Poster

choppedspleenMécanique

22 févr. 2014 (il y a 3 années et 6 mois)

54 vue(s)

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
.