Distillation theoretical stage

Relative volatility Ratio of the K values of two components a measure of the ease with which the two components can be separated by distillation. Theoretical stage Contact process between vapor and liquid such that the exiting vapor and liquid streams are in equilibrium. 

Fractional vacuum distillation is the method used to separate terpene mixtures into their components. The terpene chemist usually has in the laboratory a range of columns with differing numbers of theoretical stages. Experimental distillation in the laboratory is useful in providing data for manufacturing plants that produce commercial quantities of terpene products. 

McCabe-Thie/e Example. Assume a binary system E—H that has ideal vapor—Hquid equiHbria and a relative volatiHty of 2.0. The feed is 100 mol of = 0.6 the required distillate is x = 0.95, and the bottoms x = 0.05, with the compositions identified and the lighter component E. The feed is at the boiling point. To calculate the minimum reflux ratio, the minimum number of theoretical stages, the operating reflux ratio, and the number of theoretical stages, assume the operating reflux ratio is 1.5 times the minimum reflux ratio and there is no subcooling of the reflux stream, then ... 

Fig. 11. Limiting conditions in binary distillation, (a) Minimum reflux and infinite number of theoretical stages (b) total reflux and minimum number of...

Computer solutions entail setting up component equiUbrium and component mass and enthalpy balances around each theoretical stage and specifying the required design variables as well as solving the large number of simultaneous equations required. The expHcit solution to these equations remains too complex for present methods. Studies to solve the mathematical problem by algorithm or iterational methods have been successflil and, with a few exceptions, the most complex distillation problems can be solved. 

In order to determine the packed height it is necessary to obtain a value of the overall number of transfer units methods for doing this are available for binary systems in any standard text covering distillation (73) and, in a more complex way, for multicomponent systems (81). However, it is simpler to calculate the number of required theoretical stages and make the conversion ... 

Heat Sensitivity. The heat sensitivity or polymerization tendencies of the materials being distilled influence the economics of distillation. Many materials caimot be distilled at their atmospheric boiling points because of high thermal degradation, polymerization, or other unfavorable reaction effects that are functions of temperature. These systems are distilled under vacuum in order to lower operating temperatures. For such systems, the pressure drop per theoretical stage is frequently the controlling factor in contactor selection. An exceUent discussion of equipment requirements and characteristics of vacuum distillation may be found in Reference 90. 

The variable that has the most significant impact on the economics of an extractive distillation is the solvent-to-feed (S/F) ratio. For closeboiling or pinched nonazeotropic mixtures, no minimum-solvent flow rate is required to effect the separation, as the separation is always theoretically possible (if not economical) in the absence of the solvent. However, the extent of enhancement of the relative volatihty is largely determined by the solvent concentration and hence the S/F ratio. The relative volatility tends to increase as the S/F ratio increases. Thus, a given separation can be accomplished in fewer equihbrium stages. As an illustration, the total number of theoretical stages required as a function of S/F ratio is plotted in Fig. 13-75 7 for the separation of the nonazeotropic mixture of vinyl acetate and ethyl acetate using phenol as the solvent. 

FIG. 13-75 Number of theoretical stages versus solvent-to-feed ratio for extractive distillation, a) Close-boiling vinyl acetate-etbyl acetate system with phenol solvent, (h) A2eotropic acetone-methanol system with water solvent. 

Example 10 Calculation of Multicomponent Batch Distillation A charge of 45.4 kg mol (100 Ih-mol) of 25 mole percent heuzeue, 50 mole percent monochlorohenzene (MCB), and 25 mole percent orthodichloro-henzene (DCB) is to he distilled in a hatch still consisting of a rehoiler, a column containing 10 theoretical stages, a total condenser, a reflux drum, and a distillate accumulator. Condenser-reflux drum and tray holdups are 0.0056 and... 

The recommended method to use to determine the actual theoretical stages at an actual reflux ratio is the Erbar/Maddox relationship. In the graph, N is the theoretical stages and R is the actual reflux ratio L/D, where L/D is the molar ratio of reflux to distillate. N, is the minimum theoretical stages and R, is the minimum reflux ratio. 

After actual theoretical trays are determined (see Actual reflux and theoretical stages) one needs to estimate the actual physical number of trays required in the distillation column. This is usually done by dividing the actual theoretical trays by the overall average fractional tray efficiency. Then a few extra trays are normally added for offload conditions, such as a change in feed composition. 

We may encounter problems in the purification of substances with a high normal boiling point. If purification only requires a small number of theoretical stages. Short Path Distillation (SPD), in which pressures can be as low as 0.001 bar, can prove useful. Many vitamins and pharmaceuticals can be processed without deterioration of quality. It is now common to use mechanical vacuum pumps with proper condensers preceding the pump. 

The actual stage can be a mixing vessel, as in a mixer-settler used for solvent extraction applications, or a plate of a distillation or gas absorption column. In order to allow for non-ideal conditions in which the compositions of the two exit streams do not achieve full equilibrium, an actual number of stages can be related to the number of theoretical stages, via the use of a stage-efficiency factor. 

Sieve plates are used, similar to those used for distillation and absorption. The stage efficiency for sieve plates, expressed in terms the height of an equivalent theoretical stage (HETS), will, typically, range from 1 to 2.5 m. 

Consider first total reflux conditions, corresponding with the minimum number of theoretical stages. The bottom of a distillation column at total reflux is illustrated in Figure 9.13. 

Subscript D refers to the distillate. Equation 9.33 predicts the number of theoretical stages for a specified binary separation at total reflux and is known as the Fenske Equation5. 

Packed fractional distillation columns run in the batch mode are often used for low-pressure drop vacuum separation. With a trayed column, the liquid holdup on the trays contributes directly to the hydraulic head required to pass through the column, and with twenty theoretical stages that static pressure drop is very high, e.g., as much as 100-200 mm Hg. 

The rate of withdrawal of the sidestream is 10 per cent of the column feed rate and the external reflux ratio is 2.5. Using the enthalpy composition method, determine the number of theoretical stages required, and the amounts of bottom product and distillate as percentages of the feed rate. 

A mixture of chlorinated phenols can be represented as an equivalent binary with 90% 2,4-dichlorphenol (DCP) and the balance 2,4,6-trichlorphenol with a relative volatility of 3.268. Product purity is required to be 97.5% of the lighter material, and the residue must be below 20% of 2,4-DCP. It is proposed to use a batch distillation with 10 theoretical stages. Vaporization rate will be maintained constant. 

Figure 13.14. A centrifugal packed fractionator, trade name HIGEE, Imperial Chemical Industries. Units have been operated with 500 times gravitational acceleration, with 3-18 theoretical stages, up to 36 in. dia, employing perforated metal packing. For distillation, one unit is needed for rectification and one for stripping. Units have been used primarily for gas stripping and on offshore platforms because of compactness [Ramshaw, Chem. Eng., 13-14 (Feb. 1983)].

Use of HETP Data for Absorber Design Distillation design methods (see Sec. 13) normally involve determination of the number of theoretical equilibrium stages N. Thus, when packed towers are employed in distillation applications, it is common practice to rate the efficiency of tower packings in terms of the height of packing equivalent to one theoretical stage (HETP). 

Figure 14-8 illustrates the graphical method for a three theoretical stage system. Note that in gas absorption the operating line is above the equilibrium curve, whereas in distillation this does not happen. In gas stripping, the operating line will be below the equilibrium curve. 

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