Dhruv; Dennis,

Product degradation, can in many instances, be derived from first principles. The steps to do so are given with associated references following the steps:

1. derive the particle strength that resists breakage, by size, in laboratory tests - this establishes the surface energy by measuring degree of breakage, for a group of necessary particle sizes to establish size range continuity, from a known kinetic energy delivery to each size and its resulting surface area liberated by size.

2. model each necessary single particle size breakage behavior, from step 1 lab tests with measurements of particle physical properties (size, shape, density, elasticity, poisson ratiotensile strength; surface energy constant), classification of shapes and strengths, by sizes, using a discrete grain breakage model (DGB). This is an extension of DEM with a fracture FEM model added within each particle subgroup. See our website referenced below.

3. generate representative population of particles, by size, et al, for modeling by DGB model in a pneumatic CFD (weakly compressible) flow field with particles to obtain collision (normal and tangential) energy spectrum and frequency of collision for each representative particle size. This discrete set can then be used to produce a continuum over the particle size range.

4. define differential(energy/paricle size) equation (CDI developed IP) properties that explicitly resolves breakage for all partilce sizes -- assumes a reasonable homogenous behavior of breakage.

5. use population balance model (PBM) to extrapolate step 3 and 4 to cover up to two maginitudes of sizes beyond the DEM modelled size range, which is typically 10:1. A 4 decade size range can be established that defines the particle breakage shift from the original particle continuum.

CDI has developed such a model (1995-1999) and have applied it to cruching and grinding mills and have completed a 1.5 year due-diligence program.

The above process is costly for a one-of. Our hope is to establish a database such that one has to simply run the flow model to obtain the energy spectra that can then predict the degradatio of fines from the base size distribution.

REFERENCES:

1 L. K. Nordell and A. V. Potapov Comminution Simulation Using Discrete Element Method (DEM) Approach - From Single Particle Breakage to Full-Scale SAG Mill Operation SAG Annual Convention, Vancouver, BC September-October, 2001

2 X. Qiu, A. Potapov, M. Song, L. Nordell Prediction of Wear of Mill Lifters using Discrete Element Method SAG Annual Convention, Vancouver, BC September-October, 2001



3 M. Song, X. Qiu, A. Potapov, L. Nordell MILLSTAT - A Software Package for Statistical Analysis of Mill Databases SAG Annual Convention, Vancouver, BC September-October, 2001



4 J. A. Herbst and L. K. Nordell Optimization of the Design and SAG Mill Internals Using High Fidelity Simulation SAG Annual Convention, Vancouver, BC September-October, 2001

Lawrence Nordell

www.conveyor-dynamics.com ■