Coupled flow and geomechanics problems in porous media

Abstract:  Coupling of geomechanics and flow in a poroelastic porous media has several energy and environmental applications including subsidence events and ground water remediation. The geomechanical effects account for the influence of deformations in the porous media caused due to the pore pressure whereas the changes in the pore structure due to mechanical stresses affect the flow field.  Single phase quasi-static Biot model is typically used to model these coupled flow and deformation processes. 

We report here some of the developments in suitable iterative schemes for such models and their extensions. Our work has two components: 1. Developing suitable iterative schemes for the extensions of the Biot model to include more physics such as fractures and non-linearities, 2. Developing multirate schemes by exploiting the different time scales of mechanics and flow solve by taking coarser time step for mechanics and smaller time steps for flow. The iterative multirate schemes combine the advantages of both implicit and explicit approaches. They are efficient, allow larger time steps, are robust, and the decoupling allows us to solve the linear systems efficiently. We rigorously analyse the convergence and stability properties of some of the iterative and explicit multirate schemes.

This work is done in collaboration with Tameem Almani (Austin), Mary F. Wheeler (Austin), Vivette Girault (Paris), Florin Radu (Bergen), and Jan Nordbotten (Bergen).