Crystallization Kinetics of SAPO -۳۴ in Ultrasonic -Assisted Hydrothermal Synthesis: A Population Balance Modeling Approach

In this study, a population balance model was developed to describe the crystallization behavior of SAPO -۳۴ synthesized under ultrasonic -assisted hydrothermal conditions at three different temperatures: ۱۸۰, ۲۰۰, and ۲۲۰°C. Ultrasound was introduced during the aging stage to intensify nucleation and improve mixing and mass transfer within the synthesis medium. The resulting samples were characterized using XRD, FESEM, BET, and DLS techniques to determine the physicochemical properties of the synthesized SAPO -۳۴. The modeling approach was based on crystallinity data obtained from XRD patterns and incorporated conventional kinetic expressions for homogeneous nucleation and diffusion-limited crystal growth. Adjustments were made to the model to account for the influence of ultrasonic treatment, particularly in enhancing the local supersaturation and facilitating transport phenomena. The population balance equations were solved within a batch reactor framework using the Grey Wolf Optimization algorithm for parameter estimation. The model successfully predicted the crystallization profiles, nucleation and growth rates, and crystal size distributions under ultrasound -assisted conditions. The comparison between experimental results and model predictions revealed a strong consistency, especially regarding the mean crystal size. It was found that ultrasound significantly increased the nucleation rate and contributed to a narrower and more uniform particle size distribution. These findings demonstrate the potential of ultrasonic -assisted synthesis to fine-tune the properties of SAPO -۳۴ and highlight the efficacy of population balance modeling in understanding and optimizing complex crystallization systems relevant to industrial applications such as catalysis and adsorption.

کلیدواژه ها:

SAPO -۳۴ ، Ultrasonic ، Population Balance ، zeolite crystallization