The multiple convolution integral: A new method for modeling multistage continuous leaching reactors

A new method is presented for modeling multiparticle leaching kinetics in multistage continuous reactors at steady state. The method involves recasting the kinetics of any given leaching reaction into a linear function of time, and then solving a multiple convolution integral over residence time for the mass-weighted probability density of the resulting time-linear variable after passing through N mixed-how reactors in series. The fraction of leachable solids unreacted is then found by integrating this probability density function over all values of the time-linear variable, which is a known function of particle size. The entire model may be solved numerically in a single step using Gaussian quadrature. This new method represents an alternative to both the segregated flow model and the population balance model, combining the simplicity and ease of application of the former with the rigorousness of the latter. Copyright (C) 1996 Elsevier Science Ltd