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MATERIAL_TRANSFORM_GENERAL

The Material Transform Process Model is documented here.

This option specifies the material transform process model, which is a child of flow and a peer of transport. Under the SIMULATION block, the process model is included by adding the MATERIAL_TRANSFORM block:

SIMULATION
  SIMULATION_TYPE SUBSURFACE
  PROCESS_MODELS
    SUBSURFACE_FLOW flow
      MODE GENERAL
    /
    SUBSURFACE_TRANSPORT transport
      MODE GIRT
    /
    MATERIAL_TRANSFORM <name_string>
    /
  /
END

where <name_string> is a user-defined name for the process model. There are currently no additional options for this block. Functionality is currently available for problems utilizing flow modes (such as GENERAL, TH, and RICHARDS) and/or reactive transport with UFD_DECAY.

The details of the process model are included in the MATERIAL_TRANSFORM_GENERAL block, which lists several MATERIAL_TRANSFORM objects that can be associated with a MATERIAL_PROPERTY.

Supported models that can be included in a MATERIAL_TRANSFORM object include the following:

ILLITIZATION

The illitization function allows for a time- and temperature-dependent change from smectite to illite to be evaluated during the simulation, which in turn can be used to impart a commensurate change in permeability and/or sorption.

Required Blocks and Cards

ILLITIZATION_FUNCTION <string>

Opens an illitization block, where <string> indicates the type of illitization model to be employed.

Supported ILLITIZATION_FUNCTIONs (along with their required cards):

  • DEFAULT (HUANG)

    • SMECTITE_INITIAL

    • THRESHOLD_TEMPERATURE

    • SHIFT_PERM

    • SHIFT_KD

    • EA

    • FREQ

    • K_CONC

  • GENERAL (CUADROS_AND_LINARES)

    • SMECTITE_INITIAL

    • SMECTITE_EXPONENT

    • THRESHOLD_TEMPERATURE

    • SHIFT_PERM

    • SHIFT_KD

    • EA

    • FREQ

    • K_CONC

    • K_EXP

Illitization Parameter Definitions

In the DEFAULT model (ref. 1), for a given time step \(i+1\), the time rate of change of smectite \(\left(\frac{df_{S}}{dt}\right)\) into illite is based on the smectite fraction \(f_{S,i}\) and potassium cation concentration \([K^{+}]\). It is defined as follows:

\(\left.-\frac{df_{S}}{dt}\right|^{i+1}=\left\{{\begin{array}{cc} [K^{+}]\cdot (f_{S}^{i})^{2}\cdot A\exp{\left(-\frac{E_{a}}{\mathcal{R}T^{i+1}}\right)} & T^{i+1}\geq T_{th} \\ 0 & T^{i+1}<T_{th} \\ \end{array} } \right.\) [1/s]

where \(A\) is the frequency term, \(E_{a}\) is the activation energy, \(\mathcal{R}\) is the ideal gas constant, \(T^{i+1}\) is the temperature in Kelvin, and \(T_{th}\) is the threshold temperature. The value of \([K^{+}]\) is currently implemented as a constant.

The time-integrated smectite fraction is evaluated as:

\(f_{S}^{i+1} = \frac{f_{S}^{i}}{1-[K^{+}]\cdot A\exp{\left(-\frac{E_{a}}{\mathcal{R}T^{i+1}}\right)}\cdot (t^{i+1}-t^{i})\cdot f_{S}^{i}}\)

The illite fraction is defined as the complement of the smectite fraction:

\(f_{I}^{i+1} = 1 - f_{S}^{i+1}\)

A scale factor \(F\) is defined that ranges from 0 to 1 and is based on the relative change in the fraction of illite:

\(F^{i+1}= \frac{f_{I}^{i+1}-f_{I}^{0}}{f_{S}^{0}}\)

This is used to modify the permeability and/or soprtion based on a user-specified function (see SHIFT_PERM and SHIFT_KD below).

In the GENERAL model (ref. 2), the time rate of change of smectite is defined with the potassium concentration raised to exponent \(m\) and the smectite fraction raised to exponent \(n\), where the temperature-dependent Arrhenius term is simplified as \(k(T)\):

\(\left.-\frac{df_{S}}{dt}\right|^{i+1}=\left\{{\begin{array}{cc} [K^{+}]^{m}\cdot (f_{S}^{i})^{n}\cdot k(T) & T^{i+1}\geq T_{th} \\ 0 & T^{i+1}<T_{th} \\ \end{array} } \right.\) [1/s]

The frequency term \(A\) in \(k(T)\) must be defined in units that correspond to the choice of \(m\) and \(n\). The time-integrated smectite fraction is evaluated based on the choice of \(n\):

\(f_{S}^{i+1}=\left\{{\begin{array}{cc} \left\{[K^{+}]^{m}\cdot k(T)\cdot (n-1)(t^{i+1}-t^{i})+(f_{S}^{i})^{1-n}) \right\}^{\frac{1}{1-n}} & n>1 \\ f_{S}^{i}\cdot \exp{\left\{-k(T)\cdot[K^{+}]^{m}\cdot(t^{i+1}-t^{i})\right\}} & n=1 \\ \end{array} } \right.\)

SMECTITE_INITIAL <float>

The initial fraction of smectite in the material relative to illite, \(f_{S}^{0}\) (default of 1.0).

SMECTITE_EXP <float>

The exponent of the smectite fraction, \(n\).

THRESHOLD_TEMPERATURE <float>

The temperature in Celsius at and above which the illitization process occurs, \(T_{th}\) (default of 0°C).

SHIFT_PERM <string> <float> (optional)

Factors are provided to modify the original permeability tensor \(k_{j}^{0}\) based on changes to the smectite/illite composition. This entry consists of the function type <string> and the functional parameters \(C_{k}\) <float> (see below). Simulations utilizing this feature must have an active flow mode.

DEFAULT/LINEAR - \(C_{k,1}\)

\(C_{k,1}\) is the factor applied to the relative change in the illite fraction \((F)\) that is used to isotropically modify the original permeability. The change in a given permeability component \(k_{j}^{i+1}\) at time step \(i+1\) as a result of illitization is computed as:

\(k_{j}^{i+1}=k_{j}^{0}\left(1+C_{k,1}\cdot F^{i+1} \right)\)

This suggests that when all of the original smectite is transformed to illite, the permeability has been enhanced by a factor of \(1+ C_{k,1}\).

QUADRATIC - \(C_{k,1}, C_{k,2}\)

\(k_{j}^{i+1} = k_{j}^{0}\left[1 + C_{k,1}\cdot F^{i+1} + C_{k,2}\cdot (F^{i+1})^{2}\right]\)

POWER - \(C_{k,1}, C_{k,2}\)

\(k_{j}^{i+1} = k_{j}^{0}\left[1 + C_{k,1}\cdot(F^{i+1})^{C_{k,2}}\right]\)

EXPONENTIAL - \(C_{k,1}\)

\(k_{j}^{i+1} = k_{j}^{0}\exp{\left(C_{k,1}\cdot F^{i+1}\right)}\)

SHIFT_KD (optional)

For specified elements, factors are provided to modify original sorption distribution coefficients, \(K_{d}^{0}\), based on changes to the smectite/illite composition. In this sub-block, one list entry consists of the element \(e\) <string>, the function type <string>, and the functional parameters \(C\) <float> (see below). Simulations utilizing this feature must have an active transport mode and elements listed must be present in the UFD_DECAY process model.

DEFAULT/LINEAR - \(C_{1}\)

\(K_{d,e}^{i+1} = K_{d,e}^{0}\left(1 + C_{1,e}\cdot F^{i+1}\right)\)

QUADRATIC - \(C_{1}, C_{2}\)

\(K_{d,e}^{i+1} = K_{d,e}^{0}\left[1 + C_{1,e}\cdot F^{i+1} + C_{2,e}\cdot (F^{i+1})^{2}\right]\)

POWER - \(C_{1}, C_{2}\)

\(K_{d,e}^{i+1} = K_{d,e}^{0}\left[1 + C_{1,e}\cdot(F^{i+1})^{C_{2,e}}\right]\)

EXPONENTIAL - \(C_{1}\)

\(K_{d,e}^{i+1} = K_{d,e}^{0}\exp{\left(C_{1,e}\cdot F^{i+1}\right)}\)

EA <float>

The activation energy in the temperature-dependent Arrhenius term, \(E_{a}\) [J/mol].

FREQ <float>

The frequency term, or coefficient used to scale the temperature-dependent Arrhenius term, \(A\) [L/mol-s].

K_CONC <float>

The initial concentration of potassium cation in the material, \([K^{+}]\) [M].

K_EXP <float>

The exponent of the potassium cation concentration, \(m\).

Optional Blocks and Cards

Test Illitization Model

TEST
Including this keyword will produce output (.dat file) for an illitization model that includes:

  1. initial smectite fraction \((f_{S}^{0})\),

  2. temperature \((T)\),

  3. time \((t)\),

  4. illite fraction \((f_{I})\),

  5. \(\frac{df_{I}}{dT}\),

  6. scale factor \((F)\)

Examples

Material with transform named “mtf_bentonite” containing illitization model

 #================================= subsurface ================================

 ...

 MATERIAL_PROPERTY buffer
   ID 1
   POROSITY 3.5d-1
   TORTUOSITY_FUNCTION_OF_POROSITY 1.4d+0
   SOIL_COMPRESSIBILITY 1.6d-8
   SOIL_COMPRESSIBILITY_FUNCTION LEIJNSE
   SOIL_REFERENCE_PRESSURE 1.01325d+5
   ROCK_DENSITY  2.7d+3
   HEAT_CAPACITY 8.3d+2
   CHARACTERISTIC_CURVES cc_bentonite
   THERMAL_CHARACTERISTIC_CURVES cct_bentonite
   MATERIAL_TRANSFORM mtf_bentonite
   PERMEABILITY
     PERM_ISO  1.0d-20
   /
 /

...

#=========================== pm material transform ============================

MATERIAL_TRANSFORM_GENERAL

  MATERIAL_TRANSFORM mtf_bentonite
    ILLITIZATION
      ILLITIZATION_FUNCTION DEFAULT
        THRESHOLD_TEMPERATURE 2.50000d+1 C
        EA                    1.17152d+5 J/mol
        FREQ                  8.08000d+4 L/mol-s
        K_CONC                2.16000d-3 M
        SMECTITE_INITIAL      0.95000d+0
        SHIFT_PERM   DEFAULT  9.90000d+2
        SHIFT_KD
          Sr  QUADRATIC   -2.50000d-1 -2.50000d-1 # Sr must be listed in UFD Decay
          Tc  EXPONENTIAL -6.94000d-1             # Tc must be listed in UFD Decay
          Cs  LINEAR      -5.00000d-1             # Cs must be listed in UFD Decay
          Np  POWER       -5.00000d-1  5.00000d-1 # Np must be listed in UFD Decay
        /
      END
      TEST
    END
  END

END # MATERIAL_TRANSFORM_GENERAL

References

  1. Huang, W.-L., J. M. Longo, and D. R. Pevear (1993). An experimentally derived kinetic model for smectite-to-illite conversion and its use as a geothermometer. Clays and Clay Minerals 41(2), 162-177. https://doi.org/10.1346/CCMN.1993.0410205

  2. Cuadros, J., and Linares, J. (1996). Experimental kinetic study of the smectite-to-illite transformation. Geochimica et Cosmochimica Acta 60(3), 439-453. https://doi.org/10.1016/0016-7037(95)00407-6