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<p>The iterative sequential fixed stress coupling scheme (SC) for coupled flow and geomechanics has proven to be unconditionally stable. However, SC suffers from poor outer loop convergence, particularly evident in tightly coupled poromechanics problems. This work addresses the issue of slow sequential convergence by applying nonlinear acceleration to the outer loop. First, a coupling strength indicator, coupling strength ratio (CSR), is introduced. CSR is a&#xa0;function of fluid and rock properties, and reservoir models with stronger coupling are characterized by higher CSR values. Numerical examples prove CSR to be a suitable metric of the coupling strength, and the linear convergence rate of the fixed point SC scheme renders it ill-suited for such tightly coupled models. To that end, Aitken relaxation is applied to the porosity update after the mechanics subproblem to improve the outer loop convergence rate. Numerical examples show significant computational gains in terms of fewer outer loops needed to converge to the same residual tolerance.</p>

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Nonlinear Acceleration of the Iterative-Sequentially Coupled Flow and Geomechanics Fixed Stress Scheme

  • 期刊论文

  • 发表日期：

    2025年6月19日

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  • Sohail Waziri,
  • Guotong Ren,
  • Pavel Tomin,
  • Baris Guyaguler

摘要

The iterative sequential fixed stress coupling scheme (SC) for coupled flow and geomechanics has proven to be unconditionally stable. However, SC suffers from poor outer loop convergence, particularly evident in tightly coupled poromechanics problems. This work addresses the issue of slow sequential convergence by applying nonlinear acceleration to the outer loop. First, a coupling strength indicator, coupling strength ratio (CSR), is introduced. CSR is a function of fluid and rock properties, and reservoir models with stronger coupling are characterized by higher CSR values. Numerical examples prove CSR to be a suitable metric of the coupling strength, and the linear convergence rate of the fixed point SC scheme renders it ill-suited for such tightly coupled models. To that end, Aitken relaxation is applied to the porosity update after the mechanics subproblem to improve the outer loop convergence rate. Numerical examples show significant computational gains in terms of fewer outer loops needed to converge to the same residual tolerance.