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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.
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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).
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