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:

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. $$K_{xxd}$$ = $$K_{yyd}$$ = $$K_{zzd}$$).
 * &bull; &bull; &bull;

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.
 * &bull; &bull; &bull;

First-order fluid exchange coefficient
Scope: .dprops
 * 1) val First-order fluid exchange rate, $${\alpha}_{wd}$$ in Equation 2.69.
 * &bull; &bull; &bull;

Interface k
<tt>Scope: .dprops</tt>
 * 1) val Interface hydraulic conductivity [L T−1], $$K_a$$ in Equation 2.69.
 * &bull; &bull; &bull;

Convert pm k to macropore k
<tt>Scope: .dprops</tt>
 * 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.
 * &bull; &bull; &bull;