Nonlinear Multigrid for Efficient Reservoir Simulation

Max la Cour Christensen, Klaus Langgren Eskildsen

AbstractThe subject of this thesis is a thorough investigation of the application of nonlinear multigrid techniques, specifically the Full Approximation Scheme (FAS), for simulation of subsurface multiphase porous media flow. The main motivation for addressing this topic is a need for higher resolution and efficient simulations leading to better decision making in the production of oil and gas. Higher resolution simulations require efficient utilization of many-core parallel architectures. Current numerical methods employed in industrial reservoir simulators are memory intensive and not readily scalable on large-scale distributed systems and modern many-core architectures such as GPUs or Intel MICs.
In a first step, we investigate alternative numerical methods to establish algorithmic performance in serial computations. The nonlinear multigrid technique FAS uses local linearization, which allows for local components suitable for parallel implementation. Furthermore, FAS is a memory lean algorithm. To our knowledge, very little work is published on FAS for reservoir simulation. Molenaar, [36], considers the application of FAS on a simple 2D immiscible two-phase no gravity homogeneous example. To our knowledge, FAS has not been applied successfully to more complicated heterogeneous reservoir problems.
Two reservoir simulators have been implemented in C++ in serial. The first simulator is based on conventional techniques with global linearization in Newton’s method and state-of-the-art choice of methods for the linear solver. The second simulator is based on the nonlinear multigrid method FAS. Both simulators solve the same system of PDEs governing 3D three-phase flow of oil, water and gas in a subsurface porous medium taking into account gravitational effects. The same discretization techniques are used for both simulators. For spatial discretization, the Finite Volume Method is used and for temporal integration, the backward Euler method is used. This enables fair comparisons between the conventional methods and FAS.
The two reservoir simulators have been tested extensively to compare the nonlinear multigrid approach FAS with the conventional techniques applied in modern reservoir simulation. It has been demonstrated that, without loss of robustness, FAS outperforms the conventional techniques in terms of algorithmic and numerical efficiency for the model equations considered. Furthermore, memory comparisons have been carried out, which show that FAS provides a significant memory reduction in comparison with conventional techniques. This memory reduction is an attractive feature, which enables higher resolution simulation for the beforementioned modern many-core architectures.
TypeMaster's thesis [Academic thesis]
Year2012
PublisherTechnical University of Denmark, Department of Applied Mathematics and Computer Science
AddressMatematiktorvet, Building 303B, DK-2800 Kgs. Lyngby, Denmark, compute@compute.dtu.dk
SeriesM.Sc.-2012-103
NoteDTU supervisor: Allan P. Engsig-Karup, apek@dtu.dk, DTU Compute
Electronic version(s)[pdf]
Publication linkhttp://www.compute.dtu.dk/English.aspx
BibTeX data [bibtex]
IMM Group(s)Scientific Computing


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