(78b) New Mass Flow Limiting Lines Based on Segregation Pattern and Magnitude

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 reported as the means of solving segregation problems. Generally this 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 process flow is steady state, but the segregation pattern is not radial but axial, then segregation can sometimes be a problem in a mass flow designs. In addition, 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.

Using the radial stress theory one can compute the expected velocity profiles in a variety of process geometries. Using slope stability models one can relate the cascade behavior of cohesive material down a pile or slope. Imposing these velocity profiles in a bin or hopper and using particle tracking techniques one can compute the time any particle in any portion of the bin might exit the system. Imposing a segregation profile on the material placed in the bin, and then tracking groups of particles with a segregation concentration in a region of the bin, can help in determining when and how segregated material might exit the bin. If we do enough of these calculations, we can relate the velocity profile to the segregation intensity exiting the bin. Thus, we can define mass flow limiting line relationships that are a function of desired segregation intensity for a process. Selection of a mass flow design would then depend on the segregation pattern and the desired segregation intensity the process can live with. The work presented in this paper computes new mass flow lines for conical and Diamondback® hoppers subject to segregation issues.

We have also used the radial stress velocity profiles in the bin to compute the residence time distribution for steady flow in the process equipment. We then impose an axial segregation pattern and compute the reduction in segregation intensity leaving the output. We can then relate this reduction to the velocity profile in the bin and develop new mass limiting lines to give the desired segregation intensity leaving the bin. This information should provide the engineer a better method to design hoppers and bins so as to solve segregation issues. Some of this work has been done for conical geometries, but we will extend this work to plane flow bins like the Diamondback hoppers® that have stacked hopper sections.