h1. Analysis of the effect of alum dose and flocculator length on flocculation


h2. Procedure

In Experiment 2 we investigated the effect of alum dosage on flocculator performance. The procedure for [Experiment 1|Experiment 1 Varying flow rate] contains information on the general setup used in this experiment. We used the same setup as in Experiment 1, but instead of varying flow rate, we varied the alum dosage. The plant flow rate was held constant at 5 mL/s (shear rate of 57.563 s-1, calculated using equation 1.9 of [Ian's Thesis |^Ian Tse MS Thesis.doc]) and we used influent turbidities of 5, 25, 50, 100 and 500 NTU and three different flocculator lengths (28 m, 56 m, and 84 m).
To investigate alum dosage at a given turbidity and length, we first planned to vary the alum dose over a large range, incrementing the dose in set intervals while holding the plant flow rate (shear), influent turbidity, and residence time constant. We decided to first run an experiment at each value of influent turbidity at a length of 28 m and then repeat the experiment with the same alum dosage values at a flocculator length of 84 m. If we found a significant difference between the 28 and 84 m lengths for the same alum dosage and influent turbidity, we would then plan to test a third time at 54 m in order to understand the development of any trends we observed. Table 1 shows the alum ranges we tested for each flocculator length and influent turbidity:
*{_}TABLE 1:_* _Alum dose ranges tested and the increment used (mg/L)._
|| Flocculator Length (m) || 5 NTU || 25 NTU || 50 NTU || 100 NTU || 500 NTU ||
| 28 | 10-50 | 10-50 | 10-66 | 20-60 | 10-90 |
| Interval | 5 | 5 | 7 | 5 | 10 |
| 56 | 10-50 | 10-50 | 10-66 | 20-60 | 10-90 |
| Interval | 5 | 5 | 7 | 5 | 10 |
| 84 | 10-50 | 10-50 | 10-66 | 20-60 | 10-90 |
| Interval | 5 | 5 | 7 | 5 | 10 |
The alum dose was varied in process controller using the increment function shown in Figure 1:
!Alum Dose Calculation.JPG!
*{_}FIGURE 1:_* _Process Controller setpoints used to vary the alum dose._
The data was analyzed using the same methods as in [Experiment 1| Experiment 1 Varying flow rate].
We plan to continue narrowing down the optimal alum dose ranges for each influent turbidity and length, and hope to learn whether or not increasing flocculator length will in fact improve performance as expected and how long this trend continues.

The following Process Controller Files were used in our experiments:
[5 NTU One Length Test File |^5NTU 2796cm  5mls Alum 10-50mgL  by 5mgL.pcm]
[5 NTU Three Length Test File |^5NTU 8388cm  5mls Alum 10-50mgL  by 5  mgL.pcm]
[25 NTU One Length Test File |^25NTU 2796cm  5mls Alum 10-50mgL  by 5mgL.pcm]
[25 NTU Three Length Test File |^25NTU 8388cm  5mls Alum 10-50mgL  by 5mgL.pcm]
[50 NTU One Length Test File |^50NTU 2796cm  5mls Alum 10-63mgL  by 7mgL.pcm]
[50 NTU Three Length Test File |^50NTU 8388cm  5mls Alum 10-66mgL  by 7  mgL.pcm]
[100 NTU One Length Test File |^100NTU 2796cm 5mls-1 alum 20-60mgL-1 by 5mgL-1.pcm]
[100 NTU Three Length Test File |^100NTU 8388cm  5mls Alum 20-60mgL  by 5  mgL.pcm]
[500 NTU One Length Test File |^500NTU 2796cm  5mls Alum 10-90mgL  by 10mgL.pcm]
[500 NTU Three Length Test File |^500NTU 8388cm  5mls Alum 10-90mgL  by 10  mgL.pcm]

h2. Results and Discussion

The goal of this experiment is to study the effects of different alum doses and flocculator lengths in order to find the most effective way to improve the design of the actual AguaClara flocculator. However, before beginning any analysis, we must first be aware of the characteristics of a good flocculator. What defines a good flocculator? A good flocculator must: first, have large enough resulting flocs at the end of the flocculator so that they will weigh down, sink, and settle out in the sedimentation tank; second, have the floc size under control to an optimal size-overly large flocs hinder floc blanket formation as they will settle out before the floc particles can ever become fluidized; and third, have a low resulting turbidity indicating the production of clean water. The use of alum facilitates this process; however, too much alum can create oversize flocs that settle out in the flocculator before reaching the sedimentation tank. In addition, the over use of alum will be expensive; cost efficiency is essential in the building of the AguaClara plant. To find an ideal alum dosage for a particular influent turbidity, in our experiments, we have varied the alum doses within certain range and are going to see which dosage works best for each situation. The same goes to the different flocculator lengths; overly long flocculators will cause flocs to settle out before reaching the sedimentation tank and in addition will not be cost efficient. To find an ideal length, we have set up three apparatuses with varying tube lengths: 2796 cm, 5600 cm, and 8800 cm. For each alum dosage range, we will change the length of the flocculator in order to find the ideal combination of flocculator length and alum dose.

There are two important graphs that give the best overview of the experiment: the gamma PDF graph and the residual turbidity graph. The gamma PDF graph shows the probability of reaching a certain floc size for each run of experiment with varying alum dosage. The y-axis represents the probability and the x-axis represents the floc size. The residual turbidity graph is the gamma PDF graph focused at a certain range of sedimentation velocity. We chose this range based on our knowledge on capture velocity. Capture velocity is the minimum speed flocs must be in for them to settle in the sedimentation tank; any particle with a smaller velocity than this will not sink. Given that the capture velocity is 0.12 mm/sec, the residual turbidity graph focuses on the flocs that fail to reach this velocity. The turbidity from these particles shows the resulting turbidity produced after flocculation.

On November 12, 2009, an experiment was conducted with the turbidity set around 5 NTU, flocculator length of 2796 cm, flow rate of 5 mL/s, and alum dosage ranged from 10 to 50 mg/L.

The data processor fails to fit a curve into the gamma PDF graph due to the lack of efficient flocculation and trend/difference among the turbidity produced by the varying alum doses. Because the experiment was conducted with such a low influent turbidity, there are less colloidal particles present in the water and less probability for these particles to collide with one another. Hence, for this experiment, the shortness of the flocculator and the limited effect of the alum caused the failure of producing a significant improvement in the turbidity of the water. There will need to be a higher collision potential for these particles to successfully collide and create bigger flocs necessary for a successful flocculation. The residual turbidity graph (Figure 1) shows the resulting mean turbidity settling down to around 2 NTU starting from the alum dose of 20 mg/L.

*1*
!5NTULength1_RisidualTurbidity.png|align=center,width=400,height=400!
*{_}FIGURE 1:_* _The graph plots the residual turbidity vs. sedimentation velocity for each Alum dose ranging 10 mg/L~50 mg/L_
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On November 17, 2009, an experiment was conducted with the turbidity set around 5 NTU, flocculator length of 8800 cm, flow rate of 5 mL/s, and alum dosage ranged from 10 to 50 mg/L.

Looking at the gamma PDF curve (Figure 2A) the alum dosage of 10 mg/L demonstrates an unusual behavior compared to the other doses; it has a very narrow distribution focused at a particular sedimentation velocity. We suspect that this has been resulted from an unexpected presence of a large floc that has not necessarily been produced from the flocculator. From the residual turbidity graph (Figure 2B), there is also an unusual trend with the alum dose 40 mg/L; its turbidity unexpectedly peaks and results in an unusually high mean turbidity. In figure 2A, the alum doses 20 and 30 mg/L have wider distributions of floc sizes compared to those of other alum doses. Overall, there seems to be discrepancies between the data recorded in the two graphs. From the values of mean turbidity at settling state, from 10 to 45 mg/L the mean turbidity seemed to start at a value of .608 NTU then rise to about .725 at 25mg/L, then rises to .829 and then back down to .755 at 35 mg/L.

*2A*
!5NTULength3_GammaPDF.png|align=center,width=400,height=400!
*2B*
!5NTULength3_RisidualTurbidity.png|align=center,width=400,height=400!
*{_}FIGURE 2A:_* _The graph plots normalized turbidity vs. sedimentation velocity for each Alum dose ranging 10 mg/L~50 mg/L_; *{_}FIGURE 2B:_* _The graph plots the residual turbidity vs. sedimentation velocity for each Alum dose ranging 10 mg/L~50 mg/L_
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On November 11, 2009, an experiment was conducted with the turbidity set around 25 NTU, flocculator length 2796 cm, flow rate of 5 mL/s, and alum dosage ranged from 10 to 50 mg/L.

In the gamma PDF graph (Figure 3A), the alum dosage 10 mg/L shows a larger distribution of floc sizes with more probability to produce smaller flocs. In addition, looking at the residual turbidity graph (Figure 3B), the resultant turbidity this dosage gives is significantly higher than the rest. The residual turbidity graph also shows the alum doses 15 mg/L and 20 mg/L to be producing a slightly higher resultant turbidity. From the values of mean turbidity at settling state, starting from the alum dosage 35 mg/L, the mean turbidity settles down to a constant value around 2.5 NTU.

*3A* !25NTULength1_GammaPDF.png|align=center,width=400,height=400!
*3B* !25NTULength1_Residual turbidity.png|align=center,width=400,height=400!
*{_}FIGURE 3A:_* _The graph plots normalized turbidity vs. sedimentation velocity for each Alum dose ranging 10 mg/L~50 mg/L_; *{_}FIGURE 3B:_* _The graph plots the residual turbidity vs. sedimentation velocity for each Alum dose ranging 10 mg/L~50 mg/L_
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On October 20, 2009, an experiment was run with the set up of influent turbidity around 100 NTU, flocculator length of 2796 cm, flow rate of 5 mL/s, and an alum dosage ranging from 20 to 55 mg/L. The data obtained from this experiment was processed through Mathcad for a simplified overview of the results in graphic form.

Looking at the gamma PDF graph (Figure 4A), the alum dosage of 20 mg/L gives a widely distributed probability of reaching different floc sizes with a comparably low probability to reach its highest sedimentation velocity. In addition, the residual turbidity graph (Figure 4B) shows a high turbidity for this alum dose in its lower velocity range. Thus the alum dose 20 mg/L seems to be inefficient for this particular influent turbidity and flow rate. The mean turbidity resulting from alum dose 55 mg/L is out of normal range; its NTU value is significantly lower than the values given from the previous, lower alum dosages. Hence, the result from this dosage is doubtful. Overall, after the alum dose of 35 mg/L (except for 55 mg/L), the mean turbidity settles down to a constant value around 1.4 NTU.

*4A* !100NTULength1_GammaPDF.png|align=center,width=400,height=400!
*4B* !100NTULength1_RisidualTurbidity.png|align=center,width=400,height=400!
*{_}FIGURE 4A:_* _The graph plots normalized turbidity vs. sedimentation velocity for each Alum dose ranging 20 mg/L~55 mg/L_; *{_}FIGURE 4B:_* _The graph plots the residual turbidity vs. sedimentation velocity for each Alum dose ranging 20 mg/L~55 mg/L_
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On November 18, 2009, an experiment was ran with the set up of influent turbidity around 100 NTU, flocculator length of 8800 cm, flow rate of 5 mL/s, and an alum dosage ranging from 20 to 55 mg/L.

Looking at the gamma PDF graph (Figure 5A), all of the alum dosages give a similar result with their likeliness to produce similarly sized flocs at a similar probability. The residual turbidity graph (Figure 5B) shows alum doses 30 mg/L and 35 mg/L giving comparably higher resultant turbidities. Unlike the expected trend, rather than improving the turbidity of the water, the graphs show the deterioration of efficiency with more alum; the resulting turbidity seems to slightly increase with a larger amount of alum. Overall, there seems to be not much change with the increasing of alum dosage.

*5A*
!aguaclara graph 2pdf.jpg|align=center,width=400,height=400!
*5B*
!aguaclara graph 1_cropped.jpg|align=center,width=400,height=400!
*{_}FIGURE 5A:_* _The graph plots normalized turbidity vs. sedimentation velocity for each Alum dose ranging 20 mg/L~55 mg/L_; *{_}FIGURE 5B:_* _The graph plots the residual turbidity vs. sedimentation velocity for each Alum dose ranging 20 mg/L~55 mg/L_
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On Oct 27, 2009, another experiment was conducted with the turbidity set around 500 NTU, flocculator length 2796 cm, flow rate of 5 mL/s, and alum dosage ranging from 10 to 90 mg/L.

In both graphs (Figure 6A, Figure 6B), the alum dosage 10 mg/L gives a comparably different result from the rest; it produces a significantly higher settling turbidity and a large amount of smaller flocs. The overall mean turbidity for this dosage is almost twice the following dosages. After the alum dose 50 mg/L, the mean turbidity settles down to a constant value around 2.5 NTU.

*6A* !500NTULength1_GammaPDF.png|align=center,width=400,height=400!
*6B* !500NTULength1_RisidualTurbidity.png|align=center,width=400,height=400!
*{_}FIGURE 6A:_* _The graph plots normalized turbidity vs. sedimentation velocity for each Alum dose ranging 10 mg/L~90 mg/L_; *{_}FIGURE 6B:_* _The graph plots the residual turbidity vs. sedimentation velocity for each Alum dose ranging 10 mg/L~90 mg/L_
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On Nov 19, 2009, another experiment was conducted with the turbidity set around 500 NTU, flocculator length 8388 cm, flow rate of 5 mL/s, and alum dosage ranging from 10 to 90 mg/L.

As shown in Figure 7A, there is no big differences between the floc size distribution except for the lowest alum dose. As the previous experiment (500 NTU, length 2796 cm), the distribution is narrow wich means that we are producing flocs of almost the same size. Besides, the mean floc size seems to be the same than previously.

*7A*
!500NTULength3_GammaPDF.png|align=center,width=400,height=400!
*7B*
!500NTULength3_RisidualTrubidity.png|align=center,width=400,height=400!
*{_}FIGURE 7A:_* _The graph plots normalized turbidity vs. sedimentation velocity for each Alum dose ranging 10 mg/L~90 mg/L_; *{_}FIGURE 7B:_* _The graph plots the residual turbidity vs. sedimentation velocity for each Alum dose ranging 10 mg/L~90 mg/L_
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h2. Conclusion

_Effect of length of the flocculator on residual turbidity_:
The length of the flocculator has different effects on the residual turbidity depending on the initial effluent turbidity. In the next figures (fugures 8 and 9), we are comparing the mean residual turbidity as a function of the alum dose at 2 different lengths of flocculator, 2796 cm and 8388 cm (3*2796 cm) and for different influent turbidity, 5NTU (figure 8) and 500 NTU (figure 9) .
As shown in figure 8, at 5 NTU the length has a real effect on flocculation. Low turbidity water is more difficult to flocculate than water with high turbidity because the collision potential required to make large flocs has to be higher. There are few colloidal particles in the water so the average volume occupied by a floc or a particle is bigger so that the average time between collisions is greater leading to a higher collision potential.
{latex}
\large
$$
\psi _{needed} = {1 \over 6}\left( {{6 \over \pi }} \right)^{{1 \over 9}} d^{{2 \over 3}} \varphi _{Floc_0 } ^{{{ - 8} \over 9}} \left( {{d \over {d_0 }}} \right)^{{{8\left( {D_{fractal} - 3} \right)} \over 9}}
$$

{latex}
with
{latex}
\large
$$
\phi _{Floc_0 } = {{Volume_{floc} } \over {Volume_{suspension} }}
$$

{latex}
With a longer flocculator, the residence time is longer and the colloidal particles have more time to collide and form big flocs with a higher terminal velocity than the one at the end of the shorter flocculator. If the terminal velocity of the flocs is bigger, it means that more flocs are going to settle and it will reduce the residual velocity. As shown on figure 8, the residual turbidity is smaller for the longer flocculator.
With an effluent water of 500 NTU, the difference between the two lengths of flocculator can't really be seen in figure 9. The mean residual turbidity is even a little bit higher with the longer flocculator at high alum dose. This could be explained by the fact that we break up flocs. A high turbidity water is easier and faster to flocculate so we are making really big flocs even with the smaller flocculator and as the flocs grow bigger and bigger, they are easier to break. The hypothesis is that a sort of equilibrium is established in the flocculator. Flocs are growing but at one point they are too big and fluid shear stresses break the flocs into smaller fragments. But then these smaller fragments can flocculate again. After some time, a steady state is reached between flocculation and fragmentation and the floc size distribution stay the same. That's why the same residual turbidity is observed for the two lengths of flocculator: the steady state is reached in the two flocculators. !5NTU length 1 and 3.png|align=center,width=500,height=400!
*Figure 8*: _Plot of the residual turbidity as a function of alum dose at two different flocculator length, 796 cm and 8388 cm, for an effluent water of 5 NTU_ !500 NTU length 1 and 3.png|align=center,width=500,height=400!
*Figure 9*: _Plot of the residual turbidity as a function of alum dose at two different flocculator length, 796 cm and 8388 cm, for an effluent water of 500 NTU{_}{_}Effect of the alum dose on flocculation_:
The next figure (figure 10) we are plotting the residual turbidity as a function of alum dose for water with a different influent turbidity in the short flocculator (2796 cm). We can observe a similar behavior between the plots. At the beginning, the residual turbidity is decreasing when we increase alum dose and then we reach a limit where the residual turbidity is almost constant when we increase alum dose. These results mean that we could optimize the cost by using the minimum alum dose that gives the minimum effluent turbidity.
We can also observe on this figure that at a given alum dose, the mean residual turbidity is different for each influent turbidity. The highest residual turbidity is found for 500 NTU then 25 NTU and 5 NTU. The lowest residual turbidity is found for an influent water of 100 NTU. This could be explained by the fact that two phenomena are happening at the same time. For the low turbidity, 5 NTU and 25 NTU, as I explained earlier, it is longer to produce large flocs and the residence time in the 2796 cm long flocculator might be too short so the residual turbidity is relatively high. For the high influent turbidity, 500 NTU, we reach a steady state in the flocculator but as we are starting with a really high turbidity, the residual turbidity is high too. Logically, the optimum result should be found for a medium influent turbidity and it is found for 100 NTU. !residual turbidity_length1.png|align=center,width=500,height=400!
*Figure 10*:_Plot of the residual turbidity as a function of alum dose at different influent turbidity with a 2796 cm long flocculator{_}The following steps of this analysis will consist in doing further experiments with wider alum range and more influent turbidity. The size distribution of flocs will be analized to see what would be the influence of different flocculator lengths and different alum doses on a floc blanket.
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