Data Analysis
New Tasks for Spring 2013
Floc sedimentation velocity vs coagulant dose
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Process the data from Karen Swetland’s research to extract the average floc sedimentation velocity as a function of coagulant dosage. It should be possible to assess which coagulant, PACl or alum, produces flocs with a higher sedimentation velocity given the same aluminum concentration. This task does not require any additional laboratory work. It will require writing code to streamline the data extraction process. Think carefully about the best way to measure the time at which the turbidity is at 50% of the flocculated water turbidity. Some data smoothing or line fitting may be needed to get a reasonable estimate of the time. Create graphs of mean floc size as a function of coagulant dose for each of the turbidities that are available. Determine if the ratio of mass of coagulant per mass of clay is a good predictor of floc sedimentation velocity. Analyze the results using the insights from our new flocculation model that emphasizes the role of fractional surface coverage. Determine if equilibrium floc size can be predicted from the fractional surface coverage or if a more complex analysis is required. Make sure to take into account that for low turbidity samples more of the coagulant ends up on the flocculator walls. |
Past Research
Overview
During each experiment,data are automatically recorded in an Excel file (see example). The address for the excel file is recorded into the Meta file which is a spreadsheet with all the directories of the experimental data that will be/has been analyzed. Process Controller will be referring to the Meta file in order to acquire appropriate information on the experiment being analyzed; the Meta file will be an address book for Data Processor to efficiently access data.
The first graphs produced by the Mathcad file are the plots of the raw turbidity data vs. time and raw turbidity vs. settling velocity. The settling velocity (Vs) is calculated by dividing the distance between the ball valve and the zone illuminated by the infrared LED (z) of FRETA by the time elapsed(t).
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h1. Data Analysis h2. Overview During each experiment,data are automatically recorded in an Excel file (see example). The address for the excel file is recorded into the Meta file which is a spreadsheet with all the directories of the experimental data that will be/has been analyzed. Process Controller will be referring to the Meta file in order to acquire appropriate information on the experiment being analyzed; the Meta file will be an address book for Data Processor to efficiently access data. The first graphs produced by the Mathcad file are the plots of the raw turbidity data vs. time and raw turbidity vs. settling velocity. The settling velocity (Vs) is calculated by dividing the distance between the ball valve and the zone illuminated by the infrared LED (z) of FRETA by the time elapsed(t). {latex} \large $$ V_s = {z \over t} $$ {latex} |
For
...
experiments
...
involving
...
varying
...
alum
...
dosage,
...
another
...
graph
...
was
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produced
...
to
...
obtain
...
the
...
residual
...
turbidity
...
vs.
...
settling
...
velocity.
...
Residual
...
turbidity
...
is
...
the
...
turbidity
...
resulting
...
from
...
the
...
flocs
...
that
...
failed
...
to
...
reach
...
the
...
capture
...
velocity,
...
which
...
is
...
0.12
...
mm/s
...
for
...
the
...
sedimentation
...
tanks
...
of
...
the
...
AguaClara
...
plants.
...
From
...
this,
...
we
...
can
...
get
...
the
...
mean
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residual
...
turbidity
...
for
...
each
...
variation
...
of
...
alum
...
dose.
...
The
...
mean
...
residual
...
turbidity
...
is
...
the
...
mean
...
of
...
all
...
the
...
raw
...
turbidity
...
measured
...
after
...
a
...
time
...
of
...
approximately 22
...
min
...
till
...
the
...
end
...
of
...
the
...
sedimentation
...
state.
...
It
...
corresponds to
...
a
...
range
...
of
...
sedimentation
...
velocities
...
from
...
0.12
...
mm/s
...
to 0.089 mm/s. See example of the residual turbidity graph: Analysis Alum Dose Experiment.
TThen data smoothing and normalization are performed on the raw turbidity data. The smoothing allows us to exclude outlying data points caused by really large flocs passing in front of the light sensor of FRETA, which create turbidity fluctuations. The normalization allows us to compare data sets with varying influent turbidities. The plot of normalized turbidity vs. Vs (settling velocity) can be interpreted as a cumulative distribution function (CFD) of turbidity with respect to Vs. A CFD describes the probability that a variable is less than or equal to some value.
To make the analysis more robust, the experimental data was fit to a gamma distribution. Then a derivative of the CFD of the gamma distribution gives a probability distribution of the particle population with respect to Vs. From the fitted data, the data processor retrieves the mean sedimentation velocity for each alum dose as well as the coefficient of variation of the distribution. The coefficient of variation is the standard deviation of the distribution divided by the mean. It is an indication of the width of the sedimentation velocity distribution.
For more discussion of the data analysis, see Ian Tse's thesis(Chapter I, data analysis). See an example of the gamma PDF graph: Example of Analysis Alum Dose Experiment.
Analysis Process
The data analysis process of the current project emphasizes organization and accuracy. The following is a step-by-step guide for the analysis process.
1. Go to the file containing the desired experimental data
2. Skim through the datalog (excel sheet with experimental data) to check for any apparent error. (Wrong influent turbidity, no variation in alum dose...)
3. If no apparent error is found, open the Meta file and record the appropriate information**
--------------------------------------------------------------------------------------------
...
**Meta
...
File
...
Information
...
-The
...
Meta
...
File
...
is
...
like
...
as
...
an
...
address
...
book
...
for
...
the
...
datalogs.
...
It
...
is
...
important
...
to
...
update
...
this
...
file
...
after
...
an
...
experiment
...
for
...
the
...
Data
...
Processor
...
to
...
access.
...
The
...
steps
...
following
...
will
...
show
...
how
...
information
...
is
...
recorded
...
into
...
the
...
Meta
...
File:
...
a.
...
Put
...
the
...
appropriate
...
ID
...
Tag
...
number
...
in
...
the
...
A
...
column
b.
...
If
...
the
...
duration
...
of
...
the
...
experiment
...
was
...
three
...
days,
...
put
...
the
...
first
...
day
...
in
...
the
...
B
...
column,
...
the
...
second
...
day
...
in
...
the
...
C
...
column,
...
and
...
the
...
third
...
day
...
in
...
the
...
D
...
column;
...
if
...
the
...
experiment
...
only
...
lasted
...
for
...
2
...
days,
...
C
...
column
...
will
...
be
...
left
...
as
...
zero,
...
and
...
the
...
following
...
will
...
be
...
applied
...
for
...
an
...
experiment
...
with
...
a
...
one
...
day
...
duration-only
...
the
...
B
...
column
...
will
...
be
...
filled.
...
c.
...
Record
...
the
...
appropriate
...
directory
...
and
...
flocculator
...
length
...
in
...
column
...
F
...
and
...
G
d.
...
Column
...
J
...
will
...
be
...
adjusted
...
according
...
to
...
the
...
datalog;
...
it
...
will
...
be
...
the
...
first
...
row
...
in
...
the
...
datalog
...
where
...
the
...
settle
...
state
...
has
...
been
...
activated.
...
**Note,
...
for
...
most
...
experiments,
...
start
...
row
...
is
...
not
...
adjusted
e.
...
Comment
...
on
...
the
...
experiment
...
the
...
datalog
...
is
...
referring
...
to
...
(eg.
...
influent
...
turbidity,
...
alum
...
dose,
...
etc.)
...
Remember
...
to
...
save
...
the
...
Meta
...
file.
...
If
...
not,
...
the
...
Data
...
Processor
...
won't
...
be
...
able
...
to
...
access
...
the
...
data!
...
----------------------------------------------------------------------------------------------
...
4.
...
Open
...
Data
...
Processor
...
on
...
MathCad
...
5.
...
Change
...
the
...
directory
...
Data
...
Processor
...
is
...
referring
...
to
...
for
...
data
...
(Enter
...
the
...
ID
...
tag)
...
*
...
*
...
**Reference
...
address
...
will
...
be
...
located
...
at
...
the
...
top
...
of
...
Data
...
Processor,
...
and
...
only
...
the
...
last
...
portion
...
of
...
the
...
directory
...
will
...
need
...
to
...
be
...
changed-which
...
is
...
the
...
ID
...
tag
...
appearing
...
on
...
the
...
Meta
...
file.
...
To see where to put the MetaID, see figure 1
Figure 1: MetaID location in Data Processor
6.
...
Run
...
the
...
Data
...
Processor;
...
this
...
program
...
will
...
automatically
...
give
...
graphic
...
forms
...
of
...
the
...
data
...
and
...
calculate
...
needed
...
values.
...
7.
...
In
...
the
...
data
...
processor
...
you
...
will
...
need
...
to
...
change
...
a
...
value.
...
FirstFittedcolumn.
...
The
...
Data
...
processor
...
cannot
...
fit
...
the
...
data
...
for
...
alum
...
dose
...
too
...
low.
...
This
...
will
...
enable
...
you
...
to
...
eliminate
...
the
...
data
...
that
...
would
...
not
...
be
...
fitted
...
from
...
the
...
data
...
vector. To see where to put the fixed FirstFittedcolumn see figure 2.
Figure 2: FirstFittedColumn location in Data Processor