# A Multipoint Flux Approximation Method Based Of Harmonic Points (MPFA- H) For The Numerical Simulation Of Coupled Poroelastic Problems

## Palavras-chave:

Geome- chanics, Finite Volume Method, Multipoint flux approximation, Poroelasticity, Reservoir Simulation## Resumo

Reservoir simulation is an important tool for the prediction of oil and gas production. However, some

physical phenomena were either neglected or oversimplified in the simulations, in order to facilitate the process

of developing a simulation tool to analyze the fluid flow within the rock reservoir. One such phenomenon is the

mechanical behavior of the reservoir and surrounding rocks, and how it affects rock properties, and consequently,

the fluid flow behavior through the porous media, which, in turn, influences its mechanical behavior, since fluid

pressure contributes to the rock deformation. These effects are well observed in wellbore stability and reservoir

subsidence, as both can severally change the production behavior, if not considered. In this work, Biot’s theory of

consolidation is used to derive the governing equations of both the process of rock deformation and fluid flow in

the porous rock and their coupling. In the petroleum reservoir community, usually, these problems are solved using different numerical methods: The Finite Element Method (FEM) is used for the geomechanics problem while the Finite Volume Method (FVM) is employed for the fluid flow problem. However, in the present paper, we propose a full finite volume formulation for both problems based on the use of the Multi-Point Flux Approximation using Harmonic Points (MPFA-H), which was extended to handle the geomechanical problem. The MPFA-H method is very robust and flexible. Using the same basic strategy for both problems has the advantage of producing a locally conservative formulation, which is important for multiphase flow modeling, and the use of the same data structure which eases the simulation tool development, is expected to increase numerical stability, accuracy, and simulation speed. We use a sequential solution method in which the equations for solid deformation and fluid flow are solved separately and the solutions of each problem exchange information in all time steps, using the fixed-strain split. The solutions obtained with the strategy described are verified using benchmarks found in literature.