M.H. Moys

Residence time distributions and mass transport in the froth phase of the flotation process

Abstract A comprehensive description of some aspects of the physical behaviour of the froth phase of the flotation process has been provided by two mathematical models. Both are formulated in terms of familiar design and control variables (e.g. cell dimensions, froth depth, gas rate) and the froth stability, α, defined as the ratio between the volume flowrate of air in the concentrate stream and the volume flowrate of air in bubbles crossing the froth/slurry interface which have a finite probability of entering the concentrate stream. The first model provides a description of the two-dimensional streamline behaviour of the froth as it moves towards the concentrate weir. The second model is a two-stage approximation of this behaviour and provides a simple and tractable model of froth behaviour which can easily be incorporated in existing models of the flotation process. This model involves two more parameters: the residence time ratio δ, which provides a means for estimating the minimum froth phase residence time (it can be given the value 0.5 unless it is possible and practical to measure it more accurately); and the froth removal efficiency, e, which is a measure of the efficiency with which the available froth chamber volume is used. RTD measurements using two-phase froths have shown that these models constitute a good description of physical reality, and that e and α can be obtained as functions of control variables such as gas rate, froth height and frother concentration. Insights obtained from this work have led to the development of a method for froth removal which produces an unambiguous improvement in the performance of the flotation cell. The second model can be used to investigate the effect of control actions and scale-up on cell performance.

A discrete element method investigation of the charge motion and power draw of an experimental two-dimensional mill

Abstract The Discrete Element Method (DEM) has the potential to be a powerful tool for the design and optimisation of mills. However, for DEM to gain acceptance within the minerals processing industry, it is necessary to show that the results obtained from a DEM simulation are valid, and that this validity extends over a wide range of mill operating conditions. Real grinding mills are complex multi-phase devices with a range of particle dynamics and material processes that depend on the exact operating point of the mill. Mill conditions will generally vary statistically over time. It is therefore difficult in this type of environment to systematically verify DEM, where some degree of precision in the mill operation is required. With these considerations in mind a programme of both experimental and DEM simulation work was developed. A “two-dimensional” laboratory mill was built in such a way that precise power measurement and monitoring of charge motion was possible. DEM simulation runs were matched to the experimental conditions. In this account of the work, particular attention is given to the effect of mill speed on power and charge motion, and also of particle behaviour at mill speeds above the critical. DEM predicts the power draft and charge motion of the mill well at speeds below the critical speed. At super-critical speeds, the centrifuging of material in the load was predicted, but power predictions were not as accurate.

Measurement of impact behaviour between balls and walls in grinding mills

Experimental results of impacts of balls on walls mimicking the collision events in grinding mills are reported. The materials for balls include steel, malachite, glass as well as a billiard ball and a cricket ball. The walls used for the impact target are steel liner, rubber liner, and slate plate. Through the measuring of translational and rotational velocities, we present the impact properties as coefficient of normal restitution, coefficient of tangential restitution and impulse ratio (or dynamic coefficient of friction). The results obtained can be used to determine explicitly the mode of behaviours (roll or slide) of the contact point during impact. They can also be used to determine parameters for discrete element method simulation.

Measurement of the radial and tangential forces exerted by the load on a liner in a ball mill, as a function of load volume and mill speed

Abstract A laboratory grinding mill of diameter 0.36 m was modified to allow the measurement of the radial and tangential forces exerted by the load in the mill on lifter bars of varying profiles. Four load beams were used to achieve these measurements. Electrical conductivity measurements were used to determine when the load was “locked in” to the liners. The mill was instrumented to allow accurate measurement of the torque drawn by the mill. The above measurements were obtained for mill speeds varying between 10% and 135% of critical speed, load volume varying between 0% and 37% of mill volume, for seven different liner profiles. Steel balls of diameter 3, 4 and 5 mm were used as media (equal proportions of each); no ore was used. The measurements provide detailed and quantitative information about the forces exerted on the liner and about the behaviour of the load in the mill. Analysis of these data should provide insights relevent to the optimisation of mill performance with reference to liner and media wear and power consumption, i.e. the major factors determining operating costs in rotary mills.

The effect of grate design on the behaviour of grate-discharge grinding mills

Abstract A model for the effect of flowrate and viscosity of slurry on the hold-up of slurry in a grate-discharge grinding mill has been developed. Given detailed specifications of the grate design (such as the area in the grate within which the holes are situated, the number of holes per m 2 and the hole size) and the flowrate and viscosity of the slurry flowing through the mill, the model provides estimates of the volume of slurry held up in the mill and the distribution of this slurry down the length of the mill. The model has been assessed using data obtained from milling tests performed on a 2.5-kW pilot mill in which grate design, slurry flowrate and slurry viscosity were varied. It was shown that only three parameters need to be determined by regression on the experimental data to ensure that the model is able to predict the holdup in the mill to within 8%. The application of this model to grate design and circuit optimisation is briefly discussed. The grinding rate G (t/h of new −75 μm material) and power consumption E (kWh/t of new −75 μm material) were also measured in the above-mentioned tests. Using multilinear regression it was shown that G was not affected by grate design in the region of operation covered by the experiments, while E was only a weak function of grate design.

Progress in measuring and modelling load behaviour in pilot and industrial mills

Abstract The need for an accurate and comprehensive understanding of load behaviour in industrial mills is outlined, and the implications of the availability of techniques for measuring load behaviour in these mills for both design and control is explored. Some research performed on a pilot mill used to investigate the effect of grid liners on autogenous milling is described. Considerable slip between liners and load occurred, with the result that a simple torque model (taking into account the orientation of the load and the slurry pool as measured by conductivity probes passing through the mill shell) was adequate for describing mill power at high mill speeds. The different behaviour of overflow and discharge mills as affected by slurry and load volume was explored. Some work involving the measurement of the axially distributed behaviour of the load in an industrial mill is then described. Liner movement, load orientation (measured with conductivity probes) and load temperature were measured as a function of axial position. The load orientation was found (surprisingly) to be almost independent of axial position but was a strong function of load volume. The axial temperature profile correlated in a logical fashion with other operating conditions. The relevance of these measurements for mill control is explored.

The use of the discrete element method and fracture mechanics to improve grinding rate prediction

Abstract The Discrete Element Method (DEM) is a numerical technique that can simulate the interaction of discrete particles in dynamic environments such as fluidised beds, jigs, flow in bins, screens and mills. This technique has great application potential in comminution modelling at micro-process level. The DEM is being used to determine the grinding rate of ore particles in an Autogenous mill. The frequency of the contact events and the associated energy dissipations derived from the simulation are used to determine the particle failure rate. The probability of particle failure also depends on the inherent fracture properties of a material; hence fracture tests were conducted on an ore sample using a drop-weight impact test machine to obtain a probability fracture model. A second model that uses energy dissipation spectra from the DEM and probability fracture model calculations has been proposed. Though the model tends to over-predict breakage generally, there are indications that the model is responsive to changes in the load behaviour.

Assessment of discrete element method for one ball bouncing in a grinding mill

Abstract The Discrete Element Method (DEM) has been used to simulate tumbling, vibration, centrifugal, and Hicom Nutating mills in minerally processing research. Information about mills such as power draw, torque, load behavior, velocity, impact force and energy can be produced by DEM simulation. It is a promising and potentially powerful vehicle for the design and optimization of mills. The validation of DEM simulation results has been carried out to a limited extent. This paper introduces a specially designed two-dimensional mill which is the prototype producing what the DEM simulates. The entire trajectories of a single ball at different mill speeds were recorded and the velocities before and after its impact with the mill shell were calculated. By comparing with the simulated trajectories and velocities, it is confirmed that the coefficient of friction of ball–wall, μbw, determines the toe and shoulder positions of the charge and the coefficient of restitution of ball–wall, ebw, determines the bouncing velocity after impact. However, the simulation parameters (μbw, ebw) for the best fit to the experimental data are not the same as these with which the mill run stably during simulation. A lot of minor collisions were observed in the simulations, which were not found in previous simulations and experiments. The ability of DEM to fairly accurately model single-ball behavior is established.

Load behavior and mill power

Abstract Load orientation is conventionally described by using shoulder and toe positions and a chord connecting the shoulder and toe position with its slope equivalent to the angle of repose of mill load. This model suffers a marked discrepancy with the true load orientation at low ball filling or high speed of rotation. One reason for this discrepancy is that the load in a mill will dilate and change shape substantially at high speed. It means that the distribution of grinding elements in the mill chamber does not match the above description at all. So some torque-arm power models based on load behavior failed to predict power draw with a satisfactory accuracy at high speed. In this paper, experimental position density plots (PDPs) are used to describe load behavior in a tumbling mill. A PDP is a digital, visual and statistical representation of the charge distribution in a mill. It is constructed by superimposing a number of independent digitized images of a mill load at steady state. Not only the parameters about load behavior, such as dynamic angle of repose, shoulder angle, and toe angle, are determined from PDP, power drawn by the entire load and en masse load can be calculated as well by use of the torque-arm model directly.

A technique to measure velocities of a ball moving in a tumbling mill and its applications

A technique has been developed to film the entire trace of a ball tumbling in a rotary two-dimensional (2D) mill. With careful calibration, the positions of the ball before and after impact with the mill shell were precisely determined with an image analyzer. Because the image formation process was accurately timed using a digital strobe, the instantaneous speeds of the ball along its trajectory can also be calculated. This makes it possible to (1) investigate the end effect in the experimental two-dimensional mill; (2) evaluate the energy loss during impacts; (3) determine dynamic coefficient of restitution that is an essential parameter in Discrete Element Method (DEM) simulation. Furthermore, this technique permits the charge motion to be analyzed quantitatively in great detail hereby providing precise calibration of the DEM.