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The coal fired power plants are one of the oldest, most common and wide spread generators of electricity. They utilise heat generated by burning coal, that is pulverised in different type of grinding machines selected based on the coal type that is being processed, to produce steam power. For bituminous coal, vertical spindle pulverisers are the preferred and most common equipment for pulverisation. In this thesis, the vertical spindle pulverisers were of interest and their operation is modelled. In order to achieve this goal, a sampling procedure was developed to collect samples from these pulverisers. A standard procedure for sample analyses was followed; and when required, new experimental and sampling tools were developed and manufactured. A multi-component data set of five industrial scale surveys was produced for the pulveriser operating at different coal and air flow conditions. The multi-component data are based on size and ash content as well as density for one test and the feed samples. The selected samples were classified into size-by-size density bins by float/sink density analysis. One of the general outcomes of using multi-component data was confirmation of the mineral matter accumulation in the mill showing its dependency on size. Moreover, the multi-component data were utilised to calculate the flow rates and unknown particle size distributions of the mill interior streams by mass balancing. Hence, the mill interior streams particle size distributions and flow rates, as well as size-by-size ash content distributions were obtained; thus the circulating loads that develop in the pulveriser were calculated. This information was used in constructing the ball feed stream via combining the reject streams with the coal fed to the pulveriser, which is the key stream to compute comminution information and model parameters. The mass balanced streams information were utilised to evaluate the classifications that occur in the pulveriser. The model parameters describing the classification curves that correspond to the two different zones in the pulveriser were found to be closely related to the operational conditions. A 3D multi-component breakage function was developed with the results obtained from compressive breakage tests. It is observed that the coal and mineral matter differ in breakage behaviour. This difference was incorporated into the 3D breakage model in order to be able to predict the breakage of these component particles and their composites. The mass balanced stream information together with the multi-component breakage function was utilised to successfully determine the rate of breakage of particles in the grinding zone. The model parameters describing the rate of breakage of the particles were found to be related to the operational variables. A demonstration of the developed approach was done using a simulator which linked comminution and classification models based on size and density components, to work in closed circuit operation. The classification function used in the overall simulation model was changed to an efficiency curve model based on settling velocities of particles to enable integration of both density and size of particles into the model; rather than employing empirical relations developed based only on particle size. Similarly, parameters for rate of breakage of particles have differed from that of parameters calculated during the computations for open circuit grinding conditions. The results obtained from the simulation studies were satisfactory in describing the existing conditions that occur in the pulveriser at all the sampled conditions. In conclusion, a mathematical model of an industrial scale ball-and-race pulveriser was developed by determining the effect of operational variables on the comminution and classification operations within the pulveriser.

This paper examines the hypothesis that the manual selection of rocks for inspection, testing or analysis is invariably biased towards the heavier (larger) particles in the population being sampled. If the property of interest, such as assay or breakage potential, is size-related then such a bias would lead to systematic errors in the estimation of this property. To test the hypothesis, human volunteers were asked to select a sample of 10 rocks from a tray of 100 rocks of known weights, with and without a blindfold, in duplicate. This was repeated for a number of different rock size ranges in the range −50 + 19 mm. A statistical analysis of the results confirms the hypothesis that in almost all cases the samples were of larger weight than that expected from the known weight of the population of rocks. The magnitude of the bias depended on conditions but was highest for the widest size range. It is also shown that the volunteers produced different results to each other. The blindfold reduced the bias in the narrow size ranges but increased it for the wide size range. These effects are likely to be less important for populations of narrow size range, but where a truly unbiased sample is required strategies are proposed using randomisation processes. Relying on unmoderated human selection will lead to samples which overestimate the weight of the population.

Single relations that can be used to calculate both the terminal settling velocities of spheres and the equivalent diameter of particles from their settling velocities are developed. The literature going back to Newton is reviewed and the relations developed tabulated. It is shown how the standard drag curve has developed into the dimensionless velocity versus dimensionless diameter curve. No relations that cover the full range that can conveniently be used for both velocity and diameter calculation were found, however a relation by Concha and Almendra covers most of the range. The standard drag curve data are constructed by utilizing 535 data points available in the literature in a Reynolds number range of 2.4 × 10−5 to 2 × 105. The settling velocities are corrected for experiments in finite width columns that do not satisfy the infinite medium dimensions. The data are converted to the dimensionless diameter and dimensionless velocity terms, which is more convenient for calculation purposes. The data are...

The breakage of a coal in compression tests has been studied with the aim of obtaining an appearance function giving the distribution resulting from the breakage of each particle type, which can be used in the simulation of vertical spindle mills that are commonly used in coal fired power plants. The appearance functions from the compression tests were found to take a linear form on logit axes (log(x/(x m − x))), thus giving a simpler description than is available on other axes. In common with other breakage analysis methods the lines can be identified by the percent passing one tenth of the initial size, the t 10 parameter. An exponential relation between t 10 and specific energy was found for each particle group defined by size and density and the parameters of the exponential relation were related to the particle size and density. It was found for this particular coal that breakage did not preferentially concentrate either coal or mineral matter. The relations developed allow the generation of a three dimensional breakage-appearance function for the breakage of both size and density components which can be used in the simulation of a pulveriser for the coal tested. The paper also demonstrates the type of test work required for the generation of appearance functions for other types of coal.

A new approach to identify multivariable Hammerstein systems is proposed in this paper. By using cardinal cubic spline functions to model the static nonlinearities, the proposed method is effective in modelling processes with hard and/or coupled nonlinearities. With an appropriate transformation, the nonlinear models are parameterized such that the nonlinear identification problem is converted into a linear one. The persistently exciting condition for the transformed input is derived to ensure the estimates are consistent with the true system. A simulation study is performed to demonstrate the effectiveness of the proposed method compared with the existing approaches based on polynomials. (C) 2006 Elsevier Ltd. All rights reserved.

In this paper, a new control design method is proposed for stable processes which can be described using Hammerstein-Wiener models. The internal model control (IMC) framework is extended to accommodate multiple IMC controllers, one for each subsystem. The concept of passive systems is used to construct the IMC controllers which approximate the inverses of the subsystems to achieve dynamic control performance. The Passivity Theorem is used to ensure the closed-loop stability. (c) 2005 Elsevier Ltd. All rights reserved.

A flexible design for computer programs to simulate mineral processing plants has been developed. A relaxation method is used to give rapid calculation of circulating loads and a Monte Carlo technique may be used to calculate accuracy estimates. Computer programs for the simulation of crushing and grinding plants have been written. An example, of the use of these, optimises a multi-stage grinding circuit. The design of a system of data structures for Fortran is presented to show how to increase the flexibility of future process simulation programs.A model building technique has been developed to take advantage of both theoretical and empirical information about the unit being modelled. The procedure is presented as a series of steps and a proposal to automate these steps is presented. An improved regression technique using spline functions in one or more variables instead of analytic functions was developed to aid the model building. This multiple spline regression has been extended to include, periodic spline functions. An example, to show how an analytic base for the model building technique can be derived, develops a matrix theory of comminutioi machines.Data from a large scale industrial crushing plant has been collected and used in the model building technique to obtain models of a cone crusher and a vibrating screen. These models were combined to produce a model of the complete crushing plant . Simulation of the plant was used to design and evaluate a control system which when installed on the plant provided a 15% to 20% increase in plant capacity, The optimum control settings for a delay line in this plant were also calculated. Further simulations have been used to calculate the operating curves for this plant under automatic control.

(2002). Application of a rock abrasion model to pilot-plant and plant data for fully and semi-autogenous grinding. Mineral Processing and Extractive Metallurgy: Vol. 111, No. 1, pp. 39-43.

The step size determines the accuracy of a discrete element simulation. The position and velocity updating calculation uses a pre-calculated table and hence the control of step size can not use the integration formulas for step size control. A step size control scheme for use with the table driven velocity and position calculation uses the difference between the calculation result from one big step and that from two small steps. This variable time step size method chooses the suitable time step size for each particle at each step automatically according to the conditions. Simulation using fixed time step method is compared with that of using variable time step method. The difference in computation time for the same accuracy using a variable step size (compared to the fixed step) depends on the particular problem. For a simple test case the times are roughly similar. However, the variable step size gives the required accuracy on the first run. A fixed step size may require several runs to check the simulation accuracy or a conservative step size that results in longer run times.

The Mathews method of predicting open-stope stability was first proposed in 1980. The initial stability graph was based on a limited number of case studies, primarily from deep, North American, steeply dipping open stopes in strong rocks of medium to good quality. Since then new data have been added by various practitioners to modify, update and validate the method and support its use as a preliminary open-stope design tool.The original Mathews method has been extended with use of a significantly increased database of mining case histories. The format of the Mathews stability graph has been changed to reflect the broader range of stope geometries and rock mass conditions now captured within the database. The extended database now contains in excess of 400 case histories.Logistic regression has been performed on this larger database to delineate and optimize placement of the stability zones statistically. Isoprobability contours have been generated for all stability outcomes. The advantage of the l...

When examining a rock mass, joint sets and their orientations can play a significant role with regard to how the rock mass will behave. To identify joint sets present in the rock mass, the orientation of individual fracture planes can be measured on exposed rock faces and the resulting data can be examined for heterogeneity. In this article, the expectation–maximization algorithm is used to fit mixtures of Kent component distributions to the fracture data to aid in the identification of joint sets. An additional uniform component is also included in the model to accommodate the noise present in the data.

Discrete element simulations not only require the calculation of the contact forces in the normal direction but also in the tangential direction. The dynamic friction model used for tangential calculations should include sliding and rolling friction models. A simple coefficient of rolling friction is found insufficient for the calculation of linear and angular motion in discrete element simulation. It is shown how sliding and rolling friction can be introduced into efficient calculation methods for discrete element simulation.

The contact force calculation using in discrete element simulation is typically calculated by single spring and damping models. It is found that the commonly used linear model gives unrealistic behaviour. A non-linear model of Tsuji [4] combined with the correct separating time gives more realistic results. Single spring and damping does not allow particles with different surface properties. A double spring and damping model: each particle with a separate spring and damping, is presented in this paper so that the different surface properties of each particle can be taken into account. To simply the calculations for particles with different surface properties, two methods of matching double spring-damping models to single spring-damping models are presented in this paper.

Discrete element models can be widely applied in simulation of many types of physical systems including mineral processing and mining. The simulation process requires the calculation of the motion of each discrete element. The existing calculation methods are time consuming and often have been simplified to give unrealistic behaviour. A fast calculation method using a realistic force model has been developed. This method sepa rates the solution of the differential equation of motion from the discrete element simulation process. It can result in improved accuracy and speed in certain types of simulations.

The Halton, Sobol, and Faure sequences and the Braaten-Weller construction of the generalized Halton sequence are studied in order to assess their applicability for the quasi Monte Carlo integration with large number of variates. A modification of the Halton sequence (the Halton sequence leaped) and a new construction of the generalized Halton sequence are suggested for unrestricted number of dimensions and are shown to improve considerably on the original Halton sequence. Problems associated with estimation of the error in quasi Monte Carlo integration and with the selection of test functions are identified. Then an estimate of the maximum error of the quasi Monte Carlo integration of nine test functions is computed for up to 400 dimensions and is used to evaluate the known generators mentioned above and the two new generators. An empirical formula for the error of the quasi Monte Carlo integration is suggested.

Discrete element simulations can be used to model the behaviour of both fluids and contacting particles in a very flexible manner. These simulations have wide applications in both mining and mineral processing. They require the calculation of forces between the discrete elements used in the simulation typically by assuming spring, dashpot and slider components at the contact points. The accuracy of the simulations depends on the assumptions mide in the calculation of interelement forces. The different methods that can be used to calculate the forces have been examined and unrealistic behaviour found for most of methods commonly used. The non-linear force formula of Tsuji et al., Powder Technol., 71 (1992) 239, with the particles separating when the force returns to zero rather than when the distance between the centres exceeds the sum of the radii is found to give realistic results.

Monte Carlo and quasi Monte Carlo (ie using low discrepancy sequences) methods (Bratley & Fox 1988, Joe & Sloan 1993, Krommer & Ueberhuber 1994, Lyness 1989, Niederreiter 1978, Sloan & Kachoyan 1987) are used to approximate an integral by the average value of function samples:[EQUATION 1]where v is the volume of integration (taken here to be the unit multi-dimensional cube) and x is a vector with an element for each of the dimensions of the multidimensional space. In the case of Monte Carlo the points x p are chosen at random, while in quasi Monte Carlo the points are chosen to cover the integration volume as uniformly as possible. For numerical integration over a large number of dimensions these two techniques are often the only methods available.

Unknown parameter relations within a non-linear model can be investigated by linearising and the creation of an artificial zero point from which the parameter relation can be constructed using linear regression techniques.

The flow split between the products of a hydrocyclone is one of the least understood aspects of hydrocyclone operation. This split is greatly influenced by the air core diameter, so an understanding of the air core behaviour would greatly assist in predicting flow splits. A program of combined theoretical and experimental investigation of the factors that control the air core in a hydrocyclone is being undertaken. Rietema type simplifications of the Navier Stokes equations have been extended to include the prediction of air core diameter. The equations which are indirect in their original form have been converted to give a direct solution for the dimensionless pressure and air core diameter ratio. An experimental program using simplified test units has been undertaken. This has obtained pressure drop, air core diameter and velocity profile data over a considerable range of operating conditions. This data is being used to identify and correct deficiencies in the theoretical analysis, and to investigate the range of validity of the resulting relations. The aim is to produce simple relations that can be used to improve the accuracy of typical simulations of hydrocyclone performance, and also to provide some guidance in the design of hydrocyclones.

Deficiencies in the description of pulp properties is a major factor limiting improvements in modelling of the flow within mineral processing separation devices such as jigs and cyclones. Two factors severely hamper the development of accurate descriptions of pulp rheology - the large number of variables which influence pulp behaviour and the difficulty of making accurate measurements of pulp viscosity. Many factors make measurements of pulp viscosity difficult, including wall effects, turbulence, setting and the physical size of particles, particularly at high shear rates. This paper examines the measurement of pulp viscosity using capillary viscometers, and in particular the high shear rate regions for which turbulent flow (or the transition to turbulent flow) occurs. The results show a marked difference in the behaviour of the pulps in this regime compared to Newtonian fluids. This is significant for hydrodynamic simulations of pulps at high shear rates.

This paper presents an evaluation study of the use of newly developed clustering tools for on-stream analysis instrument calibration at Western Mining Corporation's Leinster Nickel Operations. In this application, data corresponding to different ore types are present. This causes unsatisfactory instrument calibration using existing methods. The clustering program is able to identify the distinct regions and superior predictive capabilities from the equipment are demonstrated. The use of an on-line expert system (which utilises the clusters as its knowledge base) to enhance analyser performance and identify instrument and plant anomalies is also discussed.

A technique for fitting a linear expression to data with errors in all or any of the variables is described. The form of the errors is restricted to the product of a row (data set) and a column (variable) error value. This form covers many practical cases and allows the development of an efficient algorithm.

Data from ball mills with a wide range of diameters are analyzed using detailed mathematical/numerical models. Analysis shows the relative power inefficiency of large ball mills is due to their inefficient breakage of coarse particles. The models developed can be used to scale-up mill behavior. The behavior of large mills at Bougainville and Pinto Valley is compared. It is concluded that the mills are equally inefficient at grinding coarse particles. Differences in coarseness of total mill feed are shown to account for the fact that Pinto Valley mills achieved design throughput whereas Bougainville mills did not.

Airport mean wind and gust speed data is used with past and future simulated data to estimate the maximum gust speed for a 500 year return period. It is demonstrated that the instantaneous speeds lead to the same result as data giving maximums over some time period. The airport mean wind speed was related to the gust speed, and the future simulations related to the past simulations. However, the relation between measured airport data and the simulations is poor. A Weibull distributions fitted to the upper part of the gust data is extrapolated to give the 500 year return period. An alternative approach using techniques similar to some actuarial analyses is also demonstrated.