Flow rates multicomponent distillation

Open-loop behavior of multicomponent distillation may be studied by solving modifications of the multicomponent equations of Distefano [Am. Inst. Chem. Eng. J., 14, 190 (1968)] as presented in the subsection Batch Distillation. One frequent modification is to include an equation, such as the Francis weir formula, to relate liquid holdup on a tray to liquid flow rate leaving the tray. Applications to azeotropic-distillation towers are particularly interesting because, as discussed by and ihustrated in the Following example from Prokopalds and Seider... 

Fast and satisfactory mass transfer calculations are necessary since we may have to repeat such calculations many times for a rate-based distillation column model or two-phase flow with mass transfer between the phases in the design and simulation process. The generalized matrix method may be used for multicomponent mass transfer calculations. The generalized matrix method utilizes the Maxwell-Stefan model with the linearized film model for diffusion flux, assuming a constant diffusion coefficient matrix and total concentration in the diffusion region. In an isotropic medium, Fick s law may describe the multicomponent molecular mass transfer at a specified temperature and pressure, assuming independent diffusion of the species in a fluid mixture. Such independent diffusion, however, is only an approximation in the following cases (i) diffusion of a dilute component in a solvent, (ii) diffusion of various components with identical diffusion properties, and (iii) diffusion in a binary mixture. 

FIG. 13-109a Responses after a 30 percent increase in the feed flow rate for the multicomponent-dynamic-distillation example of Fig. 13-100. Profiles of liquid mole fractions at several times. 

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. 

Multicomponent rectification Consider a multicomponent mixture of m-species continuously fed into a distillation column (Acrivos and Amundson, 1955 Amundson, 1966 Ramkrishna and Amundson, 1985). Let and be the compositions of the ith species on the nth plate for the liquid phase and the vapor phase, respectively. Based on constant molal overflow of liquid with a downflow rate L and a vapor upward flow rate V, the steady-state mass balance for the ith species in the rectifying section above the nth plate leads to the equation... 

Qualitative leap to the second stage (i.e., to the distillation theory of ideal multicomponent mixtures) was realized by Underwood (1945,1946a, 1946b, 1948). Underwood succeded in obtaining the analytical solution of the system of distillation equations for infinite columns at two important simplifying assumptions -at constant relative volatilities of the components (i.e., which depend neither on the temperature nor on mixture composition at distillation column plates) and at constant internal molar flow rates (i.e., at constant vapor and liquid flow rates at all plates of a column section). The solution of Underwood is remarkable due to the fact that it is absolutely rigorous and does not require any plate calculations within the limits of accepted assumptions. 

We now examine the general case of separation of a multicomponent mixture by means of sharp extractive distillation in a column with two feeds at a set flow rate of entrainer in the mode of minimum reflux. The conditions of sections joining are similar to the conditions of sections joining of the two-section column and depend on the number of components in the product or in the pseudoproduct of each section (trir, trim, and tits) (i.e., on the dimensionality of the working and separatrix bundles of the sections). 

The entrainer flow rate influences expenditures for separation not only in extractive distillation column itself, but also in the column of the entrainer recovery. In the case of separation of a multicomponent azeotropic mixture in an autoextractive distillation column (see Chapter 8), the intermediate columns can be located between this column and the column of autoentrainer recovery. In this case, the flow rate of the entrainer also influences expenditures for separation in the intermediate columns. In connection with the aforesaid, the necessity arises to carry... 

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. 

Both modes usually are conducted with constant vaporization rate at an optimum value for the particular type of column construction. Figure 13.9 represents these modes on McCabe-Thiele diagrams. Small scale distillations often are controlled manually, but an automatic control scheme is shown in Figure 13.9(c). Constant overhead composition can be assured by control of temperature or directly of composition at the top of the column. Constant reflux is assured by flow control on that stream. Sometimes there is an advantage in operating at several different reflux rates at different times during the process, particularly with multicomponent mixtures as on Figure 13.10. 

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