The Froth Factor And What It Tells You About Your Coal Flotation Circuit

Froth removal rate is perhaps the most important parameter in scaling up from laboratory tests to plant froth flotation circuits. The WEMCO froth factor, the percentage of the froth height over the lip of the cell, accounts for the difference between laboratory and plant froth removal rates. As laboratory tests are generally run with a high pulp level, laboratory results are directly comparable to plant results only when a high froth factor (high pulp level) is run in the plant. When a plant does not have a high pulp level, laboratory results must be modified by using a ratio between laboratory and plant kinetics to predict plant results. This ratio, which accounts for the froth factor is important in testing any new reagents or reagent dosage levels. CQ Inc. researchers have used predictive scale-up equations using this froth factor coupled with equations for kinetics and the residence time distribution in the froth flotation cells. These equations show that modifying the froth factor in the plant can have a large impact on flotation cell yield and reagent use. EQUATIONS DESCRIBING FROTH FLOTATION Scaling up from laboratory- to plant-scale coal froth flotation has been the subject of much research and debate over the years. Determining the proper rate equation to describe flotation kinetics and an equation to describe the residence time distribution in a bank of flotation cells have been particular areas of study. As shown in Tables 1 and 2, various rate equations and residence time distribution equations have been proposed in the literature. These equations consist of one or two parameters giving the rate constant(s) in units of time-1 and a parameter for recovery at infinite time, [Roo]. Dowling, Klimpel, and Aplan (1985) evaluated the rate equations in Table 1 for their ability to fit froth flotation kinetic data and found that all of the equations give reasonably low standard errors. Several of these equations, however, proved to have superior confidence limits for the parameters. Other equations have also been proposed to describe the recovery versus time profile. Most recently, Diao et al. (1992) proposed a first-order form with a sine wave distribution. As indicated in Table 2, investigators have suggested many equations to describe the residence time distribution in continuous froth flotation. To measure the water residence time distribution in a bank of cells, a soluble tracer is often used, with the level of tracer being measured over time at the tailings discharge. This response is then put on a dimensionless basis as described by Austin et al. (1984) in order to compare mixing behavior between cells or under different conditions. Coal flotation cells are generally of the flow-through or hog-trough variety allowing for some degree of backmixing and short-circuiting. While the water residence time distribution (see Figure 1) at the end of one cell in a bank of 1.4 cu ft WEMCO froth flotation cells may approximate perfect mixing conditions (Arnold, 1989), the water residence time distribution at the end of a bank of cells does not. Figure 2 shows the RTD for various flotation cell types compared to that for perfect mixers in series. To better describe the water residence time distribution in coal froth flotation cells, Van Orden (1986) used an equation similar to the perfect-mixers-in-aeries equation. This