Download retention time =1

Analysis and modeling of complex flow in a stormwater treatment wetland
Tim Granata
Abstract
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.
flow through
wetland
A residence time distribution (RTD) is the probability distribution that a particle entering a
wetland will exit at a given time. This can be measured by introducing a conservative
tracer into a wetland (AWWARF, 1996):
A given flow through a wetland
tracer input
mass
time
together with a conservative
tracer introduced at the input
Wetland Monitoring
The outflow concentration of an introduced pulse of
Rhodamine WT dye tracer determined the Residence
Time Distribution (RTD) (Levenspiel, 1972):
FLOW FROM
TREATMENT
WETLAND
STORMFLOW
FROM FARM
A 500m2 stormwater treatment wetland in
Columbus Ohio was monitored over the
summer of 2003. Sondes measured flow
and suspended solids at all inflows and
outflows to the wetland. Logging depth and
suspended solids data automatically every 10
minutes, the sondes were able to capture
short-lived storm events. A total of 19 storm
events (>1cm of rainfall) were recorded
during this summer.
C(t )V( t )
C' ( t ) 
M
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).
Y
YSI 6600 WATER QUALITY
AND FLOW PROBE
DISCHARGE
TO STREAM
AGRI DRAIN WATER
LEVEL CONTROL BOX
CONTROL BOX
Key to symbols
The wetland was surveyed so
that outlet depths could be used
to determine wetland volume as
a function of time, V(t).
An adjustable weir at the outlet
allowed controlled adjustments
of the wetland depth
t
Cin(t) Inlet concentration
C´(t)
RTD function
Developing the RTD Model
V(t)
Wetland volume
Q(t)
Flow rate
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.
M
Dye mass
Φ
Normalized time
X
RTD matrix
kv
Volumetric rate
constant
time
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.
Predicted Output concentration when kv=0
C (t )
f (t ) C
 (t )  X exp(
f (t ) k v  t )
C in (t )
Predicted Output concentration
when kv>0
time
centroid
tracer output
concentration
Yield a unique residence time
distribution (RTD) at the
output
time
retention time
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 normalized time
variable, Φ, has interesting properties, which are explored in this project.
centroid
normalized
concentration
Normalized RTD:
retention
time =1
theoretical retention times, Φ
The RTD can be normalized
to represent the dispersion of
the system without pulses
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 input differential is treated like a tracer pulse with associated
RTD. The RTD can be denormalized to yield a concentration-versus-time curve. The
resulting set of curves can be summed to create an outlet concentration prediction:
mass flux
Pollutant inflow flux
during storm
Applying denormalized RTDs to each
input differential
time
time
Σ
The RTD can be used
to model the output
of a wetland, if the
influx of a constituent
is known
concentration
Predicted Output concentration without
reaction (Tracer)
Predicted Output concentration
with reaction
time
Analyzing sedimentation rates with the model
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. Rates are plotted versus
hydraulic loading since particle size and thus sedimentation rates generally increase with
flow rates (Braskerud, 2002).
Standard PFR model
Results & Discussion
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.
Wetland suspended solids flux input
used as the model input
Investigating time series
time
RTD:
time
Outlet concentration
C ' t n 1  t nm   Cin t nm   Qin t nm 

t
V t n1 
Q(t )

dt 
V (t )
to
t
V-NOTCH WEIR
C(t)
X n,m
Martin Quigley
Calculating the RTD
Y
Introduction
Virginie Bouchard
Materials & Methods
Y
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 dynamic flow- 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. This
study also demonstrated that Residence Time Distribution (RTD) modeling with reaction
kinetics of suspended solids during storm events produces a better explanation of outflow
data than possible with steady, plug-flow models. Using only input 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.
Larry Brown
concentration
Jay Martin
concentration
Jeff Holland
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 time, t, and lags of dynamically
normalized time, Φ.
A much higher correlation peak
Opposite trends occurred when time and
occurred in cross correlations
Φ lags were compared at different
with Φ lags than with t lags:
managed water levels:
RTD model
There is less
unexplained variance
in the sedimentation
rates determined by
the 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. This effect
demonstrates that the RTD method is effective for modeling wetland constituents.
Acknowledgments
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. This study would not have
been possible without funding from the Ohio Agricultural and Research Development Center and
generous donations from Agri Drain Corporation.
Cross correlation peak
positions in Φ are
similar to those of RTDs.
The parameter Φ
is a more
consistent
explanatory
variable of
constituent flow
through wetlands
than time, t.
Correlations in t are dependent on
flow intensity, but correlations in
Φ are intrinsic to the system, and
therefore reinforce one another.
RTD peak Φ values can
be a metric of hydraulic
efficiency, or efficient
flow distribution in a
wetland (Persson et al.,
1999).
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.
References
AWWARF, 1996. Tracer Studies in Water Treatment
Facilities: A Protocol and Case Studies. American
Water Works Research Foundation, Denver, CO.
Nauman, E. B., and B. A. Buffham, 1983. Mixing in
Continuous Flow Systems. John Wiley & Sons, New
York.
Braskerud, B. C., 2002. Design considerations for
increased sedimentation in small wetlands treating
agricultural runoff. Water Sci. Technol. 45, 77-85.
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.
Kadlec, R. H., 2000. The inadequacy of first-order treatment
wetland models. Ecol. Eng. 15, 105-119.
Thackston, E. L., F. D. Shields, and P. R. Schroeder, 1987.
Residence Time Distributions of Shallow Basins. J.
Environ. Eng.-ASCE 113, 1319-1332.
Levenspiel, O., 1972. Chemical reaction engineering, 2nd
edition. Wiley, New York.
Werner, T. M., and R. H. Kadlec, 1996. Application of
residence time distributions to stormwater treatment
systems. Ecol. Eng. 7, 213-234.