Vapor liquid phase behavior

Fig. 10.12. Vapor-liquid phase behavior for the Lennard-Jones fluid. Solid triangles and hollow squares indicate the results of the particle addition/deletion and volume scaling variants of the flat-histogram simulation using the Wang-Landau algorithm. Crosses are from a histogram reweighting study based on grand-canonical measurements at seven state points. The solid line is from Lotfi, et al. [76], Reprinted figure with permission from [75]. 2002 by the American Physical Society...

Trust, D. B. Kurata, F. Vapor-Liquid Phase Behavior of the Hydrogen-Carbon Monoxide-Propane Systems AIChE J. 1971,... 

Oag, R.M., PI. King, C.J. Mellor, M.W. George, J. Ke and M. Poliakoff, Probing the Vapor-Liquid Phase Behaviors of Near-Critical and Supercritical Fluids Using a Shear Mode Piezoelectric Sensor, Analytical Chemistry, 75, 479-485 (2003). 

In most industrial processes coexisting phases are vapor and liquid, although liquid/liquid, vapor/solid, and liquid/solid systems are also encountered. In this chapter we present a general qualitative discussion of vapor/liquid phase behavior (Sec. 12.3) and describe the calculation of temperatures, pressures, and phase compositions for systems in vapor/liquid equilibrium (VLE) at low to moderate pressures (Sec. 12.4).t Comprehensive expositions are given of dew-point, bubble-point, and P, T-flash calculations. 

The most commonly encountered coexisting phases in industrial practice are vapor and liquid, although liquid/liquid, vaporlsolid, and liquid/solid systems are also found. In this chapter we first discuss the nature of equilibrium, and then consider two rules that give the lumiber of independent variables required to detemiine equilibrium states. There follows in Sec. 10.3 a qualitative discussion of vapor/liquid phase behavior. In Sec. 10.4 we introduce tlie two simplest fomiulations that allow calculation of temperatures, pressures, and phase compositions for systems in vaporlliquid equilibrium. The first, known as Raoult s law, is valid only for systems at low to moderate pressures and in general only for systems comprised of chemically similar species. The second, known as Henry s law, is valid for any species present at low concentration, but as presented here is also limited to systems at low to moderate pressures. A modification of Raoult s law that removes the restriction to chemically similar species is treated in Sec. 10.5. Finally in Sec. 10.6 calculations based on equilibrium ratios or K-values are considered. The treatment of vapor/liquid equilibrium is developed further in Chaps. 12 and 14. 

The relationship between temperature and pressure for which two phases co-exist at equilibrium is called the vapor pressure curve. This diagram summarizes all the vapor-liquid phase behavior for a one-component system. 

Cg), which are important components in gasoline. The vapor-liquid phase behavior of two-component systems is a little more complicated, because I have an additional variable — composition — as well as T and P. Instead of a single temperature at which both liquid and vapor can co-exist, there is a range of temperatures. 

Figure 21.1.5 Classification of vapor-liquid phase behavior of binary systems.

Gamma/Phi Approach For many XT E systems of interest the pressure is low enough that a relatively simple equation of state, such as the two-term virial equation, is satisfactoiy for the vapor phase. Liquid-phase behavior, on the other hand, may be conveniently described by an equation for the excess Gibbs energy, from which activity coefficients are derived. The fugacity of species i in the liquid phase is then given by Eq. (4-102), written... 

In systems that exhibit ideal liquid-phase behavior, the activity coefficients, Yi, are equal to unity and Eq. (13-124) simplifies to Raoult s law. For nonideal hquid-phase behavior, a system is said to show negative deviations from Raoult s law if Y < 1, and conversely, positive deviations from Raoult s law if Y > 1- In sufficiently nonide systems, the deviations may be so large the temperature-composition phase diagrams exhibit extrema, as own in each of the three parts of Fig. 13-57. At such maxima or minima, the equihbrium vapor and liqmd compositions are identical. Thus,... 

Case I. At sufficiently low pressures, the solubility curve does not intersect the coexistence curve. In this case, the gas solubility is too low for liquid-liquid immiscibility, since the coexistence curve describes only liquid-phase behavior. Stated in another way, the points on the coexistence curve are not allowed because the fugacity f2L on this curve exceeds the prescribed vapor-phase value f2v. The ternary phase diagram therefore consists of only the solubility curve, as shown in Fig. 28a where V stands for vapor phase. 

In our discussion of (vapor + liquid) phase equilibria to date, we have limited our description to near-ideal mixtures. As we saw in Chapter 6, positive and negative deviations from ideal solution behavior are common. Extreme deviations result in azeotropy, and sometimes to (liquid -I- liquid) phase equilibrium. A variety of critical loci can occur involving a combination of (vapor + liquid) and (liquid -I- liquid) phase equilibria, but we will limit further discussion in this chapter to an introduction to (liquid + liquid) phase equilibria and reserve more detailed discussion of what we designate as (fluid + fluid) equilibria to advanced texts. 

A brief discussion of sohd-liquid phase equihbrium is presented prior to discussing specific crystalhzation methods. Figures 20-1 and 20-2 illustrate the phase diagrams for binary sohd-solution and eutectic systems, respectively. In the case of binary solid-solution systems, illustrated in Fig. 20-1, the liquid and solid phases contain equilibrium quantities of both components in a manner similar to vapor-hquid phase behavior. This type of behavior causes separation difficulties since multiple stages are required. In principle, however, high purity... 

There are many types of phase diagrams in addition to the two cases presented here these are summarized in detail by Zief and Wilcox (op. cit., p. 21). Solid-liquid phase equilibria must be determined experimentally for most binary and multicomponent systems. Predictive methods are based mostly on ideal phase behavior and have limited accuracy near eutectics. A predictive technique based on extracting liquid-phase activity coefficients from vapor-liquid equilibria that is useful for estimating nonideal binary or multicomponent solid-liquid phase behavior has been reported by Muir (Pap. 71f, 73d ann. meet., AIChE, Chicago, 1980). 

Care should be exercised in using the coefficients from Table 4.14 to predict two-liquid phase behavior under subcooled conditions. The coefficients in Table 4.14 were determined from vapor-liquid equilibrium data at saturated conditions. 

So far, the separation of azeotropic systems has been restricted to the use of pressure shift and the use of entrainers. The third method is to use a membrane to alter the vapor-liquid equilibrium behavior. Pervaporation differs from other membrane processes in that the phase-state on one side of the membrane is different from the other side. The feed to the membrane is a liquid mixture at a high-enough pressure to maintain it in the liquid phase. The other side of the membrane is maintained at a pressure at or below the dew point of the permeate, maintaining it in the vapor phase. Dense membranes are used for pervaporation, and selectivity results from chemical affinity (see Chapter 10). Most pervaporation membranes in commercial use are hydrophyllic19. This means that they preferentially allow... 

Membranes can also be used to alter the vapor-liquid equilibrium behavior and allow separation of azeotropes. The liquid mixture is fed to one side of the membrane, and the permeate is held under conditions to maintain it in the vapor phase. Most separations use hydrophyllic membranes that preferentially pass water rather than organic material. Thus, pervaporation is commonly used for the dehydration of organic components. 

In this definition, the activity coefficient takes account of nonideal liquid-phase behavior for an ideal liquid solution, the coefficient for each species equals 1. Similarly, the fugacity coefficient represents deviation of the vapor phase from ideal gas behavior and is equal to 1 for each species when the gas obeys the ideal gas law. Finally, the fugacity takes the place of vapor pressure when the pure vapor fails to show ideal gas behavior, either because of high pressure or as a result of vapor-phase association or dissociation. Methods for calculating all three of these follow. 

Obtain (or plot from data) a phase diagram for the benzene/toluene system. Vapor-liquid equilibrium behavior of binary systems can be represented by a temperature-composition diagram at... 

In looking for a water/toluene azeotrope, we run into the problem that these two species generally form two liquid phases, a water-rich one and a toluene-rich one. We cannot ignore this two-liquid phase behavior, lest we get nonsensical answers. An azeotrope occurs when the composition for the combined liquid phases equals that for the vapor phase. Having /f-values for a species set to unity, as we di.scussed above, means that the composition for that species for the combined liquid phases matches that for the vapor phase. Whether allowing for two liquid phases or not, water and toluene form a binary azeotrope for a... 

The olefin metathesis system is used, with the physical properties and reaction kinetics being taken from the literature (Okasinski and Doherty 1998). The reaction is considered only to occur in the liquid phase with a negligible heat of reaction and ideal vapor-liquid equilibrium behavior at atmospheric pressure. The specifications for column operation are taken from Hoffmaster and Hauan (2006). The goal is to convert a pure pentene feed into product streams of butene and hexene with a purity of at least 98 mole percent using a feed flow of 2 kmol/h and a distillate to feed ratio of 0.5. 

In addition to vapor (V), high-density liquid (L2), or low-density liquid (Li) phase behavior, reservoir fluids, oils, and other organic fluids exhibit a variety of multiphase behaviors and critical phenomena as noted in Fig. 1. These include liquid-vapor (LiV or L2V), liquid-liquid (L1L2), and liquid-liquid-vapor (L1L2V) phase behavior and associated critical phenomena. 

This review discusses a newly proposed class of tempering Monte Carlo methods and their application to the study of complex fluids. The methods are based on a combination of the expanded grand canonical ensemble formalism (or simple tempering) and the multidimensional parallel tempering technique. We first introduce the method in the framework of a general ensemble. We then discuss a few implementations for specific systems, including primitive models of electrolytes, vapor-liquid and liquid-liquid phase behavior for homopolymers, copolymers, and blends of flexible and semiflexible... 

Chapter 14 describes the phase behavior of binary mixtures. It begins with a discussion of (vapor + liquid) phase equilibria, followed by a description of (liquid + liquid) phase equilibria. (Fluid + fluid) phase equilibria extends this description into the supercritical region, where the five fundamental types of (fluid + fluid) phase diagrams are described. Examples of (solid + liquid) phase diagrams are presented that demonstrate the wide variety of systems that are observed. Of interest is the combination of (liquid + liquid) and (solid + liquid) equilibria into a single phase diagram, where a quadruple point is described. 

---