Abstract

In addition to artificial fractures generated by hydraulic fracturing technology, natural fractures distributed in reservoirs will also affect the fluid flow process. To study the transient behavior of the pressure in fluid flows in reservoirs containing natural fractures, a semi-analytical model for vertically fractured wells with complex natural fracture networks was established. This model was based on the linear source function theory and the fracture discretization and coupling methods. It was solved by the Stehfest numerical inversion and the matrix transformation. The results of the study on the fluid flow stages in a reservoir with natural fractures indicated that the presence of natural fractures increased natural fracture flows. These flows were dominated by natural fractures and fracture interference stages and were different from the fluid flows observed in vertically fractured wells with a single main fracture. The sensitivity analysis on the influences of the fluid flow factors in the reservoirs with three types of natural fractures could provide a more detailed reference for the identification of the reservoir parameters and the transient characteristics of the flow stage. The different characteristic curves of the fluid flow in the reservoirs with different scale natural fractures could also provide a theoretical basis for determining the distribution of natural fractures in reservoirs.

References

1.
Hubbert
,
M. K.
,
1957
, “
Darcy's Law and the Field Equations of the Flow of Underground Fluids
,”
Int. Assoc. Sci. Hydrol.
,
2
(
1
), pp.
23
59
.
2.
Hovanessian
,
S. A.
,
1961
, “
Pressure Studies in Bounded Reservoirs
,”
Soc. Pet. Eng. J.
,
1
(
4
), pp.
223
228
.
3.
Earlougher
,
R. C.
,
Ramey
,
H. J.
,
Miller
,
F. G.
, and
Mueller
,
T. D.
,
1968
, “
Pressure Distributions in Rectangular Reservoirs
,”
J. Pet. Technol.
,
20
(
2
), pp.
199
208
.
4.
Gringarten
,
A. C.
, and
Ramey
,
H. J.
,
1973
, “
The Use of Source and Green's Functions in Solving Unsteady-Flow Problems in Reservoirs
,”
Soc. Pet. Eng. J.
,
13
(
5
), pp.
285
296
.
5.
Gringarten
,
A. C.
,
Ramey
,
H. J.
, 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
.
6.
Gringarten
,
A. C.
,
Ramey
,
H. J.
, and
Raghavan
,
R.
,
1975
, “
Applied Pressure Analysis for Fractured Wells
,”
J. Pet. Technol.
,
27
(
7
), pp.
887
892
. SPE-5496-PA.
7.
Cinco-Ley
,
H.
,
Ramey
,
H. J.
, and
Miller
,
F. G.
,
1975
, “
Unsteady-State Pressure Distribution Created by a Well With an Inclined Fracture
,”
SPE 50th Annual Fall Meeting of the Society of Petroleum Engineers of AIME
,
Dallas, TX
,
Sept. 28–30
, OnePetro, Paper No. SPE-5591-MS.
8.
Resurreicao
,
C. E. S.
, and
Fernando
,
R.
,
1991
, “
Transient Rate Behavior of Finite-Conductivity Asymmetrically Fractured Wells Producing at Constant Pressure
,”
SPE 66th Annual Technical Conference and Exhibition
,
Dallas, TX
,
Oct. 6–9
, OnePetro, Paper No. SPE-22657-MS.
9.
Rodriguez
,
F.
,
Cinco-Ley
,
H.
, and
Samaniego-V
,
F.
,
1992
, “
Evaluation of Fracture Asymmetry of Finite-Conductivity Fractured Wells
,”
SPE Prod. Eng.
,
7
(
2
), pp.
233
239
. SPE-20583-PA.
10.
Luo
,
W. J.
, and
Tang
,
C. F.
,
2015
, “
Pressure-Transient Analysis of Multiwing Fractures Connected to a Vertical Wellbore
,”
Soc. Pet. Eng. J.
,
20
(
2
), pp.
360
367
. SPE-171556-PA.
11.
Huang
,
Y.
,
Cheng
,
S. Q.
,
He
,
Y. W.
,
Li
,
S.
, and
Yu
,
H. Y.
,
2016
, “
Pressure-Transient Analysis of a Well with a Double-Segment Vertical Fracture
,”
Comput. Theor. Nanosci.
,
13
(
4
), pp.
2496
2503
.
12.
Suarez-Rivera
,
R.
,
Burghardt
,
J.
,
Stanchits
,
S.
,
Edelman
,
E.
, and
Surdi
,
A.
,
2013
. Understanding the Effect of Rock Fabric on Fracture Complexity for Improving Completion Design and Well Performance, IPTC-17018-MS.
13.
Hou
,
B.
,
Chen
,
M.
,
Li
,
Z. M.
,
Wang
,
Y. H.
, and
Diao
,
C.
,
2014
, “
Propagation Area Evaluation of Hydraulic Fracture Networks in Shale Gas Reservoirs
,”
Pet. Explor. Dev.
,
41
(
6
), pp.
833
838
.
14.
Tan
,
P.
,
Jin
,
Y.
,
Han
,
K.
,
Hou
,
B.
,
Chen
,
M.
,
Guo
,
X. F.
, and
Gao
,
J.
,
2017
, “
Analysis of Hydraulic Fracture Initiation and Vertical Propagation Behavior in Laminated Shale Formation
,”
Fuel
,
206
, pp.
482
493
.
15.
Luo
,
W. J.
,
Tang
,
C. F.
, and
Zhou
,
Y. F.
,
2019
, “
A New Fracture-Unit Model and Its Application to a Z-Fold Fracture
,”
Soc. Pet. Eng. J.
,
24
(
1
), pp.
319
333
. SPE-194024-PA.
16.
Zhang
,
Q. S.
,
Wang
,
X. Z.
,
Wang
,
D. H.
,
Zeng
,
J.
,
Zeng
,
F. H.
, and
Zhang
,
L.
,
2018
, “
Pressure Transient Analysis for Vertical Fractured Wells With Fishbone Fracture Patterns
,”
J. Nat. Gas Sci. Eng.
,
52
, pp.
187
201
.
17.
Li
,
Z.
,
Chang
,
X.
,
Yao
,
Z. X.
, and
Wang
,
Y. B.
,
2019
, “
Fracture Monitoring and Reservoir Evaluation by Micro-Seismic Method
,”
Chin. J. Geophys.
,
62
(
2
), pp.
707
719
.
18.
Al-Rbeawi
,
S.
,
2018
, “
Performance-Based Comparison for Hydraulically Fractured Tight and Shale-Gas Reservoirs With and Without Non-Darcy-Flow Effect
,”
SPE Reservoir Eval. Eng.
,
21
(
4
), pp.
0981
1006
.
19.
Molenaar
,
M. M.
,
Hill
,
D.
,
Webster
,
P.
,
Fidan
,
E.
, and
Birch
,
B.
,
2012
, “
First Downhole Application of Distributed Acoustic Sensing for Hydraulic-Fracturing Monitoring and Diagnostics
,”
SPE Drill. Completion
,
27
(
1
), pp.
32
38
. SPE-140561-MS.
20.
Chen
,
Z.
,
Liao
,
X.
,
Liu
,
Q.
,
Wang
,
L.
,
Wang
,
S.
,
Tang
,
X.
, and
Zhang
,
J.
,
2019
, “
Pressure Transient Analysis in Fractured Horizontal Wells with Fracture Networks
,”
SPE Western Regional Meeting
,
San Jose, CA
,
Apr. 23–26
, OnePetro, Paper No. SPE-195286-MS.
21.
Dejam
,
M.
,
Hassanzadeh
,
H.
, and
Chen
,
Z. X.
,
2018
, “
Semi-Analytical Solution for Pressure Transient Analysis of a Hydraulically Fractured Vertical Well in a Bounded Dual-Porosity Reservoir
,”
J. Hydrol.
,
565
, pp.
289
301
.
22.
Taleghani
,
A. D.
, and
Olson
,
J. E.
,
2014
, “
How Natural Fractures Could Affect Hydraulic-Fracture Geometry
,”
Soc. Pet. Eng. J.
,
19
(
1
), pp.
161
171
. SPE-167608-PA
23.
Zhou
,
D. S.
,
Zheng
,
P.
,
Peng
,
J.
, and
He
,
P.
,
2015
, “
Induced Stress and Interaction of Fractures During Hydraulic Fracturing in Shale Formation
,”
ASME J. Energy Resour. Technol.
,
137
(
6
), p.
062902
.
24.
Chen
,
Z. M.
,
Liao
,
X. W.
,
Zhao
,
X. L.
, and
Zhu
,
L. T.
,
2016
, “
Influence of Magnitude and Permeability of Fracture Networks on Behaviors of Vertical Shale Gas Wells by a Free-Simulator Approach
,”
J. Pet. Sci. Eng.
,
147
, pp.
261
272
.
25.
Teng
,
W.
,
Jiang
,
Y.
,
Jiang
,
R.
,
He
,
J.
,
Gao
,
X.
, and
Liu
,
Z.
,
2016
, “
Pressure Transient Analysis of Complex Fracture Networks in Shale Gas Reservoirs With Multiple-Porosity Transport Mechanisms
,”
SPE Argentina Exploration and Production of Unconventional Resources Symposium
,
Buenos Aires, Argentina
,
June 1–3
, OnePetro, Paper No. SPE-180970-MS.
26.
Ren
,
Z. X.
,
Wu
,
X. D.
,
Liu
,
D. D.
,
Rui
,
R.
,
Guo
,
W.
,
Chen
,
Z. M.
,
Zhang
,
J. M.
,
Wu
,
X. J.
,
Zhang
,
H.
, and
Tang
,
Z. G.
,
2016
, “
Semi-analytical Model of the Transient Pressure Behavior of Complex Fracture Networks in Tight oil Reservoirs
,”
J. Nat. Gas Sci. Eng.
,
35
, pp.
497
508
.
27.
Stehfest
,
H.
,
1970
, “
Algorithm 368: Numerical Inversion of Laplace Transforms [D5]
,”
Commun. ACM
,
13
(
1
), pp.
47
49
.
28.
Borges
,
J. U. A.
, and
Jamiolahmady
,
M.
,
2009
, “
Well Test Analysis in Tight Gas Reservoirs
,”
Soc. Pet. Eng.
,
2
(
1
), pp.
1178
1198
.
29.
Chaudhry
,
A. U.
,
2004
,
Application of Pressure Derivative in Oil Well Test Analysis
,
Elsevier Inc.
,
Amsterdam
.
30.
Liao
,
X. W.
, and
Shen
,
P. P.
,
2002
,
Modern Well Test Analysis
,
Petroleum Industry Press
,
Beijing
, pp.
56
126
.
You do not currently have access to this content.