Steady-state design of the esterifications of acetic acid with five different alcohols (C1-C5) was explored in Chapter 7. This chapter explores the control of these five reactive distillation systems using three different flowsheets. The degree of process nonlinearity is computed quantitatively based on the fraction of "sign reversal" for all tray temperatures or based on Allgower's nonlinearity measure.1'2 These measures provide useful information about potential problems in closed-loop control. Next, a systematic design procedure is proposed to devise control structures for all three types of flowsheets for these five esteri-fication systems. The simulation results reveal that reasonable control can be achieved for all five systems with different degrees of asymmetry in closed-loop responses as predicted by the nonlinearity measures. Two-temperature control and one-temperature-one-composition control are studied. Simulation results clearly show that simple decentralized control provides a workable solution for highly nonlinear reactive distillation columns with various flowsheet configurations.
In Chapter 7 we showed that the esterification of acetic acid with different types of alcohols (C1-C5) can be classified into three types of flowsheets (types I—III), which were shown in
'P. H. Menold, F. Allgower, and P. K. Pearson, Nonlinear structure identification of chemical processes, Comput. Chem. Eng. 21, S137-S142 (1997).
2T. Schweickhardt and F. Allgower, Quantitative nonlinearity assessment: An introduction to nonlinearity measure, In P. Seferlis and M. C. Georgiadis, Editors, Integration of Process Design and Control, Elsevier, Amsterdam, 2004.
Reactive Distillation Design and Control. By William L. Luyben and Cheng-Ching Yu
Copyright # 2008 John Wiley & Sons, Inc.
Figure 7.2. The gradual change in the process configuration is the direct consequences of two factors: increased immiscibility (Fig. 7.3) and the shift of the boiling point ranking of the two products (water and acetate). Table 7.5 gives the optimized design for the production of methyl acetate (MeAc, type I), ethyl acetate (EtAc, type II), isopropyl acetate (IPAc, type II), butyl acetate (BuAc, type III), and amyl acetate (AmAc, type III) systems.
Steady-state analysis indicates that the type I and type III systems are more economical than the type II system. This chapter explores the dynamic controllability of these three flowsheets. Of more importance, we want to devise a systematic approach to the control of these three types of reactive distillations. All of the results are obtained from steady-state and dynamic simulations using Aspen Plus and Aspen Dynamics.
Manipulated Inputs. Before delving into a detailed quantitative analysis, we need to identify the manipulated variables for these three different types of processes. As pointed out by Luyben,3 it is important to maintain stoichiometric balance for neat reactive distillation. Al-Arfaj and Luyben4 chose to use one of the feedrates. In this chapter the feed ratio is used as one manipulated variable. In addition to holding the stoichiometric balance, we need to control two product compositions using two manipulated variables. However, for reactions such as A + B , C + D, if the conversion is properly maintained and the product flowrates are equally distributed, one-end composition control will do a fairly good job.
Following Al-Arfaj and Luyben,4 for the type I flowsheet of MeAc production we chose to control the bottoms composition using vapor boilup while fixing the reflux ratio.
For the type II flowsheet, the product composition of water from the first column (reactive distillation column) is determined by the LL equilibrium, so no composition control is necessary. However, the reflux ratio of the reactive distillation column is fixed. The acetate product is withdrawn from the bottoms of the stripper and the composition is controlled by manipulating the vapor boilup as shown in Figure 13.1.
Similar to the type II flowsheet, a decanter is used for the type III flowsheet to separate the water from the overhead condensate and therefore composition control is not necessary. The organic phase is totally refluxed back to the column. However, the bottoms acetate composition is controlled by changing the reboiler duty. Note that all of the control structures mentioned in this section use temperature control. In summary, the manipulated variables are
Type I: feed ratio and reboiler duty (fixed reflux ratio)
Type II: feed ratio and reboiler duty in the stripper (fixed organic reflux ratio in reactive distillation column)
Type III: feed ratio and reboiler duty (organic phase totally refluxed)
Nonlinearity and Output Multiplicity. Once the manipulated variables are determined, we can evaluate the process nonlinearity for these three different types of flowsheets. The tray temperatures are treated as the state variables. The manipulated variables are the heat input QR and feed ratio FR. The upper and lower bounds of the steady-state
3W. L. Luyben, Economic and dynamic impact of the use of excess reactant in reactive distillation systems, Ind. Eng. Chem. Res. 39, 2935-2946 (2000).
4M. A. Al-Arfaj and W. L. Luyben, Comparative control study of ideal and methyl acetate reactive distillation, Chem. Eng. Sci. 57, 5039-5050 (2002).
Figure 13.1 Process flowsheets and temperature control configurations for (a) type I, (b) type H, and (c) type m systems.
gains between the tray temperatures and the manipulated variables (QR and FR) are obtained for a range of input variations. We made —5% to + 5% changes in the heat input and — 1% to +1% changes in the feed ratio. Note that, for a truly linear system, the upper and lower bounds should coincide with each other. Figure 13.2 clearly shows that the reactive distillation columns exhibit strong nonlinearity for all five systems but with different degrees of severity. Moreover, the sign reversal is also observed for all five systems for both QR or FR changes. The sign reversal indicates that the steady-state gain of a specific tray temperature changes sign as the magnitude of the same manipulated variables varies.
The results presented here are rather unconventional because chemical processes are known to be quite nonlinear but not to this degree in such a consistent manner. Two measures are used to differentiate the degree of nonlinearity for these three types of reactive distillation systems. One obvious choice is the fraction of trays that exhibit sign reversal.
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