Liquid-vapor phase equilibria

Boltzmann, L. 18. 19 Boltzmann constant 337 Boltzmann distribution law 514-23 bubble-pressure curve in vapor + liquid phase equilibrium 406... 

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. 

The digital simulation of a distillation column is fairly straightforward. The main complication is the large number of ODEs and algebraic equations that must be solved. We will illustrate the procedure first with the simplified binary distillation column for which we developed the equations in Chap. 3 (Sec. 3.11). Equimolal overflow, constant relative volatility, and theoretical plates have been assumed. There are two ODEs per tray (a total continuity equation and a light component continuity equation) and two algebraic equations per tray (a vapor-liquid phase equilibrium relationship and a liquid-hydraulic relationship). 

For any fixed gas composition, the dewpoint la a function of both the pressure and temperature of the gas. The question of what gas dewpoint limitation is necessary to prevent condensation of liquids in the gas pipeline Introduces a somewhat complex problem of vapor-liquid phase equilibrium under high pressure pipeline conditions, and the interrelated problem of the flowing pressure-teoperature profile for the gas in a pipeline. Gas of different compositions will behave somewhat differently, but we can... 

Vapor-liquid phase equilibrium is assumed on each tray, so the vapor composition can be calculated from the known relative volatility a = 1.5 and liquid composition ... 

Assume that vapor/liquid phase equilibrium can be represented by Raoult s law, because of the low pressure and the similarity of the species ... 

Thermodynamic properties (i.e., fugacities, entropies, and enthalpies) are required by this simulating program in the calculations of vapor/liquid phase equilibrium, compression/ expansion paths, and heat balances. Fugacities are required for the individual components of the existing vapor and liquid mixtures. Enthalpies and entropies are required for the vapor mixture or the liquid mixture. Also, mixture densities are required for both phases. 

The vapor-liquid phase equilibrium is represented by the modified Raoult s law (Eq. 1.191)... 

Vapor-liquid phase equilibrium calculations have to be conducted for the estimation of solubility in the vapor phase (16,17). Alternatively, a cubic EOS can be applied for the estimation of properties of the liquid phase. The equality of fugacity in the two phases can be written as... 

Gamma-Phi Method for Vapor-Liquid Phase Equilibrium... 

Vapor-Liquid Phase Equilibrium Calculations with the I PVDW Model... 

Furthermore, for most vapor mixtures allow pressure, 0,- is very close to unity (there are exceptions to this assumption for example, associating gases such as hydrogen fluoride or acetic acid), and that leads to the equilibrium relation we used in this monograph to calculate the vapor-liquid phase equilibrium by the direct use of activity coefficient methods ... 

Consequently, the continuous variation of specific volume of the vapor-liquid mixture at fixed temperature and pressure is a result of the continuous change in the fraction of the mixture that is vapor. The conclusion, then, is that an isotherm such as that shown in Fig. 7.3-2 is an approximate representation of the real phase behavior (shown in Fig. 7.3-3) by a relatively simple analytic equation of state. In fact, it is impossible to represent the discontinuities in the derivative dP/dV)T that occur at and v with any analytic equation of state. By its sigmoidal behavior in the two-phase region, the van der Waals equation of state is somewhat qualitatively and crudely exhibiting the essential features of vapor-liquid phase equilibrium historically, it was the first equation of state to do so. 

Figure 3.2. Vapor-liquid phase equilibrium. (E. J. Henley and E. M.

The basics of vapor-liquid phase equilibrium have been reviewed in this chapter. A good understanding of VLB is indispensable in the design and control of distillation systems. These basics will be used throughout this book. 

Fig. 2.9 Comparison of phase equilibrium calculations using SAFT (dashed lines) and PC-SAFT (solid lines) [76]. (a) Vapor-liquid phase equilibrium of polyethylene-toluene at T=393 K. Filled symbols are experimental data for polymer molecular weight...

The basic equation for the vapor-liquid phase equilibrium forms the major design criteria for apparatus that separate liquid mixtures by distillation or selective absorption. 

Vapor-Liquid Phase Equilibrium of Multicomponent Mixtures... 

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. 

In the following section, the vapor-liquid phase equilibrium condition is derived for two different arrangements ... 

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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