Resilience test with piecewise constant heat capacities

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). 

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. 

To allow algebraic equations to be used to locate ATm, assume that the heat capacities can be approximated by piecewise constant functions of temperature, with discontinuities at temperature breakpoints TBRj. Then for each exchanger, Arm can occur only at either end or at a breakpoint location inside the exchanger. However, a remaining difficulty is that since the intermediate stream temperatures are not known before the resilience test, the breakpoint locations are also not known a priori. 

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See also in sourсe #XX -- [ , ]

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