Solution of Poroelastic Equations with Different Base Variables Using Equation-based Modeling

M. H. Akanda [1], Y. Cao [1], A. J. Meir [1],
[1] Department of Mathematics & Statistics, Auburn University, Auburn, AL, USA
Published in 2015

Poroelasticity equations describe the interaction between fluid flow and solids deformation within a porous medium. Modeling of poroelasticity is coupling between elastic deformation of porous materials and Darcy’s law. Poroelasticity has numerous real world applications such as in reservoir engineering, bio-engineering, environmental engineering etc. We have used quasi-static poroelastic equations for modeling. The equations are independently transformed into two different formulations: stress-displacement-pressure formulation and increment of fluid content-rotation variables-pressure gradients formulation. The main advantage of using different formulations is to enforce different boundary conditions and hence gives us greater flexibility to handle real life applications. For each case, different admissible boundary conditions are provided knowing its well-posedness associated with the boundary conditions. Because of non-standard formulation, equation-based modeling is used for simulation.