Phase splitting

When a mixture contains components with a broad range of volatilities, either a partial condensation from the vapor phase or a partial vaporization from the liquid phase followed by a simple phase split often can produce an effective separation. This is in essence a single-stage distillation process. However, by its very nature, a single-stage separation does not produce pure products hence further separation of both liquid and vapor streams is often required. 

Consider the single-stage phase split shown in Fig. 3.1a. Overall material balances and component material balances can be written as... 

If a vapor from the phase split is either predominantly product or predominantly byproduct, then it is removed from the process. If the vapor contains predominantly unconverted feed material, it is normally recycled to the reactor. In these cases, there is no need to carry out any separation on the vapor. 

If the vapor stream consists of a mixture of unconverted feed material, products, and byproducts, then some separation of the vapor may be needed. The vapor from the phase split is difficult to condense if the feed has been cooled to cooling water temperature. If separation of the vapor is needed, one of the following methods can be used ... 

Assume initially that a phase split can separate the reactor effluent into a vapor stream containing only hydrogen and methane and a liquid stream containing only benzene, toluene, and diphenyl and that the liquid separation system can produce essentially pure products. 

Determine the relation between the fraction of vapor from the phase split sent to purge (a) and the fraction of methane in the recycle and purge (y). 

The estimated composition of the reactor effluent is given in Table 4.2. This calculation assumes that all separations in the phase split are sharp. 

Given the estimate of the reactor effluent in Example 4.2 for fraction of methane in the purge of 0.4, calculate the.actual separation in the phase split assuming a temperature in the phase separator of 40°C. Phase equilibrium for this mixture can be represented by the Soave-Redlich-Kwong equation of state. Many computer programs are available commercially to carry out such calculations. 

TABLE 4.3 Vapor-Liquid Phase Split Using the Soave-Redlich-Kwong Equation of State... 

Repeat the calculation from Example 4.2 with actual phase equilibrium data in the phase split instead of assuming a sharp split. 

The reader might wish to check that if the temperature of the phase split is increased or its pressure decreased, the separation between hydrogen, methane, and the other components becomes worse. 

The temperature of the phase split is well above the critical temperatures of both hydrogen and methane, leading to large K values. On the other hand, the K values of the benzene, toluene, and diphenyl are very low, and hence the assumption of a sharp split in Example 4.2 was a good one. 

Example 4.6 Calculate the process jueld of benzene from toluene and benzene from hydrogen for the approximate phase split in Example 4.2. 

As for LLE, an expression for G capable of representing hquid—hquid-phase splitting is required as for VLE, a vapor-phase equation of state for computing ( ) is also needed. Moreover, VLLE calculations can in principle and sometimes in practice be carried out with an equation of state vahd for ah. coexisting phases. 

Thermodynamics of Liquid—Liquid Equilibrium. Phase splitting of a Hquid mixture into two Hquid phases (I and II) occurs when a single hquid phase is thermodynamically unstable. The equiUbrium condition of equal fugacities (and chemical potentials) for each component in the two phases allows the fugacitiesy andy in phases I and II to be equated and expressed as ... 

For most LLE applications, the effect of pressure on the Yi < an be ignored, and thus Eq. (4-327) constitutes a set of N equations relating equilibrium compositions to each other and to temperature. For a given temperature, solution of these equations requires a single expression for the composition dependence of suitable for both liquid phases. Not all expressions for suffice, even in principle, because some cannot represent liquid/liquid phase splitting. The UNIQUAC equation is suitable, and therefore prediction is possible by the UNIFAC method. A special table of parameters for LLE calculations is given by Magnussen, et al. (Jnd E/ig Chem Process Des Dev, 20, pp. 331-339 [1981]). 

FIG. 13-13 Vap or-liqiiid equilibrium data for an n-biitanol-water system at 101.3 kPa (1 atm) phase splitting and heterogeneous-azeotrope formation. 

Table 13-1, based on the binary-system activity-coefficient-eqnation forms given in Table 13-3. Consistent Antoine vapor-pressure constants and liquid molar volumes are listed in Table 13-4. The Wilson equation is particularly useful for systems that are highly nonideal but do not undergo phase splitting, as exemplified by the ethanol-hexane system, whose activity coefficients are snown in Fig. 13-20. For systems such as this, in which activity coefficients in dilute regions may...

The first three of these are solely X T.E-based approaches, involving a series of simple distillation operations and recycles. The final approach also relies on distillation (X T.E), but also exploits another physical phenomena, liqnid-hqnid phase formation (phase splitting), to assist in entrainer recovery. This approach is the most powerful and versatile. Examples of industrial uses of azeotropic distillation grouped by method are given in Table 13-18. 

Figure 8. Fractionation of polyethylene owing to phase splitting in ethylene solution molecular weight distributions in equuibrium phases at 260°C and 900...

Based on the above, we can develop an "adaptive" Gauss-Newton method for parameter estimation with equality constraints whereby the set of active constraints (which are all equalities) is updated at each iteration. An example is provided in Chapter 14 where we examine the estimation of binary interactions parameters in cubic equations of state subject to predicting the correct phase behavior (i.e., avoiding erroneous two-phase split predictions under certain conditions). 

Once the best set of interaction parameters has been found, these parameters should be used with the EoS to perform the VLE calculations. The computed values should be plotted together with the data. A comparison of the data with the EoS based calculated phase behavior reveals whether correct or incorrect phase behavior (erroneous liquid phase splitting) is obtained. 

If the correct phase behavior i.e. absence of erroneous liquid phase splits is predicted by the EoS then the overall fit should be examined and it should be judged whether it is "excellent". If the fit is simply acceptable rather than "excellent", then the previously computed LS parameter estimates should suffice. This was found to be the case for the n-pentane-acetone and the methane-acetone systems presented later in this chapter. 

Therefore, although the stability function was found to be positive at all the experimental conditions it becomes negative at mole fractions between 0 and the first measured data point. Obviously, if there were additional data available in this region, the simplified constrained LS method that was followed above would have yielded interaction parameters that do not result in prediction of false liquid phase splitting. 

When a mixture contains components with large relative volatilities, either a partial condensation from the vapor phase or a partial vaporization from the liquid phase followed by a simple phase split can often produce an effective separation1. 

One extremely powerful feature of heterogeneous distillation is the ability to cross distillation boundaries. It was noted previously that distillation boundaries divide the compositions into two regions that cannot be accessed from each other. Decanters allow distillation boundaries to be crossed, as illustrated in Figure 12.32. The feed to the decanter at F is on one side of the distillation boundary. This splits in the decanter to two-liquid phases E and R. These two-liquid phases are now on opposite sides of the distillation boundary. Phase splitting in this way is not constrained by a distillation boundary, and exploiting a two-phase separation in this way is an extremely effective way to cross distillation boundaries. 

Figure 12.32 Phase splitting can be used to cross distillation boundaries.

If the liquid from the phase split requires separation, then this can normally be accomplished by distillation, except under special circumstances. A distillation sequence is most often required with products and byproducts removed from the process and unreacted feed material recycled. In some situations, byproducts might be recycled for reasons discussed in the previous section. 

The liquid stream can readily be separated into relatively pure components by distillation, the benzene taken off as product, diphenyl as an unwanted byproduct and the toluene recycled. It is possible to recycle the diphenyl to improve selectivity, but it will be assumed that is not done here. The hydrogen feed contains methane as an impurity at a mole fraction of 0.05. The production rate of benzene required is 265 kmol-lr1. Assume initially that a phase split can separate the reactor effluent into a vapor stream containing only hydrogen and methane, and a liquid containing only benzene, toluene and diphenyl, and that it can be separated to produce essentially pure products. For a conversion in the reactor of 0.75,... 

This calculation assumes that all separations in the phase split are sharp. 

When a mixture in a reactor effluent contains components with a wide range of volatilities, then a partial condensation from the vapor phase followed by a simple phase split can often produce a good separation. If the vapor from such a phase split is difficult to condense, then further separation needs to be carried out in a vapor separation process such as a membrane. The liquid from the phase split can be sent to a liquid separation unit such as distillation. 

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