Thermodynamic Modeling of Adsorption Isotherms Using VST-UNIQUAC: A Novel Approach for Solid-Liquid Equilibrium

Abstract

Based on the vacancy solution theory (VST) and using the UNIQUAC activity coefficient model, a new adsorption isotherm model (VST-UNIQUAC) is developed for solid-liquid equilibrium systems. Following VST, the solid-liquid equilibrium system is considered as a solution consisting of the adsorbate and adsorbent where the adsorbate is the solute and vacancies play the role of the solvent. The UNIQUAC equation is used to account for the non-ideality or the solute-solvent interaction in the vacancy solution. The parameters of the proposed model are calculated by using the optimization of experimental data for different single-component adsorption systems at various temperatures. The new isotherm is used to correlate the isotherms of 12 different organic compounds on activated carbon, each one at different temperatures. The accuracy of the present isotherm is presented by the coefficient of determination (R²), average absolute deviation percent (AAD%), and root mean square error (RMSE) and compared with those results obtained using Wilson, Van Laar, and NRTL equations. It is shown that the proposed VST-UNIQUAC model correlates the adsorption equilibrium with significantly higher accuracy, achieving R² values consistently above 0.98 and AAD% values ranging from 2% to 17%, which is substantially better than the deviations obtained from other models. The VST-UNIQUAC isotherm demonstrates superior capability in describing adsorption behavior across different temperatures, making it a reliable tool for design and optimization of adsorption processes in industrial and environmental applications.                                                                                   

Keywords: Adsorption isotherm, Vacancy solution theory, Thermodynamics of adsorption, UNIQUAC, Activated carbon, Solid-liquid equilibrium