building an sdat file for Kd approach in X1t

[B_Kimball]

I am trying to model uranium attenuation in X1t using a simple Kd approach. I am using the Pb example and the associated Pb-Kd.sdat file as my template for this. The header of the Pb-Kd.sdat file states that the Kd value is given in units of mol/g solid. In other words, the sorbed concentration (mol/g) is provided instead of the actual Kd value (e.g., L/kg). Why is this the case?

On a related note, is it possible to utilize the Kd approach in X1t using Kd values that change with the pH of the system?

Thank you.

Pb-Kd.sdat

[Brian Farrell]

Hi, 

The Kd model implemented in most geochemical modeling software, including the GWB, is what is called the “reaction Kd model” or “activity Kd model”. The Kd approach as strictly defined (as you’d find in a purely hydrologic model) implies, but does not specify, a chemical reaction. In reaction modeling, we write a specific chemical reaction (such as >UO2++ = UO2++) and define Kd’, the apparent distribution coefficient, as the ratio of sorbed mass to the activity of the free ion, rather than the concentration of the entire component.

For use in geochemical models, traditional Kd values need to be corrected by the value of the free ion’s activity coefficient, as well as the fraction of the component present as the free species. For more information, please see 9.1, Distribution coefficient (Kd) approach, in the Geochemical and Biogeochemical Reaction Modeling text. The Kd.sdat template, installed with the software in the Gtdata folder, provides a similar explanation in the notes. If you’re referring to the Pb-Kd.sdat file used in our RTM workshop and the GWB Online Academy, the workbook exercise description provides a true Kd value (units of cm3/g) and includes the information needed to convert that to the Kd’ (units of mol/g) specified in the surface dataset.

The GWB does not account for changing Kd values with pH. A more robust approach would be to use a surface complexation model, which the GWB does indeed include. You can account not only for pH effects, but mass balance on the sorbing sites, competition of different ions for those sorbing sites, and electrostatic effects. A simple generalized composite approach to surface complexation modeling, if you can parameterize it, would likely be much better than any Kd model.

Hope this helps,

Brian Farrell
Aqueous Solutions LLC
 

[B_Kimball]

Thanks Brian. Your description of the "activity Kd model" does help.

I have tried using both the Kd approach and a surface complexation model (SCM) to account for uranium attenuation along the flow path. In reference to a SCM, you said the magic words: "if you can parameterize it." I have the age-old problem of desiring more site-specific data to inform my SCM. When I try to incorporate a SCM with the FeOH+.sdat database and our estimates of HFO concentrations in the aquifer, the predicted attenuation of uranium is much lower than we observe in the field. A Kd model gets me closer to what we observe, but as you imply, these models are not ideal, especially when the pH of the system is changing. I will continue to think about this.

Thank you.

[Brian Farrell]

I'm glad to hear it helped. Good luck with your modeling.

Cheers,
Brian

[CShort]

Hi Brian,

Bryn and I have been talking about this and I'd like to follow up. For a simple model, I'm using REACT to calculate a Kd for uranium at some pH with ferrihydrite present as a sorbent phase. The output is set up to show the Kd.

To use that Kd in a subsequent X1T model, I can create a Kd surface dataset. Easy so far.

Is it appropriate to use the Kd that REACT spits out in my surface dataset, or does it need to be converted to an activity-Kd? In other words, does REACT provide an activity-Kd or a plain-old-Kd?

[Brian Farrell]

Hi Clark,

The distribution coefficient was originally just an observation geochemists made. At some point, it was used in a predictive sense in hydrologic models that care only about the total concentration of a component (Kd approach in the strict sense), and later in geochemical models which account for speciation (the activity Kd approach). The Kd that React reports is simply the observation. You could have a model with any number of sorbing surfaces (Kd, Freundlich, Langmuir, ion-exchange, two layer), and the reported Kd reflects the net effect of all those surfaces under the conditions of the model. 

To use the reported Kd (units of l/kg) in a predictive sense in the GWB, it would need to be converted from a “true Kd” to the “activity Kd” (units of mol/g) when you create a surface dataset.

It’s important when reporting the Kd to ensure that the mineral mass of the system is completely defined. The mineral mass can be composed of individual minerals as well as inert volume. Then, when you set up your X1t model, you should be sure to define mineral mass consistently. If you don’t, the Kd won’t be applicable to your system.

For more information, please see 6.49 inert and 6.53 Kd in the GWB Command Reference.

Hope this helps,

Brian
 

[CShort]

Thanks Brian - very helpful, as always!