Storage Models
The continuity equation (Equation 4-2) allows flexible specification of relationships between parameters like density or permeability with respect to variables such as pressure, temperature, concentration, and more.
Expanding the time-derivative term and defining the porosity and density as functions of the pressure and using the chain rule results in
By inserting the definition of fluid compressibility χf = (1/ρ)(∂ρ/∂p) to the right-hand side and rearrange the following expression is obtained
Using this relation, the generalized governing equation (Equation 4-2) takes the following form:
(4-4)
In this equation, Sp 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 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 4-4 in the Porous Medium node, which explicitly includes different storage models to choose from:
From density and porosity, where the storage directly depends on changes in porosity or fluid density
Linearized storage, which defines Sp using the compressibility of the fluid χf and of the porous matrix χp according to
.