Numerical solution of particle size distribution equation: Rapid expansion of supercritical solution (RESS) process

Abstract

The present study aimed to numerically simulate the rapid expansion of the supercritical solution (RESS) process including particle generation, hydrodynamics, and solving the population balance equation (PBE) to predict the particle-size distribution (PSD) of solid-supercritical carbon dioxide binary systems. Energy, momentum, and mass equations, in addition to the extended generalized Bender equation of state (EoS), were applied to predict the hydrodynamic behavior of a supercritical solution under several operating conditions using a nozzle and expansion vessel. The tetraphenylporphyrin (TBTPP) solubility in supercritical carbon dioxide was calculated using the Peng–Robinson EoS/Kwak–Mansoori as a mixing rule. Subsequently, TBTPP, aspirin, ibuprofen, and salicylic acid nucleation as well as the supersaturation rate were calculated. Finally, we solved the time dependence of the parameters of the size distribution numerically. The established models are compared over a wide parameter range using a reference model that refers to the method of moment log-normal size distribution functions through the RESS process to predict a solid PSD. The results obtained are presented with and without coagulation phenomena. The average absolute percent deviation of solubility of TBTPP was 3.98, and the hydrodynamic behavior of supercritical carbon dioxide showed a similar trend as the results presented in the published research work. Furthermore, a particle size distribution prediction using coagulation showed acceptable agreement with the experimental PSDs.