Presently, predicting the production performance of fractured reservoirs is often challenging because of the following two factors: one factor such as complicatedly connected and random distribution nature of the fractures and the other factor includes the limitations of the understanding of reservoir geology, deficient fracture-related research, and defective simulators. To overcome the difficulties of simulating and predicting fractured reservoir under complex circumstances of cross flow, a simplified model, which assumes cross flow only exists in the oil phase segment, is constructed. In the model, the pressure distribution of a single fracture can be described by solving an analytical mathematical model. In addition, due to research and field experience which indicate that cross flow also exists in the mixed-phase segment after water injection, the simplified model is modified to consider cross flow in the whole phase. The model constructed here is applicable for fractured reservoirs especially for a low-permeability fracture reservoir, and it moderately predicts future production index. By using iterative methods, the solution to the model can be feasibly obtained and related production performance index formulas can be derived explicitly. A case study was performed to test the model, and the results prove that it is good.

References

References
1.
Warren
,
J. E.
,
1963
, “
The Behavior of Naturally Fractured Reservoirs
,”
Soc. Pet. Eng. J.
,
3
(
3
), pp.
245
255
.
2.
Evans
,
R. D.
, and
Lekia
,
S. D. L.
,
1990
, “
A Reservoir Simulation Study of Naturally Fractured Lenticular Tight Gas Sand Reservoirs
,”
ASME J. Energy Resour. Technol.
,
112
(
4
), pp.
231
238
.
3.
Guo
,
T.
,
Li
,
Y.
,
Ding
,
Y.
,
Qu
,
Z.
, and
Gai
,
N.
,
2017
, “
Evaluation of Acid Fracturing Treatments Inshale Formation
,”
Energy Fuel
,
31
(
10
), pp.
10479
10489
.
4.
Noroozi
,
M.
,
Moradi
,
B.
, and
Bashiri
,
G.
,
2010
, “
Effects of Fracture Properties on Numerical Simulation of a Naturally Fractured Reservoir
,”
Trinidad and Tobago Energy Resources Conference
,
Port of Spain, Trinidad
,
June 27–30
, pp.
1
12
.
5.
Hillgartner
,
H.
,
Paino
,
W. F.
, and
Hadhrami
,
F.
,
2011
, “
Integrated Reservoir Modeling for Water Flood Development in a Heterogeneously Fractured Carbonate Reservoir, North Oman
,”
SPE Reservoir Characterisation and Simulation Conference and Exhibition
,
Abu Dhabi, UAE
,
Oct. 9–11
, pp.
1
9
.
6.
Karimi-Fard
,
M.
, and
Firoozabadi
,
A.
,
2003
, “
Numerical Simulation of Water Injection in Fractured Media Using the Discrete-Fracture Model and the Galerkin Method
,”
SPE Reservoir Eval. Eng.
,
6
(
2
), pp.
117
126
.
7.
Belhaj
,
H.
, and
Mnejja
,
M.
,
2011
, “
Hydraulic Fracture Simulation of Two-Phase Flow: Discrete Fracture Modelling/Mixed Finite Element Approach
,”
SPE Reservoir Characterisation and Simulation Conference and Exhibition
,
Abu Dhabi, UAE
,
Oct. 9–11
, pp.
1
9
.
8.
Moinfar
,
A.
,
Narr
,
W.
,
Hui
,
M. H.
,
Mallison
,
B. T.
, and
Lee
,
S. H.
,
2011
, “
Comparison of Discrete-Fracture and Dual-Permeability Models for Multiphase Flow in Naturally Fractured Reservoirs
,”
SPE Reservoir Simulation Symposium
,
The Woodlands, TX
,
Feb. 21–23
, pp.
1
17
.
9.
Moinfar
,
A.
,
Varavei
,
A.
,
Sepehrnoori
,
K.
, and
Johns
,
R. T.
,
2013
, “
Development of a Coupled Dual Continuum and Discrete Fracture Model for the Simulation of Unconventional Reservoirs
,”
2013 SPE Reservoir Simulation Symposium
,
The Woodlands, TX
,
Feb. 18–20
, pp.
1
17
.
10.
Lough
,
M. F.
,
Lee
,
S. H.
, and
Kamath
,
J.
,
1997
, “
A New Method to Calculate Effective Permeability of Gridblocks Used in the Simulation of Naturally Fractured Reservoirs
,”
SPE Reservoir Eng.
,
12
(
3
), pp.
219
224
.
11.
Philip
,
Z.
,
Jennings
,
J.
,
Olson
,
J.
,
Laubach
,
S.
, and
Holder
,
J.
,
2005
, “
Modeling Coupled Fracture-Matrix Fluid Flow in Geomechanically Simulated Fracture Networks
,”
SPE Reservoir Eval. Eng.
,
8
(
4
), pp.
300
309
.
12.
Oda
,
M.
,
1985
, “
Permeability Tensor for Discontinuous Rock Masses
,”
Geotechnique
,
35
(
4
), pp.
483
495
.
13.
Yao
,
J.
,
Li
,
Y. J.
, and
Huang
,
Z. Q.
,
2009
, “
Calculation of Equivalent Permeability Tensors of Fractured Oil Reservoirs Using Boundary Element Method
,”
Pet. Geol. Recovery Efficiency
,
16
(
6
), pp.
80
83
.
14.
Li
,
Y. J.
,
Yao
,
J.
,
Huang
,
Z.
, and
Zhang
,
K.
,
2010
, “
Calculation of Equivalent Permeability Tensor and Study on Representative Element Volume for Modeling Fractured Reservoirs
,”
Chin. J. Hydrodyn.
,
25
(
1
), pp.
1
7
.
15.
Li
,
Y. J.
,
Yao
,
J.
, and
Huang
,
Z. Q.
,
2011
, “
Research on Permeability Characteristics of Single-Fractured Porous Media
,”
Spec. Oil Gas Reservoirs
,
18
(
4
), pp.
94
97
.
16.
Gringarten
,
A. C.
, and
Raghavan
,
R.
,
1974
, “
Unsteady-State Pressure Distributions Created by a Well With a Single Infinite-Conductivity Vertical Fracture
,”
Soc. Pet. Eng. J.
,
14
(
4
), pp.
347
360
.
17.
Zeng
,
J.
,
Wang
,
X.
,
Guo
,
J.
, and
Zeng
,
F.
,
2017
, “
Composite Linear Flow Model for Multi-Fractured Horizontal Wells in Heterogeneous Shale Reservoir
,”
J. Nat. Gas Sci. Eng.,
38
, pp.
527
548
.
18.
Liu
,
S.
,
He
,
H.
,
Zhao
,
Q. Y.
, and
Zhou
,
D. S.
,
2018
, “
Staggered Extension Laws of Hydraulic Fracture and Natural Fracture
,”
ActaPetroleiSinica
,
39
(
3
), pp.
320
326
, 334.
19.
Kazemi
,
H.
,
Gilman
,
J. R.
, and
Elsharkawy
,
A. M.
,
1992
, “
Analytical and Numerical Solution of Oil Recovery From Fractured Reservoirs With Empirical Transfer Functions (Includes Associated Papers 25528 and 25818)
,”
SPE Reservoir Eng.
,
7
(
2
), pp.
219
227
.
20.
Barreto
,
A. B.
,
Pires
,
A. P.
, and
Peres
,
A. M.
,
2012
, “
A New Rigorous Analytical Solution for a Vertical Fractured Well in Gas Reservoirs
,”
SPE Latin America and Caribbean Petroleum Engineering Conference
,
Mexico City, Mexico
,
Apr. 16–18
, pp.
1
10
.
21.
Wang
,
W. D.
,
Mohammad
,
S.
, and
Su
,
Y. L.
,
2016
, “
Analytical Solutions for a Quad-Linear Flow Model Derived for Multistage Fractured Horizontal Wells in Tight Oil Reservoirs
,”
ASME J. Energy Resour. Technol.
,
139
(
1
), p.
012905
.
22.
Zhang
,
K.
,
Zhang
,
X. M.
, and
Zhang
,
L. M.
,
2016
, “
Assisted History Matching for the Inversion of Fractures Based on Discrete Fracture-Matrix Model With Different Combinations of Inversion Parameters
,”
Comput. Geosci.,
5
(
5–6
), pp.
1
19
.
23.
Cossio
,
M.
,
Moridis
,
G.
, and
Blasingame
,
T.
,
2012
, “
A Semi-Analytic Solution for Flow in Finite-Conductivity Vertical Fractures Using Fractal Theory
,”
SPE Latin America and Caribbean Petroleum Engineering Conference
,
Mexico City, Mexico
,
Apr. 16–18
, pp.
1
25
.
24.
Alharthy
,
N.
,
Kurtoglu
,
B.
,
Kazemi
,
H.
, and
Torcuk
,
M. A.
,
2013
, “
Analytical and Numerical Solutions for Multiple-Matrix in Fractured Reservoirs: Application to Conventional and Unconventional Reservoirs
,”
SPE Unconventional Resources Conference-USA
,
The Woodlands, TX
,
Apr. 10–12
, pp.
1
23
.
25.
Hannes
,
H.
,
Tayfun
,
B.
, and
Günter
,
Z.
,
2014
, “
Numerical Simulation of Complex Fracture Network Development by Hydraulic Fracturing in Naturally Fractured Ultratight Formations
,”
ASME J. Energy Resour. Technol.
,
136
(
4
), p.
042905
. 10.1115/1.4028690
26.
Liu
,
S.
,
He
,
H.
, and
Wang
,
H.
,
2018
, “
Mechanism on Imbibition of Fracturing Fluid in Nanopore
,”
Nanosci. Nanotechnol. Lett.,
10
(
1
), pp.
87
93
.
27.
Zhang
,
L. M.
,
Zhang
,
X. M.
,
Zhang
,
K.
,
Zhang
,
H.
, and
Yao
,
J.
,
2017
, “
Inversion of Fractures With Combination of Production Performance and In-Situ Stress Analysis Data
,”
J. Nat. Gas Sci. Eng.,
42
, pp.
232
242
.
28.
Zhang
,
M.
, and
Luis
,
F. A.
,
2018
, “
A General Boundary Integral Solution for Fluid Flow Analysis in Reservoirs With Complex Fracture Geometries
,”
ASME J. Energy Resour. Technol.
,
140
(
5
), p.
052907
.
29.
Rui
,
Z.
,
Wang
,
X.
,
Zhang
,
Z.
,
Lu
,
J.
,
Chen
,
G.
,
Zhou
,
X.
, and
Patil
,
S.
,
2018
, “
A Realistic and Integrated Model for Evaluating Oil Sands Development With Steam Assisted Gravity Drainage Technology in Canada
,”
Appl. Energy
,
213
, pp.
76
91
.
30.
Rui
,
Z.
,
Cui
,
K.
,
Wang
,
X.
,
Chun
,
J.
,
Li
,
Y.
,
Zhang
,
Z.
,
Lu
,
J.
,
Chen
,
G.
,
Zhou
,
X.
, and
Patil
,
S.
,
2018
, “
A Comprehensive Investigation on Performance of Oil and Gas Development in Nigeria: Technical and Non-Technical Analyses
,”
Energy
,
158
, pp.
666
680
.
31.
Fadairo
,
A. S. A.
,
Ako
,
C.
, and
Falode
,
O.
,
2011
, “
Modeling Productivity Index for Long Horizontal Well
,”
ASME J. Energy Resour. Technol.
,
133
(
3
), p.
033101
.
32.
Zhang
,
K.
, and
Zhang
,
X. M.
,
2017
, “
Inversion of Fractures Based on Equivalent Continuous Medium Model of Fractured Reservoirs
,”
J. Pet. Sci. Eng.,
151
, pp.
496
506
.
33.
Tamagawa
,
T.
,
Matsuura
,
T.
,
Anraku
,
T.
,
Tezuka
,
K.
, and
Namikawa
,
T.
,
2002
, “
Construction of Fracture Network Model Using Static and Dynamic Data
,”
SPE Annual Technical Conference and Exhibition
,
San Antonio, TX
,
Sept. 29–Oct. 2
, pp.
1
12
.
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