A constrained pressure-temperature residual (CPTR) method for non-isothermal multiphase flow in porous media.

*(English)*Zbl 1452.76101Summary: For both isothermal and thermal petroleum reservoir simulation, the constrained pressure residual (CPR) method is the industry-standard preconditioner. This method is a two-stage process involving the solution of a restricted pressure system. While initially designed for the isothermal case, CPR is also the standard for thermal cases. However, its treatment of the energy conservation equation does not incorporate heat diffusion, which is often dominant in thermal cases. In this paper, we present an extension of CPR: the constrained pressure-temperature residual (CPTR) method, where a restricted pressure-temperature system is solved in the first stage. In previous work, we introduced a block preconditioner with an efficient Schur complement approximation for a pressure-temperature system. Here, we extend this method for multiphase flow as the first stage of CPTR. The algorithmic performance of different two-stage preconditioners is evaluated for reservoir simulation test cases.

Reviewer: Reviewer (Berlin)

##### MSC:

76M10 | Finite element methods applied to problems in fluid mechanics |

65F08 | Preconditioners for iterative methods |

65F10 | Iterative numerical methods for linear systems |

65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |

65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |

76S05 | Flows in porous media; filtration; seepage |

##### Keywords:

preconditioning; iterative methods; porous media; thermal reservoir simulation; multiphase flow
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\textit{T. Roy} et al., SIAM J. Sci. Comput. 42, No. 4, B1014--B1040 (2020; Zbl 1452.76101)

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