Vapor pressure, multicomponent liquid system

Relative volatility is the volatility separation factor in a vapor-liquid system, i.e., the volatility of one component divided by the volatility of the other. It is the tendency for one component in a liquid mixture to separate upon distillation from the other. The term is expressed as fhe ratio of vapor pressure of the more volatile to the less volatile in the liquid mixture, and therefore g is always equal to 1.0 or greater, g means the relationship of the more volatile or low boiler to the less volatile or high boiler at a constant specific temperature. The greater the value of a, the easier will be the desired separation. Relative volatility can be calculated between any two components in a mixture, binary or multicomponent. One of the substances is chosen as the reference to which the other component is compared. 

Multicomponent distillations are more complicated than binary systems due primarily to the actual or potential involvement or interaction of one or more components of the multicomponent system on other components of the mixture. These interactions may be in the form of vapor-liquid equilibriums such as azeotrope formation, or chemical reaction, etc., any of which may affect the activity relations, and hence deviations from ideal relationships. For example, some systems are known to have two azeotrope combinations in the distillation column. Sometimes these, one or all, can be broken or changed in the vapor pressure relationships by addition of a third chemical or hydrocarbon. 

Separation systems include in their mathematical models various vapor-liquid equilibrium (VLE) correlations that are specific to the binary or multicomponent system of interest. Such correlations are usually obtained by fitting VLE data by least squares. The nature of the data can depend on the level of sophistication of the experimental work. In some cases it is only feasible to measure the total pressure of a system as a function of the liquid phase mole fraction (no vapor phase mole fraction data are available). 

In addition to equilibrium between the liquid-phase water in the sample and the vapor phase, the internal moisture equilibrium of the sample is important. If a system is not at internal moisture equilibrium, one might measure a steady vapor pressure (over the period of measurement) that is not the true water activity of the system. An example of this might be a baked good or a multicomponent food. Initially out of the oven, a baked good is not at internal equilibrium the outer surface is at a lower water activity than the center of the baked good. One must wait a period of time in order for the water to migrate and the system to come to internal equilibrium. It is therefore important to remember the restriction of the definition of water activity to equilibrium. 

When a liquid hydrocarbon mixture is present, the Lw-V-Lhc line in Figure 4.2b broadens to become an area, such as that labeled CFK in Figure 4.2c. This area is caused by the fact that a single hydrocarbon is no longer present, so a combination of hydrocarbon (and water) vapor pressures creates a broader phase equilibrium envelope. Consequently, the upper quadruple point (Q2) evolves into a line (KC) for the multicomponent hydrocarbon system. 

The phase behavior of multicomponent hydrocarbon systems in the liquid-vapor region is very similar to that of binary systems. However, it is obvious that two-dimensional pressure-composition and temperature-composition diagrams no longer suffice to describe the behavior of multicomponent systems. For a multicomponent system with a given overall composition, the characteristics of the P-T and P-V diagrams are very similar to those of a two-component system. For systems involving crude oils which usually contain appreciable amounts of relatively r on-volatile constituents, the dew points may occur at such low pressures that they are practically unattainable. This fact will modify the behavior of these systems to some extent. 

If you apply the Gibbs phase rule to a multicomponent gas-liquid system at equilibrium, you will discover that the compositions of the two phases at a given temperature and pressure are not independent. Once the composition of one of the phases is specified (in terms of mole fractions. mass fractions, concentrations, or. for the vapor phase, partial pressures), the composition of the other phase is fixed and, in principle, can be determined from physical properties of the system components. 

Eew multicomponent systems exist for which completely generalized equilibrium data are available. The most widely available data are those for vapor-liquid systems, and these are frequently referred to as vapor-liquid equilibrium distribution coefficients or K value. The K values vary with temperature and pressure, and a selectivity that is equal to the ratio of the K values is used. Eor vapor-liquid systems, this is referred to as the relative volatility and is expressed for a binary system as... 

The development of SCF processes involves a consideration of the phase behavior of the system under supercritical conditions. The influence of pressure and temperature on phase behavior in such systems is complex. For example, it is possible to have multiple phases, such as liquid-liquid-vapor or solid-liquid-vapor equilibria, present in the system. In many cases, the operation of an SCF process under multiphase conditions may be undesirable and so phase behavior should first be investigated. The limiting case of equilibrium between two components (binary systems) provides a convenient starting point in the understanding of multicomponent phase behavior. 

It is more complicated to calculate LLE in multicomponent systems accurately than to describe vapor-liquid or solid-hquid equilibria. The reason is that in the case of LLE the activity coefficients have to describe not only the concentration dependence but also the temperature dependence correctly, whereas in the case of the other phase equilibria (VLE, SLE) the activity coefficients primarily have to describe the deviation from ideal behavior (Raoult s law resp. ideal solid solubility), and the temperature dependence is mainly described by the standard fugacities (vapor pressure resp. melting temperature and heat of fusion). 

Coefficients of the equadon of state and of the equation for transport properties are stored for each substance. Parameters of the critical point and coefficients of equations for calculadon of the ideal-gas functions, the saturated vapor pressure and the melting pressure are kept also. The thermal properties in the single-phase region and on the phase-equilibrium lines can be calculated on the basis of well-known relations with use of these coefficients. The system contains data for 30 reference substances monatomic and diatomic gases, air, water and steam, carbon dioxide, ammonia, paraffin hydrocarbons (up to octane), ethylene (ethene), propylene (propene), benzene and toluene. The system can calculate the thermophysical properties of poorly investigated gases and liquids and of multicomponent mixtures also on the basis of data for reference substances. 

Most of the multicomponent systems are non-ideal. From thermodynamic viewpoint, the transfer of mass species i at constant temperature and pressure from one phase to the other in a two-phase system is due to existing the difference of chemical potential 7t, x p between phases, in which /t,- p =p + T Fln where y, is the activity coefficient of component i is p at standard state. In other words, for a gas (vapor)-liquid system, the driving force of component i transferred from gas phase to the adjacent liquid phase along direction z is the... 

To predict vapor-liquid or liquid-liquid equilibria in multicomponent systems, we require a method for calculating the fugacity of a component i in a liquid mixture. At system temperature T and system pressure P, this fugacity is written as a product of three terms... 

For mixtures containing more than two species, an additional degree of freedom is available for each additional component. Thus, for a four-component system, the equihbrium vapor and liquid compositions are only fixed if the pressure, temperature, and mole fractious of two components are set. Representation of multicomponent vapor-hquid equihbrium data in tabular or graphical form of the type shown earlier for biuaiy systems is either difficult or impossible. Instead, such data, as well as biuaiy-system data, are commonly represented in terms of ivapor-liquid equilibrium ratios), which are defined by... 

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. 

For a pressure at which partial evaporation occurs and both liquid and vapor are present in finite quantities the calculation of the composition of the liquid and the vapor in a multicomponent system is more complex but can be carried out in the following manner. 

Calculation of Bubble-Point Pressure and Dew-Point Pressure Using Equilibrium Constants. Since the total pressure P

bubble-point and dew-point pressure as was done in the case of ideal solutions. A method will now be presented for calculating the bubble-point pressure and the dew-point pressure, which is applicable to both binary and multicomponent systems which are non-ideal. At the bubble point the system is entirely in the liquid state except for an infinitesimal amount of vapor. Consequently, since ti, = 0 and n — n% equation 19 becomes... 

For a multicomponent system this computation would be considerably more difficult since the composition and amounts of liquid and vapor at each pressure would have to be calculated by the trial-and-error method using equations 18 and 19 in Chapter 5. 

The molecular weight distribution of the polymer does have another effect on the phase diagram. Figure 3.24B shows that at pressures below the LEV line, vapor and liquid exist in equilibrium. But if the molecular weight distribution of the polymer is large, the LEV line becomes an area. This is because the system is now truly a multicomponent system. The EEV line... 

Also, at a pressure higher than the equilibrium pressure at each temperature only two liquid phases exist, while below the equilibrium pressure only a single liquid and a vapor exist. Therefore, in a binary mixture, at each temperature there is only a single pressure at which two liquids and a vapor are present, which may be difficult to determine experimentally. However, because of the extra degrees of freedom, states of liquid-liquid-vapor equilibrium are much easier to find in ternary and other multicomponent systems. B... 

A straightforward, but tedious, route to obtain information of vapor-liquid and liquid-liquid coexistence lines for polymeric fluids is to perform multiple simulations in either the canonical or the isobaric-isothermal ensemble and to measure the chemical potential of all species. The simulation volumes or external pressures (and for multicomponent systems also the compositions) are then systematically changed to find the conditions that satisfy Gibbs phase coexistence rule. Since calculations of the chemical potentials are required, these techniques are often referred to as NVT- or NPT- methods. For the special case of polymeric fluids, these methods can be used very advantageously in combination with the incremental potential algorithm. Thus, phase equilibria can be obtained under conditions and for chain lengths where chemical potentials cannot be reliably obtained with unbiased or biased insertion methods, but can still be estimated using the incremental chemical potential ansatz [47-50]. 

Bertucco et al. investigated the effect of SCCO2 on the hydrogenation of unsaturated ketones catalyzed by a supported Pd catalyst, by using a modified intemal-recycle Berty-type reactor [63]. A kinetic model was developed to interpret the experimental results. To apply this model to the multiphase reaction system, the calculation of high-pressure phase equilibria was required. A Peng-Robinson equation of state with mixture parameters tuned by experimental binary data provided a satisfactory interpretation of all binary and ternary vapor-liquid equilibrium data available and was extended to multicomponent... 

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