Immobile water in X1t

[Tom Meuzelaar]

[admin notice: the below is from the former GWB users group email distribution list. This message was originally posted 12/13/2005]

 

Posted by: Janet Hering

 

Hi All,

 

I would like to include immobile water in 1xt but I'm not sure if

this is possible. This would mean defining some volume of the node(s) that

could undergo (only) diffusive exchange with the advecting fluid. As far

as I can see, there's no mention of this in the Reactive Transport Modeling

Guide. If anyone can provide some suggestions for how to do this, I'd be

very appreciative.

 

Thanks, Janet

 

Posted by: Craig Bethke

 

Janet,

 

If the stagnant and flowing waters are in good diffusive communication (i.e., they maintain approximately equivalent compositions), you need make no special adjustments. By the divergence theorem (or simple reasoning), change in the chemistry of an elemental volume depends on the rate at which the components enter the volume, less the rate at which they leave; the details of how water moves within the volume does not enter into the problem.

 

If however the stagnant and flowing waters develop differing compositions over the course of the run (or are different initially), the problem is not as simple. For example, water may be flowing along fractures while the various components diffuse into and out of the intact blocks of rock between the fractures. (Of course the preferred flow paths don't need to be fractures, but this is a common case.)

 

You can solve this problem explicitly with X2t. Example: set the left-side column of nodes to be the fracture. Its width is the fracture half-width and flow enters the bottom and exits the top. Now, to the right, set some additional columns of nodes containing stagnant water, to represent the intact matrix.

 

Formally, the additional columns would extend over the half-width of the matrix blocks. Commonly diffusion affects the matrix only quite close to the fracture, depending on the time span of the simulation, so there may be a practical need for just a relatively few columns (~10 should be plenty) of limited width.

 

After you have run the simulation, you will see not only the predicted change in chemistry within the fracture with time and along the direction of flow, but the chemical and mineralogical effects of the diffusing species within the rock matrix.

 

It is also possible to attempt a lumped parameter model in which you reduce the multi-dimensional problem to one dimension. Such a configuration is known as a dual porosity model. Doing so of course involves a number of simplifications with which you may or may not feel comfortable. You may not for example be able to consider mineral precipitation/dissolution or surface complexation within the matrix.

 

X1t is not set up as a dual porosity model, although you can probably use custom rate laws to dummy up such a configuration if you feel it is necessary. I believe that PHAST can be linked to PhreeqC to trace certain dual porosity models, but have never tried this myself.

 

In any event, I think you'll probably be happiest if you start by constructing the full model using X2t, as described above. You would then have a baseline for considering any simplified models you may end up attempting.

 

Hope this helps,

Craig