Data Fluctuation

Data Fluctuation Experiment

Objectives

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 acquired a 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 Procedures

Our team re-ran an experiment multiple times 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 flow rate (Q) of 3.1 mL/sec. We repeated this experiment ten times in a row. We looked at the effluent turbidity from the settling state (600 seconds), and computed the ensemble average of the turbidity over the 10 runs and also the standard deviation about the ensemble mean at each 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 7: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 8: Time Averaged data over 60s of the Effluent Settling Turbidities from 10 consecutive experiments using a 50ft Flocculator and turbidimeter position at the top.

Discussion

The effluent turbidity standard deviations for both the top and bottom positions have a large range (Figures 1 and 2), and there is a trend of increasing standard deviations as the settling state time increases. The maximum standard deviation for the effluent turbidity when the turbidimeter was in its standard position (top) is 12.4. The maximum standard deviation for the effluent turbidity when the turbidimeter was in its new position (bottom) is 14.2. As expected, the influent turbidity standard deviations in both positions are 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.

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.

The effluent turbidity data for each run was time averaged over a 60 second interval (Figure 3, 4, 5) to get a smoother curve. Graphing the raw effluent turbidity data is noisy and hard to make any clear conclusions. From these graphs, we can determine that the number run in a set of runs does not affect the settling turbidity. There is no trend between the number run in a set and the settling turbidity. This is good news for our research, because most of the data from last semester was collected during a large experiment that involved 30 or more runs. Now that we know that the number of runs does not affect the settling turbidity, we can conclude that our data from each run in our large experiments from last semester are not affected by the other runs in the experiment.