressure, thickness, number of frac stages, andhorizontal well length. Thus such comparisons as provided by these dimensionless plots are only one aspect of an overallintegrated characterization and simulation. The dimensionless plots are most useful when trying to make developmentdecisions such as well spacing within one specific unconventional play.

Example 7: Synthetic Example of Conventional Reservoir with Strong Fault-Related FracturingThis final short example shows the importance of shape factor (or fracture intensity). This is a synthetic example based onconcepts from the previous examples. It has moderate API oil and limited aquifer drive. It has a strong fault related fracturingalong several large faults. The Gilman plot is shown in Figure 5(A). The band running through the plot is a result of severalmore highly fractured zones. The excess permeability ratio is generally higher than the other cases. A 10-year, multi-wellsimulation of depletion is shown in Figure 5(B). All cases have the same properties except that shape factor is increased by afactor of 10 or decreased by a factor of 10 compared to the base case relations. The main differences in decline are a result ofdifferences in water production. Of note here is the large long-term difference in oil production; however, the first 3-yearsshow very minimal differences. This is typical of the types of responses we see in NFR. The short term impact of fracturespacing differences are difficult to determine from production response, but have a significant impact on long-term behavior.Differences are seen more quickly in injection processes.

The final comparison of the average properties for the different cases is shown in Figure 6. Table 1 provides the data. Thesefigures are a plot of the average values from Table 1. Averages themselves are not sufficient for estimating reservoirresponse; however, they do more clearly show the relative differences between different reservoirs. There is generally anincreasing trend of excess permeability with increasing storage ratio as expected. Case 4 is an outlier because of the very lowmatrix porosity. Figure 6(B) shows lower inter-porosity flow ratio as excess permeability increases. This trend is not strongbecause as excess permeability increases, matrix shape factor may also increase. For all these cases, the average inter-porosity flow parameter is greater than the value of 50 that might indicate rapid matrix-fracture equilibration for single-phaseflow. However, as shown in Figure 6(B), the long-term behavior is still very sensitive to the value of A. This is because oflimited fluid transfer rate for capillary and gravity dominated flow relative to transport through the fracture network.

SummaryPerformance evaluation, laboratory studies and modeling of fields with long histories has provided much information aboutthe nature of the fractured networks, fluid transfer mechanisms and indications of how the effective network properties relateto directly measurable properties like image and production logs, pressure transients and tracer tests. However, thecharacterization and modeling process still requires extensive calibration with dynamic data. Therefore we still must oftenrely on analogue reservoirs and prior experiences to estimate the flow characteristics and future behavior in NFR for fieldswith less production history. Much emphasis in modern workflows is being placed on improvements in characterization ofthe fracture network; however, reservoir flow behavior is also very dependent on the effectiveness of matrix-fracture transfermechanisms.

As a general recommendation for NFR simulation, is it important to identify intrinsic (e.g. lithologic) and extrinsic (e.g.structural) controls on fracture distribution and intensity and relate these to well performance (e.g. productivity and waterbreakthrough) in order to develop algorithms for distributing the fracture network properties in a 3-D static geomodel. Thesimulation model must honor the variability and should not be an overly simplified model in order to capture theheterogeneous nature of the reservoirs. Fracture-matrix transfer must be studied via laboratory experimentation, fine-gridmodeling and analogous reservoirs.

The new classification plot illustrated here provides a means to compare characteristics of different reservoirs including thevery important aspect of matrix-fracture transfer. Inter-porosity fluid transfer is not directly incorporated in the Nelson plot.Our new classification concept can be used to understand differences in dynamic performance of NFR for purposes ofanalogue selection or screening of potential recovery processes. We compared several characterized NFR reservoirs(including unconventional systems) via the new classification plot and their differences and performance were summarized.

12 CSUG/SPE 146580

AcknowledgementsAs mentioned in the Introduction, many of the background concepts were a result of unpublished collaborative efforts withDr. H. Kazemi, Colorado School of Mines. We would like to acknowledge his many contributions to the ideas presentedhere. We would also like to acknowledge Ron Nelson, PhD, Broken N Consulting for providing a modified schematic of hiswell-known distribution of fracture reservoir types.

NomenclatureA area, ft2B formation volume factor (FVF), RB/STBb harmonic decline factorc compressibility, psia-1d distance, ftD depth, ftD decline factor, 1/dayh height or thickness, ftk permeability, mdL matrix block dimension, ftln natural logarithmn exponent, power-law equationp pressure, psiaP10 linear fracture intensity measure, 1/LP32 volumetric fracture intensity factor, 1/LP33 volume of fractures per unit volumeq flow rate, STB/Dr radius, ftS saturation, fractiont time, daysV volume, ft3w width, ftx distance in x-direction, fty distance in y-direction, ftz distance in z-direction, ft difference or change in values porosity, fraction interfacial tension, dyne/cm difference in value inter-porosity flow parameter, dimensionless mobility, md/cp viscosity, cp Pi, constant density, lb/ft3

shape factor, ft-2

fracture-matrix flow rate, STB/D storativity ratio, dimensionless partial derivative gradient operator

divergence operator for a vector

SubscriptsA areac capillaryD dimensionlesse effective, externalexr excess ratiof fractureg gasi initial

CSUG/SPE 146580 13

i,j,k indicesm matrixo oilp effective porosityqmax maximum rater relativet totalth thresholdv verticalw waterx,y,z directions

ReferencesAraujo, H., Gilman, J. R., and Kazemi, H.: "Analysis of Interference and Pulse Tests in Heterogeneous Naturally Fractured Reservoirs",

SPE 49234 presented at the 1998 SPE Annual Technical Conference and Exhibition, New Orleans, LA (Sep. 27-30, 1998).

Arevalo-V., J. A., Samaniego-V., F., Lopez-C., F. F., Urquieta-S., E.: On the Exploitation Conditions of the Akal Reservoir ConsideringGas Cap Nitrogen Injection SPE 35319, Intl. Petroleum Conference & Exhibition of Mexico, Villahermosa, Mexico, (March 5-7.1996).

Ata, E. and Michelena, R. J.: Mapping distribution of fractures in a reservoir with P-S converted waves: The Leading Edge, 14, p.664-673(1995)

Beliveau, D., Payne, D. A. and Mundry, M.: Waterflood and CO2 flood of the Fractured Midale Field, J. Pet. Tech, 881-887,(September, 1993).

Campanella, J. D., Wadleigh, E. E., and Gilman, J. R.: Flow CharacterizationCritical for Efficiency of Field Operations and IOR, SPE58996 presented at the 2000 SPE International Petroleum Conference and Exhibition in Mexico, Villahermosa, Mexico (Feb. 1-3,2000).

Chang, M-M: Deriving the Shape Factor of a Fractured Rock Matrix, U.S. Department of Energy (National Institute for Petroleum andEnergy Research, Bartlesville, OK, NIPER-696 (DE93000170) (Sept. 1993).

Chen, H. Y., Poston, S. W., and Wu, C. H.: "Characterization of the Austin Chalk Producing Trend," SPE 15533 presented at the 61st SPEAnnual Technical Conference, New Orleans, LA (Oct. 1986).

Chen, H. L., Lucas, L. R., Nogaret, L. A. D., Yang, H. D., and Kenyon, D. E.: Laboratory Monitoring of Surfactant Imbibition WithComputerized Tomography, SPE Res. Engr. and Eval., (February 2001).

Christiansen, R. L., Gilman, J. R., Jargon, J. R., Kazemi, H., and Smith, R. E.: "Enhanced Oil Recovery in Naturally Fractured Reservoirs,"AIChE 51d presented at the 1989 AIChE Summer National Meeting Philadelphia, PA (August 1989).

Dershowitz, W., LaPointe, P., Eiben, T., and Wei, L.: Integration of Discrete Fracture Network Methods with Conventional SimulatorApproaches, SPE Res. Eval. & Eng., 165-170, (April 2000).

Dershowitz, W., Hermanson, J., Follin, S. and Mauldon, M.: "Fracture intensity measures in 1-D, 2-D, and 3-D and sp, Sweden,PacificRocks 2000, Girard, Liebman, Breeds & Doe (eds) c 2000 Balkema, Rotterdam, ISBN 90 5809 155 4. pg 849-853.

Dykstra, H.: "The Prediction of Oil Recovery by Gravity Drainage", J. Pet. Tech. 818-830, (May 1978).

Gale, Julia F. W.: Specifying Lengths of Horizontal Wells in Fractured Reservoirs, SPE Res. Eval. & Eng., 266-272, (June 2002).

Gauthier, B. D. M., Garcia, M., and Daniel J. -M.: Integrated Fractured Reservoir Characterization: A Case Study in a North AfricaField, SPE Res. Eval. and Engr., 284-294 (Aug. 2002).

Gilman, J. R. and Kazemi, H.: "Improvements in Simulation of Naturally Fractured Reservoirs," Soc. Pet. Engr. J. 695-707 (Aug. 1983).

Gilman, J. R. and Kazemi, H.: "Improved Calculations for Viscous and Gravity Displacement in Matrix Blocks in Dual-PorositySimulators," J. Pet. Tech, 60-70 (Jan. 1988).

Gilman, J. R., Tiss, M. Jargon, J. R., and Hinchman, S. B.: Dual-Porosity Simulation of the Zebbag Reservoir, Ezzaouia Field, Presentedat the Second ECLIPSE International Forum, Houston, TX, (April 15-19, 1996).

Gilman, J. R.: "Practical Aspects of Simulation of Fractured Reservoirs ", presented at the Seventh International Forum on ReservoirSimulation, Schlosshotel Bhlerhhe, Bhl/Baden-Baden, Germany (June 23rd - 27th, 2003).

14 CSUG/SPE 146580

Hallenbeck, L.D., Sylte, J.E., Ebbs, D.J., Thomas, L.K.: Implementation of the Ekofisk Field Waterflood SPE Form. Eval., , p. 284,(1991).

Haws, G. W. and Hurley, N. F.: "Applications of Pressure-Interference Data in Reservoir Characterization Studies, Big Horn Basin,Wyoming", SPE 24668 presented at the 67th SPE Annual Technical Conference and Exhibition, Washington, DC, (Oct. 4-7, 1992).

Heinemann, Z.E. and Mittermeir, G.M. Rigorous Derivation of the Kazemi-Gilman-Elsharkawy Generalized Dual Porosity Shape FactorPaper B044 presented at the 10th European Conference on the Mathematics of Oil Recovery - Amsterdam, The Netherlands, (Sept. 4-7, 2006)

Hossain, M. M., Rahman, M. K. and Rahman, S. S.: A Shear Dilation Stimulation Model for Production Enhancement from NaturallyFractured Reservoirs, SPE Journal, 183-195, (June 2002).

Iwere, F.O., Moreno, J. E., Apaydin, O. G., Len Ventura, R., Garcia, J. L. Vug Characterization and Pore volume Compressibility forNumerical Simulation of Vuggy and Fractured Carbonate Reservoirs SPE 74341, SPE International Petroleum Conference andExhibition, Villahermosa, Mexico, (Feb. 2002).

Kazemi, H., Merrill, L. S., Porterfield, K. L., and Zeman, P. R.: Numerical simulation of Water-Oil flow in Naturally Fractured Reservoirs,Soc. Pet. Eng. J. 317-26, (Dec. 1976).

Kazemi, H., Gilman, J. R., and El-Sharkawy, A. M.: "Analytical and Numerical Solution of Oil Recovery from Fractured Reservoirs UsingEmpirical Transfer Functions," Soc. Pet. Eng. Res. Engr., 219-227, (May 1992).

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Table 1. Average properties for all cases

Case kfe f km m ft2 L

ftf/(f+m) kfe/km kmmd/ft2 A=

(Akmkfe+

Case 1 1.97E+01 0.0004 2.53E+00 0.1149 0.0152 40.4 0.0033 29.73 3.52E-02 13653.30

Case 2 6.59E+01 0.0038 3.51E+00 0.2364 0.0284 21.4 0.0177 49.70 8.56E-02 10541.45

Case 3 4.64E+02 0.0054 5.48E+01 0.1250 0.0407 16.2 0.0456 66.60 2.19E+00 33423.98

Case 4 1.99E+00 0.0037 1.16E-02 0.0280 0.0050 92.5 0.0872 411.51 3.00E-05 202.67

Case 5 1.08E-01 0.0033 5.06E-03 0.0909 0.0013 82.4 0.0362 29.26 6.95E-06 413.15

Case 6 4.01E-04 0.0010 3.52E-05 0.0770 0.0032 50.0 0.0131 14.04 1.13E-07 1957.22

Case 7 5.26E+01 0.0058 1.38E+00 0.1449 0.0070 47.5 0.0387 926.13 6.75E-03 1276.83

+A=160acres for all cases

16 CSUG/SPE 146580

Figure 1. Idealization of a fractured systemwith fracture spacing Lx and fracture width wf

Figure 3. Gilman Plot for conventional reservoirs, Cases 1 to 4. A) Carbonate, light oil, pressure depletion via horizontal and verticalwells, moderate aquifer influx, B)Carbonate, light oil, pressure maintenance via gas and water injection in horizontal wells, C)Sandstone, heavy oil, waterflood via vertical wells; D)Quartzite, low matrix permeability, gas reservoir with vertical and horizontalwells

LxLx

wf

Gilman Plot

1.00

10.00

100.00

1000.00

0.0000 0.0200 0.0400 0.0600 0.0800 0.1000

f f/(f f+fm)

k fe/k

m

>0. to 1478.>1478. to 4441.>4441. to 9510.>9510. to 15581.>15581. to 22050.>22050. to 29327.>29327. to 39029.>39029. to 51233.>51233. to 74122.>74122. to 229912.

lA=(Adkms)/kfe

Intellectual Property of iReservoir.com, Inc

0.10

1.00

10.00

100.00

1000.00

0.0000 0.0100 0.0200 0.0300 0.0400

k fe/k

m

ff/(ff+fm)

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>0. to 2163.

>2163. to 5056.

>5056. to 28388.

>28388. to 68730.

>68730. to 135408.

>135408. to 213857.

>213857. to 341834.

>341834. to 622681.

>622681. to 6452860.

>6452860. to 793982524.

lA=(Adkms)/kfe

Intellectual Property of iReservoir.com, Inc

Figure 2. Modified schematic distribution of fracturereservoir types I-III relative to reservoir porosity andpermeability. Courtesy Ron Nelson, PhD, Broken NConsulting (after Nelson, 2001).

1.00

10.00

100.00

1000.00

0.0000 0.0200 0.0400 0.0600 0.0800 0.1000

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m

ff/(ff+fm)

Gilman Plot

>0. to 16.>16. to 19.>19. to 22.>22. to 25.>25. to 30.>30. to 37.>37. to 47.>47. to 58.>58. to 91.>91. to 33739.

lA=(Adkms)/kfe

Intellectual Property of iReservoir.com, Inc

0.10

1.00

10.00

100.00

1000.00

0.0000 0.0050 0.0100 0.0150 0.0200

k fe/k

m

ff/(ff+fm)

Gilman Plot

>0. to 735.

>735. to 1349.

>1349. to 2389.

>2389. to 4118.

>4118. to 6993.

>6993. to 11847.

>11847. to 20576.

>20576. to 39851.

>39851. to 90546.

>90546. to 872404.

lA=(Adkms)/kfe

Intellectual Property of iReservoir.com, Inc

IType II

III

% of Total Porosity

%of

Tota

lPer

mea

bilit

y

100 % kf

100% km100% fm 100% ff

M

All Fractures

Little or No Fractures

A B

C D

CSUG/SPE 146580 17

Figure 4. Gilman Plot for unconventional oil reservoirs, Cases 5 and 6: A) Unconventional, light oil, pressure depletion viahydraulically fractured horizontal wells; B) Unconventional, light oil/condensate with free gas phase, pressure depletion viahydraulically fractured horizontal wells (single-well characterization)

Figure 5. A) Gilman Plot for synthetic example and B) Normalized production for 10-yr forecast with shape factor increased by afactor of 10 or decreased by a factor of 10 compared to base simulation

Figure 6. Comparison of A) average values for all cases in Nelson Plot and B) plot of inter-porosity flow ratios

Gilman Plot

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10.00

100.00

1000.00

0.0000 0.0200 0.0400 0.0600 0.0800 0.1000

ff/(ff+fm)

k fe/k

m

>0. to 152.>152. to 202.>202. to 248.>248. to 296.>296. to 358.>358. to 449.>449. to 575.>575. to 755.>755. to 1007.>1007. to 4969.

lA=(Adkms)/kfe

Intellectual Property of iReservoir.com, Inc

1.00

10.00

100.00

1000.00

0.000 0.005 0.010 0.015 0.020

k fe/k

m

ff/(ff+fm)

Gilman Plot

>0. to 1001.>1001. to 1112.>1112. to 1224.>1224. to 1390.>1390. to 1613.>1613. to 1891.>1891. to 2225.>2225. to 2781.>2781. to 3615.>3615. to 4283.

lA=(Adkms)/kfe

Intellectual Property of iReservoir.com, Inc

1.00

10.00

100.00

1000.00

10000.00

0.0000 0.0200 0.0400 0.0600 0.0800 0.1000

k fe/k

m

ff/(ff+fm)

Gilman Plot

>0. to 14.>14. to 34.>34. to 71.>71. to 139.>139. to 265.>265. to 464.>464. to 855.>855. to 1521.>1521. to 3286.>3286. to 47463.

lA=(Adkms)/kfe

Intellectual Property of iReservoir.com, Inc

Case 1

Case 2Case 3

Case 4

Case 5

Case 6

Case 7

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0.0000 0.0200 0.0400 0.0600 0.0800 0.1000

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k m

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Case 1Case 2

Case 3

Case 4

Case 5

Case 6 Case 7

10.00

100.00

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10000.00

100000.00

1.00 10.00 100.00 1000.00

l A=(

Akm

s)/

k fe

kfe/km

A B

A B