Optimal Products Amount (per batch) and Composition:
Product Amount, kmol_Composition
Optimal No. of Batches: NB = 1047.1
Profit:
Optimal Design and Operation =15,168.0 $/yr
Base Case Operation (Nad and Spiegel, 1987) = 11,165.2 $/yr
Solution Statistics:
No. of Outer Loop Function Evaluations, NF = 10
No. of Outer Loop Gradient Evaluations, NG = 6
Total CPU time, hr on SPARC-10 = 5.23
The optimum results for different times allocated to each separation duty are summarised in Tables 7.4 and 7.5. They clearly show that the time allocation plays an important role in determining the size of the column as well as the operation policy. The more difficult the separation (Separation 1) is the larger is the number of plates required and the lower is the yearly profit achieved. The situation reverses as the separation becomes easy (Separation 2). Table 7.4 also presents two extreme cases, where a column designed for separation 2 is allocated 100 % of the time to Separation 1 (la) and one designed for separation 1 is allocated 100% to Separation 2 (5a). Case la shows a significant drop (66 %) in profit compared to case 1, however for case 5a this is only 3 % when compared to case 5. This clearly shows that an easy separation task can easily be accommodated in a column which was designed for a more difficult separation without losing much profit, but the reverse situation might have significant impact on the profit, and in many cases might not even give a feasible separation.
Table 7.3. Input Data and Product Specifications using Binary Mixtures (Simple Dynamic Model, Multiple Duties). [Mujtaba and Macchietto, 1996]j
Column: Still Capacity = Batch size, BO, kmol = 10.0
Condenser Vapour Load, kmol/hr = 10.0 Column Holdup, kmol:
Duties: Total Plant Operation Time, Hyr, hr/yr = 8000.0
Total time horizon, H, hr = 8000.0
No. of mixtures and fraction of time horizon for each mixture: M-2; 0, ,02 = variable
Mixtures:
Feed Composition for Mixture 1 and 2, (mole fraction) Xfi-Xf2= <0.5, 0.5>
Relative Volatility: Mixture 1 = <1.5, 1.0>, Mixture 2 = <2.5, 1.0> Specifications:
Purity of distillate products (mole fraction) x'D! = x'D2 = 0.95
Costs:
Cdi = CD2 = 20.0 $/kmol, CBfl = CBf2 = Csul = Csu2 = 0.0 CF1 = CF2 = 2.0 $/kmol, OCj, OC2 and ACC as in section 7.3
Case |
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