Mathematically, the behavior of fluid-saturated porous materials is usually modeled as the interaction between two interpenetrating systems (mechanics and flow), where the behavior of one directly influences the other. For instance, mechanical deformation impacts pore volume and permeability, thereby affecting fluid flow, while fluid pressure influences the stress on the solid matrix and subsequently affects its deformation. Numerical solutions for such systems may involve coupling different types of simulators or solving a single set of equations simultaneously.
In many applications, especially those related to geomechanics, mechanical deformations are typically small and remain within the elastic behavior range of the solid material. Linear poroelasticity theory is commonly applied in such cases, where constitutive laws linking stresses, strains, pressures, and fluid flow are linear. Quasi-static poroelasticity assumes instant equilibrium between the mechanical system, fluid pressure, and external forces, while dynamic poroelasticity incorporates inertia, kinetic energy, and can be used to describe wave propagation through the combined medium.
