Tube Floc Settling Data Analysis

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Data source

Data from previous experiments were collected using Process Controller and saved in Excel files. The data of interest (i.e. effluent turbidity) was stored in a file corresponding to the date of experiment run and the status file indicated the state of treatment process (i.e. flocculation state, settling state, etc). Data was extracted using Meta Data and analyzed in the steps provided below.

Model fitting

In the settling state (state 4 or 5, depending on the experimental and software setup), the analysis of settling dataset starts from its maximum turbidity reading. This will eliminate the data fluctuation due to a sudden stop of flow. Data is normalized to the maximum reading of dataset and converted to a positive hyperbolic curve for data interpretation. The dataset will now read as the cumulative amount of settling in the tube. A hyperbolic curve can be linearized using double reciprocal method (or Lineweaver-Burke plot), where the Y-axis is the reciprocal of the cumulative amount of settling and X-axis is the terminal velocity. The length of tube shone by the light is assumed to be 5 cm.

Equations

Assuming the dataset follows a hyperbolic curve function, therefore it can be represented as:

Y = t/(K+t)

where
Y is 1 - NTU/NTU _max
t is the time [T]
K is the flocs are settling.

This simplification will enable the team to extract an important parameter of the curve (i.e. K)

Terminal velocity is the velocity of the flocs settling in the column. Assuming d as the length of tube shone by the light, t can be redefined as:

t = d/V

where
V is the terminal velocity

Equation (1) thus becomes:

Mathcad files

1. By extracting the data using Meta Data files, we were able to pick sets of settling data of interest and plot and analyze them individually or collectively to see any trends.
2. Data fluctuation shows that ...

Model fitting

We're proposing polynomial fit as an option to evaluate the data and error analysis algorithm is utilized to see which equations fit each datasets the best.

[Another datasets example] is also analyzed to determine which polynomial fit suits the best. From sum squared error analysis, the third and fourth degree of polynomial were found to be the best.[Another raw sedimentation data] was looked at different angle to get a better sense of parameters that actually effect the curve.

Data is normalized and Lineweaver-Burke data analysis was applied.

We were interested to find out how much the data fluctuates during settling in a given experiment if repeated several times and how this might impact our results.

Data is [linearized] using double reciprocal analysis and the equations can be viewed here.

Apart from analyzing past datasets, the team also interested to analyze datasets from new setup. The new setup can be viewed here and the analysis of experimental runs can be viewed [here].