Events

Speaker:  Dr. Hamdi Tchelepi, Professor at Stanford University

Title of Seminar: “Linear and Nonlinear Solvers for Scalable Reservoir Simulation”

Abstract: Reservoir Simulation (RS) entails numerical solution of the equations that govern the flow dynamics in subsurface formations. RS is a primary tool for making predictions of reservoir performance and quantifying the uncertainty associated with the predictions. It is getting increasingly more difficult to scale the RS capabilities to keep up with the enormous growth in both the resolution of the RCM (Reservoir Characterization Model) and the complexity of the enhanced recovery processes. In order to meet this scalability challenge, we have to deal effectively with (1) the multiscale nature of the RCM, and (2) the nonlinear coupling of the conservation laws and associated constitutive relations. We address both of these issues.

First, we describe an Algebraic MultiScale (AMS) framework for flow and transport in heterogeneous porous media. The focus is on the AMS based linear solution of the pressure equation. The design and implementation of the multiscale linear solver on emerging parallel architectures is discussed. We then shift focus and address the scalability obstacles due to the strong nonlinear coupling of the physics. The evolution of the coupled nonlinear systems of equations that describe multi-component, multiphase flow in subsurface formations is usually dealt with by marching forward in time using small increments (time steps). In essence, the governing equations and associated constitutive relations are linearized around the latest estimate of the solution; as a result, the size of the time step that can be used depends very strongly on the ability of the nonlinear solver to converge. Industrial reservoir simulators employ sophisticated – often problem-specific - heuristics to guide the time stepping and the nonlinear solver, which is almost always based on the Newton method. This `damped Newton’ nonlinear solution strategy has become a serious bottleneck in our ability to scale reservoir simulators with the increase in the RCM size and the complexity of the flow physics. The severity of the nonlinear challenge increases dramatically as the spatial and temporal scales of interest increase in range and complexity. We describe a nonlinear solver based on constructing trust regions of the numerical flux functions, and we show that unconditionally convergent iterative schemes can be obtained. We discuss the connections between the trust-region approach and the continuation-Newton framework. We argue that combining multiscale formulations with trust-region nonlinear solvers provides a pathway to RS scalability. 

Biography:   Dr. Hamdi Tchelepi is Professor of Energy Resources Engineering at Stanford University. He is codirector of the Industrial Consortium on Reservoir Simulation Research (SUPRI-B), and the Stanford Center for Computational Earth and Environmental Sciences (CEES). Before joining Stanford, he was a Research Scientist with the Chevron Energy Technology Company, where he was involved with the development of the Intersect Reservoir Simulator (Chevron-Schlumberger). Current research areas include (1) multiscale formulations and solution methods for compositional processes, (2) scalable parallel linear solvers, (3) flux-based nonlinear solvers, (4) stochastic formulations for uncertainty quantification, and (5) pore-scale simulation of multiphase flow. Tchelepi holds a PhD in Petroleum Engineering from Stanford University.