3. Electronic Theses and Dissertations (ETDs) - All submissions
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Item The application of the attainable region analysis in comminution.(2008-06-09T10:03:28Z) Khumalo, NgangezweABSTRACT This work applies the concepts of the attainable region for process synthesis in comminution. The attainable region analysis has been successfully applied for process synthesis of reactor networks. The Attainable Region is defined as the set of all possible output states for a constrained or unconstrained system of fundamental processes (Horn, 1964). A basic procedure for constructing the attainable region for the fundamental processes of reaction and mixing has been postulated in reaction engineering (Glasser et al., 1987). This procedure has been followed in this work to construct the candidate attainable region for size reduction processes as found in a size reduction environment. A population balance model has been used to characterise the evolution of particle size distributions from a comminution event. Herbst and Fuerstenau (1973) postulated the dependency of grinding on the specific energy. A specific energy dependent population balance model was used for the theoretical simulations and for the fitting of experimental data. A new method of presenting particle size distributions as points in the Euclidian space was postulated in place of the traditional cumulative distribution. This allows successive product particle size distributions to be connected forming a trajectory over which the objective function can be evaluated. The curve connects products from successive batch grinding stages forming a pseudo-continuous process. Breakage, mixing and classification were identified as the fundamental processes of interest for comminution. Agglomeration was not considered in any of the examples. Mathematical models were used to describe each fundamental process, i.e. breakage, mixing and classification, and an The application of the attainable region analysis in comminution Abstract algorithm developed that could calculate the evolution of product particle size distributions. A convex candidate attainable region was found from which process synthesis and optimisation solutions could be drawn in two dimensional Euclidian space. As required from Attainable Region Theory, the interior of the bounded region is filled by trajectories of higher energy requirements or mixing between two boundary optimal points. Experimental validation of the proposed application of the attainable region analysis results in comminution was performed. Mono-sized feed particles were broken in a laboratory ball mill and the products were successfully fitted using a population balance model. It was shown that the breakage process trajectories were convex and they follow first order grinding kinetics at long grind times. The candidate attainable region was determined for an objective function to maximise the mass fraction in the median size class 2. It was proved that the same specific energy input produces identical products. The kinematic and loading conditions are supposed to be chosen as a subsequent event after the required specific energy is identified. Finally the fundamental process of classification was added to the system of breakage and mixing. The attainable regions analysis affords the opportunity to quantify exactly the reduction in energy consumption due to classification in a comminution circuit, thus giving optimal targets. Classification showed the potential to extend the candidate attainable region for a fixed specific energy input. The boundary of the attainable region is interpreted as pieces of equipment and optimum process conditions. This solves both the original process synthesis and successive optimisation problems.Item Electric rock breaking for south african ore bodies(2007-02-28T12:48:09Z) Ilgner, Hartmut JohannesAlthough pulsed power has been used in many parts of the world over the last few decades to initiate high-voltage discharges through rock, no systematic test work on South African ore bodies and related rock types has been done so far. As part of CSIR Miningtek’s integrated approach of combining underground comminution with a novel Tore© hydrotransport system, which has been shown to operate well with coarse particles up to 10 mm, various rock types were fragmented in single discharge mode under laboratory conditions. The work was conducted at the University of the Witwatersrand’s high-voltage laboratory with a custom-designed test rig. The rig configuration was based on a critical review and analysis of the literature and on assessments of existing test facilities elsewhere. Core samples with diameters ranging from 16 to 48 mm were cut from test specimens with thicknesses ranging from 8 to 48 mm. Rock types included Ventersdorp Contact Reef, Carbon Leader, Elsburg Formation, UG2 and Merensky, as well as pure quartz, shales, lava and dykes. A six-stage Marx generator provided a voltage rise time of 2 000 kV/μs to create a discharge through the rock, in preference to a discharge through the surrounding water, which acts as an insulator at ramp-up times faster than 0,5 μs. High-speed photography, and an analysis of the voltage and current signals for various rock types and for water alone, were used to quantify the potential benefits of rock breaking by electric discharge. It was found that some Kimberlite specimens and mineralised gold-bearing reefs were much easier to fragment than hanging wall or footwall material. Merensky reef appeared to be more susceptible than the less brittle UG2 material. A correlation was derived between the dynamic resistivity of various rock types, measured at 16 MHz excitation frequency, and the electrical breakdown strength at which discharge took place. The fragments created had a more cubical shape than would be created by conventional impact crushing. However, the high voltage requirements of about 30 to 35 kV per millimetre of rock thickness would necessitate not only efficient mechanical and electrical contact between the electrodes and the rock, but also considerable safety features for underground installations. The clearly identified, preferential fracturing of reef rock types, compared with the hanging or footwall materials, suggests that the greater benefit of electric rock breaking may lie in primary rock breaking as a mining method, rather than in secondary comminution of broken rock to enable hydraulic transportation by pipeline to surface.Item Effects of grinding media shapes on ball mill performance(2006-10-31T06:53:13Z) Lameck, Niyoshaka Nistlaba StanleyComminution is an important process in mineral processing, power plants, cement production and pharmaceutical industries. It is costly and an inefficient process in terms of energy requirements and steel consumption related to grinding media and liners. Spherical grinding media are predominantly used in final stages of ore grinding. The spherical balls change shape through breakage and wear. Though this is universal in milling, its contribution and effect on milling kinetics, load behaviour and mill power is not fully established. One area that is usually ignored is the relationship between media shape and mill power. The objective of this dissertation was to investigate how media shape affects grinding. Ball size distribution inside an industrial mill was analysed in terms of shapes and sizes. Load behaviour, mill power and breakage as affected by media shapes were studied in a pilot laboratory mill. An inductive proximity probe, light emitting diode, phototransistor and video photographs were used to determine the load orientation in terms of toe and shoulder positions. A load beam was used to measure the torque exerted by the charge. The variation in load orientation and mill power with speed among different media shapes was observed. Higher shoulder positions were noted with cylpebs than with worn and spherical balls. The power increased to a maximum with increasing mill speed for all media shapes reaching its peak at different mill speeds for the three shapes studied. Variations of breakage rates with media shapes were found; higher breakage rates were noted with spherical media but the differences narrows with decreasing feed size and increasing material fractional filling U. Considering that worn balls in an industrial mill charge constitute about 15 to 40 percent and that the highest difference in breakage rate observed being nine percent for purely one shape charge; it is very doubtful whether it is worthwhile in attempting to develop techniques for removing worn balls from the mill.