Stuides on slurry reactors

Abstract

Bubble column slurry reactors (BCSRs) are used for three phase contacting in petroleum, petrochemical, and chemical industries and in pollution control. The main objectives of the present work are:

to analyse and evaluate the effects of backmixing in each phase on the performance of semibatch, cocurrent, and countercurrent BCSRs, and to design modal control systems for output regulation in the face of disturbances entering the reactor.

The steady state and dynamic performance of the reactors are analysed by applying the axial dispersion model for the gas and liquid phases, and the sedimentation–diffusion model for the solid phase. Isothermal conditions and pseudo–steady state distribution of the solid particles are assumed. A common mode of operation of the reactors is one in which a sparingly soluble gas dissolves in the liquid and reacts with it at the surface of suspended catalyst particles to give a liquid product. The present analysis is mainly based on this type of operation. The reaction is assumed to be first order with respect to the diffusing component and zero order with respect to the other components. The resulting system equations consist of partial differential equations of boundary value type with variable coefficients.

Semibatch BCSR For a semibatch BCSR, analytical solutions are derived for the steady state concentration distribution and conversion of the diffusing component for several combinations of mixing conditions in the gas and slurry phases. The solution is evaluated to determine the effects of backmixing in each phase on concentration profiles and conversion at different levels of operating variables such as feed slurry concentration, particle diameter, etc. Reactor behaviour is strongly affected by the distribution of solid particles. Conversion increases with increased mixing in the slurry phase; the well mixed slurry phase gives the highest conversion because of uniform distribution of solid particles. The model is applied to the experimental data reported by Pruden and Weber (1970) on hydrogenation of methylstyrene on palladium black in a semibatch BCSR. The model fits the data quite adequately.

Cocurrent and Countercurrent BCSR The equations of the steady state dispersion model for cocurrent and countercurrent BCSRs are solved by the orthogonal collocation method, and the effects of mixing are numerically evaluated. Because of sedimentation and dispersion effects, the average concentration of solid particles in the cocurrent reactor is higher than in the feed slurry. Conversion of the gas component increases with decreased slurry phase mixing. Conversion reaches a minimum with respect to particle size-an interesting behaviour unique to cocurrent reactors. In countercurrent BCSRs, the distribution of solid particles is such that the average concentration in the reactor is less than that in the feed slurry. This distribution leads to the occurrence of a maximum (depending on operating conditions) in liquid and solid phase concentration profiles in the lower part of the reactor. Increased backmixing in the slurry phase gives higher conversion. When measured in terms of average rate per unit weight of catalyst, the performance of countercurrent reactors is superior, even though cocurrent reactors yield higher conversions and higher rates.

Consecutive Reaction (A B C) The effect of backmixing in each phase of a cocurrent BCSR on the steady state yield of product B in a consecutive reaction system (A B C) is analysed. The trends in the effects on B yield follow those obtained for conversion of the gas component.

Dynamic Behaviour The set of PDEs describing the dynamic performance of a cocurrent BCSR (for a first order reaction) is converted into ODEs using orthogonal collocation. The resulting stiff system is solved using the GEARB routine. Effects of backmixing on reactor dynamics are evaluated at different operating levels. The time to reach steady state decreases as dispersion in gas or slurry phases decreases. Catalyst concentration in the feed slurry has a profound influence on transient behaviour.

Control System Design A state variable model of the cocurrent reactor is developed by spatial discretization, resulting in a 22 state model-too large for practical control design, and many states are unmeasurable. A reduced fourth order model retaining four measurable states is developed using the moments matching method. Based on this reduced model, proportional modal feedback, feedforward, and combined feedback–feedforward control systems are designed for output regulation under disturbances in catalyst loading. The inlet gas composition is used as the manipulated variable. Digital simulation on the original 22 state model shows that simple feedback control gives the best results.