An improved equation for the overall heat transfer coefficient in packed beds

A one-point collocation analysis is performed on the two-dimensional pseudohomogeneous model of a fixed bed heat-exchanger. The analysis is based on a single radial collocation point whose position depends on the wall Blot number. The resulting improved equation for the overall heat transfer coefficient U is 1/U = 1/h(w) + R(t)/3k(r) Bi + 3/Bi + 4 which gives an error less than 3.8% in the exact asymptotic value of U over the entire range of Bi. A formula is also given for U', the overall heat transfer coefficient based on the difference between tube wall and bed center temperatures. The synthesis of vinyl acetate in a fixed bed reactor was simulated. Use of the conventional one-dimensional model with the improved equation for U, combined with the equation for U' to obtain bed center temperatures, gave predictions of acetylene conversion and bed center temperature in good agreement with those of the two-dimensional model. A criterion for the neglect of radial temperature gradients in a fixed bed; reactor is derived which is more stringent than criteria currently available in the literature.