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What boundary condition to use for contaminant infiltration?

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Hi all

This question arises in a FEMWATER model I am doing, but it is a general question that would be relevant in any contaminant model. It concerns what kind of boundary condition to use to represent infiltration of contaminant into a contaminated site.

In my model I have a water recharge rate of 0.002 L/T and the contaminant concentration in the recharge is 10.0 M/L^3. So the contaminant flux is 0.02 M/L^2/T. I have been using the FEMWATER "variable" boundary conditions to represent this, which are basically specified flux conditions.

For water, this sets V = qp on the boundary face,

where

V = Darcy flux (to be determined)

qp = water flux (p for precipitation)

For contaminant, it sets V C - theta D . grad C = V Cv on the boundary face,

where

C = concentration (to be determined)

theta = moisture content (= porosity if saturated)

D = dispersion coefficient tensor

Cv = concentration in recharge

The problem I am having is after I have solved the model, I calculate the water and contaminant fluxes across the boundaries to do a mass balance. The water flux across this boundary is correctly qp, but the contaminant flux is much higher than V Cv. When I set the dispersion tensor to zero, however, the contaminant flux then matches V Cv more closely.

The transport boundary condition seems to be acting more like a specified concentration bc than a specified flux one. This results in contaminant mass being added to the system to satisfy the dispersion equation. How do I set a boundary condition that gives the correct flux of contaminant into the system?

Edited by woodward
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Hmmm, I just found the following comment in Zheng & Bennett (2002) Applied Contaminant Transport Modeling (page 285):

"There is in fact no transport boundary condition, taken alone, which can specify the total rate at which solute mass enters or leaves at a boundary, except for the special case of zero..."

I guess if you could specify two boundary transport conditions on a face, a specified flux and a specified flux gradient ... but FEMWATER doesn't allow this ...

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Hi woodward,

I do not know femwater very well, but the internal boundary condition formulations might be comparable to FEFLOW. If femwater uses the so-called convective form of the transport equation, a mass flux boundary condition might mean only the dispersive part of the mass flux. If at the same location you have a fluid-flux boundary condition, there will be an additional advective part in the sense of a zero-gradient boundary condition. So the total mass inflow will be much higher than defined. You can find a more theoretical description of this in http://www.feflow.info/uploads/media/white_papers_vol1_01.pdf , chapter 6. Practically it means that a mass-flux bc is not really useful in the convective form if you have fluid-flow boundary condtions at the same locations. In FEFLOW, this problem is solved by letting the user choose between the convective and the divergence formulation.

Best regards,

Peter

Edited by PeterS
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• 3 weeks later...

Hi woodward,

I do not know femwater very well, but the internal boundary condition formulations might be comparable to FEFLOW. If femwater uses the so-called convective form of the transport equation, a mass flux boundary condition might mean only the dispersive part of the mass flux. If at the same location you have a fluid-flux boundary condition, there will be an additional advective part in the sense of a zero-gradient boundary condition. So the total mass inflow will be much higher than defined. You can find a more theoretical description of this in http://www.feflow.info/uploads/media/white_papers_vol1_01.pdf , chapter 6. Practically it means that a mass-flux bc is not really useful in the convective form if you have fluid-flow boundary condtions at the same locations. In FEFLOW, this problem is solved by letting the user choose between the convective and the divergence formulation.

Best regards,

Peter

Thanks Peter

It looks like FEMWATER uses the convective form only.

Simon

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