Vapor-liquid equilibrium calculations applications

Many modifications of the original Redlich/Kwohg equation that appear in the literature are intended for special-purpose applications. The SRJt equation, developed for vapor/liquid equilibrium calculations, is designed specifically to yield reasonable vapor pressures for pure fluids. Thus, there is no assurance that molar volumes calculated by the SRK equation are more accurate than values given by the original Redlich/Kwong equation. 

For vapor-liquid equilibrium calculations up to moderate pressures, the B equation is suitable and convenient for the vapor phase for its applicability and simple form. Formulas have been derived from statistical theory for the calculation of virial coefficients, including B, from intermo-lecular potential energy functions, but intermolecular energy functions are hardly known quantitatively for real molecules. B is found for practical calculations by correlating experimental B values. Pitzer [1] correlated B of normal flnids in a generalized form with acentric factor to as the third parameter. 

In a significant departure from conventional practice, Chueh and Prausnitz (11,12) proposed that the critical constraints on the RK equation be relaxed, and that parameters b and c be treated as empirical constants, determined separately for the liquid phase and for the vapor phase of a given substance. The conventional RK expression for (T) was retained the application was to vapor-liquid equilibrium calculations, in which the vapor-phase version of the equation was used for computation of vapor-phase fugacity coefficients, but in which the liquid-phase version was used only for Poynting corrections. Thus, they proposed that... 

This paper has dealt with the characteristics of equations of state required by industry, has discussed a number of equations that are used in Industrial vapor-liquid equilibrium calculations, and has covered a number of everyday and sometimes unusual practical applications of equations of state. In all three areas an attempt was made to analyze the shortcomings, deficiencies, and handicaps of specific equations of state as well as equations of state in general, from an industrial viewpoint. It is hoped that some of the material discussed in this paper will prove advantageous in future equation of state development work. 

We will see in Chapter 8 that Raoult s law, modified by adding an activity coefficient to account for nonideal behavior, is applicable and widely used for vapor-liquid equilibrium calculations and some other kinds of equilibrium calculations. 

In practice vapor-liquid equilibrium calculations using an equation of state, that is applicable to both phases, can be carried out with sufficient accuracy only for systems that are up to moderately nonideal, typically hydrocarbon mixtures alone or with such gases as H2S, CO, CO2, etc. Furthermore, since separation of such systems by distillation - because of their typically low boiling point temperatures at atmospheric pressure - is carried out at high pressures, this methodology represents what is traditionally referred to as the High Pressure or Equation of State approach to... 

Vapor/liquid equilibrium (XT E) relationships (as well as other interphase equihbrium relationships) are needed in the solution of many engineering problems. The required data can be found by experiment, but such measurements are seldom easy, even for binaiy systems, and they become rapidly more difficult as the number of constituent species increases. This is the incentive for application of thermodynamics to the calculation of phase-equilibrium relationships. 

A model is needed to calculate liquid-liquid equilibrium for the activity coefficient from Equation 4.67. Both the NRTL and UNIQUAC equations can be used to predict liquid-liquid equilibrium. Note that the Wilson equation is not applicable to liquid-liquid equilibrium and, therefore, also not applicable to vapor-liquid-liquid equilibrium. Parameters from the NRTL and UNIQUAC equations can be correlated from vapor-liquid equilibrium data6 or liquid-liquid equilibrium data9,10. The UNIFAC method can be used to predict liquid-liquid equilibrium from the molecular structures of the components in the mixture3. 

Measurements of binary vapor-liquid equilibria can be expressed in terms of activity coefficients, and then correlated by the Wilson or other suitable equation. Data on all possible pairs of components can be combined to represent the vapor-liquid behavior of the complete mixture. For exploratory purposes, several rapid experimental techniques are applicable. For example, differential ebulliometry can obtain data for several systems in one laboratory day, from which infinite dilution activity coefficients can be calculated and then used to evaluate the parameters of correlating equations. Chromatography also is a well-developed rapid technique for vapor-liquid equilibrium measurement of extractive distillation systems. The low-boiling solvent is deposited on an inert carrier to serve as the adsorbent. The mathematics is known from which the relative volatility of a pair of substances can be calculated from the effluent trace of the elutriated stream. Some of the literature of these two techniques is cited by Walas (1985, pp. 216-217). 

K values are useful for vapor-liquid equilibrium (vie) calculations. Five vie calculations are basic in applications ... 

As the first illustration of the use of these equations, consider vapor-liquid equilibrium in the hexane-triethylamine system at 60°C. These species form an essentially ideal mixture. The vapor pressure of hexane af this temperature is 0.7583 bar and that of triethylamine is 0.3843 bar these are so low that the fugacity coefficients at saturation and for the vapor phase can be neglected. Consequently, Eqs. 10.1-3 and 10.1-4 should be applicable to this system. The three solid lines in Fig. 10.1-1 represent the two species partial pressures and the total pressure, which were calculated using these equations and all are linear functions of the of liquid-phase mole fraction the points are the experimental results. The close agreement between the computations and the laboratory data indicates that the hexane-triethylamine mixture is ideal at these conditions. Note that this linear dependence of the partiaLand total pressures on mole fractions predicted by Eqs. 10.1-2 and 10.1-3 is trae only for ideal mixtures it is not true for nonideal mixtures, as we shall see in Sec. 10.2. 

Prausnitz (1,2) has discussed this problem extensively, but the most successful techniques, which are based on either closed equations of state, such as discussed in this symposium, or on dilute liquid solution reference states such as in Prausnitz and Chueh (3), are limited to systems containing nonpolar species or dilute quantities of weakly polar substances. The purpose of this chapter is to describe a novel method for calculating the properties of liquids containing supercritical components which requires relatively few data and is of general applicability. Used with a vapor equation of state, the vapor-liquid equilibrium for these systems can be predicted to a high degree of accuracy even though the liquid may be 30 mol % or more of the supercritical species and the pressure more than 1000 bar. 

Forty years ago these computed variables were calculated using pneumatic devices. Today they are much more easily done in the digital control computer. Much more complex types of computed variables can now be calculated. Several variables of a process can be measured, and all the other variables can be calculated from a rigorous model of the process. For example, the nearness to flooding in distillation columns can be calculated from heat input, feed flow rate, and temperature and pressure data. Another application is the calculation of product purities in a distillation column from measurements of several tray temperatures and flow rates by the use of mass and energy balances, physical property data, and vapor-liquid equilibrium information. Successful applications have been reported in the control of polymerization reactors. 

Equation-of-state approaches are preferred concepts for a quantitative representation of polymer solution properties. They are able to correlate experimental VLE data over wide ranges of pressure and temperature and allow for physically meaningful extrapolation of experimental data into unmeasured regions of interest for application. Based on the experience of the author about the application of the COR equation-of-state model to many polymer-solvent systems, it is possible, for example, to measure some vapor pressures at temperatures between 50 and 100 C and concentrations between 50 and 80 wt% polymer by isopiestic sorption together with some infinite dilution data (limiting activity coefficients, Henry s constants) at temperatures between 100 and 200 C by IGC and then to calculate the complete vapor-liquid equilibrium region between room temperature and about 350 C, pressures between 0.1 mbar and 10 bar, and solvent concentration between the common polymer solution of about 75-95 wt% solvent and the ppm-region where the final solvent and/or monomer devolatilization process takes place. Equivalent results can be obtained with any other comparable equation of state model like PHC, SAFT, PHSC, etc. 

In the above equations, the values of A and B are similar to those given for a binary, but in this case, considerable care must be exercised with respect to the subscripts. Thus An is equal to i/ 2, A32 is equal to 63/62, and similarly for other subscripts. It should be pointed out that for a ternary mixture, there are only two independent A terms. Any other A terms can be calculated from these two by multiplication or division. The three activity coefficient equations contain only the values of A and B associated with the three binary mixtures possible from the three components. If the Van Laar equation for multicomponent mixtures is applicable, the only information needed is the vapor-liquid equilibrium data for the binary mixtures. 

The perturbation methods were discussed in detail and applications to polar-nonpolar mixtures described the potential power of these techniques. The energy and distance scaling parameters for each component are obtained from pure component vapor pressure data. Dipole or quadrupole moments ate obtained from Independent measurements. An energy interaction parameter is evaluated from vapor-liquid equilibrium data at one temperature. An effective equation of state for these mixtures is obtained from the formalizm using this small set of data. More work must be done to improve the accuracy of the calculations to provide design data but it clearly shows promise and continued effort should be productive. 

We proceed now to use bubble and dew point calculations in the following Examples that represent typical applications of vapor-liquid equilibrium to distillation column design. 

Values of the activity coefficients are deduced from experimental data of vapor-liquid equilibria and correlated or extended by any one of several available equations. Values also may be calculated approximately from structural group contributions by methods called UNIFAC and ASOG. For more than two components, the correlating equations favored nowadays are the Wilson, the NRTL, and UNIQUAC, and for some applications a solubility parameter method. The fust and last of these are given in Table 13.2. Calculations from measured equilibrium compositions are made with the rearranged equation... 

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