From arteries to boreholes: Transient response of a poroelastic cylinder to fluid injection

TL;DR

This paper investigates how nonlinear poroelastic effects influence the transient response of a cylinder to fluid injection, emphasizing the importance of boundary conditions and driving method in the system's dynamics.

Contribution

It provides a detailed analysis of the separate and combined effects of kinematic and constitutive nonlinearities on poroelastic transient response, highlighting the role of driving method.

Findings

Nonlinearities can either speed up or slow down the response.

Imposed fluid pressure results in faster response than imposed fluid flux.

Driving method significantly affects the transient evolution.

Abstract

The radially outward flow of fluid through a porous medium occurs in many practical problems, from transport across vascular walls to the pressurisation of boreholes in the subsurface. When the driving pressure is non-negligible relative to the stiffness of the solid structure, the poromechanical coupling between the fluid and the solid can control both the steady-state and the transient mechanics of the system. Very large pressures or very soft materials lead to large deformations of the solid skeleton, which introduce kinematic and constitutive nonlinearity that can have a nontrivial impact on these mechanics. Here, we study the transient response of a poroelastic cylinder to sudden fluid injection. We consider the impacts of kinematic and constitutive nonlinearity, both separately and in combination, and we highlight the central role of driving method in the evolution of the response. We show that the various facets of nonlinearity may either accelerate or decelerate the transient response relative to linear poroelasticity, depending on the boundary conditions and the initial geometry, and that an imposed fluid pressure leads to a much faster response than an imposed fluid flux.