Modelling large mass removal in adsorption columns

Abstract

A novel mathematical model is developed to describe column adsorption when the contaminant constitutes a significant amount of the fluid. This requires tracking the variation of pressure and velocity, in addition to the usual advection–diffusion–adsorption and kinetic equations describing concentration and adsorption rates. The model goes beyond previous work, based on a simple linear kinetic equation, to include both physical and chemical adsorption. Using rigorous mathematical techniques we are able to simplify the governing equations to obtain an approximate analytical solution. The advantage of such analytical solutions is that the effect of system parameters on the behaviour is clearly defined and, in this case, only a single unknown needs to be fitted to the data. The simplicity of the solution is advantageous when testing new configurations and optimising operating conditions. Fitting a single unknown from an explicit expression is significantly more efficient than fitting multiple parameters to the base system of equations. The analytical solution shows excellent agreement with breakthrough data for multiple experiments. For the most extreme case of 69% CO our model had a Sum of Squares Error of 0.01 and an R = 0.99, compared to values 4.8, 0.94 for the standard constant velocity model.

This publication is part of the research projects PID2020-115023RBI00 and TED2021-131455A-I00 (funding T. Myers and F. Font) financed by MCIN/AEI/ 10.13039/501100011033/, by ‘‘ERDF A way of making Europe’’ and by ‘‘European Union NextGenerationEU/PRTR’’. A. Valverde acknowledges support from the Margarita Salas UPC postdoctoral grants funded by the Spanish Ministry of Universities with European Union funds - NextGenerationEU. T. Myers and M. Calvo- Schwarzwalder thank CERCA Programme/Generalitat de Catalunya for institutional support. This work is supported by the Spanish State Research Agency, through the Severo Ochoa and Maria de Maeztu Program for Centres and Units of Excellence in R&D (CEX2020-001084- M). F. Font is a Serra-Hunter fellow from the Serra-Hunter Programme of the Generalitat de Catalunya. F. Font gratefully acknowledges the SRG programme (2021-SGR-01045) of the Generalitat de Catalunya (Spain).

Peer Reviewed

Postprint (published version)