Porous Diffusion Constitutive Equation

Porous Diffusion Constitutive Equation = {model_name}

Description / Usage

This required card is used to specify the species diffusion model for the gas phase in a porous medium. Just now there is only one option, but plans are to expand the options to include multicomponent diffusion models (cf. Diffusion Constitutive Equation card). It is important to note that this model specification only applies to the gas phase of each component. Liquid phase species diffusive transport has not been implemented as of 12/19/01.

Definitions of the input parameters are as follows, with only a single permissible value:

DARCY_FICKIAN

Name of the model for the diffusion constitutive equation in the porous gas phase.

This model simply implies that gas species can be transported relative to the solid skeleton phase not only by a pressure gradient, as in Darcy’s law, but also by Fickian diffusion.

Examples

The following sample input card uses the APREPRO variable model_name (which is set to DARCY_FICKIAN.

Porous Diffusion Constitutive Equation = {model_name}

Technical Discussion

Currently, the DARCY_FICKIAN model is the only option for the porous diffusion equation and it only applies to one phase. When this card is parsed, it is contained in a solvent species loop. When we allow more than one volatile species, we will eventually allow for other diffusion constitutive equation models, e.g. of the Stefan-Maxwell type. Also, we will have to build a phase dependence into this card, as the diffusion law may be different in the liquid and in the gas. Right now, we do not allow for diffusion transport (viz. by a chemical potential or concentration gradient) in the liquid phase of a porous medium. Please consult references below for theoretical discussion.

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)