Resilience test with flow rate uncertainties

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). 

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). 

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. 

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). 

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. 

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