Equilibrium ideal Langmuir model

Fundamentals of sorption and sorption kinetics by zeohtes are described and analyzed in the first Chapter which was written by D. M. Ruthven. It includes the treatment of the sorption equilibrium in microporous sohds as described by basic laws as well as the discussion of appropriate models such as the Ideal Langmuir Model for mono- and multi-component systems, the Dual-Site Langmuir Model, the Unilan and Toth Model, and the Simphfied Statistical Model. Similarly, the Gibbs Adsorption Isotherm, the Dubinin-Polanyi Theory, and the Ideal Adsorbed Solution Theory are discussed. With respect to sorption kinetics, the cases of self-diffusion and transport diffusion are discriminated, their relationship is analyzed and, in this context, the Maxwell-Stefan Model discussed. Finally, basic aspects of measurements of micropore diffusion both under equilibrium and non-equilibrium conditions are elucidated. The important role of micropore diffusion in separation and catalytic processes is illustrated. 

At higher loadings (beyond the Henry s law region) the equilibrium isotherms for microporous adsorbents are generally of Type I form in Brunauer s classification [2]. Several different models have been suggested to represent such isotherms, the simplest being the ideal Langmuir expression [3] ... 

Figure 10.9 Comparison between the band profiles predicted by the ideal model and the numerical solution of the equilibrium-dispersive model for a Langmuir isotherm. Constant column efficiency, 2000 theoretical plates, (a) Classical C vs. f profile. Sample size given as loading factor, (b) Reduced profiles, plots of bC vs. (t — fo)/(fR,o — to)- Sample size given as apparent loading factor, m = [Icq/(1 + J q)] NLj. Similar chromatograms, corresponding to intermediate loading factors, are given in Figure 10.8.

Ideal Model, Shortcut for Langmuir Isotherms The procedure described so far requires a detailed knowledge of the adsorption equilibrium. Naturally, the more accurately the isotherm parameters have been determined, the more reliable are the obtained operating parameters ntj. However, as discussed in Section 6.5.7, experimental determination of isotherm parameters might consume quite a lot of time and substance. 

In contrast to the binary Langmuir or SSTM models, the ideal adsorbed solution theory does not lead to a simple explicit relation for the adsorbed-phase composition and loading in terms of the partial pressures. Calculation of the equilibrium for a particular gas-phase composition therefore requires a trial and error procedure. 

We estimated the N2 desorption characteristics from these zeolites under two idealized but common concepts of operation of PSA processes. They are (a) isothermal evacuation of an adsorbent column which is initially equilibrated with a binary gas mixture of N2 (yi=0,79) and O2 (y2=0.21), and (b) isothermal and isobaric desorption of pure N2 from an adsorbent column by flowing a stream of pure O2 (called purging) through the column. The adsorbers are initially at a pressure of one atmosphere and at a temperature of 30 C in both cases. Analytical model solutions are available for the above described desorption processes when they are carried out under local equilibrium conditions and when the adsorbates follow Langmuir isotherms [1,6]. 

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