In a recent R&D note by Huang et al. (1984), an analytical solution for a packed bed reactor with a first-order reaction is derived. The solution is obtained by the Laplace-transform method and by inversion in the complex plane. Since the transform contains branch points a , so called second Bromwich contour (McLachlan, 1953) is used to obtain the solution in the time domain.Some criticism is also made of an earlier analytical solution of the same problem (but without chemical reaction) given by Rasniuson and Neretnieks (1980). We are supposed to have used the first Bromwich contour (McLachlan, 1953) in our derivation. Since the Laplace transform contains branch points, they contend, this procedure is not valid. This statement is correct. However, in our analytical inversion, neither the first nor second Bromwich contour is used. Instead, we integrate along the imaginary axis. This integration path follows direct application of the complex inversion integral for the Laplace transform. We would like to clarify our analytical inversion of the Laplace transform and discuss relative merits of various methods.Under very general conditions, the inversion integral of the Laplace transform is given (Churchill, 1972; Doetsch, 1976) by:

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