# 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: - -
${\displaystyle K_{xx}}$  7.438 × 10−5 m s−1
${\displaystyle K_{yy}}$  7.438 × 10−5 m s−1
${\displaystyle K_{zz}}$  7.438 × 10−5 m s−1
Specific storage ${\displaystyle S_{sd}}$  1.0 × 10−4 m−1
Porosity 0.375 -
Volume fraction of porous medium ${\displaystyle w_{d}}$  0.01 -
Unsaturated flow relation type Pseudo-soil -

Note that the default state of the hydraulic conductivity tensor (${\displaystyle K_{d}}$  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. ${\displaystyle K_{xxd}}$  = ${\displaystyle K_{yyd}}$  = ${\displaystyle K_{zzd}}$ ).

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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], ${\displaystyle S_{sd}}$ , but defined in a similar way to ${\displaystyle S-s}$  in Equation 2.10.
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## Porosity

Scope: .grok .dprops

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

Scope: .dprops

1. val Volume fraction [L3 L−3], ${\displaystyle w_{d}}$  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, ${\displaystyle {\alpha }_{wd}}$  in Equation 2.69.
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## Interface k

Scope: .dprops

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

Scope: .dprops

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

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

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

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

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

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

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

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