A simulation model for settling tanks with varying cross-sectional area

A quasi-one-dimensional model of the process of continuous sedimentation in clarifier-thickeners (settlers) with variable cross-sectional area is presented. The partial differential equation (PDE) model extends the settler model advanced by Bürger et al. (2013 Bürger, R., Diehl, S., Farås, S., Nopens, I., and Torfs, E. (2013). A consistent modelling methodology for secondary settling tanks: A reliable numerical method, Water Sci. Technol. 68(1), 192–208.Crossref], PubMed], Web of Science ®] , Google Scholar]), which assumes a constant cross section. A reliable numerical method that handles the special features of the nonlinear PDE is presented along with an advantageous time-step condition for continuous and batch sedimentation under the condition of a variable cross-sectional area. Simulations of continuous sedimentation show the effect of change of cross-sectional area in the concentration inside the vessel and in the underflow. Simulations of batch settling in cones illustrate the versatility of the numerical scheme to include a vertex, where the area shrinks to zero.