A numerically stable sequential implicit algorithm for finite-strain elastoplastic geomechanics coupled to fluid flow
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Copyright 2015, Society of Petroleum Engineers. We propose a numerically stable algorithm for coupled flow and finite-strain multiplicative elastoplastic geomechanics in this study, extending small deformation to large deformation problems. The proposed algorithm first solves flow, being energy dissipative, and then solve mechanics. Energy-dissipation at the flow step can be achieved by fixing the first Piola-Kirchhoff total stress field. In this sense, the proposed algorithm is an extension of the fixed stress sequential method in coupled flow and geomechanics. Although fixing the first Piola-Kirchhoff total stress field provides theoretical unconditional stability, we fix the second Piola-Kirchhoff total stress field in this study, based on the assumption that the difference between the two is small, because the constitutive relations are formulated by the second Piola-Kirchhoff total stress. In space discretization, we use the finite element method for mechanics with the total Lagrangian approach scheme, while employing the finite volume method for flow. Geometrical nonlinearity from the total Lagrangian approach results in full-tensor permeability even though the initial permeability is isotropic. To deal with full-tensor permeability, we use the multipoint flux approximation in flow. In time discretization, the backward Euler method is used. We show by the energy method that the proposed algorithm is unconditionally stable, i.e., the proposed operator splitting and sequential algorithm are contractive and B-stable, respectively. Then, we present numerical examples of coupled finite-strain geomechanics and flow.
