EPA-600/D-84-099
A DIAGENETIC OXYGEN EQUIVALENTS MODEL OF SEDIMENT OXYGEN DEMAND
Dominic M. Di Toro
Environmental Engineering and Science Program
Manhattan College, Bronx, New York 10471
December 1983
~t5X?
°° 16n
Presented at the 56th Annual Water Pollution Control Federation
Conference. Session on Modeling the Sediment Oxygen Demand Process.
October 2-7, 1983
-------
Introduction
The consumption of oxygen in the overlying water by sediments is an
important component in the oxygen balance of most natural waters. Con-
ventional practice is to specify the magnitude of this sink using direct
uptake measurements. Unfortunately, if the management alternative being
investigated affects the supply of particulate organic material to the
.sediment then the use of the existing sediment oxygen demand (SOD) for
dissolved oxygen projections may be in error. Examples include the oxy-
gen consequences of phosphorus loading reductions where algal carbon
decay in the sediment is a principle DO sink. In general the evaluation
of the control of point and non-point sources which contribute to, or
affect the flux of particulate organic matter to the sediments require a
model of sediment oxygen demand.
At first glance, this task appears to be quite complicated since
both aerobic «ind anaerobic reactions in sediments are involved. Biolog-
ically mediated reactions (e.g. methane production and consumption) as
well as inorganic reactions (e.g., sulfide oxidation) are all candidates
for consideration. Layered models which distinguish zones of oxygen con-
sumption and nitrate reduction (Vanderborght and Billen, 1975; Jahnke et
al., 1982) and a three layer model including methane formation (Klapwijk
and Snodgrass, 1983) have been proposed. The many conceivable additional
ronctions involving vnrious electron donor and acceptor pairs are the
significant complicating feature since their explicit inclusion seems
unavoidable.
It is the purpose of this paper to present a model of sediment oxy-
gen demand which attempts to solve the problem in a fashion which ulti-
mately dispenses with the complexity and relates sediment oxygen demand
-------
to the flux of the oxygen equivalents of all reduced substances in the
interstitial water without specific regard to their identity. In fact,
since a simple aggregate measure of the oxygen equivalents is available
- chemical oxygen demand - a conclusion implicit in the model is that
SOD can be determined by measuring the COD flux directly, or by
measuring the interstitial water COD profile and measuring or estimating
sediment-water mass transfer or diffusion coefficient. Alternately, SOD
can be calculated from a mass balance model of oxygen equivalents in the
sediment itself. A calculation of the detailed redox chemistry of the
sediment interstitial water is also possible and may be required for a
detailed understanding of the situation. However, the COD flux methods
may suffice in roost cases.
The justification for this procedure is based upon two assumptions:
(1) that the redox chemistry is at, or reasonably near, thermodynamic
equilibrium which leads to the conclusion that COD flux and sediment oxy-
gen demand are identical; (2) that the transport coefficients of the dis-
solved chemical species involved are independent of their identity which
dispenses with the requirement that detailed redox chemistry be computed.
If these assumptions are practical approximations, then sediment oxygen
demand (the flux of dissolved oxygen from the overlying water to the sed-
iment) is equal to the upward flux of dissolved oxygen equivalents, i.e.,
dissolved COD, from the sediment. The latter is computed from the decay
rate of sedimentary particulate organic COD in the sediment, and the ver-
tical transport mechanisms of diffusion and sedimentation. The demon-
stration of this fact requires that a model of sediment - interstitial
water interactions and transport be formulated and analyzed.
-------
Structure of the Analysis.
The model presented below is based on a number of somewhat different
approaches to the analysis of sediment behavior and redox reactions. The
first are exemplified by the mass balance models of observed increases
or decreases in interstitial water concentrations of substances which are
essentially unreactive or, as in the case of radicmuclides, have known
decay rates (Goldberg and Koide, 1963, Lerman and Taniguchi, 1972). Ana-
logous formulations are available for bacterially_ mediated reactions
which can be assumed to follow simple zero or first order kinetics
(Berner, 1974, 1980). These latter are often called diagenetic models
and are based on the principle of mass conservation expressed as a mass
balance equation. They account for the mass fluxes of diffusion due to
molecular and mechanical mixing of the intersitital waters, of advection
due to sedimentation and compaction, and the effects of the particulate
organic matter decomposition reactions. Typically these models are
applied to a single constituent of interest, e.g. ammonia. For multiple
constituents a conceptual simplification is available if the reactions
are thought of as being driven by the decay of organic matter of a fixed
stoichiometry (Richards, 1965). This is also a mass balance approach
since equivalents of each electron acceptor are treated similarly and the
quantities of substances utilized or produced are in stoichiometric
ratios. Both of these approaches utilize the fundamental concept of mass
balance expressed either as an algebraic stoichiometric relation or as a
mass balance differential equation.
The second principle of importance is that of chemical equilibrium,
in particular the observation that interstitial waters are in, or ap-
proach, chemical equilibrium. For certain inorganic dissolved species
-------
and certain redox reactions this is a well known approximation that has
been tested by a number of investigators (e.g. Garrells and Christ,
1965; Kramer, 1964; Thorstenson, 1970). The evidence comes from evalu-
ating the mass action equations. Mass balance is not usually a factor
in these evaluations. While it has often been pointed out that overall
and complete thermodynamic equilibrium is never attained for all species
in all settings it is also clear that certain reactions occur so quickly
that they are virtually in equilibrium over the t_ime scale of sediment
mass transport and diagenetic reactions. Thus, while not as universally
applicable as the principle of mass balance, it is nonetheless a useful
approximation in certain contexts.
The model of sediment behavior presented below is a synthesis of
these ideas. The equations of mass balance and chemical equilibrium are
combined into a single structure for the analysis of sediment intersti-
tial water concentrations. Since bacterially mediated kinetics are in
fact responsible for many of the redox reactions which affect intersti-
tial water concentrations, it might seem at first glance that the prin-
ciple of chemical equilibrium is of little value in this context. How-
ever, it has been pointed out that the thermodynamically predicted
sequence of oxidation-reductions is commonly observed in nature as oxi-
dation of organic material occurs (Stumrn, 1966) so that this appears to
be a reasonable simplification of the complex reaction kinetics actually
taking place. The assumption is also quite convenient since equilibrium
calculations are independent of the reaction pathways and no detailed
specification of the kinetics are necessary. Only the thermodynamic con-
stants of the species of interest are required If detailed species con-
centrations distributions are to be computed.
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If reactions are known not to occur for kinetic reasons even if they
are theroodynanically favored, tbey can be prevented from occurring in
the equilibrium calculation as well. Thus, a distinction is made between
fast, slow, and prohibited reactions. Fast reactions are those which are
assumed to be in (metastable) thermodynamlc equilibrium over the time
scale of the analysis. Slow reactions are those for which the kinetics
are important and must be specified. Prohibited reactions are those
which are thought not to occur at all during the time scale of the analy-
sis even if they are thermodynamically favored. The nitrogen system is
the most important example for which thermodynamic equilibrium is not
useful. If it happens that most reactions are of the fast type then the
approach presented below is a major simplification since the number of
parameters required to specify the behavior of the species of interest
is substantially reduced and a comprehensive analysis is possible.
The major complicating feature of such an analysis is that the chem-
ical species in the interstitial waters that are affected by the fast
reactions are also subject to transport via diffusion and other mechan-
isms. Hence mass transport and rapid reactions are both simultaneously
affecting concentrations. As various species are transported the reac-
tions adjust in complex ways to maintain equilibria. The technique pre-
sented below for analyzing coupled mass transport with rapid reversible
reaction kinetics is based on a transformation of the species mass bal-
ance equations into a set of smaller and simpler equations. These equa-
tions do not explicitly contain the sources and sinks due to the fast
reversible kinetic reactions that cause the analytical and computational
difficulties. As a result they can then be solved more directly together
with the mass action equations for which there are available compute-
-------
tional codes (e.g., Deland, 1967; Morel and Morgan, 1972.)
Conservation of Mass Equations.
Consider the simplest setting, a one-dimensional vertical analysis
of N chemical species with names, A , at temporal steady state. Let D
81 i
be the diffusion coefficient porosity product of species A and let w
be the corrected (Imboden, 1975) advective velocity of A , the velocity
induced by the sedimentation of mass relative to a coordinate system
fixed with respect to the sediment surface, corrected for compaction, and
assume they are constants in depth. Suppose that there exists N fast
reversible chemical reactions involving the species A . The rate at
which A is produced by reaction j is v .R , where R is the difference
between the backward and forward reaction rates of the j fast rever-
sible reaction and v.. is the reaction stoichiometry. Let S. be the net
source of A due to other reactions which are occurring at slow rates
and, therefore, not explicitly included in the fast reversible reaction
set. For this situation the conservation of mass equations for the con-
centration of each species, [A.], are:
2
d[A ] d[A ] N
dz j = l
The difficulty with solving these coupled nonlinear equations directly
is that the forward and backward reaction rates for each fast reaction,
R , correspond to very short time scales. Further, all that is usually
known for these fact reactions is the ratio of the forward to backward
reaction rate, i.e., the equilibrium constant. Finally, there are N
S
coupled nonlinear equations to be solved simultaneously, which can be a
substantial computational burden for a realistic sediment calculation.
-------
It has been suggested (Shapiro, 1962; Galant et al.; 1973) that var-
ious transformations be employed to make eqs. (1) more tractable. The
crux of the idea is to eliminate the terms I. v^^^ which cause the dif-
ficulty and replace eqs. (1) with an alternate set of equations. The
following fact (Di Toro, 1976) leads to a convenient choice for the
transformation: Let B., j-1,..., N be the names of N components and
let a,, be the quantity of component B in species A., i.e. its stoichi-
ometry in terms of the components. The components are the building
blocks of the species. For example, the constituent atoms can be used
as components. Then, for a set of component conserving reactions the
formula matrix with elements a,. is orthogonal to the reaction matrix
with elements v , i.e.:
N
lS v^ an • ° k-l.....N ; J-1.....H, (2)
k*l
The physical fact embodied in these equations is that any reasonable
reaction stolchiometry must conserve the component concentrations. This
is apparent if the components that make up the species are thought of as
the neutral atoms, together with electrons to provide the appropriate
charges. All physically realistic (non-nuclear) reactions must conserve
atoms and charge, and eq. (2) is just a statement of that fact. It is
also apparent that the specific choice of components is not important
since any consistent choice is a linear combination of neutral atoms and
electrons and, therefore, must also be conserved. This fact suggests
that the conservation equations be transformed by multiplying eqs. (1)
by the transpose of the formula matrix yielding:
N 2 N N N
Is (-D i- + * i- ) a [A ] - ES aS + Er R ES a v (3)
i-1 dz IK i ±-1 IK i j.! 3 j.j IK 31
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But the orthogonality relation, eq. (2), implies that the terns involv-
ing R are zero so that eq. (3) becomes:
N d2[Aj N d[A.] N
£ ''"D< IP" * £ "'•'" -**- * i-I '"< ''
This is the fundamental simplification which makes the analysis tract-
able. The transformed equations are no longer functions of the fast
reversible reactions. They are influenced only by the species mass
transport coefficients and the slow reactions, S^ -
It is clear from the derivation of the transformed equations that
the simplifications introduced, namely temporal steady state and spa-
tially invariant transport coefficients, do not restrict the applicabil-
ity of the transformation technique. The method is directly applicable
to more general equations which consider temporarily and spatially vari-
able parameters.
Species Independent Transport
If D and w are not species dependent, the summations I. aijttAil
in the left-hand side of the above equation become the component
concentrations, [B ], by the definition of a . Therefore, the transfor-
mation yields conservation of mass equations for the N component concen-
trations:
d2[B 1 d[B 1 N
-I) -i- + w * - Is n..S. k-1 N (5)
.2 dz , IK 1 c
dz i«l
These equations are independent of the fast reversible reactions, which
can now be assumed to be at equilibrium. Once the spatial distribution
of the N components, B. , are calculated from eq. (5) the N -N equilib-
-------
riuro mass action equations for A., can be used in conjunction with the
N stoichionetric algebraic component mass balance equations to solve
for the concentrations of the N species, [A ], at any depth of interest,
independent of any other depth, a considerably simplified computational
task. Thus the components can be treated in exactly the same way as any
other variable in simple mass transport calculation, without regard to
the reversible reactions, so long as the mass transport coefficients are
independent of the species.
For precipitation-dissolution reactions which may be of importance
in sediments this simplification amounts to assuming that the solid
phase is subject to the same mass transport as the interstitial water,
which is clearly not the case. For species-dependent mass transport
eqs. (3) must be addressed directly and a method for their numerical
solution, which is a good deal less elaborate than what would be required
for eqs. (1), is available (Di Toro, 1980).
Sediment Oxygen Demand.
To apply these general principles to the modeling of sediment oxygen
demand it is important to realize that the assumption of species indepen-
dent transport for the fast reactants is all that is required for each
component mass balance equation (5) to be independent of the other compo-
nent equations and the detailed species distribution. Therefore we need
only to be concerned with the oxygen consuming component of the sediment
chemistry.
Consider the following model formulation. Assume that the principle
rate limiting kinetic reaction occurring in sediments is the bacterial
conversion or, as it its termed, the diagenesis of partlculate sedimen-
-------
tary organic material, C H.O N(s), into ao available reactive fora,
C H.O N(aq), after which it reacts reversibly and rapidly with all other
dissolved species in the interstitial water. In order that species-inde-
pendent transport is a reasonable assumption the possibility of precipi-
tation or dissolution of solid phase chemical species e.g. Fe(OH).(s),
is specifically excluded as is the possibility of gas phase formation
(bubbles). Thus the model includes the possibility of aqueous phase
redox reactions but excludes the possibility of other phase formations
and dissolutions which would have different mass transport coefficients.
In fact, as shown subsequently, even in the presence of a distinct gas
phase, this simplified approach is useful. The modifications required
for consideration of solid phase interactions are discussed below.
Schematically the reaction sequence is:
-»• C^CMUaq) * Aj «-...«- ^ (6)
where A.,..., \, are the rapidly reacting dissolved species being con-
s
sidered. The initial rate limiting reaction controls the rate of the
entire reaction set since it is assumed that all other reactions occur
rapidly.
The key to a comprehensible result is the intelligent choice of the
components which Isolates oxygen in oxic conditions. A number of possi-
bilities are:
C H.O N(s) = a[C] + b[H] + cfO] +[N] (7)
a b c
the neutral atoms, or the more conventional choice for chemical equilib-
rium calculations:
CaHb°cN(s) m*lC02] +61H+1 + *le~} + 6 1H2°J
However, the best choice is simply:
10
-------
*
CaVcN(s) " a[C02] * BI°2] * 6[H201 + [NH3]
so Chat particulate organic matter is thought of as being composed of the
*
components: oxidized carbon, C02, the oxygen required to oxidize the car-
*
bon (the COD), 0-> an<* ammonia. That is:
CflHbOcN(s) = (CO*)Q(0*)e(NH*) (10)
The superscript is used to denote components rather than the species
CO-(aq) and 0 (aq). The production or consumption of H^O is ignored
since it is present in excess. If species independent transport is a
reasonable assumption then each component distribution is independent
of each other and each component can be considered separately. This is
the principle simplification.
Since oxygen consumption is our primary concern, consider the dia-
genetic decay of particulate COD via a first order reaction for a purely
advective sediment model which is the conventional formulation for sta-
tionary sediments in lakes and estuaries (Berner, 1980). The mass bal-
ance equation for this situation is:
. _K[PCOD] (11)
dz
so that the vertical distribution of particulate COD in the sediment is:
[PCODKz) , e-Kz/w
w
where Jp.-.^ is the particulate COD flux from the overlying water to the
i CiUL)
sediment surface. The source of oxygen equivalents to the intersitital
wnter is -K[COD](z), the negative sign corresponding to the convention
that positive COD is oxygen consumed so that positive COD produces nega-
tive oxygen equivalents. Thus, the oxygen equivalent component equation
is:
11
-------
d2[0*I
»
dz
(13)
whose solution is:
_ e-Kz/w)
where [0_] is the oxygen component concentration at z=o.
The computation of the surface flux of oxygen equivalents follows
from its definition J * * -D d[02]/dz and applying 'this to eq. (14)
yields:
2
where n * KD/w . The fraction n/(l+n) is that portion of JpCOD which is
mineralized and returned to the sediment-water interface. The remainder
is buried via sedimentation of interstitial water as shown subsequently.
If the particulate COD is composed of various fractions with differ
ent diagenetic reaction rates, K , then by superposition of solutions:
2
where p * KD/w . For example, if a portion of the particulate COD flux
is the labile fraction of algal carbon with a relatively rapid reaction
rate, then n » 1 and all the PCOD flux returns as oxygen equivalents
flux. Refractory particulate COD on the other hand may react so slowly
that n < 1 and only a portion is returned. The remainder is buried
faster than the reaction can decompose it and diffusion transport it to
the sediment-water interface. Table 1 presents examples of the fraction
of organic matter that actually reacts diagenetically , the observed
12
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TABLE 1. DECOMPOSABLE FRACTION AND-SEDIMENT REACTION RATES
Component
COD
COD
Organic N
Organic C
Organic N
Organic C
Fraction
Reacted
(a}
0.13-0.25V '
0.13-0.48(a)
0.41
0.67
0.52{C)
0.45(C)
Reaction Rate
(yr"1)
0.55-1.9
2.4-3.6
0.60(b)
0.013
0.0172
0.029
0.196
n Sediment
English River Muds
Sewage Solids and
Inert Material
L.I. Sound (Foam Site)
3.9
52.0 Lake Greifensee
390 Lake Erie Central Basin
2700 "
Reference
Fair et al., 1941
it
Berner, 1980
rt
Di Toro and
Guerriero, in press
(a)
(b)
(c)
Assuming 0.5 kgC/kg VSS, 2.67 kg02/kgC
The larger value in bioturbation zone.
<
Considering refractory and unreactive fractions only. Labile fraction mineralizes rapidly in the first surface
layer.
-------
diagenetic reaction rates and n. The reacted fraction corresponds to
the difference between the initial (t-o for batch reaction experiments)
or surface (z-o for the analysis of sediment core data) and final (t-"»,
z»w/k) organic matter concentrations. The fact that unreacted sedimen-
tary organic matter is found at depth indicates that only a fraction of
PCOD reacts diagenetically. Thus in eq. (15) and subsequently, JpcOD
refers to the flux of labile and diagenetically reactive PCOD to the sed-
iment.
The importance of the correction T)/(l+n) can be estimated from the
examples listed. For the lake examples the correction is ^ 1. For
coastal and pelagic ocean sediments, Toth and Lerman (1977) have observed
2 2
a correlation between K and w for ammonia: K/w *• 0.01 yr/cm . For an
ammonia diffusivity in sediments of ^ 10~ cm /sec (Li and Gregory,
1974), n
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OXYGEN EQUIVALENTS MODEL OF SOD
I
[PCOD]
SEDIMENT - WATER
INTERFACE
SEDIMENTATION
PCOD —+~ - 02
DIAGENESIS
REACTION
I
SEDIMENTATION
&
DIFFUSION
:ig. 1 Schematic representation of the dlagenetic oxygen equivalents
model of SOD.
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It remains only to argue that the flux of oxygen equivalents to the
sediment is equal to the sediment oxygen demand itself. Consider the
sediment-water interface with aerobic overlying water. At the surface
there exists a region, however small, which is aerobic. For the choice
of components CO^ and 0?, the thermodynamic equilibrium for a region
where dissolved oxygen exists is that all carbon will exist as inorganic
carbon, C0? - ZCO?(aq), and that all oxygen equivalents are dissolved
oxygen itself since no other oxic species of oxygen equivalents exists
*
for the C-H-0 system. The reason for the choice of components C0_ and
0? is that the thermodynamic equilibrium solution for the case that
09(aq) > 0 can be obtained by inspection without any numerical calcula-
tions. It is simply that (>2(aq) « 02. In general the idea is to choose
the components for all the species involved in redox reactions at the
oxidation states which are known to be present in oxic conditions. Thus,
_ £ Oo. if
SOT - SO,, Fe(III) = Fe(III) etc. are chosen as components. Species
4 4
in the sulfur system would be represented as:
SO" = SO* (17)
4 4
HS~ = SO* + 1 H+ - 2 0* (18)
4 2.
the carbon-hydrogen-oxygen system as:
02(aq) - 0* (19)
C02(aq) - CO* (20)
CH4(aq) = CO* + 2 H20* - 2 0* (21)
the Iron system ns:
Fc3* = Fe*(ll]) (22)
Fe2 + = Fe(in)* - H* + 1/2 ^0* - 1/4 0* (23)
and so on. Note that for this choice of components the only species
that contains the component 0_ that is known to be present in signifi-
16
-------
cant concentrations in oxic conditions is 0 (aq) itself. Thus the molar
concentration of 02 must be accounted for by CL(aq) so that [0»] =
[02(aq)]. It follows that their gradients are equal in oxic conditions,
d[02]/dz = d[02(aq)]/dz. Therefore SOD, which is the flux of 0_(aq) at
the sediment-water Interface, z=o, is:
d[0 (aq)]
SOD = - D
dz
z=o " J02(aq) " J0* = TT1T JPCOD (24)
Note that the argument that JD . .= J * requires that thermodynaroic
equilibrium is achieved where 0 (aq) > 0. This is equivalent to assuming
that all reduced compounds are completely oxidized in the aerobic zone
at or near the sediment-water interface.
This may not be entirely the case so that a modification of the
form:
particulate COD •*• soluble COD •*• oxygen equivalents (25)
Kl K2
where KI is the diagenetic reaction rate and K is a faster, but still
finite, reaction rate which considers the soluble COD as a slow reactant
which can diffuse to the interface and escape as an unoxidized flux of
COD as well as being converted to oxygen equivalents. Some evidence that
this is the case is suggested by experimental measurements summarized in
Table 2. Aerobic dissolved COD fluxes have been measured together with
anaerobic COD fluxes and SOD. It is important to note that the differ-
ence JQ* (02(aq) = 0) - JQ* (0 (aq) > 0) equals the measured SOD, con-
firming the model prediction that the reacted COD flux under aerobic con-
ditions equals the SOD. An empirical correction to account for incom-
plete reaction is to introduce a fraction, f *, of the anaerobic COD flux
which actually reacts aerobically so that:
17
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TABLE 2. COMPARISON OF OBSERVED COD FLUX AND SOD
Anaerobic COD
flux
(g02/n.2-d)
10.6-11.9
0.408
Aerobic COD
flux
(g02/m2-d)
3.7-4.2
0.092
Difference
(g02/m2-d)
6.4-8.2
0.316
Observed SOD
(g02/tn2-d)
7.3
0.292
Reference
Fillos & Molof (1972)
Lauria & Goodman (1983)
oo
-------
SOD - f0* JQ* (26)
From the data in table 2, fQ* ^ 0.65 - 0.80. Fig. 2 illustrates the
model framework with f * - 1 and n large for the sake of clarity.
The upward flux of dissolved COD is equal to the downward flux of
*
oxygen equivalents by the definition of 0^. In the aerobic zone the
oxidation is complete assuming f * = 1 and thermodynamic equilibrium pre-
vails. All the carbon exists as inorganic carbon and the dissolved oxy-
*
gen concentration equals 0_ so that the downward flux of dissolved oxygen
is equal to the upward flux of COD.
The specific geometric and transport model used for the sediment is
not critical. For example a well mixed sediment layer of depth, H, may
b'e more appropriate. Also the sequence of particulate COD oxidation need
not be restricted to a single first order reaction. For example if sed-
imenting algal and detrital carbon are the sources of particulate COD,
then both labile, PCOD.., and refractory, PCOD , components can be consid-
ered. The reaction sequence is:
K*
PCOD, •»• f PCOD - (1 - f ) 0-
r T r 2
PCODr
(27)
r *
where f is the refractory PCOD component of the algal carbon. The mass
balance equations are analogous to eq. (A) and at steady state the oxygen
equivalents flux becomes (Di Toro and Connolly, 1980):
JPCOD JPCOD f
Jn* - - 5 - - - + - 5 - (1 - f + - - — ) (28)
__
where D1 is the effective interstitial diffusion rate for the well mixed
layer. In fact for this type of model the parameter D'/H, a mass trans-
19
-------
FLUXES OF INTERSTITIAL WATER COD, OXYGEN EQUIVALENTS,
AND DISSOLVED OXYGEN
I [o2<«q)l
N>
O
OD(aq)
O
AEROBIC LAYER , Oj > O
Oj = 02(aq)
COj=£C02(aq)
ANAEROBIC LAYER , o£< O
O? = - COD(aq)
COj = Z C02(aq) + TOC(aq)
Fig. 2 Equilibrium thermodynamic distributions ci carbon and oxygen
components in the ncrnbic nnd rin.terobic layer?.
-------
fer coefficient is the more fundamental parameter group. The dimension-
less group vH/D* controls the rate of burial of PCOD relative to the
upward diffusion of 0.. The residence time decay product of PCOD and
PCOD respectively in the active layer are w/K H and w/K H. If these
groups are all small relative to one then J * » JprnD * JPCOD an(* al*
the PCOD flux to the sediment returns as SOD. This single layer model
in its time variable form has been applied as a component in oxygen bal-
ance calculation for Lake Erie (Di Toro and Connolly, 1980) and in the
Potomac Estuary (Thomann and Fitzpatrick, 1983).
Relationship of SOD to Sediment Ammonia Flux
A consequence of the diagenetic reaction which liberates negative
oxygen equivalents to the interstitial water is that the nitrogeneous
component of the organic matter is also released. If it is assumed that
(1) the fraction of sediment COD and nitrogen that diagenetically reacts
is constant for all sediments, (2) that interstitial water COD and
ammonia are transported to the sediment-water interface without reactions
and that species-independent transport obtains, (3) that all the COD oxi-
dizes (f * = 1) and no ammonia oxidizes, then one would expect that the
°2
ratio of SOD to ammonia flux should be a constant ratio. Fig. 3 presents
simultaneous measurements from field observations and laboratory experi-
ments for various sediments. If the Redfield stoichiometry (Redfield et
al., 1963) was representative of the reactive portion of organic matter
then the ratio should be 15 gO /gN. The data indicate a range of from
15-30 gO^/gN for most data and a suggestion that at higher SOD fluxes (>
2
2gO /m -d) only a fraction (f * *> 1/2) of the COD flux is actually oxi-
2
dized. The higher ratio suggests that a portion of the ammonia flux to
21
-------
STOICHIOMETRIC FLUX RELATIONSHIP
(DIRECT MEASUREMENTS)
10.0
CVI
' 1.0 -
o
o>
Z
UJ
5
UJ
>
o
H-
UL
z
lit
o
>•
X
o
N
0.1 —
0.01
0.001
FIELD DATA
D POTOMAC ESTUARY (Callender.'82)
+ SAQINAW RIVER (Chiaro/80)
A NARRAGANSETT BAY (Hale.'SO)
0 BUZZARDS BAY (Rowe/75)
t> EEL POND (Rowe.'75)
x E. PACIFIC OCEAN (Smith/79)
O CHOPTANK RIVER (Smith/83)
V EMS - DOLLARD ESTUARY (van der Loeff/(
LAB DATA
• Fillos & Molof (1972)
• Fillos & Swanson (1975)
I I
0.01
0.1
AMMONIA FLUX FROM SEDIMENT (gN/m2- d)
Fig. 3 Observed relationship between SOD and ammonia flux from
sediments. Data are from paired observations.
22
-------
Che sediment water interface is oxidized to nitrate. This would both
reduce the ammonia flux and increase the SOD, producing a higher ratio.
This possibility is discussed subsequently. Considering the variation
of observed COD/C and C/N ratios of particulate sediment organic matter
and the lack of Interstitial water COD/NH.-N data which would be neces-
A
sary to more rigorously test this simple stoichiometric relationship,
the comparison supports the diagenetic oxygen equivalents model.
The Effect of Solid Phase Reactions
The validity of the eq. (26) which relates the SOD to the flux of
particulate COD to the sediment-water interface depends directly on the
applicability of the assumption of species independent transport since
it is this assumption that decouples the component equations from each
*
other and allows the mass balance of 0. to be independent of the other
* * *
components: CO-, SO, , Fe(III) , etc. Species independent transport is
approximately true for dissolved species - ionic diffusion coefficients
in sediments differ by approximately a factor of two (Li and Gregory,
1974) - but it is surely not true for solid phase species. Thus a cor-
rection is required for the mass balance equations.
Instead of a detailed analysis of the species-dependent transport
equations, consider the mass balance that results from the situation
illustrated in fig. 4. The flux of organic PCOD to the sediment is bal-
anced by the flux of oxygen equivalents to the sediment and the loss via
burial. To see this in terms of oxygen equivalents consider eq. (15) in
the form:
23
-------
EFFECT OF SOLID PHASE FORMATION
K>
JpCOD
PCOD
>
DISSOLVED Oj
\
SOLID PHASE Oj
X
DIAGENESIS //
/
.WITHOUTOjU)
WITH O% (8)
FORMATION
1 W Oj(aq)
1 W 0^(8)
Fig. 4 Mass balance analysis of reduced solid phase formation.
-------
Jo* " JPCOD " TT~n~ JPCOD (29)
From eq. (14) the negative term on the right hand side of this equation
is: w{[02] - [O^^} where [C^]^
at large depth (Kz/w » 3). Thus:
is: w{[02] - [O^^} where [C^]^ is the oxygen equivalents concentration
w{t02- (°2V (30>
Note that eq. (14) indicates that the oxygen equivalents concentration
[0^ would either be less than (if JpCOD > 0) or equal to [0*]Q (if
0) so that the advective transport term is always negative or
zero (i.e. J * < JpCOD) which is physically reasonable since some dis-
solved COD is buried with the interstitial water and does not exert an
SOD. When reduced solid phases form, e.g. Fe(OH) , FeS, etc., the oxygen
* *
equivalents are in both dissolved, 0 (aq) and solid phases, 0 (s). Both
of these are buried via sedimentation so that:
J0* - JPCOD * w{t°2(aq>l. * l°2(s>]. - l°Jl0>
*
The additional flux, w[0_(s)]oo, of solid phase oxygen equivalents reduces
J * since [O^^)]^ is a negative number. From a practical point of view,
the term w[00] , the entrainment flux of overlying water, is usually neg-
2(aq)]Q
3 * 2
ligible: e.g. w < 10 cm/yr, [0(aq)] < 10 g/m so that w[0^ < l 8/'ni ~
-yr, and eq. ( 31) becomes
J0; 1 JPCOD + W[°2]» (32)
*
where [0-]^ is the bulk oxygen equivalents concentration of the sediment
(aqueous and inorganic solid phase). Thus the proper correction is to
25
-------
decrement (add a negative number to) J * to account for the loss due to
burial of the reduced solid phases which fora. Based upon the relation-
ship observed between ammonia flux and SOD (fig. 3) this correction is
probably not significant. A calculation for Lake Erie, presented subse-
quently, also supports this conclusion. With the exception of this cor-
rection the formation of various reduced solid phases has no other effect
on the steady state oxygen-equivalents flux and, therefore, the SOD since
ultimately the only source of oxygen equivalents ±s via the sediment-
water interface.
The Effect of Ammonia Production
The production of elevated interstitial water concentrations of
ammonia is perhaps the most commonly observed consequence of the diagen-
esis reaction. The examples which follow illustrate the phenomena as
does the relationship between ammonia flux and SOD (fig. 3). It is con-
ventional to assume that ammonia is conservative in the anaerobic zone
and computations based on this assumption are representative of the
observations (Berner, 1980).
With regard to sediment oxygen demand, it is possible that ammonia
in the aerobic zone can nitrify to a significant extent and consume oxy-
gen as a consequence. However if the aerobic layer is thin and the over-
lying water DO is depressed then nitrification is unlikely since nitrify-
ing bacteria require ^ 1-2 mg 0 /£ for nitrification.
Tf nitrification is occurring in the sediment then it is also pos-
sible that a portion of the nitrate produced diffuses into the anaerobic
region where it is denitrified. The overall reaction in that case would
be
26
-------
I NH3 + i °2 * i N2 * I H2° (33)
so that the stoichiometric consumption ratio is 1.7 g02/g NH_-N instead
of 4.57 g02/gNH -N for nitrification. Typical carbon/nitrogen ratios of
sediments ^ 10 so that even for no denitrification the ratio of carbon
to nitrogen assiciated SOD would be ^ (10)(2.67)7(4.57)(1) «= 5.8 that is
^ 86% of the total SOD is derived from carbon associated diagenesis.
With denitrification considered the percentage is higher. Hence it is
possible that ^ 10-30% additional SOD could be generated by the ammonia
and nitrification. However for most cases the thin aerobic layer and
low DO concentrations preclude the reaction and ammonia escapes to the
overlying water without exerting an SOD.
The Effect of Nitrate flux to the Sediment
Nitrate in the overlying water is subject to the same diffusive flux
as is O.(aq) so that denitrification in the sediment clearly occurs. Un-
like the other electron acceptors considered above, however, its function
is different. Nitrate reduction is not a reversible process and, there-
fore, cannot be included in the fast reaction set. It must be considered
explicitly. However the rate of denitrification is most probably rapid
relative to the diagenesis rates so that an explicit slow reactant
approach with its attendant reaction rate is not necessary. Rather it
is assumed that all nitrate delivered to the anaerobic zone is rapidly
reduced. Since the nitrogen gas produced at this location is a non-
reversible endproduct, its formation is a permanent sink of dissolved COD
and, therefore, a constant source of oxygen equivalents.
27
-------
As a simple approximation, assume that the depth of deoitrif ication,
L, is at 0- - 0 the aerobic-anaerobic transition depth. At this depth
nitrate is rapidly consumed so that [NO~](L) - 0. The situation is
illustrated in fig. 5. The flux of nitrate to the sedimentwater inter-
face is:
d[NO,] D[NO ]
where [N0~] is the overlying water nitrate concentration. The oxygen
equivalents mass balance equation now has an additional term due to the
source of oxygen equivalents provided by denitrif ication:
' N°3 * T N2 * H+ + I V * t °2 (35)
Thus:
d2[0*] d[0*] ,
-D— f ^-d^--fJpcoDe 7 +JNO/(Z-L) (36)
dz 3
where J' 6(z - L) is the delta function source of oxygen equivalents
3 5
at location L; J = • J . and J is 8*veo *>y e T ^ _ T«
J0* JPCOD 1 + T, JN03
In order to evaluate J* - D[NO_] /L the depth of zero nitrate concen-
NU- J O
J *
tratlon, L, is required. From the condition that 0- » 0 at z « L, eq.
28
-------
EFFECT OF DENTRIFICATION
10
SOURCES OF O2
-K [PCOD]
DIAGENESIS
DENTRIFICATION
POINT SOURCE
WITHOUT
NO3—»-N
Jo$
'
NITRATE DISTRIBUTION
WITH
N
Fig. 5 Framework for the analysis of the effect of overlying nitrate
reduction on SOD.
-------
(37) yields:
L . --. - - - (39)
n JPCOD
for the case that KL/w and wL/D « 1, corresponding to a snail aerobic
depth. Using this expression in eq. (34) and eq. (38) yields:
Thus the presence of nitrate as an irreversible source of oxygen equiva-
lents reduces the flux of 0_ to the sediment by the ratio: [O-(aq)] /
([02(aq)]Q + |- [NO~]Q). For example if 02(aq) - 1 mg/J, and N03-N = 0.1
mg/£ then the 'ratio is: 0.78.
It is disturbing to note that two sets of experiments designed to
test this effect (Edwards and Rolley, 1965; Andersen, 1978) both found
no significant reduction of SOD as overlying water nitrate concentration
increased (0-20 tngN/£) although increased nitrate flux to the sediment
was observed. These results are most puzzling. It may be that the
steady state assumptions used to obtain eq. (40) did not apply to the
experimental observation which may reflect transient conditions. Alter-
nately the presence of Increased nitrate flux to the sediment may
increase the rate at which diagenesis occurs so that temporarily at least
a greater supply of dissolved COD is available that just balances the
Increase in available oxygen equivalents from the nitrate flux. Again
this would reflect n transient phenomena. In any case experimental
investigations are required which are designed to evaluate the full oxy-
gen equivalents mass balance before eq. (40) is regarded as more than a
speculation. However the underlying fact that a nitrate flux to the sed-
30
-------
intent coupled with an N. flux from the sediment is a net source of 0.
(i.e. a net sink of dissolved COD) seems inescapable. Thus either more
dissolved COD is produced in the presence of nitrate, or eventually the
SOD decreases, since the mass balance of oxygen equivalents must apply
at steady state.
It is interesting to note that the oxygen equivalents viewpoint pre-
dicts that the presence of sulfate in the overlying water has no direct
effect, with the exception of the possibility of formation of solid phase
reduced sulfur compounds that are lost by burial. The reason is that sul-
fate reduction produces HS , S , etc. which are reversibly oxidizable.
Hence their formation do not provide sinks of dissolved COD which escape
oxidation in the aerobic zone as does N?. Rather, they function as
reversible intermediates that transport dissolved COD upward and oxygen
equivalents downward. Hence their absolute concentration is unimportant.
If they are present in only small amounts, other species are available
to perform the same function. This fact explains the observation that
SOD's in fresh and salt water are of the same order of magnitude (e.g.
fig. 3) whereas the overlying water sulfate concentrations differ by mul-
tiple orders of magnitude.
Application to Chesapeake Bay Sediments
The purpose of this example is to illustrate the utility of the for-
mulation that assumes species-independent transport and redox equilibrium
for analyzing sediment chemistry and to relate the results to SOD. The
data, from Chesapeake Bay sediments (Troup, 1974; Reeburgh, 1967), have
been averaged in order to obtain a representative set of observations
which are brondly characteristic of the anaerobic sediments of upper
31
-------
Chesapeake Bay. The solution of eq. (4) for each component, B, , is as
before:
lB.](z) - [B.1 + k ° (1 - e'**7*) k-1 H (41)
k k ° 1+KD/w2 C
where [B, ] are the component boundary concentration at z-o, the sedi-
K O
Bent-water Interface and a, is the stoicbionetrlc coefficients of com-
ponent k In C H-0 N(s), whose concentration is c at z-0. For components
a D c o
that are not part of the stolchiometry of the sedimentary organic natter,
their concentrations are constant in depth.
In order to apply this analysis to a specific setting it is neces-
sary to have estimates of the stoichiometry of sedimentary organic mat-
ter, a, , the rate of exponential decrease of the organic matter, K/w,
2
and the leading constant, c /(1+KD/w ) as required by eq. (41). For the
calculations presented below the latter two parameter groups are es-
timated from the observed ammonia profile. Ammonia Is assumed to be
conservative In the anaerobic portion of the sediment and therefore pro-
vides a useful tracer for this purpose. The concentrations of the re-
maining chemical components are established from observations at the
sediment-wflter interface.
The carbon and oxygen equivalents stoichiometry of the sedimentary
organic m.iterlal cnn best be obtained from direct measurements. For
this illustration an estimate is chosen in order to reproduce the ob-
served profiles of sulfate and total inorganic carbon. Table 3 lists
the components considered, the boundary concentrations at the sediment
surface, and the estimated stoichiometry. Fig. 6 illustrates the calcu-
lated depth distribution of the components used in the calculation. The
choice of components is arbitrary with the exception of the electron,
32
-------
Table 3
Components and Parameter Values for Chesapeake Bay Sediaeot Analysis
Component
B
Boundary
Concentration
Organic Mottter
Stoichio»etry(a)
co.
2
H20
K
Ar
H2S
H+
e
NH4*(C)
1.001
1060.1
1.0
0.01325
15.0
pH-7.«(b)
-123.0
0.0625
16.0
0.0
1.0
0.0
0.0
50.0
51.0
1.0
(a) Corresponds to C.-HL-.O-.N
lo DU J/
(b) Reid constant in the calculation consistent with observation
-------
CHESAPEAKE BAY SEDIMENTS
U)
COMPONENT CONCENTRATIONS , mM
-80 -40 0 40 80
120
Fig. 6 Computed depth distribution of component concentrations.
-------
which simplifies the chemical equilibrium calculations. With regard to
SOD, it can be seen that there must be a flux of electrons to the sedi-
ment-water interface where they react with the terminal e-acceptor,
02(aq) to produce SOD. This is just an alternate viewpoint since elec-
trons and oxygen equivalents are related via:
•--K°-»*-X
With the distribution of the components established it remains to compute
the concentrations of species which result at chemical equilibrium for
the reactions assumed to be taking place. The calculation is conven-
tional (DeLand, 1967); the two phases and species considered are listed
in Table 4 together with the appropriate mass action equilibrium con-
stants for the component stoichiometry as indicated. The gas phase forms
spontaneously if the sum of the partial pressures exceeds the hydrostatic
pressure at the depth of the sediment. The partial pressures of the
gases in this phase follow from the mass action and mass balance equa-
tions.
The results of the computation described above are shown in fig. 7.
*\
The ammonia data are used to estimate w/K = 30 cm. and a,c /(1+KD/w ) =
A.6 mM - NH . Both the ammonia and sulfate data reflect what appears to
be a relatively more rapid reaction rate in the top 10 cm. of the sedi-
ment, followed by a slower rate in the deeper sediment. For this illus-
tration the parameters have been chosen as an approximate average of the
rates. The observed magnitude of the sulfate decrease determines the
electron stoichiometric coefficient and, therefore, the electron to
nitrogen ratio of the sedimentary organic material. The carbon to nitro-
gen ratio is determined by fitting the observed total inorganic carbon
increase as shown in fig. 7c.
35
-------
CHESAPEAKE BAY SEDIMENTS
-10.0 10.0 30.0 50.0 70.0 90.0 11O.O
SEDIMENT DEPTH (cm)
2O.O
16.0
s
S 12.0
IK
o
09 8.0
4.0
0
*•*
1
\
\
4n
I
i\
\
\n T (wso?
L "
. -\, . ' J . I
-10.0 10.0 30.0 50.0 70.0
SEDIMENT DEPTH (cm)
90.0 110.0
75.0
60.0
^"%
E 45.0
*^
CM
§30.0
w
15J)
(c) TOTAL CO.
-10.0 10.0 30.0 50.0 70.0 00.0 110.0
SEDIMENT DEPTH (cm)
Fig. 7 Observed and computed interstitial water concentrations of
ammonia, sulfate, and total carbon dioxide profiles for K/w
30 cm., c /(1+KD/w ) - A.6 nM and C.,He-0.-N stoichiotoetry.
O ot ID Ju Jt
-------
Table 4. Species, Equilibrium Constants and Component Stoichiometry
Species
o2
co2
H+
KH4*(NH.
H20
OH~
HCO~
C°3
N0~-
CH4
Ar
NO-
N2
so;
HS~
H2S
s:
-la
AQUEOUS PHASE
204.9
3.17
-0.378
) -0.430
-0.0053
32.95
18.19
41.66
283.6
-49.68
6.515
216.9
122.2
98.8
18.88
2.58
50.84
K Component Stoichioroetry
GAS PHASE a
198.0 2 H20 -4 E- -4 H+
1.386 1 C02
1 H+
•f * (M
26.23 1 NH4 1 NH4 VD;(-1 H+)
3.59 1 H20
1 H20 -1 H+
1 C02 1 H20 -1 H+
1 C02 - 1 H20 -2 H+
1 NH.+ 3 H00 -8 E- -10 H+
4 2
-54.59 1 C02 8 H+ 8 E- -2 H2P
1.386 1 Ar
1 NH.+ 2 H-0 -8 H+ -6 E-
4 2
116.2 2 NH4+ -8 H+ -6 E-
1 H2S 4 H20 -10 H+ -8 E-
1 H2S -1 H+
0.0 1 H2S
1 H2S -2 H+
'J-' Fnr -•imiBniK: r>ha«o rnnrpntmr ions In mole/1 and eas ohase concentrations in mole
fractions.
Included in the calculation for ammonia conservative.
Temperature - 15°C, Ionic Strength - 0.39 and a total pressure of four atmos-
pheres. Calculated using the thermodynamic constants of Vagman et al (1968)
except as indicated, and corrected for sediment temperature assuming the tabu-
lated values of AH° and S° are constants. Ionic strength corrections are made
using the Davies modification of the Debye-Huckel activity coefficients (Stumm
and Morgan, 1970). Aqueous solubility for the dissolved gases are obtained from
Atkinson and Richards (1967) and Yammamoto et al (1976) and CH4» Harvey (1966)
for CO , and Weiss (1970) for N and Ar, corrected for the observed chloride con-
centration and temperature.
37
-------
With the stoichiotnetry fixed, the methane concentration and the be-
havior of the gas phase are determined by the equilibrium assumption and
the solubilities of the dissolved gases. The calculated and observed
dissolved methane, nitrogen and argon are shown in fig. 8. These data
provide independent support for the calculation since the free
parameters have been estimated using the other data.
A number of features are noteworthy. The calculation correctly re-
produces the observed rapid increase of methane commencing at a depth of
20 cm and reaching a plateau concentration of approximately 6mM at 50 cm
after which the increase is very gradual. The dissolved nitrogen and
argon concentrations are calculated to remain constant, consistent with
'the inert nature of argon and the absence of denitrification, until a
depth of approximately 40 cm, after which both concentrations decrease.
The nearly constant methane concentration and the decline in dissolved
nitrogen and argon results from the equilibrium between the interstitial
water concentrations and a gas phase which forms. As the partial pres-
sure of methane increases with depth due to the increasing quantity of
dissolved COD which has reacted, the sum of the partial pressures also
increases until it equals the total fluid pressure, at which point a gas
phase forms. This is calculated to occur at approximately 35 cm. As
depth increases more methane is formed, and, since the interstitial
waters are saturated with methane, the additional production causes the
gas phase to expand. The larger gas phase volume provides a greater
dilution volume for the nitrogen and argon gas. Thus the partial pres-
sures of both nitrogen and argon in the gas phase decrease and, conse-
quently, since the interstitial waters are assumed to be in equilibrium
38
-------
CHESAPEAKE BAY SEDIMENTS
1O.U
8.0
f 6.0
I 4.0
O
2.0
0
-1
(a) CH4 (aq)
/T^^^
./
0.0 10.0 30.0 50.0 70.O 90.0 110.0
SEDIMENT DEPTH (cm)
M
750
600
450
300
150
(b)
-10.0 10.0 30.0 50.0 70.0 00.0 110.0
SEDIMENT DEPTH (cm)
20.0
16.0
12.0
- 8.0
4.0
(c) ARGON
00
-10,0 10.0 30.0 50.0 70.0
SEDIMENT DEPTH (cm)
90.0 110.0
Fig. 8 Observed and computed interstitial water concentrations of
dissolved methane, nitrogen, and argon.
39
-------
with the partial pressures in the gas phase, their concentrations also
decrease.
However, the actual quantity of the decrease is different for N2 and
Ar due to their differing solubilities. The calculated and observed
N-/Ar ratio, shown in fig. 9a, illustrates this behavior which, as
pointed out by Reeburgh (1969, 1974), is evidence in support of the ex-
istence of gas bubbles.
The behavior of the ratio of total aqueous CO to annnonia, fig. 9b,
is similar although the underlying mechanism is different. To a depth
of 20 cm the ratio is constant at the stoichiometric ratio of the sed-
imentary organic matter. As methane starts to form the proportions of
ECO-(aq) and CH.(aq) produced is a result of the stoichiometry of the
organic material and this agreement with observation is further evidence
that the calculation is a consistent interpretation of the observed.
concentrations.
The lack of dissolved methane in the zone of sulfate reduction is a
direct consequence of the assumption that the fast reactions involving
these species are reversible and approximate thermodynamic equilibria.
In kinetic terms this is equivalent to assuming that there exists a set
of reactions which allows the oxidation of methane with sulfate as the
terminal electron acceptor. As has been pointed out (Barnes and
Goldberg, 1976; Reeburgh, 1976; Martens and Berner, 1977), this is the
only plausible explanation for these and similar observed profiles in the
presence of mass transport. That this reaction is rapid relative to the
slow sedimentary organic matter decay is an approximation that appears
to be reasonable. If the kinetics of this reaction were slower the
result would be methane diffusing into the zone of sulfate reduction.
-------
CHESAPEAKE BAY SEDIMENTS
(a)
r RATIO
40
35
k.
<
><30
25
20
•*
V
) MEAN
isTDT DEV.
DEPTH INTERVAL
-10. 10 30 50 70
SEDIMENT DEPTH (cm)
(b) ZCO2/NH4 RATIO
90
20
18
16
a
12
10
MEAN
_^_ STD7DEV.
DEPTH INTERVAL
h
110
-------
Although no interstitial water COD data are available, it is
straightforward to compute the SOD to be expected from this sediment.
Each component's vertical distribution is given by eq. (41) with the
appropriate leading stoichiometric coefficient. The differing surface
boundary conditions [B. ] do not affect the gradient and therefore the
iC O
flux. Thus:
ito*]
°2 4[e~] 1[NH*] NH3
where:
' ""3 " 1 * KD/W2
2 2
For D ^ 1.0 cm /d the result is an SOD of ^ 1.5 gO /m -day, an entirely
reasonable estuarine value.
The purpose of the preceding example is to illustrate the results
that can be obtained using a simple species-independent transport model
of sediment redox reactions. A more detailed analysis of these data is
available (Di Toro, 1980) which considers independent gas phase trans-
port. The important point is that the reaction sequence is reasonably
reproduced with a minimum of effort and that the computed SOD is within
the expected range of observation. Another application for which the
calculation of sediment oxygen demand is the primary focus is presented
below.
Application to Lake Erie
The original application of oxygen equivalents for the modeling of
sediment oxygen demand was to Lake Erie, particularly the Central Basin
42
-------
(Di Tore and Connolly, 1980). The concern was the hypolimnetic depletion
of dissolved oxygen due to algal respiration and sediment decomposition.
The original formulation was restricted to a 5 cm well-mixed active
layer. The computation reproduced the observed SOD, only if an addi-
tional flux of oxygen equivalents from the deeper sediment was included.
For the calculation presented below, the hypolimnetic water column and
the entire active sediment column is jointly considered. The model is
one dimensional vertically and at steady state in the sediment. The
water column calculations reflect the average conditions for t « 50 days
from the onset of stratification.
The nitrogen system transformations are implemented as slow kinetic
reactions with sequential first order reactions representing the reaction
pathway: Org-N -»• NH_ •* N0_ •*• N_. Ammonia decay is allowed only in the
water column and denitrification occurs only in the sediment. The carbon
and oxygen equivalents calculation are implemented using slow kinetics
for the diagenesis of the refractory portion and the faster mineraliza-
tion reaction of the labile and dissolved portion. The end products are
* *
the components C02 and 0_ which react to produce the species concentra-
tions as in the Chesapeake Bay example. No gas phase forms in this exam-
ple. The reaction rates and boundary conditions imposed at the thermo-
clinc are listed in Table 5.
The cnlibrjitlon procedures and the sources of data are described
elsewhere (Di Toro and Guerriero, in press). The purpose of this presen-
tation is to illustrate the results of the use of the oxygen equivalents
method. Fig. 10 presents the nitrogen cycle and fig. 11 presents the
carbon and oxygen results. Each plot illustrates the hypolimnetic con-
cen trations (top half) and sediment concentrations (bottom half) either
43
-------
TABLE 5
Lake Erie Nitrogen and Carbon Reaction Rates and Boundary Conditions
Nitrogen
Carbon
Particulate Unreactive
Particulate Refractory
Particulate Labile
Dissolved Organic
Ammonia
Nitrate
Nitrogen Gas
Chlorophyll (d)
Reaction
Rate (/day)
0.0
0.029 (/yr)
0.01
0.03
0.07(a)
2.0
-------
as a>g/kg of water or dry sediment for participates, or mg/£ of intersti-
tial water for dissolved species. When a discontinuity appears in the
computed curve it is due to a plotting scale change at the sediment-water
interface. Concentrations are continuous across the sediment-water
interface. Particulate slow reactants are settling and dispersing in
the water column and only sedimentating in the sediment. Dissolved slow
reactants and fast reactant components are dispersing in both the water
column and the interstitial water. The diagenetic reaction of particu-
late refractory organic matter and the more rapid mineralization of par-
* *
ticulate labile and dissolved organic matter produce NH,, CO- and ()„.
Ammonia builds up in the interstitial water and diffuses to the overlying
bypolimnion where it nitrifies to nitrate. N0~ in turn diffuses into the
*
sediment where it denitrifies to N2> and acts as a source of 0_. The
dissolved N. concentration is calculated and, as shown in fig. 10, is
less than observations, indicating that either more denitrification is
occurring or that it is occurring deeper in the sediment and N more is
retained as a result.
The carbon-oxygen computations, fig. 11, follow the same pattern.
The slight difference between observed and computed PCOD is due to the
assumed COD/Org C ratio of 2.67. The diagenetic reaction is responsible
for the gradients of POC and PCOD. The labile particulates mineralize
rapidly and are recycled in the first surface layer. Interstitial water
COD brackets the few available observations. ZC02 and CH interstitial
water distributions are reasonably reproduced as is the dissolved oxygen
2
and sulfate distribution. The computed SOD - 230 mg/tn -d is slightly
2
lower than the observed range: 280 - 350 mg02/m -d (see the summary in
Adams et al., 1982).
45
-------
LAKE ERIE CENTRAL BASIN -SUMMER 1970
PARTICULATE SPECIES
CHLOROPHYLL A-/AQ/I
15
PON -mg/l
o 0.3
c
CM
Q. o
UJ
O
*•* 2
u
o
CM
o
CJ
HYPOLIMNION
SEDIMENT-WATER
*+• INTERFACE
SEDIMENT
3000
mg/kg 3000
DISSOLVED SPECIES
DON -mg N/l AMMONIA - mg N/l
0.5
0.2
0 0.5
NITRATE-mg N/l
0 0.6
N2 -mg N/l
o 15
o
eg
o
e^
16
0 0.0 0
Fig. 10 Computed nnd observed hypolitnnion and sediment distributions
of nitrogen species.
46
-------
LAKE ERIE CENTRAL BASIN - SUMMER 1970
PARTICULATE SPECIES
POC - mg/kg PCOD - mg/kg
I 0.4 O.a 024
o
CM
CL o
UJ
O
*•% o
E -
o
^^
o
CM
O
ex
o
t^
6QflOO
COD - O2/l
40 80
35,000 0
DISSOLVED SPECIES
- mg C/l CH4- mg C/l
30 60 (
0.05
Q. o
UJ
O
*^ o
e -
o
«^
o
fi
o
cv
o
fj
100
75
20
DO - mg Oj>/l SULPHATE -mg
0. O
UJ
o
<-. o
E -
o
w
O
CM
15 0
r»
30
O
fj
Fig. 11
0 15 0 30
Computed and observed hypolimnioo and sediment distributions
of organic and Inorganic carbon species, oxygen and oxygen
equivalents, and sulphate.
47
-------
It is interesting to note that an attempt to quantify the individual
components of the flux of reduced species to the sediment-water interface
(Adams et al., 1982) accounted for only one-third of the measured SOD.
It is probable that missing SOD is due to mineralization of labile par-
ticulate components at the interface and the presence of other reduced
species. Unfortunately no COD concentrations or fluxes were measured.
It is interesting to note that the SOD predicted by eqs. (32) and
(40) is quite close to the value obtained numerically. The flux of PCOD
which reacts diagenetically is estimated from the hypolimnetic boundary
concentration and aqueous settling velocity (w = 0.3 m/d) so that w
a a
[POC] = 122 mgC/m -d and JpcOD * 326 mg02/m2-d. The correction for
burial is unimportant, n » 1, and for denitrification: [00] = 2 mg/&
2. Q
and [NO~]Q - 0.33 mg N/*, so that the correction is 0.68 and JQ* = 222
2 2
mgO^/m -d. Loss of solid phase oxygen equivalents can be estimated from
sediment ferrous iron concentration ^ 30 g Fe/kg so that 07(s) ^ -4.3
2
g 02/kg and w 02(s) = -19 mg 02/m -d for a deep sedimentation velocity
of w = 0.164 cm/yr. Thus the total SOD = 203 mg 02/m -d. The denitri-
ficfltion correction is significant while the solid phase burial is less
so.
Summary and Conclusions
The diagenetic oxygen equivalents model of SOD yield the following
relationships. At thernodynamic equilibrium the SOD (= J .) is equal
to the flux of oxygen equivalents to the sediment water interface, which
in turn is equal to the flux of dissolved COD from the interface.
J,
02(aq)
48
-------
The COD flux that actually oxidizes is the difference between the anaero-
bic and aerobic COD flux. To correct for this incomplete oxidation an
empirical fraction, f *, is introduced:
j « f * j * (45)
where
JCOD|O -o " Jcoo|o9>o
f o* . _1_ ?_ (46)
Available data indicate that f * ^ 0.65 - 0.80. The diagenetic equations
predict that, at steady state:
V2 • TT7 JPCOD (47)
where JT,rnn is the flux of diagenetically reactive particulate COD to
t L«wlJ
the sediment. Available data (Table 1) indicate that the reactive frac-
tion is ^ 0.5 for sediments. The correction due to burial of intersti-
tial water and reduced solid phase formation is
*[°i (48)
where [0_] is the oxygen equivalents of the interstitial water and re-
duced inorganic solid phase. Alternately if Jornr. is interpreted as the
total (reactive + diagenetically inert) particulate COD, and [O-l^ is the
total organic + inorganic bulk oxygen equivalents concentration then eq.
(48) is simply a flux balance of total oxygen equivalents.
Corrections for the oxidation of diagenetically produced ammonia are
likely to be small. Predicted effects of overlying water nitrate concen-
trations can be significant but are directly contradicted by experimental
evidence that suggests no effect.
49
-------
From the point of view of mechanisms, the principle factor is
the flux of dlagenetically reactive particulate COD to the sediment. For
steady state situations the reaction rate, diffusion coefficient and sed-
2
imentation velocity enter the calculation only as n • KD/w and the cor-
rection just accounts for burial of interstitial water COD by sedimenta-
tion. Thus except for rare cases when H is not large, the steady state
SOD is predicted to be Independent of diffusion and reaction.
This suggests that the observed increases of SOD due to increased
effects on stream velocity (Whittemore, 1983) or biological mixing of
sediments are transitory, time variable phenomena. The increased surface
mass transfer indeed causes an increased oxygen equivalents flux but this
increased flux exceeds the rate of production of dissolved COD and even-
tually the interstitial 0- distribution readjusts so that the SOD is
reduced to JL,rn . From a mass balance point of view this conclusion is
Jr L«UL/
inescapable. Increased surface mass transfer does not increase the
supply of PCOD to the sediment. Therefore the quantity of oxygen equiv-
alents available to be exerted as SOD is fixed and cannot exceed the
supply. The increased SOD observed at high stream velocities must be
counterbalanced by a lower SOD during more quiescent periods so that the
average SOD is equal to the average diagenetically reactive PCOD flux to
the sediment. Increases in SOD due to the presence of benthic fauna may
be attributable to a larger fraction of the total PCOD flux being reacted
but the upper limit is again the flux of PCOD to the sediment.
The effect of overlying water dissolved oxygen concentration on SOD
(e.g. Edwards? and Rolley, 1965) can also be interpreted in light of the
oxygen equivalents model. It is known that reducing overlying DO reduces
the measured SOD flux. What appears to be occurring is that a portion
50
-------
of the upward dissolved COD flux is escaping to the overlying water as
unoxidized COD, i.e. f * is decreasing. Thus the overall oxygen demand
of the sediment is not actually decreased. That fraction of J which
COD
is not exerted at the sediment-water interface is transferred to the
overlying water where it may react as a volumetric sink of DO. Whether
it is a rapid or slow reaction is not clear. However it would be incor-
rect in dissolved oxygen models to reduce SOD at low DO concentrations
and not also properly account for the unoxidized flux of interstitial
water COD.
The division of SOD into chemical and biological components by
inhibiting the bacteria actually examines the portion of the flux of
oxygen equivalents that is oxidized at the interface either bacterially
(presumably the organic carbon components) or chemically (the reduced
Fe, Mn, and S= species) (Walker and Snodgrass, 1983). However it is
clear that the source of SOD is sedimentary PCOD biological reactions.
The fact that some of the oxidation occurs chemically at the interface
is a consequence of the species distribution of electron acceptors that
mediate the transport of oxygen equivalents that were biologically
produced in the sediment.
With regard to laboratory measurements of SOD from either intact
cores or grab samples of sediments, it is clear that the realism of the
simulation of the field situation is directly related to either preserv-
ing the interstitial profile of oxygen equivalents, or allowing enough
time to pass so that the profile is reestablished. For certain cases
this time may be so long, since diagenetic reaction rates are slow (Table
1), that grab sample experiments are meaningless and only intact cores
can be used. A clear distinction should be made between experiments
51
-------
that are designed to measure the diagenesis and mineralization rates, and
those that measure the flux of oxygen*equivalents. The latter depend on
preserving both the interstitial water oxygen equivalents concentration
and duplicating the mass transport mechanisms in the measurement proced-
ure.
The observations of SOD as a function of sediment depth can be
interpreted in this light as well. The sludge incubation experiments of
Fair et al. (1941) demonstrated an increasing SOD with increasing depth
of sludge. Since the incubators were initially homogeneous it is reason-
able to expect that the total production of COD(aq) was linearly increas-
ing with depth, and if all the COD flux were oxidized at the interface
then the SOD should be linearly increasing with depth in these experi-
ments. A less than linear relationship was found and attributed to an
increasing loss of methane to the overlying water. Thus f * was decreas-
ing as sediment depth increased, producing the observed dependency.
By contrast Edwards and Rolley (1965) observed no depth effect and
McDonnell and Hall (1969) observed a slight effect. Both these studies
were based upon incubating intact cores. A depth dependency in this
case would only be observed if (1) a significant portion of the diagene-
sis is occurring below the depth of the collected core and (2) if suffi-
cient time elapses between collection and incubation so that the effect
of the missing lower layers can diffuse to the interface. An estimate
of this time is t ^ £ /AD so that short cores (^ 5 cm) could exhibit a
reduced SOD if the time interval exceeded ^ 10 days. However in most
cases no depth effect should be observed.
The time variable behavior of SOD can be understood in terms of the
time to steady state. For the fractions of PCOD that are mineralized at
52
-------
reasonably rapid rates (^ O.Ol/day) the SOD would respond to changes in
PCOD loading within one year. However for the fraction due to the
refractory component which mineralizes at slow diagenetic rates (Table
1) the response time for changes in PCOD loading is multiple years. Thus
for practical purposes, it is essential that the fraction of SOD derived
from labile and refractory components be quantified since only the former
fraction will respond rapidly to loading changes.
Perhaps the most important consequence of the oxygen equivalents
model of SOD is the implications with regard to field measurements and
laboratory experiments. Direct measurements of aerobic and anaerobic
COD fluxes together with SOD measurements give a direct check since mass
balance of oxygen equivalents must apply. Direct measurements of inter-
stitial water COD and NH, (the convenient tracer) together with estimates
or measurements of the sediment-water mass transfer coefficient provide
an additional framework for SOD estimates. Controlled laboratory experi-
ments that are designed to further validate the predictions of the oxygen
equivalents model are also necessary. The puzzling lack of an effect of
overlyinr nitrate concentrations requires further investigation. The
proposed model provides a framework for the design of these experiments
and the evaluation of the results.
Further effort is also indicated with regard to integrating the
oxygen equivalents model into conventional BOD-DO calculations. Field
data sets which are suitable should either be located or generated so
that fixed validation of these methods can proceed.
The oxygen equivalents model of SOD provides a simple,
comprehensible framework within which to understand the phenomena of
SOU. However it is certain that further refinements will be required as
53
-------
these ideas are integrated into the practice of modeling dissolved oxygen
in situations where SOD is an important component of the problem.
Acknowledgements
The original impetus for this work came during the development of
the Lake Erie eutrophication and dissolved oxygen model. The observation
by Nelson Thomas that a fixed SOD was inadequate for making projections
began the process. The research was supported in part by: EPA research
grants R803030 and CR805229. The contributions and support of the mem-
bers of our group at Manhattan College: John Connolly, Joanne Guerriero,
Donald O'Connor, Robert Thomann, Richard Winfield; the members of the
Large Lakes Research Station, Grosse lie, Mich: Nelson Thomas, William
Richardson, Victor Blerman, and Uayland Swain, and colleagues at
HydroQual, Mahway, N.J.: Thomas Gallagher and Paul Paquin are appre-
ciated.
54
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REFERENCES
Adams, D.D., Matisoff, G., Snodgrass, V.J. 1982. Flux of reduced
chemical constituents (Fe , Mn , NH. , and CH.) and sediment oxygen
demand in Lake Erie. In Sediment/Freshwater Interaction, ed. P.G Sly,
Dr. W. Junk Pub. The Hague-Boston-London, p. 405-414.
Andersen, J.M. 1978. Importance of the Denitrification Process for the
Rate of Degradation of Organic Matter in Lake Sediments in Interactions
Between Sediments and Fresh Water, ed. H.I. Golterman, W. Junk, B.V.
• Publ. The Hague.
Barnes, R.O., and Goldberg, E.D. 1976. Methane production and consump-
tion in anoxic marine sediments. Geology 4, pp. 297-300.
Berner, R.A. 1974. Kinetic models for the early diagenesis of nitrogen,
sulfur, phosphorus and silicon in anoxic marine sediments. In The Sea.
Vol. 5, E.D. Goldberg (Ed.). J. Wiley and Sons, N.Y. pp. 427-450.
Berner, R.A. 1980. Early Diagenesis. A Theoretical Approach.
Princeton Univ. Press, Princeton, N.J.
Callender, E., Hammond, D.E. 1982. Nutrient Exchange Across the Sedi-
ment-Water Interface in the Potomac River Estuary. Est. Coastal Shelf
Sci. 15. p. 395-413.
55
-------
Chiaro, P.S., Burke, D.A. 1980. Sediment Oxygen Demand and Nutrient
Release. J. Env. Engr. ASCE 106(EEI) p. 177-195.
DeLand, E.G. 1967. Chemist - The Rand Chemical Equilibrium Program
RM-5404-PR Rand Corp., Santa Monica, Calif.
Di Toro, D.M. 1976. Combining chemical equilibrium and phytoplankton
models - a general methodology. ln_ Modeling Biochemical Processes in
Aquatic Ecosystems. R. Canale (Ed.). Ann Arbor Science Press, Ann
Arbor, Mich. pp. 233-256.
,Di Toro, .D.M. 1980. Species Dependent Mass Transport and Chemical
Equilibria: Application to Chesapeake Bay Sediments. In Proc. 2nd
American-Soviet Symposium on the Use of Mathematical Models to
Optimize Water Quality Management. EPA-600/9-80-033, p. 85-121.
Edwards, R.W., Rolley, H.L.J. 1965. Oxygen Consumption of River Muds.
J. Ecology 53(1). p. 1-19.
Fair, G.M., Moore, E.W., Thomas, H.A. Jr. 1941. The Natural
Purification of River Muds and Pollutional Sediments. Sewage Works J,
13(2). p. 270-307.
Fillos, J., Molof, A. 1972. Effect of Benthal Deposits on Oxygen and
Nutrient Economy of Flowing Waters. J. WPCF 44(4), p. 644-662.
56
-------
Fillos, J., Swanson, H.R. 1975. The Release Rate of Nutrients from
River and Lake Sediments. J. WPCF 47(5), p. 1032-1042.
Galant, S., Appleton, J.P. July 1973. The Rate-Controlled Method of
Constrained Equilibrium Applied to Chemical Reactive Open Systems,
Fluid Methanics Laboratory, MIT, No. 73-6.
Garrells, R.M. and Christ, C.L. 1965. Solutions, minerals and equilib-
rium. Harper, N.Y. 450 p.
Goldberg, E.D. and Koide, M. 1963. Rates of sediment accumulation in
. the Indian Ocean. In Earth Science and Meteorltics. J. Geiss and
E.D. Goldberg (Eds.). North-Holland Pub. Co., Amsterdam, pp. 90-102.
Hale, S.S. 1980. The Role of Benthic Communities in the Nitrogen and
Phosphorus Cycle of An Estuary. Univ. of Rhode Island Marine Reprint
#57.
Imoboden, D.M. 1975. Interstitial transport of solutes in non-steady
state accumulations and compacting sediments. Earth . Planet . Sci.
Letters 27. pp. 221-228, 1975.
Jahnke, R.A., Emerson, S.R., Murray, J.W. 1982. A Model of Oxygen
Reduction, Denitrification, and Organic Matter Mineralization in
Marine Sediments. Limnol. Oceanogr. 27(4), p. 610-623.
57
-------
Klapwijk, A., Snodgrass, W.J. 1982. Biofilm Model for Nitrification,
Denitrification, and Sediment Oxygen Demand in Hamilton Harbor. 55th
Annual Water Pollution Control Fed. Conf., St. Louis, Mo. See this
volume (Snodgrass and Lai).
Kramer, J.R. 1964. Theoretical model of the chemical composition of
fresh water with application to the Great Lakes. Pub. No. 11, Great
Lakes Research Division, Univ. of Mich. p. 147.
Lauria, J.M., Goodman, A.S. 1983. Mass Flux Measurement of Sediment
Oxygen Demand. This volume.
Lerman, A. and Taniguchi, H. 1972. Strontium 90 - diffusional transport
in sediments of the Great Lakes. J. Geophic. Res. 77(3). p. 474.
Li-Y-H, Gregory, S. 1974. Diffusion of ions in sea water and deep-sea
sediments. Geochim. et Cosmochim. Acta 38. pp. 703-714.
Martens, C.S. and Berner, R.A. 1977. Interstitial water chemistry of
anoxic Long Island Sound sediments. I. Dissolved gases. Limnol. and
Occanogr. 22(1). pp. 10-25.
Morel, F., Morgan, J.J. 1972. "A Numerical Technique for Computing
Equilibria in Aqueous Chemical Systems". Envir. Sci. and Technol.
6(1), p. 58.
58
-------
Redfield, A.C., Ketchun, B.H., Richards, F.A. 1963. The influence of
organisms on the composition of seavater. In The Sea, Vol. (2), M.N.
Hill (ed), Wiley-Interscience, N.Y. p. 26-77.
Reeburgh, W.S. 1967. Measurements of gases in sediments. Ph.D. Thesis.
Johns Hopkins Univ., Baltimore, Md.
Reeburgh, W.S. 1969. Observations of gases in Chesapeake Bay sediments.
Limnol. and Oceanogr. p. 368.
Reeburgh, W.S. and Heggie, D.T. 1974. Depth Distributions of Gases in
• Shallow Water Sediments. Natural Gases in Marine Sediments, ed. Isaac
R. Kaplan Plenum Press, N.Y., pp. 27-46.
Richards, F.A. 1965. Anoxic Basins and Fjords. Chemical Oceanography,
ed. J.P. Riley and G. Skirrow, Vol. 1, Chapt. 13, pp. 611-644, Academic
Press, N.Y.
Rowe, G.T., Clifford, C.H., Smith, K.L. Jr. 1975. Benthic nutrient
regeneration and its coupling to primary productivity in coastal
waters. Nature 255, p. 215-217.
Shapiro, N. June 1962. Analysis by Migration in the Presence of Chemi-
cal Reaction, Rand Corp., Santa Monica, Calif., p. 2596.
59
-------
Smith, K.L., White, G.A., Laver, M.B. 1979. Oxygen uptake and nitrient
exchange of sediments measured in situ using a free vehicle grab res-
pirometer. Deep Sea Res. 26A, p. 337-346.
Smith. L.K., Fisher, T.R. 1983. Sediment Oxygen Demand and Nutrient
Fluxes Associated with the Sediment-Water Interface. This volume.
Stumro, W. 1966. Redox potential as an environmental parameter: Concep-
tual significance and operational limitation. 3rd Intl. Conf. on Water
Pollut. Res. Munich, Germany, Paper No. 13. pp. 283-308.
Thomann, R.V., Fitzpatrick, J.J. 1982. Calibration and Verification of
a Mathematical Model of the Eutrophication of the Potomac Estuary
HydroQual, Inc., Mahwah, N.J. and Metropolitan Washington Council of
Governments, Wash., D.C.
Thorstenson, D.C. 1970. Equilibrium distribution of small organic
molecules in natural waters. Geochim. et. Cosmochim. Acta. 34. pp.
745-770.
Toth, D.J. and Lerman, A. 1977. Organic matter reactivity and sedimen-
tation rates in the ocean. Am. J. Sci. 277, p. 465-485.
Troup, R. 1974. "The Interaction of Iron with Phosphate, Carbonate and
Sulfide in Chesapeake Bay Interstitial Waters: A Thermodynamic Inter-
pretation", Ph.D. Thesis, Johns Hopkins Univ., Baltimore, Md.
Environmental Protection Agency
n 5, Librarv (Di;L-lG)
G. Dearb-rn Kt -et. Room 1670
Chicago. JL 60604 60
-------
Vanderborght, J., and Blllen, G. 1975. Vertical distribution of nitrate
concentration in interstitial water of marine sediments with nitrifica-
tion and denitrlficatlon. Linmol. Oceanogr. 20, p. 953-961.
Van der Loeff, M.M.R., van Es, F.B., Helder, W., deVries, R.T.P. 1981.
Sediment Water Exchange of Nutrients and Oxygen on Tidal Flats in the
Ems-Dollard Estuary. Neth. J. Sea Res. 15(1), p. 113-129.
Walker, R.R., Snodgrass, W.J. 1983. Modelling Sediment Oxygen Demand
in Hamilton Harbor. This volume.
Whitteroore, R. 1983. The Significance of Interfacial Velocity Effects
on the Exertion of SOD. This volume.
61
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