Adsorption of Gas Mixtures: Effect of Energetic Heterogeneity The ideal adsorbed solution (IAS) theory of adsorption of gas mix- tures is extended to the case of energetic heterogeneity. A heteroge- neous ideal adsorbed solution (HIAS) behaves ideally on a particular site, but energetic heterogeneity causes a segregation in the composi- tion of the adsorbed phase. Equilibrium properties are obtained by inte- grating over a multivariate energy distribution based upon perfect posi- tive correlation of site energies. The fact that predictions from HlAS are always an improvement over IAS indicates that heterogeneity is a factor that must be considered in theories of mixed-gas adsorption. Errors in HlAS predictions may be caused by steric exclusion of the larger mole- cules from micropores accessible to smaller molecules. Introduction zyxwvutsrqp Langmuir (191 8) was the first to recognize the importance of the spatial variation of the potential energy of adsorption, and Ross and Olivier (1964) established the methodology for studying heterogeneity of solid adsorbents in terms of an adsorp- tion integral equation. Several recent reviews (House, 1983; Jaroniec and Brauer, 1986) were devoted to surface heterogene- ity and numerical techniques for solving the integral equation for the energy distribution. Hoory and Prausnitz (1967) were the first to extend the adsorption integral equation to mixtures. They studied the bivariant Gaussian distribution, and Jaroniec and Borbwko (1 977) used the bivariant log normal distribution. In both cases the appropriate energy distribution is derived from experimental data for single-gas adsorption, and a correlation parameter zyxwvuts p is used to fit data zyxwvutsrqp for binary gas adsorption. For adsorbates with similar chemical characteristics, such as CH4 and C2Hs, a strong correlation (p zyxwvutsrqpon = 1) between the energy distributions was obtained. A value of p = 0 means no correlation between adsorp- tive energies and randoin matching of sites. In the random case the bivariant energy distribution is the product of the energy dis- tributions of the individual gases (Jaroniec, 1975), but this is a “gross approximation” (House, 1983) and unrealistic from a physical point of view. This paper is a continuation of the work cited above. The HlAS method developed in this paper is thermodynamic in nature, in the sense that it is not associated with a specific D. P. Valenzuela, A. L. Myers Department of Chemical Engineering University of Pennsylvania Philadelphia, PA 19104 0. Talu Chemical Engineering Department Cleveland State University Cleveland, OH 44 1 15 I. Zwiebel Chemical and Bio Engineering Department Arizona State University Tempe, AZ 85287 energy distribution or a particular equation for the pure-gas adsorption isotherm. Adsorption Integral Equation The specific amount N (mol/kg) of a pure gas adsorbed on a heterogeneous adsorbent at pressure zyx P and temperature T is given by the integral (Ross and Olivier, 1964): N = zyxw r” n(T, P, dt zyx JO wheref(t) is the probability density function for the distribution of adsorptive energies, and n is the specific adsorption if the sur- face were homogenous and characterized by energy t. The individual amount Ni of ith component adsorbed on a heterogeneous surface from a gas mixture containing r compo- nents is (Jaroniec and Rudzinski, 1975): * g(C1, €2,. . . , e,) dtl dt,. . . dt, (2) g(tl, t2, . . . , t,) is the joint probability density function for the distribution of adsorption energies and y is the gas composition vector {y,, zyxwvu y,, . . . , y,}. The joint distribution reflects the fact that each site on the surface is characterized by r adsorption energies. n, is the amount of ith component that would be AIChE Journal March 1988 Vol. 34, No. 3 397