Mathematical model of the water sorption kinetics of UBC

• A mathematical model of water sorption kinetics of UBC was investigated.
• The Elovich model was one of the best but it is still almost empirical as it is.
• The Elovich model was converted by adding equilibrium concept to the original.
• A Converted-Elovich model could estimate sorption rate under any given condition.
• The Converted-Elovich model had an aspect of non-linear Langmuir model.

The water sorption kinetics of UBC (Upgraded Brown Coal) and its feedstock coals, including raw and dried coals, were investigated. A pseudo 1st order model was suitable for the desorption of raw coal, and a pseudo 2nd order and Elovich model was determined for both sorptions of the UBC and dried coal. This finding corresponded with the fact that the water adsorption status of the surface of the coal was modified through drying. The finding also indicated that the water sorption by the UBC and dried coal can be explained by similar kinetic models. These models were empirical, and the constants of the equations were determined from existing data. Therefore, the models cannot predict the sorption rate for given environmental conditions, such as temperature, relative humidity and initial moisture. To solve this problem, the Elovich model was converted by variable transformation to include the equilibrium moisture. The constants of the converted model could be determined for any given condition. The converted-Elovich model resembled the Langmuir model with regards to the driving force, although the force acted in a non-linear way, which was unlike the original Langmuir model. The reason why the constants could be determined was explained through this resemblance. Therefore, the converted-Elovich model was demonstrated to be effective not only in the fitting of existing data but also in the estimation of the sorption rate for any given conditions. The model was close to theoretical.

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