## Exclusion effects in model

A discussion forum for Hydrus-1D users.
Jialan Zhu
Posts: 20
Joined: Tue Sep 29, 2015 11:43 pm
Location: USA

### Exclusion effects in model

Hi,
I have questions about Exclusion effects (size exclusion and ion exclusion) simulation with HYDRUS.
I’m currently studying bacteria transport in presence of surfactant in vadose zone. Surfactants enhance the effects of Exclusion.
I’m wondering if HYDRUS-1D can model this exclusion effect in unsaturated condition. And I’m considering using two-site model (attachment-detachment and straining).
According to C-Ride manual, the equation for water content accessible to colloids θc is water content θ minus the water content not accessible to colloids θim: θc=θ-θim . The θim is a constant input parameter in the model. So it is possible that θc is negative when θim is larger than θ under variably saturated conditions. How does HYDRUS deal with this problem?
Thanks
Jialan

Jirka
Posts: 5216
Joined: Sat Mar 16, 2002 3:47 pm
Location: USA
Location: Riverside, CA

### Re: Exclusion effects in model

θim has to be set to a value that is smaller than any θ value encountered during the simulation. To avoid crashes (divisions by zero), HYDRUS will set the mobile water as follows:
θm =amax1(θ - θim ,0.001)
J.

Jialan Zhu
Posts: 20
Joined: Tue Sep 29, 2015 11:43 pm
Location: USA

### Re: Exclusion effects in model

Dear Jirka,
What I’m doing right now is fitting colloid transport parameters with bacteria breakthrough curves under different surfactant concentrations.
According what you said in another postings: there are two ways to model exclusion effects with HYDRUS, one is “mobile-immobile solute transport concept”, another is “the Kd adsorption coefficient”. I have two questions:
1. What is this Kd? The detachment coefficient for attachment-detachment site?
2. If it is, what parameters I need consider (θim, Kd, or both) in parameter fitting with inverse model?
Your suggestions will be highly appreciated.
Jialan

Jirka
Posts: 5216
Joined: Sat Mar 16, 2002 3:47 pm
Location: USA
Location: Riverside, CA

### Re: Exclusion effects in model

1. Kd is the distribution coefficient, which is used to calculate the retardation factor. It is used for instantaneous sorption, contrary to kd, which would be a kinetic sorption rate (attachment). Kd is sometimes given a negative value to result in retardation less than 1 (i.e., to model anion exclusion).
2. You should be fitting simultaneously θim and Kd since they will likely be correlated.
J.

Jialan Zhu
Posts: 20
Joined: Tue Sep 29, 2015 11:43 pm
Location: USA

### Re: Exclusion effects in model

Thank you very much!
Jialan

Jialan Zhu
Posts: 20
Joined: Tue Sep 29, 2015 11:43 pm
Location: USA

### Re: Exclusion effects in model

Hi, Jirka
We appreciate the response to our previous questions about using HYDRUS-1, which were helpful for us to ask a fundamental question:

Can we use HYDRUS-1 to simulate the exclusion effect under variably saturated condition using ThImob combined with two-site model?

We understand that some researchers represent the Exclusion effect by modifying a couple parameters (one option: Theta-s and K-s) and running saturated condition.

We obtained a steady state unsaturated capillary pressure head profile of a soil column (~15% to 75% saturation, corresponding h from ~40 to ~20 cm, with theta-s ~0.4), and used it to solve for water flow for input to the transport model for various values of ThImob.

But it doesn’t yield reasonable results; there are 3 aspects:
1. A value of exactly zero has a much different relative concentration (lower than 1)
2. The relative concentration with ThImob greater than 0 increased to maximum of 1; attachment/straining effects should make it lower.
3. For larger values of ThImob (the stronger the Exclusion effect), the longer the breakthrough time, which contradicts the expected Exclusion effect.

We are hoping to use HYDRUS simulate Exclusion effect under variably saturated conditions, and when successful, will submit to the library of projects on your HYDRUS web site.
Thank you,

Jialan Zhu (PhD candidate) and Gerard Lennon (professor), Lehigh University

Jirka
Posts: 5216
Joined: Sat Mar 16, 2002 3:47 pm
Location: USA
Location: Riverside, CA

### Re: Exclusion effects in model

Note that we already have similar examples (MIMTSM) in the library of HYDRUS projects at:
http://www.pc-progress.com/en/Default.aspx?h1d-lib-vzj

These projects are discussed in Figure 11 of:
Šimůnek, J., and M. Th. van Genuchten, Modeling nonequilibrium flow and transport processes using HYDRUS, Vadose Zone Journal, doi:10.2136/VZJ2007.0074, Special Issue “Vadose Zone Modeling”, 7(2), 782-797, 2008.
Figure 11.png (80 KiB) Viewed 14089 times
J.

Jialan Zhu
Posts: 20
Joined: Tue Sep 29, 2015 11:43 pm
Location: USA

### Re: Exclusion effects in model

I read the paper and ran the projects. But according to water flow profile information, it looks like it's under saturated condition (h =0, theta = theta_s)...

My question is that is it possible that input known variably saturated water flow profile (negative pressure head at the nodes) and run solute transport model, like this

Jirka
Posts: 5216
Joined: Sat Mar 16, 2002 3:47 pm
Location: USA
Location: Riverside, CA

### Re: Exclusion effects in model

I do not see any reasons why this should not be possible. J.

Jialan Zhu
Posts: 20
Joined: Tue Sep 29, 2015 11:43 pm
Location: USA

### Re: Exclusion effects in model

It would be great helpful to me if you could check my h1d file.

I’m not sure HYDRUS 1D can simulate colloid transport under variably saturated condition because all the examples look like under saturated condition. And I used a variably saturated water content profile and yielded a weird result:
I used “Two Kinetic site model (Particle Transport using attachment/detachement, chemical nonequilibrium)” and 0, 0.1, 0.2, and 0.3 as the value of ThImob. BTC of ThImob = 0 showed a different pattern. And when ThImob > 0, the larger the ThImob the longer the breakthrough time.

After I read the paper you refered (thank you very much it’s a very helpful paper), I thought maybe I should use “Dual-porosity model with two site sorption in the mobile zone”. But I don’t find place to input transport parameters for attachment/detachment site and straining site.

So now I don’t know where the problem is.

Jialan
Attachments
Example_Ecoli transport.zip

Jirka
Posts: 5216
Joined: Sat Mar 16, 2002 3:47 pm
Location: USA
Location: Riverside, CA

### Re: Exclusion effects in model

There is a lot of problems with your project. The main problems are:
1. You deselected water flow, while specifying flux BC. If you deselect water flow, the program will keep the initial conditions constant and will not consider boundary conditions. Why would you deselect water flow?
2. This is your water content profile:
Water Content Profile.png (37.89 KiB) Viewed 14021 times
Clearly, you cannot specify the immobile water content to be 0.1, 0.2, 0.3 (your graph above), when your initial water content is only about 0.07 in the top of the domain. Through which domain would flow occur?

The program can simulate exclusion under unsaturated conditions. However, the problem has to be defined realistically and be physically meaningful.

J.

Jialan Zhu
Posts: 20
Joined: Tue Sep 29, 2015 11:43 pm
Location: USA

### Re: Exclusion effects in model

1. This is actually the steady state water flow profile under my BCs. I did water flow simulation separately. The water flow remained steady state during the experiment. So I input steady state water flow profile in colloid transport model to save calculation.

2. Yes, I should have used smaller values. I used big values ThImob because I thought it would show the effect of ThImob more clearly, and theta_m=amax1(theta-theta_1m, 0.001), the program won't crash.

And I tried use small values ThImob (smaller than 0.07), and found two problems:

1. Still, BTCs of ThImob>0 have different pattern with ThImob=0; bigger ThImob, longer breakthrough time;

2. the program doesn't calculate colloid concentration (showed NaN in Obs_Node.out) when I set ThImob smaller than 0.04 which is residual water content.

Jialan

Jirka
Posts: 5216
Joined: Sat Mar 16, 2002 3:47 pm
Location: USA
Location: Riverside, CA

### Re: Exclusion effects in model

When you do not have a constant pressure head, you cannot assume that you define your steady state profile correctly. Actually, in your case the velocity profile looks as follows:
Velocity Profile.png (33.92 KiB) Viewed 14012 times
which is clearly unrealistic for steady-state conditions. If you do not have a constant pressure head profile, you need to simulate water flow to correct such problems.

J.

Helya
Posts: 3
Joined: Mon May 10, 2021 2:02 pm

### Re: Exclusion effects in model

Hi there,

I read all the question forums about the combined use of MIM model and attachment/detachment of colloids,. However, still found the question that was asked in 2016 by a user named Julian is still unanswered and the discussion went off of the main subject which is " the Hydrus availability to simulate colloid transport (attachment/detachment and straining) in unsaturated conditions when a dual-porosity model is also considere.

The suggested paper "Simunek and Van Genuchten, 2008" was referred to as an example to the question in this forum, but it was not really the same condition! The example explained in Fig 11 of the mentioned paper just explains the sensitivity of F_em and alpha under saturated condition and nothing related to the unsaturated condition and whether it is possible to simulated straining using the available model in Hydrus "dual-porosity model with two sorption sites"!

I have the same question and I would appreciate it if anyone can answer it:
Briefly, I want to simulate colloid behavior in unsaturated porous media under transient flow conditions; I selected the dual-porosity model with two-site sorption in the mobile zone (since I observed tailing in the tracer BTC, indicative of physical non-equilibrium transport). However, based on my experimental data, I also observed depth-dependant straining in the colloid retention profile (i.e., higher retention at the top of the column). Is there any way this model can account for depth-dependent straining?

Or I should just ignore the tracer tailing and sacrifice it for the observed straining of colloids and just go with an equilibrium model for tracer and attachment/detachment model for colloids (because the attachment/detachment model can describe straining for colloids)?!!

Jirka
Posts: 5216
Joined: Sat Mar 16, 2002 3:47 pm
Location: USA
Location: Riverside, CA

### Re: Exclusion effects in model

The model that is available in HYDRUS is called in the GUI “Dual-Porosity Model with Two-Site Sorption”. In the manuscript (S+VG, 2008), it is called “Dual-Porosity Model with One Kinetic Site”. This model has one kinetic and one instantaneous site in the mobile zone (i.e., a two-site sorption model), and an additional instantaneous site in the immobile zone (longer residence => no need for kinetics). This model is described on page 788. The kinetics is described using the first-order equation (21e), not the attachment/detachment equation (which can obviously be converted to the first-order equation). This model does not allow nonlinearity (i.e., blocking or straining).

You can use the standard “Two Kinetic Sites Model” (eq. 18 on page 788), which allows straining and blocking. At the same time, you can specify the “Immobile water content”, but the particles will be entirely excluded from this immobile domain (i.e., they will move faster). Then, theta in eq. 18 will be in fact theta_m (mobile water content, i.e., total water content minus immobile water content).
J.