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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