# Category 8: Porous Equations#

The following conditions are applied as boundary conditions to the porous-flow equations. These conditions include strong Dirichlet conditions, such as hard sets on porous phase pressure on a boundary as a constant or function of position, weak-form conditions, such as a specified phase flux from a convective mass transfer model or a constant flux, and a host of interfacial conditions for impregnation, etc. The porous flow equations are actually scalar equations that represent component mass balances. Specifically, there is one component mass balance for the liquid phase, one for the gas phase, and one for the solid phase. The corresponding three dependent variables in these balances are the liquid phase pressure, the gas phase pressure, and the porosity, respectively. These variables are related to the flow through a boundary by their normal gradients (Darcy’s law formulation) and to the local inventory of liquid and gas through the saturation function. These implicit terms can often lead to some confusion in setting the boundary conditions so it is recommended that the user consult the supplementary documentation referenced in the following porous boundary condition cards.

## POROUS_LIQ_PRESSURE#

BC = POROUS_LIQ_PRESSURE NS <bc_id> <float1> [float2]


### Description / Usage#

(DC/POR_LIQ_PRES)

This Dirichlet boundary condition is used to set the liquid phase pore pressure at a noden set. It can be applied to a node set on a boundary of a POROUS_SATURATED, POROUS_UNSATURATED or POROUS_TWO_PHASE medium type (see Media Type card).

 POROUS_LIQ_PRESSURE Boundary condition name (bc_name). NS Type of boundary condition (), where NS denotes node set in the EXODUS II database. The boundary flag identifier, an integer associated with that identifies the boundary location (node set in EXODUS II) in the problem domain. Value of liquid phase pressure. [float2] An optional parameter (that serves as a flag to the code for a Dirichlet boundary condition). If a value is present, and is not -1.0, the condition is applied as a residual equation. Otherwise, it is a “hard set” condition and is eliminated from the matrix. The residual method must be used when this Dirichlet boundary condition is used as a parameter in automatic continuation sequences.

### Examples#

The boundary condition card

BC = POROUS_LIQ_PRESSURE NS 101 {pcmin}


sets the porous liquid pressure at the boundary denoted by node set 101 to the value represented by the APREPRO variable {pcmin}.

### Technical Discussion#

Setting the porous liquid pressure to a value cannot be done independently of the saturation as the two are related through the vapor pressure curve for simulations in partially saturated media (see Saturation model card). Keep in mind that when using this card in these situations, you are setting also the saturation level based on the capillary pressure, defined as $$p_{gas}$$ - $$p_{liq}$$ = $$p_c$$ . The convention in Goma is that when the capillary pressure $$p_c$$ is greater than zero, the saturation level is less than unity, viz. the medium is partially saturated. When $$p_c$$ is less than zero, i.e., when the liquid phase pressure is greater than the gas phase pressure, then the medium is saturated (in this case the capillary pressure is poorly defined, though). Also, for Media Type options of POROUS_UNSATURATED, the ambient gas pressure is constant within the pore space and is set by the Porous Gas Constants card in the material file. This boundary condition, when setting the liquid phase pressure, must be used with consideration of these definitions.

For saturated media (viz. Media Type of POROUS_SATURATED), this discussion is not relevant. In this case, one must only consider the pressure level as it may effect the isotropic stress in poroelastic problems.