(716e) A First Principles Based Dae Model for Phase Change Heat Exchangers for Process Optimization

Phase changes occur one in basic operational tasks using heat exchangers, not only in chemical process plants but also in power plants and buildings. Most utility systems depend on the Carnot cycle principle which uses latent heat and compression work to provide heating or cooling effect. Refrigeration systems are an example of reverse Carnot cycles where excess heat is absorbed at lower temperature and pressure to evaporate a refrigerant and is disposed of at a higher temperature and pressure. Heat pumps are a more general form of refrigeration systems, and can be used on both sides for heating and cooling purposes. Due to their higher efficiency and multiple utility characteristics, heat pumps are becoming more popular in the process industry.

Optimal design of heat pumps depends on the type of refrigerant and the design of heat exchangers - evaporators and condensers. In this talk, we present a physics-based first principle model for phase changes inside heat exchangers, and relate the overall design to the performance of the heat exchanger. The heat exchange between fluids inside the heat exchanger is modeled using steady state differential heat equations along with the phase change dynamics being calculated using non-smooth algebraic equations. A simultaneous differential-algebraic equation (DAE) model is proposed with both the differential and algebraic equation system with consistent initial conditions for the optimal design of phase change heat exchangers. The non-smooth DAE is reformulated using complementarity constraints as shown in Baumrucker et al. (2008) and solved using successive relaxation methods presented in Caspari et al.(2019). The exchanger structure (shells, baffles and tube passes) is used to split the heat exchanger geometry into small elements which are used to discretize the detailed DAE model and correlate the exchanger area with the overall design.

As such, these detailed DAE models cannot be solved simultaneously inside a process model for optimization problems. Instead, a Trust Region Filter based strategy (Eason and Biegler, 2018) is used to embed the detailed DAE models into process models using reduced order models. The simplified models are updated in each iteration using the zero and first order derivatives from the detailed DAE model, guaranteeing the convergence to a KKT point of the overall problem. We will discuss the performance of the method using network case studies from the literature and comment on its effectiveness in handling phase changes.

References:-

• Baumrucker, B. & Renfro, J. & Biegler, Lorenz. (2008). MPEC problem formulations and solution strategies with chemical engineering applications. Computers & Chemical Engineering. 32. 2903-2913.
• Caspari, Adrian & Lüken, Lukas & Schäfer, Pascal & Vaupel, Yannic & Mhamdi, Adel & Biegler, Lorenz & Mitsos, Alexander. (2019). Dynamic Optimization with Complementarity Constraints: Regularization for Direct Shooting.
• Eason, J.P. and Biegler, L.T. (2018), Advanced trust region optimization strategies for glass box/black box models. AIChE J, 64: 3934-3943