Peaks in the breakthrough curve with transport and kinetics

[GautierLaurent]

Hello,

I am running a reactive transport model with two mineral phases:
 - one is a copper bearing mineral needing low pH for being dissolved (here Atacamite)
 - the other tends to neutralize pH (here Calcite), thus limiting the dissolution of the first mineral.

My problem is that in some configurations I got peaks in the breakthrough curves.
The way I understand this is that in each cell the Atacamite only start to significantly dissolve when Calcite is gone,
and when all the Atacamite has been dissolved in one cell then it takes some time before Cu can be significantly recovered from the next one.
The attached examples illustrate the problem.
This is a simplified version of what I am trying to model.
In the actual models the output might even go back to 0 after each peak depending on the relative proportion of each phase.

This is of course not realistic and I understand it is due to the discretization.
I tried to increase the number of cells, which limits the effect but without completely removing it (see files with _2 suffix).

Is there any way I could improve this result besides using a very large number of cells?

best regards

[dlparkhurst]

I am not sure what an "improved" result would look like. I think we agree that PHREEQC is solving the problem correctly as defined.

First, you have ignored dispersion, which may well affect the rates of reaction and may result in a quite different copper concentration just by increasing the dispersivity in your simulation. One conceptual model is that there are many 1D flow paths with different flow rates and the result at the end of the system is some mixture of the water from the different flow paths. I assume that would tend to remove the oscillations.

Assuming that calcite must be removed before the copper dissolution can proceed at a fast rate, another approach could be to put the two reactants in the stagnant zone of a dual porosity transport. In that way, there could be reaction in all cells, but the calcite would be removed fastest from the initial cells. I don't know for sure, but I think the copper would increase more monotonically at the end of the system.

I don't really have an answer for you, but I think the problem is more in the conceptualization. In particular, I think the problem is in the assumption that there are pure reaction fronts along a single flow path.

[GautierLaurent]

Thanks for your reply.

I am not sure either what an improved result would look like.
When I am increasing the number of cells, the result tends to have the same overall shape but only smoother.
So, I guess I would like to get a similar "smooth" result but without paying the price of an extremely fine spatial resolution.
My hope was that there would be some parameters controlling the way the reactions are solved that would bring a less costly solution.
I do agree with you that PhreeqC is solving the problem correctly with the parameters I gave it.

I agree dispersion is a good suggestion. Sorry I forgot to mention I already made attempts that way but without success.
I was trying to make my question simple and straight to the point.
I estimated dispersivity should be around 0.1 to 1 m at most in my case, and velocity is rather small.
In the end, it has little effect on the result and doesn't really affect the peaks.
I think dispersivity has a limited contribution to the result here as compared to the chemical effects, mainly because of the small velocity.
But it has a huge effect on the simulation time because it is dividing the time steps by tens to hundreds.
That's why I was using a 0 dispersivity in my attempt to get rid of these peaks.
I though I could always add dispersivity to refine the result once this problem is solved.

I see what you mean with the dual porosity model. Actually, in this study I have also been investigating the effect of dual porosity parameters.
So I have also run dual porosity models and I get similar peaks.
Although, you are right that, in the models where the stagnant zone is large, the peaks are less important.
However, that's not really a solution because I would like to be able to change the dual porosity parameters to fit my experimental data so I don't really have enough degrees of freedom with these parameters.

I think you have a point that the assumption of pure reaction fronts along a single flow path is the problem here.
If not with dispersivity, do you see a way to tackle this through the way kinetic rates are defined?
I guess there could be a way to use kind of homogenized kinetics rate that would account for this complex reaction front, but I don't have a clear mind about how to achieve that, and I am far to be sure this is a practical way to go.

Anyway, I'll always have the solution to increase the resolution and with dispersivity it might do the trick.

Thanks a lot for your help.

[dlparkhurst]

Sounds like you have considered most of the options.

I would probably try using PHAST. It does not have the restrictions on cell length and velocity, plus it is parallelized, so it is much easier to adjust numbers of cells and cell lengths, and it will run much faster. PHAST also has more numerical dispersion (depending on weighting), which may be a benefit in this case.

[GautierLaurent]

Ok. At least now I know I haven't missed anything obvious.

Thanks for the suggestion of using PHAST.
I did not consider it for this problem but it sounds like a very good idea.
I'll keep that in mind.

Thanks a lot for your time.

[dlparkhurst]

Phast4Windows should allow you to set up and run your problem. Chemistry is defined with a PHREEQC input file.

Here's a rough version of your problem. I rounded space and time, so you will need to fix the details.

[GautierLaurent]

Thanks a lot.
I will give it a try.