Efficient Multi-Stage Preconditioners for Highly Heterogeneous Reservoir Simulations on Parallel Distributed Systems

摘要

Large-scale reservoir simulation is still a big challenge due to the difficulty of solving linear systems resulted from the Newton methods.For black oil simulation,more than 90%of running time is spent on the solution of linear systems.The problem is getting worse when developing parallel reservoir simulators using parallel distributed systems with tens of thousands of CPUs.Efficient linear solvers and precon- ditioners are critical to the development of parallel reservoir simulators. Here we introduce our work on developing parallel preconditioners for highly heterogeneous reservoir simulations.A family of new Constrained Pressure Residual(CPR)-like preconditioners and advanced matrix pre-processing techniques are developed,including two new three-stage preconditioners and one four-stage preconditioners.A pressure system is solved by an algebraic multi-grid method,and the entire linear system is solved by the restricted additive Schwarz(RAS)method(one of the domain decompo- sition methods).To overcome a convective issue in reservoir simulation,a parallel potential-based matrix reordering method is employed to stabilize our preconditioners.Matrix decoupling methods,such as an alternative block factorization(ABF)strategy and a Quasi-IMPES(implicit pressure explicit saturation) strategy,are also applied.With the restricted additive Schwarz and algebraic multi-grid methods,our preconditioners have good scalability for parallel computers. Our preconditioners have been applied to oil-water and black oil benchmark simulations.For the SPE 10 project,which is a big challenge for a linear solver because of highly heterogeneous permeability and porosity,our preconditioners with the GMRES linear solver are stable and efficient.When using 64 CPUs, the number of iterations of our linear solvers is less than 40.When applying our method to a standard black oil simulation with 100 millions of grid blocks,the number of iterations of our linear solvers is only two using 3,072 CPU cores.Our numerical experiments show that our preconditioners and linear solvers are stable with a large number of CPUs and are efficient for highly heterogeneous simulations.