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A random model for mineral liberation by size reduction

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... Desde o trabalho clássico de Gaudin [2], inúmeros estudos têm sido conduzidos com intuito de desenvolver modelos capazes de predizer a evolução da liberação mineral com a redução do tamanho das partículas [3][4][5][6][7][8][9][10][11][12][13][14], porém, na prática, ainda não há modelos com aplicação difundida, e a determinação das malhas de liberação e de moagem é determinada com base em testes de laboratório. O modo mais direto de se definir em qual tamanho as fases minerais presentes em um determinado minério apresentam grau de liberação satisfatório para o processo de concentração consiste em determinar as curvas de qualidade de produto versus malha de moagem, ou seja, submeter o minério a moagem em diversas malhas granulométricas com posterior concentração e avaliar em qual tamanho se obtém a qualidade química especificada para o produto. ...
... A abordagem heurística foi utilizada na prática por alguns autores em estudos de otimização em processos de cominuição e concentração [20,21]. O fato de ser possível replicar o grau de liberação de um mineral de interesse em uma faixa de tamanho para diferentes malhas de cominuição a partir da amostra cominuída em uma única 3 ...
... Liberation models aiming to predict mineral liberation based on the ore texture and independently from the comminution process parameters are commonly referred to as texture-based liberation models (Gaudin, 1939;King and Schneider, 1998a;Wiegel and Li, 1967). These models are decoupled from the breakage and size reduction phenomena affected by the mill operating parameters in contrast to the integrated liberation and size reduction models (Andrews and Mika, 1975;Wiegel, 1976). ...
... Others (Evans et al., 2013;Hsih and Wen, 1994) explicitly define the contrary, in which the breakage is considered random if it does not follow these explicit definitions of non-random breakage. Other definitions such as random breakage through examples have also been offered (Ferrara et al., 1989;Gaudin, 1939;Gay, 1999;Wiegel and Li, 1967). In this study, the contrary definition of random breakage as suggested by Evans et al. (2013) and Parian et al. (2018) is used in which the breakage is defined as random if the breakage is not preferential in any mineral nor phase boundaries. ...
Article
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Prediction of mineral liberation is one of the key steps in establishing a link between ore texture and its processing behavior. With the rapid development of X-ray Microcomputed Tomography (µCT), the extension of liberation modeling into 3D realms becomes possible. Liberation modeling allows for the generation of particle population from 3D texture data in a completely non-destructive manner. This study presents a novel texture-based 3D liberation model that is capable of predicting liberation from 3D drill core image acquired by µCT. The model takes preferential, phase-boundary, and random breakage into account with differing relative contributions to the liberation depending on the ore texture itself. The model was calibrated using experimental liberation data measured in 3D µCT. After calibration, the liberation model was found to be capable of explaining on average of around 84% of the variance in the experimental liberation data. The generated particle population can be used for particle-based process simulation to evaluate the process responses of various ore textures subjected to various modes of breakage.
... For the same degree of ore particle liberation, the mine's conventional comminution design currently needs a reduction down to 113 µm, which requires far more energy and is thus considerably less efficient. Besides particle size reduction, one of the most important and complex parameters in comminution is the particle liberation to separate ore minerals from gangue efficiently to achieve a high recovery of the commodity minerals [12]. incomplete particle liberation during size reduction poses a serious problem to efficient recovery of commodity minerals with potential loss of value minerals to the waste stream. ...
... problems in the dewatering of the tailings dams. Based on some early theoretical considerations, one author [12] stated vaguely that "some systems exhibit a tendency to fracture at grain boundaries", which "would result in significantly better liberation than expected". Surprisingly, little improvement of conventional comminution systems materialised after this 50-year-old statement or at least not until the Vero Liberator was invented in 2012. ...
Article
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Mining and mineral processing industry are under pressure from political and social stakeholders to deliver products more sustainably with a much smaller environmental impact. Technical innovations to achieve these goals include reduction in energy consumption, waterless mineral processing, coarse particle liberation, and safe dry stacking of tailings. Traditional, largely abrasional comminution in robust ball and SAG mills is known for its inefficiency with respect to breakage and energy consumption. Earlier theoretical predictions and numerical modelling postulated that more efficient impact breakage should occur at higher impact energies from higher operational velocities. The VeRo Liberator impact crusher operates in such a mechanical high-velocity regime and achieves very high particle size reduction ratios and degrees of particle liberation at very low energy consumption and without using process water. These step-changing comminution results are achieved from high frequency, high-velocity impacts with an efficient momentum transfer that leads to the effective disintegration of the feed material. The empirically tested results have been experimentally simulated and confirmed in static and dynamic uniaxial load tests and high-velocity impact gas cannon tests. The VeRo Liberator technology has currently achieved TRL 7 and several units operate currently at mining operations and test facilities in South Africa.
... • The dispersed phase model was composed of core A phases dispersed in a B phase matrix. The core phase could be spherical [20][21][22][28][29][30], regularly-shaped [16,30,31], or irregularly-shaped [32]. This differed from the Boolean model (below) because the core phases did not overlap with each other. ...
... This differed from the Boolean model (below) because the core phases did not overlap with each other. The maximum F v did not reach 1.0, and was limited to the packing density of the core phases except when the core phase was aligned in a cubic manner [16,31]. ...
Article
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An effective correction method for stereological bias is required because of the importance of accurate assessment of mineral liberation of ore particles. Stereological bias is error caused by the estimation of a three-dimensional liberation state based on two-dimensional sectional measurements. Recent studies have proposed a stereological correction method based on sectional particle texture analysis, which employs numerical particle models. However, the applicability of this method to unfamiliar particle systems, with different shape and texture characteristics from the numerical particle model, has not been thoroughly investigated. In this study, the viability of the method for examination of the internal structure and shape of unfamiliar particles, was assessed using four types of particle systems, based on combinations of two types of internal structures (Boolean and Voronoi) and two types of particle shapes (spherical and irregular). Seven different texture analysis indices were utilized for composition distribution correction with regard to each of the four types of particle systems. The results suggested that a model based on the angular second moment and/or entropy, employed by the spatial gray level dependence method, showed the greatest viability for assessment of unfamiliar particle internal structure and/or shape.
... Division of this texture into particles of various sizes allows the calculation of the proportion of fully liberated particles for a given particle-to-grain size ratio. This idea was developed further by Wiegel and Li (1967) to include a randomised distribution of mono-sized grains and retained an analytic solution to the liberation distribution function. Extended models that include full grain size distributions and calculation of the full liberation spectrum have been developed, for example by Gay (2004a), Stamboliadis (2008) and Wiegel (2006Wiegel ( , 2010. ...
... Fig. 8 illustrates the texture simulated using the new model. Fig. 9 shows good agreement between the calculated liberation distribution and Wiegel and Li's (1967) model. There are slight differences at the coarser sizes, which are probably due to differences in the assumptions used construct the texture volume. ...
Article
We present a novel methodology for numerically reconstructing a three-dimensional (3D) texture for simulating multi-mineral rock and estimating the particle properties and liberation characteristics of its breakage products. A stochastic geometrical model has been developed to describe the intact structure of ores at any scale, potentially containing several mineral types, each with unique grade and grain size distribution parameters. Additional controls over the intact texture include the ability to vary the proportion of grain inclusions within grains of a different mineral phase and by varying the degree of spatial clustering of grains within the texture. Repeated random 2D and 3D sectioning of the 3D texture to simulate particle production and to calculate their compositions is used to generate outputs comparable to reports from mineral liberation analysis systems; including density distributions, liberation distributions, and particle class distributions. These outputs enable texture parameters to be fitted to corresponding measured liberation data and is demonstrated for a four-mineral sulphide ore, yielding a realistic distribution of particle properties, essential for accurately modelling particle separations.
... Модель Годена стала основой для многих последующих работ в данном направлении, однако, будучи слишком идеализированной, сама по себе она оказалась непригодной для практического использования. 15 Усовершенствованную модель случайного раскрытия двухфазной руды предложил Р.Л.Уигл [114]. Им были получены математические выражения для вероятности образования раскрытых частиц P i и сростов P mq минеральных фаз [113]: ...
... В подошве верхнего горизонта залегает пачка железнослюдкомагнетитовых (гематито-магнетитовых), карбонато-магнетитовых и силикато-магнетитовых кварцитов с прослоями слаборудных кварцитов и межрудных сланцев. В зависимости от минерального состава руды 114 подразделены на 4 основных типа: магнетитовые, силикатомагнетитовые, железнослюдко-магнетитовые и слаборудные. ...
Thesis
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The stereological method for evaluation of mineral liberation degree in iron ores was developed. To control locked and free particles have used image analiser IBAS II. The theory on reconstruction of volume particle distributions from mesured plane sections of multi-phase despersed materials was added with Markov chains equation to describe unified comminution and liberation processes.
... Two primary approaches for setting the grinding target exist: modeling and experimental determination. Predicting liberation after comminution has long been a challenge [1,2,3,4,5,6,7,8,9,10,11,12] without widespread application to date. One practical approach involves liberation heuristics, assuming a constant particle composition distribution within a size fraction regardless of the overall particle size distribution [13]. ...
... However, there is not much information about the effect of petrographical and mineralogical properties in mineral processing operations because these properties are difficult to incorporate into the plant circuit design and relevant information can be treated as categorical variables rather than numerical variables. Wiegel & Li (1967), King & Schneider (1998), and Gay (2004b) discussed the effects on the comminution properties of the modal composition derived from the petrographic, mineralogical properties of a given rock (ore or mineral), however, they found the findings in the material's model composition too complex to translate practically into a plant circuit design. Before attempting to model the comminution properties of a particular ore, the lack of knowledge about the effects of grain size, mineral grade, and mineral composition, among ore control parameters, on the breakage rate and liberation must be addressed. ...
Article
Full-text available
Especially in terms of energy costs, data on chemical, petrographical, and mineralogical analyses of ores or minerals can provide very important information for their production in the desired size distribution. Therefore, suitable crushing and grinding machines can be selected, taking into account the data affecting the comminution such as grain size, texture, metamorphism, and mineral or element contents. However, in most mineral processing plants, these data are rarely used to understand the response of ores or minerals to comminution. Analysis of the relationships between the chemistry, petrography, and mineralogy of ores and the breakage mechanism during crushing or grinding has been the subject of researchers in the comminution field in recent years. This study is a review of studies done so far on the relationships between the comminution and the chemical, petrographic and mineralogical properties of different ores and minerals, and their effect on concentration.
... This suggests that achieving its critical level when a particle falls apart should be possible by one single step and it can happen at a considerably good liberation factor, too. As a matter of fact, there is nothing new in it, the first mention looks back around 55 years (Wiegl et al., 1967). ...
Conference Paper
The mining industry has traditionally relied on conventional fossil-based fuel sources to meet its growing energy demand. The industry is now tasked with responding to the challenges of increasing fuel prices while commodity prices tighten, resulting in ever-narrowing operating margins and increased opposition from communities to new conventional energy sources. So far, research about such decision-making on the use of renewable energy in production scheduling (PS) problem for open pit mining operations is underdeveloped. Due to the conflicting nature of economic and environmental objectives, the PS becomes a multi-objective problem. In this paper, a multi-objective gravitational search algorithm is used to provide Pareto optimal solutions which present the possible tradeoff between the cost and environmental objectives of the PS problem. To solve the problem, the weighted sum method is applied to convert multi-objective optimization to scalar optimization. The numerical results demonstrate the effectiveness of the proposed approach in solving multi-objective PS problems.
... Gaudin's approach has been revised over the years and improved to represent mineral systems better. As an example, Wiegel and Li (1967) took the volume grade of the target mineral into consideration by modifying the element size and number. This approach was later adapted to formulate the solitary grain model (Wiegel, 2011), useful for low-grade ores (less than 5% V/V). ...
Thesis
http://hdl.handle.net/20.500.11794/67317 The global efficiency of a mineral processing plant often depends on the performance of the grinding circuit, since there is a compromise to achieve the particle size liberating the targetted minerals in order to obtain high purity concentrates while maintaining low operating costs, which are largely influenced by the energy consumption. In recent years, companies have been facing more demanding performance targets, stronger competition, and more stringent environmental and safety regulations. Additional challenges are inherent to the grinding circuits themselves, e.g. the nonlinear responses, high degree of intercorrelation of the different variables, and material recirculations. Another crucial aspect that has not been reported yet is the effective integration of mineral liberation in control and optimisation schemes. Although it is a key piece of information directly related to the performance of the concentration stage, most strategies focus exclusively on the particle size. This is understandable given that it is currently impossible to measure the liberation distribution online. Based on an existing mineral processing plant simulation library, this research addresses these problems by (1) developing a mineral liberation model aiming at linking the grinding and concentration stages; (2) programming a phenomenological autogenous/sem-iautogenous (AG/SAG) mill model, required to complement the simulation toolbox, and validating it through calibration; (3) coupling a grinding circuit simulator to a concentration process by means of the liberation model, and (4) developing a plantwide control and optimisation scheme considering mineral liberation data explicitly to evaluate the economic benefits.
... Various studies have investigated the stereological bias in volumetric liberation measurement, using geometrical models (e.g., [4][5][6]), experimentation (e.g., [7][8][9]), or numerical simulations (e.g., [10][11][12][13][14]). However, to the author's knowledge, only the correction method proposed by the author is available for addressing the stereological bias in surface exposure measurement [15]. ...
Article
Full-text available
In mineral processing, surface exposure, in which the particle surface is composed of one phase, is important, because the extent of the surface exposure determines the efficiency of floatation. In general, surface exposure is calculated based on two-dimensional (2D) measurement of particle sections. However, such 2D measurement is known to result in a form of error called stereological bias. The stereological bias associated with surface exposure has not been thoroughly studied. In this study, as a means of empirically validating the findings of a previous, numerical study, the stereological bias involved in measuring the surface exposure of binary particles was experimentally investigated using artificial particles and X-ray CT analysis. Three types of binary particle samples were utilized, and significant stereological bias in surface exposure measurement was observed in each case. Then, the effect of particle shape (aspect ratio for the global shape, and corrected sphericity for the surface roughness) on the stereological bias was investigated. It was confirmed that the effect of particle shape was negligible compared to the effect of the internal mineral structure of the particle. This result supports those of the previous, numerical study.
... Other forms of non-random breakage include preferential breakage in which crack propagation occurs more frequently in one of the mineral phases [7]. To model the liberation of minerals, many researchers have assumed the breakage to be random in order to reduce the complexity of the problem [8][9][10], since in this case the selection function will be independent of particle size and the ore texture [11]. Briefly, random breakage can be defined as the independence of the failure process from both the mineralogical and mechanical characteristics during the grinding process [12]. ...
Article
Full-text available
In mineral processing, liberation of valuable mineral from gangue minerals is the most important stage before the concentration process. Comminution, which leads to liberation, includes two types of random and non-random breakages. The contribution of random and non-random breakage is very important in modelling the liberation phenomenon. In this paper, a simulator based on 2D Voronoi tessellation is introduced which can simulate random, preferential and detachment breakages of binary ores (valuable and gangue mineral). This simulator has been validated by image analysis of fragmented artificial ores which were made in different grades and comminuted in different energy levels by a drop weight device. The data obtained from images of comminuted particles were processed using the codes prepared in MATLAB®. Results showed that for the samples used in this study, the proportion of the intergranular breakage changes as the grade of the ore changes, with an agreement between simulations and experiments, independently from the energy level of comminution.
... The present study models the non-preferential breakage of binary materials composed of a core phase (phase A) dispersed in a matrix phase (phase B) is modeled. In this state, the liberation of phase A occurs when the particle size is considerably smaller than the phase A size [4,19]. The ratio of the particle size to phase A size exerts a significant influence on stereological bias for the liberation of phase A [14]. ...
Article
Full-text available
Two-dimensional (2D) measurements of the cross-sections of polished mineral samples suffer from an overestimation of the degree of liberation known as stereological bias. Stereological bias is believed to be affected by the particle texture, i.e., the stereological bias of a simple locking particle is high, while the bias of a particle with a complex texture is negligible. However, scant work has been performed on the development of a quantitative and versatile modeling of stereological bias. We performed a series of numerical simulations: modeling particle assembly using the discrete element method; modeling the binary texture of particles by imposing phase patterns to the particles; systematical generation of 8608 types of phase patterns; liberation assessments in 2D and in three-dimension (3D) based on the error-free geometrical calculation; and stereological bias assessment by a comparison between liberations in 2D and 3D. Through these simulations, the correlation between the stereological biases of the phases and particle texture was investigated. Finally, the particle texture complexity was assessed using the fractal dimension of image intensity, and stereological bias for the matrix phase was successfully correlated with the fractal dimension and area fraction of the core phase. Fractal dimension and area fraction values are easily obtained by 2D measurements and subsequent image analysis. These results may lead to the establishment of a versatile stereological correction model that depends only on measurable 2D parameters.
... The model was based on binomial distribution of cubic mineral grains in the ore matrix. Later, this concept was refi ned by Wiegel to develop a model to predict the proportion of free gangue and free valuable mineral in a given particle size range for a given grain size and volumetric ore grade (Wiegel, 1964). The model correlated well with sizeby-size Davis tube test data and directly measured average grain sizes for magnetite bearing iron ores (Wiegel, 1974). ...
Article
This study was initiated by plant sampling. Raw data generated by sample analysis were mass balanced and used for performance assessment and model fitting. Evaluation of mass-balanced data indicated that the ball mill circuit at the Ispat Inland Minorca plant was the bottleneck limiting throughput. A team of engineers developed performance improvement ideas to alleviate the load around the circuit. These included modifications that have a direct effect on the circuit, such as makeup bau size, volumetric ball charge, critical speed, percent solids in the mill, more efficient hydrocyclones, and replacing of hydrocyclones with stack sizers. Other modifications that have indirect effects-namely, dry cobbing, improved fine screening, and separate grinding of fine screen oversize-were also simulated. Simulations were carried out using an improved version of Usim Pac mineral processing simulation software. Improvements included incorporation of magnetic separator, hydroseparator, and fine screen models into the software. Although the simulations were aimed at reducing the load around the ball mill, complete plant simulations were carried out to determine the effects of modifications on downstream flows and to simulate the upstream effects of increased feed rates. Results of simulations indicated that all the modifications would provide some degree of benefit to the circuit/plant performance. However, the most promising and feasible alternative was the use of finer makeup balls with more efficient hydrocyclones. The finer makeup ball size modification was immediately implemented in the plant, and substantial improvements in throughput were obtained. Plant sampling was repeated to quantify benefits from this modification. Mass-balanced data indicated a very good fit between actual and predicted performances. As a result of simulation-based modifications at the plant, throughput was increased more than 10%. Further improvements are expected following replacement of existing 15-in. cyclones by more efficient 20-in. units.
... The model was based on binomial distribution of cubic mineral grains in the ore matrix. Later, this concept was refi ned by Wiegel to develop a model to predict the proportion of free gangue and free valuable mineral in a given particle size range for a given grain size and volumetric ore grade (Wiegel, 1964 ). The model correlated well with sizeby-size Davis tube test data and directly measured average grain sizes for magnetite bearing iron ores (Wiegel, 1974). ...
Article
Full-text available
In 1998, the Concentrator Modeling Center was established within the Coleraine Minerals Research Lab, Coleraine, Minnesota, to develop models for simulation of iron ore processing plants, and to assist plant operators in improving performance of their aging plants. The short-term objective was to develop necessary models for reliable simulation using conventional techniques, while the long-term objective was set as liberation-based modeling and simulation of these plants. The short-term objective was achieved in 2002 after the development of models for magnetic separators, hydroseparators and fine screens. A project funded by the U.S. Department of Energy was carried out to demonstrate the capability in improving iron ore processing at the Minorca plant. As a result of this study, a 10% improvement in throughput at the plant was obtained, and simulation became a desired tool for plant operators. A significant step in the long-term objective was reached in 2005 with the development of a liberation model. This was followed by incorporation of models capable of processing liberation data into the software. By early 2007, the Concentrator Modeling Center had the capability of performing liberation-based simulation of entire plants.
... A lot of liberation models have been developed from old days (for example, Gaudin, 1939;Wiegel and Li, 1967;Steiner, 1975;Andrews and Mika, 1976;King, 1979;Kiss and Schornert, 1980;Klimpel and Austin, 1983;Meloy and Gotoh, 1985;Peterson and Herbst, 1985;Barbery, 1992;Schneider, 1995) but only some of them have considered preferential breakage at phase boundaries (King, 1994;Wang et al., 1994;Hsih and Wen, 1995;Owada, et al., 2001Owada, et al., /2003Owada, et al., / 2005 and it seems that the applicability of the models are not determined yet depending on the materials which have different characteristic phase boundaries. We developed several models in which various indices of "Preferential Breakage Probability (PBP)" were defined and the applicability of each index was discussed in the paper in relation to the property of phase boundaries of target materials. ...
Article
Full-text available
Liberation degree is one of the most important indices for clarifying the limit of subsequent component separation not only in mineral processing but also in solid waste processing. Authors created several models considering preferential breakage at phase boundary and defined various kinds of indices of "Preferential Breakage Probability". Experimental validation was also carried out for synthetic composite materials as test samples which have different property of phase boundaries. The results were discussed in terms of the applicability of the models depending on the boundary property. "Preferential Breakage Probabilities" defined in the models were considered useful to quantify the facility of liberation for various materials and to determine comminution methods / conditions for achieving good liberation.
... On the other hand, the nature of boundaries between intergrown minerals indicates whether mineral grains will break at the boundaries or not (Petruk, 1995), and therefore, the ease or difficulty of liberating the mineral of interest. Based on textural attributes a variety of mathematical models have been developed for predicting mineral liberations (Gaudin, 1939;Wiegel and Li, 1967;King, 1982;Gay, 2004). However, the application of these models is not widely spread and liberation is commonly estimated from laboratory testwork. ...
Article
A combined grinding and liberation model was studied to predict the liberation characteristics of iron ore comminuted by a ball mill. Comminution characteristics were obtained using the one-size-fraction method; then, the iron ore samples were crushed and separated into several narrow-size fractions by screening. The size fractions were further divided into three classes by magnetic separation, namely concentrate, middling, and tailings. Subsequently, various size classes were subjected to ball milling, and the results were analyzed in the kinetic grinding model. The mineralogical textures of the ground products were analyzed using mineral liberation analysis. The beta distribution and Andrews–Mika diagram characterized the distribution of the iron content within the size fractions. The breakage characteristics of the iron ore samples varied slightly with the iron content. However, the liberation characteristics were well-described by adjusting the four parameters of the beta distribution. The variation in grinding kinetics with composition and liberation model parameters was used in the combined liberation–comminution model to predict the evolution of the size–composition matrix as grinding proceeded. The predicted results align with the experimental results. The developed model can construct a yield–recovery graph and calculate the liberation efficiency to determine the size reduction threshold for efficient separation.
Article
A review of the literature reveals that methods for simulating the coupled behavior of size reduction and liberation are limited to binary mineral systems containing one composite particle class. The aim of this paper is to describe the development of a mathematical model to simulate such behavior for binary and ternary systems containing multiple classes of composite particles. A modified Leven-berg-Marquardt algorithm and a finite difference Jacobian are used in conjunction with the developed model and a set of constrained equations to estimate all kinetic parameters. This estimation scheme is validated for a binary ore (sphalerite-dolomite) with five composite particle classes using experimental data.
Article
Raw coal was ground in a Hardgrove mill, and mineral liberation from coal was investigated by float-sink test and electron probe microanalyzer (EPMA). Based on EPMA, associated conditions of mineral were determined. Analyses of energy-size reduction show that energy efficiency decreases with time. For +0.074 mm progenies, yields of particles in −1.5 g.cm⁻³ decrease with the increase of size and time, and products in +1.8 g.cm⁻³ show the opposite trend. EPMA of 0.25–0.125 mm, 1.5–1.8 g.cm⁻³ products ground for 10 min indicates that only part of minerals are liberated. For −0.074 mm products, the yield of particles in −1.5 g.cm⁻³ decreases by 23.36% in last several minutes, but ash content of +1.8 g.cm⁻³ also decreases by 13.18%. Since breakage of raw coal in last 9 min does not reduce particle size obviously, and liberation degree cannot be improved dramatically, closed grinding of 10 min in Hardgrove mill is proper to balance the size reduction and mineral liberation.
Article
Comminution modeling aims to predict the size and liberation distribution of mineral particles and the required comminution energy. The current state-of-the-art comminution models provide a calculation of neither particle size distribution, grinding energy and throughput dependency with neither a broad understanding of how the mineral grade varies by size nor the liberation distribution of the product. The underlying breakage mechanisms affect the liberation of mineral grains and are dependent on modal mineralogy and mineral texture (micro structure). It has also been a challenge to model comminution systems to predict the optimal energy and size for better mineral liberation because of the variability of the mineral particle properties i.e. grains arrangement and composition. A detailed mineralogical study was carried out in order to broaden the understanding of the nature and distribution of comminuted particles in a ball mill product. Focusing on iron ore samples the study showed how the particle breakage rate decreases when the particles reach the grain size of the main mineral component. Below that size, comminution does not increase mineral liberation and therefore in most of the cases passing over that boundary is only a waste of energy. The study involving iron ores from Malmberget and Kiruna, Northern Sweden, showed that certain shortcuts can be applied to empirically model the mineral liberation distribution of the particles in a ball mill based on the mineral grade-by-size pattern from a geometallurgical program. In Malmberget and Kiruna the mineral grade-by-size pattern is depending on the mineral distribution and grain size of gangue as well as magnetite or hematite minerals. A significant difference between mineral breakage of the same grade and gangue minerals can be observed due to texture differences.
Article
Mineral liberation is a key step in many mineral processing flow sheets and is achieved by breaking large pieces of ore into smaller particles which are suitable for the subsequent separation process. The ore being broken consists of mineral grains which may exhibit a range of properties affecting how they break. In the literature on mineral liberation the breakage of ore is frequently described as random or non-random, with several types of non-random breakage identified. With numerous researchers investigating this topic over the years, a variety of definitions of random and non-random breakage in mineral liberation have been presented in the literature. This paper examines the published work in this area and provides a comprehensive review of random and non-random breakage published in the literature on mineral liberation. It does not aim to revise the definition of these terms but to review the wide range of descriptors used by researchers in this field and identify common approaches to defining random breakage. The definition could be summarised as random liberation being the independence of breakage from both ore properties and mechanical properties during comminution.
Article
In previous work at Virginia Tech, a population balance model describing the simultaneous processes of size reduction and mineral liberation has been developed. Experimental verification of this model, however, has been limited to a binary mineral system containing only one composite particle class. When considering multiple classes of composite particles, estimation of model parameters becomes more difficult. In the present work, a procedure for estimating model parameters for a multiple composite class model has been developed. Emphasis is placed on direct experimental determination of these parameters. The physical significance of the breakage rate function and the liberation function in characterizing the liberation process is also discussed.
Article
To recycle steelmaking slags for their iron, manganese and lime contents, removal of the phosphorus-bearing dicalcium silicate and calcium phosphate is essential. Slow-cooling of slags was necessary to promote sufficient grain growth to achieve liberation. In situ grain size distribution determination showed that a high soaking temperature, a long soaking time, a very slow cooling rate and the addition of fluorspar promoted grain growth. High gradient magnetic separation on slow-cooled slags removed much of the dicalcium silicate. Liberation modeling was used to discuss the breakage and beneficiation characteristics of the slow-cooled slags.
Article
A review is given of the applications of random sets and integral geometry in fragmentation and liberation models of ores and minerals. Although attempts have been made in the past to apply such mathematical techniques to the comminution of solids, it is shown that it would not result in major progress. In liberation modeling, the approach can lead to fruitful results. A model of liberation prediction is developed that can be calibrated for ore texture and breakage using image analyzers. The model is demonstrated for the case of a Poisson polyhedra ore texture and monodisperse fragment size. The model enables prediction of the complete composite particle distribution and is valuable for integration of ore breakage models with minerals separation models.
Article
A model describing size reduction and mineral liberation during grinding has been extended to include multiple classes of composite particles. The majority of the model parameters have been directly determined using computerized image processing equipment to analyze the products from batch grinding tests. A coarse-grained sphalerite ore from Tennessee, representing a nearly ideal binary mixture of sphalerite and dolomite, has been used to experimentally validate the model for the case of dry batch grinding. In all cases, excellent agreement has been observed between the model predictions and the experimental results.
Article
A.M. Gaudin espoused the use of the Rubik's-cube arrangement of mineral grains to conceptually describe binary mineral liberation. That idealized concept has been examined, modified, tested, and extended over the past 40 years, resulting in a useful quantitative model for describing the liberation of medium-grade ores. This paper describes the background and rationale for accepting this approach for modeling mineral liberation as part of an overall mineral process simulation capability. As much of the size reduction used for liberation is aimed at lower-grade mineral deposits, comments have been included concerning extending the approach to low-grade ores.
Article
Several mineral process modeling and simulation packages are currently available for use in evaluating the performance of alternative process flow schemes. A critical link that has been missing from these packages is the ability to quantitatively model the effect of size reduction on the liberation of the valuable and waste minerals in the ore being processed. Although there have been several approaches taken to this problem over the past 25 years, none of them has led to a satisfactory conclusion. A technique was developed for measuring the effective liberation characteristics of magnetic taconite ores, and a program was constructed that makes use of these liberation characteristics in simultaneously simulating both size reduction and mineral liberation as it occurs in tumbling mills. This is an especially important step in the modeling of magnetic taconite processes, where magnetic rejection of low-grade wastes between grinding stages mandates that a predictive capability be available. The current application is specific to magnetic taconite, but it is possible that a similar approach could be used for other types of mineral systems.
Article
A stochastic model of mineral texture is discussed and used to demonstrate that grain association within the intact texture has a significant effect on the liberation characteristics of breakage products. The majority of previous models have simulated texture and liberation of binary systems. This new model is able to simulate complex multi-component (multi-mineral) aggregate textures and their breakage products. Grain size distributions can be defined for each of several minerals. Mineral-mineral associations can be controlled by inserting mineral grains within grains of another mineral. Repeated Monte Carlo sampling of the aggregate is used and the liberation properties of the fragments are calculated. These are analysed to generate data in a similar form as reported by mineral liberation analysis systems, including density distributions, liberation distributions, and particle class distributions. Simulations results are presented where the model has been fitted to complex sulphide ores with four minerals. Comparison of the simulated particles and experimental data show that the model is able to reproduce similar particle class distributions as measured by QEMSCAN. The texture of real complex ores can be simulated and fitted to conventional mineral liberation analysis data. The model should provide a useful and practical means of modelling the effects of mineral texture on separation processes and in geometallurgical models.
Article
The interrelationship between mineral liberation and leaching behaviour of a gold ore is ill defined, mainly due to the complexity of both leaching and mineral liberation. This study presents a neural network approach to modelling the liberation of gold bearing ores. A complete mineralogical analysis of unmilled and milled ores, including gold deportment and gangue content are used as inputs to a self-organizing neural net, which generates order preserving topological maps. The arrangement and shapes of these clusters are coupled to unmilled free gold data to predict gold liberation in milled ores (absolute error: 8.1%). Moreover, the self-organizing maps were diagnostic of the quality of data used, indicating that the relationship between particle size and gangue material content requires further investigation.
Article
A well-defined geometric model for a mineral system and its liberation by size reduction is used to show the relationship between true volumetric particle composition and the composition estimates obtained by the measurement of linear intercepts or areas of simulated polished sections of particles. Based on this information, a transformation is developed between the areal measurements and the volumetric composition for this idealized mineral system.
Article
The floatability of minerals is closed related with their crystal chemistry characteristics The crystal chemistry characteristics includes chemical composition, chemical bonds, crystal structure and the relation among them, which decide the surface properties of minerals after dissociating in the solution, and then influence the floatability. So it has very important theoretical significance to study crystal chemistry characteristics of minerals for learning the physical, chemical and surface properties; and deep study on application of crystal chemistry in flotation is one of important ways for settling out the separation of some refractory minerals and for developing harmonious technology of mineral processing. Methods of research on mineral crystal chemistry include research of crystal structure and cell parameters, calculation of crystal chemical parameters and so on. Computer simulation for flotation is an effective method to grasp the essence of interaction between minerals and flotation reagents, so it is also a crystal chemical method used in flotation. In this paper, a review of these research methods is carried out with some examples taken for illuminatation based on abundant experimental results.
Article
New liberation model was created considering preferential breakage at phase boundaries of solid materials for evaluating facility with disassembly and solid/solid separation in the area of material recycling. Two kinds of models have been developed in the paper, one is a prototype and simplest model and the other one involves the concept of strength distribution at phase boundary. These models include the modification of the Wiegel model, one of the most popular and acceptable liberation models, as well as the definition of "preferential breakage probability" at phase boundary. The indices could become good measures to evaluate the product design and to describe suitability of disassembly and/or compositional separation for material recycling. Concept, structure, simulation results, and validation of these models are shown in the paper.
Article
Some of the mineral deposits that are being processed today, and especially those expected to be processed in the future, have relatively low compositions of the valuable mineral. With these low-grade ores, it is necessary to be able to design processes that are sufficiently low-cost to permit exploitation. One approach to minimizing the capital and operating costs for these processes is to use the capabilities of computer process simulation in the design phase of development, to make important technical and economic decisions regarding the evaluation of alternative process flow schemes, the selection of equipment and the choice of operating conditions. There are mathematical simulation models for most mineral processing operations, including several each for size reduction, size classification and mineral separations. To be able to tie these individual operating models together in an integrated mineral process simulation, however, it is important, in fact in some cases essential, that there be a model which describes how the mineral system responds to size reduction in making the liberated valuable and waste mineral particles available for concentration or rejection operations and the locked particles available for possible recirculation. This, then, is the role played by the mineral liberation model, showing the relationship between particle size, quantity and composition throughout the process.
Article
Recent advances at JKMRC in modelling mineral liberation required the development of a method to measure ore textural characteristics such as the mineral grain size distribution and the spatial location of mineral grains in three dimensions. This paper describes the development of this method which uses X-ray micro-tomography to provide three-dimensional (3D) measurement of the grain size distribution and spatial location of the minerals in an ore. The methodology was developed on a gold-bearing pyrite ore and used to quantify the textural characteristics which are key inputs for modelling mineral liberation in this ore during comminution. The measurement and image processing steps required to quantify the grain size distribution of the mineral of interest, pyrite, are described together with the image analysis method. The quantification of 3D mineral characteristics together with corresponding two-dimensional (2D) sections through the same particle, provided the opportunity to explore the relationship between 2D and 3D grain size data.
Article
When ore characteristics such as mineral grain size distributions are quantified using measurements on particulate samples there is an error associated with the measured values. The magnitude of this error is a function of the grade of mineral of interest, the texture of the ore and the number of ore particles measured in the analysis. In practice the desire to minimise the error due to sampling by increasing the number of particles measured must be balanced against the increase in time and cost of analysing this increased number of particles. A statistical method based on bootstrap resampling has been developed to estimate the error in measurements of textural characteristics which are quantified by automated mineralogy systems. An application of the method to estimate the error in measurements of mineral grain size distribution is presented; however, the method can equally be applied to estimate the error in other textural characteristics, for example mineral association. By estimating how the error in the characteristic of interest reduces as particle sample size increases, the bootstrap resampling approach assists mineralogists to identify how many particles must be analysed to achieve the desired variance in the measured value. Examples from a copper porphyry ore are presented to illustrate the practical applications of this methodology in quantitative mineralogy programmes.
Article
In mineral processing, the liberation of valuable mineral is of key importance in achieving high recoveries from downstream separation processes such as froth flotation and gravity concentration. To quantify mineral liberation, information on ore texture of the parent rock as well as properties of comminuted particles is essential. These properties have been quantified by statistical measures such as the proximity function and covariance function, which were extracted from SEM images of parent rock and particle polished sections, using convenient and efficient image analysis techniques based on Labview (TM) software. To quantify fully liberated particles, a phase specific line segment function has been introduced and evaluated by placing random line segments on the image. It was also found that the ore texture assumptions made by Barbery are not valid for the high grade sulphide ore tested and the general applicability of these assumptions is therefore questionable. Using the measured information above, predictive liberation models to quantify volumetric grade distribution of particles in 1D and 3D have been developed based on Barbery's work. Results show that the grade distributions of composite particles predicted from the proposed 1D model is closest to measured data than those of Barbery's 1D model. The predictions using the proposed 3D model are similar to those predicted from Barbery's model and are considered more realistic as the model does not rely on assumed ore texture but on measurements made on the parent rock and particle sections.
Conference Paper
Full-text available
The improvement in the chalcopyrite copper Bucim mine are gone forward to renewed reagent regime, including and involving new reagents for increase d recovery of copper and gold. The optimization and mathematical linear models using gradient method Box and Wilson are good example for improvement of industrial recoveries in flotation circuit. In this paper is shown optimization techniques, formatting the mathematical model and adequate model for carried out investigations. Tables and figures will show the optimal quantity in reagent regime (collectors), particle size, flotation time I rougher flotation, conditioning time etc.
Article
The interrelationship between mineral liberation and leaching behaviour of a gold ore is ill defined, mainly due to the complexity of both leaching and mineral liberation. A better understanding of this relationship could result in lower operating costs on gold extraction plants, since an increase in the efficiency of gold dissolution and a decrease in costs related to the crushing and grinding operations could be expected. In this investigation artificial neural nets were used to analyse diagnostic leaching data of gold ores obtained from South African gold mines. A self-organising neural net with a Kohonen layer was used to generate order preserving topological maps of the characteristics of both the unmilled and milled ores. The arrangement and shapes of these clusters could then be used to develop simple neural net models which were capable of predicting the degree of liberation more accurately than previously proposed models. Moreover, the neural net models were also capable of providing direct estimates of the reliability of their predictions by comparing new inputs with the data in their training bases.
Article
A physically realistic exposure model for expressing the exposure of “disseminated inclusive” mineral grains from a binary petrologic system has been applied to gold ore leaching operations. The relationship between gold exposed ratio (FE), gold grain size (d), ore particle size (D), and grain boundary fracturing factor (P), is expressed as: fE(K) = PK3−(K−2)3K3+(1−P)K3−(K−1)3K3K=Dd This equation facilitates calculation of the grain size of gold particles, which is difficult to obtain by direct measurement, as in the extraction of flour gold disseminated in sulfide or quartzite matrix. Thus, the economic benefit may be given by optimizing the grinding operation for gold liberation relative to gold recovery. The grain size of gold particles in the Chinkuashih gold mine located in Keelung, Taiwan was determined as 0.6–2.9 μm, 0.4–2 μ and approximately 10 μm for the Penshan, Hsumei and Buffalo districts, respectively. Furthermore, this model was also demonstrated to be suitable for gold samples of gold mine operations from other parts of the world.
Article
A review of problems encountered in developing prediction models for composition distribution for particles obtained by the breakage of multiphase materials is presented. The needs to characterize texture by image analysis, to describe particle production by similar methods, to relate particle production and texture, to use integral geometry methods and stochastic geometrical processes to solve the complex probability equations in the three dimensional space, are stressed. A presentation is made of models developed by other researchers, which illustrates some of their deficiencies. A complete presentation is made of a model which incorporates the required elements. A special case of the model, combining a description of texture based on a Boolean model with primary Poisson polyhedra grains, of particle production calibrated on screen fractions extracted from ground ores, independence of texture and breakage, is presented. Applications of the model to data presented by other researchers give evidence of its value especially in predicting particle composition distribution at sizes similar or coarser than grain sizes.
Article
An exact expression is derived for the fraction of particles of mesh size D that contain less than a prescribed fraction of any particular mineral. The expression is obtained entirely in terms of the distributions of linear intercept lengths of the minerals in the ore. These distributions can be obtained by line traverses across a section of the ore. No other statistical information regarding the mineral grain sizes is required. The theory is completely free of empirical constants or other parameters and in particular no assumptions are made regarding the shape of the mineral grains in the ore or of the particles.The theory predicts that the fractional liberation of mineral at mesh size D is given by: where F(l) is the distribution of linear intercept lengths for the mineral and μ is the mean linear intercept length for the mineral. N(l/D) is the linear intercept distribution function for particles of mesh size D and Du is the largest intercept length across any particle of mesh size D.The theory was confirmed experimentally for the liberation of pyrite from Witwatersrand quartzite.
Article
For three phase locked particles the volume frequency distribution surface has been defined for the first time. It is a deep U-shaped surface showing low probability of having as locked a particle with a significant amount of all three phases present. At the boundaries of the three phase diagram, the previously derived two phase curves are defined. In the center, the Ferrara point is found with three arms. The surprise is the absence of any new or unexpected features.
Article
A liberation model extended from Gaudin's model by incorporating a detachment factor, in addition to a mineral grain size distribution, is proposed. The experimental application of this simple, physically-realistic model was demonstrated to be suitable for two ore samples: magnetite in talc schist from Hwalian, Taiwan and mordenite in andesite from the northern coastal range of eastern Taiwan. Both of these samples exhibit a high ratio of grain boundary fracture during roller crushing. With data taken from published results, four rock samples including nine mineral-gangue systems may also be correlated by this model. A general increase in the estimated detachment factor with an increased hardness difference is demonstrated, suggesting that the distribution of the average mechanical strength of the mineral, gangue and their interfacial layer is the governing factor in liberation by detachment. Physical properties such as hardness, cleavage, and the mineralogical texture of ores such as crystal form and orientation which affect the tensile strength are considered to be the function of this factor. The quantitative detachment factor can be used to express the possibility of fracture along the grain boundaries during various comminution processes.
Article
The prediction of particle size and minerals distribution in products from size reduction processes is one of the fundamental problems in mineral processing. In this paper, a 2D model based on cellular automata is proposed to simulate particles generation by discriminatory size reduction. This model generates particles on images of ore textures, through the growing of nucleation seeds. The size reduction process is simulated as a growing process of seeds over representative images of the ore texture. Each particle grows according to rules related with the probability of agglomeration between different seeds. The final pattern represents the sections of particles corresponding to the mill product, for a specified milling time. Preliminary results of areal size distributions and mineral grade distribution shows values quite similar to experimental ones. The incorporation of an optimisation algorithm, will allow calibration of the model to improve these results.
Article
One of the fundamental problems in mineral processing is to predict how ores are comminuted and how minerals are distributed in the particles. In this paper, image analysis and data processing techniques are applied to support the development, calibration and validation of 2D simulation model of particles generation by size reduction, where minerals exhibit discriminatory behaviour. Based on images of ore textures, a simulation model of fracture lines propagation was developed. A modification of Nelder and Mead optimisation method was used to find out the model’s parameter values that minimise an objective function defined as the squared deviation between observed and simulated particle areal distributions taking into account the variation of the average grade of the target mineral with particle size.
Article
The optimization of grinding-flotation processes requires flotation models that react to changes in the properties of the particle population. This study analyzes the capability of usual flotation models to respond to changes in the size and composition distributions of the feed particles. A particle size and composition dependent kinetic flotation model is used to generate synthetic data for varying feed particle composition, texture and size distribution. Then, six different models are calibrated on these synthetic data and assessed for their ability to predict the effects due to changes in particle properties. In spite of the flexibility of distributed flotation rate constants for fitting the effects of particle heterogeneity, all the models predict poorly the concentrate grade because they do not account explicitly for particle composition.Pour optimiser globalement les procédés de comminution et séparation, les modèles de flottation doivent être capables de réagir de façon réaliste aux changements des propriétés de la population de particules traitée. L’objectif de cette étude est d’évaluer les compétences des modèles usuels de simulation de la flottation à réagir aux changements de composition et de dimension des particules. La méthodologie de l’étude est basée sur l’utilisation de données de flottation synthétiques pour des populations de particules de granulométrie, libération et teneur variables. Six modèles cinétiques habituels, négligeant la mixité des particules, sont calibrés sur ces données et évalués selon leur aptitude à répondre adéquatement à des perturbations des propriétés structurales des particules. Malgré la flexibilité offerte par certains modèles au niveau de la distribution des constantes cinétiques, ils prédisent mal les teneurs de concentré pour des propriétés variables des particules, car ils ne tiennent pas compte de la distribution de composition des particules.
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