mathematical modeling of mass transfer during solid-liquid extraction in fixed, expanded and fluidized-bed columns

In this paper, modeling approaches were given for explaining mass transfer during solid-liquid extraction in continuous fixed, expanded, and fluidized-bed extractors. the first approach utilizes a differential mass balance-based model, focusing on the differential mass conservation within an element of fixed and expanded-bed columns. the second approach employs a model by applying a mass balance concept to a control volume of the fluidized-bed column. the differential mass balance method segments the column into well-mixed stages, with the fluid flowing axially in an ideal plug flow regime. the solute diffusion inside the porous particles is modeled using fick’s second law of diffusion. modeling parameters like the effective diffusivity and equilibrium concentration were estimated using the batch extraction experiments. these models were developed and validated using experimental column data involving the extraction of potassium bicarbonate from polyamide 6 pellets with distilled water as the solvent. the modeling results show a good agreement with experimental data.