Vapor-liquid equilibrium construction

Since the boiling point properties of the components in the mixture being separated are so critical to the distillation process, the vapor-liquid equilibrium (VLE) relationship is of importance. Specifically, it is the VLE data for a mixture which establishes the required height of a column for a desired degree of separation. Constant pressure VLE data is derived from boiling point diagrams, from which a VLE curve can be constructed like the one illustrated in Figure 9 for a binary mixture. The VLE plot shown expresses the bubble-point and the dew-point of a binary mixture at constant pressure. The curve is called the equilibrium line, and it describes the compositions of the liquid and vapor in equilibrium at a constant pressure condition. 

The three sets of vapor-liquid equilibrium data appearing on the x-y diagram show some disagreement, so that great accuracy cannot be expected from determination of tray requirements, particularly at the low water concentrations. The upper operating line in the first column is determined by the overall material balance so it passes through point (0.995, 0.995), but the initial point on the operating line is at x = 0.53, which is the composition of the reflux. The construction is shown for 50% vaporized feed. That result and those for other feed conditions are summarized ... 

The calculations made thus far are of theoretical trays, that is, trays on which vapor-liquid equilibrium is attained for all components. Actual tray efficiencies vary widely with the kind of system, the flow rates, and the tray construction. The range can be from less than 10% to more than 100% and constitutes perhaps the greatest uncertainty in the design of distillation equipment. For hydrocarbon fractionation a commonly used efficiency is about 60%. Section 13.14 discusses this topic more fully. 

Because of the wide range of fixed x values for which data had been taken, it was possible to use interpolated data from Table II to construct a family of vapor-liquid equilibrium curves for the ammonium bromide-ethanol-water system at various constant salt concentration values—the condition most closely representing that existing from tray to tray in a... 

Your task in this problem will be to use a spreadsheet to generate a Txy diagram for a two-component system, using Raoult s law to express the vapor-liquid equilibrium distribution of each species. The spreadsheet will be constructed for the chloroform-benzene system at 1 atm (for which Raouit s law is not a very good approximation), but it can then be used for any other system by substituting different Antoine equation constants. 

Figure 3.5d shows the construction of a P-x diagram at temperature Tj, an isotherm that intersects the vapor pressure curve of the less volatile component, the LLV line, and both branches of the critical mixture curve (see figure 3.5b). At low pressures, a single vapor phase exists until the dew point curve of the vapor-liquid envelope is intersected and a liquid phase is formed. Vapor-liquid equilibrium is observed as the pressure is increased further until the three-phase LLV line is intersected, indicated by the horizontal tie line shown in figure 3.5d. There now exists a single vapor phase and two liquid phases. 

Note the difference between this method of calculation and the one used in the previous illustration. There we did vapor-liquid equilibrium calculations only for the conditions needed, and then solved the mass balance equations analytically. In this illustration we first had to do vapor-liquid equilibrium calculations for all compositions (to construct the. t- v diagram), and then for this binary mixture we were able to do all further calculations graphically. As shown in the following discussion, this makes it easier to consider other reflux ratios than the one u.sed in this illustration. 

Construction of Vapor-Liquid Equilibrium Diagrams for a Nonideal System... 

Figure 8.1.20. Vapor-liquid equilibrium curve, operating lines for enriching section and stripping section and construction of ideal stages and q Une for a feed consisting of vapor and liquid in a multistage distillation column having ideal equilibrium stages the McCabe-Thiele method.

Previously we have said little about g° other than that it was a function of temperature only and that each species had its own value of g°. We discussed standard states in Chapters 7, 8, and 9. A standard state is some state of matter that we will all agree upon as a suitable basis for constructing tables of properties. For most chemical reaction purposes we choose the standard state of some substance as the pure substance in its normal state (solid, liquid, or gas) at F = 1 atm or 1 bar, and an arbitrarily chosen T, normally = 25°C = 298.15 K for the tables of interest in this chapter. Alas, there are other standard states that are much more convenient for some problems, as discussed previously for vapor-liquid equilibrium calculations. However, if we put off for the moment saying what our standard state is, we can use the symbol ° to indicate a property in the standard state, and then say that, for any pure chemical element or compound (pure species) the partial molar Gibbs energy is the same as the pure species Gibbs energy, and in its standard state... 

Development of the turbo-expander process allowed design and construction of plants for recovery of liquid ethane, as well as the heavier hydrocarbon components. The turbo-expander extracts work from the gas during expansion from a high pressure to a lower pressure. Because of the work extraction the gas is cooled, and, by means of suitable heat exchange, temperatures as low as — 150°F (— 100°C) can easily be achieved. The separation at low pressure gives higher relative values of the vapor-liquid equilibrium constant... 

In vapor-liquid equilibria, it is relatively easy to start the iteration because assumption of ideal behavior (Raoult s law) provides a reasonable zeroth approximation. By contrast, there is no obvious corresponding method to start the iteration calculation for liquid-liquid equilibria. Further, when two liquid phases are present, we must calculate for each component activity coefficients in two phases since these are often strongly nonlinear functions of compositions, liquid-liquid equilibrium calculations are highly sensitive to small changes in composition. In vapor-liquid equilibria at modest pressures, this sensitivity is lower because vapor-phase fugacity coefficients are usually close to unity and only weak functions of composition. For liquid-liquid equilibria, it is therefore more difficult to construct a numerical iteration procedure that converges both rapidly and consistently. 

The design equations would include, in addition to the usual heat and mass balances and vapor-liquid equilibria, equations for chemical equilibria and/or reaction kinetics. The occurrence of a chemical reaction can severely restrict the allowable ranges of temperatures and phase compositions by virtue of the additional equations for chemical equilibrium/kinetics. This effect can be quantitatively analyzed by constructing a residue curve map (RCM). It explicitly shows the shifting of distillation boundaries in the presence of reaction and defines the limits of feasible distillation column operation. We illustrate this (Venimadhavan et al., 1994) by considering the reaction... 

To have a simple example, we consider an alkane(l) + aromatic(2) mixture, modeled by the Redlich-Kwong equation (8.2.1). Certain vapor-liquid phase diagrams for this mixture were displayed and discussed in 9.3. Here our objective is to compute residual enthalpies for vapor and liquid that coexist in equilibrium in particular, we want to construct an isothermal plot of vs. x and y. (We will call this an hxy diagram, even though it is that is actually plotted.) To do so, we set the temperature, pick a liquid composition Xp and then perform a bubble-P calculation to obtain values... 

With the chemical potential and pressure obtained in the form of the closed expressions (4.A.9) and (4.A.11) in Chapter 4, the phase coexistence envelope can be localized directly by solving the mechanical and chemical equilibrium conditions (1.134) and (1.135) for the vapor and liquid phase densities, Pvap and puq, whether or not the solution exists for all intermediate densities. Provided the isotherm is continuous across all the region of vapor-liquid phase coexistence, Eqs.(1.134) and (1.135) are exactly equivalent to the Maxwell construction on either pressure or chemical potential isotherm. This stems from the fact that the RISM/KH theory yields an exact differential for the free energy function (4.A. 10) in Chapter 4, which thus does not depend on a path of thermodynamic integration. 

Fig. 2-11. h, x-Diagram of a binary mixture including liquid phase and vapor phase (a). Construction of bubble point line and dew point line in the h, x-diagram using a boiling diagram (b). A, A2 and Bj, B2 state points of liquid phase and vapor phase in equilibrium. h Enthalpy... 

Figure 9.12 Vapor-liquid phase equilibrium in a benzene-toluene solution as a function of pressure at 23°C. (a) The total vapor pressure as a function of the mole fraction of benzene in the liquid, (b) The total vapor pressure as a function of the mole fraction of benzene in the vapor, (c) The pressure-composition phase diagram constructed by combining plots (a) and (b). The line/-g is the tie line corresponding to the system at point c.

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