A Boundary Element Method Applied to Pressure Transient Analysis of Geometrically Complex Gas Reservoirs

2009 ◽  
Author(s):  
Haitao Wang ◽  
Liehui Zhang
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Transient Analysis ◽  
Gas Reservoirs ◽  
Pressure Transient Analysis ◽  
Pressure Transient ◽  
Geometrically Complex ◽  
Element Method

The Dual-Reciprocity Boundary Element Method Solution for Gas Recovery from Unconventional Reservoirs with Discrete Fracture Networks

SPE Journal ◽  
2020 ◽  
Vol 25 (06) ◽  
pp. 2898-2914
Author(s):  
Miao Zhang ◽  
Luis F. Ayala
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Nonlinear Partial Differential Equations ◽  
Boundary Integral ◽  
Element Formulation ◽  
Gas Reservoirs ◽  
Gas Recovery ◽  
Infinite Conductivity ◽  
Fractured Horizontal Wells ◽  
Element Method

Summary In this paper, we present a novel application of the dual-reciprocity boundary-element formulation (DRBEM) to model compressible (gas) fluid flow in tight and shale-gas reservoirs containing arbitrary distributed finite- or infinite-conductivity discrete fractures. Compared with the standard boundary-element method (BEM), the DRBEM transforms the nonlinear domain integrals at the righthand side (RHS) of BEM formulations for nonlinear partial differential equations into equivalent boundary integrals. This transformation allows retention of the domain-integral-free, boundary-integral-only character of standard BEM approaches. The proposed approach is based on coupling DRBEM with the finite-volume method (FVM) in which a multidimensional system is solved by integrating over a line with random fractures. The resulting system of equations is solved simultaneously for fracture and matrix boundary conditions by combining DRBEM and FVM without invoking any approximation for pressure-dependent nonlinear terms such as gas viscosity and compressibility. Numerical examples and field cases are presented to test the validity and showcase the capabilities of the proposed approach. The proposed model provides a general framework that can be applied to a variety of well and fracture geometries and operating schedules, and it is used to analyze production behavior for these complex systems. To the best of the authors’ knowledge, this is the first successful application of the dual-reciprocity principle to the BEM analysis of massively fractured horizontal wells (MFHWs) performance in natural-gas formations in which nonlinear, pressure-dependent gas properties are captured without approximation.

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