Vapor-liquid equilibrium description

Basically, DESIGNER can use different physical property packages that are easy to interchange with commercial flowsheet simulators. For the case considered, the vapor-liquid equilibrium description is based on the UNIQUAC model. The liquid-phase binary diffusivities are determined using the method of Tyn and Calus (see Ref. 72) for the diluted mixtures, corrected by the Vignes equation (57), to account for finite concentrations. The vapor-phase diffusion coefficients are assumed constant. The reaction kinetics parameters taken from Ref. 202 are implemented directly in the DESIGNER code. 

DESCRIPTIONS AND LISTINGS OF SUBROUTINES FOR CALCULATION OF VAPOR-LIQUID EQUILIBRIUM SEPARATIONS... 

The (vapor + liquid) equilibrium line for a substance ends abruptly at a point called the critical point. The critical point is a unique feature of (vapor + liquid) equilibrium where a number of interesting phenomena occur, and it deserves a detailed description. The temperature, pressure, and volume at this point are referred to as the critical temperature, Tc. critical pressure, pc, and critical volume, Vc, respectively. For COi, the critical point is point a in Figure 8.1. As we will see shortly, properties of the critical state make it difficult to study experimentally. 

Figure 7 shows the predicted vapor-phase mole fractions of HC1 at 25°C as a function of the liquid-phase molality of HC1 for a constant NaCl molality of 3. Also included are predicted vapor-phase mole fractions of HC1 when the interaction parameter A23 is taken as zero. There are unfortunately no experimental vapor-liquid equilibrium data available for the HC1-NaCl-FLO system however, considering the excellent description of the liquid-phase activity coefficients and the low total pressures, it is expected that predicted mole fractions would be within 2-3% of the experimental values. 

In Chap. 6 we treated the thermodynamic properties of constant-composition fluids. However, many applications of chemical-engineering thermodynamics are to systems wherein multicomponent mixtures of gases or liquids undergo composition changes as the result of mixing or separation processes, the transfer of species from one phase to another, or chemical reaction. The properties of such systems depend on composition as well as on temperature and pressure. Our first task in this chapter is therefore to develop a fundamental property relation for homogeneous fluid mixtures of variable composition. We then derive equations applicable to mixtures of ideal gases and ideal solutions. Finally, we treat in detail a particularly simple description of multicomponent vapor/liquid equilibrium known as Raoult s law. 

The vapor pressure curve forms the basis for the description of vapor-liquid equilibrium for a pure fluid. As the temperature increases, the vapor pressure curve for the vapor-liquid situation ends at the critical pressure. In the case of a binary or multicomponent solution, the critical point is not necessarily a maximum with respect to either temperature or pressure. It is then possible for a vapor or liquid to exist at temperature or pressures higher than the critical pressure of the mixture. At constant temperature, it is then possible for condensation to take place as the pressure is decreased. At constant pressure, condensation may take place as the temperature is increased. Vaporization can take place at constant temperature as the pressure is increased and decreased. This unusual behavior can be useful in some process situations, for example, in the recovery of natural gas from deep wells. If the conditions are right, liquefaction of the product stream is possible. At the same time, the heavier components of the mixture may be separated from the lighter components. 

A rigorous mathematical description of a multistage cascade involves material and energy balances and some representation of the vapor-liquid equilibrium. The resulting set of algebraic equations is called the MESH Equations, for reasons which will soon become apparent. 

Now we will use the ideal solution model to develop a mathematical description of vapor-liquid equilibrium in a multicomponent solution. We will make the assumption that we have a system that is separated into a coexisting vapor and liquid phase. The vapor phase will be assumed to behave like an ideal gas, while the liquid phase will be assumed to behave as an ideal solution. 

The computations in three-phase distillation involve two sets of vapor-liquid equilibrium coefficients, or A -values, derived from the activity coefficients of each component in each liquid phase (Section 2.3.3). The calculations may be simplified in hydrocarbon systems if the second liquid phase is mostly 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 tlie effect a liquid phase split can have on distillation. 

The description of vapor-liquid equilibrium using an activity coefficient fop the liquid phase and an equation of state for the vapor phase is usually referred to as the y -

and (p-cp descriptions are two different methods of analysis of the equilibrium problem, and hence we consider them separately. 

For generality, using the activity coefficient description of vapor-liquid equilibrium, the equation can be rewritten as. ... 

We now turn from the qualitative description of high-pressure phase equilibria and its measurement to the quantitative description, that is, to the correlation or prediction of vapor-liquid equilibrium for hydrocarbon (and light gas). systems, of which the ethane-propylene system is merely one example. Our interest will be only in systems describable by a single equation of state for both the vapor and liquid phases, as the case in which the liquid is described by an activity coefficient model was considered in the previous section. 

In the study of the solubility of a gas in a liquid one is interested in the equilibrium when the mixture temperature T is greater than the critical temperature of at least one of the components in the mixture, the gas. If the mixture can be described by an equation of state, no special difficulties are involved, and the calculations proceed as described in Sec. 10.3. Indeed, a number of cases encountered in Sec. 10.3 were of this type (e.g., ethane in the ethane-propylene mixture at 344.3 K). Consequently, it is not necessary to consider the equation-of-state description of gas solubility, as it is another type of equation-of-state vapor-liquid equilibrium calculation, and the methods described in Sec. 10.3 can be used. 

What should be stressed is not the poor accuracy of the equation-of-state predictions for the COi-n-decane system, but rather the fact that the same, simple equation of state can lead to good vapor-liquid equilibrium predictions over a wide range of temperatures and pressures, as well as a qualitative description of liquid-liquid equilibrium at lower temperatures. 

Fig. 4.14 Vapor-liquid equilibrium in the system formaldehyde + water at 140°C. Left side model with consistent description of chemical and phase equilibrium. Right side inconsistent model...

Table 2.4-4 Adsorbed solution theories for the description or prediction of multicomponent adsorption equilibria. In the light gray area new theoretical models are listed. The theories in the double-framed area require experimental data of binary adsorptives. VLE denotes vapor liquid equilibrium. The meaning of VAE is vapor adsorbate equilibrium...

The EoS provides a good description of the vapor-liquid equilibrium (VLE) for the CO2 - Ar binary mixture far from the critical point but it progressively becomes less accurate near it, as shown in Figure 1. 

An important first step in any model-based calculation procedure is the analysis and type of data used. Here, the accuracy and reliability of the measured data sets to be used in regression of model parameters is a very important issue. It is clear that reliable parameters for any model cannot be obtained from low-quality or inconsistent data. However, for many published experimentally measured solid solubility data, information on measurement uncertainties or quality estimates are unavailable. Also, pure component temperature limits and the excess GE models typically used for nonideality in vapor-liquid equilibrium (VLE) may not be rehable for SEE (or solid solubility). To address this situation, an alternative set of consistency tests [3] have been developed, including a new approach for modehng dilute solution SEE, which combines solute infinite dilution activity coefficients in the hquid phase with a theoretically based term to account for the nonideality for dilute solutions relative to infinite dilution. This model has been found to give noticeably better descriptions of experimental data than traditional thermodynamic models (nonrandom two liquid (NRTE) [4], UNIQUAC [5], and original UNIversal Eunctional group Activity Coefficient (UNIEAC) [6]) for the studied systems. 

The cubic form of an equation of state is the simplest form which enables the description of the PvT behavior of gases and liquids and thus the representation of the vapor-liquid equilibrium with only one model. At constant temperature and aL a given pressure this equation has three solutions. These solutions may be - depending on the values of temperature and pressure - all of real type or of mixed real and complex type. Figure 2.14 shows an isotherm in the Pv-diagram, calculated with the Soave-Redlich-Kwong equation for ethanol at 473.15 K. The cho.. en temperature is lower than the critical temperature of ethanol (T = 516.2 K),... 

The aim of the introduction to this volume is to present the general relations between vapor-liquid equilibrium data and the thermodynamic functions of liquid mixtures and to describe the principles and methods of measurement and correlation. Only a very brief description of some of the methods and models which are used is given, extensive accounts are contained in many publications. 

It is, however, difficult to describe correctly both G and if by the same model with the same set of parameters. Since an accurate description of activity coefficients and hence is required for use with vapor-liquid equilibrium correlations, such an approach is rarely used. 

Film Theory and Gas-Liquid and Liquid-Liquid Mass Transfer. The history and literature surrounding interfacial mass transfer is enormous. In the present context, it suffices to say that the film model, which postulates the existence of a thin fluid layer in each fluid phase at the interface, is generally accepted (60). In the context of coupled mass transfer and reaction, two common treatments involve 1) the Hatta number and (2) enhancement factors. Both descriptions normally require a detailed model of the kinetics as well as the mass transfer. The Hatta number is perhaps more intuitive, since the numbers span the limiting cases of infinitely slow reaction with respect to mass transfer to infinitely fast reaction with respect to mass transfer. In the former case all reaction occurs in the bulk phase, and in the latter reaction occurs exclusively at the interface with no bulk reaction occurring. Enhancement factors are usually categorized in terms of reaction order (61). In the context of nonreactive systems, a characteristic time scale (eg, half-life) for attaining vapor-liquid equilibrium and liquid-liquid equilibrium, 6>eq, in typical laboratory settings is of the order of minutes. 

A rigorous simulation and optimization of reactive distillation processes usually is based on nonlinear fimctions for a realistic description of the reaction kinetics and the vapor-liquid-equilibrium. Within GAMS models, this description leads to very complex models that often face convergence problems. By using the new so-called external functions, the situation can be improved by transferring calculation procedures to an external module. 

As demonstrated by former publications, the GAMS modeling system has been successfully used for the MINLP-optimization of single reactive distillation columns (Poth et al., 2001 Jackson and Grossmann 2001). The strong nonlinear functions required for a realistic description of the reaction kinetics and the vapor-liquid-equilibrium in these cases lead to very complex GAMS models that may face convergence problems. 

A detailed description of the dynamic model used in the simulations and all the kinetic parameters, physical properties and vapor-liquid equilibrium relationships used in the simulation of this process are given in Luyben [6]. Some important parameters are the overall heat-transfer coefficient U = 150 Btu/hr-ft - F, heat of reaction X = -30,000 Btu/lb-mole of C generated and heat of vaporization AHy = 10,000 Btu/lb-mole of all components. 

To derive simple equations for the description of the vapor-liquid equilibrium and for the design of distillation columns, the liquid is considered as an ideal mixture, that is, the forces of attraction between molecules of the pure components equal those in the mixture. 

Using these parameters for predicting the vapor-liquid equilibrium in the polycarbonate/chlorobenzene system kij = 0) at 140°C leads to results shown in Fig. 4. It is obvious that the results are very unsatisfactory a description of the experimental data also fails for any other value of the binary parameter Therefore, the polycarbonate parameters m (uncertain since the molecular weight for the density data was unknown) and s/k were refitted to the binary data in Fig. 5a. Using these new parameters m/M = 0.0080, e/A = 256.97 K and Vqo = 17.114 cm /mol, the experimental data can now be described very well. 

Vapor-liquid equilibrium data, except in the special situations of ideal and regular solutions, must be determined experimentally. Descriptions of experimental methods [18], extensive bibliographies [67], and lists of data [7, 22] are available. 

These equations are the correct description, in terms of the quantities defined so far, for any vapor-liquid equilibrium of two species (if we substitute their names for those of ethanol and water). Observe that this equation has four values of y, one for each species in each of two phases. For any ideal solution, y=1.00. Mixtures of ideal gases are all ideal solutions, so if the gas (or vapor) is practically an ideal gas, then both of the ys for the gas phase in Eqs. 7.36 and 7.37 are 1.00. In Chapters 8 and 9 we will see that this is an excellent approximation, so for most pressures we normally drop those two ys out of Eqs. 7.36 and 7.37 and assume that any y we encounter is for one species in a liquid. Then we can solve Eqs. 7.36 and 7.37 for these ys, finding... 

Our objective in this Chapter is to develop an understanding of vapor-liquid equilibrium behavior at high pressures and an awareness of the methods involved - and the expected accuracy - in providing a quantitative description and prediction of it. 

We will focus our qualitative description of high pressure vapor-liquid equilibrium behavior of mixtures on two very important, from the practical point of view, areas ... 

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