The two-dimensional virial equation of state is used to describe the adsorbed phase on both homogeneous and heterogeneous surfaces. Heterogeneity is modeled by assuming that the adsorbent surface is composed of two patches. The adsorbed phase is assumed to be completely mobile, and the same virial coefficients represent adsorbate−adsorbate interactions on both patches. Experimental data for highly nonideal systems are accurately correlated using the two-patch model. A predictive approach is proposed for deducing the mixture coefficients from pure component parameters. The approach works reasonably well in predicting binary adsorption equilibria for simple systems.

Nonisothermal adsorption equilibrium data are described using the virial equation written as a polynomial function in adsorbed-phase loading and reciprocal temperature. This equation is written in terms of polynomials that are orthogonal to summation. As a result, application of the least-squares method to correlate experimental data becomes straightforward and simple, not even requiring any matrix algebra. Ill-conditioning of the normal equations for high-order polynomials is avoided. The model is successfully applied to describe nonisothermal data for different systems over a wide range of temperature and pressure.