MATHEMATICAL MODELLING OF THREE-PHASE SLURRY REACTORS
Abstract
Three-phase slurry reactors, which are characterized by a dispersed gas phase, a suspended solid phase, and a continuous liquid phase, are widely used in the chemical industry for gas-liquid-solid reactions. Understanding the physicochemical phenomena of the reactor is essential to design and control the reactor. Also, estimation of system parameters is important for reactor scale-up. The objectives of this study are to investigate the dynamic responses of the three-phase slurry reactor and to propose methods for the determination of system parameters for linear and nonlinear systems. The PM-PM-HS/ID model, which assumes perfect mixing (PM) in the gas and liquid phases and homogeneous suspension (HS) of the solid phase, is used for the study. The phenomenon of intraparticle diffusion (ID) is also considered in this model. The effect of chemical kinetics, linear or nonlinear, on the dynamics of the reactor was studied. The kinetics include a first-order reaction with respect to a single gas reactant or a single liquid reactant, a power-law type reaction with respect to a single gas reactant, a Michaelis-Menten type reaction with respect to a single gas reactant or a single liquid reactant, and a substrate inhibition type reaction with respect to a single liquid reactant. Analytical solutions were presented for first-order reaction systems under batch, semi-batch, and continuous operations. The results show that two types of responses exist if an input perturbation, i.e., the sudden introduction of catalyst into the reactor at time zero, is employed. The criteria to distinguish these two responses were obtained analytically. These criteria are independent of the parameters related to the intermediate transport processes such as liquid-solid mass transfer coefficients and intraparticle diffusion coefficient. With these criteria, simple experimental methods were proposed to obtain the intrinsic first-order rate constant directly from the experiments without considering the effect of intermediate transport processes. Numerical solutions were also presented for non-linear systems by the method of orthogonal collocation. The criteria to distinguish two responses are no longer independent of the parameters related to the intermediate transport processes. However, if the system possesses a shifting order kinetics with an extreme condition of first-order reaction, the rate constants still can be obtained by using the proposed methods. A case study was presented for the system with a Michaelis-Menten type of rate expression.
Degree
Ph.D.
Subject Area
Chemical engineering
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