Reflux Ratio Levels 0.779 0.833 0.557

Reflux Ratio Levels

Case 3

Figure 6.4. Optimal Reflux Ratio Profiles for Binary Distillation. [Mujtaba and Macchietto, 1993]e

6.4.2. Ternary Distillation (Simple Model)

Mujtaba and Macchietto (1993) considered the ternary operation described in Figure 6.2 where two main-cuts of specified purity and one off-cut are produced. In this problem, the recovery of component 1 in the off-cut 1 ( Re^ ) is fixed at 0.95. The composition of the off-cut 1 ( x\y ) is left as a decision variable to be optimised together with two the other decision variables, Re'Di (the recovery of component 1

in main-cut 1) and ReD2 (the recovery of component 2 in main-cut 2). Zero values for the off-cut and final bottom residue are assigned, with no constraints put on the compositions of either product. The input data for this problem are given in Table 6.3. The simple dynamic column model (Type III) was used for this example.

Table 6.3. Input Data for Ternary Distillation (Simple Model)1

No. of Ideal Separation Stages (including a reboiler and a total condenser) Total Fresh Feed, B0, kmol = 10 Feed Composition, xB0, mole fraction Column Holdup, kmol:


Internal Plates Relative Volatility, a Vapour Flow rate, kmol/hr Column Pressure, bar

Purity of Main-cut 1, , mole fraction

Purity of Main-cut 2, xD2, mole fraction

Recovery of component 1 in Off-cut 1, Re1^


Initial Outer Loop Decision Variables: Reo! =0.85, xlm =0.50, Re^>2 =0.85

Initial Inner Loop Decision Variables:

Reflux Ratio Levels 0.70 0.80 0.80 0.95 0.70 0.80

Reflux Ratio Levels 0.70 0.80 0.80 0.95 0.70 0.80

The reflux ratio is discretised into two control intervals for each operation task. Three cases were considered with different sales values for the two main-cuts. For all cases, the optimal recovery of component 1 in task 1 and that of component 2 in task 2, the optimal amounts of main-cut 1, off-cut 1 and main-cut 2, the optimal duration of the distillation tasks and the optimal profit are shown in Table 6.4. For

1 12 case 1, xRl was fixed a priori (= 0.6 molefraction) and ReD1 and Reƻ2 are optimised in the outer loop optimisation problem. The optimal reflux ratio policy for each case is presented in Figure 6.5, and accumulated and instant distillate composition profiles for case 2 are presented in Figure 6.6.

Case 2, where both main distillate products have the same unit value, is taken as the base case and used as a reference. Case 2 is similar to case 1 except that the composition of the off-cut was also optimised. The results are similar to case 1 in terms of recoveries and profit although the reflux ratio profiles are slightly different. Case 2 operation is slightly shorter and more profitable. The losses of component 2 in the off-cut for the two cases are close.

Table 6.4. Results For Ternary Distillation (Simple Model)8


c c


D, (kmol),

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