Iterative coupling reservoir simulation on high performance computers

In this paper, the iterative coupling approach is proposed for applications to solving multiphase flow equation systems in reservoir simulation, as it provides a more flexible time-stepping strategy than existing approaches. The iterative method decouples the whole equation systems into pressure and saturation/concentration equations, and then solves them in sequence, implicitly and semi-implicitly. At each time step, a series of iterations are computed, which involve solving linearized equations using specific tolerances that are iteration dependent. Following convergence of subproblems, material balance is checked. Convergence of time steps is based on material balance errors. Key components of the iterative method include phase scaling for deriving a pressure equation and use of several advanced numerical techniques. The iterative model is implemented for parallel computing platforms and shows high parallel efficiency and scalability.

[1]  D. W. Peaceman.  Fundamentals of numerical reservoir simulation , 1977 .

[2]  Yuanle Ma,et al.  Computational methods for multiphase flows in porous media , 2007, Math. Comput..

[3]  Hector Manuel Klie.  Krylov-Secant methods for solving large-scale systems of coupled nonlinear parabolic equations , 1997 .

[4]  K. H. Coats,et al.  Reservoir simulation: state-of-the-art , 1982 .

[5]  J. W. Watts,et al.  A New Method for Solving the Implicit Reservoir Simulation Matrix Equation , 2005 .

[6]  J. W. Watts,et al.  A Compositional Formulation of the Pressure and Saturation Equations , 1986 .

[7]  L. S.-K. Fung,et al.  An adaptive-implicit switching criterion based on numerical stability analysis , 1989 .

[8]  Hamdi A. Tchelepi,et al.  An Extensible Architecture for Next Generation Scalable Parallel Reservoir Simulation , 2005 .

[9]  Michael Andrew Christie,et al.  Tenth SPE Comparative Solution Project: a comparison of upscaling techniques , 2001 .

[10]  Magne S. Espedal,et al.  Parallel Simulation of Multiphase/Multicomponent Flow Models , 2005 .

[11]  A. G. Spillette,et al.  A High-Stability Sequential Solution Approach to Reservoir Simulation , 1973 .

[12]  R. P. Kendall,et al.  Development of a Multiple Application Reservoir Simulator for Use on a Vector Computer , 1983 .

[13]  Jun Liu,et al.  Next Generation Parallel Computing for Large-Scale Reservoir Simulation , 2005 .

[14]  Mary F. Wheeler,et al.  A parallel, implicit, cell‐centered method for two‐phase flow with a preconditioned Newton–Krylov solver , 1997 .

[15]  Graham Fleming,et al.  Development and Field Application of a High Performance, Unstructured Simulator with Parallel Capability , 2005 .

[16]  Mary F. Wheeler,et al.  Iterative Solution Methods for Modeling Multiphase Flow in Porous Media Fully Implicitly , 2003, SIAM J. Sci. Comput..

[17]  Bo Lu,et al.  Iteratively coupled reservoir simulation for multiphase flow in porous media , 2008 .

[18]  Martin J. Blunt,et al.  Tenth SPE Comparative Solution Project: a comparison of upscaling techniques , 2001 .

[19]  John Killough,et al.  Ninth SPE Comparative Solution Project: A Reexamination of Black-Oil Simulation , 1995 .

[20]  C. H. Stewart,et al.  A New Approach to the Two-Dimensional Multiphase Reservoir Simulator , 1966 .

[21]  Mary F. Wheeler,et al.  Iteratively Coupled Reservoir Simulation for Multiphase Flow , 2007 .