# HydroGeoSphere/Porous Medium (Variably-Saturated)

By default, all porous media zones (and elements) in the domain will use a constitutive relationship based on the pseudo-soil relation, as developed by Huyakorn et al. [1994]. Essentially, in the pseudo-soil relationship, the medium is assigned a nodal saturation of 1 above the water table and 0 (zero) below it. Relative permeability is applied to horizontal flow only and water travels vertically under saturated hydraulic conductivity conditions.

## Default constitutive relationship values

If you wish to use Van Genuchten or Brooks-Corey functions to describe the constitutive relationship you can do so using the instructions given in Section 5.8.3.4. Unless you modify them, the default values given in Table 5.11 will be used to define the functional relationships:

Table 5.11: Default Values for Functions Defining the Porous Media Constitutive Relationships, for the Van Genuchten and Brooks-Corey models
Parameter Value Unit
Common: - -
Residual water saturation, ${\displaystyle S_{wr}}$  0.053 -
Pore-connectivity, ${\displaystyle l_{p}}$  0.5 -
Beta (power index), ${\displaystyle {\beta }}$  3.1768 -
Van Genuchten: - -
Alpha (power index), ${\displaystyle {\alpha }}$  3.5237 m−1
Gamma (power index, computed), ${\displaystyle {\gamma }}$  1 - 1/${\displaystyle {\beta }}$  -
Brooks-Corey: - -
Exponent (computed) 2/${\displaystyle {\beta }}$  + ${\displaystyle l_{p}}$  + 2 -
Air entry pressure, ${\displaystyle {\psi }_{ae}}$  -0.16 m
Alpha (power index, computed), ${\displaystyle {\alpha }}$  -1/${\displaystyle {\psi }_{ae}}$  m−1
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## Default pressure-saturation and saturation-permeability

If you wish to use tables to describe the constitutive relationships you can do so using the instructions given in Section 5.8.3.5. Unless you modify them, the default values of water saturation versus pressure head and saturation versus relative permeability listed in Table 5.12 will be used to define the tabular relationships:

 Pressure(m) ${\displaystyle {\psi }}$ Saturation ${\displaystyle S_{w}}$ -10.0 0.053 0.0 1.0 Saturation ${\displaystyle S_{w}}$ Relative permeability ${\displaystyle k_{rw}}$ 0.053 0.053 1.0 1.0
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## Relative permeability xy

Scope: .grok .mprops

When using functions or tables to define the constitutive relationships, this instruction causes grok to apply the relative permeability to horizontal flow only so that water travels vertically under saturated hydraulic conductivity conditions, similar to the behaviour of the pseudo-soil relation. This instruction should be applied to porous media, as discussed in Section 5.8.1.

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