Computational Methods in Multiphase Flow IV 93 Experimental investigations o sedimentation o locs in suspensions o biological water treatment plants B. Zajdela 1,, A. Hribernik & M. Hribersek 1 gional Development Agency Mura Ltd, Slovenia Faculty o Mechanical engineering, University o Maribor, Slovenia Abstract This contribution deals with the movement o locs in suspensions, as they appear in biological water treatment (BWT plants. The irst part o the work deals with the description o a model BWT plant, ollowed by the deinition o a problem. The greatest attention is given to the geometrical and sedimentation characteristics o solid locs, key parameters or developing a ast numerical procedure or simulation o locs movements. An extensive analysis is presented o loc size distribution and their shapes. Based on the results o experimental investigations, the main geometrical parameters o the locs are deined and calculated. The second part o the work deals with calculating loc density, based on ree settling sedimentation tests and known empirical correlations or drag coeicient. Keywords: biological treatment plants, sedimentation, image analysis, size distribution, drag coeicient, density. 1 Introduction Today, wastewater treatment with the activated sludge is the most widespread process or removing dissoluble substances, small insoluble substances and colloidal organic pollutants rom wastewater. The eiciency o the process primarily depends on growing biological biocenoze, consuming and consequently removing unwanted substances, and secondarily on accumulating the activated sludge into sludge locs. The sludge locs are subjected to circulation inside the wastewater processing tank and in the inal phase o the locs sedimentation process, separating the cleaned water rom the accumulated doi:10.495/mpf07081
94 Computational Methods in Multiphase Flow IV impurities in the sludge [1]. The rate o sedimentation depends on the properties o the locs, such as size, shape, density, permeability, number density and type o wastewater (industrial, municipal. In the presented paper, the greatest attention is thereore given to determining the size distribution and main geometrical parameters o the sludge locs, by means o image analysis. Additionally, ree settling tests in connection with empirical models or determining o the drag coeicient (C D are used, in order to evaluate the densities o the locs. Materials and methods.1 Biological treatment plant The perormed analysis o the sludge locs concentrated on the data, obtained rom the wastewater samples o the Water treatment plant in Lendava, Slovenia. The wastewater samples, taken rom the plant, were analysed within a time period o 1-3 days. The samples were diluted and kept at 0 o C. The analysed wastewater was a mixture o technological and municipal waste water in the ratio o 75:5. Several analyse o various waste water samples were needed in order to obtain accurate and representative results.. Image analysis system Wastewater samples were investigated using a Nikon stereoscopic microscope, which allowed us to see the samples at 0-16x magniication. Pictures were taken with a high-resolution Sony CCD videocamera, computer controlled using the Lucia M (Nikon, Japan sotware package. Lucia M is a colour-image analysis sotware system, handling and analyzing High Color (3x5 bits or RGB components digital images o typical 75x54 pixels resolution. Lucia M basically recognizes two types o images binary and colour. Binary images have two possible values, 0 or background and a maximum o 6 or objects and structures. Binary images are produced by segmentation unctions such as threshold and are oten reerred to as segmented images. Figure 1: Colour and binary images o sludge loc.
Computational Methods in Multiphase Flow IV 95 Once the threshold value is deined the object can be clearly distinguished rom the background, such segmented images (ig. 1 being used or automated shape and size measurements (area, diameter, and perimeter..3 Preparation o samples The sludge sample must be suiciently diluted to avoid saturation o the image and the liquid layer thickness must be small enough to enable the use o relatively high magniications (80x, ocusing on a thin plane. By experimenting with dierent levels o dilution we discovered that some areas overlap even at the dilution ratio 1:15. Further diluting increased the isolation o the locs and at a dilution o 1:0 there was no loc overlap. As quoted in Grijspeerdt and Verstraete [], it is inherent to image analysis that smaller objects produce larger measurement errors. Objects are approximated by square pixels, resulting in a less accurate measurement o smaller objects. This problem could be solved by imposing a lower limit on the number o pixels in an object. Russ noted that 0.1% o objects comprising a number o pixels smaller than 0.1% o the total number o pixels o an image should not be taken into account [3]. In our case the size o the picture was 75x54 pixels and so 0.1% o the picture represented 394 pixels. In the case o 80x magniication this means that 0.1% o the picture was within an area o 0.001646 mm, thereore, locs smaller that this area were not analysed..4 Drag on non-spherical particles In general, the orce balance or a loc moving steadily in an ininite medium can be described as ollows [4]: ρ = 1 e = v ρ ρ 4g( ρ ρ d ρ w 3ρ wωcd (1 p w p w ρ is loc density, ρ w is the density o the water and ρ P is the density o the primary particles comprising the loc, C D is the drag coeicient, g is gravitational acceleration, v is the terminal velocity, d is the diameter o the loc, and e is porosity o the loc. In most studies, ρ P is assumed to be equal to ρ S, the dried solid density [5, 6]. Ω is the ratio o the resistance experienced by a porous loc to that o an equivalent solid sphere. Floc porosity is neglected in many studies [5, 7] and Ω is simply set to 1. The ρ is diicult to measure experimentally, thereore we decided to compute it based on data (velocity obtained rom the sedimentation properties o the locs, as ollows: (3 ρ 1 C v w D ρ = + (4 g d ρ w ( In order to evaluate the right hand side in eqn. ( geometrical data and data on the C D o the locs must be known. In the present work, the C D correlations
96 Computational Methods in Multiphase Flow IV were used o dierent authors, who have perormed comparison studies. The diameters and volumes o the locs were calculated based on image analysis. Sedimentation tests were perormed or terminal velocity. In general, C D is a unction o ynolds number ( and loc sphericity. An equal volume sphere diameter is needed as the characteristic linear dimension in order to evaluate the C D. As a consequence, the sphericity (ψ is commonly introduced in order to quantiy the extent o the particle s deviation rom the spherical-shaped (Wadell [8]: 3 p 3 p 1 6 V p V 4. 84V 3 ψ = = (6 π = (3 d s A p Ap Ap where V p is volume o the loc and A p is the surace area o the loc. Corey s shape actor (β can be used as an alternative to sphericity, with a>b>c the lengths o the three principal axes o the loc: β=c/(ab 1/ (4 When dealing with the sedimentation o particles in an ininite medium, the particle ynolds number is deined as: ψ vρ wd = (5 η where v is the terminal velocity o the loc in the medium o dynamic viscosity η which, due to the incorporation o sphericity, diers rom the classical equation or spheres: vρ wd = (6 η The starting point or derivation o a suitable expression or the C D o a nonspherical particle is the well-known expression or the sphere in a laminar low: 4 C D = (7 In the case o non-spherical locs it is most appealing to derive a correction to the expression (7. Haider and Levenspiel [9] developed an expression or C D or nonporous spherical and non-spherical locs in incompressible media: C D 4 B C = (1 + A + D 1+ (8
Computational Methods in Multiphase Flow IV 97 with the values o A, B, C and D as model constants and the equal volume sphere diameter used in the deinition o. This method is applicable or <.6 x 10 5, uncertainty is predicted to be 15-0%. They also proposed the ollowing equation or locs o Ψ > 0.67: C D = 4 73.69 e + + 5.378 e ( 4.0655ψ (0.0964+ 0.5565ψ [ 1 + { 8.1716 e }* ] ( 5.0748ψ (6.1ψ (9 Ganser [10] assumed that every loc experiences a Stokes s regime where drag is linear in velocity and a Newton s regime where drag is proportional to the square o velocity. He thus introduced two shape actors K 1 and K applicable in both the Stokes and Newton regimes, respectively, in the ollowing drag correlation: 0.6567 { 1 + 0.1118( K K } C 4 D = 1 + K K1K 1 + 0.4305 3305 K K 1 (10 with based on the equal volume sphere diameter, and K 1 and K as unique unctions o sphericity: 0.5 [( / 3 + ( / 3 ] 1 K 1 = d n d ψ (11 0.5743 1.8148( logψ K = (1 10 where d n is the equally projected area o the circles diameter. Swamee and Ojha [11] employed the equal volume sphere diameter and used the so called Corey shape actor (β in the ollowing drag expression: C D 48.5 + = 8 ( 0.35 0.8 0.64 18 0. 1+ 4.5β + 100 + 100β β + 1. 05β 0.3 1 (13 which was stated to be applicable within the range 0.3 < β <1 and 1 < <10.000. Finally, Chien [1] proposed the ollowing simple expression or drag, originating rom petroleum engineering literature: ( 5.03ψ C D = (30/ + 67.89 e (14 or 0. ψ 1 and < ~ 5000, where the equal volume sphere diameter was used.
98 Computational Methods in Multiphase Flow IV.5 Floc size distribution The presented image analysis system was applied or loc size distribution measurements. Automatic processing was perormed by allowing an appropriate threshold or the transormation o pictures into binary images. The results obtained were morphological characteristics o the locs. From the standard deviation σ analysis the minimum number o locs in a representative sample was determined to be n>400. Approximately 18 photos were needed to reach the minimum size or a representative sample. The basic sample consisted o 79 locs with the locs surace areas within the range rom 0.000004 mm to 0.0759 mm. According to the < 0,1% rule, we excluded all those locs whose areas were smaller than 0.001646 mm. 7 locs remained and were separated into 7 size classes. The details are presented in ig., showing locs requency distribution and cumulative locs surace area distribution. Following rom our observations, the average loc s equivalent diameter is 0.086837 mm and the average loc s surace area is 0.007845 mm. Number o paricle 50 40 30 0 10 0 Figure : 0,063 0,097 0,18 0,166 0,03 0,97 Mean diameter (mm 10 100 80 60 40 0 0 % area Number o particle % area Flocs requency distribution and cumulative locs surace area distribution..6 Main geometrical parameters Only observation o loc s plane projection is possible sing loc image analysis. No inormation on a loc s volume is necessary or the calculation o loc sphericity, C D and density. Due to the dierent shapes o locs it is very diicult to determine a representative three dimensional loc shape and volume. A large number o locs were, thereore, analysed. Each individual loc was rotated in order obtain loc images in three orthogonal planes (ig. 3 and then an attempt was made to create a 3D shape o a loc using its 3 orthogonal D images. The 3D loc s shape was approximated by an equivalent cuboid whose projections on the orthogonal planes were equal to those o the loc. The transormation can be written using a simple model as shown in ig. 3. 14 randomly selected locs rom the diluted sample (1:0 o waste water were processed in this way. Three replications were made or each individual loc and the proportions A = P1 A, B = P A, C = P3 A with P1,P and P3 as weighting actors, were estimated. Weighting actors P1 and P deviated only slightly rom their average values, while the scatter o weighting actor P3
Computational Methods in Multiphase Flow IV 99 was much bigger. In spite o this, the average values o weighting actors were used or the sake o simplicity and the ratio o the equivalent cuboid suraces was ound to be A : B : C = P1: P : P3 = 1: 0.89 : 0. 69. Experiments showed that the locs always set themselves up in a way that the projection surace in the horizontal plane which corresponds to the projection A (ig. 3 was the largest. Thereore, it is possible to estimate the sizes o projection planes B and C by measuring the projection o locs in plane A and considering the ratio A : B : C. The edges o the equivalent cuboids a, b and c are then determined and the volume o each loc is estimated as V=a b c. Finally the shape actors ψ and β, necessary in empirical equations or C D, are calculated. Since the constant ratio A : B : C was applied, the shape actors were equal or all locs. Eqn. (3 was applied or the prediction o loc sphericity ψ, which was ound to be ψ = 0.80 or the sampled wastewater. Corey actor β o locs was calculated rom eqn. (4 as β =0.86. B A C A = a * b c = B = b * c b = C = a * c a = B C A A B C A C B Figure 3: Equivalent cuboid; A, B, C - projection areas..7 Drag coeicient (C D A large number o ree settling tests were perormed and terminal settling velocities o locs were measured in order to estimate the suitability o the presented C D models given by eqns. (7 (14 A 50 ml glass cylinder was used and the time o travel o a single loc on a chosen distance was measured. Three replications o each settling test were made and the average terminal settling velocities was calculated. Only larger locs were selected or tests in order to improve visualisation quality. The results are shown in ig. 4. The terminal settling velocity o the locs varied between.5 and 4.7 mm/s. It increases with the locs diameter (size, which agrees with the results o other authors [13].
300 Computational Methods in Multiphase Flow IV Terminal velocity (mm/s 5,00 4,00 3,00,00 1,00 0,00 0,00 1,00,00 3,00 Equal volume sphere diameter (mm 10 8 6 4 0 ynolds number Equal volume sphere diameter vs terminal velocity Equal volume sphere diameter vs ynolds number Figure 4: Terminal velocity and ynolds number o locs. C D 14 1 10 8 6 4 0 0 4 6 8 10 C D Ganser C D Chien C D Haider1 C D Haider C D laminar C D Swamee in Ojha Figure 5: Comparison between dierent C D models. Data obtained rom the ree settling tests were used to predict the C D, ig. 5. The dierences between individual models were as high as 300%. Models proposed by Chien (eqn. (14 and Haider (eqns. (8 and (9 result in higher C D values than the perect sphere model (eqn. (7, while the models by Ganser (eqns. (10-(1 and Swamee (eqn. (13 predict lower C D values. The C D decreases with and the dierences between the individual models become smaller. However, it should not be neglected that only the largest locs were studied by ree settling tests. An average loc and its are much smaller, thus its C D is substantially higher than those presented in ig. 5, and an appropriate C D model is essential. It is evident, that models proposed by Ganser and Swamee under-predict C D value (it should not be under the C D value o the sphere. Models by Haider and Chien predict more reliable C D values which are very close together (± 10 %. Because o its simplicity and a wide application range the Chian model (eqn. (14 was chosen or application in our model..8 A loc s density A loc s density plays an important role in the sedimentation process. The sedimentation o suspended matter in the water is possible only i its density is higher than the water density. Otherwise it loats.
Computational Methods in Multiphase Flow IV 301 Using eqn. ( the locs density can be predicted i the loc s terminal velocity, C D and equivalent diameter are known. The densities o the locs used in the ree settling tests were estimated in this way. The measured terminal velocities and the loc s equivalent diameter were applied and C D predicted by the Chien model was used. The results are presented in ig. 6, where the dierence in the loc s and water densities is plotted against the loc s diameter. As can be seen the loc s density decreases with the loc s size. Flocs are ormed rom a large number o primary locs with the in-between ree space illed by water. Thereore, the loc density decreases with its size, which was also proven by other authors [13]. ρ (kg/m 3 9 8 7 6 5 4 3 1 0 0 0,5 1 1,5,5 3 Equal volume sphere diameter (mm Figure 6: Dierence o locs and water density against locs diameter. 3 Conclusion The properties o the activated sludge locs were examined. An image-analysis system was applied to determine loc size distribution. A representative waste water sample comprising 79 locs was acquired. Those locs larger than 0.1% o the whole image area were selected rom this sample and analyzed. The 3D loc shape was approximated by an equivalent cuboid whose projections on the orthogonal planes were equal to those o the loc. The ratio o the equivalent cuboid suraces was determined and used to predict loc volume and shape actors by measuring only the horizontal projection areas o the locs. Mean loc shape actors were ound to be ψ = 0.80 and β =0.86. A large number o ree settling tests were perormed and the obtained results were applied in six dierent C D models. The model proposed by Chien was selected as the most appropriate and applied in the loc-ree settling model or loc density computation. A loc s density was ound to vary with its size. The density o the smallest analysed loc was 1% higher and the density o the largest analysed loc was only 0.3 % higher than density o the water. The obtained results present a starting point or numerical simulation o a loc s motion in water, where the density o the loc, its size and its drag coeicient are key parameters or particle path computations.
30 Computational Methods in Multiphase Flow IV erences [1] Roš, M., Biološko čiščenje odpadne vode, GV založba, (001, (in slovene. [] Grijspeerdt, K. & Verstraete, W., Image analysis to estimate the settleability and concentration o activated sludge, Wat. s. 31, pp. 116-1134, 1997. [3] Russ, J. C., Computer Assisted Microscopy: the Measurement and Analysis o Images, Plenum Press, New York, 1990. [4] Huang, H., Porosity size relationship o drilling mud locs: ractal structure, Clay Clay Miner 41, pp. 373 379, 1993. [5] Tambo, N. & Watanabe, Y., Physical characteristics o locs. 1. The loc density unction and aluminum loc, Wat. s. 13, pp. 409 419, 1979. [6] Li, D.-H. & Ganczarczyk, J. J., Stroboscopic determination o settling velocity, size and porosity o activated sludge locs, Wat. s. 1, pp. 57 6, 1987. [7] Concha, F. & Almerdra, E. R., Settling velocities o particulate system, 1. Settling velocities o individual spherical particles, Int. J. Min. Process. 5, pp. 349 367, 1979. [8] Wadell, H., Sphericity and roundness o rock particles, J. Geol 41, pp. 310 331, 1933. [9] Haider, A. M., Levenspiel, O., Drag coeicient and terminal velocity o spherical and nonspherical particles, Power Technol. 58, pp.63 70, 1989. [10] Ganser, G. H., A rational approach to drag prediction o spherical and nonspherical particles, Power Technol. 77, pp. 143 15, 1993. [11] Swamee, P. K. & Ojha, C. P., Drag coeicient and all velocity o nonspherical particles, J. Hydraul. Eng. 117, pp. 660-667, 1991. [1] Chien, S. F., Settling velocity o irregularly shaped particles, SPE Drilling and Completion, pp. 81 89, 1994. [13] Lee, D. J., Chen, G. W. & Hsieh, C. C., On the re-settling test or estimating activated sludge loc density, Wat. s. 30, pp. 541 550, 1996.