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

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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

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 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.

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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

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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-

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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.

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     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-

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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-

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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

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                      *
     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

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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.

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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

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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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