Poroelasticity

Abstract

Poroelasticity is the study of elastic deformation of porous materials saturated with a fluid and the coupling between the fluid pressure and the solid deformation. Considerable progress has been made in formulating analytical and numerical models of subsurface fluid flow, but only few models explain the interrelations between fluid-flow pressure changes and seismicity. In this work, we describe the quasi-static poroelasticity system of partial differential equations consisting of the equilibrium equation for momentum conservation and the diffu- sion equation for Darcy flow. We prove existence and uniqueness of weak solutions to the equations of the quasi-static poroelasticity system and derive error estimates. We describe a coupled numerical algorithm that accounts for the interrelations between the fluid pres- sure changes and the deformation of the porous elastic material based on the finite element method using MATLAB.