Monte Carlo Assessment of the Impact of Oscillatory and Pulsating Boundary Conditions on the Flow Through Porous Media

Stress and water injection induce deformations and changes in pore pressure in the soil. The interaction between the mechanical deformations and the flow of water induces a change in porosity and permeability, which results in nonlinearity. To investigate this interaction and the impact of mechanical vibrations and pressure pulses on the flow rate through the pores of a porous medium under a pressure gradient, a poroelastic model is proposed. In this paper, a Galerkin finite element method is applied for solving the quasi-static Biot’s consolidation problem for poroelasticity, considering nonlinear permeability. Space discretisation using Taylor–Hood elements is considered, and the implicit Euler scheme for time stepping is used. Furthermore, Monte Carlo simulations are performed to quantify the impact of variation in the parameters on the model output. Numerical results show that pressure pulses and soil vibrations in the direction of the flow increase the amount of water that can be injected into a deformable fluid-saturated porous medium.