New mass flow limiting lines based on segregation pattern and magnitude

Abstract

Mass flow, by definition, means all of the mass in a hopper will move when some material is discharged from the outlet. Mass flow has been the recommended means to solve segregation issues. This generally works under conditions where the segregation pattern is radial and when the process operation is nearly steady state flow into and out of the hopper. If the segregation pattern is either axial or radial, but the mode of operation is to fill followed by completely emptying the bin, then segregation can easily be an issue – even in mass flow designs. Segregation prevention is all about velocity control, and matching the velocity to the segregation pattern and mode of operation.Ideally, one would like to estimate segregation using easily measured flow properties, segregation potential tests, and a description of the process geometry. This paper looks at a method of predicting segregation problems using flow properties like wall friction angle and effective internal friction angles coupled with the radial stress theory to compute the expected velocity profiles in a variety of process geometries. Using slope stability models, one can also relate the cascade behavior of cohesive material down a pile or slope. Imposing radial stress velocity profiles and cascade velocity profiles in a bin or hopper, then using particle tracking techniques, one can compute the time at which any particle in any portion of the bin might exit the system. Furthermore, imposing a measured segregation profile on the material initially placed in the bin, and then tracking groups of particles with an assigned segregation concentration through the bin, can help determine when and how segregated material might exit the bin. Doing enough of these calculations for a range of wall friction angles and hopper slope values, the velocity profile can be related to the segregation intensity exiting the bin as a function of these two variables. Since these two variables also determine the propensity for mass flow, this analysis can relate mass flow to segregation tendency for material subject to a filling and discharge mode of operation. Selection of an optimal mass flow design would then depend on the segregation pattern and the desired segregation intensity the process can live with.Applying this methodology to a conical hopper suggests that a material prone to segregation will segregate significantly in a funnel flow design. This is to be expected. However, this work also indicates that mass flow bins, when filled and then emptied completely, may experience significant segregation if the hopper walls are designed with traditional mass flow limits in mind. This work suggests that mass flow hoppers must be considerably steeper to mitigate segregation effects for a fill-then-empty mode of operation.