Gas holdup estimation using Maxwell equation in flotation systems: Revisited

• A bias error is found in gas holdup calculation when assuming slurry behaves as a continuous phase.
• A novel equation for estimating gas holdup in a three phase system is derived.
• Only water is assumed to behave as a continuous phase according to Maxwell model.
• Bias error increases with solid holdup and decreases with the magnitude of gas holdup.

Estimation of gas holdup from electrical conductivity measurements has been used in lab and industrial installations. The approach is based on the application of Maxwell’s model, which relates the concentration of a dispersed phase in a continuous medium to measurements of the electrical conductivity of the dispersed phase, continuous medium and the resulting mixture (dispersion). When applied to inferring the collection zone gas holdup in a three phase system and to facilitate real-time on-line measurement, the slurry is assumed to behave as the continuous medium and gas bubbles as a non-conducting dispersed phase. This article derives an equation for estimating gas holdup in a three phase system, eliminating the assumption that the slurry behaves as a continuous medium but rather as a dispersion of non-conducting solid particles in water. In this formulation only water behaves as the continuous medium in the sense of Maxwell, and gas holdup in a three phase system is then calculated from the application of the Maxwell model twice: (1) to determine solid content in a two-phase system, and (2) to determine solid plus gas holdup in a three phase system. To validate the new equation and quantify the errors incurred by assuming slurry is the continuous phase a laboratory flotation cell was instrumented to continuously measure the conductivity of two and three phase dispersions with known solids contents. As the amount of gas in a lab flotation machine is difficult to measure directly or by another indirect technique such as using pressure signals, 2.5 mm dielectric plastic spheres having a density of ca. 1.3 g/cm3 were used instead of air bubbles for validation. Experimental results demonstrated that the continuous medium assumption underestimates gas holdup and that the resulting bias error increases linearly with the solid content and decreases with the magnitude of gas holdup.