Chemical Engineering Science 57 (2002) 1409–1417 www.elsevier.com/locate/ces An analytic solution to the transient diusion-reaction problem in particles dispersed in a slurry reactor J. O. Marroquin de la Rosa a , R. Morones Escobar b , T. Viveros Garcia c , J. A. Ochoa-Tapia c ; * a Instituto Mexicano del Petr oleo, Eje Central Lazaro Cardenas 152, Mexico, D.F. 07730 Mexico b Departamento de Matematicas, ITAM, R o Hondo 1, Tizap an, San Angel, Mexico, D.F. 01000 Mexico c Area de Ingenieria Qu mica, Universidad Autonoma Metropolitana, Unidad Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, M exico, D.F., CP 09340 Mexico Received 7 November 2000; received in revised form 24 July 2001; accepted 18 September 2001 Abstract In this work, we present the solution of the equations that govern the reactant transport in a well mixed system that contains particles where diusion and rst-order reaction occur. The transport equations are coupled by an interfacial boundary condition that includes mass transfer resistance. The statement of the problem allows arbitrary time depending feed functions. The evaluation of the solution obtained by the Laplace method requires the solution of an eigenvalue problem. We discuss the evaluation of the solution, and typical results for three dierent feed functions: step, pulse and oscillatory functions are presented. The resulting equations are able to show the eect of internal and external mass transfer limitations on the particle and uid concentrations and on kinetic experimental results. ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: Diusion; Mass transfer; Modeling; Reaction engineering; Transient response; Transport processes 1. Introduction The well mixed stirred tank reactor is probably the most used model to determine reaction rate constants. This re- actor model is obtained by dierent experimental setups which simulate the conditions achieved in such a system: spatially homogeneous properties and variables (Carberry, 1964; Tajbl, Simmons, & Carberry, 1966; Berty, 1974; Weekman, 1974). Besides, stirred tank reactors have been widely used in industry, either as a single unit, as a series of tanks or as multichamber tank reactors (Rase, 1977; Car- berry, 1976; Shain, 1997). The determination of reaction rate constants and mechanisms has been frequently done from the analysis of the transient behavior of these reactor systems (Bennett, 1967; Bennett, Cultlip, & Yang, 1972; Bennett, 1976). The nonsteady-state methods permit more detailed kinetic analysis of elementary steps (Weller, 1992; Bennett, 1999). To obtain kinetic information it is necessary to describe adequately the experimental setup. This should include the * Corresponding author. Tel.: +52-5804-4648; fax: +52-5804-4900. E-mail address: jaot@xanum.uam.mx (J. A. Ochoa-Tapia). mass and heat transport resistances, both in the uid and the porous catalyst. Although care has been taken to obtain data in the absence of transport resistances, the use of dynamic techniques imposes greater restrictions than in steady-state experiments. In the case of dynamic experiments with fast enough reactions the interpretation of the data could be in- appropriate if the resistances are not taken into account even if these are small. It seems reasonable to use a model that includes the most important eects to decide which resis- tances can be safely discarded. In general, the models used to describe isothermal dy- namic experiments have not considered the presence of internal or external mass transfer resistances, even in the cases where porous particles have been used (Bennett, 1976; Li, Willcox, & Gonzalez, 1989; Weller, 1992; Bennett, 1999). Few reports in the literature have considered the presence of internal resistances (Relyea & Perlmutter, 1968; Kelly & Fuller, 1972; Towler & Rice, 1974; Datta, Croes, & Rinker, 1983). Recently, Dekker, Bliek, Kapteijn, and Moulijn (1995) have analyzed the eects of mass and heat transfer in transient experiments by numerical simula- tions. They extended the criteria for mass and heat transfer limitations on steady-state experiments to dynamic experi- 0009-2509/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved. PII:S0009-2509(02)00054-4