Estimation of the flotation rate distributions by numerical inversion of the Laplace transform

Abstract

A method for estimation of the distributed apparent rate constant in the kinetic equation describing the recovery of flotable species has been proposed. The flotation rate distribution is recognized as an inverse of the Laplace transform of the material remaining in the cell at a given time. Numerical inversion of the Laplace transform is carried out in the cumulative rate distribution mode. The Laplace integral in the flotation kinetic equation is approximated by the Lobatto quadrature formula and the cumulative distribution is evaluated by optimizing a least square objective function. The method has been tested with numerically generated data and the effects of errors in the data and presence of non-flotables have been studied. The procedure provides a simple and reliable method for estimation of the flotation rate distribution or any monotonically non-increasing or non-decreasing function.