Poroelasticity-II: On the Equilibrium State of the Fluid-Filled Penetrable Poroelastic Body

Abstract

Part-II of the paper titled "Poroelasticity-II" is devoted to defining the joint equilibrium state of a fluid and elastic penetrable material, encapsulated in a rigid volume, . One can ask different questions in respect to such an equilibrium state, such as: (1) In what physical state will the fluid be, if the porous volume of the poroelastic material is filled with a given mass of fluid? (2) What is the capacity of a volume filled with a penetrable sponge in respect to the fluid being in specific state? etc. The point is that, in the frame of the most popular theory of poroelastic materials, Biot's theory, such a question cannot be addressed because this theory is formulated as a linear theory in the neighborhood of some equilibrium state. In this article, we continue to describe our theory that can be applied to solve such problems. We consider a simplified case of a linear-elastic matrix and a fluid having a Van der Waals equation of state and address the problem of the equilibrium state.

A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs

“…Other recent considerations can be found in [39,204,260]. An elegant approach based on a Lagrangian formulation and representative elementary volume averaging can be found in [177][178][179]. The authors state that their final set of equations is equivalent to Biot's equations for homogeneous, consolidated (nondegenerated) materials with negligible porosity dynamics if at most linear waves are considered [178].…”

“…An elegant approach based on a Lagrangian formulation and representative elementary volume averaging can be found in [177][178][179]. The authors state that their final set of equations is equivalent to Biot's equations for homogeneous, consolidated (nondegenerated) materials with negligible porosity dynamics if at most linear waves are considered [178]. Consequently, the considerations in this thesis are based on Biot's equations as we are interested in consolidation phenomena.…”

Quasilinear poroelasticity: Analysis and hybrid finite element approximation

“…The first studies of poroelasticity are due to Biot [9][10][11][12][13] in which a linear mathematical model of poroelasticity theory was introduced. Subsequently, more sophisticated models of poroelasticity have been proposed, these include, various nonlinear models, and models with physically feasible boundary conditions and interface conditions, see, for example, [14][15][16].…”