An inversion approach to characterize batch flotation kinetics. (November 2019)

• Record Type: Journal Article
• Authors: Vinnett, L.; Navarra, A.; Waters, K.E.
• Is Part Of: Minerals engineering. Volume 143(2019)
• Publication Date: 2019-11
• Subjects: Flotation rate distribution -- Flotation kinetics -- Regularization -- Inversion; Mines and mineral resources -- Periodicals; Ressources minérales -- Périodiques; Mines and mineral resources; Periodicals; Electronic journals; 622
• DOI: 10.1016/j.mineng.2019.105944
• Languages: English
• ISSNs: 0892-6875

Abstract

Highlights: An inversion methodology is presented to characterize batch flotation kinetics. The product between the flotation rate distribution and R ∞ was estimated. Both parameters were decoupled, given F ( k ) is a probability density function. The approach was tested with 85 batch flotation datasets. The solution was in good agreement with the parametric Gamma approach. Abstract: This short communication presents the kinetic characterization of 85 batch flotation tests based on an inversion approach, extending the work reported by Vinnett et al. (2019). For first-order systems, the mineral recovery R ( t ) as a function of time t can be expressed as R t = R ∞ ∫ 0 ∞ 1 - e - k t F k d k, where R∞ is the maximum recovery, k is the rate constant and F ( k ) is the flotation rate distribution. An arrangement of this expression allows the estimation of R∞ F ( k ) by discretizing the integral term. A linear system is solved by a regularization approach that accounts for the fitting error of R ( t ) and the roughness of R∞ F ( k ). Thus, R∞ is obtained, given ∫ 0 ∞ F k d k = 1 . The results show a good agreement with those obtained from F ( k ) following a Gamma distribution (non-linear regression), in terms of: Sum of Squared Residuals, cross-validated R 2, F ( k ) shapes and range for the R∞ estimates.