A discretized population balance for continuous systems at steady state

TLDR: In this paper, a discretized population balance is adapted for continuous systems at steady state, in which the active mechanisms are nucleation, growth and aggregation, and a simple modification to the original discrete equations describing growth, permits the modelling of size-dependent growth effects.

Abstract: This paper is concerned with the solution of the population balance for continuous systems at steady state, in which the active mechanisms are nucleation, growth and aggregation. A discretized population balance, initially proposed by Hounslow et al. (1988a) for batch systems, is adapted for use with continuous systems at steady state. It is shown that simultaneous nucleation and growth can be described very effectively by the discrete equations. Criteria are developed for the selection of the optimal size domain. A simple modification to the original discrete equations describing growth, permits the modelling of size-dependent growth effects. Both size-independent and size-dependent aggregation are described by the discrete equations with three significant-figure accuracy. The complete set of discrete equations is used to simulate the nucleation, growth and aggregation of Nickel Ammonium Sulphate. It is shown that analysis by the approximate model must lead to underestimation of the nucleation and growth rates.