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Conservative mixing in estuaries as affected by sorption, complexing and turbidity maximum: a simple model example
Marine Chemistry, 28 (1989) 251-258 Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
251
Short C o m m u n i c a t i o n
Conservative Mixing in Estuaries as Affected by Sorption, Complexing and Turbidity Maximum: a Simple Model Example* E.K. DUURSMA and P. RUARDIJ
Netherlands Institute for Oceanic Sciences, N105, P.O. Box 59, 1790 AB Den Burg, Texel (The Netherlands) (Received October 28, 1988; revision received May 25, 1989)
ABSTRACT Duursma, E.K. and Ruardij, P., 1989. Conservative mixing in estuaries as affected by sorption, complexing and turbidity maximum: a simple model example. Mar. Chem., 28: 251-258. For a steady-state estuary containing a turbidity maximum, but having no residual sedimentation,a simulation model calculationhas been made for the correlationof concentrations of metal species with salinity.The metal species are in equilibrium between sorption to suspended matter and complexing to dissolved organic matter. Four cases are presented with differentcombinations of stabilityconstants and distribution coefficients.
INTRODUCTION
Conservative mixing of metals in river mouths and estuaries is generally defined as occurring when concentrations of these metals have a linear relation with water salinity. The question is, however, whether this may or may not occur within a dynamic system containing water-suspended matter, in which sorption and complexing processes occur and where a turbidity maximum is present. If so, conservative mixing curves of individual metal species have to be calculated on the basis of the real behaviour of metals as a function of salinity. A model example is presented where three chemical metal (Me) species (ionic, particulate and complexed) are followed through an estuarine system in which freshwater mixes with seawater. In this simplified model, estuarine mixing of freshwater with seawater takes place in a basin of equal depth and width, where the average salinity at distance x is proportional to the length of *Presented at the 10th International Symposium "Chemistry of the Mediterranean", May 1988, Primo~ten, Yugoslavia.
0304-4203/89/$03.50
© 1989 Elsevier Science Publishers B.V.
252
E.K. D U U R S M A A N D P RUARDI, I
x (proportional to average %oSx)
Fig. 1. Scheme of model estuary used for simulation model calculation. The average salinity at x, between 0 and 30%o S is proportional to the distance x, whereas width and water depth are constant at any value of x. TABLE 1 Data of parameters and constants Parameter a
River
Sea
Run 1
DOM (mg1-1) %0 S TDMET= (MET+OMET) c&,S P M ( m g l -~)
0 10
2 10
4 14
(rag 1- l ) 6 20
8 60
2.0 0.0 0.04 10 50
12 30
0.0 30.0 0.005
log Kst log Kd Equiv. wt. Equiv. wt.
14 20
18 10
16 15
20 8
2
2 4 3 3 Me=30 DOM=60
22 6
24 5
26 4
3
4
2 5
4 5
28 4
30 4
aDOM = Dissolvedorganicmatter,ableto complex Me. M E = Metal,with M E T = ionicmetal,O M E T = organiccomplexedmetal,P M E T = particulate metal. P M =Particulatematter (e.g.suspendedsediment). K,t = Organiccomplexedmetal stabilityconstant(dimensionsImequiv- ~). Kd = Distributioncoefficient(dimensionsg ml- ~). the estuarine mixing region. The mixing of freshwater and marine particulate matter occurs by inflow of seawater along the bottom from the seaward side and freshwater along the surface from the other side (Fig. 1 ), resulting in a turbidity m a x i m u m in the brackish zone. Complexing and sorption-desorption processes are supposed to occur between only the dissolved ionic metal ( M E T ) and organic complexed metal ( O M E T ) on the one hand, and M E T and particulate metal ( P M E T ) on the other hand. For freshwater, brackish water and seawater the stability factor (Kst) and distribution coefficient (Kd) are both constant, at least as far as this model is concerned. This note is intended to encourage discussion on conservative and non-conservative mixing, which is too often approached in an oversimplified way. M O D E L CALCULATION
Boundary conditions
A model estuary is considered, in which river water is mixing with seawater (including a salt wedge), and freshwater ~ i c u l a t e matter is mixing with marine particulate matter (including a turbidity m a x i m u m ).
CONSERVATIVE MIXING IN ESTUARIES
253
The conditions (within the variations with tides) are considered to be at a steady state,as long as no residual sedimentation or resuspension occurs. The only metal sources are the river and the sea. Table I presents the given data for concentrations of total dissolved metal ( T D M E T ) and dissolved organic matter ( D O M ) in river and seawater, particulatematter in suspension (PM) in the estuary and the equilibrium constants used, Kst and Kd. Reactions
The reactions of metal with the different phases (or compartments) are defined by MET +DOM
K.t, OMET
(1)
MET + PM
K,, PMET
(2)
where K~t = [ O M E T ] / ( [ M E T ] [ D O M ] )
(3)
and has dimensions of I mequiv - 1 and Kd
----
[PMET]/[MET]
(4)
and has dimensions of ml g - 1. These factorsare both supposed to be constant throughout the estuary. There is supposed to be no D O M production or decomposition, no precipitation or dissolutionof D O M and also no residual sedimentation or resuspension of P M . Reactions (1) and (2) are considered to be rapid with respect to the freshwater-seawater mixing process, and they are equally completely reversible. Simulation model The simulation model is based on a one-dimensional mixing and flushing model (Zimmerman, 1976). The model estuary is divided into 15 compartments of equal length and 2%0 salinityintervaleach, through which transport of metal, organic matter and particulate matter occurs. The steady-state distribution of P M concentrations is given in Table 1. For the transport of particulate matter, only advective transport and not diffusive transport is assumed. This advective transport is equal to the product of the river discharge and the concentration of P M at zero salinity.In this way we were able to transport silt (PM) without disturbing the given P M distribution. For the calculation,a simulation model was used for which the initialvalues of the state variables M E T , O M E T and P M E T concentrations are required
254
E.K, DUURSMA AND P, RUARDI,]
for each compartment. The metal concentration values are determined initially for a situation in the estuary for which no transport of P M occurs. In this situation, the P M E T distribution is in equilibrium with the M E T distribution, and there is a net exchange of zero between M E T and P M E T . Then, consequently M E T + O M E T = T D M E T (total dissolved metal) should behave conservatively with %o S (there is input to the estuary with subsequent mixing and discharge to the sea, but no loss or gain to the particulate phase in the estuary), which results in the formula. TDMET~ -
T D M E T o (S~ea - S) + TDMET~ea S
(5)
Ssea
in which S~ea is the salinity at sea, T D M E T o the T D M E T concentration of the river at zero salinity and TDMET~ the concentration of T D M E T at S salinity. From eqn. (3) the initial values for M E T and O M E T can be calculated T D M E T = O M E T + M E T = M E T × D O M × Kst + M E T or
MET-
TDMET 1 + ( D O M × K~t)
(6)
and OMET-
T D M E T X D O M × gst 1 + ( D O M xK~t)
(7)
P M E T can now be derived from eqns. (4) and (6), giving PMET-
T D M E T X Kd I+DOMxK~t
(8)
The border conditions for M E T , O M E T and P M E T at zero salinity are calculated in the same way from TDMETo. The magnitude of the river discharge (advective transport) is set at such a value that the flushing time is 30 days. The exchange coefficients ( E X ) , which describe the diffusive transport between the compartments of 2%o S each, are derived from the salt distribution (Zimmerman, 1976 ) EX(I,I+I)-
Q × ( S A L T ( I ) + S A L T ( I + 1) ) X0.5 ( S A L T ( I ) - S A L T ( I + 1) )
(9)
Fig. 2. Four runs of plots of metal (Me) species concentrations ionic Me (MET), organic complexed Me (OMET) and particulate Me (PMET) against salinity and for different Kst-Kavalues (Table 1). MET and OMET are expressed in mg Me 1-~ dissolved, PMET in mg Me g-i particulate matter. Identical scales have been used in (a)-(d), except one for PMET in (c). The data are the result of a 360-day run of the model.
255
CONSERVATIVE MIXING IN ESTUARIES
mg.i-1
PERIOD:360-360 ~ET,
PERIOD=360-360 MET,
a m 'o
o _
!I
PERIOD~360-360 g . I
m
:I
~ ,
b
PERIOD~360-360
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PERIOD~360-360 PMET,
m g . q "1
?
o
4
8
12 16 2 0 COMPARTMENT
24
28
RUN 1
4
8
12
20
24
28
16
20
24
28
RUN 2
PERIOD,360-360
PERIOD,360-360
PERIODz360-360
PERIOD,360-360
PERIOD,360-360
PERIOD:360-360
_ PMET*
PMET
12
RUN 3
16
COMPARTMENT
II
16
20
COMPARTMENT o~her scale for
24
PPIET
28
4
RUN 4
•
8
12
COMPARIMENT
256
E.K. DUURSMA AND P. RUARDIJ
in which Q is the river discharge (m ~ s -1) and SALT(I) is the salinity in compartment L Subsequently, the simulation model was run, starting from the equilibrium situation in which no PM transport occurred and continuing to the equilibrium situation with PM transport. This situation was reached after 360 days. It was confirmed that the initial assumption of no PM transport approached these real situations for the parameters as given in Table 1. On this basis, it was decided to use the model as given. PERIOr:369
}5/
~ERIO[;'=36:
PMET"
~6
~PMET •
a i
b
o
o
H! PER i OD : 3 6 0 ..TMET "
bl i LLLx_,rJ-2
PER I OD : 3 6 0 " 3 6 0 fMFT •
360
mgl
o
c ¸
4
8
12
16
20
24
28
4
8
RUN
"
RUN
PER ] OD : 3 6 0 PMET"
16
20
24
28
,::
36C
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360
qPMET °
I
~
,
rl ~
~
o
o
PERIOD:360
12
COMPARTMENT
COMPARTMEN]
¥
:1t
360
PERIOD:360360 qTMETo
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'P-]
4
8
12
16
20
24
28
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COMPARTMENT RUN
:3
,
other
SL.~I~
!!!!
8
IZ
I6
20
24
28
CQMPARTtIEN T RbN
4
Fig. 3. Plot of particulate Me { P M E T ) and total metal ( T M E T ) concentrations, all expressed in mg Me 1-1 water. T M E T - - M E T + O M E T + P M E T . For (a), (b) and ( d ) P M E T , seealso insets.
C O N S E R V A T I V E M I X I N G IN ESTUARIES
257
RESULTS AND DISCUSSION
Four differentcases have been calculatedwith various values of Kst and Kd (Table 1 ). The resultsare given in Fig. 2, where the concentrations of M E T , O M E T and P M E T are plotted against the %o S. For the imposed boundary conditions,the distributionof metal over the three phases (compartments) dissolvedionic,dissolvedorganic complex and particulate,differsin each case.As D O M is high in freshwater and zero in seawater, there is an apparent proportionality of O M E T with %o S, whereas M E T and P M E T can either decrease or increase with %o S, as they have non-linear correlations. The amount of metal in particulatematter (PMET, in m g I-I ) has a clear m a x i m u m at the turbiditym a x i m u m (Fig.3). The distributionof total metal ( T M E T ) depends on the factorsKst and Kd. W e can conclude from this tentative exercise that apparent linear mixing plots of concentrations of metal species with salinity do not mean that the Kd
m~ 7! 5: 3. 2
m~
Cd
Pb
Cu
7i 5: 4. 3. 2_
m6.
7! 5: 4. 3. 2_
m S. 7 5 3 2
1o'
il,i 123~
123~
il 123~
Fig. 4. Range of Kd values in differentregionssuch as (1) the Dutch Western and Eastern Scheldt estuaries (Valenta et al.,1986), (2) world rivers (Martin and Whitfield, 1983), and (3) and (4) the oceans (Mart et al.,1982; Duursma and Bewers, 1986). Figure from Valenta et al. (1986), reproduced by courtesy of 'The Science of the Total Environment'.
258
E,K. I)UURSMA AND P RUARDI3
m e t a l species will necessarily b e h a v e conservatively, b u t t h a t e x c h a n g e processes of c o m p l e x i n g a n d s o r p t i o n s h o u l d be t a k e n into account. T h i s conclusion is f u n d a m e n t a l , in spite of the fact t h a t our simulation model needs e x t e n s i o n with a m o r e realistic t r a n s p o r t model for P M a n d application to a n existing estuary. I r r e l e v a n t to this model, b u t r e l e v a n t to field conditions, is t h e p o i n t w h e t h e r the factors K~t a n d Ka can be c o n s i d e r e d to be c o n s t a n t over a c o m p l e t e range of salinity. As far as Kst is c o n c e r n e d , little i n f o r m a t i o n is available, b u t for Ka values, literature d a t a (Aston a n d D u u r s m a , 1973; D u u r s m a a n d Bewers, 1986) suggest t h a t w i t h i n one or two orders of m a g n i t u d e (Fig. 4) Kd values can be applied. Significance analyses s h o u l d reveal to w h a t e x t e n t such ranges, at high levels of Ka, are acceptable for simulation modelling of conservative mixing processes.
REFERENCES Aston, S.R. and Duursma, E.K., 1973. Concentration effects on 137-Cs, 65-Zn, 60-Co and 106-Ru sorption by marine sediments with geochemical implications. Neth. J. Sea Res., 6: 225-240. Duursma, E.K. and Bewers, J.M., 1986. Application of KdS in marine geochemistry and environmental assessment. In: T.H. Sibley and C. Myttenaere (Editors), Application of Distribution Coefficients to Radiological Assessment Models. Elsevier Applied Science Publishers, Barking, Essex, pp. 138-165. Mart, L., Rutzel, H., Klahre, P., Sipos, L., Platzek, U., Valenta, P. and Nurnberg, H.W., 1982. Comparative studies on the distribution of heavy metals in the oceans and coastal waters. Sci. Total Environ., 26: 1-17. Martin, J.M. and Whitfield, M., 1983. The significance of the river input of chemical elements to the ocean. In: C.S. Wong, E. Boyle, K.W. Bruland, J.D. Burton and E.D. Goldberg (Editors), Trace Metals in Sea Water. Plenum, New York, pp. 265-296. Valenta, P., Duursma, E.K., Merks, A.G.A., Rutzel, H. and Nurnberg, H.W., 1986. Distribution of Cd, Pb and Cu between dissolved and particulate phase in the Eastern Scheldt and Western Scheldt estuary. Sci. Total Environ., 53: 41-76. Zimmerman, J.T.F., 1976. Mixing and flushing of tidal embayments in the Western Dutch Wadden Sea. Part I. Distribution of salinity and calculation of mixing time scales. Neth. J. Sea Res., 10: 149-191. Part II. Analysis of mixing processes. Neth. J. Sea Res., 10: 397-439.
251
Short C o m m u n i c a t i o n
Conservative Mixing in Estuaries as Affected by Sorption, Complexing and Turbidity Maximum: a Simple Model Example* E.K. DUURSMA and P. RUARDIJ
Netherlands Institute for Oceanic Sciences, N105, P.O. Box 59, 1790 AB Den Burg, Texel (The Netherlands) (Received October 28, 1988; revision received May 25, 1989)
ABSTRACT Duursma, E.K. and Ruardij, P., 1989. Conservative mixing in estuaries as affected by sorption, complexing and turbidity maximum: a simple model example. Mar. Chem., 28: 251-258. For a steady-state estuary containing a turbidity maximum, but having no residual sedimentation,a simulation model calculationhas been made for the correlationof concentrations of metal species with salinity.The metal species are in equilibrium between sorption to suspended matter and complexing to dissolved organic matter. Four cases are presented with differentcombinations of stabilityconstants and distribution coefficients.
INTRODUCTION
Conservative mixing of metals in river mouths and estuaries is generally defined as occurring when concentrations of these metals have a linear relation with water salinity. The question is, however, whether this may or may not occur within a dynamic system containing water-suspended matter, in which sorption and complexing processes occur and where a turbidity maximum is present. If so, conservative mixing curves of individual metal species have to be calculated on the basis of the real behaviour of metals as a function of salinity. A model example is presented where three chemical metal (Me) species (ionic, particulate and complexed) are followed through an estuarine system in which freshwater mixes with seawater. In this simplified model, estuarine mixing of freshwater with seawater takes place in a basin of equal depth and width, where the average salinity at distance x is proportional to the length of *Presented at the 10th International Symposium "Chemistry of the Mediterranean", May 1988, Primo~ten, Yugoslavia.
0304-4203/89/$03.50
© 1989 Elsevier Science Publishers B.V.
252
E.K. D U U R S M A A N D P RUARDI, I
x (proportional to average %oSx)
Fig. 1. Scheme of model estuary used for simulation model calculation. The average salinity at x, between 0 and 30%o S is proportional to the distance x, whereas width and water depth are constant at any value of x. TABLE 1 Data of parameters and constants Parameter a
River
Sea
Run 1
DOM (mg1-1) %0 S TDMET= (MET+OMET) c&,S P M ( m g l -~)
0 10
2 10
4 14
(rag 1- l ) 6 20
8 60
2.0 0.0 0.04 10 50
12 30
0.0 30.0 0.005
log Kst log Kd Equiv. wt. Equiv. wt.
14 20
18 10
16 15
20 8
2
2 4 3 3 Me=30 DOM=60
22 6
24 5
26 4
3
4
2 5
4 5
28 4
30 4
aDOM = Dissolvedorganicmatter,ableto complex Me. M E = Metal,with M E T = ionicmetal,O M E T = organiccomplexedmetal,P M E T = particulate metal. P M =Particulatematter (e.g.suspendedsediment). K,t = Organiccomplexedmetal stabilityconstant(dimensionsImequiv- ~). Kd = Distributioncoefficient(dimensionsg ml- ~). the estuarine mixing region. The mixing of freshwater and marine particulate matter occurs by inflow of seawater along the bottom from the seaward side and freshwater along the surface from the other side (Fig. 1 ), resulting in a turbidity m a x i m u m in the brackish zone. Complexing and sorption-desorption processes are supposed to occur between only the dissolved ionic metal ( M E T ) and organic complexed metal ( O M E T ) on the one hand, and M E T and particulate metal ( P M E T ) on the other hand. For freshwater, brackish water and seawater the stability factor (Kst) and distribution coefficient (Kd) are both constant, at least as far as this model is concerned. This note is intended to encourage discussion on conservative and non-conservative mixing, which is too often approached in an oversimplified way. M O D E L CALCULATION
Boundary conditions
A model estuary is considered, in which river water is mixing with seawater (including a salt wedge), and freshwater ~ i c u l a t e matter is mixing with marine particulate matter (including a turbidity m a x i m u m ).
CONSERVATIVE MIXING IN ESTUARIES
253
The conditions (within the variations with tides) are considered to be at a steady state,as long as no residual sedimentation or resuspension occurs. The only metal sources are the river and the sea. Table I presents the given data for concentrations of total dissolved metal ( T D M E T ) and dissolved organic matter ( D O M ) in river and seawater, particulatematter in suspension (PM) in the estuary and the equilibrium constants used, Kst and Kd. Reactions
The reactions of metal with the different phases (or compartments) are defined by MET +DOM
K.t, OMET
(1)
MET + PM
K,, PMET
(2)
where K~t = [ O M E T ] / ( [ M E T ] [ D O M ] )
(3)
and has dimensions of I mequiv - 1 and Kd
----
[PMET]/[MET]
(4)
and has dimensions of ml g - 1. These factorsare both supposed to be constant throughout the estuary. There is supposed to be no D O M production or decomposition, no precipitation or dissolutionof D O M and also no residual sedimentation or resuspension of P M . Reactions (1) and (2) are considered to be rapid with respect to the freshwater-seawater mixing process, and they are equally completely reversible. Simulation model The simulation model is based on a one-dimensional mixing and flushing model (Zimmerman, 1976). The model estuary is divided into 15 compartments of equal length and 2%0 salinityintervaleach, through which transport of metal, organic matter and particulate matter occurs. The steady-state distribution of P M concentrations is given in Table 1. For the transport of particulate matter, only advective transport and not diffusive transport is assumed. This advective transport is equal to the product of the river discharge and the concentration of P M at zero salinity.In this way we were able to transport silt (PM) without disturbing the given P M distribution. For the calculation,a simulation model was used for which the initialvalues of the state variables M E T , O M E T and P M E T concentrations are required
254
E.K, DUURSMA AND P, RUARDI,]
for each compartment. The metal concentration values are determined initially for a situation in the estuary for which no transport of P M occurs. In this situation, the P M E T distribution is in equilibrium with the M E T distribution, and there is a net exchange of zero between M E T and P M E T . Then, consequently M E T + O M E T = T D M E T (total dissolved metal) should behave conservatively with %o S (there is input to the estuary with subsequent mixing and discharge to the sea, but no loss or gain to the particulate phase in the estuary), which results in the formula. TDMET~ -
T D M E T o (S~ea - S) + TDMET~ea S
(5)
Ssea
in which S~ea is the salinity at sea, T D M E T o the T D M E T concentration of the river at zero salinity and TDMET~ the concentration of T D M E T at S salinity. From eqn. (3) the initial values for M E T and O M E T can be calculated T D M E T = O M E T + M E T = M E T × D O M × Kst + M E T or
MET-
TDMET 1 + ( D O M × K~t)
(6)
and OMET-
T D M E T X D O M × gst 1 + ( D O M xK~t)
(7)
P M E T can now be derived from eqns. (4) and (6), giving PMET-
T D M E T X Kd I+DOMxK~t
(8)
The border conditions for M E T , O M E T and P M E T at zero salinity are calculated in the same way from TDMETo. The magnitude of the river discharge (advective transport) is set at such a value that the flushing time is 30 days. The exchange coefficients ( E X ) , which describe the diffusive transport between the compartments of 2%o S each, are derived from the salt distribution (Zimmerman, 1976 ) EX(I,I+I)-
Q × ( S A L T ( I ) + S A L T ( I + 1) ) X0.5 ( S A L T ( I ) - S A L T ( I + 1) )
(9)
Fig. 2. Four runs of plots of metal (Me) species concentrations ionic Me (MET), organic complexed Me (OMET) and particulate Me (PMET) against salinity and for different Kst-Kavalues (Table 1). MET and OMET are expressed in mg Me 1-~ dissolved, PMET in mg Me g-i particulate matter. Identical scales have been used in (a)-(d), except one for PMET in (c). The data are the result of a 360-day run of the model.
255
CONSERVATIVE MIXING IN ESTUARIES
mg.i-1
PERIOD:360-360 ~ET,
PERIOD=360-360 MET,
a m 'o
o _
!I
PERIOD~360-360 g . I
m
:I
~ ,
b
PERIOD~360-360
PERIOD,360-360 PMET"
PERIOD~360-360 PMET,
m g . q "1
?
o
4
8
12 16 2 0 COMPARTMENT
24
28
RUN 1
4
8
12
20
24
28
16
20
24
28
RUN 2
PERIOD,360-360
PERIOD,360-360
PERIODz360-360
PERIOD,360-360
PERIOD,360-360
PERIOD:360-360
_ PMET*
PMET
12
RUN 3
16
COMPARTMENT
II
16
20
COMPARTMENT o~her scale for
24
PPIET
28
4
RUN 4
•
8
12
COMPARIMENT
256
E.K. DUURSMA AND P. RUARDIJ
in which Q is the river discharge (m ~ s -1) and SALT(I) is the salinity in compartment L Subsequently, the simulation model was run, starting from the equilibrium situation in which no PM transport occurred and continuing to the equilibrium situation with PM transport. This situation was reached after 360 days. It was confirmed that the initial assumption of no PM transport approached these real situations for the parameters as given in Table 1. On this basis, it was decided to use the model as given. PERIOr:369
}5/
~ERIO[;'=36:
PMET"
~6
~PMET •
a i
b
o
o
H! PER i OD : 3 6 0 ..TMET "
bl i LLLx_,rJ-2
PER I OD : 3 6 0 " 3 6 0 fMFT •
360
mgl
o
c ¸
4
8
12
16
20
24
28
4
8
RUN
"
RUN
PER ] OD : 3 6 0 PMET"
16
20
24
28
,::
36C
PER I OO ~ 3 6 0
360
qPMET °
I
~
,
rl ~
~
o
o
PERIOD:360
12
COMPARTMENT
COMPARTMEN]
¥
:1t
360
PERIOD:360360 qTMETo
mgl.1~ TMET"
'P-]
4
8
12
16
20
24
28
4
COMPARTMENT RUN
:3
,
other
SL.~I~
!!!!
8
IZ
I6
20
24
28
CQMPARTtIEN T RbN
4
Fig. 3. Plot of particulate Me { P M E T ) and total metal ( T M E T ) concentrations, all expressed in mg Me 1-1 water. T M E T - - M E T + O M E T + P M E T . For (a), (b) and ( d ) P M E T , seealso insets.
C O N S E R V A T I V E M I X I N G IN ESTUARIES
257
RESULTS AND DISCUSSION
Four differentcases have been calculatedwith various values of Kst and Kd (Table 1 ). The resultsare given in Fig. 2, where the concentrations of M E T , O M E T and P M E T are plotted against the %o S. For the imposed boundary conditions,the distributionof metal over the three phases (compartments) dissolvedionic,dissolvedorganic complex and particulate,differsin each case.As D O M is high in freshwater and zero in seawater, there is an apparent proportionality of O M E T with %o S, whereas M E T and P M E T can either decrease or increase with %o S, as they have non-linear correlations. The amount of metal in particulatematter (PMET, in m g I-I ) has a clear m a x i m u m at the turbiditym a x i m u m (Fig.3). The distributionof total metal ( T M E T ) depends on the factorsKst and Kd. W e can conclude from this tentative exercise that apparent linear mixing plots of concentrations of metal species with salinity do not mean that the Kd
m~ 7! 5: 3. 2
m~
Cd
Pb
Cu
7i 5: 4. 3. 2_
m6.
7! 5: 4. 3. 2_
m S. 7 5 3 2
1o'
il,i 123~
123~
il 123~
Fig. 4. Range of Kd values in differentregionssuch as (1) the Dutch Western and Eastern Scheldt estuaries (Valenta et al.,1986), (2) world rivers (Martin and Whitfield, 1983), and (3) and (4) the oceans (Mart et al.,1982; Duursma and Bewers, 1986). Figure from Valenta et al. (1986), reproduced by courtesy of 'The Science of the Total Environment'.
258
E,K. I)UURSMA AND P RUARDI3
m e t a l species will necessarily b e h a v e conservatively, b u t t h a t e x c h a n g e processes of c o m p l e x i n g a n d s o r p t i o n s h o u l d be t a k e n into account. T h i s conclusion is f u n d a m e n t a l , in spite of the fact t h a t our simulation model needs e x t e n s i o n with a m o r e realistic t r a n s p o r t model for P M a n d application to a n existing estuary. I r r e l e v a n t to this model, b u t r e l e v a n t to field conditions, is t h e p o i n t w h e t h e r the factors K~t a n d Ka can be c o n s i d e r e d to be c o n s t a n t over a c o m p l e t e range of salinity. As far as Kst is c o n c e r n e d , little i n f o r m a t i o n is available, b u t for Ka values, literature d a t a (Aston a n d D u u r s m a , 1973; D u u r s m a a n d Bewers, 1986) suggest t h a t w i t h i n one or two orders of m a g n i t u d e (Fig. 4) Kd values can be applied. Significance analyses s h o u l d reveal to w h a t e x t e n t such ranges, at high levels of Ka, are acceptable for simulation modelling of conservative mixing processes.
REFERENCES Aston, S.R. and Duursma, E.K., 1973. Concentration effects on 137-Cs, 65-Zn, 60-Co and 106-Ru sorption by marine sediments with geochemical implications. Neth. J. Sea Res., 6: 225-240. Duursma, E.K. and Bewers, J.M., 1986. Application of KdS in marine geochemistry and environmental assessment. In: T.H. Sibley and C. Myttenaere (Editors), Application of Distribution Coefficients to Radiological Assessment Models. Elsevier Applied Science Publishers, Barking, Essex, pp. 138-165. Mart, L., Rutzel, H., Klahre, P., Sipos, L., Platzek, U., Valenta, P. and Nurnberg, H.W., 1982. Comparative studies on the distribution of heavy metals in the oceans and coastal waters. Sci. Total Environ., 26: 1-17. Martin, J.M. and Whitfield, M., 1983. The significance of the river input of chemical elements to the ocean. In: C.S. Wong, E. Boyle, K.W. Bruland, J.D. Burton and E.D. Goldberg (Editors), Trace Metals in Sea Water. Plenum, New York, pp. 265-296. Valenta, P., Duursma, E.K., Merks, A.G.A., Rutzel, H. and Nurnberg, H.W., 1986. Distribution of Cd, Pb and Cu between dissolved and particulate phase in the Eastern Scheldt and Western Scheldt estuary. Sci. Total Environ., 53: 41-76. Zimmerman, J.T.F., 1976. Mixing and flushing of tidal embayments in the Western Dutch Wadden Sea. Part I. Distribution of salinity and calculation of mixing time scales. Neth. J. Sea Res., 10: 149-191. Part II. Analysis of mixing processes. Neth. J. Sea Res., 10: 397-439.