AN IMPROVED EQUATION FOR THE OVERALL HEAT-TRANSFER COEFFICIENT IN PACKED-BEDS

A one-point collocation analysis is performed on the two-dimensional p seudohomogeneous model of a fixed bed heat-exchanger. The analysis is based on a single radial collocation point whose position depends on t he wall Blot number. The resulting improved equation for the overall h eat 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 over all heat transfer coefficient based on the difference between tube wal l and bed center temperatures. The synthesis of vinyl acetate in a fix ed 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 c onversion and bed center temperature in good agreement with those of t he two-dimensional model. A criterion for the neglect of radial temper ature gradients in a fixed bed; reactor is derived which is more strin gent than criteria currently available in the literature.