Fernando Betancourt - Academia.edu (original) (raw)

Papers by Fernando Betancourt

Chemical Engineering Research and Design, 2019

The efficient use of water has become an important issue in the mining industry, especially in co... more The efficient use of water has become an important issue in the mining industry, especially in countries where it is located in desert areas with low water reserves, as is the case in Chile. In addition, low ore grades necessitate efforts to recover the maximum amount of minerals in solid-liquid separation processes. Fine particle flocculation is a preliminary stage in various solid-liquid separation processes. The conventional flocculation process is done at low shear rates, ensuring that large flocs remain unbroken. However, it has been seen that the application of high shear rates at the beginning of the process for a short period of time significantly improves the solid removal efficiency, reducing the flocculant dosage and the duration and cost of the process, which is known as ultra-flocculation. This work presents a numerical CFD study of the hydrodynamic behavior in five hydraulic reactors for ultra-flocculation, analyzing the shear rate curve over treatment time, dissipation efficiency and average shear rates. A new mean shear rate, which uses hydraulic variables to estimate the average agitation, is also defined. It was shown that the hydraulic shear rate can be useful for developing better hydraulic designs because it provides a second view, which, added to the shear rate curve over treatment time and effective shear rate, allows a more complete judgment of the performance of the designs.

Minerals

The discrete element method (DEM) has been widely employed to model processes in different indust... more The discrete element method (DEM) has been widely employed to model processes in different industries, such as mining, agriculture, pharmaceuticals, and food. One of the main lines of research, and in which different authors propose several approaches, is the calibration of parameters. Bulk calibration (BCA) is a common approach used that does not necessarily represent the individual behavior of each particle. On the other hand, direct measurement (DMA) is another approach employed in some cases. This work presents a comparison between calibration of DEM model parameters with non-cohesive spherical and polyhedral particles using a combination of direct measurement and bulk calibration. BCA is employed to calibrate friction parameters and DMA to characterize shape of the particles and coefficient of restitution of the contact between particles. Experimental data from Draw Down Tests are used to calibrate the friction parameters. Numerical optimization of the parameters is conducted b...

Minerals Engineering, 2020

Minerals

The operation of a froth flotation column can be described by a nonlinear convection–diffusion pa... more The operation of a froth flotation column can be 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 predicts the bubble and (gangue) particle volume fractions as functions of height and time. The steady-state (time-independent) version of the model defines so-called operating charts that map conditions on the gas and pulp feed rates that allow for operation with a stationary froth layer. Operating charts for a suitably adapted version of the model are compared with experimental results obtained with a laboratory flotation column. Experiments were conducted with a two-phase liquid–bubble flow. The results indicate good agreement between the predicted and measured conditions for steady states. Numerical simulations for transient operation, in part for the addition of solid particles, are presented.

Minerals Engineering, 2020

Hydrocyclones are used for classification purposes in the mining and mineral processing industrie... more Hydrocyclones are used for classification purposes in the mining and mineral processing industries. According to their geometry and under certain operating conditions, hydrocyclones may present roping, which is a defective operation. Studies have related the roping phenomena to many variables such as hydrocyclone geometry and operating conditions. Some authors established a connection between the solids concentration of the feed and the discharge as one of the factors that generate roping. Other authors presented factors such as the apex and the vortex finder diameters, inlet pressure and the relationship between roping generation and the air core. This research aims to study the effect of inlet pressure and particle size distribution in the feed on roping in hydrocyclones. We develop a model using computational fluid dynamics (CFD) in order to study a 75-mm hydrocyclone operating with a variable flowrate and fed with two different materials. Each material is characterized by five granular phases interacting with each other and the model is validated by comparison with experimental data. The turbulence is treated using the Reynolds Stress Model (RSM) and the Eulerian Multiphase Model is used for the interactions between phases. The granular phases are described by the kinetic theory of granular flows (KTGF). The characteristics studied were: (i) air core and material distribution inside the hydrocyclone, (ii) underflow shape and spray angle, (iii) flow and solid concentrations, (iv) efficiency curve and separation size and (v) particle size distribution in the underflow and the cut sizes. According to the results, the particle size distribution of material in the feed has a direct impact on underflow behavior; when operating with coarser material the device tends to rope as the spray angle decreases. The same happens with an increase in the feed pressure. The roping condition generated by the coarse material directly affects the efficiency of the hydrocyclone, triggering an increase in separation size. The underflow particle size distribution tends to be coarser with an increase in the inlet pressure. When the inlet pressure decreases, the overflow particle distribution tends to be finer. 1.1. Experimental information Many experimental methods of analysis have been used to understand hydrocyclone performance, including Electrical Impedance Tomography (Gutiérrez et al., 2000), Laser Doppler Anemometry andvideo recordings to observe the flow inside the devices (Janse Van Vuuren et al., 2010). Most research has focused on the behavior of hydrocyclone efficiency curves (

Mining, Metallurgy & Exploration

Minerals

Shear-induced polymer-bridging flocculation is widely used in the solid–liquid separation process... more Shear-induced polymer-bridging flocculation is widely used in the solid–liquid separation process in cemented paste backfill, beneficial to water recycling and tailings management in metal mines. A flocculation kinetics model based on Population Balance Model (PBM) is proposed to model the polymer-bridging flocculation process of total tailings. The PBM leads to a system of ordinary differential equations describing the evolution of the size distribution, and incorporates an aggregation kernel and a breakage kernel. In the aggregation kernel, a collision frequency model describes the particle collision under the combined effects of Brownian motions, shear flow, and differential sedimentation. A semi-empirical collision efficiency model with three fitting parameters is applied. In the breakage kernel, a new breakage rate coefficient model with another three fitting parameters is introduced. Values of the six fitting parameters are determined by minimizing the difference between exper...

Powder Technology, 2021

Gravity thickening by deep cone thickener is popularly applied in cemented paste backfill, which ... more Gravity thickening by deep cone thickener is popularly applied in cemented paste backfill, which is essential for tailings management and green mining. To avoid rake bogging, high concentration and high flowability are required for thickened tailings slurry. These properties depend critically on the yield stress of the slurry. The yield stress, in turn, can be influenced by the flocculant dosage and the acidity (pH) that form the flocculation condition. Experiments have been performed to eventually quantify the dependence of yield stress on these two variables. The yield stress test of flocculated and thickened copper mineral tailings slurry, and the analysis of flocculant adsorption, were conducted at different pH values and flocculant dosages. It turns out that the amount of flocculant adsorbed on the tailings particles surface has a maximum with respect to pH but increases with the increasing flocculant dosage. In turn, the amount of flocculant adsorbed affects the yield stress, ...

a(s)ds; a(u) 0:This equation has been proposed as a model of aggregation by a series of authors ... more a(s)ds; a(u) 0:This equation has been proposed as a model of aggregation by a series of authors [1], [2], [3]under the assumption that a(u) = 0 at most at isolated points. We consider here the moregeneral assumption that a(u) = 0 on a bounded interval. Under the assumption that is asmooth function with a nite number of local extrema, through the use of a TV-stable schemewe prove the convergence of the approximate solution to the unique entropy solution of (1).Numerical examples illustrate our results.Keywords: Strongly degenerate parabolic equation, nonlocal ux, aggregation model, entropysoliution.Mathematics Subject Classi cations (2000): 35K65, 35Q92, 35R09, 65M06.

One-dimensional models to simulate secondary settling tanks (SST) with cylindrical geometry are w... more One-dimensional models to simulate secondary settling tanks (SST) with cylindrical geometry are widely used in wastewater treatment. One of these models is the Bürger-Diehl model developed in [3], the respective extention to the varying crosssectional area case was recently made in [1]. For the modelling, simulation and control of SST according to this model it is necessary to know the hindered-settling velocity function, which is considered a constitutive functions of the model. The traditional way to get this function is to measure the velocity of the declining sludge blanket in a vessel with constant cross-sectional area through experiments obtained from laboratory batch tests, however this method gives only one point on the flux curve. A newly developed method in [2] shows that in a vessel with varying cross-sectional area a large part of the flux function can be estimated from a single batch test, where the largest interval can be obtained with conical vessels. The identificati...

Comminution by gyratory crusher is the first stage in the size reduction operation in mineral pro... more Comminution by gyratory crusher is the first stage in the size reduction operation in mineral processing. In the copper industry, these machines are widely utilized, and their reliability has become a relevant aspect. To optimize the design and to improve the availability of gyratory crushers, it is necessary to calculate their power and torque accurately. The discrete element method (DEM) has been commonly used in several mining applications and is a powerful tool to predict the necessary power required in the operation of mining machines. In this paper, a DEM model was applied to a copper mining gyratory crusher to perform a comprehensive analysis of the loads in the mantle, the crushing torque, and crushing power. A novel polar representation of the radial forces is proposed that may help designers, engineers, and operators to recognize the distribution of force loads on the mantle in an easier and intuitive way. Simulations with different operational conditions are presented and...

Minerals

Froth flotation is a process in which hydrophobic particles attach to bubbles forming particle–bu... more Froth flotation is a process in which hydrophobic particles attach to bubbles forming particle–bubble aggregates, which are transported to the top section of the cell where they overflow to form the concentrate. Particles also reach the concentrate by entrainment, which is a non-selective process that leads to low concentrate grades. The objective of this work was to study and compare the degree of entrainment measured using three methods, in fresh and seawater, and using methyl isobutyl carbinol (MIBC) and DF-250 as frothers. The experimental results indicated that the degree of entrainment decreased in seawater. Besides, water recovery was lower in the experiments with seawater regardless of the frother that was used in the experiments, which correlated with the observed low degrees of entrainment. It is proposed that the reduction of entrainment and water recovery in seawater can be explained by a reduction of air recovery and/or more bubble coalescence in the froth. It is also p...

Chemical Engineering Science

J Chem Res S, 2004

... Publisher: Issue Date: 2004. ???metadata.dc.subject.productividad???: ARTICULOS INTERNACIONAL... more ... Publisher: Issue Date: 2004. ???metadata.dc.subject.productividad???: ARTICULOS INTERNACIONALES-1030759. ???metadata.dc.creator.projectrelation???: JOAQUIN ALBERTO CORTES GARRIDO. Description: Completo. URI: http://hdl.handle.net/10533/21284. ...

International Journal of Mineral Processing, 2015

Applied Mathematics and Computation, 2015

Chemical Engineering Research and Design, 2019

The efficient use of water has become an important issue in the mining industry, especially in co... more The efficient use of water has become an important issue in the mining industry, especially in countries where it is located in desert areas with low water reserves, as is the case in Chile. In addition, low ore grades necessitate efforts to recover the maximum amount of minerals in solid-liquid separation processes. Fine particle flocculation is a preliminary stage in various solid-liquid separation processes. The conventional flocculation process is done at low shear rates, ensuring that large flocs remain unbroken. However, it has been seen that the application of high shear rates at the beginning of the process for a short period of time significantly improves the solid removal efficiency, reducing the flocculant dosage and the duration and cost of the process, which is known as ultra-flocculation. This work presents a numerical CFD study of the hydrodynamic behavior in five hydraulic reactors for ultra-flocculation, analyzing the shear rate curve over treatment time, dissipation efficiency and average shear rates. A new mean shear rate, which uses hydraulic variables to estimate the average agitation, is also defined. It was shown that the hydraulic shear rate can be useful for developing better hydraulic designs because it provides a second view, which, added to the shear rate curve over treatment time and effective shear rate, allows a more complete judgment of the performance of the designs.

Minerals

The discrete element method (DEM) has been widely employed to model processes in different indust... more The discrete element method (DEM) has been widely employed to model processes in different industries, such as mining, agriculture, pharmaceuticals, and food. One of the main lines of research, and in which different authors propose several approaches, is the calibration of parameters. Bulk calibration (BCA) is a common approach used that does not necessarily represent the individual behavior of each particle. On the other hand, direct measurement (DMA) is another approach employed in some cases. This work presents a comparison between calibration of DEM model parameters with non-cohesive spherical and polyhedral particles using a combination of direct measurement and bulk calibration. BCA is employed to calibrate friction parameters and DMA to characterize shape of the particles and coefficient of restitution of the contact between particles. Experimental data from Draw Down Tests are used to calibrate the friction parameters. Numerical optimization of the parameters is conducted b...

Minerals Engineering, 2020

Minerals

The operation of a froth flotation column can be described by a nonlinear convection–diffusion pa... more The operation of a froth flotation column can be 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 predicts the bubble and (gangue) particle volume fractions as functions of height and time. The steady-state (time-independent) version of the model defines so-called operating charts that map conditions on the gas and pulp feed rates that allow for operation with a stationary froth layer. Operating charts for a suitably adapted version of the model are compared with experimental results obtained with a laboratory flotation column. Experiments were conducted with a two-phase liquid–bubble flow. The results indicate good agreement between the predicted and measured conditions for steady states. Numerical simulations for transient operation, in part for the addition of solid particles, are presented.

Minerals Engineering, 2020

Hydrocyclones are used for classification purposes in the mining and mineral processing industrie... more Hydrocyclones are used for classification purposes in the mining and mineral processing industries. According to their geometry and under certain operating conditions, hydrocyclones may present roping, which is a defective operation. Studies have related the roping phenomena to many variables such as hydrocyclone geometry and operating conditions. Some authors established a connection between the solids concentration of the feed and the discharge as one of the factors that generate roping. Other authors presented factors such as the apex and the vortex finder diameters, inlet pressure and the relationship between roping generation and the air core. This research aims to study the effect of inlet pressure and particle size distribution in the feed on roping in hydrocyclones. We develop a model using computational fluid dynamics (CFD) in order to study a 75-mm hydrocyclone operating with a variable flowrate and fed with two different materials. Each material is characterized by five granular phases interacting with each other and the model is validated by comparison with experimental data. The turbulence is treated using the Reynolds Stress Model (RSM) and the Eulerian Multiphase Model is used for the interactions between phases. The granular phases are described by the kinetic theory of granular flows (KTGF). The characteristics studied were: (i) air core and material distribution inside the hydrocyclone, (ii) underflow shape and spray angle, (iii) flow and solid concentrations, (iv) efficiency curve and separation size and (v) particle size distribution in the underflow and the cut sizes. According to the results, the particle size distribution of material in the feed has a direct impact on underflow behavior; when operating with coarser material the device tends to rope as the spray angle decreases. The same happens with an increase in the feed pressure. The roping condition generated by the coarse material directly affects the efficiency of the hydrocyclone, triggering an increase in separation size. The underflow particle size distribution tends to be coarser with an increase in the inlet pressure. When the inlet pressure decreases, the overflow particle distribution tends to be finer. 1.1. Experimental information Many experimental methods of analysis have been used to understand hydrocyclone performance, including Electrical Impedance Tomography (Gutiérrez et al., 2000), Laser Doppler Anemometry andvideo recordings to observe the flow inside the devices (Janse Van Vuuren et al., 2010). Most research has focused on the behavior of hydrocyclone efficiency curves (

Mining, Metallurgy & Exploration

Minerals

Shear-induced polymer-bridging flocculation is widely used in the solid–liquid separation process... more Shear-induced polymer-bridging flocculation is widely used in the solid–liquid separation process in cemented paste backfill, beneficial to water recycling and tailings management in metal mines. A flocculation kinetics model based on Population Balance Model (PBM) is proposed to model the polymer-bridging flocculation process of total tailings. The PBM leads to a system of ordinary differential equations describing the evolution of the size distribution, and incorporates an aggregation kernel and a breakage kernel. In the aggregation kernel, a collision frequency model describes the particle collision under the combined effects of Brownian motions, shear flow, and differential sedimentation. A semi-empirical collision efficiency model with three fitting parameters is applied. In the breakage kernel, a new breakage rate coefficient model with another three fitting parameters is introduced. Values of the six fitting parameters are determined by minimizing the difference between exper...

Powder Technology, 2021

Gravity thickening by deep cone thickener is popularly applied in cemented paste backfill, which ... more Gravity thickening by deep cone thickener is popularly applied in cemented paste backfill, which is essential for tailings management and green mining. To avoid rake bogging, high concentration and high flowability are required for thickened tailings slurry. These properties depend critically on the yield stress of the slurry. The yield stress, in turn, can be influenced by the flocculant dosage and the acidity (pH) that form the flocculation condition. Experiments have been performed to eventually quantify the dependence of yield stress on these two variables. The yield stress test of flocculated and thickened copper mineral tailings slurry, and the analysis of flocculant adsorption, were conducted at different pH values and flocculant dosages. It turns out that the amount of flocculant adsorbed on the tailings particles surface has a maximum with respect to pH but increases with the increasing flocculant dosage. In turn, the amount of flocculant adsorbed affects the yield stress, ...

a(s)ds; a(u) 0:This equation has been proposed as a model of aggregation by a series of authors ... more a(s)ds; a(u) 0:This equation has been proposed as a model of aggregation by a series of authors [1], [2], [3]under the assumption that a(u) = 0 at most at isolated points. We consider here the moregeneral assumption that a(u) = 0 on a bounded interval. Under the assumption that is asmooth function with a nite number of local extrema, through the use of a TV-stable schemewe prove the convergence of the approximate solution to the unique entropy solution of (1).Numerical examples illustrate our results.Keywords: Strongly degenerate parabolic equation, nonlocal ux, aggregation model, entropysoliution.Mathematics Subject Classi cations (2000): 35K65, 35Q92, 35R09, 65M06.

One-dimensional models to simulate secondary settling tanks (SST) with cylindrical geometry are w... more One-dimensional models to simulate secondary settling tanks (SST) with cylindrical geometry are widely used in wastewater treatment. One of these models is the Bürger-Diehl model developed in [3], the respective extention to the varying crosssectional area case was recently made in [1]. For the modelling, simulation and control of SST according to this model it is necessary to know the hindered-settling velocity function, which is considered a constitutive functions of the model. The traditional way to get this function is to measure the velocity of the declining sludge blanket in a vessel with constant cross-sectional area through experiments obtained from laboratory batch tests, however this method gives only one point on the flux curve. A newly developed method in [2] shows that in a vessel with varying cross-sectional area a large part of the flux function can be estimated from a single batch test, where the largest interval can be obtained with conical vessels. The identificati...

Comminution by gyratory crusher is the first stage in the size reduction operation in mineral pro... more Comminution by gyratory crusher is the first stage in the size reduction operation in mineral processing. In the copper industry, these machines are widely utilized, and their reliability has become a relevant aspect. To optimize the design and to improve the availability of gyratory crushers, it is necessary to calculate their power and torque accurately. The discrete element method (DEM) has been commonly used in several mining applications and is a powerful tool to predict the necessary power required in the operation of mining machines. In this paper, a DEM model was applied to a copper mining gyratory crusher to perform a comprehensive analysis of the loads in the mantle, the crushing torque, and crushing power. A novel polar representation of the radial forces is proposed that may help designers, engineers, and operators to recognize the distribution of force loads on the mantle in an easier and intuitive way. Simulations with different operational conditions are presented and...

Minerals

Froth flotation is a process in which hydrophobic particles attach to bubbles forming particle–bu... more Froth flotation is a process in which hydrophobic particles attach to bubbles forming particle–bubble aggregates, which are transported to the top section of the cell where they overflow to form the concentrate. Particles also reach the concentrate by entrainment, which is a non-selective process that leads to low concentrate grades. The objective of this work was to study and compare the degree of entrainment measured using three methods, in fresh and seawater, and using methyl isobutyl carbinol (MIBC) and DF-250 as frothers. The experimental results indicated that the degree of entrainment decreased in seawater. Besides, water recovery was lower in the experiments with seawater regardless of the frother that was used in the experiments, which correlated with the observed low degrees of entrainment. It is proposed that the reduction of entrainment and water recovery in seawater can be explained by a reduction of air recovery and/or more bubble coalescence in the froth. It is also p...

Chemical Engineering Science

J Chem Res S, 2004

... Publisher: Issue Date: 2004. ???metadata.dc.subject.productividad???: ARTICULOS INTERNACIONAL... more ... Publisher: Issue Date: 2004. ???metadata.dc.subject.productividad???: ARTICULOS INTERNACIONALES-1030759. ???metadata.dc.creator.projectrelation???: JOAQUIN ALBERTO CORTES GARRIDO. Description: Completo. URI: http://hdl.handle.net/10533/21284. ...

International Journal of Mineral Processing, 2015

Applied Mathematics and Computation, 2015