Loading ratio correlation

EOS, LRC (loading ratio correlation), Dubinin-Radushkevich (D-R), and Dubinin-Astakhov (D-A) are more suitable. 

This three-parameter equation behaves linearly in the Henry s law region and reduces to the Langmuir isotherm for m = 1. Other well-known isotherms include the Langmuir-Freundlich isotherm or Sips isotherm [Sips,/. Chem. Phys., 16, 490 (1948) Koble and Corrigan, Ind. Eng. Chem., 44,383 (1952)] or loading ratio correlation with prescribed temperature dependence [Yon and Turnock, AlChE Symp. Sen, 67(117), 75 (1971)]... 

Loading, of fillers, 11 305-306 Loading amplitudes, fatigue and, 14 450 Loading cycles, 13 482 Loading Ratio Correlation (LRC) Method, 1 626, 628... 

Isotherm Models for Adsorption of Matures. Of the following models, all but the ideal adsorbed solution dieory (IAST) and the related heterogeneous ideal adsorbed solution theory (H1AST) have been shown to contain some thermodynamic inconsistencies. They include Markham and Benton, die Leavitt loading ratio correlation (LRC) method, lire ideal adsorbed solution (IAS) model, the heterogeneous ideal adsorbed solution theory (HIAST), and the vacancy solution model (VSM). 

The loading ratio correlation (LRC) method for correlation of pure component sorption therms and prediction of multi-component sorption therms. 

The Loading Ratio Correlation. The equilibrium sorption therms for the pure components are correlated to the LRC model (1), which can be stated in the following manner ... 

Coefficients in loading ratio correlation (LRC), defined by equations (2) and (3)... 

The problem of predicting multicomponent adsorption equilibria from single-component isotherm data has attracted considerable attention, and several more sophisticated approaches have been developed, including the ideal adsorbed solution theory and the vacancy solution theory. These theories provide useful quantitative correlations for a number of binary and ternary systems, although available experimental data are somewhat limited. A simpler but purely empirical approach is to use a modified form of isotherm expression based on Langmuir-Freundlich or loading ratio correlation equations ... 

The Sips and related LRC (loading ratio correlation) models fail to properly predict Henry s law behavior (as required for tliemiodynamic consistency) at the zero pressure limit (8). Tliemiodynamic inconsistency of the LRC model had also been noted by the original authors (17) nevertheless, the model has been found useful in predicting multicomponent performance from single component data and correlating multicomponent data (18). However, users of models lacking thermo dynamic consistency must take due care, particularly in extrapolation beyond the range of actual experimental data. 

Recognizing the deficiency of the extended Langmuir equation, despite its sound theoretical footing on basic thermodynamics and kinetics theories, and the empiricism of the loading ratio correlation, other approaches such as the ideal adsorbed solution theory of Myers and Prausnitz, the real adsorption solution theory, the vacancy solution theory and the potential theory have been proposed. In this section we will discuss the ideal adsorbed solution theory and we first develop some useful thermodynamic equations which will be used later to derive the ideal adsorbed solution model. 

The product iqmibi) corresponds to the initial slope of the isotherm, or Henry s constant K), for component i. Hence, the adsorbent selectivity is equivalent to the ratio of the initial slopes of the isotherms of the two components, or K1/K2. It should be noted that the selectivity has resulted in a constant value simply because of the nature of the Langmuir isotherm. If, however, a different model such as the loading ratio correlation (Eq. 3.5) is used, the selectivity is likely to be dependent on the operating pressures of the PSA cycle. 

Activated carbon has also been used as adsorbent, but in spite of having the highest adsorption capacity of all adsorbents, its selectivity is very poor [25]. More recently Yang and coworkers [26,27] have introduced a new type of ion-exchange resins for paraffin/olefin separations, the Ag+-Amberlyst. In this work, we focus on the adsorption process at the atmospheric pressure using 13X zeolite for the TSA case and the Ag -Amberlyst for the VSA case. The loading ratio correlation or LRC model was adopted to represent multicomponent equilihrium isotherm over both adsorbents, being the parameters shown in Table 2. 

The gas-solid adsorption equilibrium is represented with a loading ratio correlation or Nitta et al. model isotherms. 

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