A Multilevel Preconditioner and Its Shared Memory Implementation for New Generation Reservoir Simulator

Abstract

The mathematical models in reservoir simulation are usually discretized into large linear equations, and solving them needs lots of time. Taking into account the mathematical characteristics of the black oil model, a multilevel preconditioning solution method is designed to deal with the algebraic equations in reservoir numerical simulation. Takes into account some of the properties of pressure, saturation, and implicit well variables in flow model, the multilevel preconditioner is comprised of several different iterative methods, such as algebraic multigrid method, Incomplete LU factorization, Gauss-Seidel iteration with downwind ordering and crosswind blocks and et al. The efficiency and robustness of multilevel preconditioner is proved by a million-cell benchmark problem and a real-world matured reservoir with high heterogeneity, high water-cut, geological faults, and complex well scheduling. The numerical results indicate that the proposed method is not only robust with respect to the heterogeneity, anisotropy, and number of wells but also efficient method that can solve large Jacobian system in reservoir simulation quickly and precisely.

Parallel Multi-Stage Preconditioners with Adaptive Setup for the Black Oil Model

“…As multi-core and many-core architectures become more and more popular, parallel computing for petroleum reservoir simulation is now a subject of great interest. In recent years, there has been some work on parallel algorithms for reservoir problems; see [33][34][35][36][37][38][39][40][41][42][43][44][45] and references therein. For example, Feng et al [35] designed an OpenMP parallel algorithm with high efficiency and low memory cost for standard interpolation and coarse grid operator of AMG, under the framework of Fast Auxiliary Space Preconditioning (FASP) [46].…”

Development of a Scalable Thermal Reservoir Simulator on Distributed-Memory Parallel Computers

“…A key to reservoir simulations is to develop effective solution techniques, especially preconditioners. Many preconditioners have been proposed to accelerate the solution of linear systems, such as constrained pressure residual (CPR) methods [10,11]; multiple level preconditioners [12]; multi-stage methods [13]; CPR-FP, CPR-FPF, and CPR-FFPF methods [14]; and FASP (fast auxiliary space preconditioners) [15,16]. Parallel computers have more memory and better performance, which provide excellent approaches to accelerate reservoir simulations [17][18][19][20][21][22][23][24][25][26][27][28].…”

Numerical Simulation of Two-phase Flow in Naturally Fractured Reservoirs Using Dual Porosity Method on Parallel Computers

“…Wheeler studied discretization methods, linear solvers, preconditioner techniques and developed a parallel black oil simulator [26]. For the linear solver and preconditioners, many preconditioning methods have been proposed and applied to reservoir simulations such as constrained pressure residual (CPR) methods [14,3], multi-stage methods [1], multiple level preconditioners [24], fast auxiliary space preconditioners (FASP) [9] and a family of parallel CPR-like methods [14].…”