2682
A Model of Froth Flotation with Drainage: Simulations and
Comparison with Experiments
Fernando Betancourt
Department of Metallurgical Engineering, Universidad de Concepción, Chile
Raimund Bürger
CI2MA &Department of Mathematical Engineering, Universidad de Concepción, Chile Stefan Diehl
Centre for Mathematical Sciences, Lund University, Sweden
María Martí
Departament de Matemàtiques, Universitat de València, Spain
Yolanda Vásquez
Facultad de Ciencias y Tecnología, Universidad Tecnológica de Panamá, Panama
ABSTRACT: The model of the operation of a froth flotation column is described by a nonlinear convection–
diffusion partial differential equation that incorporates the solids–flux, and drift–flux theories as well as a model
of foam drainage. The resulting model is novel and contains non-standard ingredients such as discontinuous
fluxes and degenerating diffusion accounting for foam drainage. It predicts the bubble and (gangue) particle
volume fractions as functions of height and time. The model’s steady-state (time-independent) version defines
conditions on the gas and pulp feed rates that allow for operation with a stationary froth layer. The model is
validated through experiments. The agreement between experiments and model predictions is good at the steady
state condition
INTRODUCTION
Water scarcity is a major concern for economic activities
in Chile, especially in the desert regions where most mines
are located. The main recovery unit operations used for
processing low-grade ores such as copper ores in Chilean
deposits is flotation, but unfortunately, it requires huge
amounts of process water. Therefore, it is of great impor-
tance to improve the scientific understanding of flotation
processes and develop suitable tools for the design, simu-
lation, and control of flotation devices [Quintanilla et al.
2021a, 2021b, Maldonado et al. 2009, Betancourt et al.
2023, Bascur 1991]. Among these equipment, flotation
columns have a significant role on cleaning flotation circuit
[Wills &NapierMunn 2006, Neethling &Cilliers 2002].
Is well known that a flotation column works by introduc-
ing gas close to the bottom to generate bubbles that rise
through the pulp. The hydrophobic particles (usually the
valuable mineral particles) attach to the rising bubbles,
forming at the top a froth that is removed through a laun-
der. The hydrophilic particles (slimes or gangue) do not
attach to bubbles but settle to the bottom (unless they are
trapped in the bulk upflow known as entrainment) and are
removed continuously as flotation tailings. Close to the
top, additional wash water can be injected to assist with the
rejection of entrained particles and increase froth stability
A Model of Froth Flotation with Drainage: Simulations and
Comparison with Experiments
Fernando Betancourt
Department of Metallurgical Engineering, Universidad de Concepción, Chile
Raimund Bürger
CI2MA &Department of Mathematical Engineering, Universidad de Concepción, Chile Stefan Diehl
Centre for Mathematical Sciences, Lund University, Sweden
María Martí
Departament de Matemàtiques, Universitat de València, Spain
Yolanda Vásquez
Facultad de Ciencias y Tecnología, Universidad Tecnológica de Panamá, Panama
ABSTRACT: The model of the operation of a froth flotation column is described by a nonlinear convection–
diffusion partial differential equation that incorporates the solids–flux, and drift–flux theories as well as a model
of foam drainage. The resulting model is novel and contains non-standard ingredients such as discontinuous
fluxes and degenerating diffusion accounting for foam drainage. It predicts the bubble and (gangue) particle
volume fractions as functions of height and time. The model’s steady-state (time-independent) version defines
conditions on the gas and pulp feed rates that allow for operation with a stationary froth layer. The model is
validated through experiments. The agreement between experiments and model predictions is good at the steady
state condition
INTRODUCTION
Water scarcity is a major concern for economic activities
in Chile, especially in the desert regions where most mines
are located. The main recovery unit operations used for
processing low-grade ores such as copper ores in Chilean
deposits is flotation, but unfortunately, it requires huge
amounts of process water. Therefore, it is of great impor-
tance to improve the scientific understanding of flotation
processes and develop suitable tools for the design, simu-
lation, and control of flotation devices [Quintanilla et al.
2021a, 2021b, Maldonado et al. 2009, Betancourt et al.
2023, Bascur 1991]. Among these equipment, flotation
columns have a significant role on cleaning flotation circuit
[Wills &NapierMunn 2006, Neethling &Cilliers 2002].
Is well known that a flotation column works by introduc-
ing gas close to the bottom to generate bubbles that rise
through the pulp. The hydrophobic particles (usually the
valuable mineral particles) attach to the rising bubbles,
forming at the top a froth that is removed through a laun-
der. The hydrophilic particles (slimes or gangue) do not
attach to bubbles but settle to the bottom (unless they are
trapped in the bulk upflow known as entrainment) and are
removed continuously as flotation tailings. Close to the
top, additional wash water can be injected to assist with the
rejection of entrained particles and increase froth stability