Atmospheric Boundary Conditions
I am confused with the boundary conditions that have to be imposed in an atmospheric boundary element for simulating evaporation with TOUGH2 (or TOUGHREACT). In a few slides (http://esd1.lbl.gov/files/research/projects/tough/support/initial-boundary-conditions.pdf), Stefan Finsterle proposed to select capillary function so that capillary pressure is zero for the material properties of the atmospheric element. But for evaporation, he wrote that capillary pressure according to Kelvin's equation in atmospheric element have to be assign.
I understand the value of zero for capillary pressure in the atmospheric element (not a porous media), but why assign capillary pressure and how (RH, saturation) ?
Any ideas ?
There are several ways to simulate evaporation. The most mechanistic approach is to define an air-mass fraction in the atmosphere that corresponds to the relative humidity value, and then actually simulate vapor diffusion from the land surface through the laminar boundary layer (the thickness of which depends on surface roughness and wind velocity etc.) to the well-mixed atmosphere.
Recognizing that both relative humidity and capillary pressure reflect a "water potential" (note that the relation between capillary pressure and relative humidity through Kelvin's equation is the measurement principle of a psychrometer), you may also approximate evaporation by imposing a (very strong!) capillary suction in the atmospheric block. There are quite a few subtle differences between the two approaches that cannot be explained in this post.
I highly recommend any paper written by Dani Or on the topic of evaporation. Regarding the implementation in TOUGH2, see the following two references (I also attach the papers themselves):
(1) Ghezzehei, T. A., R. C. Trautz, S. Finsterle, P. J. Cook, and C. F. Ahlers, Modeling coupled evaporation and seepage in ventilated tunnels, Vadose Zone J., 3: 806–818, 2004.
(2) Finsterle, S., and K. Pruess, Solving the estimation-identification problem in two-phase flow modeling, Water Resour. Res., 31 (4), 913–924, 1995.
I also attach a TOUGH2-EOS4 input file that simulates the ventilation experiment described in the second reference.
Hope this helps,
Thanks for your answer.
If I understand the papers you sent, one way of simulating evaporation is to impose an equivalent capillary suction according to Kelvin's law. The main advantage of such a solution is the direct relation between relative humidity in the air and the capillary pressure at the surface of the porous media, without any parameter. The main drawback is the overestimation of the suction. Is it true ?
In TOUGH2 (EOS4), this way of doing consist in defining an atmospheric boundary element that have several properties (see your example kelvin.inp), namely:
- large volume and small layer thickness;
- same material properties than the matrix except for porosity -> But why keeping the same properties ?
- all phases are perfectly mobile -> I don't understand why you can assume that liquid permeability is different from zero
- capillary pressure is constant in the element and equal to an equivalent capillary suction according to Kelvin's law (from capillary pressure function)
Another thing that I don't understand well in the file "kelvin.inp":
- in the INCON, the second value for the atmospheric boundary element is up to 13 while for the other elements the values is less than one -> Is this value of 13 overwritten by capillary pressure imposed in the capillary pressure function ?
- To what functions correspond the values of 11 for the relative permeability and capillary pressure for the MATRI rock ?
For the other method that consists in calculating a thickness for a laminar boundary layer, I will ask questions later, if I can.
(1) The suction is NOT overestimated - low relative humidity indeed constitutes a strong water potential, energy that is used to evaporate water and draw it to the surface.
(2) You want to make sure matrix properties are used between the atmosphere and subsurface (think upstream weighting!)
(3) The liquid relative permeability does not matter, as liquid saturation in the atmosphere is (and remains) zero at all times (feel free to choose any other function).
(4) You can make the relative humidity / capillary suction time dependent, if needed. This is not a limitation.
(5) It is very important that you understand what the primary variables in EOS3 (and any other EOS module) mean, specifically if MOP(19)=1. See manual Section 6.
(6) Sorry, IRP=ICP=11 is only available in iTOUGH2 (not TOUGH2). Please replace them with the van Genuchten curves (IRP=ICP=7) and appropriate parameters.
Hope this helps,
(2) But why is the porosity different ? In the case of the same porosity it will be as if the porous media have a small skin in equilibrium with the atmosphere, isn't it ? Why to prefer one to another ?
(5) Yes I know the primary variables in EOS3 and EOS4. The question is perhaps stupid but MOP(19)=0 in your example and I don't know why you impose 13 in the atmosphere boundary element.
(2) Multiple little points:
- The porosity in the atmosphere is essentially 1.0, so that's what is specified.
- The laminar boundary layer is actually in the atmosphere, not the rock.
- Since the volume of the atmosphere is huge, porosity does not matter.
- Porosity would affect the diffusion coefficient (which is not used in this scenario).
- Change porosity and see what happens!
(5) As indicated in my initial reply, the file I sent you is for EOS4; so please check Table 10 of the manual, and you'll see that the second primary variable for single-phase (gas) conditions is temperature, so 13 is the temperature in the atmosphere.
Sorry to disturb you again.
I succeed in applying a capillary pressure in order to simulate evaporation (thank you again for taking the time to answer). I try now to simulate evaporation with ions initially in the pore solution. I discussed this subject with Eric Sonnenthal in this post. I tried a lot of configuration but with any success:
- Capillary pressure equal to 5e9 in the ROCK parameters as in your kelvin example -> the problem is that ions (Na+ and Cl-) go out of the porous media whereas concentration should increase;
- Capillary pressure equal to zero in the ROCK parameters (without production in GENER) in order to ensure diffusion without convection -> no evaporation (or very few);
- I would like to impose a zero flux for ions (but not for water) but I do not know how.
Have you any idea?
I can only confirm what Eric explained to you regarding ion accumulation due to evaporation. Check the parameters that affect vapor diffusion (porosity, tortuosity, diffusion coefficients, nodal distances, etc.). Adjust them to achieve the right evaporation rate, at which point you'll get the expected increases in ion concentrations near the land surface.
As you suggested above, porosity is close to 1. Tortuosity is 0 (that is to say Millington and Quirk), diffusion coefficients for water and air in gas depend on temperature. Then, the only parameter that affect vapor diffusion is nodal ditance from atmospheric block to rock block. I will try this.