Wiley InterScience Backfile Collection 1832-2000
Chemistry and Pharmacology
Process Engineering, Biotechnology, Nutrition Technology
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.
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