Mathematical Model for a Fed-Batch Crystallization Process for Energetic Crystals to Achieve Targeted Size Distributions

In the manufacture of energetic materials including RDX, HMX, CL-20, it is a challenge to obtain the targeted size distribution. Generally blending is costly and regrinding of the crystals increases the defect densities to give rise to increased sensitivity. The ability to predict apriori the size distribution of various energetic crystalline materials upon recrystallization as a function of the operating conditions, allows the optimization of the process parameters to achieve the desired size distribution without having to regrind or blend different size populations. Here a comprehensive mathematical model of the fed-batch crystallization process consisting of two groups of equations is presented. These include first the dynamic material and energy equations, and second, a population balance model for the prediction of the number density of crystals as a function of time and size as functions of the nucleation and growth kinetics for the particles. A numerical solution to the general problem, which involves the alternate solution of the equations at each time step, was developed considering that the reactor volume changes with each time step. Typical results are presented to demonstrate the utility of the mathematical model of the recrystallization process.