Reliable Tools to Forecast Sludge Settling Behavior: Empirical Modeling

Abstract

In water- and wastewater-treatment processes, knowledge of sludge settlement behavior is a key requirement for proper design of a continuous clarifier or thickener. One of the most robust and practical tests to acquire information about rate of sedimentation is through execution of batch settling tests. In lieu of conducting a series of settling tests for various initial concentrations, it is promising and advantageous to develop simple predictive models to estimate the sludge settlement behavior for a wide range of operating conditions. These predictive mathematical model(s) also enhance the accuracy of outputs by eliminating measurement errors originated from graphical methods and visual observations. In the present study, two empirical models were proposed based on Vandermonde matrix (VM) characteristics as well as a Levenberg–Marquardt (LM) algorithm to predict temporal height of the supernatant–sludge interface. The novelty of our modeling approach is twofold: the proposed models in this study are more robust and simpler compared to other models in the literature, and the initial sludge concentration was considered as a key independent variable in addition to the more-customarily used settling time. The prediction performance of the VM-based model was better than the LM-based model considering the statistical parameters associated with the fitting of the experimental data including coefficient of determination (R2), root mean square error (RMSE), and mean absolute percentage error (MAPE). The values of R2, RMSE, and MAPE for the VM- and LM-based models were obtained at 0.997, 0.132, and 5.413% as well as 0.969, 0.107, and 6.433%, respectively. The proposed predictive models will be useful for determination of the sedimentation behavior at pilot- or industrial-scale applications of water treatment, when the experimental methods are not feasible, time is limited, or adequate laboratory infrastructure is not available.

Keywords

• sedimentation
• modeling
• Vandermonde matrix
• Levenberg–Marquardt algorithm
• water treatment