A block preconditioner for non-isothermal flow in porous media

In petroleum reservoir simulation, the industry standard preconditioner, the Constrained Pressure Residual method (CPR), is a two-stage process which involves solving a restricted pressure system with Algebraic Multigrid (AMG). Initially designed for isothermal models, this approach is often used in...

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Bibliographic Details
Published in:Journal of computational physics 2019-10, Vol.395, p.636-652
Main Authors: Roy, Thomas, Jönsthövel, Tom B., Lemon, Christopher, Wathen, Andrew J.
Format: Article
Language:English
Subjects:
Computational physics
Computer simulation
Conservation equations
Diffusion effects
Energy conservation
Heat transmission
Industry standards
Isothermal flow
Iterative solvers
Mathematical analysis
Porous media
Preconditioning
Pressure effects
Temperature effects
Thermal reservoir simulation
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Summary:In petroleum reservoir simulation, the industry standard preconditioner, the Constrained Pressure Residual method (CPR), is a two-stage process which involves solving a restricted pressure system with Algebraic Multigrid (AMG). Initially designed for isothermal models, this approach is often used in the thermal case. However, it does not have a specific treatment of the additional energy conservation equation and temperature variable. We seek to develop preconditioners which better capture thermal effects such as heat diffusion. In order to study the effects of both pressure and temperature on fluid and heat flow, we consider a model of non-isothermal single phase flow through porous media. For this model, we develop a block preconditioner with an efficient Schur complement approximation. Both the pressure block and the approximate Schur complement are approximately inverted using an AMG V-cycle. The resulting solver is scalable with respect to problem size and parallelization. •The continuous problem is used to develop a novel Schur complement approximation•The novel Schur complement approximation performs much better than simpler ones•The new preconditioner performs best in diffusion-dominated cases•Linear iterations stay almost constant with mesh refinement or parallelization
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2019.06.038