Porous Vapor Pressure#

Porous Vapor Pressure = {model_name} {integer} {float_list} [M/L-t2]

Description / Usage#

Used to specify the model for the vapor pressure for each multiphase flow component in the porous medium that is activated for Media Type POROUS_UNSATURATED or POROUS_TWO_PHASE.

Definitions of the input parameters are as follows:

{model_name}	The permissible values for the model in this class are KELVIN and FLAT for a volatile liquid, and NON_VOLATILE for a non-volatile liquid.
{integer}	All models require an integer field after the model name which is the species_number; always set to zero until a multicomponent capability exists.
{float_list}	One or more floating point numbers (<float1> through <floatn>) whose values are determined by the selection for {model_name}.

Porous vapor pressure model choices and their parameters are presented below; consult the Technical Discussion for relevant details.

KELVIN <integer> <float1> <float2>… <float5>

For the KELVIN porous vapor pressure model, the {float_list} has a five values:

<float1> - p*v, vapor pressure on a flat interface

<float2> - ρl, the liquid density

<float3> - Mw , molecular weight of liquid

<float4> - R, the gas law constant

<float5> - T, the operating temperature

FLAT <integer> <float1> <float2>… <float5>

For the FLAT porous vapor pressure model, the {float_list} has a five values (same as KELVIN above):

<float1> - p*v, vapor pressure on a flat interface

<float2> - ρl, the liquid density

<float3> - Mw , molecular weight of liquid

<float4> - R, the gas law constant

<float5> - T, the operating temperature

The FLAT option requires the same parameters as the KELVIN model but leaves out the exponential function.

NON_VOLATILE <integer>

The NON_VOLATILE model requires no additional input.

Examples#

The sample input card:

Porous Vapor Pressure = FLAT 0 {Vap_Pres} {density} {30.} {Rgas} {T}

applies the FLAT model as described above to vapor-liquid equilibrium (assumed to be single component for now) using all APREPRO-defined parameters.

Technical Discussion#

The KELVIN option is used to include the effect of vapor-pressure lowering that results in equilibrium over high curvature menisci, i.e., small pores. The equation form of this is:

The FLAT option requires the same parameters but leaves out the exponential function. The constants are still needed so that the gas-phase concentration can be calculated with the ideal gas law. The functional form is

where S is the local saturation, and ρgv is the gas phase density of vapor. This model is ad-hoc but nonetheless leads to some interesting results. It basically says that as saturation increases, the gas-liquid menisci, and correspondingly the interfacial area available for evaporation, become more concentrated and hence the gas-phase vapor concentration increases.

The NON_VOLATILE option should be set if no gas-phase transport of vapor of the liquid phase component is desired, as if the liquid phase were non-volatile. Goma, with this choice, sets the gas phase concentration of liquid vapor to zero.

For nonvolatile pore liquids, the vapor pressure on a flat interface, viz. the first required floating point on this card, should be set to zero. As of 6/13/02 this card has only been implemented for pure liquid solvents, so that no equilibrium solvent partitioning across the interface is present.

FAQs#

Sometimes system aborts can happen with the Kelvin model because of real large, negative capillary pressures. In this case, the exponential term can exceed the machine limit. This can happen well into a transient run. The user should be aware of this; consult GT-009.3 for tips related to dealing with this problem.

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)