Storage Model
Inserting Darcy’s law (Equation 7-20) into the continuity equation produces the generalized governing equation
(7-23)
Represent this equation fully in COMSOL Multiphysics because relationships between density or permeability can be freely specified, for example, and pressure, temperature, concentration, and so on.
Expand the time-derivative term in Equation 7-23
Define the porosity and the density as functions of the pressure, and apply the chain rule
Insert the definition of fluid compressibility χf = (1/ρ)(∂ρ/∂p) to the right-hand side and rearrange to arrive at
Using this relation, the generalized governing equation (Equation 7-23) takes the following form:
(7-24)
In this equation, S is the storage coefficient (SI unit: 1/Pa), which can be interpreted as the weighted compressibility of the porous material and the fluid. The storage S can be an expression involving results from a solid-deformation equation or an expression involving temperatures and concentrations from other analyses. The Darcy’s Law interface implements Equation 7-24 in the Porous Medium node, which explicitly includes different storage models to choose from, such as linearized storage which defines S (SI unit: 1/Pa) using the compressibility of fluids χf and of the porous matrix χp:
,
or the poroelastic storage where
.