Equilibrium system ideal vapor/liquid

Ideal Vapor/Liquid Equilibrium Systems, Nonideal Vapor/Liquid Equilibrium Systems, Vapor/Liquid Equilibrium Relationships,... 

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. 

Since few liquid mixtures are ideal, vapor-liquid equilibrium calculations are somewhat more complicated than for the cases in the previous section, and the phase diagrams for nonideal systems can be more structured than Figs. 10.1-1 to 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 yt, the vapor-liquid equilibrium pressure in a fixed-temperature experiment will no longer be a linear function of mole fraction, so that no.nideal solutions exhibit deviations from Raoult s law. However, all the calculational methods discussed in the previous section for ideal mixtures, including distillation column design, can be used for nonideal mix-, tures, as long as the composition dependence of the activity coefficients is taken into account. 

Up to this point we have looked at systems with fairly ideal vapor-liquid equilibrium behavior. The last separation system examined is a highly nonideal ternary system of methyl acetate (MeAc), methanol (MeOH), and water. Methyl acetate and methanol form a homogeneous minimum-boiling azeotrope at 1.1 atm with a composition of... 

More than one steady state for the same set of specified variables (output multiplicity) is one of the interesting features of azeotropic distillation. Simple distillation columns with ideal vapor-liquid equilibrium, however, may also show MSS (Jacobsen and Skogestad, 1991). The existence of output multiplicities in distillation were first reported on the ternary ethanol-water-benzene (EWB) system. Earlier simulation-based studies had reported two distinct steady states depending on the starting guesses (Bekiaris et al.. 

After heat recovery, via HXl and HX2, the reactor effluent is fed into a distillation column. The two reactants, A B, are light key (LK) and intermediate boiler (IK), respectively, while the product, X, is the heavy component (HK). The Antoine constants of the vapor pressure equation are chosen such that the relative volatilities of the components are ttA = 4, ttB = 2, and Oc=l for this equal molar overflow system (Table 1). Only one distillation column is sufficient to separate the product (C) from the unreacted reactants (A B). Ideal vapor-liquid equilibrium is assumed. Physical property data and kinetic data are given in Table 1. 

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. 

In contrast to the Gibbs ensemble discussed later in this chapter, a number of simulations are required per coexistence point, but the number can be quite small, especially for vapor-liquid equilibrium calculations away from the critical point. For example, for a one-component system near the triple point, the density of the dense liquid can be obtained from a single NPT simulation at zero pressure. The chemical potential of the liquid, in turn, determines the density of the (near-ideal) vapor phase so that only one simulation is required. The method has been extended to mixtures [12, 13]. Significantly lower statistical uncertainties were obtained in [13] compared to earlier Gibbs ensemble calculations of the same Lennard-Jones binary mixtures, but the NPT + test particle method calculations were based on longer simulations. 

The vapor pressure of a liquid in equilibrium with its vapor cannot be treated like an ideal gas that obeys the gas laws the equilibrium (liquid vapor) controls the vapor pressure. As conditions are changed, the system adjusts itself until the system reaches equilibrium again either the liquid which is present evaporates, or the vapor condenses. 

Compare convergence times, using interval halving, Newton-Raphson, and false position, for on ideal, four-component, vapor-liquid equilibrium system. The pure component vapor pressures are ... 

Ideal Mixed Micelles. The Critical Micelle Concentration (CMC) is the lowest surfactant concentration at which micelles form the lower the CMC, the greater the tendency of a system to form micelles. When the total surfactant concentration equals the CMC, an infintesimal fraction of surfactant is present as micelles therefore, the CMC is equal to the total monomer concentration in equilibrium with the micellar pseudo—phase. The CMC for monomer—micelle equilibrium is analogous to the dew point in vapor—liquid equilibrium. 

Ideal Liquid Solutions, Two limiting laws of solution thermodynamics that are widely employed are Henry s law and Raoult s law, which represent vapor—liquid partitioning behavior in the concentration extremes. These laws are used frequendy in equilibrium problems and apply to a variety of real systems (10). 

The compositions of the vapor and liquid phases in equilibrium for partially miscible systems are calculated in the same way as for miscible systems. In the regions where a single liquid is in equilibrium with its vapor, the general nature of Fig. 13.17 is not different in any essential way from that of Fig. I2.9< Since limited miscibility implies highly nonideal behavior, any general assumption of liquid-phase ideality is excluded. Even a combination of Henry s law, valid for a species at infinite dilution, and Raoult s law, valid for a species as it approaches purity, is not very useful, because each approximates real behavior only for a very small composition range. Thus GE is large, and its composition dependence is often not adequately represented by simple equations. However, the UNIFAC method (App. D) is suitable for estimation of activity coefficients. 

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 azeotropic distillation especially the systems are non-ideal which makes calculating vapor-liquid equilibrium properties more difficult than, for example, in distillation of mixtures of simple hydrocarbons. Work predicting the vapor-liquid equilibrium properties of ternary mixtures of... 

Activity and Activity Coefficient. —When a pure liquid or a mixture is in equilibrium with its vapor, the chemical potential of any constituent in the liquid must be equal to that in the vapor this is a consequence of the thermodynamic requirement that for a system at equilibrium a small change at constant temperature and pressure shall not be accompanied by any change of free energy, i.e., (d( )r. p is zero. It follows, therefore, that if the vapor can be regarded as behaving ideally, the chemical potential of the constituent i of a solution can be written in the same form as equation (7), where p,- is now the partial pressure of the component in the vapor in equilibrium with the solution. If the vapor is not ideal, the partial pressure should be replaced by an ideal pressure, or fugacity, but this correction need not be considered further. According to Raoult s... 

Let us consider vapor-liquid (or vapor-solid) equilibria for binary mixtures. For the sake of simplicity it will be assumed that all gases are ideal. In addition to the vapors of each component of the condensed phase, the gas will be assumed to contain a completely insoluble constituent, the partial pressure p of which may be adjusted so that the total pressure of the system, p, assumes a prescribed value. Therefore, C = 3, P = 2, and, according to equation (51), F = 3. Let us study the dependence of the equilibrium vapor pressures of the two soluble species p and P2 on their respective mass fractions in the condensed phase X and X2 at constant temperature and at constant total pressure. Since it is thus agreed that T and p are fixed, only one remaining variable [say X ( = l — "2)] is at our disposal p, P2 and the total vapor pressure p = p + p2 will depend only on X. ... 

A gas-liquid system in which the vapor-liquid equilibrium relationship for every volatile species is either Raoult s law or Henry s law is said to exhibit ideal solution behavior. An ideal liquid solution is a mixture of liquids that exhibits ideal solution behavior at equilibrium. 

We conclude this discussion with one final reminder. The vapor-liquid equilibrium calculations we have shown in Section 6.4c are based on the ideal-solution assumption and the corresponding use of Raoult s law. Many commercially important systems involve nonideal solutions, or systems of immiscible or partially miscible liquids, for which Raoult s law is inapplicable and the Txy diagram looks nothing like the one shown for benzene and toluene. 

It should also be noted that the symbol Ki is utilized for the mol fraction ratio y, /x, in comparing the permeate composition to the reject or raffinate composition, as will be developed in Example 19.4. This is the usual symbolism as used in phase equilibria, say that of the X-value or equilibrium vaporization ratio for correlating the behavior of vapor/liquid systems—and, ideally, reflects Raoult s law. The foregoing illustrates the general problem... 

For vapor—liquid equilibrium in binary system with ideal behavior of the vapor phase one can write/... 

It can be seen from equation (34.18) that for an ideal liquid system, the vapor will always be relatively richer than the liquid in the more volatile constituent, i.e., the one with the higher vapor pressure. For example, if, as in Fig. 21, the component 1 is the more volatile, p will be greater than p, and hence Ni/i 2 will exceed Ni/ns, and the vapor will contain relatively more of the component 1 than does the liquid with which it is in equilibrium. This fact is fundamental to the separation of liquids by fractional distillation. The limitations arising in connection with nonideal systems will be considered in 35b, 35c. 

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. 

Once the interaction energies were obtained, they were used to calculate the parameters in the UNIQUAC and Wilson models given by Eq. (24). To test the validity of the method, low-pressure vapor-liquid equilibrium (VLE) predictions were made for several binary aqueous systems. The calculations were done using the usual method assuming an ideal vapor phase (Sandler, 1999). Figures 7 and 8 show the low-pressure VLE diagrams for the binary aqueous mixtures of ethanol and acetone [see Sum and Sandler (1999a,b) for results for additional systems and values of the... 

A 1.20-g sample of water is injected into an evacuated 5.00-L flask at 65°C. What percentage of the water will be vapor when the system reaches equilibrium Assume ideal behavior of water vapor and that the volume of liquid water is negligible. The vapor pressure of water at 65°C is 187.5 mmHg. 

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