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362  Chapter 9 Operation Optimization
                  1.  Fractional recovery of the intermediate component B leaving the pre-fractio-
                      nator top.
                  2.  Fractional net recovery of the bottom component C in the overhead of the
                      pre-fractionator versus the total net flow of C to the main column.
                  3.  DTS ± a measure of temperature profile symmetry,

                  DTS =  P  (T 1, i ±T 4, i )+ P  (T 2, i ±T 5, i )(3)
                where T Ni is the temperature of tray i of section N, for the temperature location (see
                Figure 9.6).
                  The last mentioned feed back variable can easily be measured by temperature,
                while the others require a composition measurement.
                  The above self-optimizing technology can be seen as a suboptimization of a global
                optimization problem (Figure 9.7), or as part of the control layer. The global optimi-
                zation sets the feed composition (direct or indirect), next to the product specifica-
                tions. The self-optimization reacts to any disturbance to keep the unit at its opti-
                mum energy consumption. In the case of final products, the purities are often firm
                constraints, while recycle streams often have economic specifications that are sub-
                ject to change and need to be updated by global optimization.
                  The search for self-optimizing control structures is discussed by Skogestad (1999)
                in a more generic paper that is illustrated with some other examples as a reactor
                system and a simple distillation column. For a further description, see Chapter 8. In












                   Raw
                  materials                                             Product B
                           Reactor                    Product A




                                                                      Product C





                       Global optimizer                    Self optimizing control /
                                                              Unit optimizer

                Fig. 9.7. Global optimization versus unit self optimizing control.
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