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

Abstract

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.

On the optimization of the fixed‐stress splitting for Biot's equations

“…Continuous and discontinuous higher‐order Galerkin space‐time finite elements were proposed in the work of Bause et al Adaptive computations were considered, for example, in the work of Ern and Meunier . A Monte Carlo approach was proposed in the work of Rahrah and Vermolen . For a discussion on the stability of different spatial discretizations, we refer to the recent papers …”

“…17 A Monte Carlo approach was proposed in the work of Rahrah and Vermolen. 18 For a discussion on the stability of different spatial discretizations, we refer to the recent papers. 19,20 Independently of the chosen discretization, there are two popular alternatives for solving Biot's equations: monolithically or by using an iterative splitting algorithm.…”

A moving finite element framework for fast infiltration in nonlinear poroelastic media

“…where d s is the mean grain size of the soil and the porosity θ is computed from the displacement vector using the porosity-dilatation relation (see [35,47]):…”

“…Subsequently, we define the function spaces Q = {q ∈ H 1 ( t ) : q| 2 = p pump and q| 4 = 0} and W = {w ∈ (H 1 ( t )) 2 : w| 1 = (0, u vib ) T and (w • n)| 3 = 0}. Furthermore, we consider the bilinear forms [35]:…”

“…Poroelasticity problems have been attracting attention from the scientific computing community [25,31,50] (and references therein). Some recent work can be found in [19,24,25,35,42]. The simplicity of the displacement-pressure two-field formulation [31,52] is attractive and hence pursued by this paper.…”