Liquid phases vaporization calculations

The expression for the fugacity coefficient 4> depends on the equation of state that is used and is the same for the vapor and liquid phases. In calculating the mixture properties with the Peng-Robinson equation of state we have used the following combining rule ... 

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... 

For each of the conditions of temperature and pressure listed bdow for water, state whether the water is a solid phase, liquid phase, vapor phase (superheated), or is a saturated mixture, and if the latter, calculate the quality. Use the steam tables (inside the back cover) to get your answers. 

Equation of State Models for Vapor-Liquid Phase Equilibrium Calculations... 

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

Table 7.5-1 Thermodynamic Properties of Oxygen Along the Vapor-Liquid Phase Boundary Calculated Using the Peng-Robinson Equation of State...

Since ethylene is above its critical temperature, its liquid-phase vapor-pressure will have to be estimated if we are to do the vapor-liquid equilibrium calculation. However, since we need only a moderate extrapolation (from 7 = 9.2°C to T = 50°C), we will do an extrapolation of the vapor-pressure data, and not use Shair s correlation. Using vapor-pressure equation in the Handbook of Chemistry and Physics, NQfmA P P(50°C) 1223 bar for ethylene. 

When a liquid phase vaporizes to a vapor phase under its vapor pressure at constant temperature, an amount of heat called the latent heat of vaporization must be added. Tabulations of latent heats of vaporization are given in various handbooks. For water at 25°C and a pressure of 23.75 mm Hg, the latent heat is 44 020 kJ/kg mol, and at 25°C and 760 mm Hg, 44045 kJ/kg mol. Hence, the effect of pressure can be neglected in engineering calculations. However, there is a large effect of temperature on the latent heat of water. Also, the effect of pressure on the heat capacity of liquid water is small and can be neglected. 

In Figure 2.20, the experimental [110,111] surface tensions of the 1-propanol + n-hexane mixture at 298.15 K with the predicted ones by the present combined model are compared. In view of the strong nonideality of this system, the agreement is again rather satisfactory. For the same system, we have calculated the interfacial layer thickness as a function of composition of the liquid phase. The calculations are shown in Figure 2.21. This is an azeotropic system, and it is worth observing that the calculated maximum in Figure 2.21 is close to the azeotropic composition. In Ref. [106], we have shown that the interfacial layer thickness increases with the vapor pressure of the system. 

The computations in three-phase distillation involve two sets of vapor-liquid equilibrium coefficients, or /f-values, derived from the activity coefficients of each component in each liquid phase. The calculations may be simplified in hydrocarbon systems if the second liquid phase is formed by water. In these situations it is possible to assume the aqueous phase to be pure water and account only for water dissolved in the organic phase. The description of rigorous solution methods for three-phase distillation is deferred to Chapter 13. The objective at this point is to consider the effect that a liquid phase split can have on distillation. 

The separation factor i2 based on H2O (i = 1) concentrating in the vapor phase and D2O (i = 2) concentrating in the liquid phase is calculated using the atom fraction of hydrogen and the atom fraction of deuterium, which in turn are calculated from the mole fractions of individual compounds (see (1.6.1d)). For example, the atom fraction of hydrogen in vapor is given by... 

The calculated pure component 4>i =flP for -heptane works well with the (<, /< ), ) formulation in the liquid phase the calculated ( /< )is quite plausible. But in the vapor phase it does not work well at all the calculated ( /(, )makes little sense, mostly because the computed pure species 4>t=f/P is for a liquid. If we wished to treat this mixture in that way, we would have to estimate a hypothetical i=flP for n-heptane vapor (see Fig. 8.14), which would be perhaps 10 times the value shown in Table 10.3. 

In vapor-liquid equilibria, if one phase composition is given, there are basically four types of problems, characterized by those variables which are specified and those which are to be calculated. Let T stand for temperature, P for total pressure, for the mole fraction of component i in the liquid phase, and y for the mole fraction of component i in the vapor phase. For a mixture containing m components, the four types can be organized in this way ... 

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. 

In the calculation of vapor-liquid equilibria, it is necessary to calculate separately the fugacity of each component in each of the two phases. The liquid and vapor phases require different techniques in this chapter we consider calculations for the vapor phase. 

At pressures to a few bars, the vapor phase is at a relatively low density, i.e., on the average, the molecules interact with one another less strongly than do the molecules in the much denser liquid phase. It is therefore a common simplification to assume that all the nonideality in vapor-liquid systems exist in the liquid phase and that the vapor phase can be treated as an ideal gas. This leads to the simple result that the fugacity of component i is given by its partial pressure, i.e. the product of y, the mole fraction of i in the vapor, and P, the total pressure. A somewhat less restrictive simplification is the Lewis fugacity rule which sets the fugacity of i in the vapor mixture proportional to its mole fraction in the vapor phase the constant of proportionality is the fugacity of pure i vapor at the temperature and pressure of the mixture. These simplifications are attractive because they make the calculation of vapor-liquid equilibria much easier the K factors = i i ... 

As discussed in Chapter 3, at moderate pressures, vapor-phase nonideality is usually small in comparison to liquid-phase nonideality. However, when associating carboxylic acids are present, vapor-phase nonideality may dominate. These acids dimerize appreciably in the vapor phase even at low pressures fugacity coefficients are well removed from unity. To illustrate. Figures 8 and 9 show observed and calculated vapor-liquid equilibria for two systems containing an associating component. 

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. 

In modern separation design, a significant part of many phase-equilibrium calculations is the mathematical representation of pure-component and mixture enthalpies. Enthalpy estimates are important not only for determination of heat loads, but also for adiabatic flash and distillation computations. Further, mixture enthalpy data, when available, are useful for extending vapor-liquid equilibria to higher (or lower) temperatures, through the Gibbs-Helmholtz equation. ... 

Table 1 indicates that the enthalpy of mixing in the liquid phase is not important when calculating enthalpies of vaporization, even though for this system, the enthalpy of mixing is large (Brown, 1964) when compared to other enthalpies of mixing for typical mixtures of nonelectrolytes. 

Figure 3 presents results for acetic acid(1)-water(2) at 1 atm. In this case deviations from ideality are important for the vapor phase as well as the liquid phase. For the vapor phase, calculations are based on the chemical theory of vapor-phase imperfections, as discussed in Chapter 3. Calculated results are in good agreement with similar calculations reported by Lemlich et al. (1957). ... 

Finally, Table 2 shows enthalpy calculations for the system nitrogen-water at 100 atm. in the range 313.5-584.7°K. [See also Figure (4-13).] The mole fraction of nitrogen in the liquid phase is small throughout, but that in the vapor phase varies from essentially unity at the low-temperature end to zero at the high-temperature end. In the liquid phase, the enthalpy is determined primarily by the temperature, but in the vapor phase it is determined by both temperature and composition. 

The computation of pure-component and mixture enthalpies is implemented by FORTRAN IV subroutine ENTH, which evaluates the liquid- or vapor-phase molar enthalpy for a system of up to 20 components at specified temperature, pressure, and composition. The enthalpies calculated are in J/mol referred to the ideal gas at 300°K. Liquid enthalpies can be determined either with... 

This chapter presents quantitative methods for calculation of enthalpies of vapor-phase and liquid-phase mixtures. These methods rely primarily on pure-component data, in particular ideal-vapor heat capacities and vapor-pressure data, both as functions of temperature. Vapor-phase corrections for nonideality are usually relatively small. Liquid-phase excess enthalpies are also usually not important. As indicated in Chapter 4, for mixtures containing noncondensable components, we restrict attention to liquid solutions which are dilute with respect to all noncondensable components. 

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. 

Unfortunately, many commonly used methods for parameter estimation give only estimates for the parameters and no measures of their uncertainty. This is usually accomplished by calculation of the dependent variable at each experimental point, summation of the squared differences between the calculated and measured values, and adjustment of parameters to minimize this sum. Such methods routinely ignore errors in the measured independent variables. For example, in vapor-liquid equilibrium data reduction, errors in the liquid-phase mole fraction and temperature measurements are often assumed to be absent. The total pressure is calculated as a function of the estimated parameters, the measured temperature, and the measured liquid-phase mole fraction. 

Liquid-liquid equilibrium separation calculations are superficially similar to isothermal vapor-liquid flash calculations. They also use the objective function. Equation (7-13), in a step-limited Newton-Raphson iteration for a, which is here E/F. However, because of the very strong dependence of equilibrium ratios on phase compositions, a computation as described for isothermal flash processes can converge very slowly, especially near the plait point. (Sometimes 50 or more iterations are required. )... 

The computer subroutines for calculation of vapor-phase and liquid-phase fugacity (activity) coefficients, reference fugac-ities, and molar enthalpies, as well as vapor-liquid and liquid-liquid equilibrium ratios, are described and listed in this Appendix. These are source routines written in American National Standard FORTRAN (FORTRAN IV), ANSI X3.9-1978, and, as such, should be compatible with most computer systems with FORTRAN IV compilers. Approximate storage requirements and CDC 6400 execution times for these subroutines are given in Appendix J. 

S Sum of the calculated vapor or liquid phase mole frac-... 

In the calculation of vapor phase partial fugacities the use of an equation of state is always justified. In regard to the liquid phase fugacities, there is a choice between two paths ... 

The identifying superscripts I and v are omitted here with the understanding that Ji a.nd f are liquid-phase properties, whereas 9 is a vapor-phase property. Applications of Eq. (4-277) represent what is known as the gamma/phi approach to XT E calculations. 

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