(372g) A Nonsmooth Formulation for Representing Unclassified Process Streams in Work and Heat Exchange Networks (WHENs)

Pinch Analysis is a well-known methodology in Process Systems Engineering for improving efficiency through enhanced process integration. The methodology originally focused on heat integration and the synthesis of Heat Exchanger Networks (HENs). However, most chemical processes also include pressure manipulation through equipment such as compressors, expanders, pumps and valves that affect the heat sinks and sources in the process and thus the potential for heat integration. In addition, the inlet temperature to pressure-changing equipment such as compressors and expanders determines the work consumed or produced. Recently, attention has therefore been towards simultaneous work and heat integration and the synthesis of Work and Heat Exchange Networks (WHENs). The relationship between work and heat, makes the latter a significantly more complex problem than the heat integration problem alone.

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. [1] 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. [2] formulated three different extensions to the simultaneous optimization and heat integration algorithm by Duran and Grossmann [3]. 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 [4]. The nonsmooth extension is tested for WHEN targeting using a number of examples from the literature.

1. H. Yu, C. Fu, M. Vikse, C. He, and T. Gundersen. “Identifying Optimal Thermodynamic Paths in Work and Heat Exchange Network Synthesis."AIChE Journal, 65(2), (2019), 549-561.
2. H. Yu, M. Vikse, R. Anantharaman, and T. Gundersen. "Model reformulations for Work and Heat Exchange Network (WHEN) synthesis problems."Computers & Chemical Engineering, 125 (2019), 89-97.
3. M. A. Duran and I. E. Grossmann. "Simultaneous Optimization and Heat Integration of Chemical Processes." AIChE Journal, 32(1), (1986), 123-138.
4. P. I. Barton, K. A. Khan, P. Stechlinski, and H. A. J. Watson. "Computationally relevant generalized derivatives: theory, evaluation and applications."Optimization Methods and Software, 33(4-6), (2018), 1030-1072.