Resilience test active constraint strategy

The nonlinear resilience tests developed by Saboo et al. (1987a,b) are each for a rather specific case. A more general resilience analysis technique based on the active constraint strategy of Grossmann and Floudas (1985,1987) is also presented. The active constraint strategy can be used to test the resilience of a HEN with minimum or more units, with or without stream splits or bypasses, and with temperature and/or flow rate uncertainties (Floudas and Grossmann, 1987b). 

The active constraint strategy has been developed for both the resilience (flexibility) test and the flexibility index (Grossmann and Floudas, 1985, 1987). However, only the active constraint strategy for the resilience test will be discussed here. Recall that the resilience test is based upon a resilience measure x(d) ... 

The basic idea of the active constraint strategy is to use the Kuhn-Tucker conditions to identify the potential sets of active constraints at the solution of NLP (4) for feasibility measure ip. Then resilience test problem (6) [or flexibility index problem (11)] is decomposed into a series of NLPs with a different set of constraints (a different potential set of active constraints) used in each NLP. 

Floudas and Grossmann (1987b) have shown that for HENs with any number of units, with or without stream splits or bypasses, and with uncertain supply temperatures and flow rates but with constant heat capacities, the active constraint strategy decomposes the resilience test (or flexibility index) problem into NLPs which have a single local optimum. Thus the resilience test (or flexibility index) also has a single local optimum solution. 

Now the active constraint strategy for performing the resilience test can be summarized (Grossmann and Floudas, 1987) as follows. 

Example 11. The active constraint strategy is to be used to test the resilience of the same stream splitting HEN as in Example 9 (Fig. 12) in the uncertainty range 0 = TII415 < Tf < 515 K. ... 

Resilience Test with Active Constraint Strategy for Example 11... 

Different algorithms are required if the HEN resilience problem is nonlinear. Special algorithms were presented for testing the resilience of minimum unit HENs with piecewise constant heat capacities, stream splits, or simultaneous flow rate and temperature uncertainties. A more general algorithm, the active constraint strategy, was also presented which can test the resilience or calculate the flexibility index of a HEN with minimum or more units, stream splits and/or bypasses, and temperature and/or flow rate uncertainties, but with constant heat capacities. 

Several powerful HEN resilience analysis algorithms have been reviewed in this chapter, including the active constraint strategy (Grossmann and Floudas, 1985, 1987) which can test the resilience of the most general HEN. However, many common industrial HENs still cannot be analyzed with present techniques. For example, no technique has been... 

Develop techniques to test the resilience of HENs with uncertain heat transfer coefficients (e.g., heat transfer coefficients as a function of flow rate, but with uncertain function parameters). It is possible to extend the active constraint strategy to heat transfer coefficients with bounded uncertainties (not as a function of flow rate), but then the active constraint strategy may not have a single local optimum solution. 

Develop techniques to test the resilience of class 2 HENs with stream splits and/or bypasses, temperature and/or flow rate uncertainties, and temperature-dependent heat capacities and phase change. It may be possible to extend the active constraint strategy to class 2 problems. This would allow resilience testing of class 2 problems with stream splits and/or bypasses and temperature and/or flow rate uncertainties. However, the uncertainty range would still have to be divided into pinch regions (as in Saboo, 1984). 

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