A new model formulation and solution strategy for the design and simulation of multistream heat exchangers (MHEXs) is developed. Most current simulation-based models are over-constrained in the sense that they allow for only one unknown that can be adjusted to meet two requirements: the energy balance and second law feasibility. In many such models, a single adjustable temperature is set by the energy balance, so there is nothing left to adjust to satisfy the second law requirement; it is either satisfied or not based on the values given for the degrees of freedom in the problem, leading to temperature crossovers and other nonphysical solutions. The model proposed here allows for the specification of two additional parameters, such as the heat exchange area and/or the minimum temperature difference, as inputs to the model to free up two additional unknowns for simulation. The approach makes use of a modification of classical pinch analysis, as well as incorporating an explicit dependence of the heat transfer on the available heat exchange area to formulate a small nonsmooth equation system to model general MHEXs. Recent advances in automatic computation of derivative-like information for nonsmooth equations make the method tractable, and the use of state-of-the-art nonsmooth equation solving methods make the method precise and robust. Additionally, the algorithm is specifically designed such that B-subdifferential elements of the residual functions are calculated at every iteration, so the equation system is solved with a local quadratic convergence rate. A case study featuring an offshore liquefied natural gas production concept with two MHEXs, compressors and expanders is presented to highlight the flexibility and strengths of the model.
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