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

defaultPorosityTEC

real64

0

Default thermal expansion coefficient

defaultReferencePorosity

real64

required

Default value of the reference porosity

grainBulkModulus

real64

required

Grain bulk modulus

name

groupName

required

A name is required for any non-unique nodes

Example

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