Resilience test with stream splits

Heat exchanger network resilience analysis can become nonlinear and nonconvex in the cases of phase change and temperature-dependent heat capacities, varying stream split fractions, or uncertain flow rates or heat transfer coefficients. This section presents resilience tests developed by Saboo et al. (1987a,b) for (1) minimum unit HENs with piecewise constant heat capacities (but no stream splits or flow rate uncertainties), (2) minimum unit HENs with stream splits (but constant heat capacities and no flow rate uncertainties), and (3) minimum unit HENs with flow rate and temperature uncertainties (but constant heat capacities and no stream splits). 

Resilience analysis for HENS can become nonlinear and nonconvex if varying stream split fractions are allowed. In this section nonlinear feasibility and resilience tests are presented for networks with stream splits, with the assumption that the network has a minimum number of units. This assumption often is not restrictive since many stream split networks do have a minimum number of units. 

The minimum unit HEN with stream splits is resilient if < 0. This test is sufficient, but not necessary, for HEN resilience. It is necessary only if the same critical corner point maximizes all of the and vk constraint functions simultaneously. 

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). 

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). 

Saboo (1984) has generalized resilience test (32) to class 2 problems. However, his method is still limited to minimum unit HENs with no stream splits. 

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. 

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. 

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