2025 AIChE Annual Meeting

(525b) Improved Theoretical Prediction of Effective Heat Transfer Parameters in Packed Beds

Author

Anthony Dixon - Presenter, Worcester Polytechnic Institute
One approach to the perennial problem of predicting the effective radial heat transfer parameters kr and hw for the two-dimensional pseudo homogeneous fixed bed reactor model is known as model matching. The idea is that since the effective parameters reflect several heat transfer mechanisms which makes their direct correlation difficult, they could instead be related to the heat transfer parameters for the two individual phases, for which simpler correlations could be found by mass transfer or stagnant conduction experiments.

Dixon and Cresswell1 found formulas for kr and hw by extending a series–based model-matching methodology that had been first presented by Olbrich2 for the plug-flow model, to include axial terms in the model equations, which at that time were thought to be necessary to avoid length effects, by a one-term perturbation – orthogonal collocation approach. The Dixon-Cresswell formulas showed a nonlinear dependence of the effective parameters on Re, contrary to accepted wisdom. More recent work has shown the axial terms to be unnecessary, so that Olbrich’s series approach assumes new relevance. The present work shows that a one-term series approach is more accurate than the perturbation-orthogonal collocation approach and can also demonstrate nonlinear effects at lower flow rates, due to interphase heat transfer. However, Olbrich’s method is numerically cumbersome, requiring the iterative solution of coupled nonlinear equations to determine the first eigenvalue. Here we illustrate a simple approximate version of Olbrich’s equations, which is much easier to use and loses very little in accuracy of prediction of kr and hw.

References

  1. Dixon AG, Cresswell DL. Theoretical prediction of effective heat transfer parameters in packed beds. AIChE J. 25: 663-676 (1979).
  2. Olbrich WE. A two-phase diffusional model to describe heat transfer processes in a non-adiabatic packed tubular bed. Inst. Chem. Eng. Symp. Ser. 33: 101-119 (1971).