Liquid phases equilibrium predictions

At equilibrium, in order to achieve equality of chemical potentials, not only tire colloid but also tire polymer concentrations in tire different phases are different. We focus here on a theory tliat allows for tliis polymer partitioning [99]. Predictions for two polymer/colloid size ratios are shown in figure C2.6.10. A liquid phase is predicted to occur only when tire range of attractions is not too small compared to tire particle size, 5/a > 0.3. Under tliese conditions a phase behaviour is obtained tliat is similar to tliat of simple liquids, such as argon. Because of tire polymer partitioning, however, tliere is a tliree-phase triangle (ratlier tlian a triple point). For smaller polymer (narrower attractions), tire gas-liquid transition becomes metastable witli respect to tire fluid-crystal transition. These predictions were confinned experimentally [100]. The phase boundaries were predicted semi-quantitatively. 

We are interested in comparing the effectiveness of the various equations of state in predicting the (p. V. T) properties. We will limit our comparisons to Tr > 1 since for Tr < 1 condensations to the liquid phase occur. Prediction of (vapor + liquid) equilibrium would be of interest, but these predictions present serious problems, since in some instances the equations of state do not converge for Tr< 1. 

Consistent vapor-liquid equilibrium data are necessary to design all types of rectification devices. However, many industrially important mixtures are nonideal, particularly in the liquid phase, and predicting their equilibrium properties from fundamental thermodynamics is not possible. Thus, the correlating of experimental x-y-t and x-y-P data has developed as an important branch of applied thermodynamics. 

Overall, we consider the approximate group contribution-EOS-based models considered here to be promising for the prediction of gas-liquid phase equilibrium. Future... 

There are no experimental liquid-liquid phase equilibrium data for the isobutane-furfural system with which we can compare our predictions. However, binary mixtures of furfural and, separately, 2.2-dimethyl pentane, 2-methyl pentane, and hexane, which are similar to the binary mixture here, all exhibit liquid-liquid phase separation, with one phase containing between 89 and 90 mol T furfural (.vi) and the other between 6 and 7 mol % furfural (.v ). 

The discussion so far has been restricted to gas-phase reactions. One reason for this is that a large number of reactions, including many high-temperature reactions (except metallurgical reactions), occur in the gas phase. Also, the identification of the equilibrium state is easiest for gases, as nonidealities are,.generally less important than in liquid-phase reactions. However, many reactions of interest to engineers occur in the liquid phase.- The prediction of the equilibrium state in such cases can be complicated if the only information available is iifa or since liquid solutions are rarely ideal,... 

Both adsorption from a supercritical fluid to an adsorbent and desorption from an adsorbent find applications in supercritical fluid processing. The extrapolation of classical sorption theory to supercritical conditions has merits. The supercritical conditions are believed to necessitate monolayer coverage and density dependent isotherms. Considerable success has been observed by the authors in working with an equation of state based upon the Toth isoterm. It is also important to note that the retrograde behavior observed for vapor-liquid phase equilibrium is experimentally observed and predicted for sorptive systems. 

Pappa, G.D., Voutsas, E.C., and Tassios, D.P., 2001. Liquid-liquid phase equilibrium in polymer-solvent systems Correlation and prediction of the polymer molecular weight and the pressure effect. Ind. Eng. Chem. Res., 40(21) 4654. 

Short-chain branching is being used to modify properties of polyethylene and also plays an important role in liquid-liquid phase equilibrium in polymer solutions. Phase behavior during polymer production by solution (co)polymerization will therefore be affected by the molecular architecture and quantities like separation temperature and/or pressure as a function of, for instance, monomer conversion should preferably be predictable by model calculations. 

Using UNIQUAC, Table 2 summarizes vapor-liquid equilibrium predictions for several representative ternary mixtures and one quaternary mixture. Agreement is good between calculated and experimental pressures (or temperatures) and vapor-phase compositions. ... 

Two generally accepted models for the vapor phase were discussed in Chapter 3 and one particular model for the liquid phase (UNIQUAC) was discussed in Chapter 4. Unfortunately, these, and all other presently available models, are only approximate when used to calculate equilibrium properties of dense fluid mixtures. Therefore, any such model must contain a number of adjustable parameters, which can only be obtained from experimental measurements. The predictions of the model may be sensitive to the values selected for model parameters, and the data available may contain significant measurement errors. Thus, it is of major importance that serious consideration be given to the proper treatment of experimental measurements for mixtures to obtain the most appropriate values for parameters in models such as UNIQUAC. 

This equation may be applied separately to the liquid phase and to the vapor phase to yield the pure-species values ( ) and ( ) For vapor/ liquid equilibrium (Eq. [4-280]), these two quantities are equal. Given parameters Oj and bj, the pressure P in Eq. (4-230) that makes these two values equal is the equihbrium vapor pressure of pure species i as predicted by the equation of state. 

For most LLE applications, the effect of pressure on the Yi < an be ignored, and thus Eq. (4-327) constitutes a set of N equations relating equilibrium compositions to each other and to temperature. For a given temperature, solution of these equations requires a single expression for the composition dependence of suitable for both liquid phases. Not all expressions for suffice, even in principle, because some cannot represent liquid/liquid phase splitting. The UNIQUAC equation is suitable, and therefore prediction is possible by the UNIFAC method. A special table of parameters for LLE calculations is given by Magnussen, et al. (Jnd E/ig Chem Process Des Dev, 20, pp. 331-339 [1981]). 

Figure 8.23 (Solid + liquid) phase diagram for (. 1CCI4 +. yiCHjCN), an example of a system with large positive deviations from ideal solution behavior. The solid line represents the experimental results and the dashed line is the ideal solution prediction. Solid-phase transitions (represented by horizontal lines) are present in both CCI4 and CH3CN. The CH3CN transition occurs at a temperature lower than the eutectic temperature. It is shown as a dashed line that intersects the ideal CH3CN (solid + liquid) equilibrium line.

The vapor-liquid x-y diagram in Figures 4.6c and d can be calculated by setting a liquid composition and calculating the corresponding vapor composition in a bubble point calculation. Alternatively, vapor composition can be set and the liquid composition determined by a dew point calculation. If the mixture forms two-liquid phases, the vapor-liquid equilibrium calculation predicts a maximum in the x-y diagram, as shown in Figures 4.6c and d. Note that such a maximum cannot appear with the Wilson equation. 

Example 4.6 Mixtures of water and 1-butanol (n-butanol) form two-liquid phases. Vapor-liquid equilibrium and liquid-liquid equilibrium for the water-1-butanol system can be predicted by the NRTL equation. Vapor pressure coefficients in bar with temperature in Kelvin for the Antoine equation are given in Table 4.136. Data for the NRTL equation are given in Table 4.14, for a pressure of 1 atm6. Assume the gas constant R = 8.3145 kJ-kmoL -K-1. 

Care should be exercised in using the coefficients from Table 4.14 to predict two-liquid phase behavior under subcooled conditions. The coefficients in Table 4.14 were determined from vapor-liquid equilibrium data at saturated conditions. 

For the following mixtures, suggest suitable models for both the liquid and vapor phases to predict vapor-liquid equilibrium, a. H2S and water at 20° C and 1.013 bar. 

Mixtures of 2-butanol (.sec-butanol) and water form two-liquid phases. Vapor-liquid equilibrium and liquid-liquid equilibrium for the 2-butanol-water system can be predicted by the NRTL equation. Vapor pressure coefficients for the... 

The phenomenon of critical flow is well known for the case of single-phase compressible flow through nozzles or orifices. When the differential pressure over the restriction is increased beyond a certain critical value, the mass flow rate ceases to increase. At that point it has reached its maximum possible value, called the critical flow rate, and the flow is characterized by the attainment of the critical state of the fluid at the throat of the restriction. This state is readily calculable for an isen-tropic expansion from gas dynamics. Since a two-phase gas-liquid mixture is a compressible fluid, a similar phenomenon may be expected to occur for such flows. In fact, two-phase critical flows have been observed, but they are more complicated than single-phase flows because of the liquid flashing as the pressure decreases along the flow path. The phase change may cause the flow pattern transition, and departure from phase equilibrium can be anticipated when the expansion is rapid. Interest in critical two-phase flow arises from the importance of predicting dis-... 

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