Multicomponent system predicted

There are many types of phase diagrams in addition to the two cases presented here these are summarized in detail by Zief and Wilcox (op. cit., p. 21). Solid-liquid phase equilibria must be determined experimentally for most binaiy and multicomponent systems. Predictive methods are based mostly on ideal phase behavior and have limited accuracy near eutectics. A predic tive technique based on extracting liquid-phase activity coefficients from vapor-liquid equilib-... 

Figure 12. Comparisons between predicted and experimental phase distribution for multicomponent systems (----), predicted. Experimental...

To predict vapor-liquid or liquid-liquid equilibria in multicomponent systems, we require a method for calculating the fugacity of a component i in a liquid mixture. At system temperature T and system pressure P, this fugacity is written as a product of three terms... 

The most recendy developed model is called UNIQUAC (21). Comparisons of measured VLE and predicted values from the Van Laar, Wilson, NRTL, and UNIQUAC models, as well as an older model, are available (3,22). Thousands of comparisons have been made, and Reference 3, which covers the Dortmund Data Base, available for purchase and use with standard computers, should be consulted by anyone considering the measurement or prediction of VLE. The predictive VLE models can be accommodated to multicomponent systems through the use of certain combining rules. These rules require the determination of parameters for all possible binary pairs in the multicomponent mixture. It is possible to use more than one model in determining binary pair data for a given mixture (23). 

Most distillation systems ia commercial columns have Murphree plate efficiencies of 70% or higher. Lower efficiencies are found under system conditions of a high slope of the equiHbrium curve (Fig. lb), of high Hquid viscosity, and of large molecules having characteristically low diffusion coefficients. FiaaHy, most experimental efficiencies have been for biaary systems where by definition the efficiency of one component is equal to that of the other component. For multicomponent systems it is possible for each component to have a different efficiency. Practice has been to use a pseudo-biaary approach involving the two key components. However, a theory for multicomponent efficiency prediction has been developed (66,67) and is amenable to computational analysis. 

Both UNIFAC and ASOG are typically generalized to multicomponent systems in commercial software packages. An important feature of these methods is that only binary interaction information is used to generate multicomponent predictions. 

Problem Solving Methods Most, if not aU, problems or applications that involve mass transfer can be approached by a systematic-course of action. In the simplest cases, the unknown quantities are obvious. In more complex (e.g., iTmlticomponent, multiphase, multidimensional, nonisothermal, and/or transient) systems, it is more subtle to resolve the known and unknown quantities. For example, in multicomponent systems, one must know the fluxes of the components before predicting their effective diffusivities and vice versa. More will be said about that dilemma later. Once the known and unknown quantities are resolved, however, a combination of conservation equations, definitions, empirical relations, and properties are apphed to arrive at an answer. Figure 5-24 is a flowchart that illustrates the primary types of information and their relationships, and it apphes to many mass-transfer problems. 

Wilson s [77] equation has been found to be quite accurate in predicting the vapor-liquid relationships and activity coefficients for miscible liquid systems. The results can be expanded to as many components in a multicomponent system as may be needed without any additional data other than for a binary system. This makes Wilson s and... 

The equation of Krichevsky and Ilinskaya can readily be extended to high-pressure solutions of a gas in a mixed solvent, as shown by O Connell (01) and discussed briefly by Orentlicher (03). This extension makes it possible to predict the behavior of simple multicomponent systems using binary data only. 

In emulsion and foam technology much is known concerning the properties and behavior of systems which involve only two or three components. Given a particular system and data concerning concentration, temperature, and manner of mixing, we can today predict fairly well the properties of the comparatively simple emulsion or foam. However, most emulsions and foams of importance are multicomponent systems and in these systems the predictability of the action or the properties of the emulsion or foam on a theoretical basis often becomes small. 

The prediction methods given in the following sections, and those available in the open literature, are invariably restricted to binary systems. It is clear that in a binary system the efficiency obtained for each component must be the same. This is not so for a multicomponent system the heavier components will usually exhibit lower efficiencies than the lighter components. 

The prediction of efficiencies for multicomponent systems is also discussed by Chan and Fair (1984b). For mixtures of dissimilar compounds the efficiency can be very different... 

Chan, H. and Fair, J. R. (1984b) Ind. Eng. Chem. Proc. Des. Dev. 23, 820. Prediction of point efficiencies on sieve trays. 2. multicomponent systems. 

Although the methods developed here can be used to predict liquid-liquid equilibrium, the predictions will only be as good as the coefficients used in the activity coefficient model. Such predictions can be critical when designing liquid-liquid separation systems. When predicting liquid-liquid equilibrium, it is always better to use coefficients correlated from liquid-liquid equilibrium data, rather than coefficients based on the correlation of vapor-liquid equilibrium data. Equally well, when predicting vapor-liquid equilibrium, it is always better to use coefficients correlated to vapor-liquid equilibrium data, rather than coefficients based on the correlation of liquid-liquid equilibrium data. Also, when calculating liquid-liquid equilibrium with multicomponent systems, it is better to use multicomponent experimental data, rather than binary data. 

Fowle and Fein (1999) measured the sorption of Cd, Cu, and Pb by B. subtilis and B. licheniformis using the batch technique with single or mixed metals and one or both bacterial species. The sorption parameters estimated from the model were in excellent agreement with those measured experimentally, indicating that chemical equilibrium modeling of aqueous metal sorption by bacterial surfaces could accurately predict the distribution of metals in complex multicomponent systems. Fein and Delea (1999) also tested the applicability of a chemical equilibrium approach to describing aqueous and surface complexation reactions in a Cd-EDTA-Z . subtilis system. The experimental values were consistent with those derived from chemical modeling. 

Brown, T. H. and B. J. Skinner, 1974, Theoretical prediction of equilibrium phase assemblages in multicomponent systems. American Journal of Science 274, 961-986. 

In developing the thermodynamic framework for ECES, we attempted to synthesize computer software that would correctly predict the vapor-liquid-solid equilibria over a wide range of conditions for multicomponent systems. To do this we needed a good basis which would make evident to the user the chemical and ionic equilibria present in aqueous systems. We chose as our cornerstone the law of mass action which simply stated says "The product of the activities of the reaction products, each raised to the power indicated by its numerical coefficient, divided by the product of the activities of the reactants, each raised to a corresponding power, is a constant at a given temperature. ... 

As can be seen less than 2% error in this multicomponent system occurred when using ECES. This system is quite different than the NH3-CO2-H2O system since we are dealing only with strong electrolytes. For example, the second datum point predicted by ECES give the following results for the concentrations, activity coefficients and water activity in the aqueous phase. 

COMPARISON OF PREDICTED AND EXPERIMENTAL WATER CONTENTS OF MULTICOMPONENT SYSTEMS (From Reference 2)... 

Our results lead to good predictions of activity coefficients in multicomponent systems from data measured 1n simple solutions. Also, they yield values similar to those of Pitzer and Kim (8 ) as is shown in Table II. 

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