Experiment and Simulation of Sludge Batch Settling Curves: A Wave Approach Chun-Hsing Wu and Jia-Ming Chern* Department of Chemical Engineering, Tatung UniVersity, 40 Chungshan North Road, 3rd Section, Taipei 10452, Taiwan Chemical precipitation using alkaline solution is one of the most popular methods to remove heavy metals from industrial wastewaters in Taiwan. The resultant metal hydroxide precipitates are separated from wastewaters by gravity settling. To design continuous clarifiers, the settling characteristics of heavy metal sludge must be known. A series of batch settling tests were performed to gain design information for heavy metal sludge settling tank. The classic Kynch sedimentation theory and the nonlinear wave propagation theory were employed to depict the sludge band movement in batch settling tests. The variation of sludge concentration within the settling tank was viewed as a wave, and its wave velocity was calculated by the wave theory. The batch settling curves at varying initial solid concentrations were measured and satisfactorily predicted by the wave theory. Introduction The industrial wastewaters containing heavy metals are usually treated by a chemical precipitation method that uses alkaline solutions to form metal hydroxide precipitates to remove the heavy metals. The resultant metal hydroxide precipitates are separated from the wastewaters by gravity settling. 1 Efficient solid-liquid separation is crucial in a sludge settling tank design. For the design and optimization purposes of the solid-liquid separation process, a dynamic model able to describe the settling process is indispensable. To use the model for thickener design and process simulation, parameters that characterize the settling behaviors must be known. The solid flux method is one of the most popular methods for the thickener and clarifier design. 2,3 It is based on the observations of clear interfaces during batch settling tests to determine the settling velocities. A series of batch settling tests are performed to measure the initial settling velocities of the solids with different solid concentrations, and a graphic method using solid flux is applied to determine the clarifier area. Based on the solid flux concept, many methods were proposed for thickener and clarifier design and simulation. For example, Merta and Ziolo 4 reported a numerical calculation method to determine the thickener area. In their method, the thickener area can be directly obtained by differentiating the height-time relationship. Font 5 used calcium carbonate suspensions in water to test the compression zone effect in batch sedimentation. He also proposed a mathematical expression to relate the solid concentration to the solid-liquid interface height. Bhargava and Rajagopal 6 carried out a series of batch settling tests using various types of suspended materials such as ferric hydroxide flocs, aluminum hydroxide flocs, calcium carbonate, bentonite, and gray soil with different initial suspended solid concentra- tions. On the basis of their test results, they developed a model to predict the thickener area for any given initial suspended solid concentration and specific gravity. Zheng and Bagley 7 used a dynamic model of zone settling and compression to simulate the batch settling process numerically. They compared their results with the experimental data in the literature and showed good agreement between the simulated and experimental results. Vanderhasselt and Vanrolleghem 8 proposed a new parameter estimation method from a single batch settling curve using various settling velocity models. From their results, they found that the Vesilind model was superior to the Cho model in describing the settling velocity and solid concentration relation- ship, while the Cho model was better in describing the complete settling curves. Flamant et al. 9 presented a numerical model for a pilot settler by adding a one-dimensional source term and using a computational fluid dynamics (CFD) tool to simulate the settler performance. For a better interpretation of the settling phenom- ena, the solid fractions in settling tests were measured by a computerized axial tomography scanner, and rheological models were applied to simulate the solid concentration profiles. 10,11 For the purpose of designing steady-state clarifiers, the initial settling curves obtained in shorter test times to determine the settling velocities are of primary interest. However, the whole settling curves obtained in longer test times are of vital importance to the understanding of clarifier dynamics because they give more insights of the solid settling and compression information. Most studies either showed interest in the initial settling curves only or used complicated models and tools to simulate the whole settling curves. This study aims at applying the Kynch’s sedimentation theory 12 and a simple wave approach 13-17 along with the Vesilind model 18 to simulate the whole batch settling curves and compares the simulated results with the experimental data. Model Development In a batch settling test, it is assumed that the solids are initially suspended in a column with uniform concentration of X I . Upon settling, the solids move downward and settle on the bottom of the column due to gravity force. Applying the Kynch’s solid flux concept, the following first-order partial differential equa- tion can be used to describe the unsteady-state mass balance of solids in a batch test column: Without solving eq 1 for solid concentration as a function of time and position, let us view the concentration variation as a “wave” and define the concentration wave velocity as * Corresponding author. Tel.: +886-2-27002737, ext 23. Fax: +886-2-27087819. E-mail: jmchern@ttu.edu.tw. ∂X ∂t ) ∂(UX) ∂z ) U ∂X ∂z + X ∂U ∂z (1) 2026 Ind. Eng. Chem. Res. 2006, 45, 2026-2031 10.1021/ie0510730 CCC: $33.50 © 2006 American Chemical Society Published on Web 02/18/2006