From arteries to boreholes: Steady-state response of a poroelastic cylinder to fluid injection

TL;DR

This paper investigates the steady-state behavior of a poroelastic cylinder under fluid injection, emphasizing the effects of nonlinearities and boundary conditions on deformation and permeability.

Contribution

It provides a detailed analysis of nonlinear poromechanical responses, including deformation-dependent permeability, in a cylindrical geometry under various boundary conditions.

Findings

Deformation-dependent permeability significantly influences flow response.

Wall thickness and boundary constraints critically affect deformation and flow.

Nonlinear effects become prominent at high pressures or soft materials.

Abstract

The radially outward flow of fluid into a porous medium occurs in many practical problems, from transport across vascular walls to the pressurisation of boreholes. As the driving pressure becomes non-negligible relative to the stiffness of the solid structure, the poromechanical coupling between the fluid and the solid has an increasingly strong impact on the flow. For very large pressures or very soft materials, as is the case for hydraulic fracturing and arterial flows, this coupling can lead to large deformations and, hence, to strong deviations from a classical, linear-poroelastic response. Here, we study this problem by analysing the steady-state response of a poroelastic cylinder to fluid injection. We consider the qualitative and quantitative impacts of kinematic and constitutive nonlinearity, highlighting the strong impact of deformation-dependent permeability. We show that the wall thickness (thick vs. thin) and the outer boundary condition (free vs. constrained) play a central role in controlling the mechanics.