Dynamics of probabilistic time delay models

Abstract

Quantitative information on the dynamic behaviour of two general probabilistic time delay models, the gamma distributed model and the modified exponentially distributed model, is provided over wider ranges of model parameters than hitherto reported. The actual relationships that exist between the response and parameters of the gamma model, especially over an extended range of parameter values, are established relatively easily by recourse to frequency response. The results thus obtained are verified by a least squares curve fit of published experimental response data pertaining to a number of packed beds under trickle flow conditions. Certain characteristics that the modified exponential model has in common with the gamma model are identified. For both models, the existence of multiple sets of parameters for a given residence time distribution (RTD) curve (and consequent absence of unique parameter estimates) is also revealed. © 1986.