Porosity#
Porosity = {model_name} <float> []
Description / Usage#
This card is used to specify the model for the porosity, which is required for the Brinkman or Darcy formulations for flow through porous media, viz. for POROUS_BRINKMAN, POROUS_TWO_PHASE, POROUS_SATURATED, and POROUS_UNSATURATED media types (see Media Type card).
Definitions of the {model_name} and <float> parameters are as follows:
CONSTANT |
Name {model_name} of the constant porosity model.
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DEFORM |
Name {model_name} of the model for a porosity that varies with deformation of the porous medium. A conservation balance is required for the solid material skeleton and is invoked in the equation specification section (see EQ section).
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Examples#
The following is a sample input card:
Porosity = DEFORM 0.5
This model will result in a porosity of 0.5 (volume fraction of the interstitial space of a porous skeleton) in the undeformed or stress-free state, but will allow the porosity to vary affinely with the volume change invariant of the deformation gradient tensor (see technical discussion). As mentioned above, the DEFORM model requires a field equation for the mass-conservation of the solid matrix through the porous_deform equation.
Technical Discussion#
Porosity is a microstructural attribute of a porous medium which describes the fraction of volume not occupied by the solid skeleton. For rigid porous media, it is a parameter that weights the capacitance term (time-derivative term) of the Darcy flow equations for liquid solvent and gas “solvent” concentrations. It often affects the Saturation function (see Saturation card) and the permeability function (see Permeability card). The references cited below elucidate the role of the porosity parameter in these equations.
For deformable porous media, Goma uses the porosity as a measure of fraction solid concentration, as a part of a mass balance for the solid skeleton. The reason this equation is required is a result of the lack of an overall conservation law for the mixture. Instead, we close the system by individual conservation equations for all species components in the medium, including the solid; the liquid and gas phase components are accounted for with individual Darcy flow equations. The conservation law which governs the porosity assumes there is an affine deformation of the pores with the overall deformation of the solid, and hence can be written as:
where F˜ is the deformation gradient tensor, φ0 is the initial porosity, and φ is the porosity. This equation is invoked with the porous_deform option on the EQ specifications.
References#
GT-008.2: Porous Media Capabilities/Tutorial for GOMA. User Guidance for Saturated Porous Penetration Problems, August 11, 1999, P. R. Schunk
GT-009.3: GOMA’s capabilities for partially saturated flow in porous media, September 1, 2002, P. R. Schunk
SAND96-2149: Drying in Deformable Partially-Saturated Porous Media: Sol-Gel Coatings, Cairncross, R. A., P. R. Schunk, K. S. Chen, S. S. Prakash, J. Samuel, A. J. Hurd and C. Brinker (September 1996)