Volume 10
Issue 2
Environmental Development
JOURNAL OF
POLISH
AGRICULTURAL
UNIVERSITIES
Available Online: http://www.ejpau.media.pl/volume10/issue2/art-16.html
THE INFLUENCE OF BACKWASHING METHODS ON THE INITIAL EFFLUENT QUALITY DURING DEIRONING OF WATER
Tadeusz Siwiec1, Joanna Troińska2
1 Department of Civil Engineering and Geodesy,
Water Supply and Sewage Systems Section,
Warsaw Agricultural University, Poland
2 Water Supply and Sewage Systems Works Ltd., Nowy Dwor Mazowiecki, Poland
The aim of research was to determine the minimal time of initial effluent discharge during backwashing with the use of raw and treated water, as well as with variable filtration velocity and different granules equivalent diameter of the bed.
The following hypotheses were made:
minimal time of initial effluent discharge is not constant and depends on granules equivalent diameter, filtration velocity and kind of water used for backwashing iron concentration distribution in initial effluent is the multinomial function of granules equivalent diameter and filtration velocity, initial values of above distribution significantly depend on water used for backwashing ( raw water, treated water) The investigations were performed on experimental installation on universities water supply plant. Measuring parameter was concentration of iron in raw water and treated water.
The ranges of bed granulation variability were following: 0.64 – 0.80 mm; 1.00 – 1.25 mm; 1.60 – 2.00 mm. The ranges of filtration velocity were following: 11.5 m·h-1; 17.25 m·h-1; 23.0 m·h-1.
The research was carried out in combinations of all the aforementioned parameters, each bed was backwashed with both raw and treated water and for each bed filtration was performed at all the aforementioned velocities.
Approximate times of reaching the iron concentration of 0.2 mg·dm-3 for chosen cases are as follows: backwashing with treated water – [0.64 ÷ 0.80 mm] 11.5 m·h-1 It can be asserted that unequivocal schematic recommendations regarding the selection of the time at which the first portions of the effluent are to be discharged to sewage system require a more in-depth analysis and the assumed time of 10 minutes may frequently prove be too short.
0 min; 17.25 m·h-1
23 min; 23.0 m·h-1
32 min; [1.60 ÷ 2.00 mm] 11.5 m·h-1
49 min; 17.25 m·h-1
57 min; 23.0 m·h-1
58 min; backwashing with raw water – [0.64 ÷ 0.80 mm] 11.5 m·h-1
33 min; 17.25 m·h-1
35 min; 23.0 m·h-1
36 min; [1.60 ÷ 2.00 mm] 11.5 m·h-1
125 min; 17.25 m·h-1
152 min; 23.0 m·h-1
170 min;
Key words: filters, backwashing, quality of initial effluent.
INTRODUCTION
Rapid filtration is one of the most frequently applied processes of water treatment. The water flows through a bed composed of a porous material, such as sand, anthracite, pyrolusite and others. For the water treatment during filtration to be effective, a number of conditions must be fulfilled, such as the selection of suitable granulation of the bed material, the application of suitable filtration velocity and the application of a suitable and effective backwashing procedure.
During filtration water flows through tortuous paths among the granules of the bed, thus continuously altering the direction of the flow and its velocity, forming whirls and colliding with the granules of the bed. The essence of water treatment consists in that during its flow the impurities carried by the water are attached to the bed. This attachment of the impurities is the result of a number of complicated processes, amongst which are [2]:
sedimentation of heavy impurity particulates in intergranular spaces. This phenomenon occurs mostly in places where, due to low packing and jamming of particulates, spaces of larger size form, in which the flow of water is slowed down;
interception of impurity particulates by the granules of the bed occurs as a result of these particulates approaching the surface of the granules during the flow along tortuous paths inside the bed. The approaching and interception take place due to the processes of transport, the force of inertia, the force of diffusion, electrostatic forces, van der Waals forces and others [2,8]. As a result of these phenomena, the granules of the bed are covered with impurities, which create a thinner or a thicker layer. The forces of adhesion between the impurities and the surface of the bed granules are varied, which is why we talk about weaker or stronger anchoring of particulates.
The impurity particulates retained inside the filter create obstacles for the flow of subsequent portions of water through the filter and cause an increase in head loss, which, in consequence, leads to a decrease in filter efficiency. Should the head loss increase excessively, the purification of the bed, which is carried out in the process of backwashing, becomes necessary.
When the process of filtration is stopped, backwashing is initiated. Water is pumped in the direction opposite to the direction of filtration, i.e. upwards. During this process water of suitable intensity flows through the layer of the bed, which causes the forcing out of water, initially from above the bed and subsequently from the ducts between the granules of the bed [1,2,3,4]. This leads to the expansion of the bed, i.e. its elevation and loosening. During this phenomenon the bed particulates are momentarily suspended in the water and subsequently move both upwards and downwards, as well as sideways, in relation to other particulates. Since in such a situation the bed behaves like a fluid, this state is termed fluidisation. During the flow of the streams of water against the suspended granules of the bed, impurity particulates are elevated together with the backwash water. The first particulates to undergo elevation during this process are the ones loosely connected to the bed, i.e. retained in the process of sedimentation. Subsequently, particulates forced out of the surface of the granules as a result of their mutual collisions are elevated. This process is frequently termed impurity scaling. For the backwash to be effective it is necessary to provide suitable backwash velocity, adequate backwash duration and additional air pumping, which intensifies the effect of the mutual collisions of the granules [5,10,11].
It is debatable what decision should be made as to the type of water used in the process of backwashing. Some technologists prefer the use of raw water, while others prefer treated water. Without an overly in-depth analysis it is easy to formulate a number of advantages and disadvantages of both solutions.
The use of raw water lowers the cost of backwashing. It is worth noting that regardless
of whether raw or treated water is used, the washings are either way discharged to sewage system.On the other hand, the use of raw water leads to the situation in which, after backwashing has been finished, both the bed and the entire interior of the filter are filled with raw water, which should not find its way into waterworks system. Of course, after backwashing is finished and the process of filtration is engaged, the effluent does not initially, when the bed is not yet ripe, meet certain requirements and for the first few minutes it is necessary to discharge the effluent to sewage system, rather than pumping it into waterworks system. It is only after this time that the filter should be switched to deliver water to waterworks. This time is customarily called the discharge of initial effluent and is assumed to be 10 minutes [6,7,9]. Analysis of data from working water treatment plants, known for the authors, confirms that time of initial effluent discharge is nearly 10 minute. It seems illogical that, regardless of whether backwashing is carried out with the use of raw or treated water, the time of initial effluent discharge should always be 10 minutes.
The course of the filtration cycle is depicted in Fig. 1.
Fig. 1. The course of the filtration cycle |
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The main objective of the study was to determine the iron concentration distribution in initial effluent as a function of granules diameter, filtration velocity, kind of water used for backwashing and to work up equations which connect above-mentioned parameters.
The following hypotheses were made:
minimal time of initial effluent discharge is not constant and depends on granules equivalent diameter, filtration velocity and kind of water used for backwashing
iron concentration distribution in initial effluent is the multinomial function of granules equivalent diameter and filtration velocity,
initial values of above distribution significantly depend on water used for backwashing (raw water, treated water)
The aim of experimental research was to determine the minimal time of initial effluent discharge during backwashing with the use of raw and untreated water, as well as with variable filtration velocity and different granulations and granules of the bed.
MATERIALS AND METHODS
The scheme of the experimental installation constructed on the premises of the NBSW university waterworks station is depicted in Fig. 2.
The main part of the measuring station was a filtration column constructed of a Plexiglas tube with a diameter of 200 mm and a height of 2 m. The column had disk closures at the top and at the bottom, in which short segments of the tube were mounted. The segments were connected to pipe tees. The top tee was connected to a conduit supplying raw water 1, which had been previously aerated in an aerator used by the NBSW, and with another conduit, carrying away the water after the backwashing of the bed 4. The bottom tee was connected to a water supply conduit 2 and an effluent drainage conduit 5.
Fig. 2. The scheme of the research installation |
![]() |
The grate mounted in the bottom part was a board of rigid plastic (textolite) with a thickness of 12 mm, into which four typical filtration nozzles were screwed symmetrically. Each of them had 40 slots measuring 0.5 mm (width) and 30 mm (height).
The basic assumption of the research was that the measure of work efficiency would be the difference in the concentration of iron in the raw water and in the effluent, i.e. the efficiency of deironing. Because of this, the water used for the research was drawn from a well on the premises of NBSW, as it contains iron in the concentration of 2.4 mg·dm-3. In the technological sequence of the station this water is aerated in aerators and subsequently filtered through a bed in iron and manganese removers. The research filter was connected to this sequence in such a way that the raw water supply conduit was connected to the pipe after the aerator, i.e. to the pipe carrying aerated raw water. In this way the well pumps which work for the use of the station at the same time pumped a part of the water for the use of the research.
Because of the fact that the water reaching the research station was strongly aerated after entering the interior of the column, a large amount of air accumulated in its top part. The vent V served for the removal of this air.
The intensity of the water flow both during the filtration and the backwashing was measured with an Endress+Hauser Pulsmag meter, whereas the intensity of the air flow, which served to aid the backwashing of the bed, was measured with a rotameter.
The research consisted in the previous preparation of the bed, i.e. sifting quartz sand through suitable sieves in order to obtain media of suitable granulations. Subsequently the bed was placed inside the column and cleansing backwash was performed. Because of the fact that the filter worked as a gravitational one, in order to determine the filtration velocity for subsequent series initial filtration was performed, during which the relation between the velocity of the water flow through the bed and the height of the water layer above the bed was determined. Such an action allowed for the filtration velocity to be promptly determined after subsequent backwashes in order to carry out the measurements under equal conditions.
After cleansing the bed and determining the conditions, filtration cycles were commenced. The research consisted in initiating time measurement at the beginning of the filtration process and drawing samples of the effluent at subsequent intervals. Concentration of iron was determined in the samples. The first sample was always drawn after 120 seconds from the beginning of filtration and then samples were drawn in subsequent minutes. The experiment lasted at each time until the concentration of iron in the samples decreased to the normative range, i.e. to 0.2 mg·dm-3.
The ranges of bed granulation variability were following[12]:
sand bed with the granulation of 0.64 – 0.80 mm,
sand bed with the granulation of 1.00 – 1.25 mm,
sand bed with the granulation of 1.60 – 2.00 mm.
The ranges of filtration velocity were following [12]:
11.5 m·h-1
17.25 m·h-1
23.0 m·h-1
Backwashing was carried out with [12]:
raw water,
treated water.
The research was carried out in combinations of all the aforementioned parameters, i.e. each bed was backwashed with both raw and treated water and for each bed filtration was performed at all the aforementioned velocities.[12]
RESULTS AND DISCUSSION
The results of the research show iron concentration in the samples drawn at different times from the beginning of the filtration process. In order to facilitate the analysis of the results and the comparison of given series, each graph was created with reference to only one parameter, which was subject to changes. The graphs were juxtaposed in groups of three and presented in Figures. 3, 4, 5 and 6.
Fig. 3. The changes in iron concentration in the function of filtration velocity after backwashing with treated water |
![]() |
a. filtration velocity 11.5 m·h-1 b. filtration velocity 17.25 m·h-1 c. filtration velocity 23.0m·h-1 |
Fig. 4. The changes in iron concentration in the function of filtration velocity after backwashing with treated water |
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a. medium granulation of 0.64 – 0.80 mm b. medium granulation of 1.00 – 1.25 mm c. medium granulation of 1.60 – 2.00 mm |
Fig. 5. The changes in iron concentration in the function of filtration velocity after backwashing with raw water |
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a.filtration velocity 11.5 m·h-1 b. filtration velocity 17.25 m·h-1 c. filtration velocity 23.0m·h-1 |
Fig. 6. The changes in iron concentration in the function of filtration velocity after backwashing with raw water |
![]() |
a. medium granulation of 0.64 – 0.80 mm b. medium granulation of 1.00 – 1.25 mm c. medium granulation of 1.60 – 2.00 mm |
As can be seen from Fig. 3, at the initial stage iron concentration is low in all cases, which is caused by the effect of backwashing with treated water. After the backwashing has been finished, both the filter tank and the intergranular spaces are filled with treated water, i.e. with low iron concentration. After the filtration cycle is commenced, this water is forced out by the stream of water pumped into the filter. Here aerated raw water is pumped and flows around the surface of the bed and then down through the intergranular spaces. At this point the stream of raw water containing iron in high concentration is mixed with treated water remaining after the backwash. Hence iron concentration in the initial portions of the effluent increases.
After the backwash has been finished the bed is highly porous, since it is always set loosely and its intergranular spaces are large. Hence after the beginning of filtration decreasing quality of the effluent (increasing iron concentration) is observed, which is the result of worse filtration effects of the loosened bed. During filtration water flows downwards, which is why it slowly condenses the bed. It can be observed as the lowering of the top edge of the bed surface. After suitable thickening the filter begins to work properly and iron concentration in water slowly decreases to a level appropriate for a given bed, filtration velocity and iron concentration in raw water.
As can be seen from the top graph in Fig. 3, in the case of a bed with fine granulation filtration velocity has small influence on the effect of effluent degradation at the initial stage of work, since the maximum iron concentration was within the range between 0.2 and 0.3 mg·dm-3. At the filtration velocity of 11.5 m·h-1 concentration below the normative 0.2 mg·dm-3 occurred throughout, whereas at higher velocities it was reached only after ca. 22 minutes for the velocity of 17.25 m·h-1 and after ca. 30 minutes for the velocity of 23 m·h-1.
After backwashing the bed with treated water, the analyses performed after 120 seconds (the first point) show that water quality is very good and iron concentration amounts to ca. 0.1 mg·dm-3. This concentration depends to a lesser extent on filtration velocity and to a greater extent on bed granulation.
In the case of bed with coarser granulations the character of the curves is identical, whereas the times of reaching the effluent quality with iron concentration of the normative value of 0.2 mg·dm-3 differ. For the bed with the granulation of 1.0-1.25 mm the times amounted to 21 min, 38 min and 43 min, counting from the lowest to the highest filtration velocity. For the granulation of 1.6-2.0 mm the times were 50 min, 59 min and 60 min respectively.
As can be seen, these times are worryingly long if related to the recommended time of the so-called ‘initial effluent’ discharge, which in the majority of cases amounted to 10 minutes.
In order to visualise these relations, the values of the maxima and the times after which the maxima were reached are juxtaposed in Table 1.
Table 1. Coordinates of iron concentration maxima during backwashing with treated water |
Filtration velocity |
Medium granulations |
||
0.64 – 0.8 mm |
1.00 – 1.25 mm |
1.60 – 2.00 mm |
|
Maximum iron concentration (time from the beginning of filtration) |
|||
11.5 m·h-1 |
0.2 mg·dm-3 (11 min) |
0.26 mg·dm-3 (10 min) |
0.4 mg·dm-3 (20 min) |
17.25 m·h-1 |
0.28 mg·dm-3 (14 min) |
0.33 mg·dm-3 (14 min) |
0.43 mg·dm-3 (20 min) |
23.0 m·h-1 |
0.26 mg·dm-3 (14 min) |
0.38 mg·dm-3 (14 min) |
0.46 mg·dm-3 (20 min) |
As can be seen from Table 1, the values of the maxima strongly depend on the granulation of the bed. At the filtration velocity of 11.5 m·h-1 the maximal iron concentration varies from 0.2 mg·dm-3 to 0.4 mg·dm-3. At higher filtration velocities variations are also considerable: from 0.28 mg·dm-3 to 0.43 mg·dm-3 and from 0.26 mg·dm-3 to 0.46 mg·dm-3. The influence of the changes in filtration velocity is definitely not as strong, which can be assessed by analysing the values in the columns, i.e. with changing filtration velocities for given bed granulations.
The time at which the maxima were observed is also worth noting. For the granulation of 0.64-0.88 mm and 1.00-1.25 mm the maxima occurred between 10 and 14 min, whereas for the bed with the coarse granulation of 1.6-2.0 mm, they occurred only after 20 minutes.
Analysing Table 1, the following important conclusions can be drawn:
the time of ‘initial effluent’ discharge, popular in literature [6,7] determined for 10 minutes or 2 minutes [13] does not reflect the data gathered in the experiment. Maxima occurred after a time longer than 10 minutes and it is worth remembering that it is only from this time that iron concentration decreases, which means that the required concentration of e.g. 0.2 mg·dm-3 is reached considerably later.
for certain conditions initial effluent discharge may not be necessary. In this research such a situation took place for the lowest filtration velocity of 11.5 m·h-1 and the finest fraction of the bed, i.e. 0.64-0.8 mm. Under these conditions the iron concentration in the effluent, except for the maximum, did not exceed the normative 0.2 mg·dm-3. It follows from here that for this case the filter may be engaged for normal work immediately after backwashing.
The graph depicted in Fig. 4 was created with the use of the same values obtained from the analytical research but the independent variables were reversed. The top graph ‘a’ refers to the lowest filtration velocity of 11.5 m·h-1, the graph ‘b’ – to the velocity of 17.25 m·h-1 and ‘c’ – to the velocity of 23 m·h-1. The curves in each of the graphs refer to respective bed granulations. It is worth noting that one of the curves is longer in each of the graphs. This is due to the fact that for the bed with coarse granulation the research cycle had to be extended by 90 minutes, because within less than 45 minutes an effluent with values lesser than the normative ones was not obtained.
Looking at the distances between given measurement points in relation to the neighbouring curve, as well as the values of concentration maxima and the length of times required to reach normative concentration, it can be observed that bed granulation is of greater importance for the ripening of the bed than filtration velocity.
Figures 5 and 6 depict analogous results of the research obtained by backwashing the filter with raw water. The essence of the changes consists in that after backwashing has been finished both the filter tank and intergranular spaces are filled with raw water, i.e. water with iron concentration considerably exceeding the normative value. In this case it amounted to ca. 2.4 mg·dm-3.
The course of the bed ripening process is entirely different after backwashing with raw water and, contrary to what can be seen from the previous figures, a maximum does not occur here and the highest iron concentration is observed at the beginning of subsequent filtration cycles.
It can be explained by the fact that after backwashing has been finished, the entire bed including its pores is filled with raw water, i.e. exhibiting iron concentration exceeding in our case about 2 mg·dm-3. Commenced filtration cycle causes aerated raw water to flow into the filter, which prompts the oxidation of iron contained both in the water remaining in the filter after backwashing and in the water supplied to the filter in the process of filtration. During this process iron concentration in the water flowing out of the filter gradually decreases, which can be seen from the graphs depicted in Figures 5 and 6. The functions presented in these graphs do not show a maximum and the highest values of iron concentration occur at the beginning of the process. According to the applied methodology of measurement, this maximum value occurred after 120 seconds, as this was the time of drawing the first sample.
According to expectations the presentation of the curves shows considerable decrease in iron concentration with the time of filtration. However, reading from the horizontal axis, it can be observed that the time in which normative concentrations (0.2 mg·dm-3) are reached has considerably extended. As with the previous case, bed granulation has considerable influence on the time of the bed ripening. Approximate times of reaching the concentration of 0.2 mg·dm-3 for all the cases are presented in Table 2.
As can be seen from table 2 the times at which iron concentrations below 0.2 g·m-3 were reached are far longer than the recommendations for ‘initial effluent’ discharge that can be encountered.
Table 2. A juxtaposition of the times of reaching 0.2 mg·dm-3 iron concentration in the effluent |
The type of water used for backwashing |
Medium granulation |
Filtration velocity |
||
11.5 m·h-1 |
17.25 m·h-1 |
23.0 m·h-1 |
||
Treated water |
0.64-0.80 mm |
0 min |
23 min |
32 min |
1.00-1.25 mm |
21 min |
33 min |
43 min |
|
1.60-2.00 mm |
49 min |
57 min |
58 min |
|
Raw water |
0.64-0.80 mm |
33 min |
35 min |
36 min |
1.00-1.25 mm |
39 min |
48 min |
56 min |
|
1.60-2.00 mm |
125 min |
152 min |
170 min |
It is worth considering what the consequences of applying shorter times of the discharge of first water portions than the ones presented in the table 2 are.
In the case of a single-step pumping system, it must be noted that at the initial stage of the filter’s work after backwashing the concentration in the water pumped into the waterworks system will be higher than recommended. In such cases a check analysis of the water drawn from the system will show concentrations exceeding the normative ones.
In the case of a two-step pumping waterworks system with a storage tank, water with increased iron concentration (directly after backwashing) will flow to this tank. If the tank is big enough, the water coming from the first portions after the beginning of filtration will mix with the water remaining in the tank after the previous cycle and the average concentration obtained will usually be below normative values. Additionally, with long times of water retention in the tank, due to the contact of the water with air, oxidation of the iron will occur, part of which will sediment on the bottom and on the walls of the tank. A negative consequence will be the necessity of more frequent cleaning of the tank of the deposited sediments.
The experimental results were the base for mathematical model search with use of statistical analysis. The measuring points were approximated with use of first, second and third order multinomial functions. The results of equations factors a, b, c and d, also R2 and standard error are shown in Table 3. The assumption was made, that the factor a is with variable with highest power, b – lower and so on.
As it can be seen from table 3, the points received as investigation results of backwashing with use of raw water better fit to the function, because the high determination factor R2 was obtained for the quadratic and cubic equation as well. After backwashing with the treated water the points show the clear maximum what make difficult to get function well fitted to the measuring points. In this case, the acceptable value R2 was obtained for the cubic equation and further calculations were done for date a, b, c, and d.
Table 3. Equations factors a, b, c, d, determination factor R2 and standard error |
Treated water |
|||||||||
Parameters |
0.64-0.80 mm |
1.0-1.25 mm |
1.6-2.0 mm |
||||||
23 m·h-1 |
17.25m·h-1 |
11.5m·h-1 |
23 m·h-1 |
17.25m·h-1 |
11.5m·h-1 |
23m·h-1 |
17.25m·h-1 |
11.5m·h-1 |
|
Linear equation |
|||||||||
R2 |
0.8931 |
0.8403 |
0.8112 |
0.7614 |
0.7724 |
0.9490 |
0.7811 |
0.8046 |
0.7754 |
St. e. |
0.2347 |
0.2113 |
0.2588 |
0.2749 |
0.2509 |
0.1417 |
0.3118 |
0.2827 |
0.2810 |
b |
1.6762 |
1.2263 |
1.3540 |
1.3537 |
1.2163 |
1.8833 |
1.4479 |
1.3553 |
1.2383 |
a |
-0.0360 |
-0.0257 |
-0.0285 |
-0.0261 |
-0.0245 |
-0.0325 |
-0.0083 |
-0.0081 |
-0.0073 |
Parabolic equation |
|||||||||
R2 |
0.9956 |
0.9495 |
0.9679 |
0.9246 |
0.9088 |
0.9630 |
0.9410 |
0.9614 |
0.9556 |
St. e. |
0.0510 |
0.1271 |
0.1141 |
0.1653 |
0.1698 |
0.1290 |
0.1730 |
0.1343 |
0.1335 |
c |
2.0769 |
1.5311 |
1.7652 |
1.7501 |
1.5551 |
2.0129 |
1.8019 |
1.6916 |
1.5726 |
b |
-0.0842 |
-0.0624 |
-0.0779 |
-0.0737 |
-0.0652 |
-0.0480 |
-0.0229 |
-0.0220 |
-0.0212 |
a |
8.8·10-4 |
6.7·10-4 |
9.1·10-4 |
8.7·10-4 |
7.5·10-4 |
2.9·10-4 |
7.9·10-5 |
7.6·10-5 |
7.5·10-5 |
Cubic equation |
|||||||||
R2 |
0.9956 |
0.9688 |
0.9763 |
0.9837 |
0.9758 |
0.9656 |
0.9893 |
0.9913 |
0.9897 |
St. e. |
0.0551 |
0.1079 |
0.1060 |
0.0829 |
0.0945 |
0.1344 |
0.0794 |
0.0687 |
0.0695 |
d |
2.0754 |
1.7005 |
1.8909 |
2.0660 |
1.8691 |
1.9392 |
1.9917 |
1.8349 |
1.7144 |
c |
-0.0838 |
-0.1002 |
-0.1060 |
-0.1443 |
-0.1354 |
-0.0316 |
-0.0402 |
-0.0350 |
-0.0340 |
b |
8.7·10-4 |
2.4·10-3 |
2.2·10-3 |
4.1·10-3 |
4.0·10-3 |
-4.7·10-4 |
3.3·10-4 |
2.6·10-4 |
2.6·10-4 |
a |
1.8·10-7 |
-2.1·10-5 |
-1.6·10-5 |
-3.9·10-5 |
-3.9·10-5 |
9.1·10-6 |
-8.9·10-7 |
-6.7·10-7 |
-6.7·10-7 |
Raw Water |
|||||||||
Linear equation |
|||||||||
R2 |
0.3221 |
0.0185 |
0.1619 |
0.0175 |
0.0097 |
0.1398 |
0.1998 |
0.1073 |
0.2363 |
St. e. |
0.0371 |
0.0550 |
0.0352 |
0.0711 |
0.0585 |
0.0484 |
0.1117 |
0.1135 |
0.1047 |
b |
0.1669 |
0.1966 |
0.1566 |
0.2660 |
0.2204 |
0.2008 |
0.2933 |
0.2947 |
0.3094 |
a |
0.0024 |
-0.0007 |
-0.0014 |
-0.0007 |
0.0004 |
-0.0014 |
-0.0015 |
-0.0013 |
-0.0019 |
Parabolic equation |
|||||||||
R2 |
0.7736 |
0.7409 |
0.1629 |
0.3044 |
0.3160 |
0.3581 |
0.2789 |
0.6075 |
0.6220 |
St. e. |
0.0229 |
0.0302 |
0.0376 |
0.0640 |
0.0520 |
0.0447 |
0.1133 |
0.0813 |
0.0795 |
c |
0.0997 |
0.0918 |
0.1593 |
0.1900 |
0.1560 |
0.1526 |
0.2446 |
0.1755 |
0.2050 |
b |
0.0142 |
0.0177 |
-0.0019 |
0.0098 |
0.0093 |
0.0053 |
0.0021 |
0.0090 |
0.0071 |
a |
-3.5·10-4 |
-5.5·10-4 |
1.4·10-5 |
-2.4·10-4 |
-2.0·10-4 |
-1.5·10-4 |
-3.7·10-5 |
-1.2·10-4 |
-1.1·10-4 |
Cubic equation |
|||||||||
R2 |
0.8838 |
0.8776 |
0.5131 |
0.7985 |
0.7549 |
0.8608 |
0.7488 |
0.9050 |
0.8909 |
St. e. |
0.0177 |
0.0224 |
0.0310 |
0.0372 |
0.0336 |
0.0225 |
0.0723 |
0.0438 |
0.0468 |
d |
0.0543 |
0.0296 |
0.0904 |
0.0658 |
0.0600 |
0.0615 |
0.1043 |
0.0671 |
0.1023 |
c |
0.0295 |
0.0387 |
0.0213 |
0.0434 |
0.0352 |
0.0299 |
0.0221 |
0.0268 |
0.0240 |
b |
-1.5·10-3 |
-2.1·10-3 |
-1.7·10-3 |
-2.2·10-3 |
-1.7·10-3 |
-1.6·10-3 |
-5.6·10-4 |
-6.6·10-4 |
-6.2·10-4 |
a |
2.3·10-5 |
3.2·10-5 |
3.6·10-5 |
2.9·10-5 |
2.3·10-5 |
2.1·10-5 |
3.4·10-6 |
4.2·10-6 |
4.0·10-6 |
St. e. – Standard error |
Table 4. Full and shorter versions of equations for a,b,c,d calculations |
Cf. |
Full Version |
R2 |
a |
a = – 6.7·10-5·S2 + 3.11·10-7·Vf2 + 1.48·10-5·deq2 – 4.5·10-7·S·Vf + 1.54·10-5·S·deq + |
0.8141 |
b |
b = 0.006408·S2 – 2.5·10-5·Vf2 – 0.001·deq2 + 5.59·10-5·S·Vf – 0.00109·S·deq – |
0.8129 |
c |
c = – 0.15351·S2 + 0.000474·Vf2 + 0.02754·deq2 – 0.00172·S·Vf + 0.02599·S·deq – |
0.9177 |
d |
d = – 0.32328·S2 + 0.002812·Vf2 – 0.23595·deq2 + 0.007434·S·Vf – 0.03892·S·deq + |
0.9972 |
Shorter Version |
||
a |
a = – 4.5·10-5·S2 – 4.3·10-7·S·Vf + 3.71× 10-6·S·deq + 9.9·10-5·S + 8.79·10-6 |
0.6193 |
b |
b = 0.00444·S2 + 4.3·10-5·S·Vf – 0.00055·S·deq – 0.0096·S – 0.00034 |
0.7292 |
c |
c = – 0.11553·S2 – 0.00124·S·Vf + 0.022589··deq + 0.227277·S + 0.004133 |
0.8975 |
d |
d = 0.03713·S2 + 0.007427·S·Vf – 0.01275·S·deq + 0.623483·S – 0.01704 |
0.9943 |
Table 5. Correlation coefficients for a, b, c, d and S, Vf, deq |
a |
b |
c |
d |
|
S |
-0.7413 |
0.7820 |
-0.8784 |
0.9951 |
S2 |
-0.7455 |
0.7872 |
-0.8830 |
0.9948 |
Vf |
-0.1193 |
0.1077 |
-0.0836 |
0.0414 |
Vf2 |
-0.1059 |
0.0971 |
-0.0790 |
0.0454 |
deq |
-0.1282 |
-0.0541 |
0.1922 |
-0.0048 |
deq2 |
-0.1141 |
-0.0651 |
0.1998 |
-0.0069 |
S·Vf |
-0.7427 |
0.7873 |
-0.8689 |
0.9449 |
S·deq |
-0.5712 |
0.5637 |
-0.6270 |
0.8668 |
Vf·deq |
-0.1679 |
0.0247 |
0.0964 |
0.0231 |
The linear and parabolic regression analysis was performed to obtain unified multinomial equation. From this analysis it was possible to get the equations for calculations of factors a, b, c and d in function of equivalent granules diameter deq, filtration velocity Vf and iron concentration in water used for backwashing S. Calculations were done for different combinations of independent data: for all deq, Vf and S, and also for two from three: S and Vf; S and deq; Vf and deq. It appears that determination factors R2 were rather low – from 0.5 to 0.7, and only high values (above 0.99) was obtained for descriptive function calculation coefficient d as d=f(S, Vf, deq), d=f(S, deq) and d=f(S, Vf). However, the low value of R2 in calculations for a, b and c determined to look for the function of second order. The following set of variables was taken: S, Vf, deq, S2, Vf2, deq2, S·Vf, S·deq, deq·Vf. The overall equations for calculations of a, b, c, d and corresponded to them factors R2 are given in top part of table 4. To reduce number of elements in equations the correlation analyse was done to describe the influence of each element on value of each factor a, b, c and d. Results of correlation coefficients are shown in table 5. As it can be seen from table 5 the highest influence on values of factors a, b, c and d have S, S2, S·Vf and S·deq. The value for which the correlation coefficient was lower then 0.5 were cut of from the equation. The final form of equations is presented in bottom part of table 4.
CONCLUSIONS
The analysis of the initial effluent quality during deironing of water leads to the following conclusions.
Concentration of iron in initial effluent after backwashing with use of treated water shows well-marked maximum but after backwashing with use of raw water is decreasing function.
Distribution of iron concentration in initial effluent can be described as multinomial equation of the second or the third order.
Coefficients a, b, c and d which are located with suitable power can be described by parabolic equation as a function of iron concentration in water used for backwashing S, equivalent granules diameter deq and filtration velocity Vf.
Correlation coefficients show that influence S, deq and Vf are not similar. So equations which allow to calculate coefficients a, b, c and d can be describe in shorter version as a function of S2, S, S·Vf and S·deq.
In each water supply plants initial effluent discharge time after backwashing should be individually establish after examination of suitable pollution concentration in the first part of treated water as a function of time. The results can be described by multinomial function which allows to fix minimal time of initial effluent.
REFERENCES
Amirtharajah A., 1985. The interface between filtration and backwashing. Water Res.; 19, (5), 581-588. Amirtharajah A., 1988. Some theoretical and conceptual views of filtration. Journal AWWA; December, 36-46. Amirtharajah A., Wetstein D.P., 1980. Initial degradation of effluent quality during filtration. Journal AWWA; September, 518-524. Colton J.F., Hillis P., Fitzpatrick C.S.B., 1996. Filter backwash and start-up strategies for enhanced particulate removal. Water Res.; 30, (10), 2502-2507. Francois R.J., Van Haute A.A., 1985. Backwashing and conditioning of deep bed filter. Water Res.; 19, (11), 1357-1362. Heidrich Z., 1992. Wodociagi i kanalizacja. Cz. 1 Wodociagi, [Water supply and sewage systems. Part 1, Water supply] Wyd. Szkolne i Pedagogiczne, Warszawa [in Polish]. Heidrich Z., Roman M., Tabernacki J., Zakrzewski J., 1980. Urzadzenia do uzdatniania wody. Zasady projektowania i przykłady obliczeń. [Installation for water treatment. The base of designing and examples of calculation] Arkady, Warszawa [in Polish]. Ives K.J., 1980. Deep bed filtration. Theory and practice. Filtration and Separation. 17, March-April, 157-166. NBSW SGGW Dokumentacja powykonawcza, 2004. [Working Plan of Warsaw Agricultural University’s Water Supply Plant]. PROCHEM S.A. Warszawa [in Polish]. Siwiec T., 1994. Eksperymentalne badania technologicznych i hydraulicznych warunków płukania złóż wielowarstwowych, [Experimental investigations of technological and hydraulical conditions of multilayers backwashing] Międzynarodowa Konferencja “Zaopatrzenie w Wodę Miast i Wsi” PZITS Poznań, 917-934 [in Polish]. Siwiec T., 2000. Ocena metod płukania filtrów odżelaziajacych i odmanganiajacych. [Backwashing methods estimation of deironing and demanganise filters] Sympozjum Ogólnokrajowe HYDROPREZENTACJE III 2000, PZITS NOT Katowice, Wisła: 157-171 [in Polish]. Troińska J., 2001. Eksperymentalne badania wpracowywania się złóż w procesie odżelaziania wody. [Experimental research of starting up filters in deironing of water. Master thesis] Praca magisterska. Wydział Inżynierii i Kształtowania Srodowiska, Szkoła Główna Gospodarstwa Wiejskiego. (maszynopis) [in Polish]. Weber Ł., 2006. Problemy z wpracowywaniem złóż antracytowo-kwarcowych do usuwania manganu na Stacji Uzdatniania Wody we Wrzesni. [Starting up of anthracite-quartz demanganese filters on Water Spply Plant in Września] Forum Eksploatatora. 23, (2), 10-12 [in Polish].
Accepted for print: 28.04.2007
Tadeusz Siwiec
Department of Civil Engineering and Geodesy,
Water Supply and Sewage Systems Section,
Warsaw Agricultural University, Poland
Nowoursynowska St. 159, 02-776 Warsaw, Poland
Phone: +48 22 59 35 161
email: Tadeusz_Siwiec@sggw.pl
Joanna Troińska
Water Supply and Sewage Systems Works Ltd., Nowy Dwor Mazowiecki, Poland
Gen. Berlinga 100, Nowy Dwor Mazowiecki, Poland
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