Jeff Holland
Jay Martin
Tim Granata
Larry Brown
Virginie Bouchard
Martin Quigley
Tools
for
modeling
pulsed
flows
and
constituent
fluxes
in
wetlands,
although
well
developed
in
theory,
have
not
been
well
tested
in
practice
.
High

frequency
monitoring
of
suspended
solids
and
flows
in
a
stormwater
treatment
wetland
enabled
application
and
analysis
of
these
tools
.
A
dynami c
fl ow

and
volume

weighted
time
variable,
analogous
to
the
retention
time
in
steady

flow
systems,
is
one
important
tool
tested
in
this
study
.
Cross
correlations
with
time
lags
demonstrated
that
the
dynamic
time
variable
was
a
better
predictive
variable
of
pulsed
events
than
was
the
standard
time
variable
.
Thi s
s t udy
al s o
demons t r at ed
t hat
Res i denc e
Ti me
Di s t r i but i on
( RTD)
model i ng
wi t h
r eac t i on
k i net i c s
of
suspended
solids
during
storm
events
produces
a
better
explanation
of
outflow
data
than
possible
with
steady,
plug

flow
models
.
Usi ng
onl y
i nput
and
output
data,
an
RTD
model
explained
sedimentation
rates
with
less
unexplained
variance
than
the
standard,
plug

flow
model
.
The
results
of
this
study
underscore
the
utility
and
importance
of
RTD
modeling
for
complex
flows
.
Analysis and modeling of complex flow in a stormwater treatment wetland
theoretical retention times,
Φ
normalized
concentration
Normalized RTD:
centroid
retention
time =1
time
time
concentration
Predicted Output concentration without
reaction (Tracer)
Predicted Output concentration
with reaction
Pollutant inflow flux
during storm
time
mass flux
Σ
Applying denormalized RTDs to each
input differential
tracer output
concentration
time
RTD:
centroid
retention time
time
tracer input
mass
flow through
wetland
Introduction
Many
developments
have
been
made
recently
to
understand
complex
flow
in
wetlands
.
Residence
time
distribution
analysis,
originally
used
to
describe
non

plug,
or
nonideal,
flow
in
wetland
basins
(Thackston,
1987
),
has
more
recently
been
adapted
to
analyze
pulsed
conditions
(Werner
and
Kadlec,
1996
),
such
as
those
during
storm
events
.
A
residence
time
distribution
(RTD)
is
the
probability
distribution
that
a
particle
entering
a
wetland
will
exit
at
a
given
time
.
Thi s
can
be
measured
by
introducing
a
conservative
tracer
into
a
wetland
(AWWARF,
1996
)
:
The
resulting
RTD
reflects
the
dispersion
of
the
system,
but
it
is
complicated
by
the
pulsed
flow
through
the
system
.
This
pulsing
effect
can
be
removed
by
normalizing
the
time
axis
with
flow
and
volume
changes
of
the
wetland
system
.
The
nor mal i zed
t i me
var i abl e,
Φ
,
has
interesting
properties,
which
are
explored
in
this
project
.
The
Normalized
RTD
represents
the
dispersion
of
the
system
independent
of
pulsing
.
Knowing
the
RTD
allows
modeling
of
constituents
passing
through
the
system
(Nauman,
1983
)
.
Each
i nput
di ff erent i al
is
treated
like
a
t racer
pul se
wi t h
associ at ed
RTD
.
The
RTD
can
be
denormalized
to
yield
a
concentration

versus

time
curve
.
The
resul ti ng
set
of
curves
can
be
summed
to
create
an
outlet
concentration
prediction
:
A given flow through a wetland
together
with
a
conservative
tracer
introduced
at
the
input
Yield
a
unique
residence
time
distribution
(RTD)
at
the
output
The
RTD
can
be
normalized
to
represent
the
dispersion
of
the
system
without
pulses
The
RTD
can
be
used
to
model
t h e
o u t p u t
of
a
wetland,
if
the
influx
of
a
constituent
is
known
Wetland Monitoring
A
500
m
2
stormwater
treatment
wetland
in
Columbus
Ohio
was
monitored
over
the
summer
of
2003
.
S o n d e s
me a s u r e d
f l o w
and
suspended
solids
at
all
inflows
and
outflows
to
the
wetland
.
Loggi ng
dept h
and
suspended
solids
data
automatically
every
10
minutes,
the
sondes
were
able
to
capture
short

lived
storm
events
.
A
t ot al
of
19
storm
events
(>
1
cm
of
rainfall)
were
recorded
during
this
summer
.
STORMFLOW
FROM FARM
DISCHARGE
TO STREAM
Y
Y
V

NOTCH WEIR
Y
YSI 6600 WATER QUALITY
AND FLOW PROBE
AGRI DRAIN WATER
LEVEL CONTROL BOX
CONTROL BOX
FLOW FROM
TREATMENT
WETLAND
t
t
o
t
d
t
V
t
Q
)
(
)
(
M
t
t
t
)
)V(
C(
)
(
C'
The
wetland
was
surveyed
so
that
outlet
depths
could
be
used
to
determine
wetland
volume
as
a
function
of
time,
V(t)
.
Calculating the RTD
The
outflow
concentration
of
an
introduced
pulse
of
Rhodamine
WT
dye
tracer
determined
the
Residence
Time
Distribution
(RTD)
(Levenspiel,
1972
)
:
Materials
&
Methods
Developing the RTD Model
A
matrix
was
developed
to
represent
the
set
of
denormalized
RTDs
for
each
input
sample
.
The
indices
of
the
matrix
represent
the
time
reaching
the
outlet,
n

1
,
and
the
time
spent
in
the
wetland,
m

1
.
t
t
V
t
Q
t
C
t
t
C
X
n
m
n
in
m
n
in
m
n
n
m
n
1
1
,
'
time
concentration
)
(
)
(
t
f
X
t
C
)
exp(
)
(
)
(
)
(
t
k
t
C
t
C
t
f
v
in
The
matrix
set
of
RTDs
can
be
summed
by
multiplying
with
a
vector
of
first

order
sedimentation
fractions,
yielding
the
outflow
concentration
as
a
function
of
time
.
time
concentration
Predicted Output concentration when k
v
=0
Predicted Output concentration
when k
v
>0
Acknowledgments
References
Results
&
Discussion
Abstract
Applying the RTD Model
The model was
applied to the
monitored influx
during storm events.
The model output
matched closely with
the actual
concentration output,
demonstrating the
predictive value of
the RTD model.
Analyzing sedimentation rates with the model
Investigating time series
Sedimentation
rates
were
calculated
by
finding
the
rate
that
creates
the
least
square
model
fit
.
This
is
compared
with
the
standard
plug
flow
reactor
(PFR)
method
of
calculating
rates
based
on
inflow
and
outflow
concentration
and
retention
time
.
Ra t es
a r e
p l ot t e d
v er s us
h y d r a ul i c
l o ad i ng
s i n c e
p ar t i c l e
s i z e
and
thus
sedimentation
rates
generally
increase
with
flow
rates
(Braskerud,
2002
)
.
Cross
correlations
with
time
lags
between
the
input
flux
and
output
concentration
were
analyzed
.
These
are
the
same
parameters
used
in
the
RTD
model
.
Similar
cross
correlations
were
calculated
with
lags
of
t i me,
t,
and
lags
of
dynamically
normalized
time,
Φ
.
A
much
higher
correlation
peak
occurred
in
cross
correlations
with
Φ
lags
than
with
t
lags
:
Opposite
trends
occurred
when
time
and
Φ
lags
were
compared
at
different
managed
water
levels
:
The
depth

caused
shift
in
t
peaks
simply
represents
the
change
in
retention
time,
but
the
depth

caused
shift
in
Φ
peaks
may
represent
a
change
in
hydraulic
efficiency
.
Correlations
in
t
are
dependent
on
flow
intensity,
but
correlations
in
Φ
are
intrinsic
to
the
system,
and
therefore
reinforce
one
another
.
Standard PFR model RTD model
Previous
research
indicates
that
the
standard
PFR
model
breaks
down
during
nonideal
flow
(Kadlec,
2000
)
and
pulsed
flow
(Werner
and
Kadlec,
2000
)
.
The
RTD
model
explains
the
variance
of
the
rates
with
hydraulic
loading
better
than
the
standard
model
.
Th i s
e f f e c t
d e mo n s t r a t e s
t h a t
t h e
RTD
method
is
effective
for
modeling
wetland
constituents
.
To
make
this
relationship
applicable
to
all
water
levels
and
flow
rates,
the
time
axis
must
be
normalized
by
the
flow
and
volume
(Werner
and
Kadlec,
1996
)
.
t
time
C
in
(t)
Inlet concentration
C(t)
Outlet concentration
C
´
(t)
RTD function
V(t)
Wetland volume
Q(t)
Flow rate
M
Dye mass
Φ
Normalized time
X
RTD matrix
k
v
Volumetric rate
constant
Key to symbols
Wetland suspended solids flux input
used as the model input
The parameter
Φ
is a more
consistent
explanatory
variable of
constituent flow
through wetlands
than time,
t
.
Cross correlation peak
positions in
Φ
are
similar to those of RTDs.
RTD peak
Φ
values can
be a metric of hydraulic
efficiency, or efficient
flow distribution in a
wetland (Persson et al.,
1999).
time
An
adjustable
weir
at
the
outlet
allowed
controlled
adjustments
of
the
wetland
depth
There is less
unexplained variance
in the sedimentation
rates determined by
the RTD model
We
would
like
to
thank
Noel
Cressie
and
Tom
Lippman
for
their
advice
on
statistical
methods
and
experimental
design
.
We
are
also
appreciative
of
the
design
and
construction
work
done
by
Dan
Gill,
Tim
Salzman,
and
Alex
Daughtery
.
For
the
technical
assistance
of
Chris
Gecik,
Kevin
Duemmel,
and
Carl
Cooper,
we
are
greatly
indebted
.
Many
thanks
also
go
to
Mark
Schmittgen,
for
his
assistance
on
the
farm,
to
Chris
Keller
for
his
advice
on
using
dye
tracers,
and
to
James
Carleton
for
providing
suggestions
on
investigating
reaction
rates
.
Thi s
st udy
woul d
not
have
been
possible
without
funding
from
the
Ohio
Agricultural
and
Research
Development
Center
and
generous
donations
from
Agri
Drain
Corporation
.
AWWARF,
1996
.
Tracer
Studies
in
Water
Treatment
Facilities
:
A
Protocol
and
Case
Studies
.
American
Water
Works
Research
Foundation,
Denver,
CO
.
Braskerud,
B
.
C
.
,
2002
.
Design
considerations
for
increased
sedimentation
in
small
wetlands
treating
agricultural
runoff
.
Water
Sci
.
Technol
.
45
,
77

85
.
Kadlec,
R
.
H
.
,
2000
.
The
inadequacy
of
first

order
treatment
wetland
models
.
Ecol
.
Eng
.
15
,
105

119
.
Levenspiel,
O
.
,
1972
.
Chemical
reaction
engineering,
2
nd
edition
.
Wiley,
New
York
.
Nauman,
E
.
B
.
,
and
B
.
A
.
Buffham,
1983
.
Mixing
in
Continuous
Flow
Systems
.
John
Wiley
&
Sons,
New
York
.
Persson,
J
.
,
N
.
L
.
G
.
Somes,
and
T
.
H
.
F
.
Wong,
1999
.
Hydraulics
efficiency
of
constructed
wetlands
and
ponds
.
Water
Sci
.
Technol
.
40
,
291

300
.
Thackston,
E
.
L
.
,
F
.
D
.
Shields,
and
P
.
R
.
Schroeder,
1987
.
Residence
Time
Distributions
of
Shallow
Basins
.
J
.
Environ
.
Eng
.

ASCE
113
,
1319

1332
.
Werner,
T
.
M
.
,
and
R
.
H
.
Kadlec,
1996
.
Application
of
residence
time
distributions
to
stormwater
treatment
systems
.
Ecol
.
Eng
.
7
,
213

234
.
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