N. Standish

Porosity calculations of multi-component mixtures of spherical particles

Abstract It is shown that the relative maximum void contraction and the corresponding relative fractional solid volume are only the functions of size-ratio for binary mixtures, which can be determined experimentally. A linear analytical model, directly based on the experimental results of binary mixtures, is developed. The results show that the calculated porosities for ternary mixtures are within 8% relative error of measurements. Good agreement between the theoretical and experimental results was also obtained for Gaussian and log-normal size distributions. It is concluded that the porosity of multi-component mixtures of particles may be confidently predicted from the results of binary mixtures.

Gasification of single wood charcoal particles in CO2

Kinetic studies and SEM analysis have been carried out to elucidate the principal features of the gasification of wood charcoal particles in CO2 gas environment at atmospheric pressure. Variables investigated were: particle size (10–34 mm), temperature (900–1100 °C), gas concentration (20–100% CO2) and gas velocity (1–9cm/s). The results have shown that the particle gasification proceeds largely by the reaction of the outer shell, with the interior of the particle remaining relatively untouched until very high conversions have been reached, and that the overall gasification process was well represented by the shrinking core-reaction control model. The data were correlated by an empirical relationship for the rate of gasification of the particle as a function of the variables investigated. The relevance of this fuel in blast furnace ironmaking is discussed.

The kinetics of batch sieving

Abstract A detailed study of the sieving kinetics of sinter particles (4–0.5 mm) is described using a batch sieving technique with continuous weighing of the undersize stream. The results are anclysed by an equation derived from the first-order rate law for the condition of decreasing screen residue. It is shown that the rate of sieving and its efficiency are determined by the numerical values of the sieving rate constants of each of the particle sizes in the feed mixture and that near-mesh particles play a dual role in the overall kinetic process. The results also show that the presence of oversize particles in the feed enhances the sieving rate dramatically.

Studies of size segregation in filling and emptying a hopper

Abstract Studies are described of in-bin segregation, flow pattern and discharge segregation of ternary mixtures of ore and coke (−8 +6.15; −5 +4 and −2 +1 mm) in a model Paul Wurth hopper. Measuring techniques used include heap freezing, tracer addition, contour mapping and screen analyses. The results show that on filling the hopper small particles segregate in the centre, large particles segregate towards the wall and medium-size particles remain essentially unsegregated, i.e. the concentration of these particles in the hopper is essentially uniform throughout and equal to that of the feed. The concentration of the other two sizes in the hopper (C) was found to depend on feed composition (C o ), the nature of the material employed and the position in the hopper. It is shown that in-bin concentrations may be expressed by a relationship C = C o k , where k is an experimentally obtained segregation constant. It is also shown that material discharges from the hopper according to a sequence core flow-wall flow-scaffold flow, where the latter represents stagnant material at the hopper wall that discharges last. Analysis of the variances of tracer response curves indicates some material intermixing in the hopper during discharge. The extent of this intermixing in the core region follows a dispersed plug flow model exactly, whilst in the wall region intermixing is more enhanced with variance dependency there being related to the square of the material height in the hopper. In-bin segregation and flow pattern in the hopper influence size segregation in the discharging material. Concentration of the small particles in the discharge stream is high in the initial stages of discharge and low in the final stages of discharge. For large particles this pattern is reversed, whilst for medium-size particles the concentration in the discharge stream remains essentially constant throughout the discharge cycle. Experimental discharge segregation results show satisfactory agreement with industrial data. A method of predicting discharge segregation from knowledge of in-bin segregation and hopper flow pattern is suggested. This should interest a wide section of the bulk solids handling and processing industries.

A study of the packing of particles with a mixture size distribution

Abstract This paper presents a theoretical study of the packing of particles with a mixture size distribution. The theoretical treatment of this packing system is first rationalized. It is shown that the porosities of this packing system can be satisfactorily predicted by the linear-mixture packing model. The packing of binary and ternary mixtures of lognormal distributions is then generally discussed. The results indicate that the packing of particles with a mixture size distribution may be quite different from that with a discrete size distribution. The investigation is also extended to multi-component mixtures with particular reference to the packing systems encountered in engineering practice. Finally, the methods of determining the optimum particle size distribution for the maximum packing density of a given packing system are demonstrated by a typical practical example.

Characterisation of non-spherical particles from their packing behaviour

Abstract A method is proposed to define and determine the equivalent packing diameter of a non-spherical particle based on the similarity between the packing systems of spherical and non-spherical particles. The equivalent packing diameter of a particle is empirically related to its sphericity and some commonly used equivalent spherical diameters such as volume, surface and surface volume diameters. The relationship between the porosity and sphericity of monosized particles is formulated using the data reported in the literature. The possible application of the present results to predicting the porosity of non-spherical particle mixtures is discussed.

Coal agglomeration and its effect on bulk density

Abstract This paper presents an investigation of the effect of moisture content on the agglomeration and bulk density of coal. Growth mechanisms of agglomeration have been analysed based on microscopic observation and the results indicate that the relative roles of the growth mechanisms such as nucleation, coalescence and snowballing are dependent on the moisture content. It is shown that agglomeration occurs mainly to the moist nuclei coarse particles and the moist layering fine particles. Two types of porosity, namely intraporosity in an agglomerate and interporosity among the packed particles and agglomerates, are identified. The dependences of these two porosities and other properties of agglomerates, such as particle size distribution, moisture content and bulk density, on the moisture content are experimentally established. Analysis of these measured results suggests that the relationship between the bulk density and moisture content coal is dependent on the particle size distribution, particle (agglomerate) deformation and in particular, interparticle friction.

The porosity of particulate mixtures

Abstract Experimental measurements are reported of porosities in ternary mixtures of spheres and of coke particles and compared with the data existing in the literature. It was found that the porosities in the systems examined show similar behaviour which is dictated by the porosities of the pseudo-binaries of the two extreme size particles in the mixture.

Packing of multi-sized mixtures of wet coarse spheres

The effect of water addition on the packing of multi-sized coarse spheres has been experimentally investigated under standard poured packing conditions. The results indicate that porosity is strongly affected by particle characteristics such as particle sizes and their distribution, in addition to water content. The packing features in the relationship between porosity and moisture content for wet multi-sized spheres are found to be similar to those for wet mono-sized spheres, implying that the same governing mechanisms apply. The comparison between the dry and wet packing systems confirms that there is a similarity between them, suggesting that the packing of wet particles can be predicted within the framework of a packing model developed for dry coarse particles. Future work in this direction is also discussed.

A study of the effect of operating variables on the efficiency of a vibrating screen

Abstract The efficiency of screening sinter particles (0.25 – 3.5 mm) and coke particles (0.25 – 1.94 mm) in a vibratory screen (200 × 600 mm) is studied for a range of operating variables which include flow rate, deck angle, RPM, oversize in feed and mesh size. Kinetic approach is used to analyse the data and efficiency is quantified by the kinetic constants of the individual particle sizes involved. Regression analysis shows that for both materials the effect of feed rate is positive for all sizes, that of RPM and deck angle is negative for near-mesh particles and positive for other particles, whilst that of oversize is reversed, i.e., the effect is positive for near-mesh particles and negative for smaller particles. The significance of the results, which show for the first time the effect of operating variables on the screening of individual size particles in the feed, in modifying partition curves, is discussed. Comparison of the results with those reported by other workers in terms of traditional efficiency definitions is included.