P.C. Kapur

Production of reactive bio-silica from the combustion of rice husk in a tube-in-basket (TiB) burner

Rice husk, the main by-product of milling rice paddy and an agro-waste, is available in vast quantities in the rice-growing regions. On combustion, rice husk leaves behind about 20% ash composed essentially of bio-silica. This cheap and abundant source of reactive silica powder has numerous diverse applications, ranging from electronic-grade silicon to pozzolana cements. The phase composition of silica in the ash and its surface area depend critically on the temperature of combustion of the rice husk. A Tube-in-Basket (TiB) burner described here burns rice husk in a controlled manner to produce amorphous silica powder of high surface area, as characterized by X-ray and BET analyses.

Energy consumption and product size distributions in choke-fed, high-compression roll mills

Four minerals, dolomite, limestone, quartz and hematite, were ground in a laboratory-size chokefed, high-compression roll mill, a newly invented energy-efficient comminution machine. The size distributions of the ground solids were analyzed for energy-size reduction relationships and for development of a model of grinding kinetics in terms of energy expended in the mill. The results show that the size distributions are self-similar, that log median size decreases linearly with the amount of fines generated, and that the inverse of the median size increases directly with energy input, which in turn can be controlled by adjusting the milling force on the rolls. The standard population balance model of grinding kinetics, used widely for tumbling mills, must be modified in order to account for increasing energy dissipation as the bed of particles gets packed progressively more tightly during its passage through the rolls. The resulting model simulates the product size distributions as a function of energy input quite accurately. A noteworthy observation is that, unlike in ball mill grinding, the breakage rate parameters in pressurized roll mills remain relatively insensitive to particle size, and consequently most coarse and medium size particles in the feed get broken in only one pass through the rolls. This characteristic feature is reflected in the superior performance of roll mills in energy terms.

Modeling the size–density partition surface of dense-medium separators

A stochastic model is proposed for describing the size–density partition surface in dense-medium (DSM) gravity/centrifugal separators. The model is obtained by super-imposing a random walk on a simplified particle flow behavior inside the separator. The novel feature of the model is that it permits a description of the partition surface without incorporating the pivot phenomenon, i.e., without considering the partition number at the pivot point. The model also yields analytical expressions for the cut size, cut density and the ecart probable. The computed separation indices are in agreement with existing empirical relationships. Data from the published literature have been used to test the validity of the model in representing the partition surface.

Role of dispersants in kinetics and energetics of stirred ball mill grinding

Rheology of suspensions plays an important role in fine grinding of solids in stirred ball mills which exhibit superior performance in the sub-sieve grinding range than the conventional ball mills, in terms of both throughput and energy consumption. Addition of suitable dispersants to the slurry feed can result in a drastic reduction or even elimination of yield stress and permits higher solid loadings of the pulp. This investigation shows that size distributions of the comminuted products collapse onto essentially identical self-similar or self-preserving curves when particle size is rescaled by the median size, irrespective of the presence or absence of dispersants. The median size therefore is a consistent one parameter index of fineness that drives the size spectrum on its grinding trajectory which remains invariant of solid loadings and dispersant levels. The rate of change cf this characteristic length with the expenditure of specific grinding energy does not seem to vary with the addition of a dispersant. It is therefore inferred that dispersants do not effect the grinding mechanisms operating in the mill and the “speed” of grinding, that is, the inherent efficiency of the mill. However, since the rate of production of fines is directly proportional to the amount of solids present in the grinding charge, dispersants can under favourable conditions enhance the productivity or throughput of the mill significantly. A lumped parameters G-H model of grinding, when formulated in energy expended rather than in grinding time, can accurately simulate the kinetics of grinding in the stirred mill.

Analysis of single-particle breakage by impact grinding

A model is presented for breakage of single particles as a function of the impact energy. The model is based on a hazard function for test particles in impact energy in order to takes explicit cognizance of the distribution of feed particles in their resistance to breakage as well as the weakening of particles under repeated impacts. With this approach, it is possible to simulate the size spectra of progeny particles produced in impact grinding as a function of the impact energy employed, interrelate quantitatively the so-called t-family of curves, compute the primary, energy-free breakage distribution function, and predict the optimum level of impact energy for a given size reduction task. Extensive published data of Pauw and Mare on single-particle impact grinding are in agreement with the model.

The effects of aeration rate, particle size and pulp density on the flotation rate distributions

The apparent flotation rate distributions have been estimated from the flotation kinetic data by the numerical inversion of the Laplace transform. The distributions have been analyzed for their dependence on aeration rate, particle size and initial pulp density. The distribution function remains unaltered, but the argument of the function, the apparent flotation rate, is rescaled with change in the rate of aeration and particle size. The scaling factor increases rapidly with the rate of aeration and exhibits a characteristic maximum for intermediate particle size. The calculated distributions are approximately independent of the initial pulp density when dilute, but show marked divergence for concentrated pulps. Some implications of these results for modelling of flotation circuits are briefly discussed.

A search strategy for optimization of flotation circuits

We present a search technique which is tailored for the design of optimum flotation circuits from a generalized master network. The strategy is based on direct search driven by skewed random numbers. Depending on the drift of the parameters, a newly devised algorithm continuously adjusts the bias in the search, resulting in significantly accelerated convergence to the optimum or apparent optimum circuit configuration. This search strategy has been successfully tested under a wide variety of arbitrary sets of process, structural and economic constraints embedded in non-linear mixed-integer optimization problems of varying size and complexity. Some preliminary results are presented for verification. These include a reexamination of the optimum circuit design carried out by Green (1984) by a linear programming method. It is shown that there are no unique optimum circuits for this class of problems. In fact it is possible to synthesize much simpler circuits, having significantly smaller material hold-ups, which perform equally well, and also satisfy all the constraints imposed on the system. In the second example, a linear function of recovery and grade has been maximized. The ratio of weights on grade and recovery is varied from 10:1 to 1:10 in suitable steps. The optimum 3-bank circuit configuration changes from a rougher-clearner-cleaner to a rougher-scavenger-cleaner and finally to a rougher-scavenger-scavenger configuration, as one would intuitively anticipate. Moreover, the grade-recovery curve also varies smoothly in the expected manner. Interestingly, these circuits exhibit many features which are in conformity with a number of more or less empirical rules that have evolved over the years for the optimum design and operation of flotation circuits. Some of the more important implications of the design and synthesis methodology are briefly discussed.

A combined model for granule size distribution and cold bed permeability in the wet stage of iron ore sintering process

A combined mathematical model for granule size distribution and cold bed permeability in the iron ore sintering process is presented. The combined model is obtained by integrating the models for granulation and cold bed permeability. The granulation model is based on the two-stage granule growth mechanism and incorporates exclusion principle along with layer thickness postulates of granulation. The permeability model consists of equations for velocity of gases through the bed and the cold bed voidage. The velocity of gases is predicted using a modified Ergun equation. The bed voidage is related to the spread of the granule size distribution as well as the possible deformation of granules during charging by incorporating moisture and fines content of raw sinter feed. The model simulation of granule size distributions, cold bed voidage and velocity of gases under different operating conditions compare well with experimental data from a laboratory sintering unit. Starting from the size distribution of raw feed and its moisture content, the model predicts the granule size distribution and the cold bed voidage and permeability, without introducing any intermediate measurements. Moreover, it can be integrated with a sintering model in order to describe the complete iron ore sintering process in a quantitative fashion.

An improved method for estimating the feed-size breakage distribution functions

The discrete-size equation of batch grinding in cumulative fraction retained has an approximate, but adequately accurate, solution in the form of a second-order polynomial in time. For a single-size feed, the leading coefficient G of the polynomial is the product of the feed-size breakage-rate constant and the breakage distribution function. This coefficient as well as the second coefficient H are readily computed from the grinding data by solution of two linear algebraic equations, or by least squares, or by simple graphical techniques. In the last case, a new method of graphical display of grinding data as straightline plots is presented the intercepts of which are breakage distribution functions. Using both computer-generated as well as experimental grinding data, it is shown that the proposed G-H method of estimating breakage distribution functions is highly accurate, is not restricted to short grinding time data and is not subjected to any restrictive interrelationship between breakage-rate constants and breakage distribution functions. As such, this method is an improvement over the existing schemes, i.e. the method based on zero-order production of fines and the BII method, which are in fact shown to be time-restricted and grinding parameters-restricted specialized cases of the more general G-H method.

Empirical correlations for the effects of particulate mass and ball size on the selection parameters in the discretized batch grinding equation

Simple graphical procedures for determination of empirical correlations for the variations in selection parameters of the discretized batch grinding equation with the particulate mass and the size of the grinding media balls are described. The influence of the particulate mass is given by a single correlation function which is valid for all particle size intervals, as well as both starved and saturated mill loadings. The search for the correlation for the effect of ball size can be considerably simplified by plotting the data in a particular fashion which results in a self-preserving curve, independent of the particle size.