- Email: [email protected]
Experimental Analysis of Floc Size Distribution and Hydrodynamics in a Jar-Test
0263–8762/01/$10.00+0.00 # Institution of Chemical Engineers Trans IChemE, Vol 79, Part A, November 2001
EXPERIMENTAL ANALYSIS OF FLOC SIZE DISTRIBUTION AND HYDRODYNAMICS IN A JAR-TEST D. BOUYER1 , A. LINE1 , A. COCKX 1 and Z. DO-QUANG2 1
LIPE, INSA-DGPI, Toulouse Cedex, France 2 ONDEO-Services, Le Pecq, France
T
he present work concerns coagulation- occulation in drinking water treatment units. This study focuses on the link between hydrodynamics and oc size distribution. Experimental analysis of both oc size distributions and local hydrodynamics are performed in a jar-test vessel. In this study, water quality (pH) and coagulant (both type and dose) are xed. Floc size distributions are analysed by image processing. The temporal evolution of the oc size distributions is determined from a statistical analysis of experimental data. It leads to basic information on oc agglomeration kinetics. The velocity eld is analysed using Particle Image Velocimetry (PIV). The statistical analysis of the velocity eld leads to the determination of the average velocity eld and the average velocity gradients. In addition, instantaneous velocity elds and associated instantaneous velocity gradients are determined. It is shown to be important to locate their maximum values. The analysis highlights the close relationship between the characteristic size of the ocs and hydrodynamics, that can be expressed in terms of local dissipation of turbulence or in terms of velocity gradient. Keywords: mixing; agitation; local hydrodynamics; occulation; oc size distribution; water treatment.
INTRODUCTION The coagulation/ occulation step is a major process in drinking water treatment plants. The reliability of plant operation and the nal water quality together with the problems of cost control are the most important issues for water treatment professionals. The prediction of the optimum coagulant dose is the crucial question for two basic reasons: rstly, coagulant overdosing leads to high operating costs and risks leading to problems with public health concerns. Secondly, under-dosing the coagulant leads to low treatment ef ciency and insuf cient removal of solid particles in the operation of water treatment plants. This could lead to a failure to meet water quality standards. The new stringent regulations on the acceptable residual coagulant level in distributed water, impose a very strict control for the absence of any remaining aluminium or ferric salts residuals. In the present study, a jar-test is used in order to control and optimize the coagulant dosage. The present work focuses on the link between hydrodynamics and occulation. Such a local description of occulation offers many advantages: it allows a better understanding of the major role of the mixing on the oc aggregation kinetics and of the dissipation rate of the turbulent kinetic energy for the break-up and structure of large ocs. Mixing could then be optimized in the scope of occulation. The coagulation/ occulation process has been studied for many years. Smoluchowski1 rst proposed a global description of the particle collision in 1917. The analysis was restricted to simple laminar ow and the Brownian motion
was not considered. The collision rate between particles of diameter di and dj in a two dimensional ow can be derived as follows: 3
@U di dj 1 @Z 6 Camp and Stein2 generalized this expression and introduced the velocity gradient (G):
b di ; dj
b di ; dj
G
di
dj
6 where G is expressed as: G
P rV n
3
2
3
n represents the kinematic viscosity, P the global power input in the system and V the volume. P is balanced by the global kinetic energy dissipation. In laminar ow, the energy is dissipated by the mean ow, whereas for a turbulent ow, it is mostly dissipated by the turbulent motion. In turbulent ow, Saffman and Turner3 introduced the dissipation rate of the turbulent kinetic energy (e), which is equal to the power per unit mass (P=rV). Using dimensional analysis, Levich4 proposed to rely the collision rate in a turbulent ow to a turbulent diffusivity. The turbulent diffusivity is then proportional to an average eddy velocity multiplied by a length scale that is characteristic of the size of the energetic eddies. Such approaches are based on Taylor’s5 statistical analysis of
1017
BOUYER et al.
1018
Figure 1. Experimental set-up.
Table 1. Experimental conditions. Bentonite 30 mg l
1
Aluminium Peri-kinetic (coagulant) mixing 25 mg l
1
150 rpm for 180 s
Ortho-kinetic mixing 30 rpm 45 rpm 60 rpm 90 rpm 150 rpm
for for for for for
17 min 17 min 12 min 12 min 12 min
Time between each photo (s) 15 15 15 15 15
isotropic turbulence. Kramer and Clark6 discussed this point and showed that the global velocity gradient G is not suf cient to correctly predict the orthokinetic coagulation. Indeed, different systems with different vessel or impeller geometries can have the same velocity gradients, but the oc particle size distribution can be different due to local stress and strain rates. The objective of this work lies in the modelling of occulation phenomena. Such a modelling approach is based on the coupling between agitated vessel local hydrodynamics and oc aggregation kinetics and break-up. The hydrodynamics are rst studied experimentally and then simulated numerically, using CFD (Computational Fluid Dynamics) code. The experiments are done in a
Figure 2. Images of ocs (initial and nal steps). Image size: 30 mm 30 mm.
jar-test. Given different hydrodynamics induced by different impeller velocities, data acquisition of oc size distributions during occulation is performed. An image processing system allows the evolution of the ocs in the jar-test to be followed. These data will be used to develop a population balance model for the oc. In the next step, the model is coupled with hydrodynamics and implemented in the CFD code in order to numerically simulate the occulation phenomena. The experimental set-up is described below. Results on oc size distribution are discussed. Results on
Figure 3. Mean area of ocs versus time for ve impeller speeds.
Trans IChemE, Vol 79, Part A, November 2001
ANALYSIS OF FLOC SIZE IN A JAR-TEST
1019
Figure 4. Floc size distributions: (a) 30 rpm; (b) 45 rpm; (c) 60 rpm; (d) 150 rpm.
hydrodynamics are then presented. Finally, the maximum oc size is related to hydrodynamics characteristics. EXPERIMENTAL SET-UP Coagulation Process Analysis The experimental study is carried out in jar-test vessel (see Figure 1). A synthetic suspension of bentonite is used to simulate the behaviour of particles present in natural water. Aluminium is used as a coagulant during these experiments. In order to follow the oc size evolution, the PIV technique is used. It consists of illuminating a 2-dimensional sheet with a laser beam. A camera is placed perpendicular to the laser and then takes pictures at constant time intervals. Images are recorded on a PC and are then processed with Visilog 5.1. This software allows each individual particle to be identi ed and its area and perimeter in the illuminated plane to be determined. Mixing between the suspension of bentonite and the coagulant is a critical phase in the coagulation process. Just after the injection of coagulant, the tank is mixed at high speed, 150 rpm during 180 seconds. This provides an initial peri-kinetic phase that enhances the Brownian motion between colloids. The next phase consists of mixing the tank at a lower speed, limiting shear stress in order to control the oc growth and their structure. The study will focus on this second phase. The operating conditions are summarized in the Table 1 and examples of images of ocs with PIV techniques are shown in Figure 2. Trans IChemE, Vol 79, Part A, November 2001
Hydrodynamic Analysis The PIV technique is used to study hydrodynamics. It is based on the four following steps: (1) the uid ow volume under investigation is needed; (2) illuminating a slide of the ow eld with a pulsing light sheet; (3) two images of the uid ow are recorded with a short time interval between them, using a numerical CCD camera; (4) these images are processed by dividing the whole images into interrogation areas and using inter correlation techniques to get the instantaneous velocity eld. The PIV system used is the commercial system acquired from Dantec Measurement Technology. The system includes a laser (Mini Yag, 15 Hz, 30 mJ), a double image recorder camera (Kodak Megaplus ES 1.0, 1024 1024 pixels), a dedicated processor (PIV 2000) and software. The processor makes all the calculations in real time. As the processor produces vector maps, these are displayed and optionally stored by the software. The seeding material is spherical glass hollow silvered particles from Dantec (density 1.4, 10 mm < d < 30 mm). FLOC SIZE DISTRIBUTION RESULTS It is important to emphasize that this technique is an in-situ and non destructive technique. In addition, the vessel is completely closed, thus, the ow is not disturbed by
1020
BOUYER et al.
Figure 5. Mean velocity elds: (a) 30 rpm, maximum velocity: 2.9 10 velocity: 5.3 10 2 m s 1; (d) 150 rpm, maximum velocity: 12.5 10
2 2
m s 1; (b) 45 rpm, maximum velocity: 3.8 m s 1.
pumps. However, the data acquisition technique gives only two dimensional information on the oc size (perimeter, area, shape). The time evolution was recorded every 15 seconds. Floc size distributions are plotted in Figures 4(a) to 4(d). Figure 3 exhibits the evolution of the average oc area with time. The size evolution is similar in each case during the peri-kinetic phase because the impeller speed remains equal to 150 rpm. During the ortho-kinetic phase, two trends can be identi ed: the oc size increases as the occulation starts and the smallest particles are continuously captured by the bigger ones. Three observations can be deduced from Figure 3: (1) the nal oc size decreases with increasing impeller speed; (2) the steady state is reached more rapidly with increasing impeller speed (400 s at 60 rpm and more than 1000 s at 30 rpm); (3) the oc size tends to increase in the rst step then decreases in the second step. This is probably due to a
10
2
ms
1
; (c) 60 rpm, maximum
re-organization of the oc structure under the ow stress (J.Y. Botero, private communication). The oc size distributions for four impeller speeds at different times are plotted in Figures 4(a) to 4(d). Area weighted percentages are plotted versus area classes. It is possible to follow the largest ocs evolutions. At the end of the process, the number of tiny particles remains larger than the larger ocs. In each case, an initial distribution reaches a steady state during the peri-kinetic phase after 100 s. Then the distribution evolves toward larger size distributions with decreasing impeller speed. When the impeller speed remains constant (150 rpm), the size distributions slowly decrease. With increasing impeller speed, it can be seen in Figures 4(a) to 4(d) that the collision kinetic increases: large ocs are more rapidly formed and the steady state is reached earlier (after 300 s at 30 rpm, after 250 s at 45 rpm, after 200 s at 60 rpm and after only 100s at 150 rpm). These gures point out the in uence of the ow on the oc size at steady state. The ocs are bigger with decreasing impeller Trans IChemE, Vol 79, Part A, November 2001
ANALYSIS OF FLOC SIZE IN A JAR-TEST
1021
Figure 6. Average velocity gradient determined by a direct derivation of instantaneous velocity elds: (a) 30 rpm; (b) 45 rpm; (c) 60 rpm; (d) 150 rpm.
speed. The distributions reach a steady state with ocs of diameter equivalent to about 1200 mm at 30 rpm, 800 mm at 45 rpm, 600 mm at 45 rpm and 300 mm at 150 rpm. This latest observation clearly points out the importance of understanding the break-up mechanisms and the oc structure evolution. A local description of hydrodynamics is thus needed. HYDRODYNAMICS RESULTS In the present paper, the velocity eld is reported in a vertical plane, around the impeller. The impeller height is 20 mm and the size of the measurement zone is 50 50 mm2. The experiments are carried out using the PIV technique for different impeller velocities: N 30, 45, 60, 90 and 150 rpm. Mean velocity elds are obtained after statistical averaging over 1000 instantaneous velocity elds. The mean velocity elds are plotted in Figures 5(a) to 5(d). The structure of the ow is the same in each case, with induced velocities increasing with increasing impeller velocities. At the same time, the mean velocity gradient G can be derived from the statistical average of instantaneous elds. The mean velocity gradients are Trans IChemE, Vol 79, Part A, November 2001
plotted in Figures 6(a) to 6(d). In the region of the impinging jet, the maximum value of the velocity reaches 2.9 10 2 m s 1 at 30 rpm, 3.8 10 2 m s 1 at 45 rpm, 5.3 10 2 m s 1 at 60 rpm, 7.8 10 2 m s 1 at 90 rpm and 12.5 10 2 m s 1 at 150 rpm. The associated average velocity gradient reaches 9 s 1 at 30 rpm, 12 s 1 at 45 rpm, 15 s 1 at 60 rpm, 21 s 1 at 90 rpm and 33 s 1 at 150 rpm. However, such results are only meaningful in terms of statistical average. In order to better understand the local and instantaneous phenomena which can control the ocs size, different instantaneous velocity elds are presented and discussed. The instantaneous velocity elds correspond to an impeller speed about 60 rpm and are shown in Figures 7(a) to 7(c). The associated instantaneous velocity gradients have been estimated and plotted in Figures 7(d) to 7(f ). The Figures 7(a) and 7(b) correspond to 2 successive positions of the blade in the plane of measurements. Figure 7(a) shows that the blade has just passed and the plane of measurement is in the aspiration zone created behind it. The instantaneous velocity gradients reach maximum values in such a zone (100 s 1). Figure 7(b) shows that the blade is located 20 behind the plane of measurement; it
BOUYER et al.
1022
Figure 7. Instantaneous velocity elds and associated velocity gradients: (a) the blade just passed and the plane of measurement is in the aspiration zone; (b) the blade is about 20 after the plane of measurement; (c) the blade is out of the plane of measurement.
can be seen that counter-rotating vortices are generated by the blade tip, and the impinging jet on the lateral wall. The velocity gradients remain high and reach 60 s 1. Figure 7(c) corresponds to a position of the blade outside the plane of measurement. In this case, the vortices are randomly distributed. Instantaneous velocity gradients do not reach more than 40 s 1. These results indicate that the instantaneous velocity gradient can be six times larger than the averaged value. This analysis clearly points out two important results: (1) the maximum values of instantaneous velocity gradients are located in a particular region, around the blade; (2) these maximums are reached just after the passage of the blade, in the aspiration zone or in the counter-rotating vortices generated by the blade tip. During the occulation process, ocs can also be submitted to very high shear and strain stress when they are transported in the region between the blade and the vessel edge just after the blade passage. In the range of blade velocity analysed in this study, the ow regime lies in the transition range between laminar and turbulent. Nevertheless, the velocity gradient has been estimated for a turbulent ow, following: G
e n
1=2
4
where the dissipation rate of Turbulent Kinetic Energy (TKE) is estimated by an approximate balance of the turbulent kinetic equation: Dissipation Production Transport, neglecting diffusion. In this analysis, the velocity elds have been represented only in a vertical plane, where the eddies generated by the blade take place and lead to maximum values for the velocity gradient. In the region around the blade, and particularly in the eddies, the produc-
tion of TKE reaches maximum values, whereas the transport reaches maximum values in the impinging jet, between the blade and the vessel wall. In this plane, the production of TKE is derived as: Pr
uw
@U @z
@W @x
5
and its transport is expressed as follows: Tr
U
@k @x
W
@k @z
6
where u w represents the average value of the velocity uctuation correlation, and k the turbulent kinetic energy. The results are plotted in Figures 8(a) to 8(d). The maximum value of the turbulent velocity gradient reaches 35 s 1 at 30 rpm, 60 s 1 at 45 rpm, 90 s 1 at 60 rpm, 180 s 1 at 90 rpm and 360 s 1 at 150 rpm. At 30 rpm, it corresponds to four times the average value estimated by the direct derivation of the velocity eld. At 150 rpm it now corresponds to more than ten times the average value previously estimated. LINK BETWEEN MAXIMUM FLOC SIZE AND HYDRODYNAMICS These results show the importance of considering the local turbulence parameters for the determination of the velocity gradient. Starting from the previous results, the larger ocs dmax size are compared to the average velocity gradient and to the maximum value of the velocity gradient given by equation (4). Many authors have studied the relation between the maximum oc size dmax and the Trans IChemE, Vol 79, Part A, November 2001
ANALYSIS OF FLOC SIZE IN A JAR-TEST
1023
Figure 8. Average turbulent velocity gradient determined by a balance with the production and the transport of the dissipation rate of Turbulent Kinetic Energy.
average energy dissipated in the vessel7–10 using the following relation: dmax
C ex
C G
2x
7
where e represents the global power input in the vessel, C is a constant, and x a coef cient. Ducoste and Clark11 criti-
cized this approach and proposed to rely on the oc size to local parameters such as local stress and strain rate, rather than a global value of the velocity gradient. Another approach consists in relying the oc size to local values of the velocity gradient. In this paper, two different ways have been used to calculate the velocity gradient; (1) by determining the maximum value of the averaged velocity gradient calculated by a direct derivation of velocity elds, (2) by
Figure 9. Evolution of the most probable oc diameter versus the maximum value of the average velocity gradient determined by a direct derivation of the velocity elds and versus the maximum value of the turbulent velocity gradient for ve impeller speeds.
Trans IChemE, Vol 79, Part A, November 2001
BOUYER et al.
1024
taking into account turbulence for the calculation of G. Figure 9 shows that in each case, the maximum oc size follows the classical trend represented by equation (7). In laminar ow, the oc size tend to decrease by G 1 and e 1/2. In turbulent ow, the oc size decreases by G 2/3 and e 1/3. This result can be compared to the relation proposed by Hinze12, which rely the maximum size of bubbles with the dissipation rate of the turbulent kinetic energy following: Dmax e 0.4. CONCLUSION AND PERSPECTIVES This paper constitutes the rst step of a more general study on occulation. It shows the possibility of using a deterministic approach to describe the coagulation– occulation phenomena. This work is based on experimental analysis of both oc size distributions and local hydrodynamics. The temporal evolution of the oc size distributions are determined from a statistical analysis of measurements and after image processing. It leads to basic information on agglomeration kinetics. The statistical analysis of the velocity eld enables the mean velocity eld and the magnitude of mean velocity gradients to be determined. However, it is interesting to focus on instantaneous velocity elds and the associated instantaneous velocity gradients. The analysis must be completed in order to estimate the real nature of the velocity uctuations (randomly turbulent or periodically induced by the impeller). The main objective is to relate the oc size to the characteristic structures of the ow (large coherent structures or small scale turbulent structures). The major issues of the general study are to get a better understanding of the complex interactions between ocs and mixing. Thanks to a predictive model, full-scale design will be possible in order to optimize the coagulation– occulation process.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
Smoluchowski, M. V., 1917, Versuch zur Mathematishen Theorie der Koagulationskinetic Kolloider Lo¨sungen, Z Phys Sci, 92: 129. Camp, T. R. and Stein, P. C., 1943, Velocity gradient and internal work in uid motion, J Boston Soc of CE, 30: 219. Saffman, P. G. and Turner, J. S., 1956, On the collision of drops in turbulent clouds, J Fluid Mech, 1: 16. Levich, V. G., 1962, Physcochemical Hydrodynamics (Prentice Hall, Englewood Cliffs, USA). Taylor, G. I., 1938, The spectrum of turbulence, Proc Roy Soc, A164: 476. Kramer, T. A. and Clark, M. M., 2000, Turbulence in occulators: Effects of tank size and impeller type, J Colloid Inter Sci, 227: 251. Thomas, D. G., 1964, Turbulent disruption of ocs in small particle size suspension, AIChe J, 10(4): 517. Parker, D. S., Kaufman, W. J. and Jenkins, D., 1972, Floc break-up in turbulent occulation processes, J Sanit Div ASCE, SA1: 79. Sonntag, R. C. and Russel, W. B., 1987, Structure and break-up of ocs subjected to uid stresses: II. Theory, J Colloid Inter Sci, 115: 411. Kuster, K. A., Wijers, J. G. and Thoenes, D., 1996, Aggregation kinetics of small particles in agitated vessels, Chem Eng Sci, 52: 107. Ducoste, J. J. and Clark, M. M., 1997, Modelling orthokinetic coagulation in spatially varying laminar ow, AIChe J, 43(2): 328. Hinze, J. O., 1975, Turbulence (McGraw-Hill, New York, USA). Botero, J. Y. Private Communication. Melis, S., Verduyn, M., Storti, G., Morbidelli, M. and Baldyga, J., 1999, Effect of uid motion on the aggregation of small particles subject to interaction forces, AIChe J, 45(7): 1383.
ACKNOWLEDGEMENTS The authors gratefully acknowledge nancial support provided by ONDEO-Services.
ADDRESS Correspondence concerning this paper should be addressed to A. Line, INSA, DPT.GPI, Complexe Scient. Rangueil, 31077 Toulouse Cedex, France. E-mail: [email protected]
Trans IChemE, Vol 79, Part A, November 2001
EXPERIMENTAL ANALYSIS OF FLOC SIZE DISTRIBUTION AND HYDRODYNAMICS IN A JAR-TEST D. BOUYER1 , A. LINE1 , A. COCKX 1 and Z. DO-QUANG2 1
LIPE, INSA-DGPI, Toulouse Cedex, France 2 ONDEO-Services, Le Pecq, France
T
he present work concerns coagulation- occulation in drinking water treatment units. This study focuses on the link between hydrodynamics and oc size distribution. Experimental analysis of both oc size distributions and local hydrodynamics are performed in a jar-test vessel. In this study, water quality (pH) and coagulant (both type and dose) are xed. Floc size distributions are analysed by image processing. The temporal evolution of the oc size distributions is determined from a statistical analysis of experimental data. It leads to basic information on oc agglomeration kinetics. The velocity eld is analysed using Particle Image Velocimetry (PIV). The statistical analysis of the velocity eld leads to the determination of the average velocity eld and the average velocity gradients. In addition, instantaneous velocity elds and associated instantaneous velocity gradients are determined. It is shown to be important to locate their maximum values. The analysis highlights the close relationship between the characteristic size of the ocs and hydrodynamics, that can be expressed in terms of local dissipation of turbulence or in terms of velocity gradient. Keywords: mixing; agitation; local hydrodynamics; occulation; oc size distribution; water treatment.
INTRODUCTION The coagulation/ occulation step is a major process in drinking water treatment plants. The reliability of plant operation and the nal water quality together with the problems of cost control are the most important issues for water treatment professionals. The prediction of the optimum coagulant dose is the crucial question for two basic reasons: rstly, coagulant overdosing leads to high operating costs and risks leading to problems with public health concerns. Secondly, under-dosing the coagulant leads to low treatment ef ciency and insuf cient removal of solid particles in the operation of water treatment plants. This could lead to a failure to meet water quality standards. The new stringent regulations on the acceptable residual coagulant level in distributed water, impose a very strict control for the absence of any remaining aluminium or ferric salts residuals. In the present study, a jar-test is used in order to control and optimize the coagulant dosage. The present work focuses on the link between hydrodynamics and occulation. Such a local description of occulation offers many advantages: it allows a better understanding of the major role of the mixing on the oc aggregation kinetics and of the dissipation rate of the turbulent kinetic energy for the break-up and structure of large ocs. Mixing could then be optimized in the scope of occulation. The coagulation/ occulation process has been studied for many years. Smoluchowski1 rst proposed a global description of the particle collision in 1917. The analysis was restricted to simple laminar ow and the Brownian motion
was not considered. The collision rate between particles of diameter di and dj in a two dimensional ow can be derived as follows: 3
@U di dj 1 @Z 6 Camp and Stein2 generalized this expression and introduced the velocity gradient (G):
b di ; dj
b di ; dj
G
di
dj
6 where G is expressed as: G
P rV n
3
2
3
n represents the kinematic viscosity, P the global power input in the system and V the volume. P is balanced by the global kinetic energy dissipation. In laminar ow, the energy is dissipated by the mean ow, whereas for a turbulent ow, it is mostly dissipated by the turbulent motion. In turbulent ow, Saffman and Turner3 introduced the dissipation rate of the turbulent kinetic energy (e), which is equal to the power per unit mass (P=rV). Using dimensional analysis, Levich4 proposed to rely the collision rate in a turbulent ow to a turbulent diffusivity. The turbulent diffusivity is then proportional to an average eddy velocity multiplied by a length scale that is characteristic of the size of the energetic eddies. Such approaches are based on Taylor’s5 statistical analysis of
1017
BOUYER et al.
1018
Figure 1. Experimental set-up.
Table 1. Experimental conditions. Bentonite 30 mg l
1
Aluminium Peri-kinetic (coagulant) mixing 25 mg l
1
150 rpm for 180 s
Ortho-kinetic mixing 30 rpm 45 rpm 60 rpm 90 rpm 150 rpm
for for for for for
17 min 17 min 12 min 12 min 12 min
Time between each photo (s) 15 15 15 15 15
isotropic turbulence. Kramer and Clark6 discussed this point and showed that the global velocity gradient G is not suf cient to correctly predict the orthokinetic coagulation. Indeed, different systems with different vessel or impeller geometries can have the same velocity gradients, but the oc particle size distribution can be different due to local stress and strain rates. The objective of this work lies in the modelling of occulation phenomena. Such a modelling approach is based on the coupling between agitated vessel local hydrodynamics and oc aggregation kinetics and break-up. The hydrodynamics are rst studied experimentally and then simulated numerically, using CFD (Computational Fluid Dynamics) code. The experiments are done in a
Figure 2. Images of ocs (initial and nal steps). Image size: 30 mm 30 mm.
jar-test. Given different hydrodynamics induced by different impeller velocities, data acquisition of oc size distributions during occulation is performed. An image processing system allows the evolution of the ocs in the jar-test to be followed. These data will be used to develop a population balance model for the oc. In the next step, the model is coupled with hydrodynamics and implemented in the CFD code in order to numerically simulate the occulation phenomena. The experimental set-up is described below. Results on oc size distribution are discussed. Results on
Figure 3. Mean area of ocs versus time for ve impeller speeds.
Trans IChemE, Vol 79, Part A, November 2001
ANALYSIS OF FLOC SIZE IN A JAR-TEST
1019
Figure 4. Floc size distributions: (a) 30 rpm; (b) 45 rpm; (c) 60 rpm; (d) 150 rpm.
hydrodynamics are then presented. Finally, the maximum oc size is related to hydrodynamics characteristics. EXPERIMENTAL SET-UP Coagulation Process Analysis The experimental study is carried out in jar-test vessel (see Figure 1). A synthetic suspension of bentonite is used to simulate the behaviour of particles present in natural water. Aluminium is used as a coagulant during these experiments. In order to follow the oc size evolution, the PIV technique is used. It consists of illuminating a 2-dimensional sheet with a laser beam. A camera is placed perpendicular to the laser and then takes pictures at constant time intervals. Images are recorded on a PC and are then processed with Visilog 5.1. This software allows each individual particle to be identi ed and its area and perimeter in the illuminated plane to be determined. Mixing between the suspension of bentonite and the coagulant is a critical phase in the coagulation process. Just after the injection of coagulant, the tank is mixed at high speed, 150 rpm during 180 seconds. This provides an initial peri-kinetic phase that enhances the Brownian motion between colloids. The next phase consists of mixing the tank at a lower speed, limiting shear stress in order to control the oc growth and their structure. The study will focus on this second phase. The operating conditions are summarized in the Table 1 and examples of images of ocs with PIV techniques are shown in Figure 2. Trans IChemE, Vol 79, Part A, November 2001
Hydrodynamic Analysis The PIV technique is used to study hydrodynamics. It is based on the four following steps: (1) the uid ow volume under investigation is needed; (2) illuminating a slide of the ow eld with a pulsing light sheet; (3) two images of the uid ow are recorded with a short time interval between them, using a numerical CCD camera; (4) these images are processed by dividing the whole images into interrogation areas and using inter correlation techniques to get the instantaneous velocity eld. The PIV system used is the commercial system acquired from Dantec Measurement Technology. The system includes a laser (Mini Yag, 15 Hz, 30 mJ), a double image recorder camera (Kodak Megaplus ES 1.0, 1024 1024 pixels), a dedicated processor (PIV 2000) and software. The processor makes all the calculations in real time. As the processor produces vector maps, these are displayed and optionally stored by the software. The seeding material is spherical glass hollow silvered particles from Dantec (density 1.4, 10 mm < d < 30 mm). FLOC SIZE DISTRIBUTION RESULTS It is important to emphasize that this technique is an in-situ and non destructive technique. In addition, the vessel is completely closed, thus, the ow is not disturbed by
1020
BOUYER et al.
Figure 5. Mean velocity elds: (a) 30 rpm, maximum velocity: 2.9 10 velocity: 5.3 10 2 m s 1; (d) 150 rpm, maximum velocity: 12.5 10
2 2
m s 1; (b) 45 rpm, maximum velocity: 3.8 m s 1.
pumps. However, the data acquisition technique gives only two dimensional information on the oc size (perimeter, area, shape). The time evolution was recorded every 15 seconds. Floc size distributions are plotted in Figures 4(a) to 4(d). Figure 3 exhibits the evolution of the average oc area with time. The size evolution is similar in each case during the peri-kinetic phase because the impeller speed remains equal to 150 rpm. During the ortho-kinetic phase, two trends can be identi ed: the oc size increases as the occulation starts and the smallest particles are continuously captured by the bigger ones. Three observations can be deduced from Figure 3: (1) the nal oc size decreases with increasing impeller speed; (2) the steady state is reached more rapidly with increasing impeller speed (400 s at 60 rpm and more than 1000 s at 30 rpm); (3) the oc size tends to increase in the rst step then decreases in the second step. This is probably due to a
10
2
ms
1
; (c) 60 rpm, maximum
re-organization of the oc structure under the ow stress (J.Y. Botero, private communication). The oc size distributions for four impeller speeds at different times are plotted in Figures 4(a) to 4(d). Area weighted percentages are plotted versus area classes. It is possible to follow the largest ocs evolutions. At the end of the process, the number of tiny particles remains larger than the larger ocs. In each case, an initial distribution reaches a steady state during the peri-kinetic phase after 100 s. Then the distribution evolves toward larger size distributions with decreasing impeller speed. When the impeller speed remains constant (150 rpm), the size distributions slowly decrease. With increasing impeller speed, it can be seen in Figures 4(a) to 4(d) that the collision kinetic increases: large ocs are more rapidly formed and the steady state is reached earlier (after 300 s at 30 rpm, after 250 s at 45 rpm, after 200 s at 60 rpm and after only 100s at 150 rpm). These gures point out the in uence of the ow on the oc size at steady state. The ocs are bigger with decreasing impeller Trans IChemE, Vol 79, Part A, November 2001
ANALYSIS OF FLOC SIZE IN A JAR-TEST
1021
Figure 6. Average velocity gradient determined by a direct derivation of instantaneous velocity elds: (a) 30 rpm; (b) 45 rpm; (c) 60 rpm; (d) 150 rpm.
speed. The distributions reach a steady state with ocs of diameter equivalent to about 1200 mm at 30 rpm, 800 mm at 45 rpm, 600 mm at 45 rpm and 300 mm at 150 rpm. This latest observation clearly points out the importance of understanding the break-up mechanisms and the oc structure evolution. A local description of hydrodynamics is thus needed. HYDRODYNAMICS RESULTS In the present paper, the velocity eld is reported in a vertical plane, around the impeller. The impeller height is 20 mm and the size of the measurement zone is 50 50 mm2. The experiments are carried out using the PIV technique for different impeller velocities: N 30, 45, 60, 90 and 150 rpm. Mean velocity elds are obtained after statistical averaging over 1000 instantaneous velocity elds. The mean velocity elds are plotted in Figures 5(a) to 5(d). The structure of the ow is the same in each case, with induced velocities increasing with increasing impeller velocities. At the same time, the mean velocity gradient G can be derived from the statistical average of instantaneous elds. The mean velocity gradients are Trans IChemE, Vol 79, Part A, November 2001
plotted in Figures 6(a) to 6(d). In the region of the impinging jet, the maximum value of the velocity reaches 2.9 10 2 m s 1 at 30 rpm, 3.8 10 2 m s 1 at 45 rpm, 5.3 10 2 m s 1 at 60 rpm, 7.8 10 2 m s 1 at 90 rpm and 12.5 10 2 m s 1 at 150 rpm. The associated average velocity gradient reaches 9 s 1 at 30 rpm, 12 s 1 at 45 rpm, 15 s 1 at 60 rpm, 21 s 1 at 90 rpm and 33 s 1 at 150 rpm. However, such results are only meaningful in terms of statistical average. In order to better understand the local and instantaneous phenomena which can control the ocs size, different instantaneous velocity elds are presented and discussed. The instantaneous velocity elds correspond to an impeller speed about 60 rpm and are shown in Figures 7(a) to 7(c). The associated instantaneous velocity gradients have been estimated and plotted in Figures 7(d) to 7(f ). The Figures 7(a) and 7(b) correspond to 2 successive positions of the blade in the plane of measurements. Figure 7(a) shows that the blade has just passed and the plane of measurement is in the aspiration zone created behind it. The instantaneous velocity gradients reach maximum values in such a zone (100 s 1). Figure 7(b) shows that the blade is located 20 behind the plane of measurement; it
BOUYER et al.
1022
Figure 7. Instantaneous velocity elds and associated velocity gradients: (a) the blade just passed and the plane of measurement is in the aspiration zone; (b) the blade is about 20 after the plane of measurement; (c) the blade is out of the plane of measurement.
can be seen that counter-rotating vortices are generated by the blade tip, and the impinging jet on the lateral wall. The velocity gradients remain high and reach 60 s 1. Figure 7(c) corresponds to a position of the blade outside the plane of measurement. In this case, the vortices are randomly distributed. Instantaneous velocity gradients do not reach more than 40 s 1. These results indicate that the instantaneous velocity gradient can be six times larger than the averaged value. This analysis clearly points out two important results: (1) the maximum values of instantaneous velocity gradients are located in a particular region, around the blade; (2) these maximums are reached just after the passage of the blade, in the aspiration zone or in the counter-rotating vortices generated by the blade tip. During the occulation process, ocs can also be submitted to very high shear and strain stress when they are transported in the region between the blade and the vessel edge just after the blade passage. In the range of blade velocity analysed in this study, the ow regime lies in the transition range between laminar and turbulent. Nevertheless, the velocity gradient has been estimated for a turbulent ow, following: G
e n
1=2
4
where the dissipation rate of Turbulent Kinetic Energy (TKE) is estimated by an approximate balance of the turbulent kinetic equation: Dissipation Production Transport, neglecting diffusion. In this analysis, the velocity elds have been represented only in a vertical plane, where the eddies generated by the blade take place and lead to maximum values for the velocity gradient. In the region around the blade, and particularly in the eddies, the produc-
tion of TKE reaches maximum values, whereas the transport reaches maximum values in the impinging jet, between the blade and the vessel wall. In this plane, the production of TKE is derived as: Pr
uw
@U @z
@W @x
5
and its transport is expressed as follows: Tr
U
@k @x
W
@k @z
6
where u w represents the average value of the velocity uctuation correlation, and k the turbulent kinetic energy. The results are plotted in Figures 8(a) to 8(d). The maximum value of the turbulent velocity gradient reaches 35 s 1 at 30 rpm, 60 s 1 at 45 rpm, 90 s 1 at 60 rpm, 180 s 1 at 90 rpm and 360 s 1 at 150 rpm. At 30 rpm, it corresponds to four times the average value estimated by the direct derivation of the velocity eld. At 150 rpm it now corresponds to more than ten times the average value previously estimated. LINK BETWEEN MAXIMUM FLOC SIZE AND HYDRODYNAMICS These results show the importance of considering the local turbulence parameters for the determination of the velocity gradient. Starting from the previous results, the larger ocs dmax size are compared to the average velocity gradient and to the maximum value of the velocity gradient given by equation (4). Many authors have studied the relation between the maximum oc size dmax and the Trans IChemE, Vol 79, Part A, November 2001
ANALYSIS OF FLOC SIZE IN A JAR-TEST
1023
Figure 8. Average turbulent velocity gradient determined by a balance with the production and the transport of the dissipation rate of Turbulent Kinetic Energy.
average energy dissipated in the vessel7–10 using the following relation: dmax
C ex
C G
2x
7
where e represents the global power input in the vessel, C is a constant, and x a coef cient. Ducoste and Clark11 criti-
cized this approach and proposed to rely on the oc size to local parameters such as local stress and strain rate, rather than a global value of the velocity gradient. Another approach consists in relying the oc size to local values of the velocity gradient. In this paper, two different ways have been used to calculate the velocity gradient; (1) by determining the maximum value of the averaged velocity gradient calculated by a direct derivation of velocity elds, (2) by
Figure 9. Evolution of the most probable oc diameter versus the maximum value of the average velocity gradient determined by a direct derivation of the velocity elds and versus the maximum value of the turbulent velocity gradient for ve impeller speeds.
Trans IChemE, Vol 79, Part A, November 2001
BOUYER et al.
1024
taking into account turbulence for the calculation of G. Figure 9 shows that in each case, the maximum oc size follows the classical trend represented by equation (7). In laminar ow, the oc size tend to decrease by G 1 and e 1/2. In turbulent ow, the oc size decreases by G 2/3 and e 1/3. This result can be compared to the relation proposed by Hinze12, which rely the maximum size of bubbles with the dissipation rate of the turbulent kinetic energy following: Dmax e 0.4. CONCLUSION AND PERSPECTIVES This paper constitutes the rst step of a more general study on occulation. It shows the possibility of using a deterministic approach to describe the coagulation– occulation phenomena. This work is based on experimental analysis of both oc size distributions and local hydrodynamics. The temporal evolution of the oc size distributions are determined from a statistical analysis of measurements and after image processing. It leads to basic information on agglomeration kinetics. The statistical analysis of the velocity eld enables the mean velocity eld and the magnitude of mean velocity gradients to be determined. However, it is interesting to focus on instantaneous velocity elds and the associated instantaneous velocity gradients. The analysis must be completed in order to estimate the real nature of the velocity uctuations (randomly turbulent or periodically induced by the impeller). The main objective is to relate the oc size to the characteristic structures of the ow (large coherent structures or small scale turbulent structures). The major issues of the general study are to get a better understanding of the complex interactions between ocs and mixing. Thanks to a predictive model, full-scale design will be possible in order to optimize the coagulation– occulation process.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
Smoluchowski, M. V., 1917, Versuch zur Mathematishen Theorie der Koagulationskinetic Kolloider Lo¨sungen, Z Phys Sci, 92: 129. Camp, T. R. and Stein, P. C., 1943, Velocity gradient and internal work in uid motion, J Boston Soc of CE, 30: 219. Saffman, P. G. and Turner, J. S., 1956, On the collision of drops in turbulent clouds, J Fluid Mech, 1: 16. Levich, V. G., 1962, Physcochemical Hydrodynamics (Prentice Hall, Englewood Cliffs, USA). Taylor, G. I., 1938, The spectrum of turbulence, Proc Roy Soc, A164: 476. Kramer, T. A. and Clark, M. M., 2000, Turbulence in occulators: Effects of tank size and impeller type, J Colloid Inter Sci, 227: 251. Thomas, D. G., 1964, Turbulent disruption of ocs in small particle size suspension, AIChe J, 10(4): 517. Parker, D. S., Kaufman, W. J. and Jenkins, D., 1972, Floc break-up in turbulent occulation processes, J Sanit Div ASCE, SA1: 79. Sonntag, R. C. and Russel, W. B., 1987, Structure and break-up of ocs subjected to uid stresses: II. Theory, J Colloid Inter Sci, 115: 411. Kuster, K. A., Wijers, J. G. and Thoenes, D., 1996, Aggregation kinetics of small particles in agitated vessels, Chem Eng Sci, 52: 107. Ducoste, J. J. and Clark, M. M., 1997, Modelling orthokinetic coagulation in spatially varying laminar ow, AIChe J, 43(2): 328. Hinze, J. O., 1975, Turbulence (McGraw-Hill, New York, USA). Botero, J. Y. Private Communication. Melis, S., Verduyn, M., Storti, G., Morbidelli, M. and Baldyga, J., 1999, Effect of uid motion on the aggregation of small particles subject to interaction forces, AIChe J, 45(7): 1383.
ACKNOWLEDGEMENTS The authors gratefully acknowledge nancial support provided by ONDEO-Services.
ADDRESS Correspondence concerning this paper should be addressed to A. Line, INSA, DPT.GPI, Complexe Scient. Rangueil, 31077 Toulouse Cedex, France. E-mail: [email protected]
Trans IChemE, Vol 79, Part A, November 2001