R. Bertrum Diemer Jr., DuPont Engineering Research & Technology, DuPont Company, 1007 Market Street, Brandywine Building 8454, Wilmington, DE 19898 and Jon H. Olson, Chemical Engineering, University of Delaware, Colburn Laboratory, Newark, DE 19716.
Breakage models using power-law rate kernels and self-similar daughter distributions exhibit similarity solutions. The authors have exploited this to develop a matrix-inversion technique for extracting model parameters from the moments of measured product distributions. By specifying the daughter distribution parameters and the exponent in the power law, a mapping of daughter distribution moments into product distribution moments was produced. Regression resulted in a set of linear equations giving the product moments as functions of the daughter moments. Given a set of measured product moments, the daughter moments are obtained and from them, the daughter distribution parameters.
In this paper, we explore possible sources of error in the resulting models. These including (a) potentially ill-conditioned matrices in solution of the linear equation set, (b) regression error propagation, and (c) mismatch between the model and actual physics.