Resilience test uncertainty range

The resilience (flexibility) test determines whether a HEN is resilient (flexible) throughout a specified uncertainty range 0,... 

The solution 8C of max-min problem (8) defines a critical point for feasible operation—it is the point where uncertainty range 0 is closest to feasible region R if (d) 0 (Fig. 3a), or it is the point where maximum constraint violations occur if (d) > 0 (Fig. 3b). In qualitative terms, the critical points in the resilience test are the worst case conditions for feasible operation. 

Example 3 (adapted from Grossmann and Floudas, 1987). The HEN in Fig. 4 was designed for the heat capacity flow rates, target temperatures, and nominal stream supply temperatures shown. This HEN is to be tested for resilience in an uncertainty range of 10 K in all stream supply temperatures. 

It can be shown that the resilience test for this HEN is linear (see Section III,B,1). Therefore the HEN is resilient if and only if it is feasible at every vertex of the specified uncertainty range. 

A HEN is resilient in an expected uncertainty range 0(1) if and only if Fs 1. This is the same information which the resilience (flexibility) test gives. But the flexibility index tells us even more. For instance if F = 0.5, we know that the HEN is not resilient in the specified uncertainty range in addition, we know that the HEN can tolerate uncertainties only half as large as those expected. 

Example 9. Resilience of the minimum-unit stream-splitting HEN shown in Fig. 12 is to be tested in the uncertainty range 415 K < rf 515 K. The stream split constraints were derived in Example 8 from the ATm constraints on the hot ends of the exchangers. 

The resilience test correctly identifies that the HEN is not resilient in the specified uncertainty range. In order to apply the resilience test, the values °f vk.max and gjj max shown in Table V are calculated. The values of v max are all nonpositive thus the load constraints are satisfied throughout the... 

To show that this procedure is not a necessary test for resilience, consider the uncertainty range 370 K < 7f s 410 K. This uncertainty range is shown in Fig. 13. Obviously, the HEN is resilient in this uncertainty range since for every value of rf in the range, there is a value of 31 for which the network is feasible. 

The resilience test incorrectly identifies the network as not being resilient. The values of vk max and gy max for this uncertainty range are listed in Table VI. Since all the vk max are nonpositive, the load constraints are satisfied throughout the uncertainty range. To test the stream split constraints, LP (29) is applied ... 

Solution of this LP yields x = 0.0305, thus implying that the network is not resilient in the new uncertainty range. The resilience test is conservative because LP (29) looks for values of stream split fractions u which, if held... 

A HEN is resilient in a specified uncertainty range 0 if and only if X(d) 0. If (d) > 0, then at least one of the feasibility constraints fm is violated somewhere in the uncertainty range. Geometrically, the resilience test determines whether uncertainty range 0 lies entirely within feasible region R. 

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. ... 

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). 

---