A rigid body dynamics model to predict the combined effects of particle size and shape on pressure filtration

Abstract

• Developed a novel computational workflow for simulating pressure filtration. • Rigid body dynamics used to simulate cake formation with various particle shapes. • A “local” Ergun equation developed to capture spatial variations in cake structure. • Platelet-shaped particles predicted to generate low porosity and poor filterability. • Large and small particle mixtures predicted to generate spatial heterogeneities. Many theoretical studies have focused on the effects of spherical particle size on pressure filtration, a solid-liquid separation method commonly used in pharmaceutical manufacturing and other industries. While experimental studies have demonstrated the importance of particle shape as well as size on the filterability of non-spherical particles commonly produced from pharmaceutical crystallization, process models that mechanistically capture how particle morphology affects the microscopic properties of the particle cake are lacking. The objective of this study was to investigate the combined effects of particle shape and size on pressure filtration performance using rigid body dynamics simulation, a powerful method for predicting porous cake structure based on the properties of the constituent particles. Once a detailed cake structure was generated, the Ergun equation was used to predict the macroscopic flow behavior of the filtration process. This workflow was validated by comparing model predictions with filtrate flow measurements from a series of dead-end filtration experiments using spherical particles with heterogeneous size. By simulating cylindrical particles over a wide range of aspect ratios, we showed that particle shape can have a dramatic effect on cake porosity and filtrate flow with disk-shaped particles predicted to be particularly difficult to filter. Rigid body simulation allowed the prediction of local as well as average cake properties. We predicted that heterogeneously sized particles with small or large aspect ratios such as disks or needles could produce highly asymmetric cake structures characterized by densely packed and low porosities near the filter medium. A modified Ergun equation based on local particle size and porosity was developed and shown to predict substantially different filtrate flows than the standard Ergun equation based on spatially-averaged properties, especially for cylindrical particles with high aspect ratio.