Yu P, Xie W, Liu LX, Powell M (2014) Development of an Integrated Mill Model Structure for Tumbling Mills, Proceedings of the XXVII International Mineral Processing Congress ? IMPC 2014 Onemine.org
In order to develop a common mathematical and simulation platform for tumbling mills, a review of existing mechanistic models was made identifying the key aspects of grinding and slurry transport which are common to all tumbling mills. A mill model structure has been developed for all types of tumbling mills based on the population balance framework by incorporating breakage characteristics, slurry and solids transport, product classification and discharge, and energy consumption. A size-dependant breakage model developed by the JKMRC is applied. Transport is separated from breakage events and treated as a main sub-model in the new model structure. The model structure is based on dynamic time-stepping technique to enable dynamic simulation capability for non-steady-state simulation and control modelling. It is envisaged that the new model will cover a full range of milling conditions. It should enable a smooth transition between different mill types, such as from AG (Autogenous Grinding) to SAG to ball mill. The dynamic mill model structure developed here is the first step towards mechanistic modelling of grinding mills and provides great potential for the optimization of the comminution process
Liu LX, Zhou L, Robinson DJ, Addai-Mensah J (2013) A nuclei size distribution model including nuclei breakage, Chemical Engineering Science 86 pp. 19-24 Elsevier
In this work, a nucleation model that includes nuclei breakage/fragmentation is proposed. The model is based on the nucleation model of Hapgood and the Stokes deformation number calculated from the granule dynamic yield strength from the previously reported granule breakage work. It is proposed that breakage or fragmentation of primary nuclei from binder spray will occur if the Stokes deformation number exceeds a certain critical number. In the case where breakage occurs the model for secondary nuclei size distribution is proposed. To validate the model, the characteristics of the primary nuclei formed from nickel laterite ores with diluted sulphuric solutions as a binder were investigated. The nuclei were produced by dropping the binder solution onto a stationary powder bed. The mechanical integrity of the primary nuclei formed, the relationship between the nuclei diameter and binder drop diameter were studied. The Stokes deformation numbers for nickel laterite powders with different particle size in a lab scale drum granulator were calculated and the nuclei size distributions with different nickel laterite feed powders are predicted.
Liu LX, Palaniandy S, Powell MS (2014) A review of technical gaps and challenges in modelling fine grinding, Proceedings of Comminution '14 Minerals Engineering International
Xu D, Liu LX, Quast K, Addai-Mensah J, Robinson DJ (2013) Effect of Nickel laterite agglomerate properties on their leaching performance, Advanced Powder Technology 24 (4) pp. 750-756 Elsevier
Heap leaching is a widely used extraction method for low-grade minerals including nickel and cobalt. Agglomeration of fine mineral particles as a precursor to heap leaching is an important means of enhancing leaching rates and metal recoveries. Single pellet leaching behaviour of three nickel laterite ores, namely siliceous goethitic (SG), goethitic (G) and saprolitic (SAP) was investigated to assess the effect of pellet properties (binder type, binder content, porosity and dryness) on its stability, initial leaching rate and maximum Ni recovery. The column leaching performance of agglomerates of the same ores was also investigated. Both single pellet and column leaching tests showed that the ore mineralogy played a major role in the Ni extraction rate, with G-type of ore the lowest. The Ni extraction rate was also found to be directly related to the pellet/agglomerate dryness and the highest rate was obtained at an intermediate degree of dryness due to the better wetting and diffusion of acidic lixiviant into the pores in between the particles. However, no significant effect of drying on the stability of the agglomerates (measured by agglomerate slump in the column) was found in column leaching. For G type of ore, mixing it with high clay ores during agglomeration is recommended to enhance its robustness during leaching process.
Liu LX, Saeidi F, Powell MS (2014) Breakage characterisation of multicomponent ore, Proceedings of Comminution '14 Minerals Engineering International
The breakage characteristics of a two-component ore in a confined bed was studied in this work in order to predict the breakage behaviour of a multi-component ore from the properties of individual components. Bed compression tests with each single component and blended components at different bulk volumetric ratios were carried out at different volume based specific energies and the bed particle size distributions of each component in the mixtures were measured (through magnetic separation). The experimental results show that the breakage product size measured by t10 ? the cumulative mass percentage of particles less than 1/10th of the feed size, is linearly proportional to the relative bed porosity reduction, for both single component and multi-component ore. There is a minimum bed porosity reduction to be reached before any breakage occurs and the less competent the ore, the lower the minimum porosity reduction value. Theoretical analysis on bed compression breakage shows that the relationship between product size measured in t10 and the specific comminution energy (Ecs) is not unique and is dependent on the testing conditions. The analysis shows the importance of testing bed breakage at conditions that are independent of bed configurations. Furthermore, models for predicting the product t10 and specific comminution energy of multi-component ore from single component compression data are developed. By compressing the particle bed at the set porosity reduction for each component and few multi-component tests, one can predict the mixture product and mixture energy consumption at any mixture ratios without the needs to physically separate the products in the mixture test.
Weerasekara NS, Liu LX, Powell MS (2016) Estimating energy in grinding using DEM modelling, Minerals Engineering 85 pp. 23-33 Elsevier
The latest state of the art on Discrete Element Method (DEM) and the increased computational power are capable of incorporating and resolving complex physics in comminution devices such as tumbling mills. A full 3D simulation providing a comprehensive prediction of bulk particle dynamics in a grinding mill is now possible using the latest DEM software tools.
This paper explores the breakage environment in mills using DEM techniques, and how these techniques may be expanded to provide more useful data for mill and comminution device modelling. A campaign of DEM simulations were performed by varying the mill size and charge particle size distribution to explore and understand the breakage environment in mills using DEM techniques. Analysis of each mill was conducted through consideration of the total energy dissipation and the nature of the collision environment that leads to comminution.
The DEM simulations show that the mill charge particle size distribution has a strong influence on the mill input power and on the way the energy is distributed across the charge. The smaller particles experience higher energies while the larger experience less, but this variation is strongly dependent on the mill size. The results also showed that the average particle collision energy increases with increasing mill size, whereas its distribution over particle size is strongly influenced by the mill content particle size distribution. The simulations also captured the energy distribution within different regions of the tumbling charge, with the toe impact region having higher impact energies and the bulk shear region having higher tangential energies. Regardless of the mill size most of the energy is consumed by the particles in the mid-size range, which has the highest percentage mass of the total charge distribution.
Liu LX (2013) Influence of particle size on the direct compression of ibuprofen and its binary mixtures, Powder Technology 240 pp. 66-73 Elsevier
In this paper, ibuprofen from a commercial source and its fractioned samples with narrower size distribution were characterized to assess the effect of particle properties on compaction characteristics. The compaction behavior of binary mixtures of ibuprofen with spray-dried lactose was also studied. The tablet in-die densification rate and tablet out-of-die porosity and tensile strength were measured for all samples. It was found that the particle size of ibuprofen does not affect the yield stress as derived from a Heckel plot, however the yield stress increases with the increase of ibuprofen particle size in the binary mixtures. Particle size also affects the tablet out-of-die properties, with tablet porosity and tensile strength increasing with the decrease in particle size. The effect of adding a weak compacting powder such as lactose on the tablet tensile strength is very much dependent on the ibuprofen particle size and mass ratio of the binary mixtures. Mixing lactose with ibuprofen of similar size in equal mass has no effect on the tensile strength of the tablet whereas mixing it with ibuprofen of larger size reduces the strength compared to ibuprofen alone. Adding a smaller amount of lactose can lead to an increase in tablet strength, even though the particle size of ibuprofen and lactose is quite different. Theoretical analysis on the tablet strength based on particle?particle bond strength was also carried out to explain the experimental results.
Powell MS, Hilden M, Ballantyne G, Liu LX, Tavares LM (2014) The appropriate, and inappropriate, application of the JKMRC t10 relationship, Proceedings of the XXVII International Mineral Processing Congress ? IMPC 2014 pp. 133-144 Gecamin Publications
The t10 relationship developed by Narayanan and Whiten has underpinned a number of the JKMRC models and the characterisation of ore competence through impact testing with the drop weight tester. This usefulness is based on a consistent relationship between the t10 value and the overall size distribution that was noted for brittle rocks. However, like all characterisation tests this should be used only when the controlling conditions apply, which in this case is single impact breakage between two metal platens and within the range of sizes in which fragment sizes are normalizable. For any other mode of breakage the relationship should be confirmed before being applied. Soft ores or bimodal ores with widely different competence between dominant components have non-typical breakage signatures. Breakage via single point impact abrasion, compressed-bed breakage, low-energy surface breakage and incremental breakage, to name some of the other breakage modes, do not obey the general t10 relationship, so their outcomes cannot be used to provide a direct comparison. Inappropriate use of the t10 parameter can result in misleading conclusions about efficiency of energy use. These issues and alternative comparison techniques are presented and discussed in terms of choosing appropriate measures of efficiency of breakage, ore competence and energy required for comminution.
The latest state of the art on Discrete Element Method (DEM) and the increased computational power are capable of incorporating and resolving complex physics in comminution devices such as tumbling mills. A full 3D simulation providing a comprehensive prediction of bulk particle dynamics in a grinding mill is now possible using the latest DEM software tools.This paper explores the breakage environment in mills using DEM techniques, and how these techniques may be expanded to provide more useful data for mill and comminution device modelling. A campaign of DEM simulations were performed by varying the mill size and charge particle size distribution to explore and understand the breakage environment in mills using DEM techniques. Analysis of each mill was conducted through consideration of the total energy dissipation and the nature of the collision environment that leads to comminution.The DEM simulations show that the mill charge particle size distribution has a strong influence on the mill input power and on the way the energy is distributed across the charge. The smaller particles experience higher energies while the larger experience less, but this variation is strongly dependent on the mill size. The results also showed that the average particle collision energy increases with increasing mill size, whereas its distribution over particle size is strongly influenced by the mill content particle size distribution. The simulations also captured the energy distribution within different regions of the tumbling charge, with the toe impact region having higher impact energies and the bulk shear region having higher tangential energies. Regardless of the mill size most of the energy is consumed by the particles in the mid-size range, which has the highest percentage mass of the total charge distribution.
Xu D, Liu LX, Addai-Mensah J, Robinson D (2013) Mechanical strength and rewetting stability of nickel laterite pellets, Advanced Powder Technology 24 (4) pp. 743-749 Elsevier
The stability of agglomerated/pelletized ores is one of the key properties for successful heap leaching of complex, low-grade nickel laterite minerals. In this paper, single pellets of saprolitic and goethitic nickel laterite with controlled binder type (tap water and 44 wt.% H2SO4), binder content and pre-set porosity were made by a pellet press and subjected to mechanical strength and rewetting stability tests. The effect of fine/coarse particles ratio on the mechanical strength was also investigated using siliceous goethitic ore. The failure strength of the pellets under different drying conditions was measured and the time taken for the pellets to disintegrate under saturated (soaking) and leaching conditions was recorded. The results showed that, with the same type of nickel laterite, the time taken to disintegration during leaching test is proportional to the pellets tensile strength. Pellets with water as binder are more stable under soak conditions. Furthermore, failure strength for oven dried pellets is greater than that of air dried. With saprolitic nickel laterite (SAP) pellets, their mechanical strength and re-wetting stability can be enhanced by drying the wet pellets or by increasing the binder content in the pellets. The pellets mechanical strength was found to be a good indication of their stability under leaching conditions as well. However, no relationship between the two was observed for goethitic nickel laterite pellets.
Optimisation of grinding circuits is invariably dependent on sound process models together with process simulators that can solve the process models accurately. Most of the process models are solved numerically because analytical solutions are not available, which can lead to errors in the results due to the numerical approximation of mathematical equations. Whiten , and Valery Jnr & Morrell [2, 3] have developed a dynamic model with numerical simulation for autogenous and semi-autogenous mills, and validated the model with dynamic response of mills in terms of power draw, grinding charge level, slurry level and product size distribution to changes in feed rate, feed size, feed hardness and water addition [2, 3]. In this work, an analytical solution for their dynamic model of tumbling mills has been developed based on the knowledge of solutions to the first-order nonhomogeneous linear differential equations. Two algorithms, Direct Single Time method (DST) and Direct Multiple Time method (DMT), were applied to obtain the analytical solutions respectively. It was found that analytical solutions are more accurate than the traditional finite difference numerical methods. However, the DST analytical method has a drawback of numerical instability due to the accumulation of round-off errors which are amplified by exponential functions, whilst the DMT method can provide stable solutions. To test the DMT analytical method, two cases of SAG mill dynamic operation were studied with both the traditional numerical method and the newly developed analytical method, further proving the robustness and feasibility of the analytical solutions.
A mill model structure based on the population mass balance framework incorporating breakage characteristics, slurry and solids transport, product classification and discharge and energy consumption was reported in XXVII IMPC and named the Generic Tumbling Mill Model Structure Version I (GTMMS I). In this work, a new 4D (four dimensional) appearance function sub-model based on the experimental results of the JK Rotary Breakage Tester (JK RBT) was developed to describe the breakage characteristics and was applied to this new model structure. The newly developed 4D appearance function model has fewer fitting parameters and is more generic in nature. Most importantly, it is applicable to both high and low energy impact breakage. It is therefore much more versatile in comparison to the existing JKMRC t10-tn appearance function and the size-dependant JK M-p-q t10-tn appearance function. In addition, the Discrete Element Method (DEM) energy distribution model was integrated into the new model structure. With DEM results providing energy distribution information inside the mill directly, the selection function and the back-calculation method used in the existing JKSimMet modelling method are not needed in this model structure. With the above two revolutionary innovations, the previous model structure was upgraded to the Generic Tumbling Mill Model Structure Version II (GTMMS II). Furthermore, the new model structure is dynamic in nature with time-stepping technique for non-steady-state simulation. A case of the dynamic grinding of a SAG mill was studied to validate the GTMMS II. The model simulation results agreed well with the plant data. With the newly developed 4D appearance function model, the incorporation of DEM energy distribution and transport function, the Generic Tumbling Mill Model Structure Version II (GTMMS II) is an important step forward towards mechanistic modelling of tumbling mills.
The Appearance function, also known as breakage distribution function, is used to describe the breakage characteristics of an ore impacted with a certain energy. It is the bedrock of comminution modelling. The range of applicability of the majority of existing appearance functions is limited to coarser sizes above a few millimetres. In the previous work, a 4D (four dimensional) appearance function model was developed based on JKRBT test data, but its applicable range was not sufficiently broad at ?24.4 + 7.3 mm. In order to develop a more versatile appearance function model that can be used for a wide range of energy levels and feed particle sizes, drop weight tests for smaller particles with sizes ranging from 425 ¼m to 16 mm were carried out with the Mini JK drop weight tester. Combined with data up to 63 mm from Standard JK Drop Weight Tests, the outcomes were fitted to two types of 4D appearance functions - the P80-m based 4D model and the P80-m-q based 4D model. The proposed 4D models are more accurate and scalable than existing models. Most importantly, they can be used for a wide range of conditions, with feed particle size ranging from 425 ¼m to 63 mm and input specific energy from 0.1 to 2.5 kW h/t in the initial test data.
Solid pharmaceutical tablets can be manufactured via three processing technologies: direct
compression, dry granulation and wet granulation before the final compaction process. Dry
granulation using roll compaction generally involves production of ribbons, followed by milling to
produce granules and the production of tablets. The mechanical properties of ribbons produced during
roll compaction can influence breakage behaviour in a mill and hence the performance of a drug
formulation. Therefore it is important to explore critical factors that determine the quality of ribbons.
In this study, MCC Avicel PH-102 was used as the model powder for roll compaction and the
critical operating factors affecting ribbon quality were studied. MCC 102 ribbons were manufactured
at a range of process conditions (roll speed, feed screw speed and compaction pressure) using the TF
mini roll compactor with a serrated die & punch (DPS), grooved roll surface. The key ribbon
properties measured are the powder feed ratio (defined as the ratio of feed screw speed to that of roll
speed) and mass throughput ratio (defined as the mass of ribbons produced in a given time to that of
The porosity of ribbons was observed to depend significantly on powder feed ratio into the
compaction zone. Porosity remained constant at a fixed feed ratio irrespective of the absolute roll
speed and the feed screw speed conditions used. Mass throughput ratio is another factor that was
introduced to describe process efficiency i.e. to draw comparison between the amount of ribbons and
fines. The amount of ribbons and fines generated at a given process condition depends significantly
on the feed screw speed and the compaction pressure. In addition, ribbon porosity decreased with
increasing pressure but there was negligible effect on ribbon porosity when excessively high pressure
(> 60 bar) was used. Ribbon porosity was also observed to decrease with increasing feed screw speed
but the converse is true with increasing roll speed.
In conclusion, the impact of various roll compaction process parameters were critically
investigated and a detailed insight into the main factors (powder feed and mass throughput ratios)
that govern the behaviour of roll compacted ribbons was provided. In future, the focus is to relate
these process properties (and ribbon porosity) to granule size distribution from a milling process.
This work aims to build a generic dynamic model structure, which can accommodate interchangeable sub-models of each sub-process, making it amenable to continuous upgrade without the need for redevelopment, for multicomponent tumbling grinding mills. The Generic Tumbling Mill Model Structure (GTMMS) is based on a population mass balance framework which incorporates breakage characteristics, transport, classification along the mill, a discharge function, and energy consumption incorporated in a dynamic mill model structure. Version III builds on two earlier versions by incorporating energy distributions derived from discrete element modelling, an updated version of the 4D breakage appearance function which applies to a broader size range, and addresses multi-component ore breakage via the probability distribution of energy split based on material stiffness. The model has been tested against multi-component plant survey data. GTMMS III suggests a mechanistic insight into mixture prediction through component analysis and is a step forward towards the unified comminution model (UCM) with its mechanistic, generic, and dynamic prediction capability.
Single particle breakage characterisation at fine sizes for use in mill modelling has been addressed by only a few researchers and is not utilised in engineering design. This is mainly due to the challenge of accurately imparting a range of impact energies to sub-millimetre particles and then measuring the progeny size distribution for the tiny resultant mass. In order to fill this gap, a dispersed monolayer multi-particle breakage method was applied with a mini JK Drop weight tester in this work to extend the single particle breakage test from 16 mm down to 425 ¼m, covering a specific energy (Ecs) range of 0.1 - 2.5 kWh/t to provide a wide range of test conditions. A challenge that had to be addressed was switching from single particle to dispersed mono-layer due to the physical constraints of drop-height and drop mass in maintaining accuracy in input energy over the orders of magnitude required to apply the required specific range of energy input. As only a limited size range could be subjected to both single particle and mono-layer bed breakage, it was necessary to establish if the two testing techniques provide the same breakage results. A novel application of the Fréchet distance was successfully applied to quantitatively evaluate the discrepancy of progeny size distribution between single particle breakage and monolayer multiple particle breakage. Extrapolation of an empirical Fréchet distance model indicated that the application of dispersed mono-layer breakage below 2 mm provides an acceptable comparison with the single particle breakage applied to coarser sizes, thus facilitating the fitting of a single appearance function across this wide range of sizes and applied breakage energies.