# HydroGeoSphere/Dual Continuum (Saturated)

## Default Dual-Continuum Saturated Flow Properties

Unless you modify the default values, all dual-continuum zones (and elements) in the domain will be assigned the default properties which are listed in Table 5.7. These values are representative of a sand:

Table 5.7: Default Values for Dual-continuum Saturated Flow Properties
Parameter Value Unit
Name Default Sand -
Hydraulic conductivity terms: - -
$K_{xx}$  7.438 × 10−5 m s−1
$K_{yy}$  7.438 × 10−5 m s−1
$K_{zz}$  7.438 × 10−5 m s−1
Specific storage $S_{sd}$  1.0 × 10−4 m−1
Porosity 0.375 -
Volume fraction of porous medium $w_{d}$  0.01 -
Unsaturated flow relation type Pseudo-soil -

Note that the default state of the hydraulic conductivity tensor ($K_{d}$  in Equation 2.17) is that it is isotropic. It should also be noted that for dual continua, off-diagonal terms are not considered.

You can use the general methods and instructions outlined in Section 5.8.1 to modify the default distribution of saturated dual-continuum properties.

As was the case for the instructions which modify porous medium properties, the following instructions also have a scope of operation, the only difference being that they would appear in the .dprops file instead of the .mprops file.

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## K isotropic

Scope: .grok .dprops

1. kval Hydraulic conductivity [L T−1].

Assign an isotropic hydraulic conductivity (i.e. $K_{xxd}$  = $K_{yyd}$  = $K_{zzd}$ ).

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## K anisotropic

Scope: .grok .dprops

1. kvalx, kvaly, kvalz Hydraulic conductivities [L T−1] in the x-, y- and z-directions respectively.

Assigns anisotropic hydraulic conductivities.

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## Specific storage

Scope: .grok .dprops

1. val Specific storage [L−1], $S_{sd}$ , but defined in a similar way to $S-s$  in Equation 2.10.
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## Porosity

Scope: .grok .dprops

1. val Porosity [L3 L−3], $theta_{sd}$  in Equation 2.16.
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## Volume fraction dual medium

Scope: .dprops

1. val Volume fraction [L3 L−3], $w_{d}$  in Equation 2.16.

The volume fractions of the dual medium and porous medium always add up to 1.0.

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## First-order fluid exchange coefficient

Scope: .dprops

1. val First-order fluid exchange rate, ${\alpha }_{wd}$  in Equation 2.69.
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## Interface k

Scope: .dprops

1. val Interface hydraulic conductivity [L T−1], $K_{a}$  in Equation 2.69.
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## Convert pm k to macropore k

Scope: .dprops

1. val Porous medium background hydraulic conductivity $K_{bkgrd}[L/T]$ .

We can express the bulk hydraulic conductivity of a dual-continuum $K_{bulk}$  as the sum of the porous media $K_{bkgrd}$  and fracture $K_{d}$  components:

$K_{bulk}=K_{bkgrd}(1-w_{d})+K_{d}w_{d}$                          (Equation 5.11)

where $w_{d}$  is the volume fraction [L3 L−3] in Equation 2.16.

If we assume that the observed (porous medium) hydraulic conductivity is equal to $K_{bulk}$ , and supply an educated guess for $K_{bkgrd}$ , we can rearrange the equation and calculate $K_{d}$  as:

$K_{d}=[K_{bulk}-K_{bkgrd}(1-w_{d})]/w_{d}$                          (Equation 5.12)

For all elements in the currently chosen dual zones, the porous medium hydraulic conductivity is replaced by $K_{bkgrd}$  and the fracture hydraulic conductivity $K_{d}$  is set equal to the calculated value.

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