In this paper we consider algorithms that will enable scientists and engineers to readily model complex processes in porous media taking into account fluid motion and the accompanying solid deformations. Numerous field applications would benefit from a better understanding and integration of porous flow and solid deformation. Important applications in environmental engineering and petroleum engineering include carbon sequestration, surface subsidence, pore collapse, cavity generation, hydraulic fracturing, thermal fracturing, wellbore collapse, sand production, fault activation, and waste disposal, while similar issues arise in biosciences and chemical sciences as well. Here we consider solving iteratively the coupling of flow and mechanics. We employ mixed finite element method for flow and a continuous Galerkin method for elasticity. For single phase flow, we demonstrate the convergence and convergence rates for two widely used schemes, the undrained split and the fixed stress split. We discuss the extension of the fixed stress iterative coupling scheme to an equation of state compositional flow model coupled with elasticity and a single phase poroelasticity model on general hexahedral grids. Computational results are presented which include parallel simulation of carbon sequestration in saline aquifer, and single phase poroelasticity examples on an unstructured wellbore grid and an unstructured reservoir grid.


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