(372g) A Nonsmooth Formulation for Representing Unclassified Process Streams in Work and Heat Exchange Networks (WHENs)
Mathematical programming has proven effective in solving heat integration problems. Different pinch location algorithms exist in the literature that calculate the minimum utility consumption for a set of hot and cold process streams. Generally, the supply and target temperatures in these algorithms can be taken as variables in the problem. However, the classification of stream identity into hot and cold streams must be done prior to optimization. The latter presents a modeling challenge in simultaneous work and heat integration. Yu et al.  mapped the possible thermodynamic paths of variable pressure streams in WHENs. Depending on the thermodynamic path, compression/expansion temperatures can vary significantly in order to fully utilize the heat of compression (or cooling from expansion) in the process. Furthermore, an optimal configuration may require the superposition of different thermodynamic paths, through stream splitting, where the identity of streams depend on the paths chosen. Classifying stream identities a priori necessarily imposes an upper or lower bound on the compression/expansion temperatures, limiting the search space for the optimizer. Instead, pinch location algorithms must be modified to handle unclassified process streams.
Different strategies for handling cases of unknown stream identities have been proposed. Yu et al.  formulated three different extensions to the simultaneous optimization and heat integration algorithm by Duran and Grossmann . The extensions used either smooth approximations or disjunctive reformulations for the nonsmooth operators, and binary variables for the stream identities. The resulting formulation is an MINLP that was laborious to solve, even for smaller test problems. This work focuses on an alternative and more compact formulation, where nonsmooth operators replace the binary variables and disjunctive reformulations. Optimization is performed using IPOPT, and sensitivities are obtained using recent developments in nonsmooth analysis . The nonsmooth extension is tested for WHEN targeting using a number of examples from the literature.
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