A semi-analytical model for multilateral horizontal wells in low-permeability naturally fractured reservoirs

Abstract Multilateral horizontal wells (MLHWs) can significantly increase the reservoir exposure as well as connect high-permeability areas (natural fractures), and thus have been widely adopted in petroleum industry as an effective technique for efficient development of low-permeability reservoirs. Compared to vertical wells and horizontal wells, the flowing problems caused by MLHWs are more complex. In addition, extensive study has revealed that stress sensitivity of permeability in low-permeability reservoirs is obvious which cannot be ignored, especially for naturally fractured dual-porosity reservoirs. The non-linearity caused by stress sensitivity of permeability further complicates the flowing problems of MLHWs; however, so far, little work has been done in literature to simulate pressure transient dynamics of MLHWs with consideration of stress-sensitivity effect of permeability in low-permeability reservoirs. In this paper, a more rigorous analytical model for MLHWs in low-permeability naturally fractured reservoirs is presented. The model can not only consider different combinations of multiple branches, it can also consider the stress-sensitivity effect of reservoir permeability. The non-linear mathematical model can be linearized by Pedrosa transform and perturbation technique, and the final solution thus can be obtained by Laplace transformation method, finite cosine transform, element discretization and matrix theory. The presented model and corresponding solution are first validated by comparison with transient pressure responses calculated with a commercial numerical simulator for a simple case. Then the transient pressure responses are calculated, and flowing patterns and characteristic flowing periods caused by MLHWs are analyzed. A parametric analysis is also conducted to screen the critical parameters affecting the performance of multilateral horizontal wells. Analysis results suggest that stress-sensitivity of reservoir permeability has significant influence on the performance of MLHWs in low-permeability reservoirs; the parameters related to the shape of MLHWs, such as branch length, branch spacing, the angles between branch and horizontal wellbore, also can obviously affect the transient pressure dynamics of MLHWs. The proposed model in this paper can accurately simulate the transient pressure behaviors of MLHWs. It can help better understand the flowing characteristics of MLHWs, provide more accurate dynamic parameters for reservoir development, and give some insight into the design of MLHWs to obtain higher recovery.

[1]  Anil Kumar Ambastha,et al.  An Assessment of the Productivity of Multilateral Completions , 1998 .

[2]  Christine Ehlig-Economides,et al.  Principal Permeability Determination from Multiple Horizontal Well Tests , 1998 .

[3]  Michael J. Economides,et al.  Step-Pressure Test for Stress-Sensitive Permeability Determination , 1994 .

[4]  Lawrence W. Teufel,et al.  Numerical Well Test Analysis of Stress-Sensitive Reservoirs , 2001 .

[5]  D. Lu,et al.  Pressure Transient Analysis for Horizontal Well and Multi-Branched Horizontal Wells , 1996 .

[6]  Rajagopal Raghavan,et al.  An Investigation by Numerical Methods of the Effect of Pressure-Dependent Rock and Fluid Properties on Well Flow Tests , 1972 .

[7]  Colin Lyle Jordan,et al.  An Alternative Method For Horizontal & Multilateral Pressure Transient Analysis , 2009 .

[8]  R. W. Ostensen.  The Effect of Stress-Dependent Permeability on Gas Production and Well Testing , 1986 .

[9]  Don C. Ward,et al.  Effect of Overburden Pressure and Water Saturation on Gas Permeability of Tight Sandstone Cores , 1972 .

[10]  C. L. Hearn,et al.  Effect of Rock Stress on Gas Production From Low-Permeability Reservoirs , 1971 .

[11]  Turhan Yildiz.  Multilateral Pressure-Transient Response , 2000 .

[12]  J. E. Warren,et al.  The Behavior of Naturally Fractured Reservoirs , 1963 .

[13]  Michael J. Economides,et al.  Stress-Induced Permeability Reduction in Fissured Reservoirs , 1993 .

[14]  Shengnan Chen,et al.  Approximate Analytical Pressure Studies on Dual Porosity Reservoirs with Stress-sensitive Permeability , 2015 .

[15]  Khalid Aziz,et al.  A Simplified Approach to Couple Wellbore Flow and Reservoir Inflow for Arbitrary Well Configurations , 1998 .

[16]  A. V. Everdingen,et al.  The Skin Effect and Its Influence on the Productive Capacity of a Well , 1953 .

[17]  Albert C. Reynolds,et al.  Carbon Dioxide Effects on Wellbore-Pressure Response During Injection/Falloff Test , 2018 .

[18]  R. Raghavan,et al.  New Solutions for Well-Test-Analysis Problems: Part 2 Computational Considerations and Applications , 1991 .

[19]  F. G. Miller,et al.  An Investigation of Transient Flow of Reservoir Fluids Considering Pressure-Dependent Rock and Fluid Properties , 1977 .

[20]  Dominic Agyapong,et al.  A Simple Approach to Numerical Analysis of Complex Well Tests , 2003 .

[21]  Anil Kumar Ambastha,et al.  New Insights in Pressure-Transient Analysis for Stress-Sensitive Reservoirs , 1994 .

[22]  Chancell C. Condie.  Testing and Interpreting Multi-Lateral Wells , 2009 .

[23]  R. Raghavan,et al.  New Solutions for Well-Test-Analysis Problems: Part 1-Analytical Considerations(includes associated papers 28666 and 29213 ) , 1991 .

[24]  Brian George Davidson Smart,et al.  Stress Sensitivity of Low-Permeability Sandstones From the Rotliegendes Sandstone , 1993 .

[25]  O. A. Pedrosa.  Pressure Transient Response in Stress-Sensitive Formations , 1986 .

[26]  Djebbar Tiab,et al.  Transient Pressure Behavior of Dual Lateral Wells , 2003 .

[27]  Shengnan Chen,et al.  Approximate Analytical-Pressure Studies on Dual-Porosity Reservoirs With Stress-Sensitive Permeability , 2015 .

[28]  Juris Vairogs,et al.  Pressure Transient Tests in Formations Having Stress-Sensitive Permeability , 1973 .

[29]  M. Karakas,et al.  Well Test Analysis of a Well With Multiple Horizontal Drainholes , 1991 .

[30]  G. Da Prat,et al.  A New Model for Pressure Transient Analysis in Stress Sensitive Naturally Fractured Reservoirs , 1994 .

[31]  W. W. Owens,et al.  A Laboratory Study of Low-Permeability Gas Sands , 1980 .

[32]  Christopher R. Clarkson,et al.  Analysis of Transient Linear Flow in Stress-Sensitive Formations , 2013 .

[33]  Norman R. Warpinski,et al.  Hydraulic Fracturing in Tight, Fissured Media , 1991 .

[34]  F. Kucuk,et al.  Analysis of Simultaneously Measured Pressure and Sandface Flow Rate in Transient Well Testing (includes associated papers 13937 and 14693 ) , 1985 .

[35]  H. J. Ramey,et al.  The Use of Source and Green's Functions in Solving Unsteady-Flow Problems in Reservoirs , 1973 .

[36]  Jitendra Kikani,et al.  Perturbation Analysis of Stress-Sensitive Reservoirs (includes associated papers 25281 and 25292 ) , 1991 .

[37]  R. W. Ostensen.  Microcrack Permeability in Tight Gas Sandstone , 1983 .

[38]  V. Zakian.  Numerical inversion of Laplace transform , 1969 .

[39]  Khalid Aziz.  A General Single-Phase Wellbore/Reservoir Coupling Model for Multilateral Wells , 2001 .