Proposal for initial collection efficiency models for direct granular upflow filtration

Mathematical models of the filtration process are based on the mass balance in the filter bed. Models of the filtration phenomenon describe the mass balance in bed filtration in terms of particle removal mechanisms, and allow for the determination of global particle removal efficiencies. This phenomenon is defined in terms of the geometry and the characteristic elements of granule collectors, particles and fluid, and the composition of the balance of forces that act in the particle collector system. This type of resolution is well known as the trajectory analysis theory. Particle trajectory analysis by mathematical correlation of the dimensionless numbers that represent fluid and particle characteristics is considered the main approach for mathematically modeling the initial collection efficiency of particle removal in water filtration. The existing initial collection efficiency models are designed for downflow filtration. This study analyzes initial collection efficiency models, and proposes an adaptation of these models to direct upflow filtration in a granular bed of coarse sand and gravel, taking into account the contribution of the gravitational factor of the settling removal efficiency in the proposal of initial collection efficiency models.