Description

The $DIFFUSION keyword specifies the diffusion model and the corresponding diffusion model value used for the diffusion coefficient.

Parameters

The parameter is defined in subsequent line below the keyword. The first parameter indicates a diffusion model type and the second parameter gives the diffusion coefficient value [m2s-1].

$DIFFUSION	keyword
int double	diffusion-model-type, diffusion coefficient value

Diffusion-model-type

• -1: No diffusion specified
• 0: User-defined function by #CURVE (Not implemented)
• 1: Constant diffusion coefficient (unit: m²s^-1)
• 10: Temperature dependence Yaws

Fick’s law in the porous media (effective diffusion coefficient):

\[ D^* = \omega \cdot D_d \]

where omega is a coefficient that is related to the tortuosity (Empirical coefficient, lab: 0.5~0.01)

Other Diffusion model types

2:  * Variabler Diffusionswert (Zeitabhaengig). Abhaegigkeit ueber Kurve*
3:  * Worch, 1993*
 m = k[0]
 Daq = 3.595e-7*T / eta / pow(m,0.53)*1.e-4
4:  * Hayduk und Laudie, 1974*
 V = k[0]
 Daq = 13.26e-5 / pow(eta, 1.14) / pow(V, 0.589) * 1.e-4
5:  * Wilke und Chang, 1955*
 Msol = k[0]
 Vs = k[0]
 Daq = 7.4e-8* T* sqrt(msol) / eta / pow(Vs, 0.6) * 1.e-4
6:  * Stokes-Einstein (Fuer Partikel/Makromolekuele)*
 Rm = k[0]
 Kb = 1.38066e-23    /* Boltzmann Konstante [J/K]
 Daq = Kb * T / 6. /PI / Rm / eta*1.e-4
7:  * FSG-Method, Lyman et al., 1990*
 M = k[0]
 V = k[1]
 Vg = 20.1           /* Molares Volumen von Luft [cm3/mol]
 // Dg = (0.001 * pow(T, 1.75) * sqrt(1. / mg + 1. / m)) / (p*pow(pow(Vg, 1. / 3.), 2.)) * 1.e-4
8: ((GEM_REACT))
    Archie’s law
{{{
#!latex
D_e = D_{aq} \cdot \epsilon^m
D_e ... effective   diffusion coefficient 
ε   ... transport porosity
m   ... empirical constant depending on the type of porous medium
}}}
Only coupling to Richards flow implemented so far
  
9: ((GEM_REACT)) 
 De (effective diffusion coefficient) is calculated independently from element porosity. We use node porosity values with Archie’s law and do a harmonic average of the node diffusion coefficient. As Dp is part of the diffusion tensor, we modify
Dp -> Dp=Dp0*poro^(m-1)*
10: Yaw’s empirical diffusion model 
 Transport properties of chemicals and hydrocarbons: viscosity, thermal conductivity, and diffusivity of Cl to Cl 00 organics and Ac to Zr inorganic/Carl L. Yaws.