# HydroGeoSphere/Dual Continuum (Variably-Saturated)

Dual continua 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 functional relationships

If you wish to use Van Genuchten or Brooks-Corey functions to describe the constitutive relationships you can do so using the instructions given in Section 5.8.3.4. Unless you modify them, the default values given in Table 5.16 will be used to define the functional relationships:

Table 5.16: Default Values for Functions Defining the Dual Continua Constitutive Relationships, for the Van Genuchten and Brooks-Corey models
Parameter Value Unit
Residual water saturation, ${\displaystyle S_{wr}}$  0.053 -
Power index (alpha), ${\displaystyle {\alpha }}$  3.5237 m−1
Power index (beta), ${\displaystyle {\beta }}$  3.1768 -
Power index (gamma, computed), ${\displaystyle {\gamma }}$  1 - 1/${\displaystyle {\beta }}$  -
Pore-connectivity, ${\displaystyle l_{p}}$  0.5 -
Brooks-Corey exponent 2/${\displaystyle {\beta }}$  + ${\displaystyle l_{p}}$  + 2 -

## Default tabular relationships

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 5.17 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

## Relative permeability xy

Scope: .grok .dprops

When using functions or tables to define the constitutive relationships, this instruction causes HydroGeoSphere 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 dual continua, as discussed in Section 5.8.1.

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## Defining the interface between continua

When simulating a system with porous and dual continua, the constitutive relationships of the interface between the two continua must also be defined. The following instructions allow you to do this:

Interface unsaturated tables
Interface unsaturated van genuchten functions
Interface unsaturated brooks-corey functions
Interface relative permeability xy

Input is identical to the generic forms of the commands discussed in the following sections, except that the scope is restricted to .dprops.

We will now discuss instructions of a general nature which can be used to modify the default constitutive relationships for the various media, beginning with the functional relationships.