Binary Distillation Design

Part 3 of this book presents a number of major developments and applications of MINLP approaches in the area of Process Synthesis. The illustrative examples for MINLP applications, presented next in this section, will focus on different aspects than those described in Part 3. In particular, we will consider the binary distillation design of a single column, the retrofit design of multiproduct batch plants, and the multicommodity facility location/allocation problem. 

Formulation of the mathematical model here adopts the usual assumptions of equimolar overflow, constant relative volatility, total condenser, and partial reboiler. Binary variables denote the existence of trays in the column, and their sum is the number of trays N. Continuous variables represent the liquid flow rates Li and compositions xj, vapor flow rates Vi and compositions yi, the reflux Ri and vapor boilup VBi, and the column diameter Di. The equations governing the model include material and component balances around each tray, thermodynamic relations between vapor and liquid phase compositions, and the column diameter calculation based on vapor flow rate. Additional logical constraints ensure that reflux and vapor boilup enter only on one tray and that the trays are arranged sequentially (so trays cannot be skipped). Also included are the product specifications. Under the assumptions made in this example, neither the temperature nor the pressure is an explicit variable, although they could easily be included if energy balances are required. A minimum and maximum number of trays can also be imposed on the problem. 

For convenient control of equation domains, etTR = 1. N denote the set of trays from the reboiler to the top tray and let Nj be the feed tray location. Then AF = Nf + 1. N is the set of trays in the rectifying section and BF = 2. Nf — 1 is the set of trays in the stripping section. The following equations describe the MINLP model. 

The economic objective function to be minimized is the cost, which combines the capital costs associated with building the column and the utility costs associated with operating the column. The form for the capital cost of the column depends upon the vapor boilup, the number of trays, and the column diameter 

The model includes parameters for relative volatility a, vapor velocity v, tray spacing flow constant kv, flooding factor //, vapor py and liquid pL densities, molecular weight MW, and some known upper bound on column flow rates FmaX. 

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It is worth noting that the above formulation of the binary distillation design features the binary variables qi separably and linearly in the set of constraints. The objective function, however, has products of the diameter D, and the number of trays Ni which are treated as integer variables. 

Continuous binary distillation is illustrated by the simulation example CON-STILL. Here the dynamic simulation example is seen as a valuable adjunct to steady state design calculations, since with MADONNA the most important column design parameters (total column plate number, feed plate location and reflux ratio) come under the direct control of the simulator as facilitated by the use of sliders. Provided that sufficient simulation time is allowed for the column conditions to reach steady state, the resultant steady state profiles of composition versus plate number are easily obtained. In this way, the effects of changes in reflux ratio or choice of the optimum plate location on the resultant steady state profiles become almost immediately apparent. 

This illustrative example is taken from the recent work on interaction of design and control by Luyben and Floudas (1994a) and considers the design of a binary distillation column which separates a saturated liquid feed mixture into distillate and bottoms products of specified purity. The objectives are the determination of the number of trays, reflux ratio, flow rates, and compositions in the distillation column that minimize the total annual cost. Figure (1.1) shows a superstructure for the binary distillation column. 

M. L. Luyben and C. A. Floudas. Analyzing the interaction of design and control, Part 1 A multiobjective framework and application to binary distillation synthesis. Comp. Chem. Eng., 18(10) 933, 1994a. 

Bilec, R. and Wood, R. K., "Multivariable Frequency Domain Controller Design for a Binary Distillation Column," AIChE National Meeting, Houston, Texas, April, 1979. 

Algebraic Method for Binary Distillation Calculation 392 Shortcut Design of Multicomponent Fractionation 396 Calculation of an Absorber by the Absorption Factor Method 399... 

Blakely, D. M, "Cost Saving in Binary Distillation through Two-Column Designs," M. S. Dissertation, Cleinson University, Clemson, SC (1984). 

In this application, the column is designed with a computer simulation program and then the computer output is used for plotting the distillation diagram to check the design. This example, which is based on two articles by Johnson and Morgan (1985, 1986), also shows how the principles of binary distillation can be applied to multi-component mixtures. 

Having chosen the keys, the designer arbitrarily assigns small numbers to Xjj in the distillate (x h) and to x, in the bottoms (x J, just as small numbers are assigned to Xjjc and x a in binary distillation. Choosing small... 

Care must be exercised not to specify more control objectives than the available number of degrees of freedom. In such a case the system becomes overspecified and it is impossible to design a control system that satisfies all the desired control objectives. Thus it is impossible to design a control system for the ideal binary distillation column that can satisfy the following six operational (control) objectives ... 

This chapter introduces how continuous distillation columns work and serves as the lead to a series of nine chapters on distillation. The basic calculation procedures for binary distillation are developed in Chapter 4. Multicomponent distillation is introduced in Chapter 5. detailed conputer calculation procedures for these systems are developed in Chapter 6. and sinplified shortcut methods are covered in Chapter 7. More complex distillation operations such as extractive and azeotropic distillation are the subject of Chapter 8. Chapter 9 switches to batch distillation, which is commonly used for smaller systems. Detailed design procedures for both staged and packed columns are discussed in Chapter 10. Finally, Chapter 11 looks at the economics of distillation and methods to save energy (and money) in distillation systems. 

In design problems, the desired separation is set, and a column is designed that will achieve this separation. For binary distillation we would usually specify the mole fraction of the more volatile component in the distillate and bottoms products. In addition, the external reflux ratio, L D in Figure 4-6. 

To illustrate, consider a typical design problem for a binary distillation column such as the one illustrated in Figure 3-8. We will assume that equilibrium data are available at the operating pressure of the column. These data are plotted as shown in Figure 4-4. At the top of the column is a total condenser. As noted in Chapter 3 in Eq. (3=7), this means that yi = = Xq. The vapor leaving the first stage is in equilibrium... 

This section addresses the application of a dynamic optimization-based design approach to RD. The liquid-phase esterification reaction of C4 and methanol in the presence of inert nC4 in a staged RD column is used as tutorial example. Similar to the study on binary distillation (Bansal et al., 2000 Bansal, 2000) and on the synthesis of ethyl acetate by RD (Georgiadis et al, 2002), both spatial-related e.g. column diameter and heat exchanger areas) and control-related e.g. gain, set-point and reset time) design variables are optimized with respect to economic and dynamic performance in the presence of time-varying disturbances. 

The separation power base in the classic McCabe-Thiele graphical model of a binary distillation column is established by the reflux ratio, R/D, which is the ratio of the reflux flow rate divided by the distillate flow rate. For example, with a distillation column that is fed 1,000 kg/h of feed that produces 85 kg/h of distillate with 425 kg/h of reflux, the reflux ratio is 425/85 = 5. A minimum reflux ratio is required to achieve the desired separation with an infinite number of theoretical stages. The maximum reflux ratio, called total reflux, with zero distillate flow rate can be used in design calculations to determine the minimum number of theoretical stages required to achieve a desired separation. 

What is often called the McCabe-Thiele method " for binary distillation calculations deploys a y-x (or y-x) diagram, say, for the more-volatile component, here designated the more-permeable component i. This furnishes substantiation that a separation can indeed be attained by the use of recycle or reflux in a multistage or cascade operation. 

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