Modified van Genuchten model
Dear Stefan,
Regarding the paper by Luckner et al. 1989 there is a relationship between pressure head h and water content θ. In the modified van Genuchten model there is more or less the same equation replacing pressure head by capillary pressure. Can you explain me, please, why in general the capillary pressure should be the same as the pressure head? I can't find any proof of this thesis.
I'm asking that because I want to plot θ(h) and K(θ) to see whether there is a difference between analytical calculation and modelling.
3 replies
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Sebastian,
You can express any pressure as the pressure that is exerted by a column of water of a certain height, which is referred to as the pressure head. So it's simply a different unit of measurement. If you deal with water of constant density, the height to which water is sucked up above the water table in a capillary tube is the capillary pressure head. (Now think about two-phase flow, e.g., a fluid of a different density, such as oil, which rises to a different level (factor in the density ratio to water); it is then sometimes referred to as the "equivalent water head". This becomes confusing, which is the reason why we deal with pressures (rather than heads) in TOUGH2.
The real question is whether capillary pressure is a pressure at all (i.e., the driving force for viscous flow), or something else (i.e., a chemical potential). But this discussion is for another day!
Stefan
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Dear Stefan,
I'm still not satisfied. Do you set pressure head equal to capillary pressure, is it proportional to each other or is there an approximation (if so which assumptions were made) ? I understand that you can explain it in special cases (in a microscopic view) but the capillary pressure head is not constant like the pressure head (in a macroscopic view).
Sebastian
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Sebastian,
Just multiply the capillary pressure head (as defined in Luckner et al.) by water density and gravitational acceleration to get the capillary pressure in units of Pascals as defined in TOUGH2 and other multiphase flow simulators. The assumptions are those made in a formulation that is based on heads.
Stefan