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A New Fixed-Stress Split Scheme In Poroplastic Media Incorporating General Plastic Porosity Constitutive Theories
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, ECMOR XVI - 16th European Conference on the Mathematics of Oil Recovery, Sep 2018, Volume 2018, p.1 - 25
Abstract
Summary
One of the most challenging issues in reservoir modeling relies on the development of proper numerical schemes for coupling flow and geomechanics with ability to handle highly heterogeneous coefficients with complex spatial distributions while preserving local conservation properties and computational efficiency. In this challenging context substantial progress has been recently accomplished within the framework of sequential methods, where the fully-coupled system is partitioned into sub-problems with coupling enforced in an iterative fashion mainly through source terms in the pressure and equilibrium equations. Among the class of proposed schemes where hydrodynamics is solved first, we may highlight the fixed strain and stress split, where the former behaves conditionally stable whereas the unconditional stable fixed stress split is more efficient, since the source term involving the time-derivative of the total mean stress admits a much slower characteristic time scale compared to the other poromechanical variables. The extension of the fixed-stress split algorithm to the poroplastic scenario has been accomplished in [1] where additional nonlinearity was incorporated in the pressure equation by replacing the bulk modulus by the nonlinear elastoplastic tangent modulus. Such an immediate extension is valid provided the same form of the effective stress principle seated on the Biot-Willis coefficient, originally proposed by Biot for elastic rock skeleton, is preserved in the regime of nonlinear plastic deformations and used as the proportionality constant between plastic porosity and plastic deformation [1]. The generalization of the fixed stress split scheme to the scenario where this assumption is relaxed is still an open issue. This work aims at filling this gap. We develop a new generalized fixed stress split scheme for single phase flow in reservoirs characterized by irreversible deformations with ability to incorporate the plastic porosity concept not necessarily ruled by same the Biot-Willis parameter. This approach gives rise to additional complexity in the iterative formulation which needs to be handled by appropriate algorithms which are proposed herein. Numerical results illustrate the effects of the additional source term in the pressure equation steaming from the transient component of the total mean stress upon oil production, reservoir compaction and surface subsidence. In particular we highlight the opposite roles of the source term during primary/secondary recovery in both elastic and plastic regimes.
[1] J. Kim, H. A. Tchelepi, R. Juanes, Stability and convergence of sequential methods for coupled flow and geomechanics: Fixed-stress and fixed-strain splits.
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