Figure 6.8. Ternary Distillation without Off-cut Production (Case 2). a) Accumulated Distillate Composition and Reflux Ratio Profile b) Instant Distillate Composition and Reflux Ratio Profilek
6.4.3. Ternary Distillation (Detailed Model)
This example is taken from Mujtaba and Macchietto (1993) which involves separation of a ternary mixture cCyclohexane, n-Heptane, Toluene>. The initial amount of fresh feed is same as that used by Nad and Spiegel (1987) in an experimental column. However, for simplicity only a 10 stage (including reboiler and a total condenser) column is used instead of a 20 stage column used by the original authors. The multiperiod operation shown in Figure 6.2 is optimised, according to problem P2 (section 126.96.36.199). The problem specifications include the purity of the two main distillate products and the recovery of component 1 in the off-cut product. A detailed dynamic model (Type IV) was used here with rigorous non-ideal thermodynamics described by the Soave-Redlich-Kwong (SRK) equation of state. As before, 2 time intervals were used for the reflux ratio in task 1 and task 3 and one time interval for the off-cut production. The input data for this example are given in Table 6.6. The cost coefficients, also given in Table 6.6 were arbitrarily defined.
Table 6.6. Input Data for Ternary Distillation (Detailed Model)1
No. of Ideal Separation Stages (including a reboiler and a total condenser) Total Fresh Feed, B0, kmol Feed Composition, xB0, mole fraction Column Holdup, kmol:
Internal Plates Condenser Vapour Load, kmol/hr Column Pressure, bar
Purity of Main-cut 1, x^j, mole fraction
Purity of Main-cut 2, xD2 , mole fraction
Recovery of Component 1 in Off-cut 1, Re'ßl = 0.95 Costs:
Initial Outer Loop Decision Variables: ReJ,i =0.80, 4i = 0.50, Re|2 =0.70
Initial Inner Loop Decision Variables:
The optimal recoveries of component 1 and 2 in the main-cuts, off-cut composition, amount of each cut, duration of each task and reflux ratio profiles for each task are given in Table 6.7. They show that the desired product purities can be achieved to yield a maximum productivity for the operation of $2.0 per hr. The accumulated and instant distillate composition profiles for the optimal operation are shown in Figure 6.9. This example demonstrates that the proposed method can indeed tackle realistic problems.
The computational statistics for the problem are:
• 5 function and 3 gradient evaluations outer loop problem.
• 10-15 function and 7-12 gradient evaluations for the first and third inner loop problems.
• 5-7 function and 4-5 gradient evaluations for the second inner loop problem.
• Approximately 30 minutes CPU for one complete function evaluation of the outer loop using a SPARC-1 Workstation.
This increased computation load is as expected for such a problem due to the use of a detailed model with rigorous thermodynamics.
Table 6.7. Results for Ternary Distillation (Detailed Dynamic Model)™.
Optimal Recovery of Component 1 in Main-cut 1, Re^i = 0.779
Optimal Duration of Task 1, th hr =3.40
Optimal Off-cut 1 Composition, xlRl, mole fraction = 0.492
Optimal R1, kmol = 0.508
Optimal Duration of Task 2, t2, hr = 2.77
Optimal Recovery of Component 2 in Main-cut 2, Re^ = 0.762
Optimal Duration of Task 3, t3, hr = 2.18
Reflux Ratio Profile:
Reflux Ratio Levels 0.875 0.911 0.933 0.831 0.876
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