CFD Study of Heat Transfer near and at the Wall of a Fixed Bed Reactor Tube: Effect of Wall Conduction Anthony G. Dixon* Department of Chemical Engineering, Worcester Polytechnic Institute, 100 Institute Road, Worcester, Massachusetts 01609-2280 Michiel Nijemeisland and E. Hugh Stitt Johnson Matthey Catalysts, P.O. Box 1, Belasis Avenue, Billingham, Cleveland TS23 1LB, U.K. The inclusion of conduction in the tube wall of a packed bed reactor tube under conditions typical of steam reforming was studied. Computational fluid dynamics (CFD) was used to obtain detailed flow and temperature fields in a representative wall segment of the tube for packings of spheres, full cylinders, and cylinders with internal voids. The average wall temperature was not affected by the inclusion of wall conduction. Radial temperature profiles in the bed were also unaffected by wall conduction, but the temperature distribution on the wall changed considerably. The inclusion of wall conduction narrowed the distribution of temperatures on the tube wall, suppressing extreme temperatures. The simulations predicted that a wide enough temperature range would persist on the tube wall to have significant implications for tube life. Introduction Applications of CFD simulations in reaction engineer- ing are increasing rapidly. 1,2 Packed bed reactor model- ing using CFD has usually involved the replacement of the actual packing structure with an effective con- tinuum, to which the averaged Navier-Stokes equa- tions are applied, with a pressure drop model to obtain a reduced description of the velocity field. Recently, there has been an upsurge of interest in examining the detailed flow phenomena in a packed bed, taking into account the actual packing structure. This has been done for isothermal flows by automata-based simulation methods such as the lattice Boltzmann method. 3 These studies have been extended to isothermal reacting flows with good agreement between the computations and the experimental results. 4,5 CFD simulation of simultaneous heat transfer and fluid flow has been based on finite volume or finite element solution of the continuum equations of change, for both fluid and solid regions in the original packing geometry. The potential of CFD for fixed bed reactor design for low tube-to-particle diameter ratio (low-N) tubes was noted by Dixon and Nijemeisland, 6 and calculations for isothermal full beds of N ) 5 were presented by Esterl et al. 7 and for nonisothermal beds of N ) 4 by Dixon and Nijemeisland. 6 CFD has been applied to complex fixed bed geometries, 8 to pressure drop and flow in beds of spheres 9 and structured packings, 10,11 and to determine the heat and mass transfer between particles and the surrounding fluid. 12 A major emphasis in our work has been on under- standing the relationship between flow and heat trans- fer near the tube wall for inert spherical particles. 13 A parallel effort has studied particles with heat sinks placed inside them to mimic the thermal effects of steam reforming reactions for both spheres 14 and beds of commercial catalyst particles of cylindrical shape with internal voids. 15 Our previous results showed that, in tubes with a constant wall temperature boundary condition, the wall heat flux showed structure. A repetitive pattern of pointwise heat flux was identified for packings of spheres, which could be qualitatively correlated with near-wall flow structures and the arrangement of spheres in the wall layer. 13 These studies showed that there was a strong local variation in wall flux in fixed bed tubes. For tubes with constant wall heat flux, 15 we were again able to qualitatively link the near-wall flow patterns to near-wall temperature maps and thus to regions of better or worse heat transfer. But we did not present wall temperatures, as our earlier models were run without wall conduction. For our heat transfer studies with constant wall temperature this was obvi- ously not an issue. For simulations intended to reflect industrial steam reforming practice, however, a more realistic wall boundary condition is the imposition of constant wall heat flux, leading to a solution that gives temperature profiles on the wall. Since temperature is not constant, conduction in the wall could be expected to have a strong effect on the temperature patterns found there. Tube wall temperature is an important parameter in the design and operation of steam reformers. The tube material is exposed to an extreme thermal environment. Gradual creep of the tube material is inevitable, leading to premature failure of the tubes if the tube temperature is not constrained. The effects of tube temperature on the residual strength of a tube are generally considered by use of the Larson-Miller parameter (P): 16 where T ) material temperature (K), t ) time (h), and K is a material-dependent constant. The value of this parameter is plotted against the rupture stress of the * To whom correspondence should be addressed. Tel.: 508- 831-5350. Fax: 508-831-5853; E-mail: agdixon@wpi.edu. P ) T log(t) + K 1000 (1) 6342 Ind. Eng. Chem. Res. 2005, 44, 6342-6353 10.1021/ie049183e CCC: $30.25 © 2005 American Chemical Society Published on Web 04/14/2005