Deriving the ideal ore texture for microwave treatment of metalliferous ores

High power density microwave treatments on metalliferous ores have historically been shown to reduce ore competency prior to beneficiation at economically feasible energy inputs. However, the relationship between mineralogical textural features and the extent of the microwave-induced fracturing had previously been limited to qualitative descriptions or simplistic two-phase numerical models, which could not account for the complex mineral assemblages in real ores. In this paper, mineralogy, grain size, dissemination, textural consistency and mineral associations were determined for 13 commercially exploited nickel, copper and lead-zinc ores using a Mineral Liberation Analyser (MLA). The ores were subjected to high power density microwave treatments at up to 25kW in a single mode cavity with microwave energy inputs of approximately 0.5-10kWh/t, and the subsequent reductions in ore competency were measured by the Point Load Test. The ores that demonstrated the greatest reductions in strength typically contained between approximately 2%wt to 20%wt of highly microwave-absorbing minerals, with a native grain size d50 greater than approximately 500µm, constrained by hard matrix minerals such as quartz and feldspar. Texturally consistent ores with a high proportion of amenable textures also demonstrated the highest average reductions in strength. These findings support the qualitative descriptions and numerical modelling results available in the literature and provide a baseline for selecting likely candidate ores for microwave treatments in the future

Increasing the grind size for effective liberation and flotation of a porphyry copper ore by microwave treatment

In this paper, mineralogy, grain size, dissemination, textural consistency and mineral associations were determined for a commercially exploited porphyry copper ore using a Mineral Liberation Analyser (MLA). The ore was subjected to high power density microwave treatments in a single mode cavity at 15 kW and approximately 2 kW h/t. The untreated and microwave-treated samples were subsequently milled to two grind sizes near the nominal plant grind size and a size-by-liberation analysis performed. The analysis revealed that equivalent liberation could be obtained at a grind size approximately 50–60 μm coarser than the nominal plant grind due to the microwave treatment. Flotation testing indicated that an increase in copper recovery of approximately 1% could be achieved, or that a grind size increase of approximately 30 μm may potentially yield equivalent copper recovery due to the microwave-enhanced liberation observed. However, statistical analyses demonstrated that it is difficult to attain confidence in recovery increases of approximately 1% even when conducting batch flotation tests in triplicate. The ore under investigation had previously been shown to produce only modest average reductions in strength (∼8%) under similar microwave treatment conditions due to a prevalence of many unfavourable textures. However, the preferential association of copper minerals with a hard matrix mineral (quartz) and a hard microwave-absorbent mineral (pyrite) resulted in a significant change in liberation behaviour

Towards large scale microwave treatment of ores: Part 1 – Basis of design, construction and commissioning

Despite over thirty years of work, microwave pre-treatment processes for beneficiation of ores have not progressed much further than laboratory testing. In this paper we present a scaleable pilot-scale system for the microwave treatment of ores capable of operating at throughputs of up to 150tph. This has been achieved by confining the electric field produced from two 100kW generators operating at 896MHz in a gravity fed vertical flow system using circular choking structures yielding power densities of at least 6x108 W/m3 in the heated mineral phases. Measured S11 scattering parameters for a quartzite ore (-3.69±0.4dB) in the as-built applicator correlated well with the simulation (-3.25dB), thereby validating our design approach. We then show that by fully integrating the applicator with a materials handling system based on the concept of mass flow, we achieve a reliable, continuous process. The system was used to treat a range of porphyry copper ores

Towards large scale microwave treatment of ores: Part 2 - Metallurgical testing

A pilot scale microwave treatment system capable of treating 10-150t/h of material at 10-200kW was designed, constructed and commissioned in order to understand the engineering challenges of microwave-induced fracture of ores at scale and generate large metallurgical test samples of material treated at approximately 0.3-3kWh/t. It was demonstrated that exposing more of the ore to a region of high power density by improving treatment homogeneity with two single mode applicators in series yielded equivalent or better metallurgical performance with up to half the power and one third the energy requirement of that used with a single applicator. Comminution testing indicated that A*b values may be reduced by up to 7-14% and that the Bond Ball Mill Work Index may be reduced by up to 3-9% depending on the ore type under investigation. Liberation analysis of the microwave-treated ore indicated that equivalent liberation may be achievable for a grind size approximately 40-70µm coarser than untreated ore, which is in agreement with laboratory scale investigations reported in the literature at similar or higher doses. Flow sheet simulations further indicated that reduced ore competency following microwave treatment could potentially yield up to a 9% reduction in specific comminution energy (ECS) at a nominal plant grind of P₈₀190µm, or up to 24% reduction at a grind of P₈₀290µm, for a microwave energy input of 0.7-1.3kWh/t. Throughput could also be increased by up to approximately 30% depending on grind size, ore type and equipment constraints. To date, approximately 900t of material has been processed through the pilot plant, approximately 300t of which was under microwave power. Metallurgical testing has demonstrated that comminution and liberation benefits are achievable at doses lower than that previously reported in the literature, which allow high throughputs to be sustained with low installed power requirements providing a pathway to further scale-up of microwave treatment of ores

Selberg Supertrace Formula for Super Riemann Surfaces III: Bordered Super Riemann Surfaces

This paper is the third in a sequel to develop a super-analogue of the classical Selberg trace formula, the Selberg supertrace formula. It deals with bordered super Riemann surfaces. The theory of bordered super Riemann surfaces is outlined, and the corresponding Selberg supertrace formula is developed. The analytic properties of the Selberg super zeta-functions on bordered super Riemann surfaces are discussed, and super-determinants of Dirac-Laplace operators on bordered super Riemann surfaces are calculated in terms of Selberg super zeta-functions.Comment: 43 pages, amste

Low-Prandtl-number B\'enard-Marangoni convection in a vertical magnetic field

The effect of a homogeneous magnetic field on surface-tension-driven B\'{e}nard convection is studied by means of direct numerical simulations. The flow is computed in a rectangular domain with periodic horizontal boundary conditions and the free-slip condition on the bottom wall using a pseudospectral Fourier-Chebyshev discretization. Deformations of the free surface are neglected. Two- and three-dimensional flows are computed for either vanishing or small Prandtl number, which are typical of liquid metals. The main focus of the paper is on a qualitative comparison of the flow states with the non-magnetic case, and on the effects associated with the possible near-cancellation of the nonlinear and pressure terms in the momentum equations for two-dimensional rolls. In the three-dimensional case, the transition from a stationary hexagonal pattern at the onset of convection to three-dimensional time-dependent convection is explored by a series of simulations at zero Prandtl number.Comment: 26 pages, 9 figure

Towards a Simple Model of Compressible Alfvenic Turbulence

A simple model collisionless, dissipative, compressible MHD (Alfvenic) turbulence in a magnetized system is investigated. In contrast to more familiar paradigms of turbulence, dissipation arises from Landau damping, enters via nonlinearity, and is distributed over all scales. The theory predicts that two different regimes or phases of turbulence are possible, depending on the ratio of steepening to damping coefficient (m_1/m_2). For strong damping (|m_1/m_2|<1), a regime of smooth, hydrodynamic turbulence is predicted. For |m_1/m_2|>1, steady state turbulence does not exist in the hydrodynamic limit. Rather, spikey, small scale structure is predicted.Comment: 6 pages, one figure, REVTeX; this version to be published in PRE. For related papers, see http://sdphpd.ucsd.edu/~medvedev/papers.htm

Supercoherent States, Super K\"ahler Geometry and Geometric Quantization

Generalized coherent states provide a means of connecting square integrable representations of a semi-simple Lie group with the symplectic geometry of some of its homogeneous spaces. In the first part of the present work this point of view is extended to the supersymmetric context, through the study of the OSp(2/2) coherent states. These are explicitly constructed starting from the known abstract typical and atypical representations of osp(2/2). Their underlying geometries turn out to be those of supersymplectic OSp(2/2) homogeneous spaces. Moment maps identifying the latter with coadjoint orbits of OSp(2/2) are exhibited via Berezin's symbols. When considered within Rothstein's general paradigm, these results lead to a natural general definition of a super K\"ahler supermanifold, the supergeometry of which is determined in terms of the usual geometry of holomorphic Hermitian vector bundles over K\"ahler manifolds. In particular, the supergeometry of the above orbits is interpreted in terms of the geometry of Einstein-Hermitian vector bundles. In the second part, an extension of the full geometric quantization procedure is applied to the same coadjoint orbits. Thanks to the super K\"ahler character of the latter, this procedure leads to explicit super unitary irreducible representations of OSp(2/2) in super Hilbert spaces of $L^2$ superholomorphic sections of prequantum bundles of the Kostant type. This work lays the foundations of a program aimed at classifying Lie supergroups' coadjoint orbits and their associated irreducible representations, ultimately leading to harmonic superanalysis. For this purpose a set of consistent conventions is exhibited.Comment: 53 pages, AMS-LaTeX (or LaTeX+AMSfonts

Understanding microwave induced sorting of porphyry copper ores

Global demand for minerals and metals is increasing. It has been established that the impact of mining and mineral processing operations must be reduced to sustainably meet the demands of a low grade future. Successful incorporation of ore sorting in flow sheets has the potential to improve energy efficiency by rejecting non-economic material before grinding. Microwave heating combined with infra-red temperature measurement has been shown to distinguish low and high grade ore fragments from each other. In this work, experimentally validated 2-D finite difference models of a theoretical two phase ore, representing typical fragment textures and grades, are constructed. Microwave heating is applied at economically viable energy inputs and the resultant surface thermal profiles analysed up to 2 minutes after microwave heating. It is shown that the size and location of grains can dramatically alter surface temperature rise at short thermal measurement delay times and that the range of temperatures increases with increasing fragment grade. For the first time, it is suggested that increasing the delay time between microwave heating and thermal measurement can reduce the variation seen for fragments of the same grade but different textures, improving overall differentiation between high and low grade fragments

Pilot scale microwave sorting of porphyry copper ores: Part 1: laboratory investigations

Microwave treatment followed by infrared thermal imaging (MW–IRT) has been proposed as a potential excitation-discrimination technique to facilitate sorting of porphyry copper ores. A continuous, high throughput (up to 100t/h), belt–based microwave cavity operating at up to 100kW has been designed to interface directly with commercially available sorters at industrially relevant scales. In this paper, the fragment-by-fragment thermal response of 16 porphyry copper ore samples following microwave treatment in the bespoke system is evaluated to elucidate key performance criteria and identify likely candidate ores for microwave sorting. Microwave treatment energy dose was found to be the driving force behind the ultimate average temperature fragments experience, with other process variables (e.g. belt speed, power, belt mass loading, thermal equilibration time) having little effect on sortability performance. While fragment mineralogical texture and ore textural heterogeneity were shown to influence the average temperature rise of the fragment surface presented to the thermal camera, in most cases this variability did not adversely affect sortability performance. An abundance of microwave-heating gangue minerals (e.g. iron sulphides, iron oxides and hydrated clays) was shown to be the dominant source of deviation from intrinsic sortability. However, low average moisture content and co-mineralisation of copper and iron sulphides (or bulk sulphide sorting) was found to mitigate the deviation and provide better sortability performance. An attractive separation could be proposed for many of the ores tested, either to remove a large proportion of barren fragments from ore-grade material or concentrate a large proportion of copper values from waste-grade material