Vapor-Liquid Equilibrium VLE at Low Pressures

This chapter discusses low-pressure VLE. At high pressures, VLE is different, mostiy because we approach the critical pressures of the vapor-liquid mixtures. Chapter 10 starts from what we see in this chapter and shows how the experimental behavior and our mathematical approaches to it change at high pressures. 

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In most industrial processes coexisting phases are vapor and liquid, although liquid/liquid, vapor/solid, and liquid/solid systems are also encountered. In this chapter we present a general qualitative discussion of vapor/liquid phase behavior (Sec. 12.3) and describe the calculation of temperatures, pressures, and phase compositions for systems in vapor/liquid equilibrium (VLE) at low to moderate pressures (Sec. 12.4).t Comprehensive expositions are given of dew-point, bubble-point, and P, T-flash calculations. 

VPLQFT is a computer program for correlating binary vapor-liquid equilibrium (VLE) data at low to moderate pressures. For such binary mixtures, the truncated virial equation of state is used to correct for vapor-phase nonidealities, except for mixtures containing organic acids where the "chemical" theory is used. The Hayden-0 Connell (1975) correlation gives either the second virial coefficients or the dimerization equilibrium constants, as required. 

Henry s lxm> Constant Henry s law for dilute concentrations of contaminants in water is often appropriate for modeling vapor—liquid equilibrium (VLE) behavior (47). At very low concentrations, a chemical s Henry s constant is equal to the product of its activity coefficient and vapor pressure (3,10,48). Activity coefficient models can provide estimated values of infinite dilution activity coefficients for calculating Henry s constants as a function of... 

Two early studies of the phase equilibrium in the system hydrogen sulfide + carbon dioxide were Bierlein and Kay (1953) and Sobocinski and Kurata (1959). Bierlein and Kay (1953) measured vapor-liquid equilibrium (VLE) in the range of temperature from 0° to 100°C and pressures to 9 MPa, and they established the critical locus for the binary mixture. For this binary system, the critical locus is continuous between the two pure component critical points. Sobocinski and Kurata (1959) confirmed much of the work of Bierlein and Kay (1953) and extended it to temperatures as low as -95°C, the temperature at which solids are formed. Furthermore, liquid phase immiscibility was not observed in this system. Liquid H2S and C02 are completely miscible. 

At low system pressures, the Poynting correction is near unity and can be ignored. Thus the overall vapor-liquid equilibrium (VLE) relationship for most of the mixture systems in the following chapters (excluding acetic acid system) can be described as the following equation ... 

The measurement techniques used at high pressure are similar in principle to tho.se used at low pressure, but different in practice since leakproof metal tubing, fittings, and equilibrium cells (frequently with sapphire windows to enable one to see inside the cell) are used. Also, circulation of the vapor, liquid, or both to ensure that there is good contact between the phases and that equilibrium is obtained is usually done by pumps, rather than by heating to promote boiling, as is the case at low pressures. One example of a high-pressure dynamic VLE cell is shown in Fig. 10.3-4. 

Figure 11.3-3 shows the vapor-liquid and liquid-liquid equilibrium behavior computed for the system of methanol and n-hexane at various temperatures. Note that two liquid phases coexist in equilibrium to temperatures of about 43°C. Since liquids are relatively incompressible, the species liquid-phase fugacities are almost independent of pressure (see Illustrations 7.4-8 and 7.4-9), so that the liquid-liquid behavior is essentially independent of pressure, unless the pressure is very high, or low enough for the mixture to vaporize (this possibility will be considered shortly). The vapor-liquid equilibrium curves for this system at various pressures are also shown in the figure. Note that since the fugacity of a species in a vapor-phase mixture is directly proportional to pressure, the VLE curves are a function of pressure, even though the LLE curves are not. Also, since the methanol-hexane mixture is quite nonideal, and the pure component vapor pressures are similar in value, this system exhibits azeotropic behavior. 

The presence, thus, of nonideality in both phases characterizes high pressure vapor-liquid equilibrium as compared to that at low pressure, where the main source of nonideality is in the liquid phase. And as a result, high pressure VLE calculations can be more complex than those at low pressures. 

In low-pressure VLE (see (Chapters 8 and 9) we normally begin with experimental data, calculate liquid-phase activity coefficients, use those to estimate the appropriate constants in a suitable liquid-phase activity coefficient equation, and then use that plus a suitable estimate of the vapor-phase nonideality (often the ideal gas law or the L-R rule for low-pressure VLE) to calculate equihbrium phase concentrations. In LLE we most often begin with some kind of liquid-phase activity coefficient equation, use it to calculate the composition of the equilibrium phases (without going through the intermediate step of calculating activity coefficients), and then compare the predicted to the experimental equilibrium concentrations, adjusting our equations as needed to get agreement. Then we use the equation to estimate other data points, the values at other temperatures, and so on. 

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