Distillation multicomponent, model

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. 

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. 

Availability of large digital computers has made possible rigorous solutions of equilibrium-stage models for multicomponent, multistage distillation-type columns to an exactness limited only by the accuracy of the phase equilibrium and enthalpy data utilized. Time and cost requirements for obtaining such solutions are very low compared with the cost of manual solutions. Methods are available that can accurately solve almost any type of distillation-type problem quickly and efficiently. The material presented here covers, in some... 

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Even if you were only half awake when you read the preeeding chapter, you should have recognized that the equations developed in the examples eonstituted parts of mathematical models. This chapter is devoted to more complete examples. We will start with simple systems and progress to more realistic and complex processes. The most complex example will be a nonideal, nonequimolal-overflow, multicomponent distillation column with a veiy large number of equations needed for a rigorous description of the system. 

As a more realistic distillation example, let us now develop a mathematical model for a multicomponent, nonideal column with NC components, nonequimolal overflow, and inefficient trays. The assumptions that we will make are ... 

The general model was developed in Sec. 3.12. Table 5.8 gives a fairly general program for continuous multicomponent distillation. 

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. 

Reactive absorption, reactive distillation, and reactive extraction occur in multicomponent multiphase fluid systems, and thus a single modeling framework for these processes is desirable. In this respect, different possible ways to build such a framework are discussed, and it is advocated that the rate-based approach provides the most rigorous and appropriate way. By this approach, direct consideration... 

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. 

S. Griiner, S. Schwarzkopf, I. Uslu, et ah, Nonlinear model predictive control of multicomponent distillation columns using wave models. Proceedings, jth International Symposium on Advanced Control of Chemical Processes. Vol. 1,... 

A. Kienle, Low-order dynamic models for ideal multicomponent distillation processes using nonlinear wave propagation theory. Chem. 

The model equations for multicomponent distillation under constant boilup rate (Robinson, 1969) are ... 

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... 

For single separation duty, Bernot et al. (1991) presented a method to estimate batch sizes, operating times, utility loads, costs, etc. for multicomponent batch distillation. The approach is similar to that of Diwekar et al. (1989) in the sense that a simple short cut technique is used to avoid integration of a full column model. Their simple column model assumes negligible holdup and equimolal overflow. The authors design and, for a predefined reflux or reboil ratio, minimise the total annual cost to produce a number of product fractions of specified purity from a multicomponent mixture. 

Although the widely used equilibrium-stage models for distillation, described above, have proved to be quite adequate for binary and closeboiling, ideal and near-ideal multicomponent vapor-liquid mixtures. 

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