The main purpose of this investigation is to model the results related to biosorption using COMSOL (Multiphysics 4.3a), and to solve the advection-dispersion equation by using both linear and Langmuir models. A bidimensional model was then proposed to study the mass transfer in the process of copper ions sorption in a dynamic mode on cider vinegar residues. Sorption tests were realized by evaluating the influence of flow rate (0.75, 1, and 2.65 ml min-1 ), bed height (3.5, 7 and 8.5 cm), and copper initial concentration (169 and 300 mg L-1 ). For all cases, the mathematical formulation was solved by assuming that the column is homogeneous and the sorption is instantaneous. The corresponding results were exploited through breakthrough curve profiles, where it was shown that the solutions obtained by the "Langmuir COMSOL" model coincide with the experimental values. In contrast, the linear model has been unable to fit them. The optimal results were analyzed by Thomas, Adam-Bohart Yoon Nelson, and Ogata-Bank models, which proves that the Thomas method is well adapted with a satisfactory correlation coefficient (0.93). Further, the model validation was performed by determining the residual root mean square error, which was found less than 0.3, thereby indicating a reasonable concordance between the estimated and experimental points. The high sorption capacity obtained was around of 41.37 mg g-1 , which suggests that the cider vinegar residues can be exploited as a low-cost, available, and effective sorbent biomass in the field of the treatment of industrial effluents. PRACTITIONER POINTS: Cider vinegar residues (CVR) as low cost biosorbent were studied for continuous biosorption. A successful COMSOL model was proposed and validated. CVR is an effective biosorbent for copper fixed bed biosorption. High sorption capacity was around of 41.37 mg g-1 under optimal conditions.
Keywords: COMSOL; biosorption; cider vinegar residues; copper; modeling.
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