Vapor-liquid mixtures equilibrium concepts

As stated earlier, distillation is a widely used separation technique for liquid mixtures or solutions. The formation of these mixtures is straightforward, and is usually spontaneous, but the separation of a mixture into its separate constituents requires energy. One of the simplest distillation operations is flash distillation. In this process, part of the feed stream vaporizes in a flash chamber, and the vapor-liquid mixture, which is at equilibrium, is separated. The vapor is rich in the more volatile component, but complete separation is usually not achieved. A simple schematic showing the necessary equipment for flash distillation is given in Figure 10.3. We will illustrate the concepts by using a simple case of the flash distillation of a binary mixture. 

These models are semiempirical and are based on the concept that intermolecular forces will cause nonrandom arrangement of molecules in the mixture. The models account for the arrangement of molecules of different sizes and the preferred orientation of molecules. In each case, the models are fitted to experimental binary vapor-liquid equilibrium data. This gives binary interaction parameters that can be used to predict multicomponent vapor-liquid equilibrium. In the case of the UNIQUAC equation, if experimentally determined vapor-liquid equilibrium data are not available, the Universal Quasi-chemical Functional Group Activity Coefficients (UNIFAC) method can be used to estimate UNIQUAC parameters from the molecular structures of the components in the mixture3. 

A modified local composition (LC) expression is suggested, which accounts for the recent finding that the LC in an ideal binary mixture should be equal to the bulk composition only when the molar volumes of the two pure components are equal. However, the expressions available in the literature for the LCs in binary mixtures do not satisfy this requirement. Some LCs are examined including the popular LC-based NRTL model, to show how the above inconsistency can be eliminated. Further, the emphasis is on the modified NRTL model. The newly derived activity coefficient expressions have three adjustable parameters as the NRTL equations do, but contain, in addition, the ratio of the molar volumes of the pure components, a quantity that is usually available. The correlation capability of the modified activity coefficients was compared to the traditional NRTL equations for 42 vapor—liquid equilibrium data sets from two different kinds of binary mixtures (i) highly nonideal alcohol/water mixtures (33 sets), and (ii) mixtures formed of weakly interacting components, such as benzene, hexafiuorobenzene, toluene, and cyclohexane (9 sets). The new equations provided better performances in correlating the vapor pressure than the NRTL for 36 data sets, less well for 4 data sets, and equal performances for 2 data sets. Similar modifications can be applied to any phase equilibrium model based on the LC concept. 

The theory and conditions for phase equilibrium are well established. If more than one phase is present, then the chemical potential of a component is the same in all phases present. As chemical potential is linked functionally to the concepts of fugacity and activity, models for phase behavior prediction and correlation based on chemical potentials, fugacities, and activities have been developed. Historically, phase equilibrium calculations for hydrocarbon mixtures have been fragmented with liquid-vapor, liquid-liquid, and other phase equilibrium calculations, subject to separate and diverse treatments depending on the temperature, pressure, and component properties. Many of these methods and approaches arose to meet specific needs in the chemical process industries. Poling, Prausnitz,... 

Few liquid mixtures are ideal, so vapor-liquid equilibrium calculations can be more complicated than is the case for the hexane-triethylamine system, and the system phase diagrams can be more structured than Fig. 10.1-6. These complications arise from the (nonlinear) composition dependence of the species activity coefficients. For example, as a result of the composition dependence of y, the equilibrium pressure in a fixed-temperature experiment will no longer be a linear function of mole fraction. Thus nonideal solutions exhibit deviations from Raoult s law. We will discuss this in detail in the following sections of this chapter. However, first, to illustrate the concepts and some of the types of calculations that arise in vapor-liquid equilibrium in the simplest way, we will assume ideal vapor and liquid solutions (Raoult s law) here, and then in Sec. 10.2 consider the calculations for the more difficult case of nonideal solutions.. ... 

Despite widespread use of the ideal K-value concept in industrial calculations, particularly during years prior to digital computers, a sound thermodynamic basis does not exist for calculation of the fugacity coefficients for pure species as required by (4-85). Mehra, Brown, and Thodos discuss the fact that, for vapor-liquid equilibrium at given system temperature and pressure, at least one component of the mixture cannot exist as a pure vapor and at least one other component cannot exist as a pure liquid. For example, in Fig. 4.3, at a reduced pressure of 0.5 and a reduced temperature of 0.9, methane can exist only as a vapor and toluene can exist only as a liquid. It is possible to compute vl or f v for each species but not both, unless vl = vy, which corresponds to saturation conditions. An even more serious problem is posed by species whose critical temperatures are below the system temperature. Attempts to overcome these difficulties via development of pure species fugacity correlations for hypothetical states by extrapolation procedures are discussed by Prausnitz. ... 

To find a concept to describe the technical importance of gas solubility, the mixture is assumed to be infinitely dilute, or an ideally diluted solution. With a large excess of solvent, when the gas component i is dissolved, the mole fraction x,- in the solution tends to 0 (x, - 0). At vapor-liquid equilibrium, Henry s law for an ideally diluted solution may be applied to the gas solubility of component / in the solvent... 

In this chapter we shall consider applications of stability theory to critical phenomena of liquid-vapor transitions and separation of binary mixtures. When the applied pressure and temperature are altered, systems can become unstable, causing their physical state to transform into another distinct state. For example, when the temperature of a two-component liquid mixture (such as hexane and nitrobenzene) changes, the mixture may become unstable to changes in the composition the mixture then separates into two phases, each rich in one of the components. In Chapters 18 and 19 we shall see that in far-from-equilibrium systems, loss of stability can lead to a wide variety of complex nonequilibrium states. We shall also look at how a system that can undergo internal transformations responds to a rapid change in temperature. This leads us to the concept of configurational heat capacity. 

As far as the oil phase is concerned, it is, with rare exception, always a mixture, sometimes an awkward one like a crude oil. Also in this case, it has been recently understood that there can exist some individual behavior among oil molecules and that a mixture would not behave as a pure component provided that there is an opportunity to do so [60]. This behavior is not exceptional but rather the normal one. For instance, in the well-known vapor-liquid equilibrium, the difference in composition between the two phases is the fundamental concept underlying the distillation processes. Such a situation could be found also in liquid-liquid phase equilibria. 

Methods to estimate the thermal conductivity of liquid mixtures have been reviewed by Reid et al. (1977, 1987) and Rowley et al. (1988). Five methods are summarized by Reid et al. (1987), but three of these can be used only for binary mixtures. The two that can be extended to multicomponent mixtures are the Li method (Li 1976), and Rowley s method (Rowley et al. 1988). According to the latter the Li method does not accurately describe ternary behavior. Furthermore, it was indicated that the power law method (Reid et al. 1977 Rowley et al. 1988) successfully characterizes ternary mixture behavior when none of the pure component thermal conductivities differ by more than a factor of 2. But, the power law method should not be used when water is present in the mixture. Rowley s method is based on a local composition concept, and it uses NRTL parameters from vapor-liquid equilibrium data as part of the model. These parameters are available for a number of binary mixtures (Gmehling Onken 1977). When tested for 18 ternary systems, Rowley s method gave an average absolute deviation of 1.86%. 

Yj is the mole fraction of component i in the vapor phase Xj is the mole fraction of component i in the liquid phase Kj is the equilibrium constant of component i for a given T and P, is considered the key concept used in the compntation of phase behavior of hydrocarbon mixtures in oil and gas streams... 

In this simple distillation process, it is assumed that the vapor formed within a short period is in thermodynamic equilibrium with the liquid. Hence, the vapor composition xp is related to the hquid composition xb by an equiUbrium relation of the form xp = fixs)- The exact relationship for a particular mixture may be obtained from a thermodynamic analysis depending on temperature and pressure. For a system following the ideal behavior given by Raoult s law, the equilibrium relationship between the vapor composition y (or xp) and liquid composition x (or xb) of the more volatile component in a binary mixture can be approximated using the concept of constant relative volatility a), and is given by ... 

---