Biot Porosity Model

Overview

According to the poroelasticity theory, the porosity (pore volume), \(\phi\), can be computed as

\[\phi = \phi_{ref} + \alpha ( \epsilon_v - \epsilon_{v,\,ref} ) + (p - p_{ref}) / N.\]

Here, \(\phi_{ref}\) is the porosity at a reference state with pressure \(p_{ref}\) and volumetric strain \(\epsilon_{v,\,ref}\). Additionally, \(\alpha\) is the Biot coefficient, \(\epsilon_v\) is the volumetric strain, \(p\) is the fluid pressure and \(N = \frac{K_s}{\alpha - \phi_{ref}}\), where \({K_s}\) is the grain bulk modulus.

Parameters

The Biot Porosity Model can be called in the <Constitutive> block of the input XML file. This porosity model must be assigned a unique name via the name attribute. This name is used to assign the model to regions of the physical domain via a materialList attribute in the <ElementRegions> block.

The following attributes are supported:

Name	Type	Default	Description
defaultReferencePorosity	real64	required	Default value of the reference porosity
defaultThermalExpansionCoefficient	real64	0	Default thermal expansion coefficient
grainBulkModulus	real64	required	Grain bulk modulus
name	string	required	A name is required for any non-unique nodes

Example

<Constitutive>
   ...
   <BiotPorosity name="rockPorosity"
                 grainBulkModulus="1.0e27"
                 defaultReferencePorosity="0.3"/>
   ...
</Constitutive>