Binary system, vapor-liquid

Obtain (or plot from data) a phase diagram for the benzene/toluene system. Vapor-liquid equilibrium behavior of binary systems can be represented by a temperature-composition diagram at... 

FKiURE IS Behavior of selected binary systems vapor and liquid compositions using Raoult s law at 1 atm. 

Literature references for vapor-liquid equilibria, enthalpies of mixing and volume change for binary systems. 

Two additional illustrations are given in Figures 6 and 7 which show fugacity coefficients for two binary systems along the vapor-liquid saturation curve at a total pressure of 1 atm. These results are based on the chemical theory of vapor-phase imperfection and on experimental vapor-liquid equilibrium data for the binary systems. In the system formic acid (1) - acetic acid (2), <() (for y = 1) is lower than formic acid at 100.5°C has a stronger tendency to dimerize than does acetic acid at 118.2°C. Since strong dimerization occurs between all three possible pairs, (fij and not... 

Figure 4-4. Representation of vapor-liquid equilibria for a binary system showing moderate positive deviations from Raoult s law.

An adequate prediction of multicomponent vapor-liquid equilibria requires an accurate description of the phase equilibria for the binary systems. We have reduced a large body of binary data including a variety of systems containing, for example, alcohols, ethers, ketones, organic acids, water, and hydrocarbons with the UNIQUAC equation. Experience has shown it to do as well as any of the other common models. V7hen all types of mixtures are considered, including partially miscible systems, the... 

Figure 4-7. Vapor-liquid equilibria and activity coefficients in a binary system showing a weak minimum in the activity coefficient of methanol.

Figure 4-8. Vapor-liquid equilibria for a binary system where both components solvate and associate strongly in the vapor phase.

To illustrate calculations for a binary system containing a supercritical, condensable component. Figure 12 shows isobaric equilibria for ethane-n-heptane. Using the virial equation for vapor-phase fugacity coefficients, and the UNIQUAC equation for liquid-phase activity coefficients, calculated results give an excellent representation of the data of Kay (1938). In this case,the total pressure is not large and therefore, the mixture is at all times remote from critical conditions. For this binary system, the particular method of calculation used here would not be successful at appreciably higher pressures. 

Our experience with multicomponent vapor-liquid equilibria suggests that for system temperatures well below the critical of every component, good multicomponent results are usually obtained, especially where binary parameters are chosen with care. However, when the system temperature is near or above the critical of one (or more) of the components, multicomponent predictions may be in error, even though all binary pairs are fit well. 

For systems of type II, if the mutual binary solubility (LLE) data are known for the two partially miscible pairs, and if reasonable vapor-liquid equilibrium (VLE) data are known for the miscible pair, it is relatively simple to predict the ternary equilibria. For systems of type I, which has a plait point, reliable calculations are much more difficult. However, sometimes useful quantitative predictions can be obtained for type I systems with binary data alone provided that... 

Figure 15 shows results for a difficult type I system methanol-n-heptane-benzene. In this example, the two-phase region is extremely small. The dashed line (a) shows predictions using the original UNIQUAC equation with q = q. This form of the UNIQUAC equation does not adequately fit the binary vapor-liquid equilibrium data for the methanol-benzene system and therefore the ternary predictions are grossly in error. The ternary prediction is much improved with the modified UNIQUAC equation (b) since this equation fits the methanol-benzene system much better. Further improvement (c) is obtained when a few ternary data are used to fix the binary parameters. 

In Equation (24), a is the estimated standard deviation for each of the measured variables, i.e. pressure, temperature, and liquid-phase and vapor-phase compositions. The values assigned to a determine the relative weighting between the tieline data and the vapor-liquid equilibrium data this weighting determines how well the ternary system is represented. This weighting depends first, on the estimated accuracy of the ternary data, relative to that of the binary vapor-liquid data and second, on how remote the temperature of the binary data is from that of the ternary data and finally, on how important in a design the liquid-liquid equilibria are relative to the vapor-liquid equilibria. Typical values which we use in data reduction are Op = 1 mm Hg, = 0.05°C, = 0.001, and = 0.003... 

Phase transitions in binary systems, nomially measured at constant pressure and composition, usually do not take place entirely at a single temperature, but rather extend over a finite but nonzero temperature range. Figure A2.5.3 shows a temperature-mole fraction T, x) phase diagram for one of the simplest of such examples, vaporization of an ideal liquid mixture to an ideal gas mixture, all at a fixed pressure, (e.g. 1 atm). Because there is an additional composition variable, the sample path shown in tlie figure is not only at constant pressure, but also at a constant total mole fraction, here chosen to be v = 1/2. 

Solute/Solvent Systems The gamma/phi approach to X T.E calculations presumes knowledge of the vapor pressure of each species at the temperature of interest. For certain binary systems species I, designated the solute, is either unstable at the system temperature or is supercritical (T > L). Its vapor pressure cannot be measured, and its fugacity as a pure liquid at the system temperature/i cannot be calculated by Eq. (4-281). 

Outlined below are the steps required for of a X T.E calciilation of vapor-phase composition and pressure, given the liquid-phase composition and temperature. A choice must be made of an equation of state. Only the Soave/Redlich/Kwong and Peng/Robinson equations, as represented by Eqs. (4-230) and (4-231), are considered here. These two equations usually give comparable results. A choice must also be made of a two-parameter correlating expression to represent the liquid-phase composition dependence of for each pq binaiy. The Wilson, NRTL (with a fixed), and UNIQUAC equations are of general applicabihty for binary systems, the Margules and van Laar equations may also be used. The equation selected depends on evidence of its suitability to the particular system treated. Reasonable estimates of the parameters in the equation must also be known at the temperature of interest. These parameters are directly related to infinite-dilution values of the activity coefficients for each pq binaiy. 

TABLE 13-1 Constant-Pressure Liquid-Vapor Equilibrium Data for Selected Binary Systems... 

Table 13-1, based on the binary-system activity-coefficient-eqnation forms given in Table 13-3. Consistent Antoine vapor-pressure constants and liquid molar volumes are listed in Table 13-4. The Wilson equation is particularly useful for systems that are highly nonideal but do not undergo phase splitting, as exemplified by the ethanol-hexane system, whose activity coefficients are snown in Fig. 13-20. For systems such as this, in which activity coefficients in dilute regions may...

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... 

Relative volatility is the volatility separation factor in a vapor-liquid system, i.e., the volatility of one component divided by the volatility of the other. It is the tendency for one component in a liquid mixture to separate upon distillation from the other. The term is expressed as fhe ratio of vapor pressure of the more volatile to the less volatile in the liquid mixture, and therefore g is always equal to 1.0 or greater, g means the relationship of the more volatile or low boiler to the less volatile or high boiler at a constant specific temperature. The greater the value of a, the easier will be the desired separation. Relative volatility can be calculated between any two components in a mixture, binary or multicomponent. One of the substances is chosen as the reference to which the other component is compared. 

Multicomponent distillations are more complicated than binary systems due primarily to the actual or potential involvement or interaction of one or more components of the multicomponent system on other components of the mixture. These interactions may be in the form of vapor-liquid equilibriums such as azeotrope formation, or chemical reaction, etc., any of which may affect the activity relations, and hence deviations from ideal relationships. For example, some systems are known to have two azeotrope combinations in the distillation column. Sometimes these, one or all, can be broken or changed in the vapor pressure relationships by addition of a third chemical or hydrocarbon. 

A minimum HETP or HTU represents a maximum separation efficiency with a representing the relative volatility, i.e., vapor and liquid phase compositions of the more volatile component in a binary system ... 

Vapor-Liquid Equilibria in Binary and Multicomponent Systems... 

It is known that the three-phase line H G in the binary system H2S-H20 lies below the liquid vapor line (LG) of pure H2S. Likewise, after addition of CHC13 the four-phase line lies... 

Increasing the temperature increases the vapor pressures and moves the liquid and vapor curves to higher pressure. This effect can best be seen by referring to Figure 8.14, which is a schematic three-dimensional representation for a binary system that obeys Raoult s law, of the relationship between pressure, plotted as the ordinate, mole fraction plotted as abscissa, and temperature plotted as the third dimension perpendicular to the page. The liquid and vapor lines shown in Figure 8.13 in two dimensions (with Tconstant)... 

So far, we have considered only one type of binary (liquid -I- liquid) equilibrium. Examples can be found in the literature where a lower critical end point (LCEP) is obtained instead of a UCEP, and where both a LCEP and a UCEP are obtained for the same system. Also, (liquid + liquid) equilibria can be combined with (vapor + liquid) equilibria to give interesting (fluid + fluid)... 

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 binary and multicomponent systems. Predictive methods are based mostly on ideal phase behavior and have limited accuracy near eutectics. A predictive technique based on extracting liquid-phase activity coefficients from vapor-liquid equilibria that is useful for estimating nonideal binary or multicomponent solid-liquid phase behavior has been reported by Muir (Pap. 71f, 73d ann. meet., AIChE, Chicago, 1980). 

Data at two temperatures were obtained from Zeck and Knapp (1986) for the nitrogen-ethane system. The implicit LS estimates of the binary interaction parameters are ka=0, kb=0, kc=0 and kd=0.0460. The standard deviation of kd was found to be equai to 0.0040. The vapor liquid phase equilibrium was computed and the fit was found to be excellent (Englezos et al. 1993). Subsequently, implicit ML calculations were performed and a parameter value of kd=0.0493 with a standard deviation equal to 0.0070 was computed. Figure 14.2 shows the experimental phase diagram as well as the calculated one using the implicit ML parameter estimate. 

Leu and Robinson (1992) reported data for this binary system. The data were obtained at temperatures of 0.0, 50.0, 100.0, 125.0, 133.0 and 150.0 °C. At each temperature the vapor and liquid phase mole fractions of isobutane were measured at different pressures. The data at 133.0 and 150.0 are given in Tables 14.9 and 14.10 respectively. The reader should test if the Peng-Robinson and the Trebble-Bishnoi equations of state are capable of describing the observed phase behaviour. First, each isothermal data set should be examined separately. 

Vapor-Liquid Equilibria of Coal-Derived Liquids Binary Systems with Tetralin... 

Blanco, B., S. Beltran, J.L. Cabezas, and J. Coca, "Vapor-Liquid Equilibria of Coal-Derived Liquids. 3. Binary Systems with Tetralin at 200 mrnHg", J. Chem. Eng. Data, 39,23-26 (1994). 

Schwartzentruber J., F. Galivel-Solastiuk and H. Renon, "Representation of the Vapor-Liquid Equilibrium of the Ternary System Carbon Dioxide-Propane-Methanol and its Binaries with a Cubic Equation of State. A new Mixing Rule", Fluid Phase Equilibria, 38,217-226 (1987). 

Zeck S., and H. Knapp, "Vapor-Liquid and Vapor-Liquid-Liquid Phase Equilibria for Binary and Ternary Systems of Nitrogen, Ethane and Methanol Experiments and Data Reduction", Fluid Phase Equilibria, 25,303-322 (1986). 

Solution To determine the location of the azeotrope for a specified pressure, the liquid composition has to be varied and a bubble-point calculation performed at each liquid composition until a composition is identified, whereby X = y,-. Alternatively, the vapor composition could be varied and a dew-point calculation performed at each vapor composition. Either way, this requires iteration. Figure 4.5 shows the x—y diagram for the 2-propanol-water system. This was obtained by carrying out a bubble-point calculation at different values of the liquid composition. The point where the x—y plot crosses the diagonal line gives the azeotropic composition. A more direct search for the azeotropic composition can be carried out for such a binary system in a spreadsheet by varying T and x simultaneously and by solving the objective function (see Section 3.9) ... 

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