Poroelastoplastic reservoir modeling by tangent stiffness matrix method

Abstract

As oil and gas extraction activities move into deeper rock formations, many experimental studies and field investigations indicate rock exhibits a plastic behavior rather than a pure linear elastic behavior, so poroelastoplasticity must be taken into account in the reservoir simulation. Because reservoir rock is a porous material consisting of a compressible solid matrix and number of compressible fluids occupying the pore space, fully coupled modeling is required for reservoir simulation considering solid-fluid interaction, complex stress conditions and nonlinear behaviors. But the computational process could be cumbersome when constant tangent stiffness method is used to address the poroelastoplastic behavior. In this paper, a fully coupled poroelastoplasticity reservoir model based on Drucker-Prager yield criterion is implemented the tangent stiffness method, and the computational efficiency is compared with the constant stiffness method. The accuracy of these two methods is demonstrated in one-dimensional consolidation. In a case study, these two methods are used to analyze the stresses and pore pressure of a reservoir and computing results and running efficiency are compared. Also, the linear elastic and nonlinear solutions are compared in one-dimensional consolidation and reservoir modeling. It shows that the difference between results by constant stiffness method and tangent stiffness method is very small, while the tangent stiffness method shows significantly fewer iteration numbers and shorter running time than the constant stiffness method.

Keywords

Poroelastoplasticity / Reservoir simulation / Finite element methods / Tangent stiffness method

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