Studies 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 where a sparingly soluble gas dissolves in the liquid and reacts with it at the surface of the 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. 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 the concentration profiles and on the conversion at different levels of the operating variables such as feed slurry concentration, particle diameter, etc. The reactor behaviour is strongly affected by the distribution of the solid particles. Conversion increases with increasing mixing in the slurry phase; the well mixed slurry phase gives the highest conversion because of the associated uniform distribution of the 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. 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 processes, the average concentration of the solid particles in the cocurrent reactor is higher than the concentration in the feed slurry. Conversion of the gas component increases with decrease in slurry phase mixing. The conversion reaches a minimum with respect to particle size-an interesting behaviour that occurs only in cocurrent reactors. In countercurrent BCSRs, the distribution of solid particle concentration is such that the average concentration of the particles 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 the profiles of concentration in the liquid and solid phases in the lower part of the reactor. Increased backmixing in the slurry phase gives higher conversion. The performance of countercurrent reactors, measured in terms of the average rate per unit weight of catalyst, is superior to that of cocurrent reactors although the latter yield higher conversions and higher rates. The effects of backmixing in each phase of a cocurrent BCSR on the steady state yield of product B in a consecutive reaction A B C are also analysed. The trend in the effects on the yield of B of different process variables is similar to that obtained for the effects of these variables on the conversion of the gas component. The set of partial differential equations that describes the dynamic performance of a cocurrent BCSR (for a simple first order reaction) is converted into ordinary differential equations by the orthogonal collocation method. The resulting equations are found to be stiff and are solved using the GEARB routine. The effects of backmixing in each phase on reactor dynamics are evaluated at different levels of the operating variables. The time required to attain steady state decreases as dispersion in the gas or slurry phase decreases. The catalyst concentration in the feed slurry profoundly influences the transient behaviour of the reactor. A state variable model of the cocurrent flow reactor is obtained by discretising the space coordinate of the dynamic model. This gives a 22nd order model, which is too large for designing control systems, and many state variables are unmeasurable. A fourth order model, retaining only four measurable state variables, is therefore developed by applying the moments matching method of model reduction. Based on this reduced model, modal feedback, feedforward, and combined feedback–feedforward (all proportional type) control systems are designed for output regulation under disturbances in the catalyst loading variable. The inlet gas composition is considered as the manipulated variable. The performance of the control systems, when implemented on the original 22nd order model, is evaluated by digital simulation. Simple feedback control gives the best results.