Gravity Sedimentation: A One-Dimensional Numerical Model

• Main Author: Karl, Joanna Robin
• Format: Others
• Published: PDXScholar 1993
• Subjects: Sewage > Purification > Precipitation > Mathematical models; Sewage > Purification > Precipitation > Computer programs; Civil Engineering
• Online Access: https://pdxscholar.library.pdx.edu/open_access_etds/4594; https://pdxscholar.library.pdx.edu/cgi/viewcontent.cgi?article=5665&context=open_access_etds

A large fraction of the current cost of wastewater treatment is from the treatment and disposal of wastewater sludge. Improved design, energy efficiency, and performance of dewatering facilities could significantly decrease transport and disposal costs. Dewatering facilities are designed based on field experience, trial and error, pilot plant testing, and/or full scale testing. Design is generally time-consuming and expensive. A full-scale test typically consists_ of side-by-side operation of 4 to 5 full-scale dewatering units for several weeks to more than 6 months. Theoretical modeling of the physics of dewatering units such as the belt filter press, based on laboratory determined sludge properties, would better predict dewatering performance. This research developed a numerical computer model of the physics of gravity sedimentation. The model simulated the gravity sedimentation portion of the belt filter press. The model was developed from a physically-based numerical computer model of cake filtration by Wells (1990). As opposed to the cake filtration model, the inertial and gravity terms were retained in the gravity sedimentation model. Although in the cake filtration model, the inertial terms were shown to be negligible, according to Dixon, Souter, and Buchanan (1985), inertial effects in gravity sedimentation cannot generally be ignored. The region where inertia is important is the narrow interface between suspension and sediment. In the cake filtration model the gravity term was negligible due to the relatively large magnitude of the applied pressure; but in the gravity sedimentation model, since there was no applied pressure, it was necessary to consider the effect of gravity. _ Two final governing equations were developed - solid continuity and total momentum with continuity ("momentum"). ·The finite difference equations used a "space-staggered" mesh. The solid continuity equation was solved using an explicit formulation, with a forward difference in time and central difference in space. The "momentum" equation used a fully implicit formulation with a forward difference in time. The modeler could choose either a central difference or forward difference in space. Non-linear terms were linearized. Boundary Conditions and constitutive relationships were determined. Numerical errors in the numerical model were analyzed. The model was calibrated to known data and verified with additional data. The model was extremely sensitive to the constitutive relationships used, but relatively unaffected by the At or the use of central difference or forward difference for the spatial derivative term in the "momentum" equation. Correlations of the calibrated model to data with a low initial concentration show that the constitutive parameters approximate the data, but not very well. Model runs with low initial concentration required the addition of artificial viscosity to remain stable. The gravity term was always significant, whereas the inertial terms were many orders of magnitude less than gravity. However, the lower the initial concentration, the larger the inertial terms. In addition to the belt filter press, the model can also be applied to cake filtration and design of gravity sedimentation tanks as well.