Categorization of diffusion coefficient

[Farah]

Dear Hydrus Community,
I am trying to simulate bromide breakthrough curve obtained from through-diffusion experiment using inverse solution of Hydrus 1 D. Experiment was conducted through fully saturated bentonite sample . When I am trying to simulate the cumulative bottom flux(mg/m2) (calculated from cum. mass/ surface area) using effective diffusion coefficient value, De, Hydrus is showing me a lower flux compared experimental data. In other words, to fit the model a higher De value than experimental De is required. Please note that the De was calculated from the slope of the steady state part of cumulative mass vs time graph.
I have not used tortuosity in the model, and for porosity I just provided the total porosity (n=1-(dry density/grain density)).
My question is :
1. What type of diffusion coefficient is actually Hydrus yielding? Is it pore diffusion coefficient / apparent diffusion coefficient / effective diffusion coefficient.
2. If its not effective diffusion coefficient, How can I extract the Effective diffusion coefficient value from this?
3. Is there any way that I can directly provide the experimental De value in the model to fit the data?
As effective diffusion coefficient takes into account all the parameters (accessible porosity, tortuosity, viscosity, constrictivity etc) what type of porosity value should I use, total or diffusion accessible porosity ?
For your information I am sharing some information as well as my model
Bromide in 1300 kg/m3 bentonite, Background conc. 0M NaCl
Exp. De 8.20 E-7 m2/d
Fitted De 3.17 E-6 m2/d
Exp. Diffusion accessible porosity 0.131
Total porosity 0.51

Bromide in 1100 kg/m3 bentonite, background conc. 1 M NaCl
Exp. De 7.34 E-6 m2/d
Fitted De 1.85 E-5 m2/d
Exp. Diffusion accessible porosity 0.131
Total porosity 0.61

Thank you in advance for your support.
F

[Jirka]

Not sure that I understand your question. Anyway, the input to HYDRUS is the molecular diffusion coefficient in free water (D_w) and dispersivity (D_L). HYDRUS then internally calculates the Effective Dispersion Coefficient (D^w), which is used in the numerical solution. This Dispersion Coefficient is given by eq. 3.57 of the Technical Manual. At the input, you can also choose whether you want to consider tortuosity or not, and what model to use for tortuosity. If you do inverse modeling, then HYDRUS can fit these variables, i.e., D_w and D_L. Exact definitions are given on page 73 of the Technical Manual. J.

[Farah]

Thank you so much Prof. Jirka and sorry for my late reply.
I am sorry I could not make you clear about my query.
I was trying to understand what type of Diffusion coefficient Hydrus gives me when I am not using the tortuosity. Now I understand its pore water diffusion coefficient.
The question remaining is that how exactly Hydrus calculates this Diffusion Coefficient.
My target is to compare the experimental effective diffusion coefficient De with the model De. However as Hydrus is gives only pore diffusion coefficient Dp, I need to multiply this with diffusion accessible porosity, ɛ (that considers the anion exclusion). For conservative anion,
ɛ𝐷𝑎=ɛD𝑝= 𝐷𝑒.
But when I am multiplying the Dp wiith ɛ (calculated from experimental data), I am getting a different value than Experimental De. I want to understand what actually causing this difference.
Thats why I am trying to find how Hydrus is calculating the Dw value. Can you please guide me?
Thanks
Farhana

[Jirka]

Eq. 3.57. I have really nothing to add to it. This equation (and the governing CDE) is the most exact explanation of what the code does. J.