Inversion of a Laplace Transform arising from a Problem in Applied Chemical Kinetics

Abstract

THE solution to a problem (Wood, T., unpublished work) arising from an analysis of a closed circuit consisting of a stirred-tank reactor and a tubular reactor in series, with first-order, isothermal, irreversible kinetics, involves finding the inverse of the Laplace transform : where β₁, β₂, β₃ are known, positive, constants. The transform can be re-arranged: Since no tabulated transform could be found, the denominator was expanded as a power series, giving : The inverse of the transform is now readily shown to be¹: where H(t−nβ₃) = 0 when t ≤ nβ₃; H(t−nβ₃) = 1 where t > nβ₃