Energy integration in chemical plants is crucial as it provides a reduction in external utility consumption which, in turn, results in cost savings. Heat exchangers play an important role in energy integration by transferring energy from hot streams which need to be cooled to cold streams which need to be heated. Heat exchanger networks are now ubiquitous in chemical plants, and a lot of research has been done on synthesizing and optimizing such networks, and evaluating their controllability and operability. Yet, control of heat exchanger networks has not been studied extensively.
As a typical design objective of energy integrated networks is to maximize energy recovery, counter-current exchangers are preferred over co-current exchangers. Also, in order to recover as much energy as possible, high duty exchangers, which are characterized by high Stanton numbers, are frequently used. Several papers have studied the (mostly) control of heat exchangers under different assumptions on the modeling of such systems. None however has dealt with high duty exchangers explicitly.
In this talk, we present a dynamic analysis and nonlinear controller design of such heat exchangers. The dynamics of counter-current heat exchangers are described by first order hyperbolic partial differential equations (PDEs). In the case of high duty exchangers, the governing equations become stiff, and the system shows a potential of multi-time scale dynamics. We generalize singular perturbation-based model reduction for the stiff PDE model describing such exchangers to derive a nonlinear non-stiff PDE model which captures the dynamics in the slow time scale. Several numerical issues arise in the numerical simulation using finite differences due to the counter-current nature of the system. Using order of magnitude analysis, we derive a proper boundary for the spatial discretization step to ensure consistency of the numerical simulation of the full and reduced models. Subsequently, distributed nonlinear controllers are designed to allow tracking and regulation of an outlet temperature by manipulating an inlet flowrate. The advantages of using the reduced PDE model as the basis of controller design, and the efficacy of the proposed controller design are illustrated with simulations.
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