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zero flux for ions at boundary condition

Hello,

When simulating a drying process of a porous media it is possible in TOUGH2 to apply a capillary pressure at the boundary condition. However, when doing such a simulation with a porous media that contains ionic species with toughreact the ionic species get out of the porous media. Is it possible to prevent this?

 

Anthony

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  • Anthony,

    When you say "get out of the porous medium", the ions can "get out" by advection and or diffusion. Also, there is drying by evaporation and drying by capillary suction, changing the concentrations. Advection should just transport the ions with the water, leaving the same concentration. If evaporation actually occurs, then the concentrations will also increase. If diffusion of lower concentrations in the boundary block with higher values in the top layer is the problem, then you should limit diffusion between those grid blocks. This can be done by giving the boundary block a very low tortuosity (e.g., 0.00001), but not zero, or else Millington-Quirk kicks in and the tortuosities are calculated from the porosities and saturation.

    Eric

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  • Anthony,

    If you want to simulate drying so that there is only a flux of water into the air and not ions, then you should do it with eos4, setting a very low relative humidity in the boundary block and zero capillary pressure. Using the capillary pressure to approximate the drying process may be ok for the rough hydrological effect, but it is not the same as evaporative drying, so the concentrations will not come out the same. The other fixes I mentioned will limit diffusion but not advection, so it won't work if your boundary block is just imbibing water.

    Eric

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  • Eric,

    Thank you for your prompt response.

    I am in the case of evaporative drying. As mentioned by Stefan Finsterle in a previous post, 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 have chosen the second method for severals reasons I will not explain here. That is to say I have chosen a model that is not the mechanistic approach. However, to me, it is not a problem for the water. But it becomes a problem for ions since they should not actually transport or at least not much (problem of evaporative drying -> diffusion of water and not advection).

    Therefore, you are right when you say that giving the boundary block a very low tortuosity limit diffusion but not advection (that doesn't solve my problem here). Setting a very low relative humidity in the boundary block is a very good idea. Thanks. But why do we need to set a zero capillary pressure?

    Anthony

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  • Anthony,

    If I had seen Stefan's post, I could have referred to his perfect description! Unfortunately, the capillary suction approach does not give correct results for simulating evaporation when considering reactive transport or heat effects. The assignment of zero capillary suction just keeps liquid water from being transported up into the grid block, so the moisture is only making it out through vapor transport. That is the way I do it. Stefan probably can offer other options for simulating evaporation, consistent with chemical transport. Also, if you use the relative humidity approach, be sure to check that vapor diffusion is turned on. Since you are simulating reactive transport, then likely there is CO2 being transported in the gas phase, and the parameters for CO2 diffusion need to be set correctly in the thermodynamic database and in solute.inp. Just anticipating all the issues that may come up!

    good luck,

    Eric

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  • Eric,

    Thank you again for your answers and sorry to not have mentioned the Stefan's post in my first question.

    I don't know why you say that "the capillary suction approach dose not give correct results for simulating evaporation when considering reactive transport". Have you references that confirm such an affirmation (and even quantify it)? If the relative humidity value is very low, no matter, isn't it? The mechanistic approach does not give correct answer too since the laminar boundary layer thickness is not well quantified.

    I will try to assign a zero capillary suction and a very low relative humidity.

    Anthony

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  • Anthony,

    I'm not sure which would be the best references on this, but any papers on evapotranspiration, combined with papers on chloride in infiltrating water vs. precipitation (Sonnenthal et al, 1999), discuss the effect of evaporation on infiltrating water composition. I'm not sure we are talking about the same boundary condition, though. If you would like to model moisture removal from the surface into the atmosphere by evaporation, then then using the capillary suction approach will not change the concentration of conservative ions in solution at the top boundary. Conversion of moisture to vapor will directly concentrate the conservative cations in solution (Rayleigh distillation), which can be done by connecting an atmosphere block having low relative humidity and allowing only water vapor from the top surface to be transported. This will maintain the mass of cations in the surface, but not the amount of water, thus resulting in concentrating the conservative ions. Of course, this could induce mineral precipitation, so not all species would act conservatively. So it is basically the difference between having a leak in a tea kettle allowing all the water to drain out with the ions vs. boiling the water and producing the mineral scale as the water evaporates.

    Eric

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  • Eric,

    Thanks again. I think I have all the responses now.

    Anthony

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