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Floc sedimentation is a deterministic process that, under ideal conditions and the same initial conditions, should be highly repeatable. However, because we do not have ideal conditions there will invariably be statistical variance from the actual values. Moreover, the nepthalometric turbidimeter does a poor job of resolving individual flocs both temporally and spatially. For example, when we have a solution containing many large flocs slowly settling out in relatively clear water, the turbidity value will fluctuate between high and low values as flocs move into and out of the measurement volume. This is an intrinsic problem with using turbidity as a quantifying metric for how clear a solution is when large colloids are present in the suspension. For lack of a better measurement technique, we must try and estimate the mean turbidity as a function of time to infer some information about either floc concentration or floc size or both. We suspect that if we take the ensemble average of multiple realizations of the same experiment, we may be able to average out some of the higher frequency fluctuations that are caused by large flocs moving in and out of the sample volume.
Last semester, our team recorded acquired a lot large set of data , not knowing how the effluent turbidity data might vary greatly even if the same experiment were to be run twice. In order to get a better picture of the noise or high frequency data fluctuations in our past data, we wanted to design a simple experiment to quantify how much of the fluctuation can be removed through ensemble averaging the data from a large number of experimental runs.
Experiment
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Procedures
Our team re-ran a typical an experiment multiple times repeatedly to see how the effluent turbidity data fluctuated during the settling state in each experiments and to compare the data fluctuation between experiments. The experiment set up was an influent turbidity of 50 NTU, an alum concentration of 25 mg/L, a flocculator length of 25 feet, and a G flow rate (Q) of 3.1 1mL/ssec. We repeated this experiment at least ten times in a row. We extrapolated looked at the data effluent turbidity from just the settling state (600 seconds), we found and computed the ensemble average and standard deviation of the influent turbidity over the 10 runs and the effluent turbidity separately also the standard deviation about the ensemble mean at each second interval. We conducted this experiment for the typical position of the turbidimeter at the top of the settling column and at a new position of the turbidimeter at time interval.
Additionally, we decided to also investigate whether our previous assumption that flocs were settling in a discrete manner was accurate. If flocs were growing in size because smaller particles adsorbed to the large flocs as they settled, then our steady-state assumption that flocs reach a constant terminal velocity very soon after the termination of flow would be inaccurate. In order to investigate how flocs settled inside the settling column, we decided to move the sampling volume to near the bottom of the settling column to see if it would result in a different settling curve. If the flocs settled out faster for the run where we sampled from the bottom of the settling column than for the runs where we sampled at the top, then differential sedimentation does occur and neglecting it may introduce too much error.
Results
Figure 1: Standard Deviations of the Influent and Effluent Settling Turbidities from 10 consecutive experiments using the same position of the settling column (top).
Figure 2: Standard Deviations of the Influent and Effluent Settling Turbidities from 10 consecutive experiments using a new position of the settling column (bottom).
Figure 3: Ensemble Averaged data of 10 consecutive experiments using a 25ft Flocculator and turbidimeter position at the top.
Figure 4: Ensemble Averaged data of 10 consecutive experiments using a 25ft Flocculator and turbidimeter position at the bottom.
Figure 5: Ensemble Averaged data of 10 consecutive experiments using a 50ft Flocculator and turbidimeter position at the top.
Figure 6: Time Averaged data over 60s of the Effluent Settling Turbidities from 10 consecutive experiments using a 25ft Flocculator and turbidimeter position at the top.
Figure 47:Time Averaged data over 60s of the Effluent Settling Turbidities from 10 consecutive experiments using a 25ft Flocculator and turbidimeter position at the bottom.
Figure 58: Time Averaged data over 60s of the Effluent Settling Turbidities from 10 consecutive experiments using a 50ft Flocculator and turbidimeter position at the top.
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The effluent turbidity standard deviations in for both the top and bottom positions have a large range (Figure Figures 1 and 2), and there is a trend of increasing standard deviations as the settling state time increases. The max maximum standard deviation for the effluent turbidity when the turbidimeter was in its standard position (top) is 12.4. The max maximum standard deviation for the effluent turbidity when the turbidimeter was in its new position (bottom) is 14.2. The As expected, the influent turbidity standard deviations in both positions are generally consistently lower than the effluent turbidity standard deviations, and maintain at low values. We expect this because the deviations from the mean are a result of large flocs moving in and out of the sample volume.
These results definately show us some insights into our data. We see that the settling data in one experiment will not be the same as in the next experiment (when all variables of the experiment remain the same). From the data, it appears that there is no significant difference from having the turbidimeter position at the top or at the bottom of the column, except for the slight increase in the max standard deviation of the effluent settling turbidity, and the increase in range of effluent turbidity standard deviation values. For example, the standard deviation values at the end of the settling time in the top position experiment ranges from 2 to 12, whereas the range of the standard deviation values at the end of the settling time in the bottom position experiment ranges from 5 to 15.
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