Abstract

This paper presents numerical techniques for coupled simulations with different time scales and space discretizations for reservoir flow and geomechanics. We use an explicitly coupled approach together with an iterative coupling to increase stability and reduce time discretization error. An error indicator is proposed to determine when displacement must be updated and whether the explicit or iterative coupling technique is required. Under this setting, one geomechanics calculation is performed for several reservoir flow steps. For time steps without geomechanics updates linear extrapolated pore volume is used for porous flow calculations. The resulting algorithm is computationally more efficient than the iterative coupling, and it is more stable and accurate than the loosely coupled technique.

In the event that different meshes are used for the reservoir flow and geomechanics models, special treatments are required for the integration of the coupling terms over each element. To avoid complex 3D grid intersection calculations we propose to divide an element into a number of subelements and apply the midpoint integration rule over each subelement. Numerical results are presented to demonstrate the efficiency and accuracy of the proposed method for coupled simulations with different time and space discretizations.

Introduction

Numerical modeling of multiphysics and multi-processes leads to large coupled multi-field problems. Computationally efficient and accurate strategies for modeling these phenomena have been the focus of development for various operator splitting and decoupling techniques in complex hydrocarbon field simulations. Since varying time scales generally arise in the coupling of different physical processes, it can be advantageous to assign different time discretizations to individual models. In coupled reservoir flow and geomechanics, quasi-static behavior is usually assumed for the poroelastic model.Numerical results indicate that time steps for modeling mechanics may be much larger than those for flow in order to balance contributions to the global error from flow and mechanics [1].

This paper proposes a time stepping strategy that takes into account different time scales for coupling reservoir multiphase flow and geomechanics. The fluid pressures and saturations are computed using multiple time steps for each displacement time step.The latter coarse time step is selected based on a local error indicator. A major advantage of this algorithm is a reduction in computational costs.

onventionally, in a coupled simulation of a reservoir compaction and subsidence problem, the Galerkin finite element method is used for geomechanics analysis, and the cell-centered finite difference or control volume method is used for reservoir flow calculations. However, this type of discretization may not be able to capture the geomechanics effects around wellbores due to the line source treatment of wells.For some geomechanics applications (e.g. cavity generation, sand production [2], waste disposal [3] and wellbore stability) the wall of a wellbore must be discretized to accurately model the rock mechanical behavior around wells.Although applying the Galerkin method to the reservoir flow calculations can resolve this problem, it sacrifices local mass conservation.

In this paper, we present an iterative coupling algorithm for poroelasticity that allows different grids to be used for different models.To realize the wellbore geometry, unstructured hexahedral grids are generated for the stress model while rectangular grids are used for the reservoir flow calculation.In each nonlinear iteration the flow model will first compute the wellbore pressure and density. The mechanics model will then use the wellbore pressure as a traction boundary condition to solve for displacements. Special integration techniques are introduced for the coupling terms to minimize the error in local mass conservation.

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