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:
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From density and porosity, where the storage directly depends on changes in porosity or fluid density
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Linearized storage, which defines Sp using the compressibility of the fluid χf and of the porous matrix χp according to
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Poroelastic storage where
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Storage models are only available for the Subsurface Flow Module and the Porous Media Flow Module. For a detailed overview of the functionality available in each product visit https://www.comsol.com/products/specifications/.