2026
Ind. Eng. Chem. Res. 2006, 45, 2026-2031
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 Ziolo4 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. Font5 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 Rajagopal6 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 concentrations. 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 Bagley7 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 Vanrolleghem8 proposed a new parameter * Corresponding author. Tel.: +886-2-27002737, ext 23. Fax: +886-2-27087819. E-mail:
[email protected].
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 relationship, 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 phenomena, 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 theory12 and a simple wave approach13-17 along with the Vesilind model18 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 XI. 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 equation can be used to describe the unsteady-state mass balance of solids in a batch test column:
∂X ∂(UX) ∂X ∂U ) )U +X ∂t ∂z ∂z ∂z
(1)
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
10.1021/ie0510730 CCC: $33.50 © 2006 American Chemical Society Published on Web 02/18/2006
Ind. Eng. Chem. Res., Vol. 45, No. 6, 2006 2027
UX ≡ -
(∂z∂t)
X
(2)
Equation 2 defines the down-moving velocity of solids with concentration X. According to the above definition, UX > 0 stands for solids moving down, and UX < 0 stands for solids moving up. Applying the chain rule of calculus and combining eqs 1 and 2 lead to
∂X/∂t ∂U ∂(UX) )U+X ) ∂X/∂z ∂X ∂X
UX )
(3) Figure 1. Wave velocity and movement directions in a settling column.
Equation 3 can be used to calculate the moving velocity of nonsharpening waves. For self-sharpening waves, an integral mass balance gives the following equation:
U∆X )
∆(UX) ∆X
(4)
to calculate the moving velocity of sharp interface separating two zones with upstream and downstream solid concentrations. Assume that the Vesilind model18 is applicable to the heavy metal sludge:
U ) U0e-kX
(5)
where U0 and k are two model parameters that can be determined experimentally. Combining eqs 3 and 5 leads to
UX ≡ U0e-kX(1 - kX)
(6)
Figure 1, a schematic plot of UX versus X, shows that a diluted zone with a low X moves down (UX > 0) while a concentrated zone with a high X moves up (UX < 0). We can therefore consider the settling process as the propagation of two waves; C f I is the upper wave moving down, and S f I is the bottom wave moving up, with C, I, and S representing the clear zone (X ) XC ) 0), intermediate zone (X ) XI), and sediment zone (X ) XS > XI), respectively. As shown in Figure 1, the wave velocity of zero concentration (XC) is greater than that of initial concentration (XI); the faster down-moving XC wave will catch the slower down-moving XI wave. This will result in a sharp interface between zone XC and zone XI; the C|I cut interface denoted by C f I wave is therefore called a self-sharpening wave. Figure 1 also shows that the absolute value of XS wave is less than that of the XI wave. The slower up-moving XS wave cannot catch up the faster up-moving XI wave. Therefore, one transition zone XT will appear between XI and XS; the resultant T f I wave is still a self-sharpening wave but the S f T wave is a non-sharpening wave. For a nonsharpening wave, there is no sharp interface between XS and XT; there is a concentration spectrum between XS and XT, and the corresponding wave velocities are calculated by eq 6. The transition-zone concentration XT is actually the tangent point of the solid flux curve (UX versus X) passing the initial concentration XI.14 The velocities of the self-sharpening waves C|I and T|I cuts are calculated by the following equations with XC ) 0:
{
UCfI )
UIXI - UCXC ) UI ) U0e-kXI XI - XC
U I X I - U TX T UTfI ) 2/k), and eq 21 is also applicable to find the tangent point. ‚Case 3: XI g 2/k If the initial solid concentration is equal to or greater than the reflexing point concentration, the tangent point concentration is exactly equal to the initial solid concentration as shown in Figure 5. After determining the tangent point solid concentration XT, we can use eqs 7 to 19 to calculate all the intersection points and connect all the points to obtain the whole settling curve. Figure 6 schematically shows the evolution of the batch settling
Ind. Eng. Chem. Res., Vol. 45, No. 6, 2006 2029
Figure 7. Initial settling curves at different initial solid concentration.
Figure 6. Evolution of the batch settling process. Table 1. Characteristics and Heavy Metal Composition of Sludge type
pH
chemical 8.26 sludge a
density streaming (g/cm3) current 1.03
-0.71
SRFa (m/kg)
mg/g of DSCb Cu Zn
Cd
Cr
total
3.8e+11 6.2 2.9
