A study on the optimization of the arrangement of flotation circuits

The optimum utilization of available plant capacity has been investigated by simulation of a three-stage flotation circuit. By using simple models of the flotation process a wide variety of cell arrangements has been investigated and the findings tested against a number of operating flotation plants. It is concluded that the efficiency of operation of flotation systems is rather insensitive to circuit arrangement unless the circuit becomes grossly unbalanced. Circuit performance is much more sensitive to the flotation conditions and selectivity in the banks and it is only if a new circuit configuration leads to significantly improved flotation conditions that real improvements are likely. Simulation studies would require detailed modelling of such effects to be useful for circuit optimization studies.     

An analysis of the dynamic characteristics of flotation circuits by time-series analysis

Time-series analysis techniques are used to investigate the dynamic characteristics of the flotation circuits on the Renison tin concentrator in Tasmania. Routine plant-operating data provide information on the variability of feed streams, the disturbances resulting from normal manual operation, the suitability of certain locations for sitting instruments, and some simple time delays in the circuit. It is also shown how plant upsets and abnormal conditions caused by large perturbations to the operation can prove useful in such studies. Finally, a dynamic experiment is described which shows that disturbances higher in frequency than those in the feed are induced in the roughing and scavenging operations, but that these are filtered out again in the cleaner circuit. The uses and limitations of these techniques are discussed.     

The optimisation of flotation networks

The generalised optimisation of a flotation network is studied by means of using variable connections (structural parameters) and variable enhancement factors which are used instead of a flotation model to describe the separation process. The enhancement factors are functions of variables affecting the flotation process. These functional relationship may be derived by means of using a flotation model. Bounds are placed on the enhancement factors by means of either using a flotation model or by inspection of existing pilot or commercial plant data. These bounds, together with external, system and mass balance constraints and an appropriate objective function, define the general optimisation problem for a flotation network.The optimisation problem above may be solved by non-linear programming methods, however, it is easily transformable into a Linear Programme which is easy to solve. The procedure has been applied to a flotation circuit comprising three banks of cells for which an optimal set of connections and enhancement factors has been computed for varying constraints.A simulation procedure based on a gamma flotation model has been applied to one of the optimal circuits so as to compute the flotation variables.     

Dynamic model of flotation cell banks — circuit analysis

While all mineral industry flotation circuits are stable, they are sensitive to low-frequency perturbations in the feedrate. In both countercurrent and cocurrent circuits, the lead cell is more sensitive to feed variations. The frequency response predicts the amount of extra cell capacity needed to handle the maximum feed due to a sinusoidal forcing function. Feedback loops are more significant than sump delays. The countercurrent $\text{4 × 4}$ circuit floating quartz, with a 200-sec retention time, requires 75 minutes for the concentration of quartz in the input to the first cell to reach 95% of its steady-state value. Countercurrent circuits were found superior to cocurrent circuits in all respects.     

Analysis and optimization of mineral processing and coal-cleaning circuits — Circuit analysis

In mineral processing and coal cleaning operations, there are two classes of unit operations used in the separation processes. The first type — crushing, grinding, pelletizing and settling — modifies the size distribution of the feed. The second type — heavy media, sizing, flotation, magnetic, electrostatic and jigging — separates the particles. In these latter unit operations, the size distribution is not changed; rather, the feed stream is split into a product and waste stream based on subtle physical and physicochemical differences between the different types of feed particles. In separation unit operations, the mathematical functions, representing the behavior of the unit operations, are easy to manipulate. Thus, a number of theorems, useful to both the plant designer, and the plant engineer, can be proven.The work presented in this paper makes the fundamental assumption of linearity as do all current plant design analysis systems. The linearity assumption states that in a separation operation, there is no particle-particle interaction effecting the probability that a particle will be selected for the product or waste stream. In other words, if one doubles or triples the feed rate to a unit operation, the fraction of particles of a given characteristic selected to appear in the product stream remains unchanged. In actuality, this assumption is not true because higher feed rates affect the behavior of separation operations. However, when designing a plant, one can calculate the feed rate to a given unit operation and then select a piece of equipment large enough to handle the computed tonnage. Thus, the designed circuit behaves linearly.     

复杂开挖过程FLAC3D力学仿真代码生成系统研究

针对直接采用FLAC3D编制复杂开挖过程力学仿真程序所遇到的困难,开发了FLAC3D力学仿真程序代码生成系统(generating code system,简称GCS)。介绍了如何利用矿用地质软件Surpac,按空间、次序、结构功能及工程地质体属性对复杂开挖过程进行剖分,形成可编程的组件;着重解决了模型单元质心定位、单元捕捉、重组和应用程序变量到FLAC3D变量、函数、语句、数据结构之间映射等问题;使用VC++开发并给出了一个特定回采开挖过程的FLAC3D力学仿真代码生成系统实例,该应用程序以模型单元数据库为数据源,通过一系列与用户交互的页面,由用户对回采开挖过程所需步骤和参数进行选择和确认,并将这些步骤和参数传递给仿真代码生成系统,由系统自动完成FLAC3D力学仿真代码的生成。FLAC3D力学仿真程序代码生成系统架起了地质三维几何造型软件与三维计算软件之间的桥梁,可大大提高编制FLAC3D三维力学仿真代码的效率,降低程序编制的出错率,有利于应用FLAC3D软件更为深广地解决复杂岩土开挖过程中的力学问题。     

Effect of a material-flow model in prediction of particle-size distributions in open- and closed-circuit mills

A size-continuous breakage-kinetics model is postulated and supported with industrial grinding-mill data. It is shown that the kinetics parameters include the effects of possible classification at the mill discharge. The estimated parameters were then used in the kinetics model to simulate the behavior of a grinding mill in open- and closed-circuit operation. While material transport and kinetics are equally important in open-circuit operation, heavy recycle in a closed circuit makes a detailed material-transport model for grinding unnecessary. In effect, the mill can be considered as backmixed. This suggests that more emphasis should be placed on modelling the classifier than the development of detailed material-transport models for the grinding mill.     

Modelling the performance of industrial ball mills using single particle breakage data

Ball milling is an energy-intensive unit operation and usually consumes a major proportion of the power drawn by a typical mineral processing plant. Hence, substantial economic benefits can be achieved by optimal design and by operating ball milling circuits under optimum process conditions. This requires an accurate ball mill modelling technique.In the multi-segment ball mill model, the size-dependent material transport within the mill varies systematically with the amount of coarse particles present in each segment. The ore-specific breakage distribution function can be determined from single particle breakage tests conducted using a computer-monitored twin pendulum apparatus. When the ore-specific breakage distribution function is used in the multi-segment, a constant relationship between the breakage rate parameters and mill diameter is observed. Thus, the performance of an industrial ball mill can be adequately described using the ore-specific breakage distribution function together with the systematic variation of the material transport and the breakage rate functions with process conditions and mill diameter, respectively.This ball mill modelling technique is illustrated using a case study on the design of a ball milling circuit for a particular grinding requirement and another case study on modelling the performance of an industrial ball milling circuit.     

Further studies on the use of classifiers for the control of wet grinding circuits

The use of inferential particle sizing for wet grinding circuit control is well established in the literature. In this paper an analytical development is presented which yields a general inferential sizing model relating circuit product size to $\text{d}{}_{50}$ corrected for the circuits' classifier. It is then shown how the different forms of empirical equations reported in the literature can arise, depending on the range of the operating variables and the ratio of feed 50% passing size to $\text{d}{}_{50}$ corrected. Following this development, data show pilot plant and industrial plant operations to behave as predicted by the general inferential size model.     

Roughing and cleaning flotation behaviour and the realistic simulation of complete plant performance

Data are presented which illustrate a range of flotation behaviour observed for roughing and cleaning operations in industrial plants. Differences are observed in the size by size recoveries in cleaner flotation from those measured in the roughers.The implications of these differences to flotation modelling are discussed, and the importance of conducting confirmatory laboratory batch flotation tests is emphasized.Batch flotation tests have indicated that for certain minerals the flotation characteristics in the cleaner tests are substantially different from those in rougher tests conducted under the same conditions of pulp level, impeller speed, aeration rate and froth removal. The differences are most pronounced for the coarse particles.Computer simulations of a rougher-cleaner circuit have been done to illustrate the effects of these differences on predicted circuit performance. The differences are significant and arise mainly from differences in the behaviour of coarse particles.     

A rational interpretation of the role of particle size in flotation

From the examination of data from detailed plant surveys and associated laboratory batch testing, the principal effects of particle size in flotation have been identified. The current state of knowledge concerning the role of this variable is discussed in terms of the evidence presented. It is concluded that the minimum degree of hydrophobicity necessary for the flotation of a particle depends upon its size and as a result, recovery-size curves are a valuable diagnostic aid to the assessment of flotation performance. Entrainment is shown to be an important contributory mechanism to the recovery of fine particles which, when coupled with a low rate of genuine flotation, can account for much of the observed behaviour of such fines. The significance of particle size and its consequences in flotation research, in plant operations and in control schemes has been under-rated. The separate conditioning or flotation or both of separate size fractions seems inevitable as ores become increasingly difficult to concentrate.     

Beneficiation of sillimanite by column flotation—a pilot scale study

A fully automated semi-commercial flotation column incorporating state of the art instruments was designed to study the amenability of flotation column for the beneficiation of different minerals. In the present study, beneficiation of sillimanite was investigated by installing the flotation column in the flotation circuit of Orissa Sands Complex, Indian Rare Earths Limited, Chatrapur, Orissa. The effect of process parameters on sillimanite grade and recovery was investigated. At optimum conditions, the flotation column was operated continuously with a feed rate of one ton per hour and demonstrated the efficiency of the technology for the beneficiation of sillimanite. The results show that a concentrate assaying 96% sillimanite at 90% recovery can be obtained in a single column flotation stage.     

The effect of hydrodynamic conditions on true flotation and entrainment in flotation of a complex sulphide ore

The separation efficiency and selectivity of flotation are directly proportional to recoveries of the mineral species in the feed due to true flotation and entrainment. In this study, effects of the hydrodynamic conditions on true flotation and entrainment were investigated by using a fractional factorial experimental design. A method previously described in the literature was applied to determine the contributions of true flotation and entrainment in flotation of a complex sulphide ore. In order to apply the method, the kinetic flotation tests were conducted under various hydrodynamic conditions defined by some physical variables. Some of these tests were conducted in the presence and absence of a collector to evaluate the self-induced floatability. The selectivity index of the mineral species for entrainment was seen to be suitable evaluation of the non-selectivity and efficiency of the entrainment. Furthermore, the results of the size-by-size analysis of the froth products indicated that the presence of the self-induced hydrophobic particles in the feed is as important as the presence of very fine particles for accurate estimation of true flotation and entrainment in flotation of a complex sulphide ore. In addition, the estimated results for entrainment in flotation of the complex sulphide ore can be misleading. Therefore, a new approach would be necessary to determine the contributions of true flotation and entrainment in flotation of a complex sulphide ore.     

Froth structure in continuous flotation cells: Relation to the prediction of plant performance from laboratory data using process models

The paper discusses the obstacles in the way of making mathematical models of flotation circuits for use in process design; and describes also a route towards simple, but practical, models of full-scale flotation plant performance, which overcome the major problems. The principal difficulties lie in simulating the froth processes at full-scale. Timed batch tests may be used to identify the pulp-froth transfer processes, and steady-state (“equilibrium”) cell tests may be used to identify static froth concentration profiles. Froth mobility in a real cell is different from that in an “equilibrium” cell, and this paper shows how these dynamic patterns have been investigated, and may be used to simulate full-scale circuits. It is shown that it is not possible, at the present time, to completely eliminate judgement and experience from the establishment of parameter values; but the position should improve as experience accumulates.     

Predicting contaminant fate and transport in sediment caps: Mathematical modelling approaches

Sediment capping is a remedial option for managing contaminated sediments that involves the artificial placement of a layer of material over a contaminated area. Sorbent materials such as activated C and coke can be used to amend sand caps to improve cap performance. In this study, analytical and numerical modelling approaches were compared for predicting contaminant fate and transport in sediment caps using several diffusion-controlled and advection-dominated contaminant transport scenarios. An analytical tool was used to predict cap performance at steady-state. These results were compared with the results from the numerical CoReTranS model in which the effective diffusivity and degradation rates were modelled as discontinuous functions at a prescribed bioturbation depth. The numerical approach was also applied to modelling a sorptive cap. It was shown that, while the analytical approach can be used to predict steady-state contaminant transport, the numerical approach is needed to evaluate multiple sediment layers with different transport and sorption characteristics and to examine the transient performance between the time that the single layer transient is applicable (i.e., before penetration of the cap containment layer) and until steady-state in the upper layer. For the 30 cm thick sand cap that was considered in this study, the predicted time to reach steady-state conditions for a diffusion-controlled scenario is 1 ka. For an advection-dominated transport, the time to reach steady-state conditions is reduced to 100 a. The activated C-amended sand cap was more effective in isolating the contaminant within the sorbent layer for a sustained period of time (∼100 a). Results from both modelling approaches showed that capping can effectively reduce contaminant flux to the overlying water with critical variables being cap thickness, groundwater velocity, and sediment sorptivity.     

A compartment model for the mass transfer inside a conventional flotation cell

A model is developed by taking into account the simultaneous mechanisms of true flotation and entrainment in a conventional flotation cell. The total volume of the cell is divided into three compartments: pulp collection zone, pulp quiescent zone and froth region, with the mechanisms being modeled as occurring at the same time but originating at different places: true flotation from the collection zone and entrainment from the quiescent one. A particle is referred to as suspended in water or attached to an air bubble, depending upon its original state before crossing the pulp–froth interface (whether or not it remains in that state all the way to the concentrate launder). The model is obtained by solving a set of equations describing the mass conservation of solids and water between adjacent compartments. The principal mass transfer factors are identified as: the flotation rate constant, the mean residence time in the collection zone, the froth recovery of attached particles, the degree of entrainment through the froth and the water recovery from the feed to the concentrate. The development presented here allows the intricate nature of the mass transfer in a flotation cell to be reduced to one single equation, overcoming the need of numerical methods for simulation purposes. Moreover, it is shown that reliable prediction of grade and recovery can be obtained without detailed information on the pulp hydrodynamics or on any froth sub-process either than drainage, bubble bursting and bubble coalescence.     

A numerical sandbox: high-resolution distinct element models of halfgraben formation

Basin-scale tectonics and sedimentation are studied using particle flow code (PFC), a special implementation of the distinct-element method (DEM) using circular elements. Special focus is on the development and application of new techniques, which allow for strain weakening and localisation effects and, thus, the formation of discrete fault patterns in high-resolution DE models.Fundamental modelling assumptions and the procedures necessary to define the microproperties of a DE material from given rock mechanical data are first explained. Recent methodical enhancements, consisting of automatic fault detection (AFD) and intelligent crack management (ICM) algorithms are also discussed. Refined DE modelling techniques are then applied to three scenarios of extensional basin formation, i.e. the evolution of halfgrabens above detachments with simple listric and ramp–flat–ramp geometries, respectively. Numerical modelling results compare favourably with the analogue (‘sandbox’) models widely used in this kind of basin studies. Not only do they reproduce the general basin architecture (e.g. roll-over anticlines and crestal collapse grabens), but also detailed fault structure and the sequence of faulting. In addition, numerical models can describe temporal changes in mechanical material properties to model compaction and diagenesis of syntectonic sediments.     

Liberation-limited grade/recovery curves from X-ray micro CT analysis of feed material for the evaluation of separation efficiency

Procedures for 3D mineral liberation analysis by X-ray micro CT (XMT) are presented and discussed including the construction of liberation-limited grade/recovery curves for specific feed materials. In this way, actual separation efficiencies can be compared to what might be expected for a perfect separation limited only by the extent of liberation. It is shown that 3D mineral liberation analysis based on XMT is preferred to 2D section analysis which overestimates the extent of liberation. By way of example, procedures and experimental results are presented and discussed for feed material in the case of phosphate rock flotation.     

The effect of air flow rate on the kinetics of flotation. Part 1: The transfer of material from the slurry to the froth

Bubble size distributions and flotation rates were determined as a function of air flow rate and frother concentration using a specially designed batch flotation cell. This cell permitted the unambiguous determination of the flotation rate from the slurry to the froth.Flotation rate constants were determined for different size classes of silica and galena. The flotation rate constants increased to a maximum and then decreased as air flow rate was increased. This maximum was predicted by a model which considered the effect of bubble size on both the total bubble surface area and the bubble-particle collision efficiency. This work shows that collision efficiency effects, shown to exist in single-bubble/single-particle systems, are also present in flotation systems where many bubbles and particles interact.A second model for hindered flotation is proposed which assumes that the particle-capturing bubble surface differs from the particle-retaining surface. This model predicts a sharp transition from hindered to free flotation. Experimental results are presented which agree well with those derived from the model.