5 Multi-objective Optimization of Biodiesel Synthesis in Simulated Moving Bed Reactor
5.7 Design stage optimization
This problem involves optimization of SMBR performance by allowing its design parameters such as length of the column to be selected optimally. It is worthwhile to consider this problem for industrial application. The parameter which has been
considered for this is column length (Lcol). Two optimization problems were once again
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Case 2.1 Simultaneous maximization of yield and purity:
The objective functions, constraints and decision variables for this problem are the same as those of Case 1.1, with the addition of another decision variable; column length
[ ( ) ( )]. The Pareto optimal solutions are shown in Figure 5.5.
Figure 5.5a shows the Pareto set for yield and purity of biodiesel. Once again, it is observed that they act in conflicting manner. But a much higher value of purity (97%) can be obtained as compared to case 1.1 where the highest purity value obtained was 87%. Also, the highest yield value obtained in case 1.1 was 79% against a purity value of 76%. The yield in this case is 90% corresponding to value of purity being marginally more than 90% (point 1 in Figure 5.5a). Hence a drastic improvement is achieved when column length is introduced as a decision variable. The purity also acts in conflicting manner against raffinate flow rate, as is evident from Figure 5.5b. A very low value of β (≈ 0.1) is required to achieve 97% purity, indicating the requirement of a higher residence time in section P. Figure 5.5c represents that a high value of desorbent flow rate (γ≈3.5) to achieve a purity in the range of 94% to 97%. Just as in case 1.1, γ has to be kept above a threshold value; further increase in γ will not improve purity. An increase in column length also improves purity, as represented by Figure 5.5d. Larger column length means that the reactants will have more residence time, hence improving the conversion, purity and yield. As far as switch time is concerned, it has increased to about 11 minutes as compared to 5 minutes in Case 1.1. This is due to the introduction of column length as a decision variable. A higher Lcol value means indicates requirement of a higher residence
time before a switch is made.
This optimization problem asserts that SMBR performance can be improved if design parameters are also optimized along with operating parameters. A high value of both yield and purity were obtained when column length was also introduced as a decision variable
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Figure 5.5 Pareto solutions for maximizing yield and purity with column length as a design stage parameter
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Case 2.2 Maximization of purity and minimization of desorbent consumption:
The objective functions, constraints and decision variables for this problem are the same as those of Case 1.2, with the addition of another decision variable; column length [ ( )
( )]. The Pareto optimal solutions are shown in Figure 5.6.
Figure 5.6a shows the relation between γ and purity. At lower values of γ, a linear relation exists with purity. However after that, the graph becomes exponential; indicating that a slight increase in purity would require a very high desorbent consumption, just as in case 1.2. Hence, γ should be just high enough above a threshold value (≈ 2 in this case). Further increase is not necessary.
Figure 5.6b shows the dependence of purity on raffinate flow rate. β is fairly constant at a low value (≈ 0.1). Hence purity is not sensitive to it when column length is a decision variable and minimization of desorbent consumption is an objective. The same trend is shown by switch time; it is fairly constant at around 9 minutes (Figure 5.6c). The dependence of purity on column length is fairly uniform, showing requirement of a high column length for high purity (Figure 5.6d).
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Figure 5.6 Pareto solutions for maximizing purity and minimizing desorbent consumption
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5.8 Conclusions
Multi-objective optimization studies were carried out on the performance of a reactive SMB for synthesis of biodiesel. The NSGA algorithm was used to obtain the Pareto optimal solutions. Optimization of both existing set-up and design-stage were studied. Two multi-objective optimization problems were solved involving two objective functions for each mode of operation. Simultaneous maximization of yield and purity as well as maximization of purity and minimization of desorbent consumption were considered as objective functions. It was observed that a yield and purity of above 90% can be achieved by optimizing both operating and design stage parameters. This study extols the usefulness of multi-objective optimization for improvement of design and operation of reactive SMB system for its practical application and successful implementation on industrial scale.
5.9 References
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