Multicomponent Distillation in Tray Columns

Let us now try to extend the model of binary distillation developed in Section 12.1.1 to multicomponent systems. The extension is based on the work of Toor (1964b) and the starting point is the material balance Eqs. 12.1.4, which must now be combined in n — 1 dimensional matrix form as 

The vapor-phase diffusion fluxes at any point are expressed using Eq. 7.3.11 (once again 

Equation 12.2.2 may be integrated over the dispersion height to give = [CKAy ) 

As in the binary case, we assume the integrand in Eq. 12.2.5 to be independent of froth height in order to complete the integration to give the overall number of transfer units. 

If the matrix of overall numbers of transfer units is known, (a topic we address 

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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. 

The design of both types of distillation columns is a fascinating subject to which a great many books and papers have been devoted (some were cited above). The modeling of mass transfer on distillation trays and the use of these mass transfer models in the simulation of multicomponent distillation and absorption columns are the aspects of the process design function that we shall consider in this book. 

Chapter 12 presents models of mass transfer on distillation trays. This material is used to develop procedures for the estimation of point and tray efficiencies in multicomponent distillation in Chapter 13. Chapter 14 uses the material of Chapter 12 in quite a different way in an alternative approach to the simulation and design of distillation and absorption columns that has been termed the nonequilibrium stage model. This model is applicable to liquid-liquid extraction with very little modification. Chapter 15 considers the design of mixed vapor condensers. 

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... 

Many industrial columns use temperatures for composition control because direct composition analyzers can be expensive and unreliable. Although temperature is uniquely related to composition only in a binary system (at known pressure), it is still often possible to use the temperatures on various trays up and down the column to maintain approximate composition control, even in multicomponent systems. Probably 75 percent of all distillation columns use temperature control of some tray to hold the composition profile in the column. This prevents the light-key (LK) impurities from dropping out the bottom and the heavy-key (HK) impurities from going overhead. 

If one or more unit operations have been given infeasible specifications, then the flowsheet will never converge. This problem also occurs with multicomponent distillation columns, particularly when purity specifications or flow rate specifications are used, or when nonadjacent key components are chosen. A quick manual mass balance around the column can usually determine whether the specifications are feasible. Remember that all the components in the feed must exit the column somewhere. The use of recovery specifications is usually more robust, but care is still needed to make sure that the reflux ratio and number of trays are greater than the minimum required. A similar problem is encountered in recycle loops if a component accumulates because of the separation specifications that have been set. Adding a purge stream usually solves this problem. 

Two different approaches have evolved for the simulation and design of multicomponent distillation columns. The conventional approach is through the use of an equilibrium stage model together with methods for estimating the tray efficiency. This approach is discussed in Chapter 13. An alternative approach based on direct use of matrix models of multicomponent mass transfer is developed in Chapter 14. This nonequilibrium stage model is also applicable, with only minor modification, to gas absorption and liquid-liquid extraction and to operations in trayed or packed columns. 

Chan, H., Tray Efficiencies for Multicomponent Distillation Columns, Ph.D. Thesis in Chemical Engineering, The University of Texas at Austin, TX, 1983. 

RAPID ESTIMATES OF MULTICOMPONENT DISTILLATION AND MINI> UM TRAYS IN DISTILLATION COLUMNS... 

The general methods of design for multicomponent distillation apply. Since in most cases all the components of the feed streams are found in the bottoms, the method of Lewis and Matheson can be used, starting at the bottom and computing to the top. There will be an optimum solvent-circulation rate small solvent rates require many trays, but the column diameters are small large ratios require fewer trays but larger column diameters and greater solvent-circulation costs. 

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. 

Total reflux exists in a distillation column, whether a binary or multicomponent system, when all the overhead vapor from the top tray or stage is condensed and returned to the top tray. Usually a column is brought to equilibrium at total reflux for test or for a temporary plant condition which requires discontinuing feed. Rather than shut down, drain and then re-establish operating conditions later, it is usually more convenient and requires less... 

The model of a multicomponent batch distillation column was derived in Sec. 3.13. For a simulation example, let us consider a ternary mixture. Three products will be produced and two slop cuts may also be produced. Constant relative volatility, equimolal overflow, constant tray holdup, and ideal trays are assumed. 

In fact, through use of matrix models of mass transfer in multicomponent systems (as opposed to effective diffusivity methods) it is possible to develop methods for estimating point and tray efficiencies in multicomponent systems that, when combined with an equilibrium stage model, overcome some of the limitations of conventional design methods. The purpose of this chapter is to develop these methods. We look briefly at ways of solving the set of equations that model an entire distillation column and close with a review of experimental and simulation studies that have been carried out with a view to testing multicomponent efficiency models. 

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