Vapor-liquid equilibrium principle

The design of a distillation column is based on information derived from the VLE diagram describing the mixtures to be separated. The vapor-liquid equilibrium characteristics are indicated by the characteristic shapes of the equilibrium curves. This is what determines the number of stages, and hence the number of trays needed for a separation. Although column designs are often proprietary, the classical method of McCabe-Thiele for binary columns is instructive on the principles of design. 

In principle, the parameters can be evaluated from minimal experimental data. If vapor-liquid equilibrium data at a series of compositions are available, the parameters in a given excess-free-energy model can be found by numerical regression techniques. The goodness of fit in each case depends on the suitability of the form of the equation. If a plot of GE/X X2RT versus X is nearly linear, use the Margules equation (see Section 3). If a plot of Xi X2RT/GE is linear, then use the Van Laar equation. If neither plot approaches linearity, apply the Wilson equation or some other model with more than two parameters. 

Take a mixture of two or more chemicals in a temperature regime where both have a significant vapor pressure. The composition of the mixture in the vapor is different from that in the liquid. By harnessing this difference, you can separate two chemicals, which is the basis of distillation. To calculate this phenomenon, though, you need to predict thermodynamic quantities such as fugacity, and then perform mass and energy balances over the system. This chapter explains how to predict the thermodynamic properties and then how to solve equations for a phase separation. While phase separation is only one part of the distillation process, it is the basis for the entire process. In this chapter you will learn to solve vapor-liquid equilibrium problems, and these principles are employed in calculations for distillation towers in Chapters 6 and 7. Vapor-liquid equilibria problems are expressed as algebraic equations, and the methods used are the same ones as introduced in Chapter 2. 

The SRK and PR equations follow the principle of corresponding states in the three-parameter form only the commonly available critical properties T, p, and are required to apply the equation to a substance. The simple vdW mixing rules work well with these equations. Hence they are widely used for the calculation of vapor-liquid equilibrium in mixtures. 

The data reduction of vapor-pressure osmometry (VPO) follows to some extent the same relations as outlined above. However, from its basic principles, it is not an equilibrium method, since one measures the (very) small difference between the boiling point temperatures of the pure solvent drop and the polymer solution drop in a dynamic regime. This temperature difference is the starting point for determining solvent activities. There is an analogy to the boiling point elevation in thermodynamic equilibrium. Therefore, in the steady state period of the experiment, the following relation can be applied if one assumes that the steady state is sufficiently near the vapor-liquid equilibrium and linear non-equilibrium thermodynamics is valid ... 

A modification of the corresponding-state principle by introducing a parameter related to the vapor pressure curve is reasonable, because experimental vapor pressure data as a function of temperature are easy to retrieve. Furthermore, the vapor-liquid equilibrium is a very sensitive indicator for deviations from the simple corresponding-state principle. The value Tr = 0.7 was chosen because this temperature is not far away from the normal boiling point for most substances. Additionally, the reduced vapor pressure at Tr = 0.7 of the simple fluids has the value = 0.1 (log = —1). As a consequence, the acentric factor of simple fluids is 0 and the three-parameter correlation simplifies to the two-parameter correlation. 

Given an adequate force field, molecular simulation is in principle capable of yielding predictions of thermodynamic properties for a broad range of thermodynamic conditions. To this end, different simulation techniques can be employed, which can be divided in MD and MC. Here, some simulations tools for predicting thermodynamic properties that are important for chemical engineering, i.e., vapor-liquid equilibrium and transport properties, will be addressed briefly. 

Coupling of photocatalysis and MD could avoid fouling problems related to the use of pressure-driven membrane separations (Mozia, Tomaszewska, Morawski, 2007). MD is a separation process that is based on the principle of vapor—liquid equilibrium. The nonvolatile components (e.g. ions, macromolecules, etc.) are retained on the feed side, whereas the volatile components pass through a porous hydrophobic membrane and then they condense in a cold distillate (usually distilled water). 

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. 

For calculation of the equilibrium compositions of the liquid phase either the equilibrium constants of the dissociation and polycondensation reactions have to be known or they can be computed by methods which use the approach of minimizing Gibbs free energy [200-202]. In addition, ab initio modeling techniques such as density functional theory (DFT) in combination with reactive molecular dynamic (MD) simulations could be used. Once the liquid phase system is modeled, there are in principle two options to describe the vapor-liquid equilibrium. Either equations of state (EOS) or excess Gibbs free energy models (g -models) may be used to describe the thermodynamics of the liquid... 

Leach, J. W., Chappelear, P. S. Leland, T. W. (1968). Use of molecular shape factors in vapor-liquid equilibrium calculations with the corresponding states principle. AIChE J., 14, 568-576. 

The general principles of design of multicomponent fractionators are the same in many respects as those for binary systems, but the dearth of adequate vapor-liquid equilibrium data imposes severe restrictions on their application. These are especially needed for liquids which are not ideal, and the danger of attempting new designs without adequate equilibrium data or pilot-plant study for such solutions cannot be overemphasized. Inadequate methods of dealing with tray efficiencies for multicomponents represent another serious problem still to be solved. 

Process engineer One who uses the principles of heat balance, hydraulics, vapor-liquid equilibrium, and chemistry to solve plant operating problems and optimize operating variables. Your authors are process engineers. 

Distillation columns can be used to separate chemical components when there are differences in the concentrations of these components in the liquid and vapor phases. These concentration differences are analyzed and quantified using basic thermodynamic principles covering phase equilibrium. Vapor-liquid equilibrium (VLE) data and analysis are vital components of distillation design and operation. 

A few of the simplest EOSs are based on theory (or had theory found for them after their utility was shown). The more complex EOSs start with the simple EOSs and add terms that have no theoretical basis at all, but with which they can match the experimental data to higher and higher pressures. We would all like one EOS that represented the liquid, the gas, the solid, and the two-phase or three-phase mixtures of gas, liquid, and solid. In principle, it should be possible to devise such an EOS, but none has been foimd so far. However, for making up tables like the steam tables, EOSs have been found that describe both the liquid and the gas to within the uncertainties of the best experimental PvT measurements. These EOSs also describe the two phase regions, but their values there do not correspond to reality (see Chapter 10). We will also see that simpler forms of these EOSs are widely used in vapor-liquid equilibrium calculations. 

The vdW EOS is not very good at representing experimental PvT data, but it has had a profound influence on thermodynamics. Fairly simple, totally empirical modifications of it by Redlich and Kwong, Soave, and Peng and Robinson are very widely used in vapor-liquid equilibrium calculations, as discussed in Chapter 10 and Appendix F. Furthermore, it led to the principle of corresponding states, discussed below, which is very useful. 

In the previous sections of this chapter, VLE has mostly concerned equilibrium of vapors and liquids (see Section 3.2.1 for the distinction between gases and vapors). In all of the plots previously presented in this chapter, both of the species can exist as a pure liquid at the temperature of interest. In all of the figures shown so far, the vapor-liquid equilibrium region extends over the whole range of Do the same ideas and equations apply to gas-liquid equilibrium, such as the air-water system we spent so much time on in Chapter 3 In principle, yes in practice, yes and no. 

Stepanova and Velikovskii (1970) stated that deviation from ideal behavior is connected with fugacity and activity. A paper on the prediction of vapor-liquid equilibrium for polar-nonpolar binary systems by Finch and Van Winkle is mentioned here because of the terminology and the principles involved. The 12 systems examined comprised systems such as ethylbenzene-hexylene glycol, n-octane-cellosolve, toluene-phenol, and n-heptane-toluene. It was pointed out that whereas the Scatchard-Hildebrand theory has had some success in predicting the vapor-liquid equilibria for nonpolar binary systems, it has proved to be unsatisfactory in the quantitative prediction of such equilibria for polar-polar systems and for polar-nonpolar systems. 

Phase equilibrium can be viewed as a dynamic process on the molecular level. We will discuss this perspective by considering a system containing a pure species in vapor-liquid equilibrium, but the principles can be applied to liquid-solid, vapor-solid, and even solid-solid phase equilibria. 

The pressure-temperature phase diagrams also serve to highlight the fact that the polymorphic transition temperature varies with pressure, which is an important consideration in the supercritical fluid processing of materials in which crystallization occurs invariably at elevated pressures. Qualitative prediction of various phase changes (liquid/vapor, solid/vapor, solid/liquid, solid/liquid/vapor) at equilibrium under supercritical fluid conditions can be made by reference to the well-known Le Chatelier s principle. Accordingly, an increase in pressure will result in a decrease in the volume of the system. For most materials (with water being the most notable exception), the specific volume of the liquid and gas phase is less than that of the solid phase, so that... 

The field of membrane separations is radically different from processes based on vapor-liquid or fluid-solid operations. This separation process is based on differences in mass transfer and permeation rates, rather than phase equilibrium conditions. Nevertheless, membrane separations share the same goal as the more traditional separation processes the separation and purification of products. The principles of multi-component membrane separation are discussed for membrane modules in various flow patterns. Several applications are considered, including purification, dialysis, and reverse osmosis. 

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