The prediction of the outermost trajectory of media in a grinding mill for lifter bars with rounded or worn profiles

This thesis presents the analysis of the path of a ball on the inside of a ball mill for lifter bars with rounded or worn profiles. The model predicts the response of a single ball with particular reference to the balls trajectory after departure from the lifter bar and incorporates the effect of friction, mill rotational speed, lifter height as well as different lifter bar profiles. The out of plane travel of the particles are ignored and hence the system is reduced to a two dimensional problem. A set of experiments were performed on a model perspex mill in order to obtain data by which the theory could be compared. The lifter bar is analysed using a parabolic expression which allows the shape to be changed to model various stages oflifter wear. Two possible formulations are investigated in determining the motion of the particle on the lifter bar. The first formulation assumes the ball to roll on the lifter bar until a limiting friction is reached after which the ball will slide along the lifter. The second formulation considers the ball to have a pure sliding motion on the lifter

Optimization and performance of grinding circuits: the case of Buzwagi Gold Mine (BGM)

Buzwagi Gold Mine (BGM) is operated by Acacia Mining and located in the Lake Victoria Goldfields of central Tanzania. The mine commenced its operation since April 2009 and treats a sulphide copper-gold ore to produce gold in form of doré bars and a concentrate containing gold, copper and silver. The BGM comminution circuit includes a primary crushing stage with a gyratory crusher and a two grinding circuits using a Semi-Autogenous Grinding (SAG) mill and a ball mill. The SAG mill circuit also includes a single-deck screen and a cone crusher while the ball mill circuit utilizes hydrocyclones. Currently, the grinding circuits are inefficient in achieving the aspired product fineness of xP,80 = 125 μm even at low to normal throughputs (450-600 t/h). An evaluation and optimization study of the circuit performance was conducted to improve the product fineness through circuit surveys, experimental lab work and simulations. In three full scale sampling campaigns, size distributions and solids contents of the samples were determined at selected points in the circuit. Further, several types of breakage tests were conducted; standard Bond tests to determine ore grindability and work indices, batch grinding tests to determine parameters for breakage and selection functions , and standard ball mill tests for mineral liberation characterization by an automated mineral liberation analyzer (MLA).The tests were conducted in a size range from 0.063 to 2 mm. Then, mass balance of the circuit was calculated and the models for mills, screens and hydrocyclones were employed in MODSIM (version 3.6.24). Firstly, simulations were conducted to optimize the existing plant. Several options were evaluated such as reduction of SAG screen aperture, adjustment of cyclone feed solids content and reduction of vortex finder and apex diameters. Moreover, simulations were also evaluated for a possible modification of the existing circuit and include; partial splitting of the cyclone underflow back to SAG mill, introduction of a second classification stage as well as introduction of a second ball mill. The evaluation of breakage tests and survey data revealed the following; the Bond work index obtained for the current ore ranges between 17.20 - 18.70 kWh/t compared to 14.50 - 16.50 kWh/t which was estimated during plant design.This indicates a change in hardness of the ore during the last 7 years. Harder ore means more energy requirement for an efficient operation, the consequence of which is increased costs. Thus, a periodic review of the ore hardness for ongoing mining operation is recommended. This will help in establishing better blends as well as prediction of appropriate tonnages for the existing ore types, so as to be efficiently treated by the available plant design. The work indices of the ore blends treated during survey were correlated with their quartz content and showed a strong linear relationship (R2= 0.95). Therefore, the work index for the BGM ore could be predicted based on known quartz content of the material. Further, the model could be used as a control tool for monitoring hardness variation of the SAG mill feed. The mineral liberation studies indicated that the valuable phase (pyrite-pyrrhotite) could be liberated at relatively coarser particle sizes (200-400 µm). This implies that, there could be no problem with the efficiency of the gravity circuit for the BGM operation, where the gold contained in pyrite-pyrrhotite could be easily concentrated. However, the efficiency of flotation and cyanidation processes will still require finer feed. In overall, the liberation characteristics of the ore blends treated during survey showed minor differences. The Bond efficiency factors of 48-61 % were obtained for the BGM grinding circuit, indicating an inefficient operation. This suggests that the operation could achieve targets by lowering the throughput. Further, the SAG mill circuit was characterized by fluctuating feed size of between xF,80 =102 to 185 mm. A need for control of the feed size as well as blending ratios was recommended for an efficient operation in terms of throughput and final product size. This could be achieved through closer monitoring of the primary crusher performance and proper control of the ratios for the SAG mill feeders drawing the ore from the stockpile. The ball mill grinding efficiency was poor and could be indicated by the fraction 400 µm in the mill discharge. This was deemed due to poor hydrocyclone performance which was characterized by higher feed solids content, coarser overflow xP,80: >200 µm as well as cut sizes, xT : > 200 µm. An improvement of product fineness up to 327 µm could be achieved during the simulation and optimization of the existing design. This could be achieved by modification of the operating conditions such as reduction of SAG screen aperture from 12 mm to 10 mm, reduction of vortex finder from 280 mm to 270.3 mm, reduction of apex diameter from 150 mm to 145.6 mm as well as adjustment of the cyclone feed solids content from 66.7 to 67.1 %. Based on this result, it was concluded that the current equipment could not achieve the target product quality (i.e. xP,80 = 125 µm ). Further simulations based on flowsheet modification options showed that a second ball mill (series configuration) can help to achieve the desired product fineness as well as an increase of throughput from 618 t/h to 780 t/h. Although the circulating load increases to approximately 500 % in this configuration, it is outweighed by the benefits. Importantly, this option is cost intensive and hence may be considered as a long term solution and especially after cost-benefit analysis. Finally, the results based on optimization of the existing design is recommended as short term solution for improvement of the BGM operation. Although the fineness achieved is still low (i.e. xP,80 = 327 µm) compared to the target (i.e. xP,80 = 125 µm), this gives additional advantage in the sense that, also better hydrocyclone performance is achieved in terms of overflow product (xP,80 = 105 µm vs. > 240 µm) , cut size (xT =133.1 µm vs. > 220 µm) and circulating load (CL =350 %). The improved overflow fineness will contribute to improved efficiency for the downstream processes

Using positron emission particle tracking (PEPT) to investigate the motion of granular media in a laboratory-scale tumbling mill

Includes bibliographical references.Positron emission particle tracking is a Lagrangian, single particle tracking technique in which the trajectory of a representative tracer particle is triangulated from the decay products of the positron-emitting radioisotope with which it is labelled. Although the trajectories of a tracer particle moving in a bulk of similar particles can be of interest, it is often more informative to employ the ergodic assumption and to thus convert trajectory data in the Lagrangian reference frame of the tracer particle into a fixed Eulerian reference frame. This has, in the past, been done by dividing 3D space into voxels and assigning a location probability density to each voxel based on the number of times that triangulated tracer particle locations fall into it- a process called simple binning. A major outcome of my work has been to develop an alternative probability density based on the cumulative time spent by the tracer particle in a given voxel. This method is called residence time binning, and the resultant probability distribution- which I argue is proportional to, among other things, the mass and solidicity distributions of the tracer particle - the residence time distribution (RTD). In this work I propose, implement and test the residence time binning method, and show that it significantly outperforms the simple binning method in all situations. A second thrust of my work has been to develop a suite of general analysis routines for positron emission particle tracking (PEPT) data, based on the RTD. This suite contains routines for the triangulation, optimisation and pre-processing of PEPT data, as well as for obtaining residence time probability and time-averaged kinematic distributions in 3D space, and for aggregating and visualising the results. I have also extended this general set of routines for the special case of cylindrical symmetry through the addition of routines for the further pre-processing of RTDs, as well as for the calculation of angular measures about an arbitrary axis in space. Finally, I further extended this set of routines for application to tumbling mills. My tumbling mill analysis includes the identification of charge features and regions, and the isolation of charge in each region so-defined for further analysis. These features, particularly the shape of the bulk free and equilibrium surfaces, the angular position of the centre of circulation (CoC) of the charge, and the position of its impact toe allow me to characterise the behaviour of the charge under a range of conditions. This characterisation, together with the shear rate distributions and power draughts that I also calculate, allow me to speak meaningfully about the evolution of grinding regions in tumbling mills- information that could be used to construct charge motion and grinding models to inform the use of tumbling mills in industry. In this work, I apply these analysis routines to a small subset of the experiments performed by the UCT Centre for Minerals Research (CMR) on laboratory-scale tumbling mills, and in so-doing elucidate the behaviour of charge in its different regions- and the evolution of such behaviour with mill operating parameters- and discuss the implications of these to grinding efficacy in tumbling mills

Doctor of Philosophy

dissertationThe current study is aimed at improving the performance of autogenous grinding and semiautogenous grinding mills. In particular, the material transport issue is the focus since the efficiency of mill discharge via grate, pulp lifter channels, and discharge trunnion determines the mill throughput. The objective of this study is to develop a computational tool, and a simulation model which is built on fundamental physics of the process. Mainly, the simulation model is expected to give reasonably accurate predictions of free surface profiles inside the pulp lifter channels and volumetric flow rate out of the pulp lifter channels. Employing the computational fluid dynamics as the central component, the study puts forward the mathematical modeling of the pulp flow in the pulp lifter channels along with experimental validation of simulation results. First, past modeling studies of grinding mills are reviewed, with the focus on the material transport. Then the experimental methodology is presented. The explanations of flow dynamics are given from a theoretical point of view. Primarily, the free surface profiles and the dynamic discharge profiles are captured experimentally. The proposed model that includes rotation of the pulp lifter channel is validated by comparing the predictions of the model to experimental results. Having proved the pulp flow dynamics by the experimental study, the computational fluid dynamics methodology is employed for the prediction of plant scale mill data. The free surface profiles inside the mill are well captured by the CFD methodology, giving insight into understanding the pulp flow. The volumetric flow rate predictions conform to the experimental data as well as the plant scale mill survey data. Modeling of pulp flow in the pulp lifter channel by computational fluid dynamics is beneficial in the sense that it yields comprehensive information about the specifics of the operation, making it possible to investigate in detail such phenomena as flow back and carry over flow in semiautogenous grinding mill pulp lifter channels

Evaluating the influence of lifter face angle on the trajectory of particles in a tumbling mill using PEPT

Includes bibliographical references.The work performed in this thesis was aimed at evaluating the influence of lifter face angle on the charge kinematics for a laboratory scale mill. The study involved tracking a single particle representing the ensemble using the Positron Emission Particle Tracking (PEPT) to obtain the location of the particle with time. The particle was radiated with a radionuclide; ⁶⁸8Ga, which has a half-life of 68 minutes. The objectives of the study involved tests with different lifter face angles at different mill speeds and volumetric mill filling. After performing the tests the data was analysed to obtain probability density distributions for each test conditions from key charge descriptors. Charge descriptors such as the Centre of Circulation (CoC), shoulder angle, toe angle, the free surface and also kinematic information such as the velocity profile along a carefully chosen radial line from the centre of the mill that passes through the CoC were obtained. The time averaged velocity data was used when assessing the influence of the lifter face angle on the velocity profile. The results showed notable effects of lifter face angle on charge characteristics. No real definitive trend was observed for the CoC as the lifter face angle was altered at all mill speed and filling conditions. However, the CoC showed an outward shift toward the mill shell with an increase in mill speed but an inward shift toward the mill centre with increase in charge filling degrees. Mill speed is expected to cause a load expansion as the charge approaches centrifugation