Energy Required for Size Reduction

FIGURE 4.3 Average energy required for size-reduction equipment, O is typical product size, is typical feed size. 

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Since the surface of unit mass of material is proportional to 1/L, the interpretation of this law is that the energy required for size reduction is directly proportional to the increase in surface. 

Power required in size reduction. The various theories or laws proposed for predicting power requirements for size reduction of solids do not apply well in practice. The most important ones will be discussed briefly. Part of the problem in the theories is that of estimating the theoretical amount of energy required to fracture and create new surface area. Approximate calculations give actual efficiencies of about 0.1 to 2%. 

Assumes that the power required is constant with size reduction ratio (e.g. the energy required for 1 mm 0.5 mm = 10 cm 5 cm = — 1)... 

As mentioned earlier, the acceleration type behavior is explained by an increase in surface due to breakup of catalyst particles subjected to mechanical pressure of growing polymer chains anchored to the catalyst active centers. The smaller the particle size, the greater the mechanical energy required for further size reduction, and so the particle size—and hence the specific surface area—would reach some asymptotic value. The stationary polymerization rate would correspond to this catalyst particle size. 

Kick (1885) reckoned that the energy required for a given size reduction was proportional to the size reduction ratio and took the value of the power n as 1. In such a way, by integrating Equation 4.1, the following relation, known as Kick s law is obtained ... 

There are three well-known postulates predicting energy requirements for particle size reduction. We will cover them in the chronological order in which... 

The energy required for the comminution, or size reduction, of a material to a certain required fineness (characterized by the specific surface of the product obtained) will depend on the hardness of the material, its compressive strength, its brittleness (or its elasticity or its plasticity), the size and shape of its particles, its temperature and moisture content, and of course also on the nature of the comminuting action exerted by the grinding process employed These factors in combination determine the resistance that the material offers to size reduction and can be regarded as specific of the material. 

Size reduction (qv) or comminution is the first and very important step in the processing of most minerals (2,6,10,20—24). It also involves large expenditures for heavy equipment, energy, operation, and maintenance. Size reduction is necessary because the value minerals are intimately associated with gangue and need to be Hberated, and/or because most minerals processing/separation methods require the ore mass to be of certain size and/or shape. Size reduction is also required in the case of quarry products to produce material of controlled particle size (see Size measurement of particles). In some instances, hberation of valuables or impurities from the ore matrix is achieved without any apparent size reduction. Scmbbers and attritors used in the industrial minerals plants, eg, phosphate, mtile, glass sands, or clay, ate examples. 

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