Temperature-Dependent Relative Volatilities

Relative volatilities are fairly constant in hydrocarbon systems with similar chemical structures. However, in many systems the temperature dependences of vapor pressures of individual components are not the same. This typically results in a decrease in relative volatihty as temperature increases. If higher temperatures favor chemical kinetics and low temperatures give high relative volatihties, a mismatch may occur that can make reactive distillation unattractive. We wiU quantify these economic issues in Chapter 3. 

The reflux-dmm temperature in a conventional column would typically be 320 K because this permits the use of coohng water in the condenser. This would minimize pressure and maximize relative volatihties. The temperature in the reflux drum of the base case reactive distillation column operating at 8 bar is about 394 K (see Fig. 2.10). This is weU above the 320 K minimum and has been selected because it favors chemical kinetics. No issues of vapor-hquid equilibrium were involved in this selection because the relative volatihties were assumed to be constant and not affected by temperature. 

TABLE 2.4 Vapor Pressure Constants for Temperature Dependent a.g Case 

Now we demonstrate what happens when the relative volatihties of the components are temperature dependent. This is achieved by assuming that the relative volatility values of adjacent components are 2 when the temperature is 320 K but become smaller as the temperature increases. The value of the relative volatility of adjacent components at 390 K (a39o) is selected as a way to define this temperature dependence. The value of a39o is reduced from 2 (which corresponds to the constant relative volatihty case) to lower values. 

We will return to this problem in Chapter 3 and show how the design of the reactive column must be altered to handle cases with temperature dependence of the relative volatilities. As expected, the optimum column pressure decreases and the number of reactive trays increase as the values of a39o decrease. Reactive distillation becomes economically unattractive for a39o values of less than 1.2. 

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In the previous section, the optimum economic steady-state designs of reactive distillation columns were quantitatively compared with conventional multiunit systems for a wide range of chemical equilibrium constants. Relative volatilities (a = 2) were assumed constant. Reactive distillation was shown to be much less expensive than the conventional process. In this section we explore how temperature-dependent relative volatilities affect the designs of these two systems. 

Table 3.7 provides the optimum design results for the conventional process over a range of temperature-dependent relative volatilities. Because the column relative volatilities are only slightly lower than those of the constant relative volatility case, we assume that the three design optimization variables are the same as in the constant relative volatility case. The slightly lower relative volatilities produce small increases in the number of trays, the reflux ratios, and the vapor boilups in both columns. There is a small increase in the recycle flowrate (D2). 

Reactive Distillation. Figure 3.18 and Table 3.8 give optimum design results for the reactive distillation process for a range of temperature-dependent relative volatilities. As the a39o parameter decreases, the optimum pressure decreases. This occurs because lower pressure helps the vapor-liquid equilibrium because it lowers temperatures and hence increases relative volatilities. However, a lower temperature is unfavorable for reaction because the reaction rates are too small. The result is a rapid increase in the required number of reactive trays. 

A range of temperature-dependent relative volatilities are considered, which are the same as those studied in Chapter 3. The relative volatilities between all adjacent components are assumed to be 2 at a temperature of 320 K. This temperature corresponds to a typical reflux-drum temperature when using coohng water in the eondenser. 

The Kb method. For updating the tray temperatures, the theta method relies on the Kb method. The Kb method takes advantage of the near-linear dependence of the logarithm of the K-values and the relative volatilities on temperature over short temperature spans. Relative volatilities (a s) are calculated with respect to a base component K-value, K.bj k, at the stage temperature of the current column trial, Tjk. The base component is usually a middle boiler or a hypothetical component, The K-value of the base component for the next trial, Kbjk + 1( is calculated using a form of the bubble-point equation unique to the Kb method ... 

When the decomposition of N-phenyl-1,3,4,6-tetrahydrothieno-(3,4-c)-pyrrole-2,2-dioxide (II) was carried out in a sublimator a relatively high yield (80-95%) was obtained. However, under identical conditions, the decomposition of 5-(carboethoxyphenyl)-l,3,4,6-tetrahydrothieno(3,4-c)-pyrrole-2,2-dioxide yielded only 15% of diene product. This observation was found in agreement with the results reported by Alston (18). It was suggested that the yield from these sulfones depended on the relative volatility of the exocyclic diene formed since these dienes could undergo dimerization readily at the decomposition temperature of lbO C. 

It is evident that with the discrete cycles of the non-flame atomizers several reactions (desolvation, decomposition, etc.) which occur simultaneously" albeit over rather broad zones in a flame (due to droplet size distributions] are separated in time using a non-flame atomizer. This allows time and temperature optimization for each step and presumably improves atomization efficiencies. Unfortunately, the chemical composition and crystal size at the end of the dry cycle is matrix determined and only minimal control of the composition at the end of the ash cycle is possible, depending on the relative volatilities and reactivities of the matrix and analyte. These poorly controlled parameters can and do lead to changes in atomization efficiencies and hence to matrix interferences. 

Converse and Huber (1965), Robinson (1970), Mayur and Jackson (1971), Luyben (1988) and Mujtaba (1997) used this model for simulation and optimisation of conventional batch distillation. Domenech and Enjalbert (1981) used similar model in their simulation study with the exception that they used temperature dependent phase equilibria instead of constant relative volatility. Christiansen et al. (1995) used this model (excluding column holdup) to study parametric sensitivity of ideal binary columns. 

Determine the relevant vapor-pressure data. Design calculations involving vapor-liquid equilibrium (VLE), such as distillation, absorption, or stripping, are usually based on vapor-liquid equilibrium ratios, or K values. For the tth species, K, is defined as K, = y, /x, where y, is the mole fraction of that species in the vapor phase and x, is its mole fraction in the liquid phase. Sometimes the design calculations are based on relative volatility c/u], which equals K,/Kj, the subscripts i and j referring to two different species. In general, K values depend on temperature and pressure and the compositions of both phases. 

For ideal systems (adhering to Raoult s law) the relative volatility reduces to the ratio between two components vapor pressures. The dependency on total pressure is eliminated, and there is only a weak residual dependency on temperature. In many systems the relative volatilities can be considered constant, and this provides an easy means of calculating the vapor phase composition given the liquid phase mole fraction ... 

The lighter (lower-boiling temperature) components tend to concentrate in the vapor phase, while the heavier (higher-boiling temperature) components concentrate in the liquid phase. The result is a vapor phase that becomes richer in light components as it passes up the column and a liquid phase that becomes richer in heavy components as it cascades downward. The overall separation achieved between the distillate and the bottoms depends primarily on the relative volatilities of the components, the number of contacting trays in each column section, and the ratio of the liquid-phase flow rate to the vapor-phase flow rate in each section. 

The volatilities of the feed components relative to the solvent are generally high therefore, the design of the secondary column is primarily a function of the solvent circulation rate. The condenser duties depend on the reflux ratios in the two columns which are thus affected by the relative volatilities. The solvent cooler duty is a function of the solvent circulation rate and the recovery column reboiler temperature which is determined by the solvent volatility. The sum of the reboiler duties in... 

To obtain the composition of the top and bottom products, first calculate the relative volatility of each component using the conditions of the feed as a first guess. The relative volatility depends on temperature and pressure. The bubble point of the feed at 400 psia (27.6 bar) and at the feed composition, calculated using ASPEN [57], is 86.5 °F (130 °C). The K-values of the feed are listed in Table 6.7.1. Bubble and dew points could also be calculated using K-values from the DePriester charts [31] and by using the calculation procedures given in Chapter 3. Next, calculate the relative volatility of the feed stream, defined by Equation 6.27.18, for each component relative to the heavy key component. 

If the relative volatilities are composition-, temperature-, and pressure-dependent, we can use this composition as input to a bubble point computation. When solved, we will have new estimates for the relative volatilities. Then we can iterate the computation until all the numbers are consistent. 

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