Characterizing Partially Fractured Reservoirs by Tracer Injection

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Copyright 2003, Society of Petroleum Engineers Inc.

This paper was prepared for presentation at the SPE International Improved Oil RecoveryConference in Asia Pacific held in Kuala Lumpur, Malaysia, 2021 October 2003.

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AbstractThere is considerable interest in the petroleum industry tocharacterize partially fractured reservoirs and to develop anincreased understanding of the physics of fluid flow in thesetypes of reservoirs. This is because fractured reservoirs havedifferent behavior and there exist a large number of thesereservoirs that are not fully developed. This paper presents anumerical simulation study that was performed to investigatethe effect of rock properties on the tracer response in partiallyfractured reservoirs using a finite difference numerical

simulator. These properties include fracture intensity, fractureporosity and matrix permeability. The functional relationshipsbetween these parameters and the calculated effectivepermeabilities are also investigated. Several images, eachwith different probability of fracture intensity, were generatedrandomly. Numerical simulations of single-phase tracertransport were then performed in each of the generatedfractured models. Results show that the fracture intensity,fracture porosity and matrix permeability have a significanteffect on the tracer response in naturally fractured reservoirs.Depending on the reservoir properties, the results also showthat the flow in partially fractured reservoirs can be eithermatrix-dominated or fracture-dominated. The characteristicsof each regime and the conditions for its occurrence

are presented.

IntroductionThere is a large number of oil and gas reservoirs that arenaturally fractured. In fact, one may claim that allhydrocarbon reservoirs are naturally fractured reservoirs(NFR) to a certain degree. The question remains, however,whether or not these fractures form a fracture network thataffects the fluid flow properties. The effect of fractures

becomes important only when they occur with sufficientlength of penetration, connectivity and spacing. The behaviorof these types of reservoirs is considerably different than theconventional reservoirs (Aguilar 1980, Van Golf Racht 1982,

Saidi 1987). The difference arises from the two interactingpaths (rock matrix and fractures) for fluid flow having totallydifferent properties and communication with each other. Dueto the complexity of NFR systems, the literature discussingcharacterization and modeling of NFR is scarce compared tonon-NFR systems.

Modeling Naturally Fractured Reservoirs. Research onfractured reservoir simulation has a long history. Performance

prediction of naturally fractured reservoirs under uniform rockproperties has been the subject of many publications duringthe last three decades. Currently, there are three differenmethods being used for simulation of NFR systems: (1)continuum approach, (2) discrete fracture approach, and (3)integrated approach.Conventional single continuum approach has been applied tosimulate fractured reservoirs with fractures having smaleffects on the flow. Barenblatt et al (1960) first introduced thedual continuum (dual-porosity) approach. The authorsconsidered naturally fractured reservoirs as two homogeneousisotropic, overlapping continuums: the matrix blocks andfracture network. They assumed quasi-steady state flow from

matrix to fracture. Warren and Root (1963) later extendedthis work. The authors proposed a simplified representationof fracture networks to be used in dual-porosity simulatorsThey assumed that secondary porosity is contained within anorthogonal set of equally spaced system of fracture networkswhile the matrix blocks feed the fracture continuously. Inaddition, a no-flow condition between the matrix blocks wasassumed. In order to characterize the relationship between thetwo porosity regions, Warren and Root (1963) introduced twodimensionless parameters: inter-porosity flow coefficient ( )

and dimensionless fracture storage (). In his study, Kazem(1976) used the dual continuum approach to model NFR by amulti-layer system (dual-permeability model). The authorassumed that fractures are thin layers of high conductivity

alternating with thicker layers of matrix blocks consisting ofhigh storage capacity but low conductivity. The dual

permeability simulators allow matrix-matrix flow (Kazemi etal. 1976, Rossen 1977, Thomas et al. 1983).

In a later study, Pruess and Narasimhan (1985) introducedthe multiple interacting continua method (MINC), which isapplicable to numerical simulation of heat and multi-phasefluid flow in multi-dimensional, fractured porous media. Oneof the disadvantages of the dual-continuum approach is that itassumes fractures to be distributed regularly and welconnected. Whereas, real fracture systems are very irregularand very poorly connected (Chiles 1987, Laubach 1991Lorenz et al. 1991).

SPE 84886

Characterizing Partially Fractured Reservoirs by Tracer InjectionFuad Qasem, SPE, Ridha B.C. Gharbi, SPE, and Muhammed I. Mir, Kuwait University


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Long et al. (1985) and Dershowitz (1988) presented anapproach called discrete fracture flow models. In thisapproach, natural fractures are assumed as a system ofinteracting fracture segments instead of viewing them as acontinuum. Because this approach considers flow onlythrough the fracture space, the contribution of matrix

permeability and isolated fractures is not accounted for.

Besides this limitation, the models based upon this approachare limited in size, speed and level of sophistication requiredto simulate multiphase flow when compared to models basedupon continuum approach. This approach is typicallyapplicable for computation of flow through a single regioncontaining a large number of connected fractures.

To combine the advantages of both continuum approachand the discrete fracture network approach, integratedmethods have been introduced (Oda 1985, , Lee et al. 1997,Lough et al. 1998, Jensen et al. 1998, Park et al. 2000,Dershowitz 2000, Lee et al. 2000, Sutopo et al. 2001). In thisapproach, a discrete fracture network model of the reservoir isfirst prepared. Then, either this model directly or the

parameter distribution derived from this model is used to

provide input grid parameters for simulators based uponcontinuum (single or dual) approach. The approach retainsmany of the advantages of continuum approach along with therealism offered by the discrete fracture network approach.

Characterization of Naturally Fractured Reservoirs.

Various sources for fracture data have been used: outcropstudies, seismic, well logging, pressure transient tests, andinter-well tracer studies. The data from all these sources isintegrated to get a reliable description of fracture system bothat field scale and at local reservoir cell scale. Reliablecharacterization of fractures are now possible by developingtools for merging seismic, borehole imaging, lithological andoutcrop data together with the help of geological andgeochemical rules. Accurate seismic data yield reliablemodels of large-scale fracture networks, whereas boreholeimaging provides the actual fracture description along thewells, which enables a reliable statistical determination offractures.

Well logging data represent only properties measured ator near the well bore, so its application to characterize thefractures system in the reservoir must be done with caution.Pressure transient analyses have often been used to estimatethe equivalent fracture permeability, fracture volume, andsometimes the shape factor of the fracture network around thewell. Pressure interference tests can also indicate the globalhorizontal anisotropy of fracture permeability (i.e.

fracture orientation).Radioactive and chemical tracers have been used for

many years in ground water hydrology to analyze movementof water through porous formations. However, their use ingeothermal and petroleum reservoir engineering is relativelyrecent (Jensen 1983). The literature on the flow of tracer in

porous media can be divided into two main categories: directand inverse methods. The direct method deals with tracerresponse behavior from the knowledge of pertinent reservoirand tracer parameters. The inverse method estimates thereservoir and tracer parameters from the interpretation of thetracer response.

Inter-well tracer studies provide valuable characterizationof naturally fractured reservoirs. The applications of tracers tostudy naturally fractured reservoirs have been the subject onumerous studies (Wagner 1977, Tester et al. 1982, Ramirez1993, Shinta et al. 1993, Daltaban et al. 1994, Ramirez et al1994, Sato et al. 1994, Zellou et al. 1995, Maroongoog et al1995, Deng et al. 1995, Wattenbarger et al. 1995, Almeida et

al. 1996). Despite all these studies (only few cited here), theresponse of tracers in partially fractured reservoirs is yet to beinvestigated. In partially fractured reservoirs, the fracturenetwork does not cover the entire reservoir volume. In othewords, the fragment sizes are larger than the simulation grid

block. Therefore, the primary objective of this work is to usenumerical simulations to investigate the effect of fractureintensities on the tracer response in partially fracturedreservoirs. A secondary objective of the work is to examinehow fracture porosity and matrix permeability affect the tracerresponse in these types of reservoirs. A final objective is tostudy the functional relationship between these parameters andthe calculated effective permeabilities. First, we present themethodology that is used for this study.

MethodologyFracture Models. The conventional methods of simulatingnaturally fractured reservoirs consist of fully regular matrixnetwork, surrounded by interconnected fractures. Thisapproach is unsuitable for partially fractured reservoirs

because of their high degrees of heterogeneities. In partiallyfractured reservoirs, fracture distribution is highly irregularIn this study, a random distribution of fractures is consideredA uniform random number generator was used to generaterandom points inside a two-dimensional field of 70x71 grid(Press et al. 1992) Several images, each with differen

probability of fracture intensity, were generated using a singlerealization. Fracture intensity is defined as the ratio of thenumber of grid blocks having fractures to the total number ogrid blocks. The fracture models were generated to cover awide range of fracture intensities from 0.1 to 0.9. A fractureintensity of 0.1 represents a nearly non-fractured mediumwhile a fracture intensity of 0.9 represents a highly fracturedmedium (i.e. 90% of all grid blocks are fractured). Dependingon the depositional environment, partially fractured petroleumreservoirs can have widely varied fracture intensities rangingfrom high to low numbers. Figures 1 and 2 show 2-D

permeability maps with fracture intensities of 0.10 and 0.5respectively. The white colored blocks represent the nonfractured ones, while the dark color blocks are fractured.

Fluid Flow Models. Numerical simulations of single-phasetracer transport were performed in each of the generated 2-Dmodels. One well was placed horizontally along one side othe reservoir, while the other was placed along the oppositeside. An advanced black oil simulator IMEX (Users Guide2000), in dual permeability mode, was used for this purposeWe have used Gilman and Kazemi ( 1983) formulation forshape factor calculations. The 2-D areal model with x-y-zgrid of 70x71x1 was found to be relatively insensitive tofurther mesh refinement. For all simulation runs, the x- and y

permeability values were assumed equal in each grid-blockFracture permeability was kept constant at 1000 mdFracturing rarely increases the porosity more than a few


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percent but may dramatically increase permeabilities to valuesof several darcies. The total porosity of each grid block isassumed constant. The relationship between total porosity

(t), fracture porosity (f), and matrix porosity (m) isas follows:

mfft += 1

The water is injected continuously and across the entireinlet end through the 70 grid blocks. Injection was at aconstant rate of 100 bbl/day. Tracer injection schedule was 1lbs/bbl of water injected for 10 days. Production, constrained

by constant outlet pressure, occurred through the 70 gridblocks at the outlet end of the porous medium. Table 1 liststhe simulation input data.

A sensitivity study was carried out to investigate theeffect of fracture intensity, fracture porosity and matrix

permeability on the normalized properties of tracer produced.These include the normalized cumulative tracer produced andthe normalized rate of tracer produced. The fracture porosityand the matrix permeability were varied from 0.01 to 0.06,and from 0.5 to 35 md, respectively. As mentioned earlier, the

fracture intensity varied from 0.1 to 0.9. The total amount oftracer injected (1000 lbs) is used to normalize the cumulativetracer produced, while the tracer mass injection of 100 lbs/daywas used to normalize the rate of tracer produced.

Results and DiscussionFigures 3a and 3b show respectively the effect of fracture

intensity (FI) on the normalized cumulative tracer produced

( Dm ) and on the normalized rate of tracer produced ( Dq ),

both of which are in dimensionless form. In these simulation

runs, the fracture porosity ( f ) was assumed 0.01 and matrix

permeability ( mk ) was 5 md. The figures show the effect of

FI on the tracer response is very significant. As FIdecreases below a certain value ( 6.0FI ), the responsecurves of Figure 3a gradually become elongated or moredispersive. This corresponds to a gradual flattening of theresponse curve in Figure 3b and a shift in the peak to a latertime. In these instances, the matrix increasingly dominates theflow and the fractures play less important role as

FI decreases.On the other hand, as FI increases to higher values

( 6.0FI ), the shape of the response curves graduallybecomes less stretched (Figure 3a). This corresponds to

sharper and shortly delayed peaks for higher values ofFI

(Figure 3b). In these cases, the fractures become more andmore dominant and the matrix play lesser role as FIincreases.

These results appear to imply that there is critical value of

FI that sort matrix-dominated flow from fractured-

dominated flow. For the case of mdkm 5= , this value of

FI is on order of 0.6. Therefore, depending on the fractureintensity, the flow in partially fractured reservoirs can beeither matrix-dominated or fractured-dominated.

Figures 4a-b and 5a-b show the results of the tracerresponse when the fracture porosity was modified to 0.01 and0.06, respectively. All other parameters in these runs were

maintained constant. These figures can be compared to thebase case run of Figure 3a-b, where the fracture porosity was0.02. It can be noticed from these figures that an increase infracture porosity delays the tracer break through slightly. Foreservoirs with high values of fracture intensity, this delay

becomes more significant.Another way of looking at these data is shown in Figure

6. The figure shows the results of tracer response variationwith the fracture porosity for a given fracture intensity. Asshown, the effect of fracture porosity is more significant for

fracture intensity 6.0FI and less significant for

6.0FI . At a fracture intensity of 0.6, the response showsthe formation of two peaks. In this instance, both the matrixand the fracture play a role. The earlier peak denotes the flowfrom the fracture, while the second peak is due to the flowfrom the matrix. Therefore, this confirms that fractureintensity in the order of 0.6 represents a transition fromfracture-dominated to matrix-dominated flow for the case o

mdkm 5= .

Figure 7 shows the change in the peak arrival time at the

production well with the fracture intensity, FI for fractureporosity of 0.02 and 0.06. As shown, for low fractureintensity (matrix-dominated flow), the peak arrival time is adecreasing function of fracture intensity. On the other handfor fractured-dominated flow, the peak arrival time increaseswith fracture intensity. The point where the two curves meeindicates the transition from matrix-dominated to fractured-dominated flow. This transition, however, is a function ofracture porosity. As the fracture porosity increases from 0.02to 0.06, the transition from matrix-dominated to fracture-dominated flow occurred at higher value of fracture intensityIn addition, the rate of change of the peak arrival time in thefracture-dominated region was higher for higher fracture

porosity. Because of the low difference between the twovalues, the variation of fracture porosity from 0.02 to 0.01 didnot make a significant effect on the peak arrival time.

Figures 8a-b, 9a-b, and 10a-b show the results of thetracer response when the matrix permeability was modified to0.5, 2, and 35 md, respectively, with fracture porositymaintained at 0.02. These figures should also be compared toFigure 3a-b, where the matrix permeability was 5 md. Excepthe matrix permeability, all other parameters for these runswere maintained constant. An increase in matrix permeabilityvalues delays the break through time. This effect is more

pronounced in cases in which a variation in the matrixpermeability changes the nature of the flow (i.e. matrixdominated or fracture-dominated). In other words, the matrix

permeability plays a dominant role in deciding whether theflow is matrix-dominated or fracture-dominated.

This point is much more clear to see in Figure 11, whichshows the effect of matrix permeability on the tracer responsefor a given fracture intensity. As shown, for fracture intensityof 0.4, the matrix dominates the flow for all studied values ofmatrix permeability (0.5, 2, and 35 md). However, fofracture intensity of 0.9, the fractures dominate the flow for alcases. For reservoirs with fracture intensity of 0.6, the effecof varying the matrix permeability changes the flow to

fracture-dominated for mdkm 5.0= , and to matrix


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dominated for mdkm 35= . Therefore, higher matrix

permeability shifts the transition from matrix-dominated tofracture-dominated flow to higher values of fracture intensity.

Figure 12 shows the change in the peak arrival time at theproduction well with the fracture intensity for matrixpermeabilities of 5 and 35 md. As shown, for the case of 5md, the matrix dominates the flow up to a fracture intensity of

0.6. After this point, the fractures will take over andconsequently; the contribution from the matrix becomesinsignificant. For the case of 35 md, however, the matrix stilldominates the flow for higher values of fracture intensity.This shows that an increase in matrix permeability has shifted

the transition to higher value ofFI. Further increase in thematrix permeability will yield matrix-dominated flow nomatter what the value of the fracture intensity is. Data alsoshow that a decrease in the matrix permeability below 5 mdwill shift the transition of matrix-dominated to fracture-

dominated flow to lower values of FI. Therefore, thetransition is a function of fracture intensity, matrix

permeability and fracture porosity of the reservoir.

The effect of the reservoirs properties on the effectivepermeability ( effk ) is also investigated. The effective

permeability values for the various models having differentfracture intensity, fracture porosity, and matrix permeabilityare presented in Figure 13. As shown, the effect of fracture

intensity on effk is quite significant. With an increase in

fracture intensity, the portion of high permeability medium(fractures) is increased, and therefore the effective

permeability is increased. For matrix-dominated flow, the rate

of increase in effk is low, whereas, for fracture-dominated

flow, the rate is much higher. For the same fracture intensity,the effect of matrix permeability is to shift the effective

permeabilities to higher values. This shift is more pronouncedin cases where both the matrix and the fractures play a role(i.e. at or near the transition zone). It should also be notedthat the change in fracture porosity plays no significant effecton the effective permeability values.

ConclusionThis study was aimed at investigating the effect of rock

properties on the tracer response in partially fracturedreservoirs using a finite difference numerical simulator.Properties included fracture intensity, fracture porosity andmatrix permeability. Based on the results of reservoirsimulations of single-phase tracer response, we conclude

the following:1. Fracture intensity, fracture porosity and matrix

permeability have a significant effect on the tracerresponse in partially fractured reservoirs.

2. Depending on the reservoir properties, the flow inpartially fractured reservoirs can be either matrix-dominated or fracture-dominated. The formation of two

peaks in tracer response (one for fracture and one formatrix) indicates the transition from matrix-dominated tofracture -dominated flow.

3. The transition from matrix-dominated to fracture-

dominated flow is a function of fracture intensity (FI),

the matrix permeability ( mk ), and the fracture

porosity ( f ).

4. Higher matrix permeability and higher fracture porosityshift the transition from matrix-dominated to fracture-dominated flow to higher value of fracture intensity andvice versa.

5. The effect of fracture porosity is more significant forfractured-dominated reservoirs and less significant formatrix-dominated reservoirs.

AcknowledgmentsThe authors express their appreciation to Kuwait UniversityResearch Administration for financially supporting this workthrough a university research grant (EP 02/01).

Nomenclature

FI = Fracture Intensity

effk = Effective permeability

mk = Matrix permeability

Dm = Normalized cumulative tracer produced

Dq = Normalized rate of tracer produced

NFR = Naturally fractured reservoirs

Greek Symbols

t = Total porosity of a grid block,

f = Fracture porosity

m = Matrix porosity

References

Aguilar, R.: Naturally Fractured reservoirs, PennWell, TulsaOklahoma, 1980.

Almeida, A.R. and Cotta, R.M.: Analytical Solution of theTracer Equation for the Homogenous Five-SpoProblem, Soc. Pet. Eng. J. (March) 31-38, 1996.

Barenblatt, G. I., Zheltov, I.P., and Kochina, I.N.: BasicConcepts in the theory of Seepage of HomogeneousLiquids in Fissured Rocks, Priklandaia Matematica IMechanica Academia Nauk, S.S.S.R., 24, No.5, 852-8641960.

Barenblatt, G.I., Zheltov, I.P.: On the Basic Equations of theSingle Phase Flow of Fluids Through Fractured PorousMedia, Dokladi Akademii Nauk, S.S.S.R., 132, No.3

542-548, 1960.Chiles, J.P.: ThreeDimensional Geometric Modeling of aFracture Network, proceedings of the conference onGeostatistical, Sensitivity and Uncertainty Methods forGroundWater Flow and Radionuclide TransporModeling, San Francisco, California, September 1987editor Bruce E. Buxton, Batelle Press, (1987) 361.

Deng, X. and Horn, R.N.: Description of HeterogeneousReservoir Using Tracer and Pressure DataSimultaneously, paper SPE 30590 presented at the SPEAnnual Technical Conference and Exhibition, Dallas, TXOctober 22-25, 1995.


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Dershowitz, B., LaPointe, P., Eiben, T., and Wei, L.:Integration of Discrete Feature Network Methods withConventional Simulator Approaches, Soc. Pet. Eng.Reservoir Eval. & Eng. 3 (2), April 2000.

Dershowitz, W. S., Doe, T. W.: Practical Applications ofDiscrete fracture Approaches in Hydrology, Mining andPetroleum Extraction, proceedings of the International

Conference on Fluid Flow in Fractured Rocks, Atlanta,Georgia, May 1988, 381.Gilman, J., and Kazemi, H.: Improvements in Simulation of

Naturally Fractured Reservoirs, Soc. Pet. Eng. J., August1983, pp. 695-707.

Jensen, C.L., Lee, S.H., Miliken, W.J., Kamath, J., Narr, W.,Wu, H., and Davies, J.P.: Field Simulation of NaturallyFractured Reservoirs Using Permeabilities Derived FromRealistic Fracture Characterization, paper SPE 48999,

presented at the SPE Annual Technical Conference andExhibition held in New Orleans, LA, Sept. 27-30, 1998.

Jensen, C.L.: Matrix Diffusion and Its Effect on theModeling of Tracer Returns From the Fracturedgeothermal Reservoir at Wairakei New Zealand,

Stanford Geothermal Program, SGP-TR-TR-71, Stanford,California, 1983.

Kazemi, H., Merill, L., Porterfield, K. and Zeman, P.:Numerical Simulation of Water-Oil Flow in NaturallyFractured Reservoirs, Soc. Pet. Eng. J. (Dec.)317-326, 1976.

Kazemi, H.: Pressure Transient Analysis of NaturallyFractured Reservoirs, Soc. Pet. Eng. J. (December) 415-462, 1969.

Laubach, S.E.: Fracture Patterns in Low PermeabilitySandstone Gas Reservoir Rocks in the rocky Mountainregion, paper SPE 21853, presented at the RockyMountain Regional Meeting and Low PermeabilityReservoirs Symposium, Denver, Colorado, April 1991.

Lee, S.H., Durlofsky, L.J., Lough, M.F., and Chen, W.H.:Finite Difference Simulation of Geologically ComplexReservoirs with Tensor Permeabilities, paper SPE38002, presented at the SPE Reservoir SimulationSymposium held in Dallas, TX, June 8-11, 1997.

Lee, S.H., Jenson, C.L, and Lough, M.F.: Efficient FiniteDifference Model For Flow in a Reservoir with Multiplelength-scale Fractures, Soc. Pet. Eng. J. (Sept.)268-275, 2000.

Long, J.C.S., Gilmour, P., and Witherspoon, P.A.: A ModelFor Steady Fluid Flow in Random Three-Dimensional

Networks of Disc-Shaped Fractures, Water ResourcesResearch 21, 1105, 1985.

Lorenz, J.C., and Hill, R.E.: Subsurface Fracture Spacing:Comparison of Inferences from Slant/Horizontal Coresand Vertical Core in Mesaverde Reservoirs, paper SPE21877, presented at the Rocky Mountain RegionalMeeting and Low Permeability Reservoirs Symposium,Denver, Colorado, April 1991.

Lough, M.F., Lee, S.H., and Kamath, J.: An EfficientBoundary Integral Formulation for Flow ThroughFractured Porous Media, Journal of ComputationalPhysics 143, 462-483, 1998.

Maroongroge, V., Saad, N., Pope, G.A., and Sepehrnoori, K.:Use of Inverse Modeling for Conditioning GeostatisticalModels to vertical tracer Profiles, paper SPE 30592,

presented at the SPE Annual Technical Conference andExhibition, Dallas, TX, October 22-25, 1995.

Oda, M.: Permeability Tensor for Discontinuous RockMasses, Geotechnique 35, 483, 1985.

Park, Y.C. and Sung, W.M.: Development of FEM reservoiModel Equipped With Effective Permeability Tensor andits Application to the Naturally Fractured Reservoir,

paper SPE 64793, presented at the SPE International Oiand Gas Conference and Exhibition held in BeijingChina, Nov. 7-10, 2000.

Press, W.H., Teukolsky, S.A., Vetterling, W.T., and FlanneryB.P.: Numerical Recipes in Fortran: The art of ScienceComputing, 2nd Edition, Cambridge UniversityPress, 1992.

Pruess, K. and Narasimhan, N.T.: A Practical Method foModeling Fluid and Heat Flow in Fractured PorousMedia, Soc. Pet. Eng. J. (Feb) 14-26, 1985.

Qasem, F.H.: Performance and Recovery Prediction inHeterogeneous Naturally Fractured Reservoirs Under theSolution Gas Drive Process, PhD Dissertation, Universityof Southern California, 1996.

Ramirez, J., Samaniego, F., Rivera J., and Rodriguez, F.Trace Flow in Naturally Fractured Reservoirs, paperSPE 25900 presented at the SPE Rocky MountainRegional/Low Permeability Reservoirs SymposiumDenver, Colorado, April 12-14, 1993.

Ramirez, S.J., Samaniego, V.F., Rodriguez, F., and RiveraR.J.: Tracer-Test Interpretation in Naturally FracturedReservoirs, paper SPE 28691, presented at the SPEInternational Petroleum Conference and Exhibition oMexico, October 10-13, 1994.

Rossen, R.H.: Simulation of Naturally Fractured Reservoirwith Semi Implicity Source Terms, Soc. Pet. Eng. J(June) 210-210, 1977.

Saidi, A.M.: Reservoir Engineering of Fractured ReservoirsGeneral Printing, Singapore, 1987.

Sato, K. and Abbaszadeh, M.: Tracer Flow and PressurePerformance of Reservoirs Containing Distributed ThinBodies, paper SPE 28444, presented at the SPE AnnuaTechnical Conference and Exhibition, New Orleans, LASeptember 25-28, 1994.

Shinta, A.A. and Kazemi, H.: Tracer Transport inCharacterization of Dual-Porosity Reservoirs, paper SPE26636, presented at the SPE Annual TechnicaConference and Exhibition, Houston, TX,October 3-6, 1993.

Sutopo, Arihara, N., Sato, K.: Simulation of NaturallyFractured Reservoirs with Effective Permeability, paper

SPE 68705, presented at SPE Asia Pacific Oil and GasConference And Exhibition held in Jakarta, Indonesia17-19 April 2001.

Tester, J.W., Bivins, R.L., and Potter, R.M.: Interwell TraceAnalyses of a Hydraulically Fractured GraniticGeothermal Reservoir, Soc. Pet. Eng. J. (August)537, 1982.

Thomas, L.K., Dixon, N.T. and Pierson, R.G.: FracturedReservoir Simulation, Soc. Pet. Eng. J. (February) 4254, 1983.

Users Guide, IMEX, Advanced Oil/Gas Reservoir Simulatorversion 2000, Computer Modeling Group, Ltd., CalgaryAlberta, Canada.


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Van Golf-Racht, T.D.: Fundamentals of Fractured ReservoirEngineering, Elsevier Scientific Publishing,Amsterdam, 1982.

Wagner, O.R.: The Use of Tracers in Diagnosing InterwellReservoir Heterogeneities Field Results, J. Pet.Technology (November) 1410, 1977.

Warren, J.E. and Root, P.J.: The behavior of naturally

fractured reservoirs, Soc. Pet. Eng. J., 3, 245-255, 1963.Wattenbarger, R. C., Aziz, A., and Orr, F.M.: High-Throughput TVD-Based Simulation of Tracer Flow,

paper SPE 29097, presented at the SPE Symposium onReservoir Simulation, San Antonio, TX,February 12-15, 1995.

Yi, T., Daltaban, T.S., and Archer, J.S.: Analysis oInterwell Tracer Flow Behavior in Transient Two-PhaseHeterogeneous Reservoirs Using Mixed Finite ElementMethods and the Random Walk Approach, paper SPE28901, presented at the SPE European PetroleumConference, London, UK, October 25-27, 1994.

Zellou, A., Ouenes, A., and Banik, A.: Improved Naturally

Fractured Reservoir Characterization Using NeuraNetworks, Geomechanics and 3-D Seismic, paper SPE30722, presented at the SPE Annual TechnicaConference and Exhibition, Dallas, TX,October 22-25, 1995.

Table 1. Simulation Input Data

Nx 70

Ny 71

Nz 1

Injection rate 100 bbl/dayTracer mass injection 1 lb/bblTotal tracer amount 1000 lbsMatrix permeability 0.5 35 mdFracture porosity 0.01 0.06Block porosity 0.2Fracture permeability 1000 mdFracture intensity 0.1 0.9


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0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5PVI

mD

0.2 0.4 0.6 0.9FI:

Figure 3a. Effect of Fracture Intensity on tracer produced

(f= 0.02, Km = 5 md)

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5PVI

mD

0.2 0.4 0.6 0.9FI:

Figure 3b. Effect of Fracture Intensity on tracer rate

(f= 0.02, Km = 5 md)

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5PVI

mD

0.2 0.4 0.6 0.9


(f= 0.01, Km = 5 md)

0

0.1

0.2

0.3

0 0.5 1 1.5PVI

qD

0.2 0.4 0.6 0.9


(f= 0.01, Km = 5 md)


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SPE 84886 9

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5PVI

mD

0.2 0.4 0.6 0.9FI:

Figure 5a. Effect of Fracture Intensity on tracer produced (f= 0.06, Km = 5 md)

0

0.1

0.2

0.3

0 0.5 1 1.5PVI

qD

0.2 0.4 0.6 0.9

Figure 5b. Effect of Fracture Intensity on tracer rate (f= 0.06, Km = 5 md)


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Figure 6 Effect offon Tracer Response for Various Fracture Intensities

a) FI = 0.4

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5

PVI

mD

0.01 0.02 0.06

c) FI = 0.6

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5

PVI

mD

0.01 0.02 0.06f:

e) FI = 0.9

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5

PVI

mD

0.01 0.02 0.06

b) FI = 0.4

0

0.1

0.2

0.3

0 0.5 1 1.5

PVI

qD

0.01 0.02 0.06

d) FI = 0.6

0

0.1

0.2

0.3

0 0.5 1 1.5

PVI

q D

0.01 0.02 0.06

f) FI = 0.9

0

0.1

0.2

0.3

0 0.5 1 1.5

PVI

qD

0.01 0.02 0.06


11/14

SPE 84886 11

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

Fracture Intensity

PeakArrivalTime,PVI

0.01 0.02 0.06

Matrix Dominated

Fracture Dominated

Figure 7: Effect of FI on Peak Arrival Time ( Km = 5 md )

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5PVI

mD

0.40 0.60 0.90


(f= 0.02, Km = 0.5 md)

0

0.1

0.2

0.3

0 0.5 1 1.5PVI

qD

0.40 0.60 0.90


(f= 0.02, Km = 0.5 md


12/14

12 SPE 84886

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5

PVI

mD

0.60 0. 70


(f= 0.02, Km = 2 md)

0

0.1

0.2

0.3

0 0.5 1 1.5PVI

qD

0.60 0.70


(f= 0.02, Km = 2 md)

0

0.2

0.4

0.6

0.8

1

0 0.3 0.6 0.9 1.2 1.5

PVI

mD

0.4 0.6 0.7


(f= 0.02, Km = 35 md)

0

0.1

0.2

0.3

0 0.5 1 1.5

PVI

qD

0.4 0.6 0.7


(f= 0.02, Km = 35 md)


13/14

SPE 84886 13

Figure 11. Effect of Km on Tracer Response for Various Fracture Intensities (f= 0.02 )

b) FI = 0.4

0

0.1

0.2

0.3

0 0.5 1 1.5P VI

qD

0.5 5 35

e) FI = 0.6

0

0.1

0.2

0.3

0 0.5 1 1.5PV I

q D

0.5 5 35

f ) FI = 0.9

0

0.1

0.2

0.3

0 0.5 1 1.5PV I

q D

0.5 5 35

a) FI = 0.4

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5PV I

mD

0.5 5 35

c) FI = 0.6

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5PV I

mD

0.5 5 35Km :

e) FI = 0.9

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5P VI

mD

0.5 5 35


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14 SPE 84886

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Fracture Intens ity

PeakArrivalTime,

PV

I

5 35

Fracture

Dominated

MatrixDominated

km:

Figure 12. Effect of FI on the Peak Arrival Time (f = 0.02)

0

100

200

300

400

500

600

700

800

900

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Fracture Intensity

EffectivePermeability,md

km = 5md

km = 35 md

Figure 13. Effect of FI on the Effective Permeability (f = 0.02)

Characterizing Partially Fractured Reservoirs by Tracer Injection

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