Differences in the dispersion and/or catalytic pellet size between laboratory and commercial reactors, operating at the same average residence time, may lead to differences in the yield of a desired product. Bounds are developed for predicting the maximal design uncertainty introduced by these phenomena for a network consisting of an arbitrary number of irreversible first-order reactions. A major advantage of these bounds is that they do not require any knowledge of the rate constants. It is shown that in a packed-bed reactor, the fractional yield loss is smaller than:where m -1 is the number of reaction steps involved in converting a reactant to the desired product, 08' is the dimensionless variance of the residence time density function, Bi,,, is the Biot number, p2 = [( V,/S,)*(I / (DJ)], and T is the average residence time.
IntroductionThe different impact of nonideal flow and/or catalytic pellet transport limitations on the performance of laboratory or pilot plant reactors and commercial ones leads to uncertainties in the scale-up procedure. These are especially important when a large number of chemical reactions occur simultaneously.In many tubular and packed-bed reactors, deviations from plug flow may be accounted for by an axial dispersion model. Many papers have examined the influence of axial dispersion or residence time distribution on the conversion or yield in reactors in which first-order reactions occur. Many investigators studied the conditions leading to optimal yield for specific reaction networks and kinetic parameters (Tichacek, 1963;Kipp and Davis, 1968;Chung and Howell, 1970;Glasser et al., 1973;Wan and Ziegler, 1973;Silverstein and Shinnar, 1975;Dang, 1984).The yield in a short laboratory reactor is affected by axial dispersion more than that of a full-scale industrial reactor operating at the same residence time. To estimate the uncertainty involved in the scale-up it is important to have an a priori estimate of the maximal deviation in the yield between a laboratory and a full-scale reactor. This information is essential for predicting the minimal length a laboratory reactor should have for specified operating conditions so that the yield of a desired product will not deviate by more than some specified value from that of a full scale reactor. Tichacek (1963) developed a rule of thumb that for two consecutive reactions, the maximum fractional reduction in the yield of an intermediate due to axial dispersion is approximately equal to 1/Pe = D,,/uL, where D, is the axial disperison coefficient. Glasser et al. (1973) and Silverstein and Shinnar (1975) conjectured that for n isothermal, irreversible, first-order, consecutive reactions, the maximal fractional yield loss of the mth species due to axial dispersion occurs when the rate constants of the first m reactions are equal. This led to a prediction that the maximal fractional yield loss of the mth species due to a small deviation from plugflow is(1)