A Continuous Mathematical Model of the One-Dimensional Sedimentation Process of Flocculated Sediment Particles

Abstract

A new continuous one-dimensional sedimentation model incorporating a new continuous flocculation model that considers aggregation and fragmentation processes was derived and tested. Additionally, a new procedure to model sediment particle size distribution (PSD) was derived. Basic to this development were three different parametric models: Jaky, Fredlund and the Gamma probability distribution (GPD) were chosen to fit three different glass micro-spheres PSDs having average particle sizes of 7, 25 and 35 microns. The GPD provided the best fit with the least parameters. The bimodal GPD was used to fit ten sediment samples with excellent results (\u3c 5% average error). A continuous flocculation model was derived using the method of moments for solving the continuous Smoluchowski coagulation equation with fragmentation. The initial sediment PSD was modeled using a bimodal GPD. This new flocculation model resulted in a new general moments’ equation that considers aggregation and fragmentation processes, which is represented by a system of ordinary differential equations. The model was calibrated using a genetic algorithm with initial and flocculated PSDs of four sediment samples and four anionic polyacrylamides flocculants. The results show excellent correlation between predicted and observed values (R2 \u3e 0.9878). A new continuous one-dimensional sedimentation model that resulted in a scalar hyperbolic conservation law was derived from the well-known Kynch kinematic sedimentation model. The model was calibrated using column tests results with glass micro-spheres particles. Two different glass microspheres particle size distributions (PSDs) were used with average diameters of 7 and 37 microns. Excellent values of coefficient of determination (R2 \u3e 0.89, except for one test replicate) were obtained for both the small and large glass micro-spheres PSDs. These results suggest that the proposed sedimentation model can be expanded to model the sedimentation process inside a sediment pond