Relative volatility. See

From Fenske s equation, the minimum number of equilibrium stages at total reflux is related to their bottoms (B) and distillate or overhead (D) compositions using the average relative volatility, see Equation 8-29. 

Step 2 Calculate the corresponding y. Recalling the definition of relative volatility (see page 51) ... 

Changinp feed composition changes reflux ratio and energy input but not in the same way for all columns. The effect depends on product purities and relative volatilities (see reference 9). 

Many mercury compounds are labile and easily decomposed by light, heat, and reducing agents. In the presence of organic compounds of weak reducing activity, such as amines (qv), aldehydes (qv), and ketones (qv), compounds of lower oxidation state and mercury metal are often formed. Only a few mercury compounds, eg, mercuric bromide/77< 5 7-/7, mercurous chloride, mercuric s A ide[1344-48-5] and mercurous iodide [15385-57-6] are volatile and capable of purification by sublimation. This innate lack of stabiUty in mercury compounds makes the recovery of mercury from various wastes that accumulate with the production of compounds of economic and commercial importance relatively easy (see Recycling). 

Hengstebeck shows how the method can be extended to deal with situations where the relative volatility cannot be taken as constant, and how to allow for variations in the liquid and vapour molar flow rates. He also gives a more rigorous graphical procedure based on the Lewis-Matheson method (see Section 11.8). 

Example 11.1 Each component for the mixture of alkanes in Table 11.2 is to be separated into relatively pure products. Table 11.2 shows normal boiling points and relative volatilities to indicate the order of volatility and the relative difficulty of the separations. The relative volatilities have been calculated on the basis of the feed composition to the sequence, assuming a pressure of 6 barg using the Peng-Robinson Equation of State with interaction parameters set to zero (see Chapter 4). Different pressures can, in practice, be used for different columns in the sequence and if a single set of relative volatilities is to be used, the pressure at which the relative volatilities are calculated needs, as much as possible, to be chosen to represent the overall system. 

Example 11.2 Using the Underwood Equations, determine the best distillation sequence, in terms of overall vapor load, to separate the mixture of alkanes in Table 11.2 into relatively pure products. The recoveries are to be assumed to be 100%. Assume the ratio of actual to minimum reflux ratio to be 1.1 and all columns are fed with a saturated liquid. Neglect pressure drop across each column. Relative volatilities can be calculated from the Peng-Robinson Equation of State with interaction parameters assumed to be zero (see Chapter 4). Determine the rank order of the distillation sequences on the basis of total vapor load for ... 

Because acrylonitrile is listed as a hazardous substance, disposal of waste acrylonitrile is controlled by number of federal regulations (see Chapter 7). Rotary kiln, fluidized bed and liquid injection incineration are acceptable methods of acrylonitrile disposal (HSDB 1988). Underground injection is another disposal method. The most recent quantitative information on amount of acrylonitrile disposed in waste sites is for 1987. Emissions were 0.9 metric tons in surface water, 152 metric tons disposed through Publicly Owned Treatment Works (POTW), 92 metric tons disposed of on land 1,912 metric tons by underground injection (TR11988). Because acrylonitrile is relatively volatile and is also readily soluble in water, release to the environment from waste sites is of concern. 

Example 2.7. To show what form the energy equation takes for a two-phase system, consider the CSTR process shown in Fig. 2.6. Both a liquid product stream f and a vapor product stream F (volumetric flow) are withdrawn from the vessel. The pressure in the reactor is P. Vapor and liquid volumes are and V. The density and temperature of the vapor phase are and L. The mole fraction of A in the vapor is y. If the phases are in thermal equilibrium, the vapor and liquid temperatures are equal (T = T ). If the phases are in phase equilihrium, the liquid and vapor compositions are related by Raoult s law, a relative volatility relationship or some other vapor-liquid equilibrium relationship (see Sec. 2.2.6). The enthalpy of the vapor phase H (Btu/lb or cal/g) is a function of composition y, temperature T , and pressure P. Neglecting kinetic-energy and potential-energy terms and the work term,... 

Figure 4.19 illustrates the effect of liquid phase mass transfer, represented by the dimensionless group Kuq (see Eqs. (55) and (57)). If the evaporation velocity is in the same order of magnitude as the liquid phase mass transfer coefficient, then the selectivity of the evaporation process vanishes though the relative volatility as well as the gas phase mass transfer coefficients remain unchanged. 

For single separation duty, Diwekar et al. (1989) considered the multiperiod optimisation problem and for each individual mixture selected the column size (number of plates) and the optimal amounts of each fraction by maximising a profit function, with a predefined conventional reflux policy. For multicomponent mixtures, both single and multiple product options were considered. The authors used a simple model with the assumptions of equimolal overflow, constant relative volatility and negligible column holdup, then applied an extended shortcut method commonly used for continuous distillation and based on the assumption that the batch distillation column can be considered as a continuous column with changing feed (see Type II model in Chapter 4). In other words, the bottom product of one time step forms the feed of the next time step. The pseudo-continuous distillation model thus obtained was then solved using a modified Fenske-Underwood-Gilliland method (see Type II model in Chapter 4) with no plate-to-plate calculations. The... 

In each selector, a logical diagram will guide the identification of a suitable separation method for the split proposed above. This is done by ranking the mixture components versus a characteristic property. For example, the relative volatility is a characteristic property for separation by simple distillation (see Appendices E and F). This approach, however, is not applicable when azeotropes are involved and other characteristic properties should be investigated, such as, for example, the chemical structure. A split becomes potential if complete by at least one method. 

The effect of physical properties on column efficiency can be roughly estimated from Fig. 8.16. For this system, viscosity is 0.35 cP (see statement of previous example) and relative volatility is 3.6, so the abscissa is 1.26. The ordinate, or column efficiency, is read to be 68 percent. 

It is reasonable to allow a pressure drop of 3 mmHg per tray. Then the reboiler pressure will be 50 + 3(157) = 521 mmHg. At this pressure, the relative volatility (from Fig. 8.22) is 1.14, and the average relative volatility in the column is then (see step 1) (1.265 + 1.14)/2 = 1.2. From Fig. 8.5, the estimated number of equilibrium stages is 107, which confirms that the initially selected 110 trays was a reasonable assumption. 

Equation-Based Design Methods Exact design equations have been developed for mixtures with constant relative volatility. Minimum stages can be computed with the Fenske equation, minimum reflux from the Underwood equation, and the total number of stages in each section of the column from either the Smoker equation (Trans. Am. Inst. Chem. Eng., 34, 165 (1938) the derivation of the equation is shown, and its use is illustrated by Smith, op. cit.), or Underwoods method. A detailed treatment of these approaches is given in Doherty and Malone (op. cit., chap. 3). Equation-based methods have also been developed for nonconstant relative volatility mixtures (including nonideal and azeotropic mixtures) by Julka and Doherty [Chem. Eng. Set., 45,1801 (1990) Chem. Eng. Sci., 48,1367 (1993)], and Fidkowski et al. [AIChE /., 37, 1761 (1991)]. Also see Doherty and Malone (op. cit., chap. 4). 

Composition profiles for the same extractive distillation column are shown in Figure 6. The water concentration in the liquid goes through a pronounced maximum at about tray number four (see Table VI), corresponding to the minimum in the relative volatility of water with respect to ethanol. In this region the ethanol concentration in the vapor increases rapidly, changing from less than 2% at tray number three to more than 50% at tray number six. This rapid increase continues to about tray number ten where the concentration of ethanol in the vapor is about... 

To 70% HF/pyridine (10-l5mL) was added the a/iridine (5-10 mmol), pure or diluted in dry benzene or CHjCi, (2 mL), dropwisc at rt. The mixture was maintained under the conditions required for each starting material (see Table 12), then poured into H2O (10-20mL). washed with EljO or CHjClj (3 X 15mL), cautiously neutralized with 10-30% NH, or sat. aq NaHCO,. and extracted with EtjO or CH,CL (3 X 20 mL). The organic extracts were then dried (MgSOJ and evaporated in vacuo. Except for relatively volatile fluoro amines (for which the pyridine and the fluoro amine w ere separated by column chromatography or recrystallization), pure fluoro amines were obtained after evaporation of the pyridine in vacuo. 

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