Optimal Sampling Times for Leaching Experiments

Abstract

In this study, an optimal sampling schedule was developed for leaching experiments with the objective of improving the confidence of the kinetic parameters. This study shows that there is an improvement in the confidence interval from uniform sampling and the method presented here. The optimal sampling times were determined by reducing the determinant of the covariance matrix associated with the kinetic constant, which can be expressed through the covariance matrix of the extracted fraction, $X,$ used to generate a function to distribute the sampling times in the experiment. The method presented here requires minimal knowledge a priori of the system to be characterized. Only the kinetic expression for the system is required. The methodology was applied to a simulated case and experimental case study of ammoniacal leaching of copper slags. The simulations conducted indicated a lower value of the standard deviation of 1.40·10⁻⁴ min⁻¹ for optimized sampling times and a value of 1.78·10⁻⁴ min⁻¹ for uniform distribution. The experimental validation results indicated a reduction of the coefficient of variation for optimized experiments of 9.3 pct (less uncertainty) from 29.7 pct (uniform sampling) to 14.6 pct (optimized sampling). Thus, the methodology proposed here is successful in decreasing the uncertainty in laboratory leaching experiments.