Dear all,
I'm trying to model the breakthrough curve for an adsorption packed bed column. By making use of a Crank-Nicolson scheme I've discretized the general mass balance equation (diffusion advection equation) where I now want to add a source term which will describe the actual adsorption.
I'm building the model according to the following article since the same assumptions are valid for my model:
http://www.sciencedirect.com/science/article/pii/S1385894710003840
I did not succed in modeling the adsorption term in the model. I'm unsure how I have to discretize this term in the axial direction. I was advised to add the adsorption term by making use of the fractional step method. Is there anyone who has experience with this?
All forms of help are highly appreciated!
Cheers,
Stijn
If you are modeling transport through a packed column of porous media, you could use the advection-dispersion equation with a retardation factor (R) to account for adsorption. If the adsorption is linear, fast, and reversible, a partitioning coefficient can be used (Kd=concentration adsorbed/concentration in mobile phase) which goes into the R factor. For an example see attached papers:
Carroll, K.C., J.F. Artiola, and M.L. Brusseau (2006) Transport of Molybdenum in a Biosolid-Amended Alkaline Soil. Chemosphere, 65: 778-785.
Cantrell, K.J., K.C. Carroll, E.C. Buck, D. Neiner, and K.N. Geiszler (2013) Single-Pass Flow-Through Test Elucidation of Weathering Behavior and Evaluation of Contaminant Release Models for Hanford Tank Residual Radioactive Waste. Applied Geochemistry, 28: 119-127.
Thanks for your reply, the method with a retardation factor seems like a good way to model the process, however if I understand it correctly this would mean that I have to determine the Kd values experimentally.
I have a description of the adsorption isotherm available which can be modeled as a Freundlich isotherm. I personally was thinking about making use of either a first order reaction scheme that will account for the adsorption (shown in the article I posted above) or by making use of the linear-driving-force model.
I've currently applied the split-operator approach which seems to work for the test equation. Any thoughts on this?
- Stijn
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