# Total Density of Solvents in Porous Media#

Total density of solvents in porous media = {yes | no}


## Description / Usage#

This post processing option can be used to trigger the computation and output of the total density of solvents as a nodal field variable to the output EXODUS II file. Three nodal variables are written, Rho_Total_Liq, Rho_Total_air and Rho_Total_solid. The mathematical details are given below in the technical discussion. This option applies to media types of POROUS_SATURATED, POROUS_UNSATURATED, and POROUS_TWO_PHASE (see Media Type card). The options are:

 yes Calculate and write the total solvent densities as a postprocessing variable to the output EXODUSII file. no Do not calculate the total solvent densities.

## Examples#

Total density of solvents in porous media = yes


This card will result in the calculation and output of the mixture density of solvent (viz., phase mixture of liquid solvent in vapor form, liquid form, and the form adsorbed in the solid skeleton for partially saturated porous flows). The form of that mixture density is given in the technical discussion.

## Technical Discussion#

In saturated flow cases, viz. for Media Type selection POROUS_SATURATED, the total solvent density is

where $$\rho_1$$ is the pure liquid density and $$\phi$$ is the porosity. Here we have assumed that no liquid solvent is adsorbed into the solid struts (currently the assumption used throughout Goma).

For partially saturated flows, viz. for Media Type selection POROUS_UNSATURATED or POROUS_TWO_PHASE, the total density is given by

where $$\rho_{gv}$$ is the density of solvent vapor in the total gas-solvent vapor mixture (see Density of solvents in gas phase in porous media card), S is the saturation (see Porous Saturation card), and $$\chi_{ls}$$ is the volume fraction of solvent in liquid phase (including any condensed species component). When calculating the total density of the liquid (Rho_Total_liq), the liquid vapor density comes from a Kelvin vapor-liquid equilibrium relation. The total density of the gas phase (Rho_Total_gas) will use a vapor density fro air and a volume fraction of zero (0) since air is insoluble. The total density of the solid in the gas (Rho_Total_solid) is zero (0).

## References#

GT-009.3: GOMA’s Capabilities for Partially Saturated Flow in Porous Media, September 1, 2002, P. R. Schunk