10.4 Grinding

Grinding is a necessary component in the processing of a number of ores. Optimizing the grinding process, however, is a difficult task requiring innovative techniques and accurate computer models. But, because of the high energy costs and the large amount of ore processed, improvements in the efficiency of grinding have a dramatic economic impact.

The grinding process is characterized by several performance measures, all of which are important in various circumstances. Generally, there are four measures that are especially important indicators of grinding efficiency: (1) fineness of the ground product, (2) energy costs associated with the process, (3) a viscosity coefficient, and (4) a viscosity exponent. Mehta, Kumar, and Schultz (1982) have developed an empirical model of grinding that accurately mirrors the response of a coal grinding process. In that work, they studied the ability of a simple genetic algorithm to optimize the performance of their computer model of a particular grinding circuit.

A genetic algorithm was used to tune the computer model of a grinding process. Only two of the four indicators of grinding efficiency are considered: fineness and energy consumption. However, the steps used to tune the models that predict fineness and energy consumption could also be used to tune models that predict viscosity characteristics. The pertinent modeling equations are:

and

where F is the weight percent of material less than 38 millimeters, E is the energy in kilowatt hours per ton, x_S is the percent solids by weight, x_B is the maximum ball size, x_M is mill speed, x_D is dispersant addition, x_ij represents the product of x_i and x_j, and C₁ through C₃₀ are the empirical constants selected so that the model equations accurately reproduce data obtained from a physical system. It is important to note that C₁ through C₁₅ can be determined entirely independent of C₁₆ through C₃₀. Thus, there are two separate 15 parameter search problems to be solved.

Development of an efficient empirical computer model of a grinding circuit actually depends on tuning 15 parameters for each of four separate model equations (only two such equations are considered here). The very same approach used in the previous sections of employing a genetic algorithm for tuning computer models can be used here. The coding scheme outlined in the hydrocyclone section can easily be used, as can the fitness function definition. Thus, all that is left is to present some results.

Figures 10.3 and 10.4 demonstrate the effectiveness of using a GA for tuning the empirical constants associated with the grinding models. In these plots, the fineness and energy data are plotted against the computer-predicted values. These figures demonstrate the ability of a GA to determine empirical constants for the grinding models.

Figure 10.3  A GA effectively tuned the fineness model of grinding as indicated in the figure in which data values are plotted against model-predicted values.

Figure 10.4  A GA effectively tuned the energy model. The plot above indicates that the empirical model accurately matched the data values over a range of values.

10.5 Column Flotation Circuit

Flotation is an established method for concentrating minerals (Sastry, 1978). Separation occurs when selected particles are rendered hydrophobic (water repellent) with chemical agents (called collectors) and are attached to air bubbles added to a vigorously stirred flotation cell containing a mineral-water slurry. The bubbles and their attached mineral particles rise to the top of the flotation cell to form a froth. The froth is collected and the mineral recovered. Such conventional flotation cells have been a cornerstone of the mineral processing industry for a number of years. However, column flotation that occurs in a taller unsthted flotation cell is becoming increasingly popular as an alternative to conventional flotation cells because of its efficiency and mechanical simplicity. Several copper-molybdenum operations in the United States and Canada are currently operating flotation columns while numerous other ventures are running pilot-plant tests (Agar, Huls, and Hyma, 1991). The popularity of these separators should continue to grow as a better understanding of the underlying mechanics of the operation is gained.

Figure 10.5 shows a schematic of a column flotation unit. The chemically treated mineral slurry (feed) is fed into the column approximately one-third of the way down from the top of the column. Bubbles are introduced at the bottom of the column. As the feed particles sink and the bubbles rise, collisions occur. Due to the chemical treatment of the feed, some particle species attach to the bubbles during collision and rise to the top to form a foam or froth zone, while others are repelled by the air thereby remaining unattached and sink to the bottom. Thus, a separation occurs.

Figure 10.5  Column flotation units are becoming increasingly popular separators because of their mechanical simplicity.

Because of the increased use of column flotation units, researcher have begun to investigate their mathematical underpinnings. The result of these efforts has been the development of systems of mathematical equations that describe column flotation, or separate events associated with column flotation. Some of the more noteworthy research has been reported by Finch and Doby (1990), Herbst and Rajamani (1989), Luttrell, Adel, and Yoon (1987), and Ynchausti, Herbst, and Hales (1988). In the current effort, the Finch and Doby model has been used because it has been well documented, is relatively straightforward to program, and provides accurate results.