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SPE 132838

Effects of Fracture Properties on Numerical Simulation of a NaturallyFractured ReservoirM.M. Noroozi and B. Moradi, SPE, Iranian Central Oil Fields Company, and G. Bashiri, Research Institute ofPetroleum Industry

Copyright 2010, Society of Petroleum Engineers

This paper was prepared for presentation at the Trinidad and Tobago Energy Resources Conference held in Port of Spain, Trinidad, 27–30 June 2010.

This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewedby 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, ormembers. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print isrestricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

AbstractEffects of Some of the fracture properties on numerical simulation of fractured reservoirs are usually not taken into consideration.

Two important fracture properties, which are used in simulation, are fracture capillary pressure and fracture relative permeabilities.Engineers usually assume the first one to be zero and the second one to be a straight line without paying attention to their

significant role in the simulation of fractured reservoirs. In addition, effects on these parameters on the behavior of fractured

reservoir model when Dual Porosity Dual Permeability (DSDP) concept is used are not investigated yet. The present study

investigates the effects of above mentioned properties through other fracture properties like fracture permeability and matrix-

fracture transfer coefficient(shape factor) to analyze completely effects of the whole fracture characteristics on numericalsimulation of a reservoir. The oil field under study is a highly fractured carbonate reservoir located in Southwest of Iran. This

 paper indicates when straight-line fracture relative permeabilities and zero fracture capillary pressure can be used in the simulation.

Effect of reservoir heterogeneity was investigated on numerical simulation too. Sensitivity analysis also has been done to clearly

indicate the behavior of the DSDP model by assuming /nonassuming zero fracture capillary pressure and straight line fracture

relative permeabilities. Sensitivity analysis was done in three main production scenarios: natural depletion, water injection, gasinjection. This sensitivity study will also show the magnitude of the error which simulation engineers are making if they use

straight-line relative permeabilities and zero capillary pressure in the fractures.

IntroductionSimulation of naturally fractured reservoirs is a challenging task from both a reservoir description and a numerical standpoint:

Flow of fluids through the reservoir primarily is through the high permeability, low effective porosity fractures surrounding

individual matrix blocks.The matrix blocks contain the majority of the reservoir pore volume and act as source or sink terms to thefractures. The rate of recovery of oil and gas from a fractured reservoir is a function of several variables, including:a) Size and

 properties of matrix block b) Size and properties of fracture blocks. The study of naturally fractured reservoirs has been the

subject of numerous papers over the last four decades. but there are some fracture properties which usually their effects is ignored by researchers and engineers .Two important fracture properties which are usually neglected are: a)  Fracture relative

 permeabilities .b) Fracture capillary pressure. Currently engineers simulating fractures reservoirs by following assumptions: a)

straight line fracture relative permeabilities. b)zero capillary pressure in the fractures.They do not know when non-straight linerelative permeabilities and non-zero capillary pressure are important and when they are not important, and they do not know the

magnitude of the error they are making by applying these simplified assumptions. De la Porte [1] investigated the effect of fracture

 properties on the synthetic model while Dual Porosity concept is used; however, the effects of fracture properties on the behavior

of the real fractured reservoir model when DSDP concept is used, is not investigated yet. In this study, one of the fractured

reservoirs of Iran has been used as a real model. ECLIPSE, which is one of the best worldwide simulators, has been used in this project to perform the simulation.simulation results with economical impact, which is analyzed, Are final oil Recovery, Oil rate,

Water injection rate, Gas oil ratio and Gas injection rate.

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Theory

Fracture Relative Permeabilities

Relative permeability functions are usually taken to be dependent on phase saturation. The two most commonly used expressionfor relative permeability for homogeneous  porous media are the X-curve and Corey curve (Corey, 1954). The X-curve describes

relative permeability as a linear function of saturation.[2] Earliest is Romm’s (1966) experiment with kerosene and water through an

artificial parallel-plate fracture lined with strips of polyethylene or waxed paper. Romm found a linear relationship between

 permeability and saturation.[3]

 His experimemits did not examine the effects of fracture aperture and roughness effects, or the

implications for reservoir scale behavior. Pruess and Tsang (1990) conducted numerical simulation for flow through rough-walledfractures. They modeled fractures as two-dimensional porous media with apertures varying with position. Their study shows that

residual saturation of the nonwetting phase is large and phase interference is greatly dependent on the presence or absence ofspatial correlation of aperture in the direction of flow.[4]Persoff et al. (1991) did experiments on gas and water flow through rough-

walled fractures using transparent casts of natural fractured rocks. The experiment showed strong phase interference similar to the

flow in porous media. [5]Persoff and pruess did other experiments on multiphase flow in rough walled fracture. [6]Their results are

compared with commonly used relative permeability relations for porous media, the X-curve and Corey curve as shown in Figure1. In 1992, Rossen and Kumar introduced a method for calculating non straight-line relative permeabilities usig the Effective

Mediumn Approach (EMA), which is based on the work of Pruess and Tsang as discussed above. EMA was used to illustrate the

effect of gravity and aperture distribution on relative permeabilities. [7] The fracture relative permeability curves used in this study

were obtained from the research by Rossen and Kumar. According to their study the main parameter used in selecting the

appropriate relative permeability curve for a specific reservoir system, with gravity and capillary forces acting, is dimensionlessfracture height, HD. That is essentially a ratio of the gravitational force to the capillary forces in the system:

 [1]

o

 Db

 H  g  H 

/

**

γ  

 ρ ∆

=   (1)

Where  ρ ∆  is the density difference between the fluids,γ    is the interfacial or surface tension between the fluids,g is gravitational

acceleration,H is fracture height and ob  is mean half-aperture of the fracture.

HD quantifies the extend of gravity segregation. HD of zero indicates complete domination of capillary forces, so simultaneous

two-phase flow is impossible. When HD is infinity, total phase segregation will allow the use of straight-line relative permeabilities

and zero capillary pressures. 

Figure 3 shows the fracture relative permeability curves associated with the various HD parameters.

According to their data, it can be shown that HD is straightly proportional to mean half-aperture of the fracture (Figure 2).

Their experiments shows that when HD  is high (greater than 10). Total phase segregation allows use of straight-line relative

 permeabihities.according to above result in oil-gas systems straight-line relative permeabihities can be used (It will be discussed in

details in gas injection section)

Fracture Capillary Pressure

Capillary pressure in the fracture of a naturally fractured reservoir would exist due to two reasons: [8] 

In vertical fractures due to gravitational segregation of the fluids and capillary rise.Due to Wettability, where fracture walls andvery narrow parts of the fractures would be covered or filled with the wetting phase, thus causing an interface between the phase to

 be present.

The fracture capillary pressures used in the study were derived by Firoozabadi and Hauge [9], varying per fracture aperture of sizes

10, 20 and 100 μm. They developed a phenomenological model, based on the Young-Laplace equation of capillarity.The model is based on assumptions regarding fracture properties,Including roughness, shape of the asperities and number of asperities in contact

with each other at opposite fracture faces. They calculate fracture capillary pressure for different waviness angels (Fig 3) and

various fracture width (Fig 4). [9] 

Based on the above results Rossen and Kumar converted fracture capillary pressure to dimensionless form(PcfD) and tabulated the

results(Table 2.3).They defined PcfD as follows:[7]

./

o

b

 p

cfD p

γ  =

  (2)

Where bo is the fracture half aperture (t= 2bo).

If bo is given in inches, and γ is given in pounds/inch; Pc (in psi) would simply be calculated as

o

cfDb

 p p

/γ  = . On the other hand,

if bo is given in microns and γ in dines/cm, then Pc (in psi) would be given by:[1] 

o

cfD

cb

 p p   γ  *145.0=   (3)

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SPE 132838 3

For example in graphical form, for a water-oil system with interfacial tension of 0.35 dynes/cm, the fracture capillary pressure

curves for different values of fracture apertures would be represented by Figure 5. 

ECLIPSE models for fractured reservoirs

Dual-Porosity Model

The most commonly used flow model for practical simulations of fractured systems is the dual-porosity model. Here the basic idea

is to dissociate the flow inside the fracture network and the matrix and to model the exchange between these two media using a

transfer function. This concept was first introduced by Barenblatt and Zheltov (1960). [10]A simplified dual-porosity version of theBarenblatt and Zheltov flow model was used, in which the block-to-block flow takes place only through the fracture network, with

the matrix feeding the fractures through a transfer function.

Dual Porosity Dual Permeability Model

The dual-porosity models discussed above do not represent inter block matrix-matrix flow. This approximation is reasonable when

large-scale flow is solely through the fractures. When matrix-matrix interblock flow is significant and must therefore be included

in the model, we require a DSDP representation.

Blaskovich et al. (1983) first introduced models of this type[11]

. By adding the matrix-to-matrix connections, the matrix blocks areno longer isolated, and contribute to the overall fluid flow. Being more general than the dual-porosity model, which is limited to

strongly connected fractured reservoirs, the Dual porosity Dual permeability model is capable of simulating a wide variety of

 problems ranging from slightly fractured to highly fractured systems. [12] 

In this study, DSDP  model  is used to describe flow in fractures. This can be done in ECLIPSE by using the DUALPERMkeyword.

Simulation Design

The main objective of the sensitivity study was to determine in which situations it would make a significant difference to the

simulated reservoir behavior to use HD, associated fracture relative permeabilities and non-zero fracture capillary pressures.

“Significant difference” was defined where the difference between the simulation with straight line fracture relative permeabilities

and zero capillary pressure and the non-straight line fracture relative permeabilities and non-zero capillary pressure is greater thantypical uncertainties in the input data .these is done by take in to account other fracture properties. So different combination of

fracture properties is used to prepare an engineering guide lines in fractured reservoir simulation.

The objective was achieved by running simulations, varying the fracture parameters mainly influencing the flow directly, i.e.effective fracture permeability, sigma. Each combination was run with each of the different sets of relative permeabilities, as

associated with the HD parameter, using a zero capillary pressure. The results were compared to the base case, which had straight-

line fracture relative permeabilities and zero capillary pressures. This was performed on three different cases:

• Reservoir with primary Depletion• Reservoir with water injection

• Reservoir with gas injection

Water injection scenario

1-Effect of Fracture Relative Permeabiliy

As can be seen in Figure 6 differences decrease with an increase of HD, with the differences for HD=5 less than about10%.Differences in ultimate oil recovery are all positive, which indicates that the recovery will always be less (slower) if non-

straight-line relative permeability curves have been used. Figure 7 shows that water injection rates in cases with a low effective

fracture permeability (for example, K f =l00mD), are always much lower than in straight-line cases. At high fracture permeabilities,

with Kf around 500 to 1000mD and HD>=1, the injectivity is the same. Figure 8 shows the differences in the output vectors that

were observed in a HD=0.5 case and Figure 9 shows how the differences reduced in the H D=5 case.As can be seen from Figure 8there are significant difference between main output vectors and base case.

Summary of cases where straight-line fracture relative permeability would make no difference in any of the results parameters are

listed in Table 1.

2-Effect of Capillary Pressure

The effect of fracture capillary pressure in the three-phase system, combined with non- straight-line fracture relative permeability,is minimal and can be ignored. A combination of HD=1 and the capillary pressure for a fracture width of 10 microns, were tested.

Figure 10 shows the differences between i) test case with HD=1 and Pc=0 and ii) Test case with HD=1 and Pc=High

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Gas injection scenario

1-Effect of Fracture Relative Permeabiliy

Straight-line relative permeabilities is used for gas –oil case in this study.this is based on the results of gas-oil density differences,

as calculated by the ECLIPSE. Figure 11 shows the density differences with pressure change. This figure clearly indicates that

minimum difference between gas and oil density is 27.3 lb/ft3. Using the minimum differences above and calculating the HD; the

results can be seen in Table 2 for various aperture widths. For this minimum difference, it was proven that HD is always greater

than 5 so straight line relative permeabilities can be used .for the other gas-oil density differences which is more than 27, HD evenwill be more than HD related to this minimum differences.Therefore gas-oil relative permeabilities in the fractures should always

 be set to straight lines.It is good to be mentioned that the expression for HD in any consistent set of units is given by Eq. (1) However; the terms on the

right side of this equation in this study are more traditionally measured in the following units:Δρ: lbm/ft3, H: ft, G: ft/sec2, gc: (lb.ft)/(lbf.sec

2), γ: dynes/cm, bo: cm, If these units are used, HD could be calculated as follows:

(3)

2-Effect of Capillary Pressure

The base case, with zero fracture capillary pressures, was compared to three cases in which the fracture capillary pressure was setto correspond to three fracture widths, as described before. The results show a clear increase in field oil recovery (FOE), higher oil

 production rates (FOPR) with increasing capillary pressure because as fracture capillary pressure decrease later and more gradualgas breakthrough will occur . It is obvious that Gas- oil ratio is inversely proportional to fracture capillary pressure (Figure 12).

Primary depletion scenario

1-Effect of Fracture Relative Permeabiliy The differences between ultimate recoveries were small between base case with straight-line fracture relative permeabilities and

test cases. As can be observed on Figure 13 all differences are less than 10% so the effect of fracture relative permeabilities can be

ignored.

2-Effect of Capillary Pressure As the main driving mechanism in this case is gravity drainage (like gas injection case), fracture capillary pressure have a

significant effect on the simulation results.Fig 14 shows the difference in ultimate oil recovery in base case(pcf =0) and the testcases (with nonzero fracture capillary pressures ) are exactly like the gas injection case as described before.

Conclusion1)  This research has shown that the use of fracture relative permeabilities in numerical simulations of this fractured reservoir

sometimes make a substantial difference in the simulated reservoir behavior and subsequently the prediction results. Thedifference up to 70 % in prediction oil recovery has been shown.

2)  The use of straight-line fracture relative permeabilities should be limited to the following water injection cases: HDfactor of 1.5: low sigma (around .001 to .0001 ft-2) and high Kf (more than 1000 mD). All cases with an HD of 5 and

higher.

3)  In gas injection case, the difference between gas and oil densities are high enough for HD to be greater than 5; so straightline fracture relative permeabilities could be used.

4)  Results from the primary depletion case approved that effect of fracture relative permeabilities are insignificant on thesimulation results.

5)  Fracture capillary pressures showed significant differences in the simulation results of gas injection case, whererecoveries were up to 60% higher. Gas-oil systems with: a) Low fracture permeability (kf=100), b) small fractures widths(

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SPE 132838 5

Acknowledgments

This work was supported by the National Iranian Oil Company (NIOC). The authors acknowledge the Iranian Central Oil Fields

Company (ICOFC), especially the R&D department, for their help in preparing this paper.

References

1)  De la Porte ,J.J.; Kossack,C.A.:"The Effect of Fracture Relative Permeabilities and Capillary Pressures on the Numerical Simulation of

 Naturally Fractured Reservoirs”, paper SPE No.95241 

2)  Corey, A.T.: “The interrelationship between gas and oil relative permeabilities”, Prod. Mon., Vol. 19, pp. 38-41, 1954

3)  Serhat,A.:”Estimation of fracture relative permeabilities from unsteady state core floods”, Journal of Petroleum Science

and Engineering 30 ,2001

4)  Pruess, K.; Tsang ,Y.W.: “ Two-Phase Relative Permeability and Capillary Pressure of Rough-Walled Fracture“,Water

Resource. Res. 1915-1926., Sept. 1990

5)  Persoff, P. K.; Pruess, K.; Myer, L.: “Two-Phase Flow Visualization and Relative Permeability Measurement in

Transparent Replicas of Rough-Walled Rock Fractures”, Proceedings 6th Workshop on Geothermal Reservoir

Engineering, Stanford University, Stanford, California, January 23-2 5, 1991

6)  Persoff, P.;Pruess,K.:“Two-Phase Flow Visualization and Relative Permeability Measurement in Natural Rough-Walled

Rock Fractures” ,Water Resources Research Vol. 31, No. 5, pp. 1175-1186, May, 1995

7)  Rossen, W.R.; Kumar, A.T.A.: “Single and Two-Phase Flow in Natural Fractures”, paper SPE No.24915 ,1992

8)  Saidi,A.M.:”Reservoir Engineering of Fractured Reservoirs(Fundamental and Practical Aspects)”,Total edition

 presse,1987

9)  Firoozabadi, A.; Hauge, J.:” Capillary pressure in fractured porous media”. JPT, 784 791. 1990

10)  Barenblatt, G. I.; Zheltov, Y. P.:”Fundamental equations of filtration of homogeneous liquids in fissured rocks”,1960

11)  Blaskovich,F.T.;Cain,G.M.; Sonier,F.; Waidren,D.;Webb,S.J.:”A multicomponent isothermal system for efficient

reservoir simulation”, paper SPE NO.11480 presented at the Middle East Oil Technical Conference, Bahrain,1983

12)  Gong.B.:”Effective Models of Fracture Reservoirs “,Stanford University,september 2007

Table 1: Summary of cases where straight-line fracture relative permeability would make no difference in any of the results

 parameters.

HD  Matrix-Fracture Effective fracture

Coefficient, Sigma permeability ,K f(0.0001 to 1 ft-2) (100 to 1000 mD)

0 None None0.5 None None

1 None None1.5 1 None1.5 0.01 None

1.5 0.001 High only

1.5 0.0001 High only5 All All

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Table 2: Gas HD calculation.

Pressure Δρ  H γ  bo  HD 

[lbm/ft3] [feet] [dynes/cm] [micro meters]

4194 27.3 5 0.66 10 99.049327.3 5 0.66 100 990.493

27.3 5 0.66 1000 9904.93

27.3 5 0.66 10000 99049.3

Figure 1:Measurement of air-water relative permeabilities in rough-walleded fractures (graph from Horne et al. 2000)

Figure 2:Dimensionless fracture height parameter, HD, vs mean half-aperture of the fracture.

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SPE 132838 7

Figure 3:Computed capillary pressure for t=100μm and different waviness angels

Figure 4:Computed capillary pressure for α=5° and various fracture width

Capillary pressure vs.saturation

00.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 0.2 0.4 0.6 0.8 1 1.2

liquid saturation

      p

      c         (      p

      s        i         )

bo=5 microns

bo=10 microns

bo=50 microns

 Figure 5: Fracture Capillary Pressures per fracture width.

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Ultimate Recovery (FOE) Differences Results

0

1020304050607080

        (        0  ,

        1  ,

      σ  ,

        1        )

        (        0  ,

        2  ,

      σ  ,

        1        )

        (        0  ,

        3  ,

      σ  ,

        1        )

        (        1  ,

        1  ,

      σ  ,

        1        )

        (        1  ,

        2  ,

      σ  ,

        1        )

        (        1  ,

        3  ,

      σ  ,

        1        )

        (        2  ,

        1  ,

      σ  ,

        1        )

        (        2  ,

        2  ,

      σ  ,

        1        )

        (        2  ,

        3  ,

      σ  ,

        1        )

        (        3  ,

        1  ,

      σ  ,

        1        )

        (        3  ,

        2  ,

      σ  ,

        1        )

        (        3  ,

        3  ,

      σ  ,

        1        )

        (        4  ,

        1  ,

      σ  ,

        1        )

        (        4  ,

        2  ,

      σ  ,

        1        )

        (        4  ,

        3  ,

      σ  ,

        1        )

Experiment No.

     %     D     i     f     f    e    r    e    n    c    e

s igma=1 s igma=0.0001

 Figure 6:Differences in Ultimate Oil Recovery (FOE) with an increase in HD towards the right.

Water Injection Rate after 1 year vs K (Sigma=1)

0

10

20

30

40

50

60

70

80

k=100 k=500 k=1000

     %     D     i     f     f    e    r    e    n    c    e   HD=0.5

HD=1

HD=1.5

HD=5

 Figure 7:Difference in water injection rates (injectivity) after 1 year of production(sigma=1).

Figure 8:Results from Case with HD=0.5 and HD=∞: Gas-oil ratio ,Oil Recovery Factor, oil production rate , water cut. The greencurves represent the base case, using straight line relative permeabilites.

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SPE 132838 9

Figure 9:Results from Case with HD=5 and HD=∞: Gas-oil ratio ,Oil Recovery Factor, oil production rate , water cut. The greencurves represent the base case, using straight line relative permeabilites.

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Figure 10:The combined effect of non-zero capillary pressure and non-straight-line relative permeabilities. Blue represents the test

case with Pc=0, and red the test case with Pc=High

Gas-Oil Density Difference vs Pressure

20

25

30

35

40

45

1000 1500 2000 2500 3000 3500 4000 4500

 Figure 11:Gas-Oil density difference with pressure change, as determined by ECLIPSE

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SPE 132838 11

Figure 12:Comparison of results, using different capillary pressure tables based on fracture aperture . green

curves(b0=0),pink curves(b0=5), light blue curves(b0=10), dark blue curves(b0=50).

        (        0

  ,        k        f  ,

        1  ,

        1        )

        (        2

  ,        k        f  ,

        1  ,

        1        )

        (        3  ,

        k        f  ,

        1  ,

        1        )

        (        4  ,        k

        f  ,

        1  ,

        1        )

        (        0  ,        k

        f  ,

        4  ,

        1        )

        (        2  ,

        k        f  ,

        4  ,

        1        )

        (        3  ,

        k        f  ,        4  ,

        1        )

        (        4  ,

        k        f  ,        4

  ,        1        )

kf="100"

kf="1000"0

1

2

3

4

5

6

7

8

9

FOE Difference (%)

Experiment number (HD, Kf, sigma,deltaP)

LIVE OIL PRIMARY RECOVERY: Difference in Oil Recovery (FOE)

kf="100"

kf="500"

kf="1000"

 Figure 13: summary of all differences in the ultimate oil.

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Figure 14:Comparison of field oil recovery in base case and test cases.

50 microns fracture aperture

10 microns fracture aperture

5 microns fracture

aperture

Fracture aperture=0