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The influence of velocity gradient on properties and filterability of suspension formed during water treatment
Separation and Purification Technology 92 (2012) 161–167
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Separation and Purification Technology journal homepage: www.elsevier.com/locate/seppur
The influence of velocity gradient on properties and filterability of suspension formed during water treatment Petra Bubakova ⇑, Martin Pivokonsky Institute of Hydrodynamics, Academy of Sciences of the Czech Republic, v.v.i., Pod Patankou 30/5, 166 12 Prague 6, Czech Republic
a r t i c l e
i n f o
Article history: Available online 23 September 2011 Keywords: Aggregation Fractal dimension Filtration Particle size distribution Velocity gradient
a b s t r a c t This paper deals with the influence of the global velocity gradient G (in the range of 28–307 s1) on properties of suspension (size and structure) formed during water treatment. Furthermore, it describes the influence of these properties on separation using depth filtration (filtration velocities of 3 and 6 m h1). The methods of image and fractal analysis were used to determine the aggregate size and structure, respectively. The experiments were conducted in a pilot plant (a mixing tank and a rapid gravity sand filter) with ferric sulphate used as coagulant. The experiments confirmed that with an increasing velocity gradient the aggregate size decreased; the aggregate size distribution narrowed (suspension was more homogenous); the fractal dimension D2 increased (aggregates were more compact) and the fractal dimension Dpf diminished (aggregates were more regular). The smallest and most compact aggregates (d 60 lm and D2 = 1.9) formed at G > 200 s1 displayed the best filterability with the time of filtration up to 78 h. On the contrary, the filtration of large and porous aggregates formed at G 30 s1 lasted only about 30 h. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction The processes of destabilisation and aggregation are often used to remove colloidal particles in water treatment. The purpose is to prepare aggregates of such properties that are suitable for reaching the maximum effectiveness of following separation step(s). Aggregate properties are influenced by conditions under which they are formed. These conditions can be divided into two groups: (1) Physicochemical conditions, i.e. the type and dose of coagulant, pH, alkalinity and temperature [1,2]. Physicochemical conditions influence primarily the destabilisation of colloidal particles and they can be optimised on the basis of routine laboratory jar testing. (2) Hydrodynamics, i.e. local/global velocity gradient, distribution of velocity field, mixing time, etc. primarily given by the geometry of a mixing tank and the stirrer shape and speed [3,4]. Hydrodynamics influences mainly the aggregation of colloidal particles and represents a crucial factor in constituting properties (size, shape and structure) of the formed aggregates. In contrast to physicochemical conditions, the optimisation requires using the pilot plant tests. Hydrodynamics influences two different processes which occur simultaneously, i.e. aggregation and break-up [5–7]. These ⇑ Corresponding author. Tel.: +420 233 109 002; fax: +420 233 324 361. E-mail address: [email protected] (P. Bubakova). 1383-5866/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.seppur.2011.09.031
processes are formed by the balance between the hydrodynamic force F (kg m s2) and the cohesive force J (kg m s2). The hydrodynamic force arises from a flow of fluid around a particle and is, thus, determined by the magnitude of the velocity gradient G (s1), cross-sectional area of the particle A (m2) and dynamic viscosity of the fluid l (kg m1 s1). The cohesive force is given by the sum of all attractive forces acting between interacting particles (e.g. van der Waals, electrostatic or hydrophobic forces). It depends particularly on particle and reagent composition (material) and determines the strength of formed aggregates [6–10]. If the cohesive force prevails (J > F), aggregation occurs. If the hydrodynamic force prevails (F > J), aggregates are not formed at all or a breakup of already existing aggregates takes place. If the aggregate strength (cohesive force J) is fixed (i.e. physicochemical conditions are kept constant), the aggregate size is limited only by the hydrodynamic force represented by the velocity gradient G. For this case, the following empirical relationship between the stable floc size (d) and the global velocity gradient (G) has been developed [3,4,11–13]:
d ¼ C G2c ;
ð1Þ
where C is the constant representing the aggregate strength and c is the coefficient representing the aggregate break-up. It is necessary to realize that this expression includes the global velocity gradient, which is just a rough estimate of hydrodynamic conditions in real mixing devices, where the uniform distribution of G cannot be usually assured. Nevertheless, it is complicated to relate the size of an individual aggregate to specific location in the mixing device with a
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defined local G, especially in a pilot plant scale. For that reason, global velocity gradients are usually used in practice. The hydrodynamic force influences not only the size of the formed aggregate but also the arrangement of the primary particles in the aggregate. If the hydrodynamic force F is distinctively lower than the cohesive force J, particles combine at the point of the first contact and aggregates of porous structure and irregular shape are formed. Conversely, if the hydrodynamic force is only slightly lower than the cohesive force, particles tend to form compact aggregates which are energetically stable. Thus, compactness of the structure decreases with the diminishing magnitude of the hydrodynamic force [14–16]. The structure of aggregates has been recently studied by means of fractal dimension calculated from the data on light scattering or image analysis [15,17]. There are interesting studies dealing with the effect of hydrodynamics on the size and structure of aggregates formed during destabilisation and aggregation, some of which have already been mentioned [3,4,9,12,15,18–20]. However, these studies examine the influence of hydrodynamics on aggregate properties without a direct relation to subsequent depth filtration. The main objective of this paper is to describe the influence of the global velocity gradient on the properties of aggregates formed during the destabilisation and aggregation in a flow mixing tank, and to explain how the character of the formed aggregates affects separation using depth filtration. 2. Experimental 2.1. Raw water and reaction conditions The experiment used raw water from the Svihov reservoir (potable water source), Czech Republic. The tests were carried out during the winter period (December–February), when raw water quality was stabilized with the following parameters: temperature in the range of 2.6–4.1 °C (3.3 °C on average), pH between 7.2 and 7.5 (7.3 on average) and alkalinity of 0.92–1.13 mmol l1 (1.04 mmol l1 on average). Ferric sulphate hydrate Fe2(SO4)3 9H2O (Analytika, Ltd., Czech Republic) served as coagulant. The dose (3.98 mg l1 of Fe) was optimized by standard jar tests [21].
Fig. 1. Pilot plant arrangement. MT – mixing tank, RGF – rapid gravity filter, CTI – centre of taken images, S – sampling site, P1–P8 – pressure probe, 1 – header tank, 2 – regulation valve, 3 – flow-meter, 4 – homogeniser with injection of coagulant, 5 – feed pipe, 6 – variable speed drive, 7 – torque-meter, 8 – overflow, 9 – flow regulator, 10 – filtrate discharge pipe, 11 – data logging.
2.2. Pilot plant tests The influence of the velocity gradient on properties and filterability of formed suspension was tested using a pilot plant installed at the Zelivka waterworks, Czech Republic. 2.2.1. Pilot plant design The pilot plant consisted of a flow rate regulation unit, dosing unit, mixing tank (MT) and rapid gravity filter (RGF), as illustrated in Fig. 1. Raw water was brought to the flow rate regulation unit, consisting of a header tank (1), regulation valve (2) and flow-meter (3). A homogenizer (4) with injection of the coagulant was placed in front of the inlet to the mixing tank. Dosed raw water flowed through the feed pipe (5) into the mixing tank made of a Plexiglas tube. The geometry of the mixing tank was as follows: the tank diameter was 280 mm, the liquid height in the tank was 1500 mm, the stirrer diameter was 240 mm and the paddle height was 40 mm. The stirrer had four paddles connected with five transverse crosspieces. The paddle stirrer was driven by a variable speed drive (6) with a torque-meter (7). In the mixing tank, the hydrodynamic conditions were characterised by the global velocity gradient G calculated according to the relationship as follows:
G¼
sffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffi Pi xM 2pfM ; ¼ ¼ Vl Vl Vl
ð2Þ
where Pi represents the power dissipated in the tank (kg m2 s3), V is the volume of the tank (m3), l is the dynamic viscosity of the fluid (kg m1 s1), x is the angular stirrer velocity (rad s1), M is the torque (kg m2 s2) and f is the stirrer frequency (s1). Global velocity gradients used in this study were G = 28, 45, 77, 114, 153, 199, 244 and 307 s1 and the retention period of the suspension in the mixing tank corresponded to T = 900 s (steady state). The suspension formed in the mixing tank was allowed to drain away through an overflow (8) to RGF. RGF consisted of a Plexiglas tube 3 m long with the inner diameter d = 140 mm with pressure probes (P1–P8) placed along the depth and a flow regulator (9) installed in the filtrate discharge pipe (10). The filter was charged with silica sand with granularity of 0.8–1.2 mm (d50 = 1.11 mm) to a filter bed depth LF = 1050 mm. The operating water depth was LW = 970 mm. During the pilot plant operation, several RGF filtration runs were evaluated at filtration velocities of mf = 3 and 6 m h1. RGF was washed using tap water. The data characterizing mixing (global velocity gradient G) and filtration (pressure drop PF and duration of filtration run TF) were used as operational parameters. The time of a filtration run TF was limited either by exhausting the pressure drop PF, or exceeding the maximum allowed Fe concentration (cFe = 0.20 mg l1) in the
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filtrate. For the purpose of verifying the reproducibility of results, three pilot plant test series were carried out. 2.2.2. Pilot plant performance evaluation The efficiency of the water treatment process was evaluated by: (1) Treated water quality parameters: residual Fe, total organic carbon (TOC) and turbidity. (2) Determining the separation efficiencies /Fe, /DOC and /Tu (%) [21]. (3) Filtration parameters: time of filtration run TF (h) and pressure drop PF (kPa) in RGF. (4) Calculation of the dirt holding capacity of the filter bed, DHC (kg m3), according to the following equation [16]
DHC ¼
T F mf css ; LF
ð3Þ
where TF is the time of the filtration run (s), mf is the filtration velocity (m s1), css is the concentration of suspended solids at the inlet to the filter (kg m3) and LF is the depth of the filtration bed (m). 2.3. Analyses of suspension properties 2.3.1. Image analysis The size of aggregates formed in the mixing tank was determined by image analysis. This image processing technique has been developed to measure the aggregate size distribution in an aggregated suspension [4,22]. It is based on three steps: (1) Illuminating a slice of flow in the aggregation reactor with a laser light sheet (width = 1.2 ± 0.1 mm) generated by a laser diode (k = 675 nm, power capacity 20 mW). (2) Recording images of the aggregate using a digital camera Pentax K20D (Asahi Co., Japan) with a Sigma AF 105/2.8 EX MACRO lens (Sigma Co., Japan). (3) Processing of the images using image analysis software (Sigma Scan 5). The centre of the taken images (CTI in Fig. 1) was situated 200 mm above the stirrer in the upper part of the mixing tank. The digital images (22 14.6 mm) taken in the RAW format (4672 3104 pixels) resulted in the pixel size of about 4.7 4.7 lm. In order to eliminate the digital background noise, only aggregates larger than 4 pixels (9.4 9.4 lm) were retained in the image analysis process. Furthermore, the images were converted from the RAW format to the BMP grey-scale format and the contour of each particle on the image was analysed. If the contour was well- defined without any shading, the aggregate data were retained in the analysis process; if the contour of the aggregate was shaded, the aggregate data were rejected from the image analysis process. This image analysis resulted in two-dimensional data. The Sigma Scan 5 software was used to calculate the projected area A and perimeter P of the imaged aggregates. The equivalent aggregate diameter d (lm) was calculated by the following equation:
d¼
pffiffiffiffiffiffiffiffiffiffiffiffi 4A=p:
163
following equation from the slope of the log–log plot of the equivalent aggregate diameter d vs. the projected area of the aggregate A [17,18,23] D
A / d 2:
ð5Þ
For the calculation of the average value of fractal dimension, this study uses all aggregates in a given image, meeting the requirements from the previous section (aggregates larger than 4 pixels with well defined contour). The number of aggregates in each image differed in dependence on the gradient used. The standard error was applied in determining the slopes from the regression lines. Densely packed (i.e. less porous) aggregates have a high fractal dimension, while a lower fractal dimension results from large, highly branched and loosely bound structures [12,17,24]. If the measurement of the aggregate perimeter P is performed with an accuracy defined by the resolution (one pixel is the smallest perimeter length unit), a fractal relationship between the measured perimeter and the projected area A of the aggregate is written as [24,25]
A / P2=Dpf ;
ð6Þ
where Dpf is the perimeter-based fractal dimension of the aggregate. Eq. (6) was used to evaluate the geometry of aggregates formed in the mixing tank. The value of Dpf is related to the aggregate surface morphology since Dpf varied between 1 (a circle) and 2 (a line). The interpretation of increasing Dpf can be as follows: as the projected area of the fractal aggregate (A) increases, the aggregate perimeter (P) increases more rapidly than for Euclidean objects, so that the boundary becomes more convoluted [24]. 3. Results and discussion 3.1. Aggregate size and size distribution For the study of the relation between the aggregate size and velocity gradient, the Eq. (1) was used. The values of c and log C can be found as constants of a power function fitted to the measured data. Fig. 2 shows that the maximum and average aggregate diameter follows the trend represented by the Eq. (1). As expected, the aggregate size decreases with an increasing global velocity gradient [3,4,11,26]. The value of c for the average and maximum aggregate diameter is equal to 0.57 and 0.68, respectively. Similar studies by other authors have provided a rather wide range of values for the coefficient c. For example, Bache et al. [26] concluded that the value of c varied between 0.44 and 0.64 for aggregates
ð4Þ
The main advantage of this size distribution measurement technique is that it is non-intrusive and therefore non-destructive. A detailed description of this technique was published in a previous paper [22]. 2.3.2. Fractal analysis A two-dimensional box-counting fractal dimension was used to characterise the aggregate structure. It was calculated by the
Fig. 2. Dependence of aggregate size (dmax and dav) on global velocity gradient (G).
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formed during the flocculation of raw water with natural organic matter. Serra et al. [3] found that the value of c was 0.95 for a suspension of latex particles mixed by a paddle stirrer. Other researchers concluded that the value of c was around 1 in laminar flow and 2/3 in turbulent flow for alumino-bentonite aggregates [13]. The values of c found by other authors are summarized in the review of Jarvis et al. [7]. This study used aggregate size distributions weighted by size, which mainly represents the largest aggregates of the population. Aggregate size distributions formed at different G are presented in a plot of cumulative frequencies of individual sizes (Fig. 3). One can see that the aggregate size distribution is narrower for higher G values. The suspension with heterogeneous aggregate size distribution becomes more homogeneous due to an increase in hydrodynamic force. Low G values form large aggregates; nevertheless, smaller aggregates occur simultaneously in the system. An example is demonstrated at the velocity gradient G = 28 s1 with the greatest variability in formed aggregates, where aggregates from 9.4 up to 6918.4 lm in size appear in the effluent from the mixing tank. On the contrary, the lowest variability in formed aggregates occurs at the global velocity gradient G = 307 s1, where only aggregates from 9.4 to 249.1 lm are present. Furthermore, Fig. 3 shows that the aggregate size distribution is practically identical at velocity gradients G P 199 s1. The influence of the hydrodynamic force on the aggregate size is, thus, indistinguishable under the conditions of G P 199 s1. 3.2. Fractal dimension Apart from their size distribution, the structure, density and geometry of aggregates greatly influence the efficiency of separation. Aggregates are typically fractal objects, for which the density decreases appreciably with an increasing aggregate size [27,28]. The D2 and Dpf fractal dimensions observed in the mixing tank during aggregation at different G values are plotted in Fig. 4. For different global velocity gradients ranging from 28 to 307 s1, the D2 fractal dimension was observed to range from 1.58 to 1.90. The D2 fractal dimension grew with an increase in the velocity gradient, indicating that the aggregates notably lost in their amorphousness but gained in the compactness at higher gradients [17,18,24]. Fig. 4 also shows that the fractal dimension increases (approaches Euclidean dimension) for smaller aggregates, which is in agreement with the work of Maggi et al. [29]. The Dpf fractal dimension generally represents the geometry (or shape) of an aggregate. The closer it approaches the value of 1, the
Fig. 4. Relationship between fractal dimensions D2 and Dpf and their dependence on global velocity gradient.
more regular the aggregates. Our measurements showed that Dpf decreased from 1.36 to 1.12 with the G value increasing. With high velocity gradients G P 199 s1, the Dpf values are lower, which indicates more compact and regular aggregates. In contrast, at low velocity gradient values of G 6 77 s1, the Dpf values are higher, which means the aggregates are more porous with irregular shape. Attention should also be given to the relationship between D2 and Dpf fractal dimensions. The same functional dependence on G (power function) as used for the aggregate size can be possibly fitted to both fractal dimensions (Fig. 4). Moreover, it follows from the figure that the extent of growth of the aggregate compactness with increasing G is very similar to the extent of growth of their regularity. Exponents of the two fitted power functions (having very similar absolute values) could confirm that. If the power functions describing D2 (Eq. (7)) and Dpf (Eq. (8)) are added up (assuming the opposite value of exponents),
D2 ¼ a1 Gb ;
ð7Þ
Dpf ¼ a2 Gb ;
ð8Þ
the following result is obtained
D2 Dpf ¼ const:
ð9Þ
The suggested Eq. (9) (illustrated in Fig. 4 as well) provides a very interesting view of the relationship between the mentioned fractal dimensions. Although it can be valid just for the presented data set and for certain conditions, it deserves more attention and further detailed research. 3.3. Filterability of aggregates formed under different hydrodynamics
Fig. 3. Particle/aggregate size distribution (PSD) at different values of global velocity gradient.
It follows from the previous results that hydrodynamic conditions are very important during the processes of destabilization and aggregation, because they influence the size distribution and the character of formed aggregates. The next step of the experiment was to find out how the properties of aggregates formed under different hydrodynamic conditions influence their filterability and the total efficiency of the water treatment process. During the pilot plant operation, three filtration runs were evaluated for each of the filtration velocities mf = 3 and 6 m h1 and for all previously mentioned G values.
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Fe (mg l ) TOC (mg l1) Turbidity (NTU) /Fe (%) /TOC (%) /Tu (%)
Raw water
28
45
77
114
153
199
244
307
0.07 4.5 2.9 – – –
0.07 1.35 <0.1 98 71 >97
0.05 1.33 <0.1 99 72 >97
0.04 1.33 <0.1 99 72 >97
0.03 1.3 <0.1 99 72 >97
0.03 1.31 <0.1 99 72 >97
0.03 1.26 <0.1 99 73 >97
0.03 1.27 <0.1 99 73 >97
0.03 1.26 <0.1 99 73 >97
The treatment efficiencies are presented in Table 1. The results show that the different properties of the aggregates formed at individual G values did not affect the separation efficiency of RGF at all. High separation efficiencies /Fe P 98%, /Tu P 97% and /TOC ranging from 71% to 73% were reached at both filtration velocities during all filtration runs. In contrast, the parameters typically characterising filterability (TF, PF and DHC) were heavily affected by the character of aggregates (see Table 2). The results of filterability of aggregates formed at selected G values are plotted as pressure diagrams in Fig. 5. In the first column, there are pressure diagrams with the filtration velocity mf = 3 m h1 and in the other with mf = 6 m h1. The course of the filtration was very similar in both cases. The influence of the velocity gradient is quite apparent from the pressure diagrams. Size-heterogeneous suspensions which were formed at G = 28 s1 (and also at G = 45 s1), with a high proportion of large, porous and irregular aggregates, were intercepted in the uppermost layer of the filter bed and only penetrated to a depth of about 220 mm (260 mm at G = 45 s1). Similar results were presented by Polasek and Mutl [30], who concluded that large aggregates of an organic-polymerformed suspension did not penetrate deep into the filter bed. In contrast to low velocity gradients, size-homogeneous suspensions with small, compact and regular aggregates formed at the velocity gradient G P 199 s1 (represented by the gradient of 244 s1 in Fig. 5) penetrated throughout the full depth of the filter bed. The extent of aggregate penetration increased with the decrease in aggregate size and increase in D2 fractal dimension. Further, it is important to note that the filtration of aggregates formed at G = 28 s1 started to proceed under negative pressure (sub-atmospheric conditions) after about 20 h of operation, which is not favourable for the filtration process. These sub-atmospheric conditions deepened with filtration time, and the filtration run ended after TF = 30 h because the total pressure drop available in the filter had been utilised. The filtration run process with aggregates formed at G = 45 s1 was very similar. The pressure provided by the water level above the medium was fully used after 28 h. The filtration of aggregates formed at G P 77 s1 operated under positive pressure at all times and ended due to the penetration of Fe into the filtrate above the limit (0.20 mg l1). The time of filtration TF depended on the size and structure characteristics of aggregates formed under different hydrodynamic conditions, and increased
Table 2 Characterisation of filtration runs. G (s1)
dav (lm)
mf = 3 m h1 TF (h)
PF (kPa)
DHC (kg m3)
TF (h)
PF (kPa)
DHC (kg m3)
28 45 77 114 153 199 244 307
1330.1 817.7 507.6 305.5 155.1 65.8 61.1 56.4
30 39 51 62 70 76 78 78
20.2 20.2 18.4 17.9 16.2 14.8 14.0 13.6
1.5 2.0 2.6 3.1 3.5 3.8 3.9 3.9
26 32 42 51 59 64 68 68
18.8 18.2 17.8 17.0 16.0 14.4 13.7 13.3
2.6 3.2 4.2 5.1 5.9 6.4 6.8 6.8
with increasing G and a drop in aggregate size. The time of filtration TF and also the pressure drop PF was practically identical for velocity gradients G P 199 s1 (see Table 2). This corresponds to findings presented previously that the aggregate size distribution and fractal dimension are practically identical at high velocity gradients (G P 199 s1). It follows from the results stated above that the best filterability of aggregates formed at different G values was recorded at dav 60 lm and D2 P 1.89. Similar results were concluded by Mutl and Knesl [31] and Pivokonsky et al. [32], who demonstrated that small (10–100 lm) and highly compact aggregates formed during aggregation in a fluidised bed of granular material are favourable for one-step separation by filtration. Furthermore, Ngo et al. [33] reported that flocs with size of about 60 lm are optimal for direct filtration. These findings are similar to that of Bai and Tien [34], who noticed that aggregates with d > 10 lm are more suitable for deep bed filtration. The comparison of the filtration velocities mf = 3 and 6 m h1 implies that the higher filtration velocity positively affected penetration of aggregates into the depth of the filter bed, which resulted in an increase of DHC (Table 2). The differences in the depth of the filter bed which was penetrated by aggregates originated from different shear stress at each filtration velocity [30,35,36]. Since the cohesion forces enabling the attachment of aggregates to the filter medium are fixed, the greater shear forces produced by water flowing through the filter bed at high filtration velocity allow aggregates to penetrate deeper into the bed. At higher filtration velocity the filtration runs ended earlier, but the DHC was approximately 1.7 times larger than with lower filtration velocity. The formation of aggregates in a mixing tank (destabilisation and aggregation) and deep-bed filtration are interrelated processes because the effectiveness of filtration is determined by the properties of the formed aggregates. There are four different aggregate types reflecting their filterability [30]: (1) Aggregates which are completely retained in the filter bed at the expense of a high pressure drop are not desirable. (2) Similarly, aggregates which generate a low pressure drop but are poorly retained are also not desirable. (3) Aggregates which are poorly retained and generate high pressure drop present the worst case. (4) Those aggregates which are completely retained and generate a minimum pressure drop represent the ideal target for aggregate formation. The results of filterability presented here show that small and highly compact aggregates with regular shape are the best solution for direct filtration. In practice, these aggregates can be formed in a mixing tank operating at high G values (G > approximately 200 s1).
mf = 6 m h1
4. Conclusions The presented results lead to the following conclusions (1) The aggregate size decreases with an increase in the value of the global velocity gradient (as expected) and confirmed to be a power function of G. The value of c for the average and maximum aggregate diameter is equal to 0.57 and 0.68, respectively.
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Fig. 5. Pressure diagrams for the rapid gravity filter – filterability of aggregates formed at selected G. Left column: mf = 3 m h1, right column: mf = 6 m h1.
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(2) With an increasing G value, the aggregate size distribution narrows, i.e. the suspension becomes more homogeneous. At low G values, considerably larger aggregates are formed; nevertheless, smaller aggregates occur simultaneously in the system. At high G values, only smaller aggregates are produced. (3) The D2 fractal dimension grows with increasing G, indicating that the aggregates become less porous and more compact. For global gradients from 28 to 307 s1, the D2 fractal dimension ranges from 1.58 to 1.90. The Dpf fractal dimension decreases (from 1.36 to 1.12) with increasing G indicating that the aggregates become more regular in shape. The relationship between the two mentioned fractal dimensions was suggested:
D2 Dpf ¼ const: (4) The suspension properties did not influence the removal efficiency of Fe/TOC/turbidity, but the effectiveness of filtration itself was affected significantly. (5) The suspensions formed at G 6 45 s1 (with a high proportion of large, porous and irregular aggregates) did not penetrate deep into the filter bed, and were intercepted in the uppermost layer. In contrast, the aggregates formed at G P 199 s1 (size-homogeneous suspensions with small, compact and regular aggregates) penetrated throughout the full depth of the filter bed. The extent of aggregate penetration (as well as the time of filtration TF) increased with the decreasing aggregate size and increasing D2 fractal dimension. (6) The aggregates of dav 60 lm and D2 P 1.89 displayed the best filterability. They provided the longest filtration runs (up to 78 and 68 h for mf = 3 and 6 m h1, respectively) and generated a minimal pressure drop (approximately 14 kPa). (7) The increase of filtration velocity mf from 3 to 6 m h1 resulted in approximately 1.7 times higher dirt holding capacity DHC.
Acknowledgements This research project was funded by the Czech Science Foundation under Project No. P105/11/0247 and Institutional Research Plan No. AV0Z20600510. References [1] J.K. van Benschoten, J.K. Edzwald, Chemical aspects of coagulation using aluminium salts – I. Hydrolytic reactions of alum and polyaluminium chloride, Water Res. 24 (12) (1990) 1519–1526. [2] C.S.B. Fitzpatrick, E. Fradin, J. Gregory, Temperature effects on coagulation using different coagulants, Water Sci. Technol. 50 (12) (2004) 171–175. [3] T. Serra, J. Colomer, B.E. Logan, Efficiency of different shear devices on flocculation, Water Res. 42 (4–5) (2008) 1113–1121. [4] D. Bouyer, C. Coufort, A. Line, Z. Do-Quang, Experimental analysis of floc size distributions in a 1-L jar under different hydrodynamics and physicochemical conditions, J. Colloid Interface Sci. 292 (2) (2005) 413–428. [5] V. Oles, Shear-induced aggregation and break-up of polystyrene latex particles, J. Colloid Interface Sci. 154 (2) (1992) 351–358. [6] R.C. Sonntag, W.B. Russel, Structure and break-up of flocs subjected to fluid stresses: II Theory, J. Colloid Interface Sci. 115 (2) (1987) 378–389.
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Separation and Purification Technology journal homepage: www.elsevier.com/locate/seppur
The influence of velocity gradient on properties and filterability of suspension formed during water treatment Petra Bubakova ⇑, Martin Pivokonsky Institute of Hydrodynamics, Academy of Sciences of the Czech Republic, v.v.i., Pod Patankou 30/5, 166 12 Prague 6, Czech Republic
a r t i c l e
i n f o
Article history: Available online 23 September 2011 Keywords: Aggregation Fractal dimension Filtration Particle size distribution Velocity gradient
a b s t r a c t This paper deals with the influence of the global velocity gradient G (in the range of 28–307 s1) on properties of suspension (size and structure) formed during water treatment. Furthermore, it describes the influence of these properties on separation using depth filtration (filtration velocities of 3 and 6 m h1). The methods of image and fractal analysis were used to determine the aggregate size and structure, respectively. The experiments were conducted in a pilot plant (a mixing tank and a rapid gravity sand filter) with ferric sulphate used as coagulant. The experiments confirmed that with an increasing velocity gradient the aggregate size decreased; the aggregate size distribution narrowed (suspension was more homogenous); the fractal dimension D2 increased (aggregates were more compact) and the fractal dimension Dpf diminished (aggregates were more regular). The smallest and most compact aggregates (d 60 lm and D2 = 1.9) formed at G > 200 s1 displayed the best filterability with the time of filtration up to 78 h. On the contrary, the filtration of large and porous aggregates formed at G 30 s1 lasted only about 30 h. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction The processes of destabilisation and aggregation are often used to remove colloidal particles in water treatment. The purpose is to prepare aggregates of such properties that are suitable for reaching the maximum effectiveness of following separation step(s). Aggregate properties are influenced by conditions under which they are formed. These conditions can be divided into two groups: (1) Physicochemical conditions, i.e. the type and dose of coagulant, pH, alkalinity and temperature [1,2]. Physicochemical conditions influence primarily the destabilisation of colloidal particles and they can be optimised on the basis of routine laboratory jar testing. (2) Hydrodynamics, i.e. local/global velocity gradient, distribution of velocity field, mixing time, etc. primarily given by the geometry of a mixing tank and the stirrer shape and speed [3,4]. Hydrodynamics influences mainly the aggregation of colloidal particles and represents a crucial factor in constituting properties (size, shape and structure) of the formed aggregates. In contrast to physicochemical conditions, the optimisation requires using the pilot plant tests. Hydrodynamics influences two different processes which occur simultaneously, i.e. aggregation and break-up [5–7]. These ⇑ Corresponding author. Tel.: +420 233 109 002; fax: +420 233 324 361. E-mail address: [email protected] (P. Bubakova). 1383-5866/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.seppur.2011.09.031
processes are formed by the balance between the hydrodynamic force F (kg m s2) and the cohesive force J (kg m s2). The hydrodynamic force arises from a flow of fluid around a particle and is, thus, determined by the magnitude of the velocity gradient G (s1), cross-sectional area of the particle A (m2) and dynamic viscosity of the fluid l (kg m1 s1). The cohesive force is given by the sum of all attractive forces acting between interacting particles (e.g. van der Waals, electrostatic or hydrophobic forces). It depends particularly on particle and reagent composition (material) and determines the strength of formed aggregates [6–10]. If the cohesive force prevails (J > F), aggregation occurs. If the hydrodynamic force prevails (F > J), aggregates are not formed at all or a breakup of already existing aggregates takes place. If the aggregate strength (cohesive force J) is fixed (i.e. physicochemical conditions are kept constant), the aggregate size is limited only by the hydrodynamic force represented by the velocity gradient G. For this case, the following empirical relationship between the stable floc size (d) and the global velocity gradient (G) has been developed [3,4,11–13]:
d ¼ C G2c ;
ð1Þ
where C is the constant representing the aggregate strength and c is the coefficient representing the aggregate break-up. It is necessary to realize that this expression includes the global velocity gradient, which is just a rough estimate of hydrodynamic conditions in real mixing devices, where the uniform distribution of G cannot be usually assured. Nevertheless, it is complicated to relate the size of an individual aggregate to specific location in the mixing device with a
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defined local G, especially in a pilot plant scale. For that reason, global velocity gradients are usually used in practice. The hydrodynamic force influences not only the size of the formed aggregate but also the arrangement of the primary particles in the aggregate. If the hydrodynamic force F is distinctively lower than the cohesive force J, particles combine at the point of the first contact and aggregates of porous structure and irregular shape are formed. Conversely, if the hydrodynamic force is only slightly lower than the cohesive force, particles tend to form compact aggregates which are energetically stable. Thus, compactness of the structure decreases with the diminishing magnitude of the hydrodynamic force [14–16]. The structure of aggregates has been recently studied by means of fractal dimension calculated from the data on light scattering or image analysis [15,17]. There are interesting studies dealing with the effect of hydrodynamics on the size and structure of aggregates formed during destabilisation and aggregation, some of which have already been mentioned [3,4,9,12,15,18–20]. However, these studies examine the influence of hydrodynamics on aggregate properties without a direct relation to subsequent depth filtration. The main objective of this paper is to describe the influence of the global velocity gradient on the properties of aggregates formed during the destabilisation and aggregation in a flow mixing tank, and to explain how the character of the formed aggregates affects separation using depth filtration. 2. Experimental 2.1. Raw water and reaction conditions The experiment used raw water from the Svihov reservoir (potable water source), Czech Republic. The tests were carried out during the winter period (December–February), when raw water quality was stabilized with the following parameters: temperature in the range of 2.6–4.1 °C (3.3 °C on average), pH between 7.2 and 7.5 (7.3 on average) and alkalinity of 0.92–1.13 mmol l1 (1.04 mmol l1 on average). Ferric sulphate hydrate Fe2(SO4)3 9H2O (Analytika, Ltd., Czech Republic) served as coagulant. The dose (3.98 mg l1 of Fe) was optimized by standard jar tests [21].
Fig. 1. Pilot plant arrangement. MT – mixing tank, RGF – rapid gravity filter, CTI – centre of taken images, S – sampling site, P1–P8 – pressure probe, 1 – header tank, 2 – regulation valve, 3 – flow-meter, 4 – homogeniser with injection of coagulant, 5 – feed pipe, 6 – variable speed drive, 7 – torque-meter, 8 – overflow, 9 – flow regulator, 10 – filtrate discharge pipe, 11 – data logging.
2.2. Pilot plant tests The influence of the velocity gradient on properties and filterability of formed suspension was tested using a pilot plant installed at the Zelivka waterworks, Czech Republic. 2.2.1. Pilot plant design The pilot plant consisted of a flow rate regulation unit, dosing unit, mixing tank (MT) and rapid gravity filter (RGF), as illustrated in Fig. 1. Raw water was brought to the flow rate regulation unit, consisting of a header tank (1), regulation valve (2) and flow-meter (3). A homogenizer (4) with injection of the coagulant was placed in front of the inlet to the mixing tank. Dosed raw water flowed through the feed pipe (5) into the mixing tank made of a Plexiglas tube. The geometry of the mixing tank was as follows: the tank diameter was 280 mm, the liquid height in the tank was 1500 mm, the stirrer diameter was 240 mm and the paddle height was 40 mm. The stirrer had four paddles connected with five transverse crosspieces. The paddle stirrer was driven by a variable speed drive (6) with a torque-meter (7). In the mixing tank, the hydrodynamic conditions were characterised by the global velocity gradient G calculated according to the relationship as follows:
G¼
sffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffi Pi xM 2pfM ; ¼ ¼ Vl Vl Vl
ð2Þ
where Pi represents the power dissipated in the tank (kg m2 s3), V is the volume of the tank (m3), l is the dynamic viscosity of the fluid (kg m1 s1), x is the angular stirrer velocity (rad s1), M is the torque (kg m2 s2) and f is the stirrer frequency (s1). Global velocity gradients used in this study were G = 28, 45, 77, 114, 153, 199, 244 and 307 s1 and the retention period of the suspension in the mixing tank corresponded to T = 900 s (steady state). The suspension formed in the mixing tank was allowed to drain away through an overflow (8) to RGF. RGF consisted of a Plexiglas tube 3 m long with the inner diameter d = 140 mm with pressure probes (P1–P8) placed along the depth and a flow regulator (9) installed in the filtrate discharge pipe (10). The filter was charged with silica sand with granularity of 0.8–1.2 mm (d50 = 1.11 mm) to a filter bed depth LF = 1050 mm. The operating water depth was LW = 970 mm. During the pilot plant operation, several RGF filtration runs were evaluated at filtration velocities of mf = 3 and 6 m h1. RGF was washed using tap water. The data characterizing mixing (global velocity gradient G) and filtration (pressure drop PF and duration of filtration run TF) were used as operational parameters. The time of a filtration run TF was limited either by exhausting the pressure drop PF, or exceeding the maximum allowed Fe concentration (cFe = 0.20 mg l1) in the
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filtrate. For the purpose of verifying the reproducibility of results, three pilot plant test series were carried out. 2.2.2. Pilot plant performance evaluation The efficiency of the water treatment process was evaluated by: (1) Treated water quality parameters: residual Fe, total organic carbon (TOC) and turbidity. (2) Determining the separation efficiencies /Fe, /DOC and /Tu (%) [21]. (3) Filtration parameters: time of filtration run TF (h) and pressure drop PF (kPa) in RGF. (4) Calculation of the dirt holding capacity of the filter bed, DHC (kg m3), according to the following equation [16]
DHC ¼
T F mf css ; LF
ð3Þ
where TF is the time of the filtration run (s), mf is the filtration velocity (m s1), css is the concentration of suspended solids at the inlet to the filter (kg m3) and LF is the depth of the filtration bed (m). 2.3. Analyses of suspension properties 2.3.1. Image analysis The size of aggregates formed in the mixing tank was determined by image analysis. This image processing technique has been developed to measure the aggregate size distribution in an aggregated suspension [4,22]. It is based on three steps: (1) Illuminating a slice of flow in the aggregation reactor with a laser light sheet (width = 1.2 ± 0.1 mm) generated by a laser diode (k = 675 nm, power capacity 20 mW). (2) Recording images of the aggregate using a digital camera Pentax K20D (Asahi Co., Japan) with a Sigma AF 105/2.8 EX MACRO lens (Sigma Co., Japan). (3) Processing of the images using image analysis software (Sigma Scan 5). The centre of the taken images (CTI in Fig. 1) was situated 200 mm above the stirrer in the upper part of the mixing tank. The digital images (22 14.6 mm) taken in the RAW format (4672 3104 pixels) resulted in the pixel size of about 4.7 4.7 lm. In order to eliminate the digital background noise, only aggregates larger than 4 pixels (9.4 9.4 lm) were retained in the image analysis process. Furthermore, the images were converted from the RAW format to the BMP grey-scale format and the contour of each particle on the image was analysed. If the contour was well- defined without any shading, the aggregate data were retained in the analysis process; if the contour of the aggregate was shaded, the aggregate data were rejected from the image analysis process. This image analysis resulted in two-dimensional data. The Sigma Scan 5 software was used to calculate the projected area A and perimeter P of the imaged aggregates. The equivalent aggregate diameter d (lm) was calculated by the following equation:
d¼
pffiffiffiffiffiffiffiffiffiffiffiffi 4A=p:
163
following equation from the slope of the log–log plot of the equivalent aggregate diameter d vs. the projected area of the aggregate A [17,18,23] D
A / d 2:
ð5Þ
For the calculation of the average value of fractal dimension, this study uses all aggregates in a given image, meeting the requirements from the previous section (aggregates larger than 4 pixels with well defined contour). The number of aggregates in each image differed in dependence on the gradient used. The standard error was applied in determining the slopes from the regression lines. Densely packed (i.e. less porous) aggregates have a high fractal dimension, while a lower fractal dimension results from large, highly branched and loosely bound structures [12,17,24]. If the measurement of the aggregate perimeter P is performed with an accuracy defined by the resolution (one pixel is the smallest perimeter length unit), a fractal relationship between the measured perimeter and the projected area A of the aggregate is written as [24,25]
A / P2=Dpf ;
ð6Þ
where Dpf is the perimeter-based fractal dimension of the aggregate. Eq. (6) was used to evaluate the geometry of aggregates formed in the mixing tank. The value of Dpf is related to the aggregate surface morphology since Dpf varied between 1 (a circle) and 2 (a line). The interpretation of increasing Dpf can be as follows: as the projected area of the fractal aggregate (A) increases, the aggregate perimeter (P) increases more rapidly than for Euclidean objects, so that the boundary becomes more convoluted [24]. 3. Results and discussion 3.1. Aggregate size and size distribution For the study of the relation between the aggregate size and velocity gradient, the Eq. (1) was used. The values of c and log C can be found as constants of a power function fitted to the measured data. Fig. 2 shows that the maximum and average aggregate diameter follows the trend represented by the Eq. (1). As expected, the aggregate size decreases with an increasing global velocity gradient [3,4,11,26]. The value of c for the average and maximum aggregate diameter is equal to 0.57 and 0.68, respectively. Similar studies by other authors have provided a rather wide range of values for the coefficient c. For example, Bache et al. [26] concluded that the value of c varied between 0.44 and 0.64 for aggregates
ð4Þ
The main advantage of this size distribution measurement technique is that it is non-intrusive and therefore non-destructive. A detailed description of this technique was published in a previous paper [22]. 2.3.2. Fractal analysis A two-dimensional box-counting fractal dimension was used to characterise the aggregate structure. It was calculated by the
Fig. 2. Dependence of aggregate size (dmax and dav) on global velocity gradient (G).
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formed during the flocculation of raw water with natural organic matter. Serra et al. [3] found that the value of c was 0.95 for a suspension of latex particles mixed by a paddle stirrer. Other researchers concluded that the value of c was around 1 in laminar flow and 2/3 in turbulent flow for alumino-bentonite aggregates [13]. The values of c found by other authors are summarized in the review of Jarvis et al. [7]. This study used aggregate size distributions weighted by size, which mainly represents the largest aggregates of the population. Aggregate size distributions formed at different G are presented in a plot of cumulative frequencies of individual sizes (Fig. 3). One can see that the aggregate size distribution is narrower for higher G values. The suspension with heterogeneous aggregate size distribution becomes more homogeneous due to an increase in hydrodynamic force. Low G values form large aggregates; nevertheless, smaller aggregates occur simultaneously in the system. An example is demonstrated at the velocity gradient G = 28 s1 with the greatest variability in formed aggregates, where aggregates from 9.4 up to 6918.4 lm in size appear in the effluent from the mixing tank. On the contrary, the lowest variability in formed aggregates occurs at the global velocity gradient G = 307 s1, where only aggregates from 9.4 to 249.1 lm are present. Furthermore, Fig. 3 shows that the aggregate size distribution is practically identical at velocity gradients G P 199 s1. The influence of the hydrodynamic force on the aggregate size is, thus, indistinguishable under the conditions of G P 199 s1. 3.2. Fractal dimension Apart from their size distribution, the structure, density and geometry of aggregates greatly influence the efficiency of separation. Aggregates are typically fractal objects, for which the density decreases appreciably with an increasing aggregate size [27,28]. The D2 and Dpf fractal dimensions observed in the mixing tank during aggregation at different G values are plotted in Fig. 4. For different global velocity gradients ranging from 28 to 307 s1, the D2 fractal dimension was observed to range from 1.58 to 1.90. The D2 fractal dimension grew with an increase in the velocity gradient, indicating that the aggregates notably lost in their amorphousness but gained in the compactness at higher gradients [17,18,24]. Fig. 4 also shows that the fractal dimension increases (approaches Euclidean dimension) for smaller aggregates, which is in agreement with the work of Maggi et al. [29]. The Dpf fractal dimension generally represents the geometry (or shape) of an aggregate. The closer it approaches the value of 1, the
Fig. 4. Relationship between fractal dimensions D2 and Dpf and their dependence on global velocity gradient.
more regular the aggregates. Our measurements showed that Dpf decreased from 1.36 to 1.12 with the G value increasing. With high velocity gradients G P 199 s1, the Dpf values are lower, which indicates more compact and regular aggregates. In contrast, at low velocity gradient values of G 6 77 s1, the Dpf values are higher, which means the aggregates are more porous with irregular shape. Attention should also be given to the relationship between D2 and Dpf fractal dimensions. The same functional dependence on G (power function) as used for the aggregate size can be possibly fitted to both fractal dimensions (Fig. 4). Moreover, it follows from the figure that the extent of growth of the aggregate compactness with increasing G is very similar to the extent of growth of their regularity. Exponents of the two fitted power functions (having very similar absolute values) could confirm that. If the power functions describing D2 (Eq. (7)) and Dpf (Eq. (8)) are added up (assuming the opposite value of exponents),
D2 ¼ a1 Gb ;
ð7Þ
Dpf ¼ a2 Gb ;
ð8Þ
the following result is obtained
D2 Dpf ¼ const:
ð9Þ
The suggested Eq. (9) (illustrated in Fig. 4 as well) provides a very interesting view of the relationship between the mentioned fractal dimensions. Although it can be valid just for the presented data set and for certain conditions, it deserves more attention and further detailed research. 3.3. Filterability of aggregates formed under different hydrodynamics
Fig. 3. Particle/aggregate size distribution (PSD) at different values of global velocity gradient.
It follows from the previous results that hydrodynamic conditions are very important during the processes of destabilization and aggregation, because they influence the size distribution and the character of formed aggregates. The next step of the experiment was to find out how the properties of aggregates formed under different hydrodynamic conditions influence their filterability and the total efficiency of the water treatment process. During the pilot plant operation, three filtration runs were evaluated for each of the filtration velocities mf = 3 and 6 m h1 and for all previously mentioned G values.
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Fe (mg l ) TOC (mg l1) Turbidity (NTU) /Fe (%) /TOC (%) /Tu (%)
Raw water
28
45
77
114
153
199
244
307
0.07 4.5 2.9 – – –
0.07 1.35 <0.1 98 71 >97
0.05 1.33 <0.1 99 72 >97
0.04 1.33 <0.1 99 72 >97
0.03 1.3 <0.1 99 72 >97
0.03 1.31 <0.1 99 72 >97
0.03 1.26 <0.1 99 73 >97
0.03 1.27 <0.1 99 73 >97
0.03 1.26 <0.1 99 73 >97
The treatment efficiencies are presented in Table 1. The results show that the different properties of the aggregates formed at individual G values did not affect the separation efficiency of RGF at all. High separation efficiencies /Fe P 98%, /Tu P 97% and /TOC ranging from 71% to 73% were reached at both filtration velocities during all filtration runs. In contrast, the parameters typically characterising filterability (TF, PF and DHC) were heavily affected by the character of aggregates (see Table 2). The results of filterability of aggregates formed at selected G values are plotted as pressure diagrams in Fig. 5. In the first column, there are pressure diagrams with the filtration velocity mf = 3 m h1 and in the other with mf = 6 m h1. The course of the filtration was very similar in both cases. The influence of the velocity gradient is quite apparent from the pressure diagrams. Size-heterogeneous suspensions which were formed at G = 28 s1 (and also at G = 45 s1), with a high proportion of large, porous and irregular aggregates, were intercepted in the uppermost layer of the filter bed and only penetrated to a depth of about 220 mm (260 mm at G = 45 s1). Similar results were presented by Polasek and Mutl [30], who concluded that large aggregates of an organic-polymerformed suspension did not penetrate deep into the filter bed. In contrast to low velocity gradients, size-homogeneous suspensions with small, compact and regular aggregates formed at the velocity gradient G P 199 s1 (represented by the gradient of 244 s1 in Fig. 5) penetrated throughout the full depth of the filter bed. The extent of aggregate penetration increased with the decrease in aggregate size and increase in D2 fractal dimension. Further, it is important to note that the filtration of aggregates formed at G = 28 s1 started to proceed under negative pressure (sub-atmospheric conditions) after about 20 h of operation, which is not favourable for the filtration process. These sub-atmospheric conditions deepened with filtration time, and the filtration run ended after TF = 30 h because the total pressure drop available in the filter had been utilised. The filtration run process with aggregates formed at G = 45 s1 was very similar. The pressure provided by the water level above the medium was fully used after 28 h. The filtration of aggregates formed at G P 77 s1 operated under positive pressure at all times and ended due to the penetration of Fe into the filtrate above the limit (0.20 mg l1). The time of filtration TF depended on the size and structure characteristics of aggregates formed under different hydrodynamic conditions, and increased
Table 2 Characterisation of filtration runs. G (s1)
dav (lm)
mf = 3 m h1 TF (h)
PF (kPa)
DHC (kg m3)
TF (h)
PF (kPa)
DHC (kg m3)
28 45 77 114 153 199 244 307
1330.1 817.7 507.6 305.5 155.1 65.8 61.1 56.4
30 39 51 62 70 76 78 78
20.2 20.2 18.4 17.9 16.2 14.8 14.0 13.6
1.5 2.0 2.6 3.1 3.5 3.8 3.9 3.9
26 32 42 51 59 64 68 68
18.8 18.2 17.8 17.0 16.0 14.4 13.7 13.3
2.6 3.2 4.2 5.1 5.9 6.4 6.8 6.8
with increasing G and a drop in aggregate size. The time of filtration TF and also the pressure drop PF was practically identical for velocity gradients G P 199 s1 (see Table 2). This corresponds to findings presented previously that the aggregate size distribution and fractal dimension are practically identical at high velocity gradients (G P 199 s1). It follows from the results stated above that the best filterability of aggregates formed at different G values was recorded at dav 60 lm and D2 P 1.89. Similar results were concluded by Mutl and Knesl [31] and Pivokonsky et al. [32], who demonstrated that small (10–100 lm) and highly compact aggregates formed during aggregation in a fluidised bed of granular material are favourable for one-step separation by filtration. Furthermore, Ngo et al. [33] reported that flocs with size of about 60 lm are optimal for direct filtration. These findings are similar to that of Bai and Tien [34], who noticed that aggregates with d > 10 lm are more suitable for deep bed filtration. The comparison of the filtration velocities mf = 3 and 6 m h1 implies that the higher filtration velocity positively affected penetration of aggregates into the depth of the filter bed, which resulted in an increase of DHC (Table 2). The differences in the depth of the filter bed which was penetrated by aggregates originated from different shear stress at each filtration velocity [30,35,36]. Since the cohesion forces enabling the attachment of aggregates to the filter medium are fixed, the greater shear forces produced by water flowing through the filter bed at high filtration velocity allow aggregates to penetrate deeper into the bed. At higher filtration velocity the filtration runs ended earlier, but the DHC was approximately 1.7 times larger than with lower filtration velocity. The formation of aggregates in a mixing tank (destabilisation and aggregation) and deep-bed filtration are interrelated processes because the effectiveness of filtration is determined by the properties of the formed aggregates. There are four different aggregate types reflecting their filterability [30]: (1) Aggregates which are completely retained in the filter bed at the expense of a high pressure drop are not desirable. (2) Similarly, aggregates which generate a low pressure drop but are poorly retained are also not desirable. (3) Aggregates which are poorly retained and generate high pressure drop present the worst case. (4) Those aggregates which are completely retained and generate a minimum pressure drop represent the ideal target for aggregate formation. The results of filterability presented here show that small and highly compact aggregates with regular shape are the best solution for direct filtration. In practice, these aggregates can be formed in a mixing tank operating at high G values (G > approximately 200 s1).
mf = 6 m h1
4. Conclusions The presented results lead to the following conclusions (1) The aggregate size decreases with an increase in the value of the global velocity gradient (as expected) and confirmed to be a power function of G. The value of c for the average and maximum aggregate diameter is equal to 0.57 and 0.68, respectively.
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Fig. 5. Pressure diagrams for the rapid gravity filter – filterability of aggregates formed at selected G. Left column: mf = 3 m h1, right column: mf = 6 m h1.
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(2) With an increasing G value, the aggregate size distribution narrows, i.e. the suspension becomes more homogeneous. At low G values, considerably larger aggregates are formed; nevertheless, smaller aggregates occur simultaneously in the system. At high G values, only smaller aggregates are produced. (3) The D2 fractal dimension grows with increasing G, indicating that the aggregates become less porous and more compact. For global gradients from 28 to 307 s1, the D2 fractal dimension ranges from 1.58 to 1.90. The Dpf fractal dimension decreases (from 1.36 to 1.12) with increasing G indicating that the aggregates become more regular in shape. The relationship between the two mentioned fractal dimensions was suggested:
D2 Dpf ¼ const: (4) The suspension properties did not influence the removal efficiency of Fe/TOC/turbidity, but the effectiveness of filtration itself was affected significantly. (5) The suspensions formed at G 6 45 s1 (with a high proportion of large, porous and irregular aggregates) did not penetrate deep into the filter bed, and were intercepted in the uppermost layer. In contrast, the aggregates formed at G P 199 s1 (size-homogeneous suspensions with small, compact and regular aggregates) penetrated throughout the full depth of the filter bed. The extent of aggregate penetration (as well as the time of filtration TF) increased with the decreasing aggregate size and increasing D2 fractal dimension. (6) The aggregates of dav 60 lm and D2 P 1.89 displayed the best filterability. They provided the longest filtration runs (up to 78 and 68 h for mf = 3 and 6 m h1, respectively) and generated a minimal pressure drop (approximately 14 kPa). (7) The increase of filtration velocity mf from 3 to 6 m h1 resulted in approximately 1.7 times higher dirt holding capacity DHC.
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