Mixture Isotherms

Ideal Adsorbed Solution Theory. Perhaps the most successful approach to the prediction of multicomponent equiUbria from single-component isotherm data is ideal adsorbed solution theory (14). In essence, the theory is based on the assumption that the adsorbed phase is thermodynamically ideal in the sense that the equiUbrium pressure for each component is simply the product of its mole fraction in the adsorbed phase and the equihbrium pressure for the pure component at the same spreadingpressure. The theoretical basis for this assumption and the details of the calculations required to predict the mixture isotherm are given in standard texts on adsorption (7) as well as in the original paper (14). Whereas the theory has been shown to work well for several systems, notably for mixtures of hydrocarbons on carbon adsorbents, there are a number of systems which do not obey this model. Azeotrope formation and selectivity reversal, which are observed quite commonly in real systems, ate not consistent with an ideal adsorbed... 

Many simple systems that could be expected to form ideal Hquid mixtures are reasonably predicted by extending pure-species adsorption equiUbrium data to a multicomponent equation. The potential theory has been extended to binary mixtures of several hydrocarbons on activated carbon by assuming an ideal mixture (99) and to hydrocarbons on activated carbon and carbon molecular sieves, and to O2 and N2 on 5A and lOX zeoHtes (100). Mixture isotherms predicted by lAST agree with experimental data for methane + ethane and for ethylene + CO2 on activated carbon, and for CO + O2 and for propane + propylene on siUca gel (36). A statistical thermodynamic model has been successfully appHed to equiUbrium isotherms of several nonpolar species on 5A zeoHte, to predict multicomponent sorption equiUbria from the Henry constants for the pure components (26). A set of equations that incorporate surface heterogeneity into the lAST model provides a means for predicting multicomponent equiUbria, but the agreement is only good up to 50% surface saturation (9). 

Fig. 50. TG curve showing the formation of alumina whiskers during oxidation of iron-aluminum alloy in wet hydrogen (2%)/argon mixture (isothermal at 1555 °C). Sample weight 1000 mg...

The only information needed to predict the mixture surfactant concentration to attain a specified adsorption level is the pure component adsorption isotherms measured at the same experimental conditions as the mixture isotherms. These isotherms are needed to obtain the pure component standard states. 

The five mixtures isotherms are linear combinations of the pure materials isotherms. At any pressure, the adsorbed volume is proportional to the weight percentages of each pure compound. This result is statistically confirmed hy an test with a threshold of 1%. The closing of the hysteresis loop always occurs at the same pressure and its height is proportional to the weight percentage of alumina in the mixture. 

Pressure Swing Adsorption (PSA) unit is a dynamic separation process. In order to create a precise model of the process and thus an accurate design, it is necessary to have a good knowledge of the mixture s adsorption behaviour. Consequently, the dilAision rates in the adsorbent particles and the mixture isotherms are extremely vital data. This article intends to present a new approach to study the adsorption behaviour of isomer mixtures on zeolites. In a combined simulation and experimental project we set out to assess the sorption properties of a series of zeolites. The simulations are based on the configurational-bias Monte Carlo technique. The sorption data are measured in a volumetric set-up coupled with an online Near Infra-Red (NIR) spectroscopy, to monitor the bulk composition. Single component isotherms of butane and iso-butane were measured to validate the equipment, and transient volumetric up-take experiments were also performed to access the adsorption kinetics. 

Presently, there are no methods that allow the theoretical calculation of isotherms. However, there are methods available that allow the calculation of mixture isotherms... 

This chapter considers the vapor-liquid equilibrium of mixtures, conditions for bubble and dew points of gaseous mixtures, isothermal equilibrium flash calculations, the design of distillation towers with valve trays, packed tower design. Smoker s equation for estimating the number of plates in a binary mixture, and finally, the computation of multi-component recovery and minimum trays in distillation columns. 

In this equation c is the mixture isothermal compressibility, and the and Ki are the component mole fractions and isothermal compressibilities at the same temperature and pressure as the mixture. Values of A were derived from VE(P, T, x) in Reference 11. This quantity was quite large for all the systems studied (10,11). Whereas the maximum VE observed was on the order of 10% of the mixture V, the maximum A M... 

Three methods were tested for calculating mixture isothermal compressibilities. The first used a mole fraction average of component values ... 

In Table VII a comparison is made between root mean square deviations from experimental binary data for the three methods. Experimental mixture isothermal compressibilities were taken from Appendix B of Reference 11. Component values for use in Equation 24 came from Appendix A of the same reference. Use of values from the correlation would have yielded slightly higher deviations for the systems containing N2. 

It is generally much better to use the Equation 25 approach than the mole-fraction average of the component values to obtain mixture isothermal compressibilities. Very little is gained by trying to optimize the deviation parameters to binary data. It would appear that = 0 is a satisfactory approximation in this method. 

Table VII. Root Mean Square Deviations (GPa-1) between Calculated Mixture Isothermal Compressibilities and Experimental Values from Reference 11, pp. 166—184, and Optimum Deviation Parameters (j) for Equation 26...

There are several methods available that allow the prediction of mixture isotherms based on general single-component information. An application can significantly reduce the necessary number of experiments. The most successful approach is the ideal adsorbed solution (IAS) theory initially developed by Myers and Prausnitz (1965) to describe competitive gas phase adsorption. This theory was subsequently extended by Radke and Prausnitz (1972) to quantify adsorption from dilute (i.e., also ideal) solutions. 

As with the selection of a suitable single-component adsorption isotherm model, a final decision about the accuracy and validity of this attractive approach to predict mixture isotherms has to be based on the results of a critical comparison between simulated and measured concentration profiles. 

Separating variables and integrating along the mixture isotherm at fixed composition, we find... 

The M-S approach allows the prediction of the mixture diffusion based on the pure component M-S diffusivities, along with the mixture isotherms (i.e., estimated using the ideal adsorbed solution theory [lAST] of Myers and Prausnitz) [101]. Experimentally, the NMR pulse field gradient technique has been used to calculate the mixture diffusion coefficients. 

The CQ2/N2 mixture isotherm calculated by the IAS model is shown in Figure 12 to give an excellent fit to that obtained expaimentally. 

Prediction of the mixture isotherm in this way requires experimental singlecomponent isotherm data for the less strongly adsorbed species up to pres-... 

Table 8.11. Pure-component ratio and separation factor (based on mixture isotherms) for benzene/cyclohexane, all at 0.1 atm...

Filippov, L.K., Coherent and incoherent frontal patterns for multi-component dynamics of adsorption Analysis of frontal-pattern isothermal dynamics for convex mixture isotherms of adsorption, Chem. Eng, Sci.. 47(5), 1199-1210(1992). 

The extended Langmuir (Markham-Benton) isotherm has limited applicability especially for liquid phase adsorption, since even singlecomponent isotherms in liquid phase are rarely explained by the Langmuir equation. There have been several trials to extend the Freundlich type equation to mixture isotherms. Fritz and Schliinder (1974) gave the following equation. 

In the previous chapter we have shown that our model gives a satisfactory description of the adsorption isotherms of pure n-alkanes and 2-methylalkanes for C4-C9 on Silicalite. In this chapter, we investigate the mixture isotherms of various alkane isomers. Experimentally, the measurement of an isotherm is more complicated for mixtures than for pure components. One not only has to measure the weight increase of the zeolite as a function of pressure, but also the change in composition of the gas mixture. To the best of our knowledge, only adsorption isotherms of mixtures of short alkanes have been measured [149, 205]. In ref. [148] we have shown that for mixtures of ethane and methane our model gives a reasonable prediction of the mixture isotherms. Here we concentrate on the mixtures of C4 through C7 isomers. 

Using the Maxwell-Stefan theory, we will closer investigate the influence of isotherm inflection on the diffusivity. When we assume that the Maxwell-Stefan diffusion coefficient (sometimes also called the corrected diffusion coefficient) is independent of the loading, the loading dependence of the conventional Pick diffusion coefficient will be completely determined by the adsorption isotherm. We will demonstrate that on the basis of mixture isotherms we can predict the membrane permeation efficiency without having to know the diffusion coefficients exactly. 

In the previous chapter, we have focussed on adsorption of pure linear and branched cdkcines on Silicalite and found that our model is able to reproduce experimental data very well. Here, we will use the same model and simulation technique to study mixtures. In figures 5.1-5.4, the mixture isotherms of C4, C5, Cg, and C7 isomers are presented. We focus on a mixture of a linear alkane and the 2-methyl isomer with a 50%-50% mixture in the gas phase. Details about these simulations can be found in chapter 4. For all mixtures we see the following trends. At low pressure the linear and branched alkanes adsorb independently. The adsorption of the two components is proportional to the Henry coefficients of the pure components. At a total mixture loading of 4 molecules per unit cell the adsorption of the branched alkanes reaches a maximum and decreases with increasing pressure. For C5, Cg and C7 mixtures, the branched alkane is completely removed from the zeolite. The adsorption of the linear alkanes however increases with increasing pressure till saturation is reached. 

There is an important advantage in being able to describe the inflection behavior accurately with the help of the dual-site Langmuir model (DSL) this is because it would then be possible to predict the mixture isotherm from only pure component data. For single components, we have... 

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