Biot Porosity Model

Overview

According to the linear thermoporoelasticity theory (Coussy, 2004) , the porosity (pore volume), $\phi$ , can be computed as

$\phi = \phi_{ref} + \alpha ( \epsilon_v - \epsilon_{v,\,ref} ) + (p - p_{ref}) / N - 3 \beta_{\phi} (T - T_{ref}).$

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, $N = \frac{K_s}{\alpha - \phi_{ref}}$ , where ${K_s}$ is the grain bulk modulus, $T_{ref}$ is the reference temperature and $\beta_{\phi} = \beta_s ( \alpha - \phi_{ref} )$ , where ${\beta_s}$ is the solid matrix thermal expansion coefficient.

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:

XML Element: BiotPorosity

Name	Type	Default	Description
defaultGrainBulkModulus	real64	required	Grain bulk modulus
defaultPorosityTEC	real64	0	Default thermal expansion coefficient
defaultReferencePorosity	real64	required	Default value of the reference porosity
name	groupName	required	A name is required for any non-unique nodes
useUniaxialFixedStress	integer	0	Flag enabling uniaxial approximation in fixed stress update

Example

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