Distillation multicomponent calculations

In this chapter consideration is given to the theory of the process, methods of distillation and calculation of the number of stages required for both binary and multicomponent systems, and discussion on design methods is included for plate and packed columns incorporating a variety of column internals. 

After evaluation of (5.1-37) the energy demand of multicomponent distillation is calculated from... 

Distillation Columns. Distillation is by far the most common separation technique in the chemical process industries. Tray and packed columns are employed as strippers, absorbers, and their combinations in a wide range of diverse appHcations. Although the components to be separated and distillation equipment may be different, the mathematical model of the material and energy balances and of the vapor—Hquid equiUbria are similar and equally appHcable to all distillation operations. Computation of multicomponent systems are extremely complex. Computers, right from their eadiest avadabihties, have been used for making plate-to-plate calculations. 

Simple analytical methods are available for determining minimum stages and minimum reflux ratio. Although developed for binary mixtures, they can often be applied to multicomponent mixtures if the two key components are used. These are the components between which the specification separation must be made frequendy the heavy key is the component with a maximum allowable composition in the distillate and the light key is the component with a maximum allowable specification in the bottoms. On this basis, minimum stages may be calculated by means of the Fenske relationship (34) ... 

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 ... 

Feed analyses in terms of component concentrations are usually not available for complex hydrocarbon mixtures with a final normal boihng point above about 38°C (100°F) (/i-pentane). One method of haudhug such a feed is to break it down into pseudo components (narrow-boihng fractions) and then estimate the mole fraction and value for each such component. Edmister [2nd. Eng. Chem., 47,1685 (1955)] and Maxwell (Data Book on Hydrocarbons, Van Nostrand, Princeton, N.J., 1958) give charts that are useful for this estimation. Once values are available, the calculation proceeds as described above for multicomponent mixtures. Another approach to complex mixtures is to obtain an American Society for Testing and Materials (ASTM) or true-boihng point (TBP) cui ve for the mixture and then use empirical correlations to con-strucl the atmospheric-pressure eqiiihbrium-flash cui ve (EF 0, which can then be corrected to the desired operating pressure. A discussion of this method and the necessary charts are presented in a later subsection entitled Tetroleum and Complex-Mixture Distillation. ... 

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... 

Relative volatility is the volatility separation factor in a vapor-liquid system, i.e., the volatility of one component divided by the volatility of the other. It is the tendency for one component in a liquid mixture to separate upon distillation from the other. The term is expressed as fhe ratio of vapor pressure of the more volatile to the less volatile in the liquid mixture, and therefore g is always equal to 1.0 or greater, g means the relationship of the more volatile or low boiler to the less volatile or high boiler at a constant specific temperature. The greater the value of a, the easier will be the desired separation. Relative volatility can be calculated between any two components in a mixture, binary or multicomponent. One of the substances is chosen as the reference to which the other component is compared. 

Yaws [124] et al. provide an estimating technique for recovery of each component in the distillate and bottoms from multicomponent distillation using short-cut equations and involving the specification of the recovery of each component in the distillate, the recovery of the heavy key component in the bottoms, and the relative volatility of the light key component. The results compare very well with plate-to-plate calculations. Figure 8-46, for a wide range of recoveries of 0.05 to 99.93% in the distillate. 

Multicomponent distillation is by far the common requirement for process plants and refineries, rather than the simpler binary systems. There are many computer programs which have been developed to aid in accurately handling the many iterative calculations required when the system involves three to possibly ten individual components. In order to properly solve a multicomponent design, there should be both heat and material balance at every theoretical tray throughout the calculation. 

Hengstebeck, R. J., An Improved Shortcut for Calculating Difficult Multicomponent Distillations, Chem. Eragjan. 13 (1969), p. 115. 

Fredenslund, A., Gmehling, J., Michelsen, M. L., Rasmussen, P. and Prausnitz, J. M. (1977a) Ind. Eng. Chem. Proc. Des. and Dev. 16, 450. Computerized design of multicomponent distillation columns using the UNIFAC group contribution method for calculation of activity coefficients. 

The complexity of multicomponent distillation calculations can be appreciated by considering a typical problem. The normal procedure is to solve the MESH equations (Section 11.3.1) stage-by-stage, from the top and bottom of the column toward the feed point. For such a calculation to be exact, the compositions obtained from both the bottom-up and top-down calculations must mesh at the feed point and match the feed composition. But the calculated compositions will depend on the compositions assumed for the top and bottom products at the commencement of the calculations. Though it is possible to... 

Colburn, A. P. (1941) Trans. Am. Inst. Chem. Eng. 37, 805. The calculation of minimum reflux ratio in the distillation of multicomponent mixtures. 

Integral condensation in which the liquid remains in equilibrium with the uncondensed vapour. The condensation curve can be determined using procedures similar to those for multicomponent flash distillation given in Chapter 11. This will be a relatively simple calculation for a binary mixture, but complex and tedious for mixtures of more than two components. 

A distillation calculation is to be performed on a multicomponent mixture. The vapor-liquid equilibrium for this mixture is likely to exhibit significant departures from ideality, but a complete set of binary interaction parameters is not available. What factors would you consider in assessing whether the missing interaction parameters are likely to have an important effect on the calculations ... 

Underwood AJV (1946) Fractional Distillation of Multicomponent Mixtures - Calculation of Minimum Reflux Ratio, 7 Inst Petrol, 32 614. 

Two other problems that fit this category are calculating the number of stages in a multicomponent distillation problem, and obtaining the material balance when complicated recycle operations occur. 

Although this problem is one of multicomponent batch distillation, the product remains of constant composition so that normal methods can be used for plate-to-plate calculations at a point value of the varying reflux ratio. 

In multicomponent distillation, A and B are the light and heavy key components respectively. In this problem, the only data given for both top and bottom products are for m-and p-xylene and these will be used with the mean relative volatility calculated in the previous problem. Thus ... 

This relation enables the composition of the vapour to be calculated for any desired value of x, if a is known. For separation to be achieved, a must not equal 1 and, considering the more volatile component, as a increases above unity, y increases and the separation becomes much easier. Equation 11.14 is useful in the calculation of plate enrichment and finds wide application in multicomponent distillation. 

The concepts NTU and HTU are defined only for binary distillations and the transfer of a single substance in absorption or stripping. Since most processes of industrial interest involve multicomponents, the HETS of packed towers is the more useful concept, and may be evaluated readily from test data and tray calculations. 

Until the advent of computers, multicomponent distillation problems were solved manually by making tray-by-tray calculations of heat and material balances and vapor-liquid equilibria. Even a partially complete solution of such a problem required a week or more of steady work with a mechanical desk calculator. The alternatives were approximate methods such as those mentioned in Sections 13.7 and 13.8 and pseudobinary analysis. Approximate methods still are used to provide feed data to iterative computer procedures or to provide results for exploratory studies. 

When data of activity coefficients of all pairs of components are known, including those with the solvent, any of the standard calculation procedures for multicomponent distillation, which include ternaries, may be used. Composition profiles found by tray-by-tray calculations in two cases appear in Figure 13.24. 

Design. When the vapor-liquid equilibria are known, in the form of UNIQUAC parameters for instance, the calculation of azeotropic distillation may be accomplished with any of the standard multicomponent distillation procedures. The Naphthali-... 

Suzuki I, Yagi H, Komatsu H, Hirata M. Calculation of multicomponent distillation accompanied by a chemical reaction. J Chem Eng Japan 1971 4 26-33. 

The rate-based models suggested up to now do not take liquid back-mixing into consideration. The only exception is the nonequilibrium-cell model for multicomponent reactive distillation in tray columns presented in Ref. 169. In this work a single distillation tray is treated by a series of cells along the vapor and liquid flow paths, whereas each cell is described by the two-film model (see Section 2.3). Using different numbers of cells in both flow paths allows one to describe various flow patterns. However, a consistent experimental determination of necessary model parameters (e.g., cell film thickness) appears difficult, whereas the complex iterative character of the calculation procedure in the dynamic case limits the applicability of the nonequilibrium cell model. 

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... 

Suzaki, Yagi, Kamatsu, and Hirat, "Calculation of Multicomponent Distillation Accompanied by Chemical Reaction", J. Chem. Eng. (Japan), vol 4, no 1, p 26, (1971)... 

Multicomponent Distillation Calculations," Journal Chem Engr. Sym, Series No. 32," 1969, Inst of Chem Engr. -London. 

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