One site sorption _Sink Solid0

[Farah]

Hello Hydrus community,
I am attempting to simulate reactive solute transport through various densities of bentonite. I am using the inverse modelling of Hydrus to simulate the breakthrough curve (cumulative bottom flux vs time) observed during a diffusion experiment. The boundary and initial conditions were (where L is the thickness of the puck)
C(0≥x≤L,t=0)=0 ;C(x=0,t>0)=C_0 ;C(x=L,t>0)=0;
I discovered that the experimental data can be explained by a one site kinetic sorption model, but only if I include the sink solid zero term in my model. I am a bit confused by this term. According to the Hydrus manual's governing equation, this term is a Zero Order Production rate. However, it is specified as a sink term in the model. Does the fact that this parameter plays a significant role in my model imply that there is some production of the solute in the system? Please note that we don’t have any source in our system.
I have used (mg, meter and day) as unit in my model and found that SinkSolid0 value in the rage of (3x10^-6)- (9.5x10^-4) per day, which indicates a very slow rate.
The only thing is that to meet the boundary condition we have kept the top boundary concentration 1000 ppm (1000000 mg/m3) during the experimental period.
My questions are:
Is Sink SolidO always means production/source rate?
If it’s a source, is the boundary condition having an effect on this term (though according to my understanding it should not).

Please assist me in resolving my confusion.
Thank you in advance.

[Jirka]

You have several problems in your projects:
1. The residual water content needs to be smaller than the saturated water content. The value is actually irrelevant (for this case), and thus you can make it equal to zero.
2. The upper solute BC should be the solute flux BC.
3. The bottom solute BC should be the zero concentration gradient.
You likely also have some problems with respect to units.

Yes, SinkSolid0 always represents a production/source rate?

J.

[Farah]

Thanks a lot Prof. Jirka,

I really appreciate your prompt reply and going through the model thoroughly.
Its great to be confirmed with the Sink Solid0 term. I will check the units again and change the residual water content into zero.

However, I am now confused by the Boundary conditions. There was no flow during the diffusion experiment, and the concentration at the boundary was maintained at a constant level. Using a peristaltic pump, 1000 ppm and 0 ppm concentration solutions were circulated at the top and bottom boundaries, respectively (to devolve the concentration gradient that drove diffusion).
I chose concentration BC for both the upper and lower BC concentrations. According to the "Help" section of Hydrus, the Concentration Flux BC for the upper boundary (liquid phase concentration of the infiltrating water) does not correspond to the experimental condition because there was no flow infiltration. As there was no free drainage, a zero conc. gradient was not specified for the lower boundary.
Please let me know if I am overlooking something.

Thanks once again.
F

[Jirka]

I have listed BCs that are usually used for column experiments. If you believe that other BCs are applicable for your conditions, clearly use those. J.

[Farah]

Thanks a lot Prof. Jirka.
Regards

[Farah]

Hello Prof. Jirka,
Thank you for your help last time.
But I have few more questions left.
As I mentioned earlier, that though I have not any source of production in my experiment I still find that the SinkSolid0 is playing a major role in my model. Being said that I would like to elaborate a little on my experimental condition.
Bentonite puck was saturated with DI water. Anion diffusion experiment was started by circulating 1000 ppm from upper boundary and DI water at the lower boundary side. The large concentration gradient between the reservoirs resulted in a non-uniform ionic concentration over the sample length. Therefore De over the domain was not constant, rather it varied depending on the local solute concentration, as ion diffusivity through bentonite depends on ionic strength (due to its effect on diffuse double layer). De measured in our experiment gives an average value over a certain range of ionic concentration. The steady-state ionic concentration distributions across the sample length (L) or distance in such case ( De∝ concentration) follows a convex curve Crank (1975) as shown in Figure attached.
I am wondering that, when I am using the SinkSolid0 term, only then I am able to obtain this type (the convex curve) of profile information. But as SinkSolid0 is a production term, and I don’t have any source of production in my experiment, can I say that Sinksolid0 covers the effect of Variable De (not constant and was higher in some cases which caused more solute to pass through the sample compared to that would have passed with a constant De). Would that be a valid claim/explanation?
Also another question, the unit of Sinksolid0 is per day, just a rate (same unit as mass transfer rate coefficient α). Generally ( not specific to my experiment) is there any way to estimate a specific concentration or percentage of upper boundary concentration from this parameter? Or how exactly it can be interpreted?

Thanks once again for your time and assistance.
F

[Jirka]

If you have no flow, then De in HYDRUS will be constant and will produce, as you have shown, for steady-state conditions, a linear concentration profile. You can indeed get the nonlinear profile when you vary De as a function of concentration (which HYDRUS does not do), or if you add some reactions, e.g., zero-order production (which is what you do, and which HYDRUS allows). Unfortunately, even if you can get the same concentration processes, these (variable De, or production) are very different processes, with very different mass balances (not adding or adding solute mass to the system). Thus, I do not think that it is justifiable to substitute one process/factor for the other. Implementing variable D, depending on concentration, would require modifying the computation code. J.

[Farah]

Many thanks Prof. Jirka, for your clarification and explanation.
Best regards,
F