Influence of charge size distribution on net-power draw of tumbling mill based on DEM modelling

Modelling and optimization of the power draw of large SAG/AG mills is important due to the large power draw which modern mills require (5-10 MW). The cost of grinding is the single biggest cost within the entire process of mineral extraction. Traditionally, modelling of the mill power draw has been done using empirical models. Although these models are reliable, they cannot model mills and operating conditions which are not within the model database boundaries. Also, due to its static nature, the impact of the changing conditions within the mill on the power draw cannot be determined using such models. Despite advances in computing power, discrete element method (DEM) modelling of large mills with many thousands of particles could be a time consuming task. The speed of computation is determined principally by two parameters: number of particles involved and material properties. The computational time step is determined by the size of the smallest particle present in the model and material properties (stiffness). In the case of small particles, the computational time step will be short, whilst in the case of large particles; the computation time step will be larger. Hence, from the point of view of time required for modelling (which usually corresponds to time required for 3-4 mill revolutions), it will be advantageous that the smallest particles in the model are not unnecessarily too small. The objective of this work is to compare the net power draw of the mill whose charge is characterised by different size distributions, while preserving the constant mass of the charge and mill speed. (C) 2004 Elsevier Ltd. All rights reserved.

Particle number emissions and source signatures of an industrial facility

The work presented was conducted within the scope of a larger study investigating impacts of the Stuart Oil Shale project, a facility operating to the north of the industrial city of Gladstone, Australia. The aims of the investigations were threefold: (a) the identification of the plant signatures in terms of particle size distributions in the submicrometer range (13-830 nm) through stack measurements, (b) exploring the applicability of these signatures in tracing the source contributions at locations of interest, at a distance from the plant, and (c) assessing the contribution of the plant to the total particle number concentration at locations of interest. The stack measurements conducted for three different conditions of plant operation showed that the particle size distributions were bimodal with average modal count median diameters (CMDs) of 24 (SD 4) and 52 (SD 9) nm. The average of all the particle size distributions recorded within the plant sector at a site located 4.5 km from the plant, over the sampling period when the plant was operating, also showed a bimodal distribution. The modal CMDs in this case were 27 and 50 nm, similar to those at the stack. This bimodal size distribution is distinct from the size distribution of the most common ambient anthropogenic emission source, which is vehicle emissions, and can be considered as a signature of this source. The average contribution of the plant (for plant sector winds) was estimated to be (10.0 +/- 3.8) x 10(2) particles cm(-3) and constituted approximately a 50% increase over the local particle ambient concentration for plant sector winds. This increase in particle number concentration compared to the local background concentration, while high compared to the clean environment concentration, is not significant when compared to concentrations generally encountered in the urban environment of Brisbane.

Flow regime, hydrodynamics, floc size distribution and sludge properties in activated sludge bubble column, air-lift and aerated stirred reactors

This paper presents a comparative study how reactor configuration, sludge loading and air flowrate affect flow regimes, hydrodynamics, floc size distribution and sludge solids-liquid separation properties. Three reactor configurations were studied in bench scale activated sludge bubble column reactor (BCR), air-lift reactor (ALR) and aerated stirred reactor (ASR). The ASR demonstrated the highest capacity of gas holdup and resistance, and homogeneity in flow regimes and shearing forces, resulting in producing large numbers of small and compact floes. The fluid dynamics in the ALR created regularly directed recirculation forces to enhance the gas holdup and sludge flocculation. The BCR distributed a high turbulent flow regime and non-homogeneity in gas holdup and mixing, and generated large numbers of larger and looser floes. The sludge size distributions, compressibility and settleability were significantly influenced by the reactor configurations associated with the flow regimes and hydrodynamics.

Application of density functional theory to analysis of energetic heterogeneity and pore size distribution of activated carbons

A new approach based on the nonlocal density functional theory to determine pore size distribution (PSD) of activated carbons and energetic heterogeneity of the pore wall is proposed. The energetic heterogeneity is modeled with an energy distribution function (EDF), describing the distribution of solid-fluid potential well depth (this distribution is a Dirac delta function for an energetic homogeneous surface). The approach allows simultaneous determining of the PSD (assuming slit shape) and EDF from nitrogen or argon isotherms at their respective boiling points by using a set of local isotherms calculated for a range of pore widths and solid-fluid potential well depths. It is found that the structure of the pore wall surface significantly differs from that of graphitized carbon black. This could be attributed to defects in the crystalline structure of the surface, active oxide centers, finite size of the pore walls (in either wall thickness or pore length), and so forth. Those factors depend on the precursor and the process of carbonization and activation and hence provide a fingerprint for each adsorbent. The approach allows very accurate correlation of the experimental adsorption isotherm and leads to PSDs that are simpler and more realistic than those obtained with the original nonlocal density functional theory.

Rotary atomizer drop size distribution database

Wind tunnel measurements of drop Size distributions from Micronair A U4000 and A U5000 rotary atomizers were collected to develop a database for model use. The measurements varied tank mix, flow rate, air speed, and blade angle conditions, which were correlated by multiple regressions (average R-2 = 0.995 for A U4000 and 0.988 for AU5000). This database replaces an outdated set of rotary atomizer data measured in the 1980s by the USDA Forest Service and fills in a gap in data measured in the 1990s by the Spray Drift Task Force. Since current USDA Forest Service spray projects rely on rotary atomizers, the creation of the database (and its multiple regression interpolation) satisfies a need seen for ten years.

Adsorption in slit pores and pore-size distribution: A molecular layer structure theory

A new approach is developed to analyze the thermodynamic properties of a sub-critical fluid adsorbed in a slit pore of activated carbon. The approach is based on a representation that an adsorbed fluid forms an ordered structure close to a smoothed solid surface. This ordered structure is modelled as a collection of parallel molecular layers. Such a structure allows us to express the Helmholtz free energy of a molecular layer as the sum of the intrinsic Helmholtz free energy specific to that layer and the potential energy of interaction of that layer with all other layers and the solid surface. The intrinsic Helmholtz free energy of a molecular layer is a function (at given temperature) of its two-dimensional density and it can be readily obtained from bulk-phase properties, while the interlayer potential energy interaction is determined by using the 10-4 Lennard-Jones potential. The positions of all layers close to the graphite surface or in a slit pore are considered to correspond to the minimum of the potential energy of the system. This model has led to accurate predictions of nitrogen and argon adsorption on carbon black at their normal boiling points. In the case of adsorption in slit pores, local isotherms are determined from the minimization of the grand potential. The model provides a reasonable description of the 0-1 monolayer transition, phase transition and packing effect. The adsorption of nitrogen at 77.35 K and argon at 87.29 K on activated carbons is analyzed to illustrate the potential of this theory, and the derived pore-size distribution is compared favourably with that obtained by the Density Functional Theory (DFT). The model is less time-consuming than methods such as the DFT and Monte-Carlo simulation, and most importantly it can be readily extended to the adsorption of mixtures and capillary condensation phenomena.

Pore size distribution analysis of activated carbons: Application of density functional theory using nongraphitized carbon black as a reference system

The application of nonlocal density functional theory (NLDFT) to determine pore size distribution (PSD) of activated carbons using a nongraphitized carbon black, instead of graphitized thermal carbon black, as a reference system is explored. We show that in this case nitrogen and argon adsorption isotherms in activated carbons are precisely correlated by the theory, and such an excellent correlation would never be possible if the pore wall surface was assumed to be identical to that of graphitized carbon black. It suggests that pore wall surfaces of activated carbon are closer to that of amorphous solids because of defects of crystalline lattice, finite pore length, and the presence of active centers.. etc. Application of the NLDFT adapted to amorphous solids resulted in quantitative description of N-2 and Ar adsorption isotherms on nongraphitized carbon black BP280 at their respective boiling points. In the present paper we determined solid-fluid potentials from experimental adsorption isotherms on nongraphitized carbon black and subsequently used those potentials to model adsorption in slit pores and generate a corresponding set of local isotherms, which we used to determine the PSD functions of different activated carbons. (c) 2005 Elsevier Ltd. All rights reserved.

Focused beam reflectance technique for in situ particle sizing in wastewater treatment settling tanks

Due to the complexities involved with measuring activated sludge floc size distributions, this parameter has largely been ignored by wastewater researchers and practitioners. One of the major reasons has been that instruments able to measure particle size distributions were complex, expensive and only provided off-line measurements. The Focused Beam Reflectance Method (FBRM) is one of the rare techniques able to measure the particle size distribution in situ. This paper introduces the technique for monitoring wastewater treatment systems and compares its performance with other sizing techniques. The issue of the optimal focal point is discussed, and similar conclusions as found in the literature for other particulate systems are drawn. The study also demonstrates the capabilities of the FBRM in evaluating the performance of settling tanks. Interestingly, the floc size distributions did not vary with position inside the settling tank flocculator. This was an unexpected finding, and seriously questioned the need for a flocculator in the settling tank. It is conjectured that the invariable size distributions were caused by the unique combination of high solids concentration, low shear and zeolite dosing. (C) 2004 Society of Chemical Industry.

Effect of granule morphology on breakage behaviour during compression

In the area of dry particle breakage, Discrete Element Method (DEM) simulations have been widely used to analyse the sensitivity of various physical parameters to the behaviour of agglomerates during breakage. This paper looks at the effect of agglomerate shape and structure on the mechanisms and extent of breakage of dry agglomerates under compressive load using DEM simulations. In the simulations, a spherical-shaped agglomerate produced within the DEM code is compared with an irregularly shaped agglomerate, whose structure is that of an actual granule that was characterised with X-ray microtomography (muCT). Both agglomerates have identical particle size distribution, coordination number and surface energy values, with only the agglomerate shape and structure differing between the two. The work here details the breakage behaviour with a number of traditional DEM output parameters (i.e., contact/cluster distributions) with showing vastly different behaviour between the two agglomerates. (C) 2004 Elsevier B.V. All rights reserved.

Pore size characterization of mesoporous materials by a thermodynamic approach: A curvature-dependent solid-fluid potential

A thermodynamic analysis of nitrogen adsorption in cylindrical pores of MCM-41 and SBA-15 samples at 77 K is presented within the framework of the Broekhoff and de Boer (BdB) theory. We accounted for the effect of the solid surface curvature on the potential exerted by the pore walls. The developed model is in quantitative agreement with the non-local density functional theory (NLDFT) for pores larger than 2 tun. This modified BdB theory accounting for the Curvature Dependent Potential (CDP-BdB) was applied to determine the pore size distribution (PSD) of a number of MCM-41 and SBA-15 samples on the basis of matching the equilibrium theoretical isotherm against the adsorption branch of the experimental isotherm. In all cases investigated the PSDs determined with the new approach are very similar to those determined with the non-local density functional theory also using the same basis of matching of theoretical isotherm against the experimental adsorption branch. The developed continuum theory is very simple in its utilization, suggesting that CDP-BdB could be used as an alternative tool to obtain PSD for mesoporous solids from the analysis of adsorption branch of adsorption isotherms of any sub-critical fluids.

Adsorption of Lennard-Jones fluids in carbon slit pores of a finite length. A computer simulation study

The adsorption of simple Lennard-Jones fluids in a carbon slit pore of finite length was studied with Canonical Ensemble (NVT) and Gibbs Ensemble Monte Carlo Simulations (GEMC). The Canonical Ensemble was a collection of cubic simulation boxes in which a finite pore resides, while the Gibbs Ensemble was that of the pore space of the finite pore. Argon was used as a model for Lennard-Jones fluids, while the adsorbent was modelled as a finite carbon slit pore whose two walls were composed of three graphene layers with carbon atoms arranged in a hexagonal pattern. The Lennard-Jones (LJ) 12-6 potential model was used to compute the interaction energy between two fluid particles, and also between a fluid particle and a carbon atom. Argon adsorption isotherms were obtained at 87.3 K for pore widths of 1.0, 1.5 and 2.0 nm using both Canonical and Gibbs Ensembles. These results were compared with isotherms obtained with corresponding infinite pores using Grand Canonical Ensembles. The effects of the number of cycles necessary to reach equilibrium, the initial allocation of particles, the displacement step and the simulation box size were particularly investigated in the Monte Carlo simulation with Canonical Ensembles. Of these parameters, the displacement step had the most significant effect on the performance of the Monte Carlo simulation. The simulation box size was also important, especially at low pressures at which the size must be sufficiently large to have a statistically acceptable number of particles in the bulk phase. Finally, it was found that the Canonical Ensemble and the Gibbs Ensemble both yielded the same isotherm (within statistical error); however, the computation time for GEMC was shorter than that for canonical ensemble simulation. However, the latter method described the proper interface between the reservoir and the adsorbed phase (and hence the meniscus).