Parameter Estimation for Multiphase Reservoir Models on Hypercubes

This paper discusses the parallel implementation of a numerical algorithm for estimating reservoir parameter distributions on hypercube parallel computers. The algorithm can be used to identify the reservoir absolute permeability distributions by matching the computed pressure values with measured pressure values obtained at observation wells (history matching). We show that the use of multilevel grids in nested iterations improves the quality of the identified permeability distributions significantly. The whole parameter identification process is very computationally intensive since a group of coupled nonlinear PDEs and a regularized least-square problem must be solved repeatedly with different parameter values at many time steps. The block SOR scheme with red and black ordering and parallel orthogonal transformation schemes were implemented to solve the algebraic equations resulting from the discretization of the governing PDEs. High speed-up has been achieved by exploring parallelism and minimizing internode communications.