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Kinetic and equilibrium approaches to estuarine chemistry
253
The Science of the Total Environment, 97/98 (1990) 253 266 Elsevier Science Publishers B.V., Amsterdam
KINETIC AND EQUILIBRIUM CHEMISTRY
APPROACHES
TO ESTUARINE
A.W. MORRIS
Natural Environment Research Council, Plymouth Marine Laboratory, Prospect Place, The Hoe, Plymouth PL1 3DH (United Kingdom)
ABSTRACT A one-box model is used to examine the relationship between freshwater residence time (T) and the time constant (half-life, tl/~) for a first-order chemical reaction in an estuary. Higher and lower limits of the ratio tl/2/T appropriate for conservative or chemical equilibrium modelling, respectively, are derived. These limits depend also on the equilibrium constant for the reaction and the initial reactant and product concentrations. For intermediate values of this ratio, the system can be described quantitatively only by using a kinetic model. Systematic inter-estuarine variability in the distributions of dissolved metals as a function of estuarine size (or hydrodynamic turnover time) is predicted by this model when the potential for sorptive particle-water exchanges is examined. However, this deduction, which is based on kinetic criteria alone, is not confirmed by evidence in the literature. Indeed, the model is contradicted in that dissolved metals appear to be most interactive in some, but not all, small estuaries and least interactive in large estuaries. It follows that the thermodynamic drive for metal interactions to occur is a necessary additional consideration. Gross thermodynamic disequilibrium with respect to particle-water metal exchange, which in turn generates highly non-conservative dissolved metal distributions, is most readily generated in small, highly dynamic systems through enhanced internal mobility of estuarine resuspendable sediment.
INTRODUCTION The preparation of this paper was prompted by the theme of the Quebec S y m p o s i u m o f O c t o b e r , 1988, n a m e l y t h e f a t e a n d e f f e c t s o f t o x i c c h e m i c a l s i n large estuaries. It considers the question: to what extent are intra-estuarine contrasts in the propagation of chemical processes, and consequently in the d i s t r i b u t i o n s o f r e a c t i v e c h e m i c a l c o n s t i t u e n t s , r e l a t e d t o e s t u a r i n e size? T h i s is e s s e n t i a l l y a q u e s t i o n o f a v a i l a b l e t i m e . I n c r e a s i n g e s t u a r i n e s i z e i m p l i e s increasing turnover time for contained water, within the whole estuary or any s e g m e n t o f it. H e n c e , a v a i l a b l e r e a c t i o n t i m e is l o n g e r i n l a r g e , r e l a t i v e t o s m a l l , e s t u a r i e s . I t is p r e d i c t a b l e t h e r e f o r e t h a t , o t h e r f a c t o r s b e i n g e q u a l , i n situ chemical processes should advance further towards thermodynamic equil i b r i u m s t a t e s a s t h e size o f t h e s y s t e m i n c r e a s e s . However, whatever the size (or water replacement time) of the estuary, the
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254 locations where, and extent by which, reactant concentration distributions deviate from the simple mixing-controlled condition also depend on the thermodynamic characteristics of the reaction and on how far source reactant concentrations deviate initially from the local equilibrium state. The interactive effects of these conditions in estuaries are examined with the aid of a one-box model relating hydrodynamic turnover time, the time constant for a chemical reaction and the degree of advancement of the reaction. Using this model, it is argued that, from kinetic considerations alone, interestuarine differences in dissolved metal distributions which are dependent on estuarine size should be apparent. This is because metal exchange reactions at particle surfaces occur at rates which are comparable to estuarine hydrodynamic residence times. However, obvious size-related contrasts in metal distributions in estuaries are not evident when reported distributions are compared. The implications of this observation are discussed. MIXING CURVES AS EVIDENCE FOR ESTUARINE CHEMICALREACTIVITY Mixing curves provide the principal practical method for identifying the occurrence of chemical reactivity in estuaries (Boyle et al., 1974). These relate the concentrations of any dissolved constituent to those of another constituent (usually salinity) which quantifies the mixed proportions of freshwater and seawater throughout the estuarine mixing zone (or any selected segment of it). Providing a number of criteria are satisfied, of which steady state is usually the most important (Loder and Reichard, 1981), a linear mixing curve indicates conservative behaviour of the constituent within the estuary (or segment). Any other relationship (concave, convex, multiple inflections) indicates addition and/or removal of the constituent. It follows that where subsidiary inputs throughout the observed mixing zone are demonstrably absent, a non-linear mixing curve invariably indicates significant in situ reactivity. Marked gradients in constituent concentrations and in ambient physicochemical conditions (especially ionic strength, pH, redox status, suspended particulate material - - often termed 'master variables' in aquatic chemistry) are characteristic of estuarine mixing zones. Hence, absolute conservativeness of any constituent throughout an estuary is theoretically a highly improbable situation. That is, a more rigorous interpretation of a linear mixing curve is that a practically detectable deviation in reactant concentration has not occurred because either: (a) reactions involving the constituent are too slow, or (b) they utilise only a very small proportion of the available concentration. Condition (b) applies generally to the abundant major (conservative) sea water cations. For example, sorptive exchanges of these are strongly influential in controlling the surface properties of estuarine suspended particles, but are ineffectual with respect to producing non-linear mixing curves. However, for many of the trace constituents of natural waters, it is more likely that linear mixing curves are a product of slow reaction kinetics. Where deviations from linear mixing curves are clearly evident, a further question is raised: is the reaction sufficiently fast to generate a close approach
255 to thermodynamic equilibrium within the mixing zone or is the observed distribution dependent on both reaction kinetics and hydrodynamic t u r n o v e r of the containing waters? To answer this question, a knowledge of both reaction rate and available reaction time is essential. The two-dimensional steady-state numerical simulation of San Francisco Bay developed by Peterson et al. (1978) provides a revealing illustration of the interaction between reaction rate and water replacement time on the detectability of chemical reactivity. Assuming typical concentrations of 200 and 40/~g at l- 1for the silicate content of freshwater and seawater, respectively, the model showed th at a hypothetical zero-order (biological) removal over the whole estuary at a rate of l p g a t l 1day 1 would generate pronounced c u r v a t u r e in the mixing curve, clearly indicative of removal, when the river discharge was 100 m3s-1. Increasing the discharge to 400 m3s i or greater with the same removal rate generated a mixing curve which deviated only slightly from linearity. Taking into account analytical and na t ura l environmental variability, such a deviation may not be distinguishable in practice. Another useful example is the study of dissolved organic carbon in the Severn E stuary reported by M a n t o u r a and Woodward (1983). In this case, field data were best fitted by a linear mixing curve. However, considering the appreciable scatter of data points about the conservative mixing line, it was calculated t h a t a first-order removal of dissolved organic carbon with a time constant of 3.6 x 10 4day i or less could not be differentiated from the conservative case at the 95% confidence level. Freshwater residence or t u r n o v e r times differ widely between estuaries, ranging for the whole estuary from the order of one tidal cycle in the smallest to more th an a year in the largest systems, with correspondingly shorter times for segments thereof. Furthermore, within any one system, t u r n o v e r times can vary substantially with season in response to changes in freshwater discharge. Significant inter- and intra-estuarine contrasts in reactive chemical distributions are expected to be generated by these differences in hydrodynamic time scales. A SIMPLE BOX MODEL Interactions between reaction rate and hydrodynamic residence time can be explored with the aid of a simple box model. Consider an estuary, or a segment Output Input Q flowrate reactant concentration [A] i
1 rapidly stirred volume V A -~--k' B
Fig. 1. The one-boxsteady-state model.
flowrate Q reactant concentration [A] product concentration [B]
256 A_..~] [ 10 3
,
,
i
~
i
[BI
10 2
~=~o ..... i.e. ca__ 5% conversion when K=I
~ 10
I I
{A]
~ : g + ~ of KT0~ .__..._~.~.__~,._
...........
conservative ~ l ~ k i n e t i c
fo -+
range ~11
',,(a) 10 3
li 2
101
~ l s h o r t residence time slow reaction
~"........... ~ equilibrium
(b>,, 10° t~]_~22 T
,
10-1
10-2
10-3
long residence time~r~ fast r e a c t i o n J
Fig. 2. Dependenceof the steady-stateratio of reactant to product ([A]/[B]) on the ratio of forward reaction half-life to hydrodynamicturnover time (t~/2/T) for the one-boxmodel. thereof, to be represented by a well-mixed box of volume V with an input volume flow rate, Q, containing a r e a c t a n t A at a concent ra t i on [A]i (Fig. 1). The r e a c t a n t A is being converted within the box to a product B by a reversible first-order reaction characterised by an equilibrium constant K and forward and reverse rate constants of k and k', respectively. For the time invariant or steady-state condition, with standing concentrations of r e a c t a n t and product within the box represented by [A] and [B], respectively, we have d[A]/dt = d[B]/dt = 0 and (Morgan, 1967): [A]/[B]
=
1 / g + 1/(k(V/Q))
For a hydrodynamic t u r n o v e r time T given by V/Q, and a chemical reaction time or half-life tl/2 for the forward reaction equal to In 2/k, we have: [A]/[B]
=
1 / g + 1/(T/tl/2)ln2
This relationship is illustrated graphically in Fig. 2, which shows the ratio of the standing concentrations of A and B as a function of the ratio of chemical half-life to hydrodynamic residence time when the chemical reaction has a K value of unity. Theoretically, true equilibrium defined by [A]/[B] = 1 / K is attained only after infinite time. In practice, an arbitrarily selected close approach, say 99% conversion, needs to be accepted; this is shown as point (b) in Fig. 2. Equilibrium modelling is appropriate for describing the chemistry of the system only when the ratio of tl/2/T is less than (b). Point (a) depends solely on the ability, in practice, to measure a significant chemical change within the system. In estuaries, this may be either the detection of a significant deviation of r e a c t a n t concen t ra t i on [A] from t ha t predicted by the theoretical dilution line or the detection of a significant yield
257 of B. For illustrative purposes, point (a) is plotted in Fig. 2 at [A]/[B] = 20, which corresponds to about a 5% conversion of A with K = 1. For values of tl/2/T greater t h a n (a), conservative behaviour of reactant A will be inferred in practice. When values of tll2/Tfall between (a) and (b), which may conveniently be termed the 'kinetic range', quantitative models of the chemistry of the system must necessarily include kinetic terms. The 'kinetic range' of tl/2/T is dependent on K and, in this example, covers about two orders of magnitude. With increasing values of K, the range widens because the reaction has effectively to proceed further in order to closely approach the equilibrium state. HYDRODYNAMIC TURNOVERTIME IN ESTUARIES For the purposes of this discussion it is convenient to use the simple concept of freshwater replacement to quantify hydrodynamic control of available reaction time. This concept is most appropriate in considerations of the fate within estuaries of dissolved chemical constituents introduced by the river. The freshwater replacement time is defined as the time required to replace the volume of freshwater contained in the whole estuary or any segment of it (inferred from the distribution of salinity) by the volume influx of the river. Since the replacement time depends on the river flow, Fr, it varies substantially with season. For example, Zimmerman (1988) has shown t h a t the whole estuary freshwater replacement time for the Ems-Dollard Estuary varies between about 10 and 70 days through the normal seasonal range of river flow. The dependence of replacement time on river discharge tends to an exponential rather than a linear relationship. Pilson (1985) showed that data for Narragansett Bay was well described by the equation T = 41.8 exp (-0.00435Fr). Figure 3 compares the ranges of whole estuary replacement times reported for a number of estuaries with estimates of their length. Because of complicated '
400
'
/
I
!
~oo
~ -LL
-o
- ~ ~
E
:
~ ~?,-" i
-zd
,-"-'if-
0 0
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" 1 !' 4/
/
/
Y 100
/
I
/
/
,/E
//
/
>
I
100
200 Length
300
(km)
Fig. 3. Seasonal ranges of whole estuary hydrodynamicturnover time (freshwater replacement time) within estuaries in relation to their length.
Tamar San Francisco Bay Severn
Estuary
10 50 200
120 235
Approx. mean freshwater replacement time, T (days)
30
Approx. length (km)
0.69 2.77
0.14
0.77 3.09
0.15
658 2630
132
K = 1
K-
1
tl/2 (days) for conservativeness is greater than
tl/2 (days) for equilibrium is less than K = 10
690 2760
138
K-
10
Half-lives for a first-order chemical reaction bounding the "kinetic range" in whole estuaries of different size. Within this range, kinetic models are required for modelling the system. Longer reaction half-lives generate practically conservative distributions; shorter half-lives are suitable for equilibrium modelling
TABLE 1
259 shape, estuarine length is not a precisely determined property. Nevertheless, it does provide a convenient illustration of the relationship between estuarine size and the range of T. The extreme T values recorded for these estuaries under normal conditions have been used to calculate chemical half-lives (for a reaction with K = 1 or 10) corresponding to points (a) and (b) of Fig. 2, which enclose the 'kinetic range'. The results listed in Table 1 illustrate the considerable inter- and intra-estuarine differences in the degree of advancement achievable by any individual chemical process. Whole estuary replacement times do not necessarily represent the total time available for the advancement of individual chemical reactions, which may be confined within a restricted region of an estuary. Particularly short replacement times are characteristic of the very low salinity zone. However, mainly because gradients in physico-chemical properties are locally very steep, this is an important site for estuarine chemical reactivity (Morris et al., 1978). In the Tamar Estuary, for example, freshwater in the segment enclosing water up to a salinity of 1%o is replaced within a few hours, even when river flow is at its summer minimum. Nevertheless, substantial removal of river introduced dissolved metals is generally observed in the low salinity region of this estuary (Morris, 1986; Ackroyd et al., 1986), indicating a very fast reaction. CHEMICALREACTIONRATES IN NATURALWATERS Rates of chemical reactions in natural waters cannot, in general, be predicted absolutely from fundamental theory. As expressed by the law of mass action, the primary control of reaction rate is exerted by the concentrations (activities, to be precise) of participating reactants. Next in importance is temperature, the influence of which is often predictable using the activation energy concept. The rates of most natural aquatic reactions also depend on ambient pH and/or pE through the participation of proton and/or electron transfers in the reaction mechanism. In estuaries, salinity-related changes in chemical reaction rates are also important and are generated both by mixingcontrolled changes in the relative concentrations of reactants and by the influence of ambient ionic strength on the activities of reacting species. Additionally, the multi-component, heterogeneous nature of natural waters provides abundant scope for catalysis or inhibition of reactions. With such uncertainties, quantification of reaction rates in natural waters must generally be based on empirical observations. It is also pertinent to note here the observation of Hoffman (1981) that very few chemical reactions of interest in natural aquatic systems follow simple first-order kinetics. Despite this, there is a general tendency to apply first-order chemical kinetics when modelling reactions for which the mechanism is unknown. Experimental rate constants describing the kinetics of trace metal sorption processes in natural waters are available only in first-order kinetic terms.
26O THE KINETICS OF SORPTION PROCESSES FOR TRACE METALS IN NATURAL WATERS T h e k i n e t i c s of t r a c e m e t a l a d s o r p t i o n a n d d e s o r p t i o n a t the s u r f a c e s of n a t u r a l p a r t i c l e s h a v e been e x a m i n e d q u a n t i t a t i v e l y by N y f f e l e r et al. (1984) a n d by J a n n a s c h et al. (1988) u s i n g r a d i o t r a c e r t e c h n i q u e s . T h e m o d e l s used to describe t h e i r r e s u l t s a r e s h o w n in T a b l e 2. In t h e s i m p l e s t (Model I), m e t a l s a r e a s s u m e d to e x c h a n g e r e v e r s i b l y b e t w e e n the dissolved s t a t e a n d a single t y p e of a d s o r p t i o n site on t h e s u r f a c e s of p a r t i c l e s w i t h first-order kinetics. H o w e v e r , in m a n y cases it was o b s e r v e d t h a t a n initial f a s t e r u p t a k e of radiot r a c e r w a s a c c o m p a n i e d by a l o n g e r - t e r m s l o w e r u p t a k e . M o d e l II w a s t h e r e f o r e f o r m u l a t e d to include the s e q u e n t i a l first-order r e v e r s i b l e t r a n s f o r m a t i o n of i n i t i a l l y a d s o r b e d m e t a l into one or m o r e s t r o n g l y b o u n d s t a t e s w h i c h are not d i r e c t l y e x c h a n g e a b l e w i t h the s o l u t i o n phase. J a n n a s c h et al. (1988) found t h a t c u r v e fitting of t h e i r e x p e r i m e n t a l k i n e t i c d a t a could n o t d i s t i n g u i s h M o d e l II f r o m M o d e l III, w h i c h describes the o v e r a l l process as a n u m b e r of p a r a l l e l first-order r e a c t i o n s in w h i c h m e t a l s are a d s o r b e d d i r e c t l y from s o l u t i o n o n t o sites of differing d e g r e e s of s o r p t i v e s t r e n g t h . T a b l e 3 lists first-order r a t e c o n s t a n t s a n d half-lives o b t a i n e d by fitting k i n e t i c d a t a for t r a c e m e t a l s o r p t i o n to M o d e l II, w i t h the r a t e k_2, w h i c h is g e n e r a l l y found to be v e r y slow, set to zero. T h e m o s t i m p o r t a n t c o n c l u s i o n f r o m t h e s e r e s u l t s is t h a t s o r p t i o n p r o c e s s e s for m e t a l s a r e in g e n e r a l sufficiently fast to be h i g h l y significant in estuaries, e v e n w i t h i n t h e r a p i d l y flushed low TABLE 2 Kinetic models describing the sorptive behaviour of trace metals onto natural particles [M]d is the concentration of dissolved metal; [M]~(n) is the concentration of metal attached to a surface site of type n. Model I - - Reversible first-order reaction; single type of solid adsorption site (Nyffeler et al., 1984) kl
[M]d ~
[M]~I~ k
Model II
1
Sequential reversible first-order reactions; initially adsorbed metal migrates into the particle lattice or is otherwise further bound (Nyffeler et al., 1984) k1 k
k2
1
k
2
Model III - - Parallel reversible first-order reactions; multiple binding sites of differing adsorptive strengths (Jannasch et al., 1988) [Mls(l~ [M]d ~
[M].... ~ . . .
TABLE 3 First-order r a t e c o n s t a n t s and c o r r e s p o n d i n g half-lives describing t h e sorptive b e h a v i o u r of some t r a c e metals on n a t u r a l particles a c c o r d i n g to Model II (Table 2) w i t h k 2 = 0 Metal
Cd Zn Sn
N a r r a g a n s e t t Bay surface s e d i m e n t (Nyffeler et al., 1984)
P u g e t Sound s u s p e n d e d particles ( J a n n a s c h et al., 1988)
k1*
k i
k2
85 (0.08) 390 (0.018) 2 × 104 (0.0003)
1.0 (7) 0.32 (22) 0.10 (69)
~ 0 ~0 ~0
Tamar E s t u a r y s u s p e n d e d particles (Glegg et al., 1988)
kl*
k 1
k2
kl*
k-1
k2
7 × 104 (0.0001) 3 x 107 (2 × 10 7)
1.9 (3.6) 2.3 (3.0)
0.16 (43) -0.5 (14)
6-55 x 103 (0.001 1.2 × 10 4)
< 4.8 (> 1.4)
~0
kl* is the particle n o r m a l i s e d r a t e c o n s t a n t in ml g 1day 1; n u m b e r s in p a r e n t h e s e s are t h e c o r r e s p o n d i n g half-lives in days for a s u s p e n d e d load of lOOmgl 1. k 1 and k 2 are in day 1; n u m b e r s in p a r e n t h e s e s are t h e c o r r e s p o n d i n g half-lives in days.
262 TABLE 4 Reported behaviour of trace metals in the lower salinity ( ~ 0-10%o)regions of estuaries of varying size Estuary
Observed dissolved metal behaviour Conservative
Large estuaries, length > 200 km Amazon Cu, Ni Changjiang Cu
Desorption Cd (?) Ni, Cd
Medium sized estuaries, 200 > length > 100km San Francisco Cu, Ni, Bay Cd, Zn Small estuaries, length < 100 km Beaulieu Zn Rhine GSta Tamar
Ref.
Removal Boyle et al. (1982) Edmond et al. (1985) Cu
Zn, Cu, Cd
Cu, Zn Cu, Zn
Eaton (1979)
Holliday and Liss (1976) Duinker and Nolting (1977) Danielsson et al. (1983) Ackroyd et al. (1986)
s a l i n i t y zones of s m a l l e r systems. This is e s p e c i a l l y t r u e for the a d s o r p t i o n of dissolved m e t a l s o n t o p a r t i c l e surfaces. DISSOLVED TRACE METAL BEHAVIOUR IN ESTUARIES T a b l e 4 s u m m a r i s e s r e p o r t s of t r a c e m e t a l b e h a v i o u r in a n u m b e r of e s t u a r i e s classified a c c o r d i n g to size. T h e i n f o r m a t i o n r e l a t e s to the l o w e r s a l i n i t y zone (0-10%o) a n d is c o n c e r n e d m a i n l y w i t h the fate of r i v e r i n t r o d u c e d dissolved m e t a l s w h e r e t h e r i v e r c o n s t i t u t e s the m a j o r dissolved m e t a l source. M o s t r e m a r k a b l y , in t w o of the w o r l d ' s l a r g e s t s y s t e m s w h e r e t h e a v a i l a b l e r e a c t i o n time is longest, c o n s e r v a t i v e b e h a v i o u r of the dissolved m e t a l s Cu (Changjiang; E d m o n d et al., 1985) a n d Cu a n d Ni (Amazon; Boyle et al., 1982) h a s b e e n observed. T h e r e w a s no e v i d e n c e for m e t a l a d s o r p t i o n in t h e s e l a r g e estuaries, a l t h o u g h s i g n i f i c a n t d e s o r p t i o n was r e p o r t e d for some m e t a l s (Ni a n d Cd in the C h a n g j i a n g and, possibly, Cd in t h e Amazon). N o t e also t h a t c o n s e r v a t i v e b e h a v i o u r of Ni, Cd, Zn a n d Cu (but w i t h a t e n t a t i v e i n d i c a t i o n of Cu r e m o v a l u n d e r low flow conditions) was r e p o r t e d by E a t o n (1979) for the medium-sized S a n F r a n c i s c o Bay. D e s o r p t i o n of m e t a l s f r o m the influx of fresh r i v e r i n e p a r t i c l e s to a n e s t u a r y is i n e v i t a b l e t h r o u g h d i s p l a c e m e n t of a d s o r b e d m e t a l s by t h e s h a r p l y i n c r e a s i n g c o n c e n t r a t i o n s of m a j o r s e a w a t e r cations. Since d e s o r p t i o n is a r e l a t i v e l y slow process (Table 3) its s i g n i f i c a n c e in e s t u a r i n e l o w e r s a l i n i t y r e g i o n s is likely to i n c r e a s e w i t h e s t u a r i n e size ( f r e s h w a t e r r e t e n t i o n time). This is b o r n e o u t by the i n f o r m a t i o n in T a b l e 4, w h i c h s h o w s t h a t d e s o r p t i o n h a s only b e e n r e p o r t e d for t h e l a r g e s t estuaries. H o w e v e r , w h e t h e r or n o t
263 desorption of any particular metal is observed will also depend on the potentially-desorbable content of that metal on the riverine particles and on the chemical affinity of the adsorption. It should also be noted that where metal removal has been observed in small estuaries (discussed below), this may in reality be a net balance of opposing adsorption and desorption reactions. Extensive uptake of dissolved metals by estuarine suspended particles at low salinities has been observed only in small estuaries, e.g. the Rhine (Duinker and Nolting, 1977) and the Tamar (Ackroyd et al., 1986). Even so, conservative behaviour has been observed in others, e.g. the Beaulieu (Holliday and Liss, 1976) and the GSta (Danielsson et al., 1983). Since metal adsorption by suspended particles is generally rapid (Table 3), these inter-estuarine contrasts cannot be attributed to kinetic factors. It must be concluded that they arise from differences in the thermodynamic potential for adsorption to occur; that is, in the ability of the suspended particle population to sustain a continuous removal of dissolved metals. Consider a hypothetical estuary where the local suspended particle population is everywhere comprised of particles oscillating between suspension and deposition at the sediment surface without particle transport through the estuarine mixing gradient. Assume also that the dissolved metal concentrations carried by the river are invariant. In this case, the adsorbed metal on particles within the estuary would tend to attain and maintain equilibrium with respect to the local dissolved metal concentrations, according to any of the models in Table 2. Desorption of metals from the fresh input of riverine particles to the estuary would be the sole particle-water metal exchange process. Where the riverine influx of a particulate metal is relatively small, this desorption may not significantly affect estuarine dissolved metal concentrations with the result that dissolved metals would show conservative estuarine distributions. The behaviour of dissolved metals in larger estuaries appears to conform with this description in that only desorption or conservativeness has been observed. Oscillations in the dissolved metal content of the freshwater would lead to corresponding oscillations in the net adsorption/ desorption balance within the estuary. However, concentrations of dissolved metals in river inputs to estuaries, especially to larger systems, do not vary greatly or rapidly so that such oscillations would be expected to have only a minor influence on particle/water exchanges within the estuary. For extensive adsorption of riverine introduced dissolved metals to occur in the low salinity zone, an appropriate thermodynamic drive for the reaction must be generated. That is, the local particle population must be depleted in adsorbed trace metals relative to equilibrium with the ambient dissolved metal concentrations. This can only be achieved by the rapid riverward transport of particles from the mid to lower reaches of the estuary such as occurs in smaller dynamic estuaries with strong tidal currents. The processes involved have been discussed by Elbaz-Poulichet et al. (1984), Morris (1986) and Ackroyd et al. (1986). In such systems, relatively large fluxes of tidally resuspendable sediment are net transported towards the head of the estuary by asymmetry in
264
30f
,
A: Large estuary
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...-""" I ] ~s s ~'J"
N.- iI Ii-..I I II 100
0 .--~ 0 I-E 30 ~ IB ....
-"~ River
2OO
i
~----
/ ' ' ' ' 1 ,~r'' ,/
/
TE=10k m
Ilestuary
201-
0 I--~ 0
t~ *~'s~...///1/
J
i 20
-[
r
_-l,,-,o,m i
Distance (km)
/
i 40 S ea --m-
Fig. 4. Ranges of salinity encounteredby a resuspended sediment particle transported through a typical tidal excursionof 10km in (A) a large (200km length)and (B) a small(40 km length)estuary. the ebb and flood tidal currents (Allen et al., 1980; Bale et al., 1985; Uncles et al., 1985). The resuspendable sediment that accumulates in the upper estuary is redistributed downestuary during short periods of storms and river spate. In addition to the effects of large internal particle fluxes, Fig. 4 shows schematically another reason why internal transport of resuspendable particles may be much more effective in influencing dissolved metal concentration distributions in small compared with large estuaries. A typical tidal excursion (TE) of the order of 10km can transport resuspended sediment particles through a much greater portion of the mixing gradient (or salinity range) of small estuaries. Consequently, appreciable disequilibrium with respect to particle-water metal exchanges is much more readily achieved in smaller estuaries. Clearly, the magnitude of internal particle fluxes and the residence times of suspended particle and resuspendable sediment populations are highly important factors in the control of metal sorption interactions in estuaries. The arguments presented above suggest that observed distributions of dissolved trace metals in estuaries are compatible qualitatively with current understanding of the mechanisms and kinetics of adsorption/desorption processes in natural waters. However, this is not to argue t h a t other potentially significant processes (precipitation/dissolution of stoichiometric solid phases, colloid flocculation, speciation changes, biotic interactions) do not also contribute to estuarine trace metal interactions. Indeed, one conclusion of this study must be that in order to quantify the importance of sorption/desorption relative to these various other processes, and consequently to compare systematically the behaviour of trace metals in estuaries of widely differing charac-
265 teristics, m o r e i n f o r m a t i o n on the k i n e t i c s of these processes, and of t h e i r k i n e t i c controls, is required. SUMMARY The r a t i o of c h e m i c a l r e a c t i o n r a t e to the time available for the reaction, as d e t e r m i n e d by the h y d r o d y n a m i c w a t e r r e p l a c e m e n t time, d e t e r m i n e s the r a n g e s of r e a c t i o n r a t e s r e q u i r i n g c o n s e r v a t i v e , equilibrium or k i n e t i c modelling in estuaries of different size. The model, used in c o n j u n c t i o n with r e c e n t kinetic m e a s u r e m e n t s of sorptive e x c h a n g e s o f dissolved metals at the surface of e s t u a r i n e suspended particles, indicates t h a t b o t h a d s o r p t i o n and d e s o r p t i o n o c c u r at rates w h i c h are significant with respect to c h a r a c t e r i s t i c e s t u a r i n e w a t e r r e p l a c e m e n t times. T h a t is, q u a n t i t a t i v e models of metal b e h a v i o u r in estuaries m u s t g e n e r a l l y be f o r m u l a t e d in d y n a m i c terms. The c o r o l l a r y t h a t i n t e r - e s t u a r i n e differences in the e x t e n t of sorption/ d e s o r p t i o n i n t e r a c t i o n s , and h e n c e in the distributions, of dissolved metals in estuaries are directly related to e s t u a r i n e size is n o t confirmed by the available literature. I n t e r - e s t u a r i n e c o n t r a s t s are a p p a r e n t , but are more complex. This indicates t h a t the t h e r m o d y n a m i c drive for a s u b s t a n t i a l r e a c t i o n to o c c u r is an i m p o r t a n t consideration. It a p p e a r s t h a t disequilibrium with respect to sorptive e x c h a n g e of metals is most r e a d i l y g e n e r a t e d in small estuaries subject to e n h a n c e d i n t e r n a l fluxes of r e s u s p e n d a b l e sediment particles driven by s t r o n g tidal currents. In o t h e r estuaries, d e s o r p t i o n of metals from influxing riverine particles appears to be the principal s o r p t i o n process. The r e l a t i v e l y slow r a t e of d e s o r p t i o n suggests t h a t this process will more readily be observed in the l a r g e s t systems, and this is confirmed by the literature. However, d e s o r p t i o n is n o t observed for all metals in large estuaries, i n d i c a t i n g variability in the m a g n i t u d e of the p o t e n t i a l l y desorbable riverine influx a n d / o r in the a d s o r p t i o n affinity. REFERENCES Ackroyd, D.R., A.J. Bale, R.J.M. Howland, S. Knox, G.E. Millward and A.W. Morris, 1986. Distributions and behaviour of dissolved Cu, Zn and Mn in the Tamar Estuary. Estuarine Coastal Shelf Sci., 23: 621~40. Allen, G.P., J.C. Salomon, P. Bassoullet, Y. Du Penhoat and C. De Grandpr6, 1980. Effect of tides on mixing and suspended sediment transport in macrotidal estuaries. Sediment Geol., 6: 69-90. Bale, A.J., A.W. Morris and R.J.M. Howland, 1985. Seasonal sediment movement in the Tamar Estuary. Oceanol. Acta, 8: 1~. Boyle, E., R. Collier, A.T. Dengler, J.M. Edmond, A.C. Ng and R.F. Stallard, 1974. On the chemical mass-balance in estuaries. Geochim. Cosmochim. Acta, 38: 1719-1728. Boyle, E.A., S.S. Huestead and B. Grant, 1982. The chemical mass-balance of the Amazon Plume -- II. Copper, nickel and cadmium. Deep-Sea Res., 29: 1355-1364. Danielsson, L.-G., B. Magnusson, S. Westerlund and K. Zhang, 1983.Trace metals in the GSta River Estuary. Estuarine Coastal Shelf Sci., 17: 73-85. Duinker, J.C. and R.F. Nolting, 1977. Dissolved and particulate metals in the Rhine Estuary and Southern Bight. Mar. Pollut. Bull., 8: 65-71. Eaton, A., 1979. Observations on the geochemistry of soluble copper, iron, nickel and zinc in the San Francisco Bay estuary. Environ. Sci. Technol., 13: 425-432.
266 Edmond, J.M., A. Spivack, B.C. Grant, Ming-Hui Hu, Zexiam Chen, Sung Chen and Xiushau Zeng, 1985. Chemical dynamics of the Changjiang estuary. Cont. Shelf Res., 4: 17-36. Elbaz-Poulichet, F., P. Holliger, W. Wen Huang and J.-M. Martin, 1984. Lead cycling in estuaries illustrated by the Gironde Estuary, France. Nature, 308: 409-414. Glegg, G.A., J.G. Titley, G.E. Millward, D.R. Glasson and A.W. Morris, 1988. Sorption behaviour of waste-generated trace metals in estuarine waters. Water Sci. Technol., 20: 113-121. Hoffman, M.R., 1981. Thermodynamic, kinetic, and extrathermodynamic considerations in the development of equilibrium models for aquatic systems. Environ. Sci. Technol., 15: 345-353. Holliday, L.M. and P.S. Liss, 1976. The behaviour of dissolved iron, manganese and zinc in the Beaulieu Estuary, S. England. Estuarine Coastal Mar. Sci., 4: 349-353. Jannasch, H.W., B.D. Honeyman, L.S. Balistrieri and J.W. Murray, 1988. Kinetics of trace element uptake by marine particles. Geochim. Cosmochim. Acta, 52: 567-577. Loder, T.C. and R.P. Reichard, 1981. The dynamics of conservative mixing in estuaries. Estuaries, 1: 64-69. Mantoura, R.F.C. and E.M.S. Woodward, 1983. Conservative behaviour of dissolved organic carbon in the Severn Estuary: chemical and geochemical implications. Geochim. Cosmochim. Acta, 47: 1293-1309. Morgan, J.J., 1967. Applications and limitations of chemical thermodynamics in water systems. In: R.F. Gould (Ed.), Equilibrium Concepts in Natural Water Systems. Advances in Chemistry Series, 67. American Chemical Society, Washington, DC, pp. 1-29. Morris, A.W., 1986. Removal of trace metals in the very low salinity region of the Tamar Estuary, England. Sci. Total Environ., 49: 297-304. Morris, A.W., R.F.C. Mantoura, A.J. Bale and R.J.M. Howland, 1978. Very low salinity regions of estuaries: important sites for chemical and biological reactions. Nature, 274: 678~80. Nyffeler, U.P., Y.-H. Li and P.H. Santschi, 1984. A kinetic approach to describe trace-element distribution between particles and solution in n a t u r a l aquatic systems. Geochim. Cosmochim. Acta, 48: 1513-1522. Peterson, D.H., J.F. Festa and T.J. Conomos, 1978. Numerical simulation Of dissolved silica in San Francisco Bay. Estuarine Coastal Mar. Sci., 7: 9~116. Pilson, M.E.Q., 1985. On the residence time of water in Narragansett Bay. Estuaries, 8: ~14. Uncles, R.J., R.C.A. Elliot and S.A. Weston, 1985. Observed fluxes of water, salt and suspended sediment in a partly mixed estuary. Estuarine Coastal Shelf Sci:, 20: 147-168. Zimmerman, J.T.F., 1988. Estuarine residence times. In: B. Kjerfve (Ed.), Hydrodynamics of Estuaries, Vol. I Estuarine Physics. CRC Press Inc., Boca Raton, FL, pp. 75-84.
The Science of the Total Environment, 97/98 (1990) 253 266 Elsevier Science Publishers B.V., Amsterdam
KINETIC AND EQUILIBRIUM CHEMISTRY
APPROACHES
TO ESTUARINE
A.W. MORRIS
Natural Environment Research Council, Plymouth Marine Laboratory, Prospect Place, The Hoe, Plymouth PL1 3DH (United Kingdom)
ABSTRACT A one-box model is used to examine the relationship between freshwater residence time (T) and the time constant (half-life, tl/~) for a first-order chemical reaction in an estuary. Higher and lower limits of the ratio tl/2/T appropriate for conservative or chemical equilibrium modelling, respectively, are derived. These limits depend also on the equilibrium constant for the reaction and the initial reactant and product concentrations. For intermediate values of this ratio, the system can be described quantitatively only by using a kinetic model. Systematic inter-estuarine variability in the distributions of dissolved metals as a function of estuarine size (or hydrodynamic turnover time) is predicted by this model when the potential for sorptive particle-water exchanges is examined. However, this deduction, which is based on kinetic criteria alone, is not confirmed by evidence in the literature. Indeed, the model is contradicted in that dissolved metals appear to be most interactive in some, but not all, small estuaries and least interactive in large estuaries. It follows that the thermodynamic drive for metal interactions to occur is a necessary additional consideration. Gross thermodynamic disequilibrium with respect to particle-water metal exchange, which in turn generates highly non-conservative dissolved metal distributions, is most readily generated in small, highly dynamic systems through enhanced internal mobility of estuarine resuspendable sediment.
INTRODUCTION The preparation of this paper was prompted by the theme of the Quebec S y m p o s i u m o f O c t o b e r , 1988, n a m e l y t h e f a t e a n d e f f e c t s o f t o x i c c h e m i c a l s i n large estuaries. It considers the question: to what extent are intra-estuarine contrasts in the propagation of chemical processes, and consequently in the d i s t r i b u t i o n s o f r e a c t i v e c h e m i c a l c o n s t i t u e n t s , r e l a t e d t o e s t u a r i n e size? T h i s is e s s e n t i a l l y a q u e s t i o n o f a v a i l a b l e t i m e . I n c r e a s i n g e s t u a r i n e s i z e i m p l i e s increasing turnover time for contained water, within the whole estuary or any s e g m e n t o f it. H e n c e , a v a i l a b l e r e a c t i o n t i m e is l o n g e r i n l a r g e , r e l a t i v e t o s m a l l , e s t u a r i e s . I t is p r e d i c t a b l e t h e r e f o r e t h a t , o t h e r f a c t o r s b e i n g e q u a l , i n situ chemical processes should advance further towards thermodynamic equil i b r i u m s t a t e s a s t h e size o f t h e s y s t e m i n c r e a s e s . However, whatever the size (or water replacement time) of the estuary, the
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© - - 1990 Elsevier Science Publishers B.V.
254 locations where, and extent by which, reactant concentration distributions deviate from the simple mixing-controlled condition also depend on the thermodynamic characteristics of the reaction and on how far source reactant concentrations deviate initially from the local equilibrium state. The interactive effects of these conditions in estuaries are examined with the aid of a one-box model relating hydrodynamic turnover time, the time constant for a chemical reaction and the degree of advancement of the reaction. Using this model, it is argued that, from kinetic considerations alone, interestuarine differences in dissolved metal distributions which are dependent on estuarine size should be apparent. This is because metal exchange reactions at particle surfaces occur at rates which are comparable to estuarine hydrodynamic residence times. However, obvious size-related contrasts in metal distributions in estuaries are not evident when reported distributions are compared. The implications of this observation are discussed. MIXING CURVES AS EVIDENCE FOR ESTUARINE CHEMICALREACTIVITY Mixing curves provide the principal practical method for identifying the occurrence of chemical reactivity in estuaries (Boyle et al., 1974). These relate the concentrations of any dissolved constituent to those of another constituent (usually salinity) which quantifies the mixed proportions of freshwater and seawater throughout the estuarine mixing zone (or any selected segment of it). Providing a number of criteria are satisfied, of which steady state is usually the most important (Loder and Reichard, 1981), a linear mixing curve indicates conservative behaviour of the constituent within the estuary (or segment). Any other relationship (concave, convex, multiple inflections) indicates addition and/or removal of the constituent. It follows that where subsidiary inputs throughout the observed mixing zone are demonstrably absent, a non-linear mixing curve invariably indicates significant in situ reactivity. Marked gradients in constituent concentrations and in ambient physicochemical conditions (especially ionic strength, pH, redox status, suspended particulate material - - often termed 'master variables' in aquatic chemistry) are characteristic of estuarine mixing zones. Hence, absolute conservativeness of any constituent throughout an estuary is theoretically a highly improbable situation. That is, a more rigorous interpretation of a linear mixing curve is that a practically detectable deviation in reactant concentration has not occurred because either: (a) reactions involving the constituent are too slow, or (b) they utilise only a very small proportion of the available concentration. Condition (b) applies generally to the abundant major (conservative) sea water cations. For example, sorptive exchanges of these are strongly influential in controlling the surface properties of estuarine suspended particles, but are ineffectual with respect to producing non-linear mixing curves. However, for many of the trace constituents of natural waters, it is more likely that linear mixing curves are a product of slow reaction kinetics. Where deviations from linear mixing curves are clearly evident, a further question is raised: is the reaction sufficiently fast to generate a close approach
255 to thermodynamic equilibrium within the mixing zone or is the observed distribution dependent on both reaction kinetics and hydrodynamic t u r n o v e r of the containing waters? To answer this question, a knowledge of both reaction rate and available reaction time is essential. The two-dimensional steady-state numerical simulation of San Francisco Bay developed by Peterson et al. (1978) provides a revealing illustration of the interaction between reaction rate and water replacement time on the detectability of chemical reactivity. Assuming typical concentrations of 200 and 40/~g at l- 1for the silicate content of freshwater and seawater, respectively, the model showed th at a hypothetical zero-order (biological) removal over the whole estuary at a rate of l p g a t l 1day 1 would generate pronounced c u r v a t u r e in the mixing curve, clearly indicative of removal, when the river discharge was 100 m3s-1. Increasing the discharge to 400 m3s i or greater with the same removal rate generated a mixing curve which deviated only slightly from linearity. Taking into account analytical and na t ura l environmental variability, such a deviation may not be distinguishable in practice. Another useful example is the study of dissolved organic carbon in the Severn E stuary reported by M a n t o u r a and Woodward (1983). In this case, field data were best fitted by a linear mixing curve. However, considering the appreciable scatter of data points about the conservative mixing line, it was calculated t h a t a first-order removal of dissolved organic carbon with a time constant of 3.6 x 10 4day i or less could not be differentiated from the conservative case at the 95% confidence level. Freshwater residence or t u r n o v e r times differ widely between estuaries, ranging for the whole estuary from the order of one tidal cycle in the smallest to more th an a year in the largest systems, with correspondingly shorter times for segments thereof. Furthermore, within any one system, t u r n o v e r times can vary substantially with season in response to changes in freshwater discharge. Significant inter- and intra-estuarine contrasts in reactive chemical distributions are expected to be generated by these differences in hydrodynamic time scales. A SIMPLE BOX MODEL Interactions between reaction rate and hydrodynamic residence time can be explored with the aid of a simple box model. Consider an estuary, or a segment Output Input Q flowrate reactant concentration [A] i
1 rapidly stirred volume V A -~--k' B
Fig. 1. The one-boxsteady-state model.
flowrate Q reactant concentration [A] product concentration [B]
256 A_..~] [ 10 3
,
,
i
~
i
[BI
10 2
~=~o ..... i.e. ca__ 5% conversion when K=I
~ 10
I I
{A]
~ : g + ~ of KT0~ .__..._~.~.__~,._
...........
conservative ~ l ~ k i n e t i c
fo -+
range ~11
',,(a) 10 3
li 2
101
~ l s h o r t residence time slow reaction
~"........... ~ equilibrium
(b>,, 10° t~]_~22 T
,
10-1
10-2
10-3
long residence time~r~ fast r e a c t i o n J
Fig. 2. Dependenceof the steady-stateratio of reactant to product ([A]/[B]) on the ratio of forward reaction half-life to hydrodynamicturnover time (t~/2/T) for the one-boxmodel. thereof, to be represented by a well-mixed box of volume V with an input volume flow rate, Q, containing a r e a c t a n t A at a concent ra t i on [A]i (Fig. 1). The r e a c t a n t A is being converted within the box to a product B by a reversible first-order reaction characterised by an equilibrium constant K and forward and reverse rate constants of k and k', respectively. For the time invariant or steady-state condition, with standing concentrations of r e a c t a n t and product within the box represented by [A] and [B], respectively, we have d[A]/dt = d[B]/dt = 0 and (Morgan, 1967): [A]/[B]
=
1 / g + 1/(k(V/Q))
For a hydrodynamic t u r n o v e r time T given by V/Q, and a chemical reaction time or half-life tl/2 for the forward reaction equal to In 2/k, we have: [A]/[B]
=
1 / g + 1/(T/tl/2)ln2
This relationship is illustrated graphically in Fig. 2, which shows the ratio of the standing concentrations of A and B as a function of the ratio of chemical half-life to hydrodynamic residence time when the chemical reaction has a K value of unity. Theoretically, true equilibrium defined by [A]/[B] = 1 / K is attained only after infinite time. In practice, an arbitrarily selected close approach, say 99% conversion, needs to be accepted; this is shown as point (b) in Fig. 2. Equilibrium modelling is appropriate for describing the chemistry of the system only when the ratio of tl/2/T is less than (b). Point (a) depends solely on the ability, in practice, to measure a significant chemical change within the system. In estuaries, this may be either the detection of a significant deviation of r e a c t a n t concen t ra t i on [A] from t ha t predicted by the theoretical dilution line or the detection of a significant yield
257 of B. For illustrative purposes, point (a) is plotted in Fig. 2 at [A]/[B] = 20, which corresponds to about a 5% conversion of A with K = 1. For values of tl/2/T greater t h a n (a), conservative behaviour of reactant A will be inferred in practice. When values of tll2/Tfall between (a) and (b), which may conveniently be termed the 'kinetic range', quantitative models of the chemistry of the system must necessarily include kinetic terms. The 'kinetic range' of tl/2/T is dependent on K and, in this example, covers about two orders of magnitude. With increasing values of K, the range widens because the reaction has effectively to proceed further in order to closely approach the equilibrium state. HYDRODYNAMIC TURNOVERTIME IN ESTUARIES For the purposes of this discussion it is convenient to use the simple concept of freshwater replacement to quantify hydrodynamic control of available reaction time. This concept is most appropriate in considerations of the fate within estuaries of dissolved chemical constituents introduced by the river. The freshwater replacement time is defined as the time required to replace the volume of freshwater contained in the whole estuary or any segment of it (inferred from the distribution of salinity) by the volume influx of the river. Since the replacement time depends on the river flow, Fr, it varies substantially with season. For example, Zimmerman (1988) has shown t h a t the whole estuary freshwater replacement time for the Ems-Dollard Estuary varies between about 10 and 70 days through the normal seasonal range of river flow. The dependence of replacement time on river discharge tends to an exponential rather than a linear relationship. Pilson (1985) showed that data for Narragansett Bay was well described by the equation T = 41.8 exp (-0.00435Fr). Figure 3 compares the ranges of whole estuary replacement times reported for a number of estuaries with estimates of their length. Because of complicated '
400
'
/
I
!
~oo
~ -LL
-o
- ~ ~
E
:
~ ~?,-" i
-zd
,-"-'if-
0 0
I /
/ /
-1"
jL-
'1t
" 1 !' 4/
/
/
Y 100
/
I
/
/
,/E
//
/
>
I
100
200 Length
300
(km)
Fig. 3. Seasonal ranges of whole estuary hydrodynamicturnover time (freshwater replacement time) within estuaries in relation to their length.
Tamar San Francisco Bay Severn
Estuary
10 50 200
120 235
Approx. mean freshwater replacement time, T (days)
30
Approx. length (km)
0.69 2.77
0.14
0.77 3.09
0.15
658 2630
132
K = 1
K-
1
tl/2 (days) for conservativeness is greater than
tl/2 (days) for equilibrium is less than K = 10
690 2760
138
K-
10
Half-lives for a first-order chemical reaction bounding the "kinetic range" in whole estuaries of different size. Within this range, kinetic models are required for modelling the system. Longer reaction half-lives generate practically conservative distributions; shorter half-lives are suitable for equilibrium modelling
TABLE 1
259 shape, estuarine length is not a precisely determined property. Nevertheless, it does provide a convenient illustration of the relationship between estuarine size and the range of T. The extreme T values recorded for these estuaries under normal conditions have been used to calculate chemical half-lives (for a reaction with K = 1 or 10) corresponding to points (a) and (b) of Fig. 2, which enclose the 'kinetic range'. The results listed in Table 1 illustrate the considerable inter- and intra-estuarine differences in the degree of advancement achievable by any individual chemical process. Whole estuary replacement times do not necessarily represent the total time available for the advancement of individual chemical reactions, which may be confined within a restricted region of an estuary. Particularly short replacement times are characteristic of the very low salinity zone. However, mainly because gradients in physico-chemical properties are locally very steep, this is an important site for estuarine chemical reactivity (Morris et al., 1978). In the Tamar Estuary, for example, freshwater in the segment enclosing water up to a salinity of 1%o is replaced within a few hours, even when river flow is at its summer minimum. Nevertheless, substantial removal of river introduced dissolved metals is generally observed in the low salinity region of this estuary (Morris, 1986; Ackroyd et al., 1986), indicating a very fast reaction. CHEMICALREACTIONRATES IN NATURALWATERS Rates of chemical reactions in natural waters cannot, in general, be predicted absolutely from fundamental theory. As expressed by the law of mass action, the primary control of reaction rate is exerted by the concentrations (activities, to be precise) of participating reactants. Next in importance is temperature, the influence of which is often predictable using the activation energy concept. The rates of most natural aquatic reactions also depend on ambient pH and/or pE through the participation of proton and/or electron transfers in the reaction mechanism. In estuaries, salinity-related changes in chemical reaction rates are also important and are generated both by mixingcontrolled changes in the relative concentrations of reactants and by the influence of ambient ionic strength on the activities of reacting species. Additionally, the multi-component, heterogeneous nature of natural waters provides abundant scope for catalysis or inhibition of reactions. With such uncertainties, quantification of reaction rates in natural waters must generally be based on empirical observations. It is also pertinent to note here the observation of Hoffman (1981) that very few chemical reactions of interest in natural aquatic systems follow simple first-order kinetics. Despite this, there is a general tendency to apply first-order chemical kinetics when modelling reactions for which the mechanism is unknown. Experimental rate constants describing the kinetics of trace metal sorption processes in natural waters are available only in first-order kinetic terms.
26O THE KINETICS OF SORPTION PROCESSES FOR TRACE METALS IN NATURAL WATERS T h e k i n e t i c s of t r a c e m e t a l a d s o r p t i o n a n d d e s o r p t i o n a t the s u r f a c e s of n a t u r a l p a r t i c l e s h a v e been e x a m i n e d q u a n t i t a t i v e l y by N y f f e l e r et al. (1984) a n d by J a n n a s c h et al. (1988) u s i n g r a d i o t r a c e r t e c h n i q u e s . T h e m o d e l s used to describe t h e i r r e s u l t s a r e s h o w n in T a b l e 2. In t h e s i m p l e s t (Model I), m e t a l s a r e a s s u m e d to e x c h a n g e r e v e r s i b l y b e t w e e n the dissolved s t a t e a n d a single t y p e of a d s o r p t i o n site on t h e s u r f a c e s of p a r t i c l e s w i t h first-order kinetics. H o w e v e r , in m a n y cases it was o b s e r v e d t h a t a n initial f a s t e r u p t a k e of radiot r a c e r w a s a c c o m p a n i e d by a l o n g e r - t e r m s l o w e r u p t a k e . M o d e l II w a s t h e r e f o r e f o r m u l a t e d to include the s e q u e n t i a l first-order r e v e r s i b l e t r a n s f o r m a t i o n of i n i t i a l l y a d s o r b e d m e t a l into one or m o r e s t r o n g l y b o u n d s t a t e s w h i c h are not d i r e c t l y e x c h a n g e a b l e w i t h the s o l u t i o n phase. J a n n a s c h et al. (1988) found t h a t c u r v e fitting of t h e i r e x p e r i m e n t a l k i n e t i c d a t a could n o t d i s t i n g u i s h M o d e l II f r o m M o d e l III, w h i c h describes the o v e r a l l process as a n u m b e r of p a r a l l e l first-order r e a c t i o n s in w h i c h m e t a l s are a d s o r b e d d i r e c t l y from s o l u t i o n o n t o sites of differing d e g r e e s of s o r p t i v e s t r e n g t h . T a b l e 3 lists first-order r a t e c o n s t a n t s a n d half-lives o b t a i n e d by fitting k i n e t i c d a t a for t r a c e m e t a l s o r p t i o n to M o d e l II, w i t h the r a t e k_2, w h i c h is g e n e r a l l y found to be v e r y slow, set to zero. T h e m o s t i m p o r t a n t c o n c l u s i o n f r o m t h e s e r e s u l t s is t h a t s o r p t i o n p r o c e s s e s for m e t a l s a r e in g e n e r a l sufficiently fast to be h i g h l y significant in estuaries, e v e n w i t h i n t h e r a p i d l y flushed low TABLE 2 Kinetic models describing the sorptive behaviour of trace metals onto natural particles [M]d is the concentration of dissolved metal; [M]~(n) is the concentration of metal attached to a surface site of type n. Model I - - Reversible first-order reaction; single type of solid adsorption site (Nyffeler et al., 1984) kl
[M]d ~
[M]~I~ k
Model II
1
Sequential reversible first-order reactions; initially adsorbed metal migrates into the particle lattice or is otherwise further bound (Nyffeler et al., 1984) k1 k
k2
1
k
2
Model III - - Parallel reversible first-order reactions; multiple binding sites of differing adsorptive strengths (Jannasch et al., 1988) [Mls(l~ [M]d ~
[M].... ~ . . .
TABLE 3 First-order r a t e c o n s t a n t s and c o r r e s p o n d i n g half-lives describing t h e sorptive b e h a v i o u r of some t r a c e metals on n a t u r a l particles a c c o r d i n g to Model II (Table 2) w i t h k 2 = 0 Metal
Cd Zn Sn
N a r r a g a n s e t t Bay surface s e d i m e n t (Nyffeler et al., 1984)
P u g e t Sound s u s p e n d e d particles ( J a n n a s c h et al., 1988)
k1*
k i
k2
85 (0.08) 390 (0.018) 2 × 104 (0.0003)
1.0 (7) 0.32 (22) 0.10 (69)
~ 0 ~0 ~0
Tamar E s t u a r y s u s p e n d e d particles (Glegg et al., 1988)
kl*
k 1
k2
kl*
k-1
k2
7 × 104 (0.0001) 3 x 107 (2 × 10 7)
1.9 (3.6) 2.3 (3.0)
0.16 (43) -0.5 (14)
6-55 x 103 (0.001 1.2 × 10 4)
< 4.8 (> 1.4)
~0
kl* is the particle n o r m a l i s e d r a t e c o n s t a n t in ml g 1day 1; n u m b e r s in p a r e n t h e s e s are t h e c o r r e s p o n d i n g half-lives in days for a s u s p e n d e d load of lOOmgl 1. k 1 and k 2 are in day 1; n u m b e r s in p a r e n t h e s e s are t h e c o r r e s p o n d i n g half-lives in days.
262 TABLE 4 Reported behaviour of trace metals in the lower salinity ( ~ 0-10%o)regions of estuaries of varying size Estuary
Observed dissolved metal behaviour Conservative
Large estuaries, length > 200 km Amazon Cu, Ni Changjiang Cu
Desorption Cd (?) Ni, Cd
Medium sized estuaries, 200 > length > 100km San Francisco Cu, Ni, Bay Cd, Zn Small estuaries, length < 100 km Beaulieu Zn Rhine GSta Tamar
Ref.
Removal Boyle et al. (1982) Edmond et al. (1985) Cu
Zn, Cu, Cd
Cu, Zn Cu, Zn
Eaton (1979)
Holliday and Liss (1976) Duinker and Nolting (1977) Danielsson et al. (1983) Ackroyd et al. (1986)
s a l i n i t y zones of s m a l l e r systems. This is e s p e c i a l l y t r u e for the a d s o r p t i o n of dissolved m e t a l s o n t o p a r t i c l e surfaces. DISSOLVED TRACE METAL BEHAVIOUR IN ESTUARIES T a b l e 4 s u m m a r i s e s r e p o r t s of t r a c e m e t a l b e h a v i o u r in a n u m b e r of e s t u a r i e s classified a c c o r d i n g to size. T h e i n f o r m a t i o n r e l a t e s to the l o w e r s a l i n i t y zone (0-10%o) a n d is c o n c e r n e d m a i n l y w i t h the fate of r i v e r i n t r o d u c e d dissolved m e t a l s w h e r e t h e r i v e r c o n s t i t u t e s the m a j o r dissolved m e t a l source. M o s t r e m a r k a b l y , in t w o of the w o r l d ' s l a r g e s t s y s t e m s w h e r e t h e a v a i l a b l e r e a c t i o n time is longest, c o n s e r v a t i v e b e h a v i o u r of the dissolved m e t a l s Cu (Changjiang; E d m o n d et al., 1985) a n d Cu a n d Ni (Amazon; Boyle et al., 1982) h a s b e e n observed. T h e r e w a s no e v i d e n c e for m e t a l a d s o r p t i o n in t h e s e l a r g e estuaries, a l t h o u g h s i g n i f i c a n t d e s o r p t i o n was r e p o r t e d for some m e t a l s (Ni a n d Cd in the C h a n g j i a n g and, possibly, Cd in t h e Amazon). N o t e also t h a t c o n s e r v a t i v e b e h a v i o u r of Ni, Cd, Zn a n d Cu (but w i t h a t e n t a t i v e i n d i c a t i o n of Cu r e m o v a l u n d e r low flow conditions) was r e p o r t e d by E a t o n (1979) for the medium-sized S a n F r a n c i s c o Bay. D e s o r p t i o n of m e t a l s f r o m the influx of fresh r i v e r i n e p a r t i c l e s to a n e s t u a r y is i n e v i t a b l e t h r o u g h d i s p l a c e m e n t of a d s o r b e d m e t a l s by t h e s h a r p l y i n c r e a s i n g c o n c e n t r a t i o n s of m a j o r s e a w a t e r cations. Since d e s o r p t i o n is a r e l a t i v e l y slow process (Table 3) its s i g n i f i c a n c e in e s t u a r i n e l o w e r s a l i n i t y r e g i o n s is likely to i n c r e a s e w i t h e s t u a r i n e size ( f r e s h w a t e r r e t e n t i o n time). This is b o r n e o u t by the i n f o r m a t i o n in T a b l e 4, w h i c h s h o w s t h a t d e s o r p t i o n h a s only b e e n r e p o r t e d for t h e l a r g e s t estuaries. H o w e v e r , w h e t h e r or n o t
263 desorption of any particular metal is observed will also depend on the potentially-desorbable content of that metal on the riverine particles and on the chemical affinity of the adsorption. It should also be noted that where metal removal has been observed in small estuaries (discussed below), this may in reality be a net balance of opposing adsorption and desorption reactions. Extensive uptake of dissolved metals by estuarine suspended particles at low salinities has been observed only in small estuaries, e.g. the Rhine (Duinker and Nolting, 1977) and the Tamar (Ackroyd et al., 1986). Even so, conservative behaviour has been observed in others, e.g. the Beaulieu (Holliday and Liss, 1976) and the GSta (Danielsson et al., 1983). Since metal adsorption by suspended particles is generally rapid (Table 3), these inter-estuarine contrasts cannot be attributed to kinetic factors. It must be concluded that they arise from differences in the thermodynamic potential for adsorption to occur; that is, in the ability of the suspended particle population to sustain a continuous removal of dissolved metals. Consider a hypothetical estuary where the local suspended particle population is everywhere comprised of particles oscillating between suspension and deposition at the sediment surface without particle transport through the estuarine mixing gradient. Assume also that the dissolved metal concentrations carried by the river are invariant. In this case, the adsorbed metal on particles within the estuary would tend to attain and maintain equilibrium with respect to the local dissolved metal concentrations, according to any of the models in Table 2. Desorption of metals from the fresh input of riverine particles to the estuary would be the sole particle-water metal exchange process. Where the riverine influx of a particulate metal is relatively small, this desorption may not significantly affect estuarine dissolved metal concentrations with the result that dissolved metals would show conservative estuarine distributions. The behaviour of dissolved metals in larger estuaries appears to conform with this description in that only desorption or conservativeness has been observed. Oscillations in the dissolved metal content of the freshwater would lead to corresponding oscillations in the net adsorption/ desorption balance within the estuary. However, concentrations of dissolved metals in river inputs to estuaries, especially to larger systems, do not vary greatly or rapidly so that such oscillations would be expected to have only a minor influence on particle/water exchanges within the estuary. For extensive adsorption of riverine introduced dissolved metals to occur in the low salinity zone, an appropriate thermodynamic drive for the reaction must be generated. That is, the local particle population must be depleted in adsorbed trace metals relative to equilibrium with the ambient dissolved metal concentrations. This can only be achieved by the rapid riverward transport of particles from the mid to lower reaches of the estuary such as occurs in smaller dynamic estuaries with strong tidal currents. The processes involved have been discussed by Elbaz-Poulichet et al. (1984), Morris (1986) and Ackroyd et al. (1986). In such systems, relatively large fluxes of tidally resuspendable sediment are net transported towards the head of the estuary by asymmetry in
264
30f
,
A: Large estuary
20
~o
...-""" I ] ~s s ~'J"
N.- iI Ii-..I I II 100
0 .--~ 0 I-E 30 ~ IB ....
-"~ River
2OO
i
~----
/ ' ' ' ' 1 ,~r'' ,/
/
TE=10k m
Ilestuary
201-
0 I--~ 0
t~ *~'s~...///1/
J
i 20
-[
r
_-l,,-,o,m i
Distance (km)
/
i 40 S ea --m-
Fig. 4. Ranges of salinity encounteredby a resuspended sediment particle transported through a typical tidal excursionof 10km in (A) a large (200km length)and (B) a small(40 km length)estuary. the ebb and flood tidal currents (Allen et al., 1980; Bale et al., 1985; Uncles et al., 1985). The resuspendable sediment that accumulates in the upper estuary is redistributed downestuary during short periods of storms and river spate. In addition to the effects of large internal particle fluxes, Fig. 4 shows schematically another reason why internal transport of resuspendable particles may be much more effective in influencing dissolved metal concentration distributions in small compared with large estuaries. A typical tidal excursion (TE) of the order of 10km can transport resuspended sediment particles through a much greater portion of the mixing gradient (or salinity range) of small estuaries. Consequently, appreciable disequilibrium with respect to particle-water metal exchanges is much more readily achieved in smaller estuaries. Clearly, the magnitude of internal particle fluxes and the residence times of suspended particle and resuspendable sediment populations are highly important factors in the control of metal sorption interactions in estuaries. The arguments presented above suggest that observed distributions of dissolved trace metals in estuaries are compatible qualitatively with current understanding of the mechanisms and kinetics of adsorption/desorption processes in natural waters. However, this is not to argue t h a t other potentially significant processes (precipitation/dissolution of stoichiometric solid phases, colloid flocculation, speciation changes, biotic interactions) do not also contribute to estuarine trace metal interactions. Indeed, one conclusion of this study must be that in order to quantify the importance of sorption/desorption relative to these various other processes, and consequently to compare systematically the behaviour of trace metals in estuaries of widely differing charac-
265 teristics, m o r e i n f o r m a t i o n on the k i n e t i c s of these processes, and of t h e i r k i n e t i c controls, is required. SUMMARY The r a t i o of c h e m i c a l r e a c t i o n r a t e to the time available for the reaction, as d e t e r m i n e d by the h y d r o d y n a m i c w a t e r r e p l a c e m e n t time, d e t e r m i n e s the r a n g e s of r e a c t i o n r a t e s r e q u i r i n g c o n s e r v a t i v e , equilibrium or k i n e t i c modelling in estuaries of different size. The model, used in c o n j u n c t i o n with r e c e n t kinetic m e a s u r e m e n t s of sorptive e x c h a n g e s o f dissolved metals at the surface of e s t u a r i n e suspended particles, indicates t h a t b o t h a d s o r p t i o n and d e s o r p t i o n o c c u r at rates w h i c h are significant with respect to c h a r a c t e r i s t i c e s t u a r i n e w a t e r r e p l a c e m e n t times. T h a t is, q u a n t i t a t i v e models of metal b e h a v i o u r in estuaries m u s t g e n e r a l l y be f o r m u l a t e d in d y n a m i c terms. The c o r o l l a r y t h a t i n t e r - e s t u a r i n e differences in the e x t e n t of sorption/ d e s o r p t i o n i n t e r a c t i o n s , and h e n c e in the distributions, of dissolved metals in estuaries are directly related to e s t u a r i n e size is n o t confirmed by the available literature. I n t e r - e s t u a r i n e c o n t r a s t s are a p p a r e n t , but are more complex. This indicates t h a t the t h e r m o d y n a m i c drive for a s u b s t a n t i a l r e a c t i o n to o c c u r is an i m p o r t a n t consideration. It a p p e a r s t h a t disequilibrium with respect to sorptive e x c h a n g e of metals is most r e a d i l y g e n e r a t e d in small estuaries subject to e n h a n c e d i n t e r n a l fluxes of r e s u s p e n d a b l e sediment particles driven by s t r o n g tidal currents. In o t h e r estuaries, d e s o r p t i o n of metals from influxing riverine particles appears to be the principal s o r p t i o n process. The r e l a t i v e l y slow r a t e of d e s o r p t i o n suggests t h a t this process will more readily be observed in the l a r g e s t systems, and this is confirmed by the literature. However, d e s o r p t i o n is n o t observed for all metals in large estuaries, i n d i c a t i n g variability in the m a g n i t u d e of the p o t e n t i a l l y desorbable riverine influx a n d / o r in the a d s o r p t i o n affinity. REFERENCES Ackroyd, D.R., A.J. Bale, R.J.M. Howland, S. Knox, G.E. Millward and A.W. Morris, 1986. Distributions and behaviour of dissolved Cu, Zn and Mn in the Tamar Estuary. Estuarine Coastal Shelf Sci., 23: 621~40. Allen, G.P., J.C. Salomon, P. Bassoullet, Y. Du Penhoat and C. De Grandpr6, 1980. Effect of tides on mixing and suspended sediment transport in macrotidal estuaries. Sediment Geol., 6: 69-90. Bale, A.J., A.W. Morris and R.J.M. Howland, 1985. Seasonal sediment movement in the Tamar Estuary. Oceanol. Acta, 8: 1~. Boyle, E., R. Collier, A.T. Dengler, J.M. Edmond, A.C. Ng and R.F. Stallard, 1974. On the chemical mass-balance in estuaries. Geochim. Cosmochim. Acta, 38: 1719-1728. Boyle, E.A., S.S. Huestead and B. Grant, 1982. The chemical mass-balance of the Amazon Plume -- II. Copper, nickel and cadmium. Deep-Sea Res., 29: 1355-1364. Danielsson, L.-G., B. Magnusson, S. Westerlund and K. Zhang, 1983.Trace metals in the GSta River Estuary. Estuarine Coastal Shelf Sci., 17: 73-85. Duinker, J.C. and R.F. Nolting, 1977. Dissolved and particulate metals in the Rhine Estuary and Southern Bight. Mar. Pollut. Bull., 8: 65-71. Eaton, A., 1979. Observations on the geochemistry of soluble copper, iron, nickel and zinc in the San Francisco Bay estuary. Environ. Sci. Technol., 13: 425-432.
266 Edmond, J.M., A. Spivack, B.C. Grant, Ming-Hui Hu, Zexiam Chen, Sung Chen and Xiushau Zeng, 1985. Chemical dynamics of the Changjiang estuary. Cont. Shelf Res., 4: 17-36. Elbaz-Poulichet, F., P. Holliger, W. Wen Huang and J.-M. Martin, 1984. Lead cycling in estuaries illustrated by the Gironde Estuary, France. Nature, 308: 409-414. Glegg, G.A., J.G. Titley, G.E. Millward, D.R. Glasson and A.W. Morris, 1988. Sorption behaviour of waste-generated trace metals in estuarine waters. Water Sci. Technol., 20: 113-121. Hoffman, M.R., 1981. Thermodynamic, kinetic, and extrathermodynamic considerations in the development of equilibrium models for aquatic systems. Environ. Sci. Technol., 15: 345-353. Holliday, L.M. and P.S. Liss, 1976. The behaviour of dissolved iron, manganese and zinc in the Beaulieu Estuary, S. England. Estuarine Coastal Mar. Sci., 4: 349-353. Jannasch, H.W., B.D. Honeyman, L.S. Balistrieri and J.W. Murray, 1988. Kinetics of trace element uptake by marine particles. Geochim. Cosmochim. Acta, 52: 567-577. Loder, T.C. and R.P. Reichard, 1981. The dynamics of conservative mixing in estuaries. Estuaries, 1: 64-69. Mantoura, R.F.C. and E.M.S. Woodward, 1983. Conservative behaviour of dissolved organic carbon in the Severn Estuary: chemical and geochemical implications. Geochim. Cosmochim. Acta, 47: 1293-1309. Morgan, J.J., 1967. Applications and limitations of chemical thermodynamics in water systems. In: R.F. Gould (Ed.), Equilibrium Concepts in Natural Water Systems. Advances in Chemistry Series, 67. American Chemical Society, Washington, DC, pp. 1-29. Morris, A.W., 1986. Removal of trace metals in the very low salinity region of the Tamar Estuary, England. Sci. Total Environ., 49: 297-304. Morris, A.W., R.F.C. Mantoura, A.J. Bale and R.J.M. Howland, 1978. Very low salinity regions of estuaries: important sites for chemical and biological reactions. Nature, 274: 678~80. Nyffeler, U.P., Y.-H. Li and P.H. Santschi, 1984. A kinetic approach to describe trace-element distribution between particles and solution in n a t u r a l aquatic systems. Geochim. Cosmochim. Acta, 48: 1513-1522. Peterson, D.H., J.F. Festa and T.J. Conomos, 1978. Numerical simulation Of dissolved silica in San Francisco Bay. Estuarine Coastal Mar. Sci., 7: 9~116. Pilson, M.E.Q., 1985. On the residence time of water in Narragansett Bay. Estuaries, 8: ~14. Uncles, R.J., R.C.A. Elliot and S.A. Weston, 1985. Observed fluxes of water, salt and suspended sediment in a partly mixed estuary. Estuarine Coastal Shelf Sci:, 20: 147-168. Zimmerman, J.T.F., 1988. Estuarine residence times. In: B. Kjerfve (Ed.), Hydrodynamics of Estuaries, Vol. I Estuarine Physics. CRC Press Inc., Boca Raton, FL, pp. 75-84.