Applications of Fractional Calculus In Chemical Engineering - Shen, Xin (Université d'Ottawa / University of Ottawa, 2018)
Fractional calculus, which is a generalization of classical calculus, has been the subject of numerous applications in physics and engineering during the last decade. In this thesis, fractional calculus has been implemented for chemical engineering applications, namely in process control and in the modeling mass transfer in adsorption. With respect to process control, some researchers have proposed fractional PIλDμ controllers based on fractional calculus to replace classical PI and PID controllers. The closed-loop control of different benchmark dynamic systems using optimally-tuned fractional PIλDμ controllers were investigated to determine for which dynamic systems this more computationally-intensive controller would be beneficial. Four benchmark systems were used: first order plus dead time system, high order system, nonlinear system, and first order plus integrator system. The optimal tuning of the fractional PIλDμ controller for each system was performed using multi-objective optimization minimizing three performance criteria, namely the ITAE, OZ, and ISDU. Conspicuous advantages of using PIλDμ controllers were confirmed and compared with other types of controllers for these systems. In some cases, a PIλ controller was also a good alternative to the PIλDμ controller with the advantage of being less computationally intensive. For the optimal tuning of fractional controllers for each benchmark dynamic system, a new version of the non-dominated sorting genetic algorithm (NSGA-III) was used to circumscribe the Pareto domain. However, it was found that for the tuning of PIλDμ controllers, it was difficult to circumscribe the complete Pareto domain using NSGA-III. Indeed, the Pareto domain obtained was sometimes fragmentary, unstable and/or susceptible to user-defined parameters and operators of NSGA-III. To properly use NSGA-III and determine a reliable Pareto domain, an investigation on the effect of these user-defined operators and parameters of this algorithm was performed. It was determined that a reliable Pareto domain was obtained with a crossover operator with a significant extrapolation component, a Gaussian mutation operator, and a large population. The findings on the proper use of NSGA-III can also be used for the optimization of other systems. Fractional calculus was also implemented in the modeling of breakthrough curves in packed adsorption columns using finite differences. In this investigation, five models based on different assumptions were proposed for the adsorption of butanol on activated carbon. The first four models are based on integer order partial differential equations accounting for the convective mass transfer through the packed bed and the diffusion and adsorption of an adsorbate within adsorbent particles. The fifth model assumes that the diffusion inside adsorbent particles is potentially anomalous diffusion and expressed by a fractional partial differential equation. For all these models, the best model parameters were determined by nonlinear regression for different sets of experimental data for the adsorption of butanol on activated carbon. The recommended model to represent the breakthrough curves for the two different adsorbents is the model that includes diffusion within the adsorbent particles. For the breakthrough experiments for the adsorption of butanol on activated carbon F-400, it is recommended using a model which accounts for the inner diffusion within the adsorbent particles. It was found that instantaneous or non-instantaneous adsorption models can be used. Best predictions were obtained with fractional order diffusion with instantaneous adsorption. For the adsorption of butanol on activated carbon Norit ROW 0.8, it is recommended using an integer diffusion model with instantaneous adsorption. The gain of using fractional order diffusion equation, given the intensity in computation, was not sufficient to recommend its use.
Keywords: fractional calculus; chemical engineering