A Population Balance Model for Shear-Induced Polymer-Bridging Flocculation of Total Tailings

Shear-induced polymer-bridging flocculation is widely used in the solid–liquid separation process in cemented paste backfill, beneficial to water recycling and tailings management in metal mines. A flocculation kinetics model based on Population Balance Model (PBM) is proposed to model the polymer-bridging flocculation process of total tailings. The PBM leads to a system of ordinary differential equations describing the evolution of the size distribution, and incorporates an aggregation kernel and a breakage kernel. In the aggregation kernel, a collision frequency model describes the particle collision under the combined effects of Brownian motions, shear flow, and differential sedimentation. A semi-empirical collision efficiency model with three fitting parameters is applied. In the breakage kernel, a new breakage rate coefficient model with another three fitting parameters is introduced. Values of the six fitting parameters are determined by minimizing the difference between experimental data obtained from FBRM and modeling result through particle swarm global optimization. All of the six fitting parameters vary with flocculation conditions. The six fitting parameters are regressed with the flocculation factors with six regression models obtained. The validation modeling demonstrates that the proposed PBM quantifies well the dynamic evolution of the floc size during flocculation under the given experimental setup. The investigation will provide significant new insights into the flocculation kinetics of total tailings and lay a foundation for studying the performance of the feedwell of a gravity thickener.

Computational and experimental study of an oil jet in crossflow: coupling population balance model with multifluid large eddy simulation

Understanding the size of oil droplets released from a jet in crossflow is crucial for estimating the trajectory of hydrocarbons and the rates of oil biodegradation/dissolution in the water column. We present experimental results of an oil jet with a jet-to-crossflow velocity ratio of 9.3. The oil was released from a vertical pipe 25 mm in diameter with a Reynolds number of 25 000. We measured the size of oil droplets near the top and bottom boundaries of the plume using shadowgraph cameras and we also filmed the whole plume. In parallel, we developed a multifluid large eddy simulation model to simulate the plume and coupled it with our VDROP population balance model to compute the local droplet size. We accounted for the slip velocity of oil droplets in the momentum equation and in the volume fraction equation of oil through the local, mass-weighted average droplet rise velocity. The top and bottom boundaries of the plume were captured well in the simulation. Larger droplets shaped the upper boundary of the plume, and the mean droplet size increased with elevation across the plume, most likely due to the individual rise velocity of droplets. At the same elevation across the plume, the droplet size was smaller at the centre axis as compared with the side boundaries of the plume due to the formation of the counter-rotating vortex pair, which induced upward velocity at the centre axis and downward velocity near the sides of the plume.