Development of a high-order accurate reservoir simulator using spectral element method

Discontinuous galerkin method;Spectral element method;Reservoir simulation;Reservoir management

Taneja, Ankur

关键词: Discontinuous galerkin method;    Spectral element method;    Reservoir simulation;    Reservoir management;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/97245/TANEJA-DISSERTATION-2017.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Reservoir simulation serves as an important tool for reservoir management to predict and optimize the future performance of a reservoir. Modeling multiphase fluid flow in porous media can be computationally challenging due to heterogeneous geologic features and sharp, moving fluid interfaces. Low-order convergence of conventional reservoir simulators, often based on finite volume or finite element methods, can be computationally prohibitive to fully resolve the physics of flows with sharp fronts. A high-order numerical scheme with strong stability properties and robustness to accurately resolve the physics of reservoir flows is thus highly desirable. The current research work focuses on the case of two-phase immiscible, incompressible fluid flow in oil reservoirs and seeks to develop a high-order accurate numerical scheme. Governing equations for two-phase incompressible flow in porous media, derived in terms of pressure p and saturation s, are a coupled system of partial differential equations (PDEs) with elliptic-parabolic nature in general. Under certain conditions, the governing equations can become elliptic-hyperbolic in nature. Computational challenges in numerically solving PDEs with discontinuous solutions or discontinuous data are identified and various numerical schemes reviewed for meeting desired goals of accuracy and stability. In particular, numerical comparisons are given for convective hyperbolic PDEs using (a) a first-order upwind finite volume method, (b) a hybrid 1st/2nd order Jameson-Schmidt-Turkel scheme, (c) explicit Runge-Kutta Discontinuous Galerkin method of Cockburn and Shu, and (d) an implicit Discontinuous Galerkin method. Based on the conclusions drawn from these schemes, a fully coupled implicit Discontinuous Galerkin spectral element method (DGSEM) is proposed to solve the two non-linear governing equations in pressure and saturation. The proposed DGSEM scheme is capable of using high-order spectral elements and controlled amount of artificial diffusion to achieve stable, robust numerical solutions. Spectral/hp-convergence of DGSEM scheme is demonstrated for quarter five-spot pattern flow in homogeneous reservoirs. Superior performance capabilities of the DGSEM scheme in resolving heterogeneous geologic features are demonstrated. A novel approach for using volumetric source terms for injection/production wells on spectral element grids not required to be conforming with geometric or geologic features is presented. Numerical results are presented for simulations with different types of geologic heterogeneities and injection/production patterns for 2D reservoirs.