Determination of lifter design, speed and filling effects in AG mills by 3D DEM

The power required to operate large gyratory mills often exceeds 10 MW. Hence, optimisation of the power consumption will have a significant impact on the overall economic performance and environmental impact of the mineral processing plant. In most of the published models of tumbling mills (e.g. [Morrell, S., 1996. Power draw of wet tumbling mills and its relationship to charge dynamics, Part 2: An empirical approach to modelling of mill power draw. Trans. Inst. Mining Metall. (Section C: Mineral Processing Ext. Metall.) 105, C54-C62. Austin, L.G., 1990. A mill power equation for SAG mills. Miner. Metall. Process. 57-62]), the effect of lifter design and its interaction with mill speed and filling are not incorporated. Recent experience suggests that there is an opportunity for improving grinding efficiency by choosing the appropriate combination of these variables. However, it is difficult to experimentally determine the interactions of these variables in a full scale mill. Although some work has recently been published using DEM simulations, it was basically. limited to 2D. The discrete element code, Particle Flow Code 3D (PFC3D), has been used in this work to model the effects of lifter height (525 cm) and mill speed (50-90% of critical) on the power draw and frequency distribution of specific energy (J/kg) of normal impacts in a 5 m diameter autogenous (AG) mill. It was found that the distribution of the impact energy is affected by the number of lifters, lifter height, mill speed and mill filling. Interactions of lifter design, mill speed and mill filling are demonstrated through three dimensional distinct element methods (3D DEM) modelling. The intensity of the induced stresses (shear and normal) on lifters, and hence the lifter wear, is also simulated. (C) 2004 Elsevier Ltd. All rights reserved.

Flexible synthesis of enantiomerically pure 2,8-dialkyl-1,7-dioxaspiro[5.5]undecanes and 2,7-dialkyl-1,6-dioxaspiro[4.5]decanes from propargylic and homopropargylic alcohols

A new approach to enantiomerically pure 2,8-dialkyl-1,7-dioxaspiro[5.5]undecanes and 2,7-dialkyl-1,6-dioxaspiro [4.5] decanes is described and utilizes enantiomerically pure homopropargylic alcohols obtained from lithium acetylide opening of enantiomerically pure epoxides, which are, in turn, acquired by hydrolytic kinetic resolution of the corresponding racemic epoxides. Alkyne carboxylation and conversion to the Weinreb amide may be followed by triple-bond manipulation prior to reaction with a second alkynyllithium derived from a homo- or propargylic alcohol. In this way, the two ring components of the spiroacetal are individually constructed, with deprotection and cyclization affording the spiroacetal. The procedure is illustrated by acquisition of (2S,5R,7S) and (2R,5R,7S)-2-n-butyl-7-methyl-1,6-dioxaspiro[4.5]-decanes (1), (2S,6R,8S)-2-methyl-8-n-pentyl-1,7-dioxaspiro[5.5]undecane (2), and (2S,6R,8S)-2-methyl-8-n-propyl-1,7-dioxaspiro[5.5]undecane (3). The widely distributed insect component, (2S,6R,8S)-2,8-dimethyl-1,7-dioxaspiro[5.5]undecane (4), was acquired by linking two identical alkyne precursors via ethyl formate. In addition, [H-2(4)]-regioisomers, 10,10,11,11-[H-2(4)] and 4,4,5,5-[H-2(4)] of 3 and 4,4,5,5-[H-2(4)]-4, were acquired by triple-bond deuteration, using deuterium gas and Wilkinson's catalyst. This alkyne-based approach is, in principle, applicable to more complex spiroacetal systems not only by use of more elaborate alkynes but also by triple-bond functionalization during the general sequence.