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.

Data repeatibility

The details of the experiment conducted to test data repeatibility can be viewed here.

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:

Equation 1

where
NTU is the effluent turbidity [-]
t is the time [T]
K is the rate of settling flocs [T].

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:

Equation 2

where
v is the terminal velocity

substitution of Equation (2) in Equation (1) yields:

Equation 3

Double reciprocal equation
Equation 4

Equations can also be viewed here.

Mathcad files

Data repeatibility

The results and discussion of data fluctuation can be viewed here.

Model fitting

By extracting the data using Meta Data files, we were able to choose any set of settling data of interest, plot and analyze them individually or collectively to see any if there is any trend to the data. We proposed polynomial fit as an option to evaluate the data and error analysis algorithm was 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 evaluated to get a better sense of parameters that actually effect the curve.

The limitation of using polynomial fit in the data analysis is hard to determine the any parameter that is responsible to describe the dataset. Each time a dataset was analyzed, the polynomial coefficients were changing and we couldn't find any trend that best described the settling data.

A hyperbolic fit was proposed and a sample of experimental dataset was normalized to its maximum turbidity reading to determine the percentage of flocs that has been settled over a period of time. Lineweaver-Burke data analysis was applied.

Examples of [data linearization] using double reciprocal analysis.

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.