A Nonsmooth Approach to Modeling and Optimization - Application to Liquefied Natural Gas Processes and Work and Heat Exchange Networks
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Despite their implicit presence in many process systems engineering applications, nonsmooth functions have repeatedly been shunned due to the existence of nondifferentiable points that cause issues for numerical solvers and gradient based optimization methods. Instead, alternative methods have been widely explored, such as providing smooth approximations around nonsmooth points, or by reformulating the function altogether using disjunctions. However, recent advances in nonsmooth analysis have provided a numerically tractable approach for computing sensitivity information for certain classes of nonsmooth functions, thus paving the way for a new paradigm in process modeling. Rather than circumventing the se of nonsmooth functions by exploring alternative options, they can instead be employed actively for implementing certain decisions into the model. Furthermore, nonsmooth formulations have the potential of reducing the overall model size wherever the previous models relied on disjunctive reformulations. Along with the new developments in nonsmooth analysis came a promising application of the framework for modeling multistream heat exchangers. Multistream heat exchangers are an integral part of natural gas liquefaction processes that, due to cooling at cryogenic temperatures, call for self-refrigeration. Nevertheless, existing process simulation software suffer from several disadvantages with regards to the modeling of multistream heat exchangers, in particular when it comes to enforcing feasible heat transfer at interior points. As a result of this, alternative modeling approaches have been explored where mixed integer programs and embedded pinch location methods are used. However, these formulations come at the expense of additional binary variables that can only be handled in an optimization environment, as well as adverse scalability to large-scale processes. The nonsmooth multistream heat exchanger, on the other hand, profits from its hybrid modeling strategy that capitalizes on assets from both an equation-oriented and a sequential-modular approach. The result is a model that could simulate the single-mixed refrigerant PRICO process with a cubic equation of state by solving a nonlinear nonsmooth equation system. Nevertheless, the PRICO process is among the most basic natural gas liquefaction processes available on the market, and has already been studied extensively. Therefore, in order to demonstrate the true capabilities of the nonsmooth framework, more complex and commercially interesting liquefaction processes must be modeled. In this thesis, simulation models for complex single mixed refrigerant and dual mixed refrigerant processes are developed. Cases are constructed, where results are compared with existing software for validation. In addition, a dual mixed refrigerant process is subjected to an optimization study using IPOPT. Although significantly larger than the PRICO flowsheet, the nonsmooth framework retains a moderate model size also for the most complex dual mixed refrigerant process, and is thus capable of simulating all cases presented here within respectable CPU times. Furthermore, it adds versatility to the designer, which makes it possible to locate feasible operating points where the current state-of-the-art process simulators cannot. Lastly, the advantages of the nonsmooth framework is expanded to the more general topic of work and heat exchange networks. Existing literature resort to mixed integer nonlinear models for dealing with unclassified process streams and locating pinch points. Although these methods are effective at handling small-scale problems, they suffer from an exponential scaling, which can become troublesome when additional variable pressure streams are considered. Here, an alternative approach using nonsmooth operators for assigning the true identity is presented. The extension achieves favorable scaling compared to existing formulations, and can be solved using a similar strategy as with the liquefied natural gas models. To test the new extension, different case studies related to exergy targeting of work and heat exchange networks are discussed.