Dynamic Mesh Adaptivity and Novel Stopping Criterion Guided by a Posteriori Error Estimates for Coupled Geomechanics Using Mixed Finite Element Method for Flow

Abstract

Flow coupled with geomechanics problems has gathered increased research interest due to its resemblance to engineering applications, such as unconventional reservoir development, by incorporating multiple physics. Computations for the system of such a multiphysics model is often costly. In this paper, we introduce a posteriori error estimators to guide dynamic mesh adaptivity and to determine a novel stopping criterion for the fixed-stress split algorithm to improve computational efficiency. Previous studies for flow coupled with geomechanics have shown that local mass conservation for the flow equation is critical to the solution accuracy of multiphase flow and reactive transport models, making mixed finite element method an attractive option. Such a discretization maintains local mass conservation by enforcing the constitutive equation in strong form and can be readily incorporated into existing finite volume schemes, that are standard in the reservoir simulation community. Here, we introduced a posteriori error estimators derived for the coupled system with the flow and mechanics solved by mixed method and continuous Galerkin respectively. The estimators are utilized to guide the dynamic mesh adaptivity. We demonstrate the effectiveness of the estimators on computational improvement by a fractured reservoir example. The adaptive method only requires 20% of the degrees of freedom as compared to fine scale simulation to obtain an accurate solution. To avoid solving enormous linear systems from the monolithic approach, a fixed-stress split algorithm is often adopted where the flow equation is resolved first assuming a constant total mean stress, followed by the mechanics equation. The implementation of such a decoupled scheme often involves fine tuning the convergence criterion that is case sensitive. Previous work regarding error estimators with the flow equation solved by Enriched Galerkin proposed a novel stopping criterion that balances the algorithmic error with the discretization error. The new stopping criterion does not require fine tuning and avoids over iteration. In this paper, we extend such a criterion to the flow solved by mixed method and further confirm its validity.