Figure 9.14. Reflux Ratio and Instant Distillate Composition Profile. [Wajge and Reklaitis, 1999]d d Reprinted from Chemical Engineering Journal, 75, Wajge, R.M. and Reklaitis, G.V., RBDOPT: a general-purpose object-oriented module for distributed campaign optimisation of reactive batch distillation, 57-68, Copyright (1999), with permission from Elsevier Science .

9.10. Optimal Design of Operating Procedures with Parametric Uncertainty

Process dynamics and uncertainties are important issues for optimal design and operation of any processes. All process models are subject to uncertainties, e.g. in physical properties, kinetics, etc.

Walsh et al. (1995) examined the effect of uncertain parameters on the optimal operation of BREAD processes and the use of control to reduce the effect of uncertainties. The study provided an important step towards the implementation of optimal operating policies on real (uncertain) processes.

As presented in the earlier chapters, the operating policy for a batch distillation column can be determined in terms of reflux ratio, product recoveries and vapour boilup rate as a function of time (open-loop control). Under nominal conditions, the optimal operating policy may be specified equivalently in terms of a set-point trajectory for controllers manipulating these inputs. In the presence of uncertainty, these specifications for the optimal operating policy are no longer equivalent and it is important to evaluate and compare their performance.

The effect of uncertainty on the performance of an operating policy can be evaluated by repetitive simulation (Leversund et al., 1993). However, if the uncertainty can be characterised by a finite set of parameterised conditions, then a multi-period approach to design and operation is appropriate (Chapter 7 and Mujtaba and Macchietto, 1996). This approach is well suited to design problems in which the key variability in the process is both known and discrete, e.g. a number of specified feed compositions. If the variability / uncertainty to be accommodated is continuous rather than discrete then the multi-period design must be augmented with a method for finding the worst-case scenarios of the uncertainty, i.e. worst-case design (Grossmann et al., 1983).

Walsh et al. (1995) used a simplified BREAD process model in conjunction with a parameterised uncertainty description to predict the performance. Worst-case design algorithm of Walsh (1993) was used to systematically determine the optimal operating policies that allow performance constraints to be met over a bounded set of uncertain parameters.

9.10.1. The Worst-case Design Algorithm

Walsh (1993) used approximate global maximisation of the maximum constraint violation to identify the worst-case scenarios for consideration in design. Control Vector Parameterisation (CVP) described in earlier chapters is used in solving the underlying dynamic optimisation problems. The general approach of worst-case design is shown in Figure 9.15. See the original reference for further details.

Figure 9.15. Worst-case Design using Outer Approximation Algorithm.

9.10.2. Case Study Process Description

Walsh et al. (1995) considered an industrial batch reactive distillation problem originally presented by Leversund et al. (1993) as a case study. A condensation polymerisation reaction between a dibasic aromatic acid (Rl) and two glycols (R2, R3) was considered. The reaction products were a polymer product (P) and water

(W). Chemical reaction occurs in the reboiler only. High conversion is achieved by removing the water in the distillate.

The process model is given in Leversund et al. (1993). As the polymer product forms a separate solid phase, this was not included in the process model. The model includes mass and energy balances, column holdup and phase equilibria and results in a set of DAEs. All thermodynamic, physical properties are calculated from library subroutines. The column description and data for the process are given in Table 9.6.

Table 9.6. Input Data for the Case Study


Initial Holdups:

Initial Charge Composition:

Initial Plate Composition:

Reaction: Reaction Rate: Rate Constants:

Reference Temperature: Column Pressure: Value of Product P:

Cost of Steam:

Accumulator + Total Condenser + 5 Plates + Reboiler

Reboiler = 20.6 kmol Plates = 0.1 kmol

Condenser =1.7 kmol Accumulator = 0

0.1505,0.4854] molefraction x° (W, R2, R3, Ri) = [0.999999, 0.000001,

0.0, 0.0] molefraction

r = k{cm (cR 2 +cR 3 ) - k2cw fcj ~ k\Q exp h = *2,o exP


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