A New Approach to Fixed Bed Radial Heat Transfer Modeling Using Velocity Fields from Computational Fluid Dynamics Simulations Mohsen Behnam, †,⊥ Anthony G. Dixon,* ,† Michiel Nijemeisland, ‡ and E. Hugh Stitt ‡ † Department of Chemical Engineering, Worcester Polytechnic Institute, 100 Institute Road, Worcester, Massachusetts 01609-2280, United States ‡ Johnson Matthey, P.O. Box 1, Belasis Avenue, Billingham, Cleveland TS23 1LB, U.K. ABSTRACT: A new velocity-based approach to fixed bed radial heat transfer is presented. Axial and radial velocity components were averaged from detailed 3D computational fluid dynamics (CFD) fixed bed simulations of computer-generated beds of spheres and used to model radial thermal convection. The convection terms were coupled with a radially varying stagnant bed thermal conductivity in a 2D pseudocontinuum fixed-bed heat transfer model. The usual effective radial thermal conductivity k r and apparent wall heat transfer coefficient h w were not used, and there were no adjustable parameters. The radial and axial temperature variation predicted by the velocity-based model agreed well with the angular-averaged temperatures from the detailed 3D CFD simulations over the range 80 ≤ Re ≤ 1900 and for N = 3.96, 5.96, and 7.99. 1. INTRODUCTION Heat transfer in fixed bed tubes is an important topic in the chemical industry because fixed beds are extensively used in applications with heat effects, such as reactors, thermal storage units, and adsorption or desorption plants. In particular, multitubular fixed bed reactors with low tube-to-particle diameter ratio (N) are used for extremely exothermic or endothermic reactions such as partial oxidations and steam reforming of methane, respectively. Heat must be rapidly transferred into or out of a narrow reactor tube, in which the tube wall has a strong influence on heat transfer and flow of reactants around the catalyst particles. These in turn affect catalyst activity, selectivity, and deactivation. Current reactor models for heterogeneous gas-solid reactors have been based on fairly radical simplifying assumptions, such as pseudohomogeneity, effective transport parameters, and uniform catalyst pellet surroundings. Despite the realization that local flow structures are critically important in determining the global behavior of a flow or transport system, 1 in many cases the hydrodynamic modeling of reactors is still based on unidirectional axial plug flow. All mechanisms for radial heat transport are lumped into an effective radial thermal conductivity k r , which is taken as constant and used to describe heat transfer up to the wall. The observed increase in resistance to heat transfer near the containing wall has been a continuing source of difficulty. The classical approach to modeling this increased resistance near the wall is to idealize it to occur at the wall, and lump all the mechanisms into a wall heat transfer coefficient, h w . Thus the near-wall resistance is misplaced, and the temperature of the near-wall particles is under-predicted (for wall heating) along with the associated reaction rate. For narrow tubes this can be a major problem. A review has recently been presented of the present state of research and understanding of radial heat transfer in fixed beds. 2 The classical effective parameter k r - h w model was extensively described and problems with typical approaches to obtaining and analyzing experimental heat transfer data to get k r and h w were explained. Current correlations for k r were evaluated, and the debate over the meaning and usefulness of h w was elaborated, in the context of the historical development of the concept. A discussion of alternatives to the k r - h w approach and their pros and cons was made, with focus on recent efforts to include limited aspects of the velocity field and local bed structure. The major finding from this review was that all current approaches to radial fixed bed heat transfer modeling suffer from serious deficiencies, which motivates the completely new development of the present work. A new approach to modeling radial heat transfer in fixed beds is proposed. The motivation for this approach is to discard the use of effective conduction to represent transport by convective motion of the fluid, which is a purely fluid mechanical phenomenon. A second motivation is to improve the prediction of temperature profiles and heat fluxes at the reactor tube wall by incorporating the physical phenomena that cause the extra resistance to heat transfer near the tube wall directly into the model, and not idealizing them at the wall with an artificial temperature jump. We therefore postulate a new type of two- dimensional pseudocontinuum model. For this work, the model is also pseudohomogeneous, but this is for convenience only and is not an essential part of the formulation. The development of this new approach depends on the use of 3D computational fluid dynamics (CFD) for full beds of particles 3,4 to obtain the necessary information on individual velocity components. The CFD simulation is then also used to provide validated temperature profiles to test the 2D pseudocontinuum model. The strategy for this development is illustrated in Figure 1. The first step is to develop 3D CFD discrete particle models for the detailed flow through a catalyst packing, to provide the detailed flow fields that are responsible Special Issue: NASCRE 3 Received: January 12, 2013 Revised: March 15, 2013 Accepted: March 20, 2013 Published: March 20, 2013 Article pubs.acs.org/IECR © 2013 American Chemical Society 15244 dx.doi.org/10.1021/ie4000568 | Ind. Eng. Chem. Res. 2013, 52, 15244-15261