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Data
...
Analysis
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New
...
Tasks
...
for
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Spring
...
2013
...
Floc
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sedimentation
...
velocity
...
vs
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coagulant
...
dose
...
| Excerpt |
|---|
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Process |
...
the |
...
data |
...
from |
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Karen |
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Swetland’s research |
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to |
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extract |
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the |
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average |
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floc |
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sedimentation |
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velocity |
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as |
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a |
...
function |
...
of |
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coagulant |
...
dosage. |
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It |
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should |
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be |
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possible |
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to |
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assess |
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which |
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coagulant, |
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PACl |
...
or |
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alum, |
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produces |
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flocs |
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with |
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a |
...
higher |
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sedimentation |
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velocity |
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given |
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the |
...
same |
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aluminum |
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concentration. |
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This |
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task |
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does |
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not |
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require |
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any |
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additional |
...
laboratory |
...
work. |
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It |
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will |
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require |
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writing |
...
code |
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to |
...
streamline |
...
the |
...
data |
...
extraction |
...
process. |
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Think |
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carefully |
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about |
...
the |
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best |
...
way |
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to |
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measure |
...
the |
...
time |
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at |
...
which |
...
the |
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turbidity |
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is |
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at |
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50% |
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of |
...
the |
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flocculated |
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water |
...
turbidity. |
...
Some |
...
data |
...
smoothing |
...
or |
...
line |
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fitting |
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may |
...
be |
...
needed |
...
to |
...
get |
...
a |
...
reasonable |
...
estimate |
...
of |
...
the |
...
time. |
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Create |
...
graphs |
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of |
...
mean |
...
floc |
...
size |
...
as |
...
a |
...
function |
...
of |
...
coagulant |
...
dose |
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for |
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each |
...
of |
...
the |
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turbidities |
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that |
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are |
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available. |
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Determine |
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if |
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the |
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ratio |
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of |
...
mass |
...
of |
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coagulant |
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per |
...
mass |
...
of |
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clay |
...
is |
...
a |
...
good |
...
predictor |
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of |
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floc |
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sedimentation |
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velocity. |
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Analyze |
...
the |
...
results |
...
using |
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the |
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insights |
...
from |
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our |
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new |
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flocculation |
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model |
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that |
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emphasizes |
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the |
...
role |
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of |
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fractional |
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surface |
...
coverage. |
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Determine |
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if |
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equilibrium |
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floc |
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size |
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can |
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be |
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predicted |
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from |
...
the |
...
fractional |
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surface |
...
coverage |
...
or |
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if |
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a |
...
more |
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complex |
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analysis |
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is |
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required. |
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Make |
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sure |
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to |
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take |
...
into |
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account |
...
that |
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for |
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low |
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turbidity |
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samples |
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more |
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of |
...
the |
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coagulant |
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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
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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
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settling
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velocity
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(Vs)
...
is
...
calculated
...
by
...
dividing
...
the
...
distance
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between
...
the
...
ball
...
valve
...
and
...
the
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zone
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illuminated
...
by
...
the
...
infrared
...
LED
...
(z)
...
of
...
FRETA
...
by
...
the
...
time
...
elapsed(t).
| Wiki Markup |
|---|
{latex} \large $$ V_s = {z \over t} $$ {latex} |
For
...
experiments
...
involving
...
varying
...
alum
...
dosage,
...
another
...
graph
...
was
...
produced
...
to
...
obtain
...
the
...
residual
...
turbidity
...
vs.
...
settling
...
velocity.
...
Residual
...
turbidity
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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
...
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:
...
...
...
...
...
.
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