Discrete element modelling of the influence of lifters on power draw of tumbling mills

Crushing and grinding are the most energy intensive part of the mineral recovery process. A major part of rock size reduction occurs in tumbling mills. Empirical models for the power draw of tumbling mills do not consider the effect of lifters. Discrete element modelling was used to investigate the effect of lifter condition on the power draw of tumbling mill. Results obtained with PFC3D code show that lifter condition will have a significant influence on the power draw and on the mode of energy consumption in the mill. Relatively high lifters will consume less power than low lifters, under otherwise identical conditions. The fraction of the power that will be consumed as friction will increase as the height of the lifters decreases. This will result in less power being used for high intensity comminution caused by the impacts. The fraction of the power that will be used to overcome frictional resistance is determined by the material’s coefficient of friction. Based on the modelled results, it appears that the effective coefficient of friction for in situ mill is close to 0.1.     

Acoustic emissions simulation of tumbling mills using charge dynamics

Knowledge of the internal variables of a mill is of importance in design and performance optimization of the mill, notwithstanding the difficulty in measuring these variables within the harsh mill environment. To overcome this problem, the research has focused on measuring the internal parameters through non-invasive measurement methods such as the use of the vibration/acoustic signal obtained from the mill. Alternatively, virtual instruments, such as discrete element methods (DEM), are employed. Here, a methodology is developed to simulate on-the-shell acoustic signal emitted from tumbling mills using the information extracted from a DEM simulator. The transfer function which links the forces exerted on the internal surface of the mill and the acoustic signal measured on the outer surface is measured experimentally. Given this transfer function and the force distribution obtained from the DEM simulation, and assuming a linear time-invariant response, the on-the-shell acoustic of a laboratory scale ball mill has been simulated. Comparison of this simulated signal with the signal measured experimentally can be used as a criterion to judge the validity of the DEM simulations, and as a tool for enhancing our understanding of both DEM simulations and the use of acoustics within the context of mineral processing. The results derived from preliminary experiments on a laboratory scale mill shows satisfactory agreement between the actual measurement and the simulated acoustic signal.     

Studies of the effect of tracer activity on time-averaged positron emission particle tracking measurements on tumbling mills at PEPT Cape Town

The statistical uncertainties associated with time-averaged positron emission particle tracking (PEPT) measurements of the position, velocity and acceleration of a small tracer particle have been investigated. Experiments were undertaken using the ECAT ‘EXACT3D’ PET scanner recently installed at the facilities of PEPT Cape Town at iThemba LABS, South Africa. Small “button” sources of ⁶⁸Ga were attached to the outer shell of a small mill and PEPT data were recorded over several half-lives, for the cases of the mill being empty and entirely filled with steel balls. The effect of tracer activity on the statistical uncertainties in the positions, velocities and accelerations derived from the measurements was investigated, as a first step towards fully quantifying the uncertainties associated with tracking particles via PEPT in laboratory-scale tumbling mills.     

A mechanistic model for slurry transport in tumbling mills

We describe a modelling approach to slurry transport in dynamic beds. Volume and time averaging are combined to obtain a dynamic replacement for the static Ergun equation. Solutions of the resulting dynamic equation are exhibited for a simple charge-motion model, which serves as the prototype for a practical slurry transport model.     

Control of the mill charge behavior in dry tumbling mills

Powder filling of a dry mill has a large influence on grinding capacity and wear rate of grinding media and liners. In particular low powder filling levels can cause extensive wear rates. This paper discusses the influence of some operating parameters of the mill circuit on powder filling, when airflow through the mill is applied. An method of warning against low powder filling levels inside the mill is shown, a piezoelectric strain transducer installed on the mill shell accomplishing this task.     

Towards a mechanistic model for slurry transport in tumbling mills

A new modelling approach to slurry transport in dynamic beds based upon combining space and time-averaged Navier–Stokes equations with a new type of cell model is described. The resulting Ergun-like equation is used to correlate pressure drop with time-averaged distributions of the porosity, superficial fluid velocity and solids velocity for data derived from positron-emission-particle-tracking (PEPT) experiments in a scaled industrial tumbling mill fitted with lifter bars, pulp lifters and a discharge grate and run with particles and re-circulating slurry.     

An experimental investigation of the effects of operating parameters on the wear of lifters in tumbling mills

Lifters are usually used with mill liners to extend their life and to enhance the grinding and crushing efficiency. Although the lifters are durable wear parts but they will gradually worn and consequently their dimensions change during the course of operation. These changes in dimensions have a significant influence on the overall economic performance of the mills. Therefore, it is useful to know the relationship between the mill operation and the lifter profile, and the influence of lifter wear on the change in lifter profile. In this work, a laboratory mill which is capable of producing the required impact and abrasion grinding was operated both wet and dry. Many factors were varied such as: velocity, charge, ore size and different material for the lifters. Also the wear rate on the top and face of lifters are compared in the different conditions. It is found that the mill charge and the mill speed significantly affect the wear rate. Also, the results showed how size distribution affects the wear rate. The results can be interpreted in terms of the wear process in industrial scale mills over different operating conditions. The experimental results provide the possibility of including the lifter wear in optimising mill performance.     

Experimental analysis of charge dynamics in tumbling mills by vibration signature technique

Up until now, real time identification of the dynamics of the charge in a tumbling mill has not been accomplished. This paper examines the possibility of correlating the vibration signature of tumbling mills to characterize the motion of the charge and the state of grinding. Vibration signals were picked up using accelerometers mounted directly on the mill shaft of a 90-cm diameter mill. The time domain signals were transformed to frequency domain by using fast Fourier transform (FFT). The Fourier spectra in the frequency domain were methodically interpreted and correlated to establish the prevailing mode of the charge motion under any operating condition. The grinding behavior under dry as well as wet grinding conditions were analyzed by following the variations in the vibration signature as a function of speed of the mill, volumetric filling, powder loading, and time of grinding.Experimental results clearly show that the dominant peak in the FFT spectra is quite sensitive to the variations in any mill operating parameter. This feature has been employed to detect undesirable operating conditions such as surging, mill over-load, etc. Finally, it is demonstrated that by proper interpretation of the vibration signature of the mill, it is possible to predict the charge dynamics and establish the state of grinding.     

Spreadsheet-based modeling of liner wear impact on charge motion in tumbling mills

Grinding remains the major constituent of the total cost of processing minerals in most applications. Charge motion is one of the key parameters affecting grinding efficiency and mill power draw. Although there have been numerous investigations on the effect of liner design on charge motion, the effect of charge profile due to liner wear during mill operation along the mill length has not received much attention. In this research, Powell’s analytical approach to calculate the charge trajectory with respect to the liner profile was used to develop a software based on Microsoft Excel© . As a case study, the liner wear profile of the Sarcheshmeh copper complex SAG mill was used to model the liner wear rate and calculate the changes of lifter face angle and lifter height during mill operation. Results were then used to determine charge motion in the SAG mill at any given operation time. The results indicated that after 4000 h of operation the lifters face angle increased from 14° to 47.1° and the height of lifters decreased from 15.2 to 5.8 cm. Modeling charge motion in the mill after 3000 h of operation showed 34° difference between the maximum and minimum of angles of impact along the mill length due to the nonuniform wear profile. It was also found that the variation in the pattern of the charge motion depends on the mill working hours and the distance of the desired point from the feed end. It was determined that the ratio of spacing to the height of lifters (S/H) plays an important role in the grinding efficiency and throughput. After 4000 h of operation, S/H ratio of the Sarcheshmeh SAG mill increased from 1.7 to 4.6.     

The application of a simplified approach to modelling tumbling mills,stirred media mills and HPGR’s

Most modern population balance models for comminution invoke the concept of a specific breakage rate function and a breakage distribution function to describe breakage kinetics. One of the difficulties of this approach is that these functions are very difficult to measure directly. Consequently, it is usual to assume that these functions can be represented by simple equations with parameters that can easily be estimated from test data using back-calculation techniques. However, these estimates can be very sensitive to small measurement errors and are usually subject to very large variances. This paper presents a simplified approach to modelling comminution processes that invoke the concept of an energy-based cumulative breakage rate function to describe breakage kinetics. This function can be estimated directly from plant data and is well-suited to multi-component modelling of individual rock types and mineral species. Examples of the application of this simplified modelling approach are described for the treatment of platinum ores using ball mills, AG/SAG mills, HPGR’s and stirred media mills.     

Validation of a model for physical interactions between pulp,charge and mill structure in tumbling mills

Modelling the pulp fluid and its simultaneous interactions with both the charge and the mill structure is an interesting challenge. The interactions have previously been modelled for dry grinding with a combination of discrete element method (DEM), smoothed particle hydrodynamics (SPH) and the finite element method (FEM), where the DEM particles or SPH particles represent the grinding balls and FEM is used to model the mill structure. In this work, the previous model is extended to include fluids with SPH. Wet milling with water and a magnetite pulp, for graded and mono-size charges are numerically modelled and validated. The internal working of the charge and the physical interaction between the charge and the mill structure is studied. The combined SPH–DEM–FEM model presented here can predict the classical DEM results, but can also predict responses from the mill structure, as well as the pulp liquid flow and pressure. Validation is conducted by comparing numerical results with experimental measurements from grinding in an instrumented small-scale batch ball mill equipped with an accurate torque metre. The simulated charge movement is also compared with high speed video of the charge movement for a number of cases. Numerical results are in good agreement with experimental measurements.     

Effects of slurry filling and mill speed on the net power draw of a tumbling ball mill

The pool of slurry is known to lower the power drawn to the mill. An attempt to ascertain this observation by relating load orientation to mill power for a range of speeds and slurry fillings was undertaken.To this end, a Platinum ore (−850 μm) was used to prepare a slurry at 65% solids concentration by mass. The Wits pilot mill (552 × 400 mm), initially loaded with 10 mm balls at 20% volumetric filling, was run at 5 different speeds between 65% and 85% of critical. The net power draw and media charge position were measured. After this, the slurried ore was gradually added to the media charge for slurry filling U between 0 and 3. A proximity probe and a conductivity sensor mounted on the mill shell provided a means of measuring both the position of the media charge and that of slurry. The data collected for the load behaviour and net power draw was later analysed.It was found that Morrell’s model could not fully explain the effect of slurry volume on net power draw especially for an under-filled media charge (i.e., for U < 1). The size of lifters and grinding balls used could be the reason for this. That is why a piece-wise function was curve-fitted to the power data to help make sense of the inconsistencies observed.     

Characterisation of superficial breakage using multi-size pilot mills

Low energy surface breakage has a high frequency of occurrence and thus plays a significant role in grinding processes. Yet this superficial breakage is poorly understood, measured and modelled – forming the focus of this work.Pilot mills of 0.8–1.8 m diameter, designed to provide a predominantly surface breakage environment with efficient removal of the resultant progeny, are utilised to characterise superficial breakage. A new rate, that of superficial breakage (1/(kW h/m²)), is introduced which measures fractional superficial breakage rate per energy provided to the surface of the material. This methodology is proposed as being suitable for understanding and characterising the surface breakage behaviour of ores.Tests were conducted on two ores with different hardness. Superficial breakage rates varied from 2 to 16 (1/(kW h/m²)) for the different ores and mill sizes, indicating a good sensitivity to ore type and the need to understand the applied stress – related to mill size. The results show that a single ‘surface breakage rate for use in mill modelling is incorrect as the rate of superficial breakage is dependent on the size of the mill and therefore the inter-particle stressing conditions.     

Conditional draw control system in block-cave production scheduling using mathematical programming

Block caving is a complex and large-scale mining method. The application of block caving is for low-grade, caveable and massive ore-bodies. Among the underground mining methods available, caving methods are favoured because of their low cost and high level of production. Generating a production schedule that will provide optimal operating strategies without geotechnical constraints is not practical in block caving. Establishing relationships among draw columns to consider depletion rates of other draw columns is complex but essential to provide a reasonable solution for real block-caving mines. This paper presents a mixed-integer linear programming (MILP) model to optimise the extraction sequence of drawpoints over multiple time horizons of block-cave mines with respect to the draw control systems. Four resolutions are formulated in this paper to guarantee practical solutions with respect to draw control managing in mined areas according to the draw rate and conditional draw rate constraints. Application and comparison of the four resolutions for production scheduling based on the draw control systems are presented using 325 drawpoints over 15 periods. The performance was analysed based on maximising the net present value (NPV) at a discount rate of 12%. The maximum obtained NPV from of the proposed MILP models is $451.07M.     

Modelling the influence on power draw of the slurry phase in Autogenous (AG), Semi-autogenous (SAG) and ball mills

The slurry level in AG/SAG and ball mills has an influence on their power draw, which in some instances can be profound. This is particularly the case with so-called slurry pooling in AG/SAG mills which can result in significant lowering of power draw. From a predictive viewpoint there are currently no published models that explicitly describe the influence of slurry level on power draw and the relationship between slurry level, slurry flow and pulp lifter design. Citic SMCC Process Technology Pty Ltd has developed such a model and in this paper its structure is described. Examples are given of both AG/SAG and ball mills of how the model responds to changes in slurry level. These examples are used to explain the observed phenomena of slurry pooling and the decrease in power draw observed in ball mills after start-up when feed is first introduced into the mill.     

Variables affecting the fine grinding of minerals using stirred mills

Base metal resources are becoming more fine-grained and refractory and minerals separation processes require these ores to be milled to increasingly finer sizes. To cope with very fine grinding to below a P₈₀ of approximately 15 μm stirred milling technology has been adopted from other industries. Neither this technology, nor the basic concepts of fine grinding, are well understood by the minerals processing industry. Laboratory studies were therefore carried out in order to investigate fine milling using different types of stirred mills. The variables analysed were stirrer speed, grinding media type and size, slurry solids content as well as the feed and product size. The results of the testwork have shown that all of these variables affect the grinding efficiency. The ratio of media size to material size was found to be of particular significance. The results were also analysed using the stress intensity approach and the optimum stress intensity ranges for the most efficient grinding were determined. Application of the results for process optimisation in the industrial size units is also discussed in this paper.     

Comparison of energy efficiency between ball mills and stirred mills in coarse grinding

Stirred mills are primarily used for fine and ultra-fine grinding. They dominate these grinding applications because greater stress intensity can be delivered in stirred mills and they can achieve better energy efficiency than ball mills in fine and ultra-fine grinding. Investigations were conducted on whether the greater performance of stirred mills over ball mills in fine grinding can be extended to coarse grinding applications. Four different laboratory ball mills and stirred mills have been tested to grind seven ore samples with feed sizes ranging from 3.35 mm to 150 μm. A case study on full scale operations of a 2.6 MW IsaMill replacing the existing 4 MW regrind ball mill at Kumtor Gold Mine in Kyrgyzstan is also included. This paper summarizes the major findings from these investigations.     

Measurement of shear rates in a laboratory tumbling mill

A methodology for characterising shear rate profiles in tumbling mills based on in situ trajectory fields from Positron Emission Particle Tracking (PEPT) experiments is presented. Experiments were carried out in a laboratory scale mill fitted with lifter bars, pulp lifters and a discharge grate, and run with radioactively labelled particles within re-circulating slurry environments. Using time-averaged velocity distributions of small PEPT tracers, a model for tangential velocity profiles along radial scan-lines is proposed from which the shear rates are derived.