Control—Binary Distillation

Some very perceptive insights into the differences between petroleum refining distillation and that in the chemical industry are offered by Tolliver and Waggoner in an extensive literature review. 

Although most existing columns do not have composition control at both ends, some columns are so equipped. Most of those reported in the literature (references 8 and 9, for example) apparently are not badly aSlicted with interaction. At least dual composition control was accomplished without decouplers. For a laboratory column Waller and associates studied six approaches to dual composition control, including those of modem control theory. Tyreus discusses multivariable control of an industrial column whose design was performed via a technique called the inverse Nyquist array. 

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Figure 3.60. Model representation of a continuous binary distillation column. PC is the cooling water controller, LC the reflux controller.

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. 

Continuous Binary Distillation Column 496 Controller Tuning Problem 427 Three-Stage Reactor Cascade with Countercurrent Cooling 287... 

Example 1.5. For a binary distillation column (see Fig. 1.6), load disturbance variables might include feed flow rate and feed composition. Reflux, steam, cooling water, distillate, and bottoms flow rates might be the manipulated variables. Controlled variables might be distillate product composition, bottoms product composition, column pressure, base liquid level, and reflux drum liquid level. The uncontrolled variables would include the compositions and temperatures on aU the trays. Note that one physical stream may be considered to contain many variables ... 

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. 

RGA Example To illustrate use of the RGA method, consider the following steady-state version of a transfer function model for a pilot-scale, methanol-water distillation column (Wood and Berry, "Terminal Composition Control of a Binary Distillation Column, Chem. Eng. Sci., 28 1707, 1973) Kn = 12.8, Ku = -18.9, K21 = 6.6, and K22 = —19.4. It follows that X = 2 and... 

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

Jafarey et al. (61) derived a simple, approximate equation for binary distillation by simplifying the solution to Smoker s equation. Their equation is powerful for predicting the effect of disturbances on column performance. This makes their equation particularly useful in computer and microprocessor control, where it can be applied to estimate the effect of disturbances and the control action needed to compensate for them. This application is highlighted in Examples 3.8 and 3.9. The Jafarey et al, equation is... 

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 relationship was used in Examples 5.7 and 5.8 to determine the number of controlled outputs in a binary distillation and a mixing process, respectively. 

Consider the feed as a pseudo-binary mixture composed of benzene (== A) and toluene + diphenyl (s B). From Example 5.7 we know that we can specify four controlled variables for a binary distillation column. In our case these are ... 

EXAMPLE 4.2. Composition control in distillation columns is Ifequently done by controlling a temperature somewhere in the column The location of the best temperature control tray is a popular subject in the. process control literature. The ideal location for controlling distillate composition xo with reflux flow by using a tray temperature would be at the top of the column for a binary system (see Fig. 4.9a). This is desirable dynamically because it keeps the measurement lags as small as possible. It is also desirable from... 

Sensitivity. Figure 18.1 shows typical temperature and composition profiles for binary distillation. Temperature is insensitive to composition below point A or above point B. Therefore, all trays above tray 8 and below tray 36 are unsuitable for temperature control from a sensitivity standpoint. Of the trays between trays 8 and 36, some are more sensitive to composition than others. 

Sundmacher and Qi (Chapter 5) discuss the role of chemical reaction kinetics on steady-state process behavior. First, they illustrate the importance of reaction kinetics for RD design considering ideal binary reactive mixtures. Then the feasible products of kinetically controlled catalytic distillation processes are analyzed based on residue curve maps. Ideal ternary as well as non-ideal systems are investigated including recent results on reaction systems that exhibit liquid-phase splitting. Recent results on the role of interfadal mass-transfer resistances on the attainable top and bottom products of RD processes are discussed. The third section of this contribution is dedicated to the determination and analysis of chemical reaction rates obtained with heterogeneous catalysts used in RD processes. The use of activity-based rate expressions is recommended for adequate and consistent description of reaction microkinetics. Since particles on the millimeter scale are used as catalysts, internal mass-transport resistances can play an important role in catalytic distillation processes. This is illustrated using the syntheses of the fuel ethers MTBE, TAME, and ETBE as important industrial examples. 

Figure 1.3 shows a schematic of the batch distillation process for the separation of a volatile compound from a binary liquid mixture. It is heated in the bottom still to generate vapors, which condense at the top to yield distillate having a higher concentration of a the volatile compound. A part of the distillate is withdrawn as product while the rest is recycled to the still. An optimal control problem is to maximize the production of distillate of a desired purity over a fixed time duration by controlling the distillate production rate with time (Converse and Gross, 1963). 

Figure 20.11 Two control configurations for a binary distillation column (a) LV (b) DV.

Figure 21.2 shows the LV configuration for the two-point composition control of a binary distillation column discussed in Example 20.9. After assigning manipulated variables to regulate the vapor and liquid inventories, the boilup rate, V, and the reflux flow rate, L, remain available to control the distillate and bottoms product compositions, and Xg, respectively. To assess the controllability and resiliency of this configuration, the disturbances are taken to be the feed composition, Xp, and the flow rate, F. The column dynamics are approximated by a linear model in transfer function form (Sandelin et al., 1990) ... 

Figure 21.2 Control of a binary distillation column using the LV configuration.

Figure 213 Closed-loop response of the LV configuration for binary distillation to the worst-case disturbance, d. = [20, 6] with the decentralized PI control—Outputs X[i (solid line), Xg (dashed line) Inputs L (solid line), V (dashed line).

EXAMPLE 21.9 Tuning PI Control Loops for a Binary Distillation Column (Example 21.8 Revisited)... 

Most engineering students are familiar with the use of spreadsheets, but they may not be familiar with the power of spreadsheets when they are coupled with VBA. VBA is an extremely useful programming language for controlling spreadsheets. Word, and other Microsoft programs. This short introduction focuses on use of VBA for spreadsheet calculations. The particular exanple is binary distillation, but the VBA programming method is applicable to many of the separation methods in this book. Readers interested in more information on VBA are referred to Microsoft (1999) or McFedries (2004). 

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 process variables for continuous binary distillation columns and four basic control strategies... 

Wood, R.K., Berry, M.W. Terminal Composition Control of a Binary Distillation Column. Chemical Engineering Science 28, 1707-1717 (1973)... 

The alternative designs generated for the two test cases (heat exchanger and binary distillation) on basis of this TCA principle prove to be remarkably well aligned with the results of a black-box, input-output controllability analysis using the steady-state disturbance sensitivity approach. 

S( — 1 if all the feed enters tray k, and is zero otherwise, and = 1 if the reflux enters tray k, and is zero otherwise. Additionally, a set of control binary variables 6f are introduced that are associated with each MV-CV pairing and are unity when the pairing exists and zero otherwise. The modelling of the control structure selection is carried our similarly to Narraway and Perkins [15]. These features lead to a mixed-integer dynamic distillation model. The principal differential-algebraic equations (DAEs) for the trays are given below. A full list of nomenclature, values of the parameters, details of the DAEs for the reboiler, condenser, reflux drum and control scheme, cost correlations for the objective function and inequality path constraints, can be found in Bansal et al, [7]. 

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