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, σ is the dimensionless variance of the residence time density function, Bim is the Biot number, p2 = [(Vp/Sx)2(1/Deτ)], and τ is the average residence time.