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MINERAL_KINETICS

Specifies coefficients for kinetic mineral precipitation-dissolution reactions. The rate law is defined through transition state theory, as detailed in section Mineral Precipitation and Dissolution of the theory guide. The reaction rate \(I_m\) for the \(m\) th mineral is defined as

(1)\[I_m = -a_m\Big(\sum_l k_{ml}(T) {\mathcal P}_{ml}\Big) \Big|1-\big(K_m Q_m\big)^{\left(\frac{1}{\lambda_m\sigma_m}\right)}\Big|^{\beta_m} {\rm sign}(1-K_mQ_m),\]

where a positive value corresponds to precipitation and a negative value to dissolution, and where

\(a_m\) = mineral specific surface area [m\(^{-1}\)]

\({\mathcal P}_{ml}\) = prefactor (a sum of prefactor rates; if activation energy is provided the Arrhenius equation is applyied to each prefactor to calculate rates at different temperatures)

\(K_m\) = equilibrium constant

\(Q_m\) = ion activity product

\(\sigma_m\) = Temkin number (default is 1)

\(\lambda_m\) = mineral scaling factor (default is 1)

\(\beta_m\) = affinity power (default is 1)

\(k_{ml}\) = rate constant

Required Cards:

MINERAL_KINETICS

Opens the block.

<string>

Specifies mineral name.

RATE_CONSTANT <float> <optional units_string>

Kinetic rate constant. If negative, then raised to power 10 (e.g. -12.d0 is converted to \(10^{-12}\)) (default units [mol/m²-sec])

Optional Cards:

ACTIVATION_ENERGY <float>

If specified, used in the prefactor calculations for temperature dependent rates. (Arrhenius) [J/mol]

AFFINITY_THRESHOLD <float>

If specified, rate is only calculated if \(K_m Q_m \geq\) threshold and \({\rm sign}(1-K_mQ_m) < 0\) corresponding to precipitation.

AFFINITY_POWER <flaot>

\(\beta_m\) in Eqn. (1) above.

DISSOLUTION_RATE_CONSTANT <float> <optional units_string>

Kinetic rate constant for dissolution that requires a complementary precipitation rate constant. If negative, then raised to power 10 (e.g. -12.d0 is converted to \(10^{-12}\)) (default units [mol/m²-sec])

MINERAL_SCALE_FACTOR <flaot>

\(\lambda_m\) in equation above.

NUCLEATION_KINETICS <string>

Name of nucleation kinetics reaction to be applied to the mineral (specified elsewhere in the NUCLEATION_KINETICS block).

PRECIPITATION_RATE_CONSTANT <float> <optional units_string>

Kinetic rate constant for precipitation that requires a complementary dissolution rate constant. If negative, then raised to power 10 (e.g. -12.d0 is converted to \(10^{-12}\)) (default units [mol/m²-sec])

PREFACTOR

Parameters for reaction rate prefactors

RATE_LIMITER <float>

Limiting reaction rate factor (see Eqn. (27) in Theory Guide, Mode: Reactive Transport for details).

SPECIFIC_SURFACE_AREA <float>

The specific surface area of the reacting mineral. (default units [m²/g])

SURFACE_AREA_FUNCTION <string>

Specifies the function used to calculate the reacting surface area \(\left[\frac{m^2_\text{mnrl}}{m^3_\text{bulk}}\right]\) for a mineral. See Changes in Material Properties in the Theory Guide.

Options: CONSTANT, POROSITY_RATIO, VOLUME_FRACTION_RATIO, POROSITY_VOLUME_FRACTION_RATIO, MINERAL_MASS

MINERAL_MASS

\(a_m = \frac{\text{SSA}\cdot\text{FMW}}{\overline{V}_m}\porosity_m\)

POROSITY_RATIO

\(a_m = a_m^0 \left(\frac{\porosity}{\porosity_0}\right)^n\)

POROSITY_VOLUME_FRACTION_RATIO

\(a_m = a_m^0 \left(\frac{\porosity_m}{\porosity_m^0}\right)^n \left(\frac{1-\porosity}{1-\porosity_0}\right)^{n'}\)

VOLUME_FRACTION_RATIO

\(a_m = a_m^0 \left(\frac{\porosity_m}{\porosity_m^0}\right)^n\)

where

\(\porosity\) = porosity \(\left[\frac{\strlength^3_\strpore}{\strlength^3_\strbulk}\right]\)

\(\porosity_0\) = initial porosity \(\left[\frac{\strlength^3_\strpore}{\strlength^3_\strbulk}\right]\)

\(a_m\) = surface area \(\left[\frac{\strlength^2_\strmnrl}{\strlength^3_\strbulk}\right]\)

\(a_m^0\) = initial surface area \(\left[\frac{\strlength^2_\strmnrl}{\strlength^3_\strbulk}\right]\)

\(\porosity_m\) = volume fraction \(\left[\frac{\strlength^3_\strmnrl}{\strlength^3_\strbulk}\right]\)

\(\porosity_m^0\) = initialvolume fraction \(\left[\frac{\strlength^3_\strmnrl}{\strlength^3_\strbulk}\right]\)

\(\overline{V}_m\) = molar volume \(\left[\frac{\strlength^3_\strmnrl}{\strmole_\strmnrl}\right]\)

FMW = molecular weight \(\left[\frac{\strmass_\strmnrl}{\strmole_\strmnrl}\right]\)

SSA = specific surface area \(\left[\frac{\strlength^2_\strmnrl}{\strmass_\strmnrl}\right]\)

\(n\) = SURFACE_AREA_VOL_FRAC_POWER [-]

\(n'\) = SURFACE_AREA_POROSITY_POWER [-]

SURFACE_AREA_POROSITY_POWER <float>

Exponent in equation for transient mineral surface area calculated as a function of porosity, \(\porosity\):

SURFACE_AREA_VOL_FRAC_POWER <float>

Exponent in equation for transient mineral surface area calculated as a function of the mineral volume fraction \(\porosity_m\). Note that the volume fraction power can be applied only if \(\porosity_m^0 > 0\) corresponding to primary minerals.

TEMKIN_CONSTANT <flaot>

Sigma in Eqn. (1) above.

VOLUME_FRACTION_EPSILON <float>

Minimum volume fraction for a kinetic mineral.

Examples

CHEMISTRY
  ...
  MINERAL_KINETICS
    Calcite
      RATE_CONSTANT 1.d-13 mol/cm^2-sec
    /
  /
  ...
END

CHEMISTRY
  ...
  MINERAL_KINETICS
    Alunite
      RATE_CONSTANT 1.d-11 mol/cm^2-sec
    /
    Chrysocolla2
      SURFACE_AREA_FUNCTION VOLUME_FRACTION_RATIO
      SURFACE_AREA_VOL_FRAC_POWER 0.666666667d0
      PREFACTOR
        RATE_CONSTANT 1.d-10 mol/cm^2-sec
        PREFACTOR_SPECIES H+
          ALPHA 0.39
        /
      /
    /
    Goethite
      SURFACE_AREA_FUNCTION POROSITY_VOLUME_FRACTION_RATIO
      SURFACE_AREA_POROSITY_POWER 0.8d0
      SURFACE_AREA_VOL_FRAC_POWER 0.666666667d0
      RATE_CONSTANT 1.d-11 mol/cm^2-sec
    /
    Gypsum
      RATE_CONSTANT 1.d-10 mol/cm^2-sec
    /
    ...
  /
END

CHEMISTRY
  ...
  MINERAL_KINETICS
    Quartz
      RATE_CONSTANT 2.d-11 mol/m^2-sec
      NUCLEATION_KINETICS simplified
      SURFACE_AREA_FUNCTION MINERAL_MASS
      SPECIFIC_SURFACE_AREA 0.041 m^2/g
    /
  /
  NUCLEATION_KINETICS
    SIMPLIFIED simplified
      RATE_CONSTANT 1.d-5
      GAMMA 1.d10
    /
  /
END