Hydraulic fracturing stimulation has become a routine for the development of shale oil and gas reservoirs, which creates large volumes of fracturing networks by helping the hydrocarbon to transport quickly into the wellbore. However, the optimal fracture spacing distance and fracture conductivity are still unclear for the field practice, even though the technique has improved significantly over the last several years. In this work, an analytical method is proposed to address it. First, the analytical production rate for a single fracture is proposed, and then, we apply Duhamel principle to obtain the production rate of a horizontal well with multifractures. Based on this model, the flow regimes and essential affecting factors including fracture spacing, fracture conductivity, and skin factor are analyzed in this work. The optimal values and suggestion are provided based on the simulation results.
Issue Section:
Petroleum Engineering
References
1.
Energy Information Administration
, 2018
, “Annual Energy Outlook 2018: With Projections to 2050
,” Government Printing Office
.2.
Huang
, X.
, Lv
, K.
, Sun
, J.
, Lu
, Z.
, Bai
, Y.
, Shen
, H.
, and Wang
, J.
, 2019
, “Enhancement of Thermal Stability of Drilling Fluid Using Laponite Nanoparticles Under Extreme Temperature Conditions
,” Mater. Lett.,
248
(11
), pp. 146
–149
. 3.
Zhang
, F.
, and Yang
, D.
, 2017
, “Effects of Non-Darcy Flow and Penetrating Ratio on Performance of Horizontal Wells With Multiple Fractures in a Tight Formation
,” ASME J. Energy Resour. Technol.
, 140
(10
), p. 032903
. 4.
Hou
, X.
, Zhang
, X.
, and Guo
, B.
, 2019
, “Mathematical Modeling of Fluid Flow to Unconventional Oil Wells With Radial Fractures and Its Testing With Field Data
,” ASME J. Energy Resour. Technol.
, 141
(7
), p. 070702
. 5.
Tan
, Y.
, Li
, H.
, Zhou
, X.
, Jiang
, B.
, Wang
, Y.
, and Zhang
, N.
, 2018
, “A Semi-Analytical Model for Predicting Horizontal Well Performances in Fractured Gas Reservoirs With Bottom-Water and Different Fracture Intensities
,” ASME J. Energy Resour. Technol.
, 140
(10
), p. 102905
. 6.
Ahn
, C. H.
, Dilmore
, R.
, and Wang
, J. Y.
, 2016
, “Modeling of Hydraulic Fracture Propagation in Shale gas Reservoirs: A Three-Dimensional, Two-Phase Model
,” ASME J. Energy Resour. Technol.
, 139
(1
), p. 012903
. 7.
Seales
, M. B.
, Ertekin
, T.
, and Wang
, Y. J.
, 2017
, “Recovery Efficiency in Hydraulically Fractured Shale gas Reservoirs
,” ASME J. Energy Resour. Technol.
, 139
(4
), p. 04290120
. 8.
Gringarten
, A. C.
, and Ramey
, H. J.
, Jr., 1973
, “The Use of Source and Green’s Functions in Solving Unsteady-Flow Problems in Reservoirs
,” SPE J.
, 13
(5
), pp. 285
–296
. 9.
Gringarten
, A. C.
, Ramey
, H. J.
, Jr., and Raghavan
, R.
, 1974
, “Unsteady-State Pressure Distributions Created by a Well With a Single Infinite-Conductivity Vertical Fracture
,” SPE J.
, 14
(4
), pp. 347
–360
. 10.
Cinco
, L.
, Samaniego
, V.
, and Dominguez
, A.
, 1978
, “Transient Pressure Behavior for a Well With a Finite-Conductivity Vertical Fracture
,” SPE J.
, 18
(4
), pp. 253
–264
. 11.
Cinco-Ley
, H.
, and Meng
, H. Z.
, 1988
, “Pressure Transient of Wells With Finite Conductivity Vertical Fractures in Double Porosity Reservoirs
,” Proceedings of the SPE Annual Technical Conference and Exhibition
, Houston, TX
, Oct. 2–5
, SPE 18172-MS.12.
Blasingame
, T. A.
, and Poe
, B. D.
, 1993
, “Semianalytic Solutions for a Well With a Single Finiteconductivity Vertical Fracture
,” Proceedings of the SPE Annual Technical Conference and Exhibition
, Houston, TX
, Oct. 3–6
, SPE 26424.13.
Kuchuk
, F. J.
, Goode
, P. A.
, Wilkinson
, D. J.
, and Thambynayagam
, R. K. M.
, 1991
, “Pressure Transient Behavior of Horizontal Wells With and Without Gas Cap or Aquifer
,” SPE Form. Eval.
, 6
(01
), pp. 86
–94
. 14.
Lee
, S. T.
, and Brockenbrough
, J. R.
, 1986
, “A New Approximate Analytic Solution for Finite-Conductivity Vertical Fractures
,” SPE Form. Eval.
, 1
(01
), pp. 75
–88
. 15.
Meyer
, B. R.
, Bazan
, L. W.
, Jacot
, R. H.
, and Lattibeaudiere
, M. G.
, 2010
, “Optimization of Multiple Transverse Hydraulic Fractures in Horizontal Wellbores
,” Proceedings of the SPE Unconventional Gas Conference
, Pittsburgh, PA
, Feb. 23–25
, SPE 131732.16.
Brown
, M.
, Ozkan
, E.
, Raghavan
, R.
, and Kazemi
, H.
, 2011
, “Practical Solutions for Pressure-Transient Responses of Fractured Horizontal Wells in Unconventional Shale Reservoirs
,” SPE Reservoir Eval. Eng.
, 14
(6
), pp. 663
–676
. 17.
Fan
, D.
, and Ettehadtavakkol
, A.
, 2017
, “Analytical Model of Gas Transport in Heterogeneous Hydraulically-Fractured Organic-Rich Shale Media
,” Fuel
, 207
(10
), pp. 625
–640
. 18.
Pang
, Y.
, Soliman
, M. Y.
, and Sheng
, J.
, 2018
, “Investigating Gas-Adsorption, Stress-Dependence, and Non-Darcy-Flow Effects on Gas Storage and Transfer in Nanopores by Use of Simplified Local Density Model
,” SPE Reservoir Eval. Eng.
, 21
(1
), pp. 73
–95
. 19.
Wang
, W. D.
, Shahvali
, M.
, 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
. 20.
Houze
, O. P.
, Horne
, R. N.
, and Ramey
, H. J.
, Jr., 1988
, “Pressure-Transient Response of an Infinite-Conductivity Vertical Fracture in a Reservoir With Double-Porosity Behavior
,” SPE Form. Eval.
, 3
(3
), pp. 510
–518
. 21.
Ozkan
, E.
, and Raghavan
, R.
, 1991
, “New Solutions for Well-Test-Analysis Problems: Part 2 Computational Considerations and Applications
,” SPE Form. Eval.
, 6
(3
), pp. 369
–378
. 22.
Stehfest
, H.
, 1970
, “Algorithm 368: Numerical Inversion of Laplace Transforms [D5]
,” Commun. ACM
, 13
(1
), pp. 47
–49
. 23.
Feng
, Q.
, Wang
, S.
, Zhang
, W.
, Song
, Y.
, and Song
, S.
, 2013
, “Characterization of High-Permeability Streak in Mature Waterflooding Reservoirs Using Pressure Transient Analysis
,” J. Pet. Sci. Eng.,
110
(8
), pp. 55
–65
. 24.
Wan
, J.
, and Aziz
, K.
, 2002
, “Semi-Analytical Well Model of Horizontal Wells With Multiple Hydraulic Fractures
,” SPE J.
, 7
(4
), pp. 437
–445
. 25.
Wilkinson
, D. J.
, 1989
, “New Results for Pressure Transient Behavior of Hydraulically Fractured Wells
,” Proceedings of the Low Permeability Reservoirs Symposium
, Denver, CO
, Mar. 6–8
, SPE 18950.26.
Luo
, W.
, Wang
, X.
, Liu
, P.
, and Tian
, Q.
, 2018
, “A Simple and Accurate Calculation Method for Finite-Conductivity Fracture
,” J. Pet. Sci. Eng.,
161
(11
), pp. 590
–598
. 27.
Chen
, Z.
, Liao
, X.
, Zhao
, X.
, Dou
, X.
, and Zhu
, L.
, 2015
, “Performance of Horizontal Wells With Fracture Networks in Shale Gas Formation
,” J. Pet. Sci. Eng.,
133
(7
), pp. 646
–664
. 28.
Chen
, Z.
, Liao
, X.
, Zhao
, X.
, Lv
, S.
, and Zhu
, L.
, 2016
, “A Semianalytical Approach for Obtaining Type Curves of Multiple-Fractured Horizontal Wells With Secondary-Fracture Networks
,” SPE J.
21
(2
), pp. 538
–549
. 29.
Jia
, P.
, Cheng
, L.
, and Clarkson
, C. R.
, 2017
, “A Laplace-Domain Hybrid Model for Representing Flow Behavior of Multifractured Horizontal Wells Communicating Through Secondary Fractures in Unconventional Reservoirs
,” SPE J.
, 22
(6
), pp. 1856
–1876
. 30.
Wang
, X.
, and Sheng
, J. J.
, 2017
, “Effect of Low-Velocity Non-Darcy Flow on Well Production Performance in Shale and Tight Oil Reservoirs
,” Fuel
, 190
(2
), pp. 41
–46
. 31.
Wang
, X.
, Yang
, Z.
, Sun
, Y.
, and Liu
, X.
, 2011
, “Experimental and Theoretical Investigation of Nonlinear Flow in Low Permeability Reservoir
,” Proc. Environ. Sci.
, 11
, pp. 1392
–1399
. 32.
Xu
, J.
, Chen
, B.
, Sun
, B.
, and Jiang
, R.
, 2019
, “Flow Behavior of Hydraulic Fractured Tight Formations Considering Pre-Darcy Flow Using EDFM
,” Fuel
, 241
(2
), pp. 1145
–1163
. 33.
Prada
, A.
, and Civan
, F.
, 1999
, “Modification of Darcy’s Law for the Threshold Pressure Gradient
,” J. Pet. Sci. Eng.
, 22
(4
), pp. 237
–240
. 34.
Javadpour
, F.
, McClure
, M.
, and Naraghi
, M. E.
, 2015
, “Slip-Corrected Liquid Permeability and Its Effect on Hydraulic Fracturing and Fluid Loss in Shale
,” Fuel
, 160
(9
), pp. 549
–559
. 35.
Afsharpoor
, A.
, and Javadpour
, F.
, 2016
, “Liquid Slip Flow in a Network of Shale Noncircular Nanopores
,” Fuel
, 180
(9
), pp. 580
–590
. 36.
Majumder
, M.
, Chopra
, N.
, Andrews
, R.
, and Hinds
, B. J.
, 2005
, “Nanoscale Hydrodynamics: Enhanced Flow in Carbon Nanotubes
,” Nature
, 438
(7064
), pp. 44
–44
. 37.
Secchi
, E.
, Marbach
, S.
, Niguès
, A.
, Stein
, D.
, Siria
, A.
, and Bocquet
, L.
, 2016
, “Massive Radius-Dependent Flow Slippage in Carbon Nanotubes
,” Nature
, 537
(7619
), pp. 210
–213
. 38.
Nie
, R. S.
, Meng
, Y. F.
, Jia
, Y. L.
, Zhang
, F. X.
, Yang
, X. T.
, and Niu
, X. N.
, 2012
, “Dual Porosity and Dual Permeability Modeling of Horizontal Well in Naturally Fractured Reservoir
,” Transp. Porous Media
, 92
(1
), pp. 213
–235
. 39.
Stehfest
, H.
, 1970
, “Remark on Algorithm 368: Numerical Inversion of Laplace Transforms
,” Commun. ACM
, 13
(10
), p. 624
. 40.
Van Everdingen
, A. F.
, and Hurst
, W.
, 1949
, “The Application of the Laplace Transformation to Flow Problems in Reservoirs
,” J. Pet. Technol.
, 1
(12
), pp. 305
–324
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