# HydroGeoSphere/Porous Medium

## Default porous media transport values

By default, all porous media zones (and elements) in the domain will be assigned default porous media transport properties which are listed in Table 5.21. Included here are parameters for modifying the porous medium so that it acts as a double-porosity medium for simulating transport, as described in Section 2.6.1.3 and also for isotopic fractionation, as described in Section 2.6.1.4.

Table 5.21: Default Values for Porous Media Transport Properties
Parameter Value Unit
Longitudinal dispersivity ${\displaystyle {\alpha }_{l}}$  1.0 m
Horizontal component of transverse dispersivity ${\displaystyle {\alpha }_{t}}$  0.1 m
Vertical component of transverse dispersivity ${\displaystyle {\alpha }_{t}}$  0.1 m
Bulk density ${\displaystyle {\rho }}$  2031.25 kg m−3
Tortuosity ${\displaystyle {\tau }}$  0.1 -
Immobile zone porosity ${\displaystyle {\theta }_{Imm}}$  0.0 -
Immobile zone mass transfer coefficient ${\displaystyle {\alpha }}$  0.0 s−1
Reverse fractionation rate ${\displaystyle k_{r}}$  0.0 s−1
Fractionation factor ${\displaystyle {\alpha }_{r}}$  0.0 -
Mass ratio, solid to water phases ${\displaystyle x_{r}}$  0.0 -
Thermal conductivity of the solids ${\displaystyle k_{s}}$  3.0 W m−1 K−1
Specific heat capacity of the solids ${\displaystyle c_{s}}$  738.0 J kg−1 K−1
Density of the solids ${\displaystyle {\rho }_{s}}$  2650.0 kg m−3

The following instructions can be applied to porous media, as discussed in Section 5.8.1, to modify the default transport parameters. For each instruction we will indicate its scope (i.e. .grok, .mprops). Recall that if an instruction is used in the prefix.grok file, it will affect the current set of chosen zones, while in a properties (e.g. .mprops) file, it will only affect the named material of which it is a part.

## Longitudinal dispersivity

Scope: .grok .mprops

1. val Longitudinal dispersivity [L], ${\displaystyle {\alpha }_{l}}$  in Equation 2.97.
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## Transverse dispersivity

Scope: .grok .mprops

1. val Horizontal component of the transverse dispersivity [L], ${\displaystyle {\alpha }_{t}}$  in Equation 2.97.
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## Vertical transverse dispersivity

Scope: .grok .mprops

1. val Vertical component of the transverse dispersivity [L], ${\displaystyle {\alpha }_{t}}$  in Equation 2.97.
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## Tortuosity

Scope: .grok .mprops

1. val Tortuosity , ${\displaystyle {\tau }}$  in Equation 2.97.
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## Anisotropic tortuosity ratio

Scope: .grok .mprops

1. y_tortratio Tortuosity ratio in the y-direction. Default value is 1.
2. z_tortratio Tortuosity ratio in the z-direction. Default value is 1.

By default, tortuosity is isotropic, since the ratio values are set to 1 in both the y- and z-directions. You may make tortuosity anisotropic by entering a value greater than 0 and less than 1. These values will be used to multiple the tortuosity, ${\displaystyle {\tau }}$  in the y- and z-directions respectively, to obtain the directional values.

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## Bulk density

Scope: .grok .mprops

1. val Bulk density [M L−3], ${\displaystyle {\rho }_{b}}$  in Equation 2.96. If this instruction is used, the value of the density of solids previously saved for this material is overwritten by the density of solids computed from the bulk density, the density of water and the porosity ${\displaystyle [{\rho }_{s}=({\rho }_{b}-{\theta }_{s}{\rho })/(1-{\theta }_{s})]}$ .
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By default, the porous medium acts a single-porosity medium (i.e. the immobile zone is inactive) because the porosity and mass transfer coefficient are set to zero. In order to activate the double-porosity feature, you can enter non-zero values for these parameters using the following two instructions:

## Immobile zone porosity

Scope: .grok .mprops

1. val Immobile zone porosity, ${\displaystyle {\theta }_{Imm}}$  in Equations 2.101, 2.135 and 2.136.
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## Immobile zone mass transfer coefficient

Scope: .grok .mprops

1. val Immobile zone mass transfer coefficient [T−1], ${\displaystyle {\alpha }_{Imm}}$  in Equation 2.134.
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## Isotope fractionation data...End

Scope: .mprops

Causes grok to begin reading a group of isotope fractionation instructions until it encounters an End instruction.

If no further instructions are issued, the default isotopic fractionation parameter values listed in Table 5.21 will be used.

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The following three instructions can be used to change these values:

## Reverse rate

Scope: .mprops

1. val Reverse fractionation rate [L−1], ${\displaystyle k_{r}}$  in Equation 2.143.
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## Fractionation factor

Scope: .mprops

1. val Fractionation factor, ${\displaystyle {\alpha }_{r}}$  in Equation 2.143.
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## Rock-water mass ratio

Scope: .mprops

1. val Isotopic rock-water mass ratio, ${\displaystyle x_{r}}$  in Equation 2.102.
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The next four instructions can be used to change the thermal properties of the porous medium:

## Thermal conductivity of solid

Scope: .grok .mprops

1. val Temperature invariant thermal conductivity of the solids [W L−1 K−1]. The bulk thermal conductivity is computed internally from the volume fractions of the solid and liquid phases.
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## Temperature-dependent thermal conductivity of solid

Scope: .grok .mprops

1. k_s1 Thermal conductivity [W L−1 K−1] at temperature ${\displaystyle t_{s1}}$ .
2. t_s1 Temperature [°C] at which the thermal conductivity is equal to ${\displaystyle k_{s1}}$ .

If that instruction is specified, the thermal conductivity of the solid phase is temperature-dependent. The bulk thermal conductivity is also temperature-dependent and is computed internally from the volume fractions of the solid and liquid phases. It is assumed here that the thermal conductivity of the solids decreases at a constant rate of 1% per 10°C increase in temperature and the relationship between thermal conductivity and temperature is defined with the pair of values ${\displaystyle (k_{s1},t_{s1})}$ .

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## Specific heat capacity of solid

Scope: .grok .mprops

1. val Specific heat capacity of the solid phase [J kg−1 K−1]. The default value is 730.0 J kg−1 K−1.
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Note that the density of the solid phase of the porous medium is now computed automatically from the bulk density and porosity.