Mobile-Immobile model

[vss0015@auburn.edu]

Greetings everyone,

I am using single porosity model for water flow and dual-porosity MIM model (physical non-eq) for a non-reactive solute transport. I wanted to ask:

1. For saturated flow conditions, considering the models I am using, will the residual water content (Qr) be zero? The saturated will be equal to porosity but I am not sure what value to use for residual water content? In Hydrus 1D manual it is given that we will consider Qr = 0 for Dual porosity model, but will the same stand for the mobile-immobile model too?
2. I am optimizing the dispersivity parameter (DL) in the solute reaction parameters. Is that dispersivity the immobile dispersivity or effective dispersivity or mobile dispersivity? I want to compare it with CXT-FIT optimised Dispersion co-efficient (D), but am not sure how these two are related?
Will the CXT-FIT optimised value of Dispersion co-efficient be effective dispersion co-efficient, mobile dispersion co-efficient or something else. Moreover, is the dispersivity parameter in hydrus effective dispersivity or mobile dispersivity?

3. I have significant macropore/preferential flow in some of my soil columns. In those columns, I have a high immobile water content optimized by HYDRUS. I am just wondering why in those columns with macropore flow, the immobile water content is more than that of columns with no macropore flow?
I hope you can provide some insights into my doubts as these things are not mentioned in research papers.

Thank you.
Vishawjot Singh Sandhu

[Jirka]

1. For saturated systems, the values of parameters theta_r, n, alpha, and l are irrelevant. Only theta_s and Ks affect the results.
2. In HYDRUS, we consider dispersivity in the mobile zone. The dispersion coefficient is calculated from it (and the diffusion coefficient). See eq. 3.54 of the HYDRUS technical manual. For the dual-porosity systems, you simply replace theta with theta_m, q with Q_m, etc.
3. In the system with macropores, the dual-porosity model (which requires two domains – mobile and immobile) likely interprets the entire matrix as being immobile, since the flow is dominated by macropores.

J.

[vss0015@auburn.edu]

Thank you Dr. Jirka for your reply. It really helps a lot.

[vss0015@auburn.edu]

Dear Dr. Jirka,

Once again, thanks for clarifying my previous questions. In continuation of my previous question. In the columns in which I have more macropores, there is more immobile water content. Does this imply it should have less alpha (mass transfer coefficient)?
I am trying to think is alpha negatively or positively correlated to immobile water content in soil? Or there is no correlation between immobile water content and mass transfer coefficient?

I have been reading contradictory papers; some say that with an increase of immobile water content, the alpha should increase as it would lead to larger regions of contact between the immobile domain and mobile domain.
I am aware that mass transfer coefficient is positively co-related with pore water velocity.
However, some papers say that with an increase in macropores or an increase in immobile water content, the mass transfer would decrease.
Even in my case, in the columns in which there are higher macropores, there is higher immobile content and lesser mass transfer coefficient.
Please let me know what your thoughts are with respect to increase or decrease of 'alpha' with respect to increase or decrease of immobile water content or the number of macropores.
Thanks in advance!

[Jirka]

I’m not aware of any straightforward correlations between these parameters. J.

[vss0015@auburn.edu]

Thank you Dr. Jirka for your swift reply. It helps a lot. Have a good day!!

[thotran11292]

Dear Jirka,

I crossed by this post. and have one question please?

"In the system with macropores, the dual-porosity model (which requires two domains – mobile and immobile) likely interprets the entire matrix as being immobile, since the flow is dominated by macropores."

You stated this. Could you explain this for me please?

Actually, i am working on unsaturated soil column experiment. In the slightly loose packed soil column with density of 1.2 g/cm3, I got considerably high immobile water content (like 90%) from HYDRUS fitting. And I think the statement you stated above could be very helpful.

Best regards

Tho Tran

[Jirka]

Obviously, this will depend very much on the conditions. However, if you use the dual-permeability model for macroporous heavy-textured soils, then you will have slow water movement in the matrix and fast movement in the fractures (during ponding or conditions close to saturations). On the other hand, if you use the dual-porosity model (with mobile and immobile water), it will likely assume that the mobile zone is in the macropores (which dominate flow during near-saturated conditions), and the immobile zone in the matrix. J.

[thotran11292]

Dear Jirka,

Thank you for your reply. It is very helpful. Can I have one more question please?
Under such condition, when we consider the Freundlich absorption, there is a term of "Fraction of sorption site in contact with mobile zone" - known as f. I crossed several papers, some assumes that as theta_mobile/theta, other assumes that as theta_immobile/theta. I tried both assumptions and the one with theta_immobile/theta gave me a so much better fitted results. But I could not understand from how that assumption the formula was derived. Do you have any recommendation/suggestion for me to understand more on this problem? Also, I actually asked HYDRUS to fit that value for me from inverse modelling, and it gave me the value that was closer to the theta_immobile/theta.

Best regards

Tho Tran

[Jirka]

The parameter Fract represents the fraction of sorption sites that is in the mobile zone and (1-Fract) is the fraction of sorption sites that is in the immobile zone. Some models, e.g., Macro, assume that all sorption sites are in the immobile zone, i.e., Fract=0. If you chose Fract=Theta_mob/Porosity, then you assume that the sorption sites are distributed proportionally to the extent of the mobile and immobile zones. However, it is likely that more sorption sites are in the immobile zone than the mobile zone, since that is usually fine-textured soil with a large surface area contrary to macropores, which have a small surface area. This is in general a fitting parameter. J.

[thotran11292]

Dear Jirka,

Thank you so much for your quick and helpful response. It does help me a lot.

Have a good day!

Best regards,

Tho Tran