Modelling Bubble Flow Hydrodynamics: Drift-Flux and Molerus Models

Minerals flotation is a widely used process to produce base metal concentrates through the selective capture of particles on the surface of bubbles. The process performance depends on the size distribution of the bubble population generated by gas dispersion, which is characterized by three variables: superficial gas velocity, gas holdup, and bubble size. A literature review revealed that current instrumentation cannot provide reliable on-line measurement of these variables except for gas velocity. There are some promising alternatives for gas holdup, but bubble size measurement will continue to be unavailable. The use of a model that integrates the three gas dispersion variables makes possible the calculation of one of the variables when knowing the values of the other two. Modelling bubble flow has been pursued using two approaches: determining the bubble terminal velocity reduction by the presence of other bubbles and regarding the bubble swarm as a packed bed through which a fluid is allowed to flow. Models based on these approaches (drift-flux and Molerus, respectively) were found in the literature and used to assess their prediction ability. Gas holdup predictions for known values of gas velocity and bubble size showed similar trends for both models; Molerus results were always higher than those obtained with the drift-flux model, and the difference between both predictions increased with bubble size and gas velocity. A relationship between bubble surface area flux and gas holdup was explored (a single line was expected); Molerus values showed a noticeable effect of bubble size, while drift-flux results showed a minor effect of bubble size only for gas holdups below 10%. Model accuracy was established using a data set collected to characterize frother roles in flotation for six commercial frothers, which included values of the three gas dispersion variables measured simultaneously and reported at the same conditions. The results indicate that bubble size predictions obtained from Molerus model are closer to the measured values than those obtained from the drift-flux model. Drift-flux predictions systematically underestimated the measured bubble size, with relative errors between 10 and 30%, while Molerus predictions showed values around the measured size with relative errors not larger than 15% (and in most cases below 10%). The accuracy of the Molerus predictions is acceptable for applications in the control of individual cells and flotation circuits operation. Further testing to assess the performance of Molerus model with data collected in lab and industrial mechanical cells and columns, where conditions in the test volume may not be stable or homogeneous, is recommended