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Block constrained pressure residual preconditioning for two-phase flow in porous media by mixed hybrid finite elements

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submitted on 2024-01-11, 10:48 and posted on 2024-01-15, 11:02 authored by Stefano Nardean, Massimiliano Ferronato, Ahmad Abushaikha

This work proposes an original preconditioner that couples the Constrained Pressure Residual (CPR) method with block preconditioning for the efficient solution of the linearized systems of equations arising from fully implicit multiphase flow models. This preconditioner, denoted as Block CPR (BCPR), is specifically designed for Lagrange multipliers-based flow models, such as those generated by Mixed Hybrid Finite Element (MHFE) approximations. An original MHFE-based formulation of the two-phase flow model is taken as a reference for the development of the BCPR preconditioner, in which the set of system unknowns comprises both element and face pressures, in addition to the cell saturations, resulting in a $$3\times 3$$ 3 × 3 block-structured Jacobian matrix with a $$2\times 2$$ 2 × 2 inner pressure problem. The CPR method is one of the most established techniques for reservoir simulations, but most research focused on solutions for Two-Point Flux Approximation (TPFA)-based discretizations that do not readily extend to our problem formulation. Therefore, we designed a dedicated two-stage strategy, inspired by the CPR algorithm, where a block preconditioner is used for the pressure part with the aim at exploiting the inner $$2\times 2$$ 2 × 2 structure. The proposed preconditioning framework is tested by an extensive experimentation, comprising both synthetic and realistic applications in Cartesian and non-Cartesian domains.

Other Information

Published in: Computational Geosciences
License: https://creativecommons.org/licenses/by/4.0
See article on publisher's website: https://dx.doi.org/10.1007/s10596-023-10238-x

Funding

Open Access funding provided by the Qatar National Library.

History

Language

  • English

Publisher

Springer Nature

Publication Year

  • 2023

License statement

This Item is licensed under the Creative Commons Attribution 4.0 International License.

Institution affiliated with

  • Hamad Bin Khalifa University
  • College of Science and Engineering - HBKU