Tubular reactor design—I Two dimensional model

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Conservation equations for a packed tubular reactor are modelled using a radially varying axial velocity, radial diffusivity and radial thermal conductivity. Radial diffusivity and thermal conductivity profiles are obtained from relations presented in this work. Instead of using a wall heat transfer coefficient, the model accounts for the higher resistance to heat flow near the reactor wall by using a lower value of the thermal conductivity. Axial diffusion is not included in the bulk of the bed, but its effect on the inlet temperature and conversion profiles are accounted for by considering axial diffusion in the pre-reaction zone. The two partial differential equations are converted into ordinary differential equations by using orthogonal collocation in the radial direction. The conventional orthogonal collocation method is modified by adding balance equations at the center of the tube, so as to improve the prediction of hot spot temperature. The model was applied to the sulfur dioxide reactor of Schuler et al. The results agreed quite well with the experimental data without the need for adjustment of parameters or constants.