Ecological Engineering 36 (2010) 1691–1699
Contents lists available at ScienceDirect
Ecological
Engineering
j o u r n a l h o m e p a g e :w w w.e l s e v i e r.c o m /l o c a t e /e c o l e n
g
Quantifying the hydraulic performance of treatment wetlands using the moment index
Mark D.Wahl a ,∗,Larry C.Brown a ,Alfred O.Soboyejo a ,Jay Martin a ,Bin Dong b
a Ohio State University,Dept.of Food,Agricultural,&Biological Engineering,United States b
Wuhan University,College of Water Resources &Hydropower,China
a r t i c l e i n f o Article history:
Received 13January 2010
Received in revid form 12July 2010Accepted 19July 2010
Keywords:
Constructed wetland Hydraulic efficiency Hydraulic index
Residence time distribution (RTD)Retention time Moment index Nominal divide Treatment wetland
a b s t r a c t
A new hydraulic index was derived according to residence time distribution theory.The approach quan-tifies hydraulic inefficiencies according to the juxtaposition of the hold back parameter relative to the residence time distribution.The index was evaluated for its ability to detect variation,for conformity with qualitative asssments,and for correlation to effluent pollutant fractions in order to asss its suitability as a predictor of treatment.
我和靓姐The moment index overcomes many of the weakness inherent in existing indices.The index can be computed from a datat considering just one volume exchange so arbitrary truncation of data due to the finite nature of data collection has no impact on the moment index.The moment index appears to be more nsitive than existing indices in detecting attenuation of a residence time distribution as well.The new index demonstrated excellent correlation to the effluent pollutant fraction predicted by a first-order reduction implying the index could be the good predictor of treatment.In addition to correlation with treatment,the moment index matched qualitative asssment precily for
eight specific cas considered.
The moment index could substantially aid in the design and management of treatment wetlands for balancing cost and efficacy by resolving some of the uncertainty associated with residence time.The index could be ud to help identify the optimal wetland configuration for maximizing residence time.Not only would it be uful in quantifying the effects of vegetation,bathymetry,and wetland shape on residence time;it could have utility in supplying the bounds for pollutant reduction.
© 2010 Elvier B.V. All rights rerved.
1.Introduction 1.1.Problem definition
Agricultural practices impact water quality as production inten-sifies through the u of chemical fertilizers and pesticides,in combination with intensive drainage practices (Zucker and Brown,1998).Drainage increas the amount of arable land and improves field trafficability.Much of Ohio and many parts of the Midwest-ern United States are intensively subsurface drained (Fauy et al.,1995).Intensively drained cropland has reduced detention storage compared with undrained cropland.As a result,more nutrients
∗Corresponding author at:The Ohio State University,Dept.of Food,Agricultural,&Biological Engineering,Agricultural Engineering Building Room 250,590Woody Hayes Drive,Columbus,OH 43210-1057,United States.Tel.:+18507482299;fax:+16142929448.
E-mail address:wahl.59@osu.edu ,wahl.59@buckeyemail.osu.edu (M.D.Wahl).
are flushed from the soil and then accumulate in surface water (Hubbard et al.,2004).Nitrogen contamination in drinking water in the form of nitrate can cau methemoglobinemia,a potentially fatal dia in infants (Vigil et al.,1965).Coastal eutrophication driven primarily by nitrogen,and sometimes phosphorus,results in harmful algal blooms and widespread hypoxia or anoxia (Howarth,2008).This is a growing concern in the Great Lakes region of the United States,as well as in the Gulf of Mexico,where hypoxia threatens to upt delicate food chains with potential impacts on commercial and recreational fishing industries.
One strategy to protect public health,promote economic vital-ity,and improve ecological health is to reduce the amount of excess nutrients entering surface waters so that cumulative downstream concentrations are not excessive (Mitsch and Goslink,2007).Conventional water treatment process ud in point source applications are generally not practical in agricultural ttings where
a large pollution component is from non-point sources.Con-structed wetlands are uful as a low-tech water treatment option in rural ttings;particularly in an agricultural landscape where intensive farming practices contribute to high nutrient and di-
0925-8574/$–e front matter © 2010 Elvier B.V. All rights rerved.doi:10.leng.2010.07.014
1692M.D.Wahl et al./Ecological Engineering 36 (2010) 1691–1699
ment loads in drainage water (Dong et al.,2009;Mao et al.,2009).With their low capital cost and minimal operational expen rel-ative to conventional water treatment,constructed wetlands are an appropriate water treatment technology in many parts of the world (Brix,1994).杭州西湖风景
Wetlands provide considerable benefit and promote biodi-versity by offering habitat for water loving plants and incts (Mitsch and Goslink,2007).Wetlands provide hydrologic bene-fits through storm water capture and detention which can delay the ont and limit the verity of downstream flooding.Additionally,wetlands remove impurities through physical,chemical,and bio-logical mechanisms (Mitsch and Goslink,2007).Conquently,constructed wetlands are an increasingly common best practice for reducing nutrient loads and other pollutants (Brix,1994;Kadlec and Knight,
1996).
Wide-scale implementation of a strategy which incorporates constructed wetlands for the treatment of agricultural runoff is challenging.Competing cost and efficacy concerns must be bal-anced (Shields and Thackston,1991).Wetlands require sufficient land area in order to handle a particular runoff volume,and in many cas that land could otherwi be ud for generating revenue.Land cost,along with lost revenue,exerts pressure to minimize the size of the wetlands.However,undersized units will be less effective at reducing nutrients.One challenge to achieving opti-mal wetland design and management is related to our ability to measure hydraulic performance.Metrics are needed that can reli-ably quantify hydraulic performance and then be ud to predict time-dependent treatment process.A new index is propod for quantifying hydraulic performance and its correlation to a first-order pollutant reduction is evaluated.
1.2.Theoretical background
1.2.1.Hydraulic residence time
Constructed wetlands are an increasingly common best practice for reducing nutrient loads and other pollutants (Brix,1994;Kadlec
and Knight,1996).Wetlands act as nutrient sinks through process including dimentation,sorption,plant uptake,and chemical or biological reductions.The process are all heavily time depen-dent so that pollutant reduction is cloly related to the amount of time an individual pollutant resides in the wetland (Fogler,1992;Kadlec and Knight,1996).The more contact time pollutants have to removal mechanisms the greater the likelihood for pollutant reduction.Management practices should aim to maximize wetland residence time to facilitate nutrient reductions.
Wetland residence time describes travel time from inlet to outlet.The term residence time is sometimes ud interchangeably with hydraulic retention time (Persson et al.,1999;Su et al.,2009).For consistency and to avoid confusion with the hydrologic concept for storm water routing through retention/detention basins,the term residence time is preferred for this discussion.Residence time is dependent on the wetland volume and flow rate.Under uniform flow conditions,or plug flow ,every parcel of water entering the inlet at t 0reaches the outlet at precily some nominal time (t n )determined as the time required for a complete volume exchange within the wetland (Kadlec and Knight,1996;Persson et al.,1999),described as:t n =
V Q
(1)
In practice,a single nominal residence time is inadequate.Each parcel of water may have a unique residence time affected by streamlines,boundary conditions,and turbulent effects (Su et al.,2009).Residence time can be considered a random variable having some type of distribution.
Residence time distributions (RTDs)are functions often described by their shape and position relative to t n .Stagnant or re-circulating zones reduce the effective volume of the wetland creating preferential flow paths that effectively shorten the aver-age residence time.Short-circuiting tends to shift the center of the distribution below the theoretical residence time,t n ,as depicted in Fig.1
a.
Fig.1.(a)Conceptual effect of short-circuiting (adapted from Holland et al.,2004).(b)Conceptual effect of mixing on residence time distribution (adapted from Holland et al.,2004).Mixing scale is reprented by the number of continuously stirred tank reactors (CSTRs)in ries.
M.D.Wahl et al./Ecological Engineering36 (2010) 1691–16991693 The shape of a RTD is generally related to the mixing.Princi-
ples of chemical reactor design can be ud to quantify mixing
effects.Fogler(1992)and Levenspiel(1999)describe treatment
wetlands as reactors modeled by a quence of tanks-in-ries.In
a continuously stirred tank reactor(CSTR)all parcels have an equal
probability of leaving the basin at any given time.The RTD for a
single CSTR is an exponential function.As the number of CSTRs-in-
ries increas,the spread of the RTD decreas.Deviations from
ideal plugflow are described by the mixing scale.Mixing scale is
the number of CSTRs required to approximate the actual residence
time distribution.Fig.1b shows the effects of mixing scale on RTD
using the tanks-in-ries approach.
Direct comparison of RTDs is possible for asssing hydraulic
performance only after normalizing for hydraulic loading,wetland
size,and tracer mass.The area under the raw RTD reprents tracer
mass.Once normalization is performed,the RTD becomes a dimen-
sionless function withflow-weighted time along the x-axis such
that the area under curve is unity.The corrected,or normalized,
RTD is esntially a probability density function of residence time
(Teixeira and Siqueira,2008).
1.2.2.Hydraulic efficiency
Treatment wetlands are frequently treated as chemical reac-
tors(Kadlec and Knight,1996).Plugflow assumes full utilization
of the entire basin volume.However,a typical wetland contains
some stagnant or slow moving zones.Such underutilized compo-
nents effectively reduce the basin volume generating preferential
flow paths and shortening the average residence time.Additionally,
exchanges occur between the preferentialflow paths and stagnant
zones due to recirculation,dispersion,and diffusion.In a free sur-
face wetland mixing can also be turbulence induced as a result of
wind shear and bioturbation(Werner and Kadlec,2000).Mixing
tends to attenuate the peak of the residence time distribution and
increas the spread.Fig.2shows the effects of short-circuiting and
mixing on residence time distribution in relation to the ideal plug
flow respon.
The term hydraulic efficiency describes hydraulic performance
in terms of departure from ideal plugflow(Thackston et al.,1987).
Holland et al.(2004)interpret this as reprentative of the capac-
ity of a wetland to effectively utilize the entire wetland volume
by uniformly distributingflow to maximize residence time.Wet-
lands with comparable ratios of volume toflow rate will have
similar nominal residence times but may have very different mea-
sured residence times depending on hydraulic performance.This
uncertainty pos challenges in predicting residence time as well
as treatment performance.
Hydraulic indices are commonly extracted from a RTD and ud
to analyze hydraulic performance.Teixeira and Siqueira(2008)
assd veral reported hydraulic indices.Most of the hydraulic
indices could be categorized as either short-circuiting indices or
mixing indices.They evaluated the indices on three criteria:(1)
the correlation of the index to the physical phenomenon it is said
to reprent;(2)the capability of the index to detect variation;
and(3)statistical variability of the index.The authors evaluated
eight short-circuiting indices and found only one index meeting
all criteria.None of the six mixing indices evaluated fulfilled every
requisite.
Persson et al.(1999)propod the commonly ud hydraulic
efficiency index( )combining theflow uniformity index(1−1/N)
and effective volume(e)as:
=e
1−
1
N
(2)
where e is defined by Thackston et al.(1987)as a ratio of mean
residence time(¯t)to nominal residence time:
e=
¯t
t n
(3)
and N is the number of CSTRs in ries.Fogler(1992)considers N
the inver of the coefficient of variation squared:
N=
t
−2
(4)
Measured RTDs typically have a long drawn out tail that asymp-
totically approaches zero concentration since small quantities of
tracer are trapped in stagnant or recirculation zones for extended
periods of time.The point when data collection is terminated will
determine the effective length of the tail and decide its overall
influence on the distribution.Hydraulic indices bad on mean res-
idence time or variance are skewed by this tail effect.Incomplete
data cannot accurately determine mean residence time(Su et al.,
2009).Fogler(1992)suggests extrapolating the tail as an exponen-
tial decay function to avoid truncation error.
Challenges persist in quantifying hydraulic efficiency.The mere
existence of so many hydraulic indices demonstrates a need for
consistency in evaluating hydraulic performance(Min and Wi,
2009).Teixeira and Siqueira(2008)expo weakness inherent in
many of the indices.Tail effects related to the arbitrary truncation
of data as a result of thefinite nature of the data collection also
整合营销策略influence hydraulic efficiency calculations.A new index is put forth
here to address the shortcomings.
1.3.Objective
A hydraulic index demonstrating strong correlation to pollutant
reduction is needed to identify the optimal wetland configuration
for maximizing residence time.Such an index should quantify the
effects from various wetland parameters that influence the RTD to
resolve some of the uncertainty associated with residence time.The
index would not only be uful in quantifying the effects of vege-
tation,bathymetry,and wetland shape on residence time;it could
have utility in supplying the bounds for pollutant reduction.Such
卡通狗狗
an index could substantially aid in the design and management of
treatment wetlands for balancing cost and efficacy.
2.Materials and methods
2.1.Measuring residence time
Wetland hydraulics are commonly assd by plottingflow
vectors or by an analysis of residence times(Somes et al.,1999).
A plot offlow vectors can be constructed from measured velocities
重阳节有哪些习俗or by numerical simulation.The vector plot can be ud to quantify
the RTD or afield tracer study might be conducted(Persson et al.,
1999).
Afield tracer study us an inert tracer introduced at a sin-
gle inlet with concentrations in the effluent stream measured as
a function of time.Puld tracer studies were conducted to mea-
sure residence time distributions at wetlands located within rice
paddy schemes in rural Hubei and Guangxi Provinces,China.Rho-
damine WT was lected as the tracer becau it is non-toxic,
receives minimal background interference,and has low adsorption
and degradation rates(Holland et al.,2004).The tracer is consid-
ered conrvative for up tofive days in a wetland environment
according to the manufacturer’s specifications.
Local irrigation canals supplied water continuously at the
wetland inlet during the tracer studies while rhodamine concen-
trations were measured at a single outlet at various time intervals.
1694M.D.Wahl et al./Ecological Engineering
36 (2010) 1691–1699
Fig.2.For ideal plug flow,a tracer pul introduced at the inlet is obrved after one volume exchange at the outlet.Short-circuiting reduces the travel time while mixing attenuates the respon at the outlet (adapted from Persson et al.,1999).
Fluctuations in flow rates were unavoidable as a result of other paddy scheme demands on the water supply canal.After initiating flow at the inlet,a period of time was required to establish quasi-steady flow at the outlet.The delay allowed water temperature to stabilize minimizing thermal gradien
ts.Flow rates were deter-mined at the inlet and outlet by measuring the water depth over a broad-crested weir inside a portable sheet metal flume at both locations.
Once the flow rate and temperature at the outlet stabilized,a slug of tracer was introduced at the inlet.Rhodamine WT concen-trations were measured with a YSI 600OMS V2sonde equipped with a rhodamine probe,temperature nsor,and data recorder.Data were collected every 5–10min.Date (mo/day/year),time (h:min:s),temperature (◦C),rhodamine concentration (g/l),and battery voltage (V)were recorded.The rhodamine probe range is 0–200g/l (detection limit 0.5g/l,resolution 0.1g/l,and preci-sion ±1g/l or 5%of reading).Standard calibration performed on the probe before each tracer study did not consider turbidity or chlorophyll corrections.2.2.RTD normalization
Direct comparison of the measured RTDs is not appropriate for basins having different volumes,tracer concentrations,flow rates,etc.A dimensionless function developed from normalized data pro-vides a means of comparing wetlands of various sizes and flow rates.Hydraulic efficiency should be bad on the normalized dis-tribution for drawing meaningful comparisons with other RTDs.Analytic challenges exist in applying residence time distribu-tion theory to variable flow systems.Nauman (1969)describes two different residence times;the average residence time for parti-cles entering a system and the average residence time for particles exiting the system.For unsteady
flow conditions the entering and exiting residence times are not equal.Tracer puls introduced dur-ing the same event may have different outlet tracer concentration profiles depending whether volumetric flow rate was increasing or decreasing.
Werner and Kadlec (1996)propod the dimensionless flow-weighted time variable to account for unsteady flow with changing basin volume described as:
=
t
t 0
Q (t )V (t )
dt
(5)
where t reprents a “dummy”variable of integration,Q (t )rep-rents the variable outflow rate,V (t )reprents a changing basin
volume due to unsteady flow,and t 0is the initial time of tracer delivery.The variable corresponds to a t amount of vol-ume exiting the system “stretching”or “compressing”time into a dimensionless form (Werner and Kadlec,1996).The theoretical res-idence time,or nominal residence time,is reprented by equal to one.This value is comparable to the nominal residence time under steady state conditions from Eq.(1)with basin volume divided by a constant flow rate.
Concentrations plotted on the y -axis become dimensionless by multiplying outflow concentration,C ( ),and volume,V ( ),at a given flow-weighted time and dividing by the total mass of the tracer:C ( )=
C ( )V ( )
M
(6)
where C ( )is the dimensionless function and M reprents the total mass of tracer.The subquent RTD with normalized con-centration plotted with respect to flow-weighted time results in a probability density function where the area below the function reprenting tracer mass equals one.2.3.Moment analysis
A moment analysis of the normalized RTD provides meaning-ful parameters for describing the distribution (Kadlec and Knight,1996;Werner and Kadlec,1996;Holland et al.,2004;Min and Wi,
2009).The zeroth moment (M ∗0
)of the dimensionless RTD function about the origin provides the fraction of tracer mass recovered:
M ∗0
=
∞
C ( )d
裙带菜蛋花汤(7)
The first moment (M ∗1
)about the origin describes the centroid of the RTD function:
M ∗1
=
∞
C ( )d
(8)
The cond moment (M ∗2
)reprents variance which describes the spread of the function:
M ∗2
=
∞
( −M ∗
1)2
C ( )d
(9)
An important check of the tracer mass balance is a zeroth moment equal to one.If substantially less is reported then the tracer may not be conrved.For ideal plug flow conditions the spread is zero while the recovery fraction and centroid are unity.Deviations from
M.D.Wahl et al./Ecological Engineering36 (2010) 1691–1699
1695
Fig.3.Residence time distribution reprented as a probability density function with cumulative distribution function int.
ideal conditions,M∗
0=M∗
蒲地蓝消炎胶囊
1
=1,and M∗
2
=0,are uful for quantify-
ing hydraulic efficiency(Werner and Kadlec,1996;Holland et al., 2004).
2.4.Quantifying hydraulic efficiency with the moment index
The moment index provides a hydraulic efficiency index that avoids reliance on mixing and short-circuiting indices and operates independent of the influence from tail effects.This approach con-siders hydraulic efficiency relative to the fraction of tracer exiting prematurely as well as the juxtaposition of residence times about what is referred to as the nominal divide in Fig.3.
The method assumes that residence times of a completely effi-cient basin will meet or exceed the nominal residence time.The portion of tracer exiting the wetland prior to the nominal divide adverly impacts hydraulic efficiency.This gment of the prob-ability density function prior to the nominal divide is considered inefficient with more weight assigned to the more verely pre-mature residence times.If the bulk of tracer exiting has a clo proximity to the nominal divide then hydraulic efficiency is high. As more tracer exits earlier,hydraulic efficiency approaches zero.
Thus when hydraulic efficiency decreas the magnitude of the moment about the nominal divide will increa proportionally. Assigning the direction of positive moment out of the page,the total moment about the nominal divide is as follows:
M divide=(t n−¯t)×Mass tracer(10) where¯t is the average residence time.After normalizing the RTD with respect to tracer mass,basin volume,andflow rate,the tracer mass reprented by the area under the curve becomes unity and t n equals one.Eq.(10)then simplifies as:
M divide=(1−¯ )(11) where¯ is the averageflow-weighted time.Generally,the moment about the nominal divide for the normalized RTD is:
M divide=
∞
(1− )C ( )d (12)
Residence times less than nominal are considered inefficient.Fig.4 shows the RTD divided into pre-nominal and post-nominal com-ponents.The pre-nominal area in thefigure is what Stamou and Noutsopoulos(1994)refers to as the hold back parameter(HBP).Only the inefficient pre-nominal portion of the distribution is counted against the computed hydraulic efficiency.
Using this approach,the pre-nominal moment about the nom-inal divide,M pre is simply the moment in Eq.(12)bounded from zero to one as expresd below:背景分明打一地名
M pre=
1
(1− )C ( )d (13)
This pre-nominal moment is merely the HBP multiplied by the moment arm from the nominal divide to the centroid of the A pre shown in Fig.4.The propod moment index is then the complement of the pre-nominal moment about the nominal divide:
Moment Index=1−M pre(14) 2.5.Pollutant reduction
In order to function as a predictor of treatment,the index should not only quantify hydraulic performance,it should also demon-strate some correlation to treatment.Kadlec and Knight(1996) suggest wetland treatment process remble afirst-order rate function of the following form:
X=e−k v t(15) where X is the fraction of pollutant remaining over time depending on some rate constant k v.Forfirst-order reactions it is possible to determine X directly from the RTD function,E(t):
X=
∞
E(t)e−k v t dt(16)
For higher order reactions,the RTD alone is not sufficient for pre-dicting pollutant reduction although the RTD still has utility in supplying bounds for the reduction(Fogler,1992).
Forty-two hypothetical residence time distributions were con-ceptualized to capture a full range of mixing and short-circuiting. Fig.5illustrates the conceptual RTDs with the time axisflow-weighted so that it is expresd in units of volume exchanges. Effects from wetland volume and hydraulic loading are normal-ized.Mixing scales ranging from a single completely mixed tank to a near approximation of plugflow are considered.The short-circuiting component is described by the ratio of mean residence time to nominal residence time ranging from0.25to1.
