Thermodynamic equilibrium in systems with multiple adsorbed and bulk phases

A new procedure is proposed for the calculation of adsorption equilibria in multicomponent systems. This methodology is capable of predicting equilibrium of one or more fluid phases with one or more adsorbed phases. The specifications are the total volume available for the bulk phases, the total area available for adsorption or total mass of adsorbent, the number of moles of each species, and the temperature. The problem is formulated and solved as a minimization of the total Helmholtz free energy, using the Peng-Robinson equation of state as a model for the bulk phases and a lattice-gas model for the adsorbed phases. As a result we obtain the number of moles of each species in each phase of the system, the volume occupied by each bulk phase and the area occupied by each adsorbed phase. There is excellent agreement between the results of our methodology and experimental data for a pure component and Monte Carlo simulation data for a binary mixture. In multicomponent systems, very interesting predictions of phase multiplicity of bulk and/or adsorbed phases are obtained. However, experimental data would be necessary to confirm the phase behavior predicted by the calculations presented here.