Efficient calculation of the equilibrium composition in multicomponent batch adsorption with the steric mass action model

Streamlined relationships are derived to predict the equilibrium composition in batch adsorption when the isotherm is described by the steric mass action (SMA) model, which is used extensively to represent macromolecule adsorption on ion exchange resins. In the general case with N components, the approach reduces the mathematical problem from a system of 2N equations to a single non-linear algebraic equation whose numerical solution is easily found. A graphical approach is also presented where isotherm lines describing mixture equilibrium values of the adsorbed concentrations of each component are plotted against the equilibrium solution concentration of a common reference species. In this case, the actual equilibrium composition is obtained at the intercept of the reference component equilibrium curve with the straight line representing the material balance for the reference species. Analytical expressions are provided for two and three-component mixtures. The graphical approach provides insight on the effects of the ratio of adsorbent and solution volumes on the equilibrium composition.