5. PP. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDC 893+01. 1984 ooo9-z5wp4 s3.00 + .oV kwmon F’rw Ltd TRANSIENT RESPONSE OF THREE-PHASE SLURRY REACTORS RAVINDRA DATTAt and ROBERT G. RINKER* Department of Chemical and Nuclear Engineering, University of California, Santa Barbara, CA 93106, U.S.A. (Received 29 November, 1982; accepted 12 September 1983) Abstract-Analytical time domain solutions are provided for the transient response of three-phase slurry reactors, with diffusion and first-order irreversible chemical reaction in catalyst particles, for the following disturbances: (a) step input of the reactant in the inlet gas stream; and @) when the catalyst particles are suddenly introduced into the reactor which has otherwise reached steady-state with the gas and the liquid phases flowing. Tbe results have been obtained for the general case of continuous slurry reactors but can be easily reduced for application to semi-batch slurry reactors in which there is no flow of the liquid phase. The results depend upon six dimensionless parameters and are expected to be useful for evaluating the rate and equilibrium constants from dynamic response experiments. Asymptotic solutions have also been obtained for the case of large Tbiele parameter (4 2 3) and some other simpler expressions have be-enderived as well for some limiting cases of practical signiticance. The results are accurate only for gaseous reactants of moderate or high solubility in the liquid phase and are not applicable lo those with low solubility. INTRODUCTION Slurry reactors find numerous applications in industry and some of these are given in a review by Chaudhari and Ramachandran[l]. Shah[2] provides a compre- hensive list of three-phase catalytic reactions which are or could be conducted in slurry reactors. In de- signing this type of reactor, the dynamic approach of parameter estimation by analyzing response of labora- tory reactors to input concentration disturbances is particularly attractive, since it offers the possibility of providing the needed information under actual oper- ating conditions from relatively few experiments. The method of moments has been applied to dy- namic response data by several investigators to esti- mate rate and equilibrium parameters in semi-batch slurry adsorbers [3]. Niiyama and Smith [4] derived the required expressions for the first absolute and second central moments for the response of semi-batch slurry adsorbers, wherein all processes were assumed to be linear. In addition, Ramachandran and Smith[S] have derived the moment equations for the case of first-order irreversible reaction, with or without ad- sorption. Misic and Smith[6] provided time domain solutions for the response of a semi-batch slurry ad- sorber with no diffusional retardation within the solid particles and with the adsorption step considered to be at equilibrium. They obtained solubility and ad- sorption isotherms as well as mass transfer coefficients. Komiyama and Smith[7J were able to obtain Freundlich-type nonlinear absorption and ad- sorption isotherms by numerical integration of the *Author to whom correspondence should be addressed. TPresent address: Chemical and Materials Engineering Program. The University of Iowa, Iowa City, IA 52242, U.S.A. breakthrough curves in addition to obtaining mass transfer coefficients, effective diffusivities and rate constants. In the work reported here, we have provided anal- ytical time domain solutions for the transient response of an isothermal three-phase catalytic slurry reactor. These solutions can be used for estimating parameters from experimental response curves without using the method of moments. The two forcing functions con- sidered are: (a) step input of reactant, and (b) sudden introduction of catalyst particles into the reactor which has otherwise reacted steady conditions relative to flow of the gas and liquid phases. These input conditions were chosen since they can he easily real- ized in the laboratory. We do not consider the case of pulse input, since for slurry reactors this is not likely to yield accurate results [4]. Although our development considers the more gen- eral case of continuous slurry reactors, the results can be easily reduced to the case of semi-batch reactors. Further, we assume that the solid particles are of spherical geometry which is quite reasonable for a slurry reactor. POEMUJATION A schematic of a continuous three phase catalytic ‘slurry reactor is shown in Fig. 1. The gas and the liquid phases flow continuously through the reactor at con- stant volumetric fiow rates. The liquid phase is as- sumed to be completely mixed. The gas is introduced at the bottom through a sparger and it is supposed that the bubbles travel upwards in plug motion through the slurry. These assumptions about the mixing states of the two phases are customary[4, 51. The reactant, A, enters the reactor only in the gas stream and not in the liquid stream. Transport of A from the gas bubbles in CES Vol. 39, No. S-H 893