LUMPED KINETICS OF MANY PARALLEL NTH-ORDER REACTIONS

The kinetics of lumped nth‐order reactions are examined both asymptotically and numerically. The lumped kinetics in most cases are Mth order at large times. There exist two critical values for n, denoted by n* and n*, which are expressed explicitly as functions of the feed properties. It is shown that (1) M = n when n > n*, (2) M is linear in n when n* < n < n*, and (3) M does not exist when n = n* or n ≤ n*. Whenever the feed contains some unconvertibles, M is independent of n for −∞ < n < n*. The overall effective rate constant is not continuous at n = n* nor at n = n*. Unexpectedly, when n > n* the lump's long‐time behavior is governed by all species, not just by the most refractory species. Although the asymptotic kinetics are developed for long times, they are useful for fitting the whole‐time behavior of the lump by an mth‐order model. This is true even when M does not exist in the asymptotic regime. Numerical experiments show that M and m behave similarly in many respects. For example, as n increases, they both become closer to n and less dependent on the feed properties. Some published data are rationalized in light of the present results. Copyright © 1990 American Institute of Chemical Engineers