Fast Computational Methods for Reservoir Flow Models

Abstract

Numerical reservoir simulation models are used in the energy industry to forecast the behavior of hydrocarbon reservoirs and connected surface facilities over long production periods. The simulation of oil and gas reservoirs requires the construction and solution of large, sparse linear systems with millions or tens of millions of unknowns at each step of a Newton iteration. The problem size and complexity of these models is growing faster than advances in computer hardware, therefore more accurate and robust numerical techniques are necessary to reduce simulation turnaround time. In this paper, we compare the computational performance of a Nonlinear Newton-Krylov solver with Inexact Newton-Krylov and Quasi-Newton methods for a compressible, three-phase fluid model with an incompressible rock model. The coupled system of nonlinear partial differential equations (PDEs) that describe fluid flow are discretized on a structured, rectangular grid using finite volumes. An implicit method is used to solve for updates to the pressure and saturations at each time step. Rock properties, like permeability and porosity are generated from the top layer of the SPE10 model problem. We conclude with results comparing different nonlinear and linear solvers and from an optimization strategy for well placement that we experimented with as part of the Institute for Mathematics and its Applications (IMA) summer industrial workshop. 1