Modelling of Chemical Exchange Reactions on the Seafloor

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Rapporttittel /Report title



Modelling of Chemical Exchange Reactions
on the Seafloor




Forfatter(e) / Author(s)

Akvaplan
-
niva rapport nr / report no:

JoLynn Carroll, Ph.D.

APN
-
414.1672.0
03


Dato / Date:


04/15/2000


Antall sider / No. of pages


24

+ 21


Distribusjon / Distribution


Unrestricted

Oppdragsgiver / Client

Oppdragsg. Ref. / Client ref.

G. Sander, Norwegian Polar Institute

Transport and

Effects Program
-
Contaminants
Section


Sammendrag / Summary

This report presents the findings of a literature investigation conducted to identify
mathematical formulations used by marine geochemists to describe sediment diagenetic
processes that are imp
ortant in controlling contaminant distributions in sediments. This work
was carried out as a subtask of the part “Geochemical Models” of the Norwegian Ministry of
the Environment and Ministry of Foreign Affairs Programme, “Transport and Fate of
C潮瑡浩湡湴
s in the Northern Seas.”


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䭲楳i楮愠i汳l潮Ⱐo栮䐮


© Akvaplan
-
niva ISBN
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-
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-
00000
-
0



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Tel. +47 77 75 03 00

Faks +47 77 75 03 01

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Contents

1.

OBJECTIVE


................................
................................
................................
.........................

3

2.

INTRODUCTION

................................
................................
................................
.................

3

3.

CONCEPTUAL FRAMEWORK

................................
................................
..........................

4

3.1.

Key Processes

................................
................................
................................
.................

6

3.1.1.

Sediment accumulation

................................
................................
................................
...

6

3.1.2.

Bioturbation

................................
................................
................................
....................

7

3.1.3.

Biochemical Reactions

................................
................................
................................
...

8

3.3.1.1

Organic matter mineralization

................................
................................
.................

8

3.3.1.2

Contaminant Reactions

................................
................................
..........................

11

4.

MATHEMATICAL APPROAC
H

................................
................................
.......................

12

4.1.


Bulk Sediment Diffusion Coefficients (D
sed
)
................................
...............................

13

4.2.


Bulk Sedimentation Rate (

)

................................
................................
.......................

14

4.3.


Linear Exchange Coefficient (K)

................................
................................
.................

14

4.4.


Bioturbation coefficient (D
b
)

................................
................................
.......................

16

4.5.


Slow Reaction Processes (

R)

................................
................................
.....................

17

5.

DISCUSSION

................................
................................
................................
......................

18

5.1

Sediment Accumulation and Bioturbation

................................
................................
....

18

5.2

Sediment Biochemical Reactions

................................
................................
.................

19

5.3

Contaminant Reactions

................................
................................
................................
.

19

6.

RECOMMENDATIONS

................................
................................
................................
.....

20

7.

REFERENCES

................................
................................
................................
....................

21

8.

APPENDIX


................................
................................
................................
.......................

24

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1.


Objective

This report presents the findings of a literature investigation conducted to identify
mathematical formulations of con
taminant transport processes to be used in marine transport
models. This work was carried out as a subtask of the part “Geochemical Models” of the
Norwegian Ministry of the Environment and Ministry of Foreign Affairs Programme,
“Transport and Fates of Cont
aminants in the Northern Seas.” We have looked for and
identified modelling approaches used by marine geochemists to describe sediment diagenetic
processes that are important in controlling contaminant distributions in sediments.

2.


Introduction

At the su
rface of the sea
-
floor, a variety of chemical and biological processes control the
cycling and ultimate burial of contaminants on the seabed. This report is concerned with
modern sediment processes. The reason for this focus is that modern sediments are th
e most
subject to a host of anthropogenic influences, including contamination by biological,
chemical and radioactive sources. It becomes of some concern to determine where such
sources might be, how the contaminants are transported and deposited, and how
they
influence the sediments and waters into which they are brought. Part of the difficulty in such
determinations is that the sediments and waters do not remain in place after they are charged
with contaminants, nor do the contaminants stay attached to th
e sediments but can later
undergo a variety of exchange reactions, diffuse or be advected away by water. Thus models
including sediment
-
related processes are required to unscramble those constituents which are
indeed in situ and those which are mobile. An
d the mobility time and distance scales must
also be provided somehow.

Traditionally, numerical models have emphasized physical transport of contaminants in
seawater as the primary pathway for distributing contaminants within the oceanic
environment. Only
more recently has increased attention been given to the biogeochemical
cycling of contaminants on the seabed. The bioavailability of contaminants and pathways of
incorporation into biological systems are in part determined by seabed processes. This
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informa
tion is needed in order to link the results of the Transport program with the work of
the Effects program.

This report is not intended to review the vast amount of available literature on oceanic
sedimentation processes or the chemical behavior of contami
nants in the environment. There
exist already a number of seminal works on these topics, see for example
(Lisitzin 1996
;
Kennett 1982
;
Stumm &
Morgan 1981
;
Berner 1980

and
Krauskopf 1979
). Instead, the aim
of this report is to present practical metho
ds that can be used by modelers to better represent
the main processes that play a key role in models that simulate the transport and fate of
contaminants in marine systems. These processes are briefly reviewed in Section 3. Section 4
presents the mathema
tical formulations used to describe changes to particulate matter after
deposition on the seafloor. Section 5 provides a suggested procedure for including the
described sediment
-
related processes into existing contaminant transport models. The report
con
cludes with Section 6, which contains recommendations derived from this investigation.

3.


Conceptual Framework

As illustrated in Figure 1, contaminant transport models must include a variety of
reservoirs and processes in order to simulate properly the beha
viour of contaminants in
natural systems. This includes the main reservoirs (atmosphere, ocean and bioturbated
sediment), and the associated fluxes between these systems. Having entered the ocean, the
main processes controlling the transport of contaminant
s are: (1) particle flux through the
water column, (2) deposition of material onto the ocean floor, (3) remineralization, and
redissolution within the water column and the sediment porewaters, (4) transport and mixing
in the water column, (5) diffusion of
sediment porewaters and interaction with bottom waters,
(6) sediment resuspension, bioturbation, and sediment accumulation. Collectively, the
processes that bring about changes in sediment subsequent to entering the ocean are known as
diagenisis
(Berner 1980)
. Diagenetic processes change the distribution and comp
osition of
both solids (e.g. particulate matter) and solutes (e.g. seawater and sediment porewater). The
important processes occurring at or near the seabed are known as sediment diagenisis and
these are discussed in Section 3.

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Figure 1:
Reser
voirs and processes associated with global ocean geochemical models
(Heinze et al. 1999)
.




OCEAN

transport

mixing

particle

rain

re
-
dissolution

export

production

LITHOSPHERE

SEDIMENT

deposition

ATMOSPHERE

weathering

river

discharge

gas

transfer

sediment

accumulation

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3.1.

Key Processes

This section provides an overview of the main processes associated with sediment
diagensis. For presentation in this report, the processes are grouped into three categories
as
indicated below.



3.1.1 Sediment Accumulation
(Deposition-Resuspension)
Redistribution of Solids
3.1.2 Bioturbation
(Advection+Bioturbation)
Redistribution of Solids
3.1.3 Biogeochemical Reactions
(remineralization+redissolution)
Solute Diffusion
Sediment Diagenisis

3.1.1.

Sediment accumulation

The particle flux through the water column to the seafloor, or sedimentation rate, varies
throughout the oceans and especially within continental margins. Sedimentation controls the
ra
te of burial on the seafloor of contaminants sorbed to particles and therefore is a controlling
variable in models of contaminant transport. Contaminants that sorb to particles in the water
column are subsequently deposited on the seabed where they become
available to organisms
living in or feeding at the sediment
-
water interface.

The process whereby sediments are permanently buried on the seafloor is known as
sediment accumulation. Sediment accumulation rates in the ocean vary over about 5 orders of
mag
nitude and depend significantly on water depth. The relationship of sediment
accumulation rate with depth is due to the inverse correlation of water depth with proximity
to continents and hence to sediment sources. The majority of sediments (56%) are burie
d
within the 0
-
200 meter depth range beyond continental margins with an additional 30%
buried within the depth range 200
-
2000 meters (Table 1, Column 3). The other variables
presented in Table 1 will be explained in later sections of this report.

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Table 1:

Global depth distribution of burial (sediment accumulation) and mineralization
rates in the ocean
(Middelburg, Soetaert & Herman 1997)
. Data represent the percentage of
the total that occurs within different depth ranges of the seafloor. Row 1 is the
column
number in the table. Column numbers are referenced in later sections of this report.


1

2

3

4

5

6

7

8

Depth Range

(m)

Area

(%)



(%)

F
b

(%)

F
c

(%)

AEROBIC

(%)

DEN

(%)

SRR

(%)

0
-
200

7

56

68

52

42

63

64

200
-
2000

9

30

27

30

30

29

29

>2000

84

14

5

18

28

8

7

1



= sediment accumulation rate

2

F
b
= organic carbon buried

3

F
c
= organic carbon mineralized

4

AEROBIC = aerobic mineralization of organic carbon

5

DEN = nitrate reduction of organic carbon

6

SRR = sulfate reduction of organic carbon


3.1.2.

Bioturb
ation

The process of bioturbation results from the burrowing and feeding of benthic macrofauna
such as worms, crabs, etc. so that particles are mixed and redistributed within a column of
sediment or alternatively, they are resuspended and redeposited or wa
shed away. There are
various ways sediments are reworked by organisms, including (1) diffusive mixing, (2)
conveyor
-
belt mixing, and (3) regenerative mixing.


Diffusive mixing
-

If sediment reworking consists of a large number of small events, the effect
a
ppears as diffusive mixing
(Boudreau 1986
a)
. The diffusion analog most closely resembles
the random burrowing of amphipods
(Robbins et al. 1979)
.


Conveyor
-
belt mixing
-

Some organisms, such as the tubificid worms, ingest sediment at
depth and excrete it at the surface in a ‘conveyor belt’ fashion
(Robbins et al. 1979)
. In this
approach, also known as n
on
-
local exchange, sediment parcels above a critical depth are
systematically replaced by parcels from immediately above (Smith, Boudreau, & Noshkin
1986).

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Regenerative mixing
-

Large macrobenthic organisms such as fiddler crabs, dig large burrows
which ar
e subsequently backfilled with surficial material. The result is that parcels at depth
are systematically and largely replaced by surficial material. This strategy is known as the
regenerative model and was developed by
(Gardner, Sharma & Moore 1987)
.


On a world
-
wid
e basis, the depth of mixing is restricted to a narrow surficial zone with a
mean of 9.8


4.5 cm
(Boudreau 1998)
. Interestingly, this depth zone does not correlate with
biological mixing intensity or water depth indicating that no single controlling factor has yet
to be identified on the basis of observati
onal data.

In the most widely used general theory, bioturbation is expressed mathematically as a
diffusive process
(Berner 1980; Guinasso & Schink 1975)
. Very few investigators have
applied the non
-
local exchange model
(Boudreau 1986b; Smith, Boudreau & Noshkin 1986)

or the regenerative model
(Gardner, Sharma & Moore 1987)

to describe sediment mixing.
However the description of mixing as a biodiffusion pr
ocess is not based on a mechanistic
model of the mixing process itself, but rather has been shown to produce a high degree of
correlation with depth profiles of tracers gathered from a number of sedimentary systems.

Similarly, non
-
biological, or physical
mixing of sediments caused by periodic processes
(e.g. bottom currents, waves and tides) and episodic events (e.g. storms and floods, turbidites)
can exchange material among different depth horizons at a single location or remove material
from one location

depositing it elsewhere.
Ruettgers van der Loeff & Boudreau (1997)

developed a resuspension theory for the distribution of particles below and above the
sediment
-
water interface and
further expanded the model to investigate how early diagentic
reactions are affected by resuspension. However, these specialized theories have yet to be
integrated into large scale transport models.


3.1.3.

Biochemical Reactions

3.3.1.1

Organic matter mineralization

Mineralization of organic matter in marine sediments is the ultimate factor determining
most diagenetic processes and the direction and rate of sediment
-
water exchanges. This
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process is carried out mainly by microorganisms which populate the sediment and
which
depend on the deposition of organic detritus from the water column as the energy source.
Organic matter deposited on the seafloor fuels a sequence of degradation reactions that
remove carbon from the sediment system (Table 2).

The breakdown of organ
ic matter leads to the exchange of particle
-
bound contaminants to
porewater and vis versa. This breakdown of organic matter proceeds via a well
-
defined
sequence of terminal electron acceptors: oxygen is consumed first, followed by nitrate and
nitrite, man
ganese oxide, iron oxides, sulfate, and finally oxygen bound in organic matter
(Froelich et al. 1979)
. In the deep
-
sea where organic matter deposition is low, oxygen is by
far the major electron acceptor in the mineralization process
(Jahnke, Emerson & Murray
1982)
. With increasing org
anic deposition, suboxic and anoxic processes become more
important
(Canfield et al. 1993; Jørgensen 1983)
. Following deposition, the organic
substrates are sequentially consumed according to their decreasing lability (affinity for
particles). As a result, the reactivity of organic matter (ability to remove organic matter from
part
icle surfaces) decreases with time during mineralization
(Stumm & Morgan 1981)
.

The important concepts relating to the mineralization process are outlined here:


Organic carbon burial rate
-

the supply of organic carbon is the starting point for the process of
organic mineralization. This s
upply rate depends significantly on water depth since water
depth is related to sediment accumulation rate
(Tromp, Van Cappellen & Key 1995)
.


Total mineralization rate
-
Following deposition, organic substrates are consumed according to
their decreasing labili
ty. As a result, the reactivity of organic matter decreases with time
during mineralization
(Middelburg 1989)
. The total amount of carbon consumed depends
upon the rate of metabolic activity and the degradability of the organic matter.


Aerobic mineralization rate
-
Oxygen is the most powerful oxidant
and is consumed first in
organic matter mineralization
(Froelich et al. 1979)
. In the deep
-
sea, where organic deposition
is low, oxygen is the major electron acceptor in the mineralization process and almost no
carbon escapes the zone of aerobic oxidation.


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Denitrification ra
te
-

Oxic carbon mineralization produces ammonium which is further
oxidized to nitrate. Nitrate
-
based mineralization (denitrification) produces ammonium and
nitrogen gas. Rates of denitrification steadily decrease with increasing water depth (Table 1,
Colum
n 7). For areas of higher organic carbon burial rates, suboxic and anoxic processes
become more important than oxic processes.


Sulfate reduction rate
-

Sulfate
-
based mineralization produces ammonium and some reduced
substance. On a global basis, oxygen an
d sulfate appear to be the primary oxidants for the
decomposition of organic matter
(Tromp, Van Cappellen & Key 1995)
.


Table 2:
Stoichiometric equations of

reactions controlling oxidation of organic matter in
sediments (Stumm and Morgan, 1981).


Process

Che
mical Reactions

Aerobic respiration

(CH
2
O)
x
(NH
3
)
y
(H
3
PO
4
)
z
+(
x
+2
y
)O
2



x
CO
2
+(
x
+
y
)H
2
O+
y
HNO
3
+
z
H
3
PO
4

Nitrate reduction

5(CH
2
O)
x
(NH
3
)
y
(H
3
PO
4
)
z+
4
x
NO
3
-

x
CO
2
+3
x
H
2
O+4
x
HCO
-
3
+2
x
N
2
+5
y
NH
3
+ 5
z
H
3
PO
4

Manganese reduction

(CH
2
O)
x
(NH
3
)
y
(H
3
PO
4
)
z
+2
x
MnO
2
+3
x
CO
2
+
x
H
2
O

2
x
Mn
++
+4
x
H
CO
-
3
+
y
NH
3
+
z
H
3
PO
4

Iron reduction

(CH
2
O)
x
(NH
3
)
y
(H
3
PO
4
)
z
+4
x
Fe(OH)
3
+3
x
CO
2
+
x
H
2
O

4
x
Fe
++
+8
x
HCO
-
3
+3
x
H
2
O+
y
NH
3
+
z
H
3
PO
4

Sulfate reduction

2(CH
2
O)
x
(NH
3
)
y
(H
3
PO
4
)
z
+
x
SO
2
-
4

H
2
S+2
x
HCO
-
3
+2

y
NH
3
+ 2
z
H
3
PO
4

Methane production

(CH
2
O)
x
(NH
3
)
y
(H
3
PO
4
)
z
+

x
CH
4
+
x
CO
2
+2

y
NH
3
+ 2
z
H
3
PO
4

x
=106;
y
=16;
z
=1


Rates of benthic mineralization are primarily determined by the flux of organic matter to
the sediments, which in turn depends on the productivity of the ocean surface and on water
depth
(Suess 1980)
. As a consequence, rates of benthic mineralization decrease over orders of
magnitude from rapidly

accumulating nearshore to slowly accumulating deep
-
sea deposits.
Fifty
-
two percent of the organic carbon supplied to the seabed is mineralized within the depth
range 0
-
200 meters (Table 1, column 5). Of the remaining 48%, thirty percent is mineralized
in
the depth zone 200
-
2000 meters and 18% is mineralized at water depths greater than 2000
meters.

Degradation pathways and kinetics of sedimentary organic matter are reviewed in detail
by
Berner (1980)
. Globally, oxygen and sulfate appear to be the primary oxidants for the
decomposition of organic detritus in marin
e sediments
(Berner & Canf
ield 1989)
. Global
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rates of organic matter decomposition via denitrification and sulfate reduction steadily
decrease with water depth, whereas rates of aerobic and total mineralization initially decrease
with depth, but then show a secondary maximum at wa
ter depths of 2500
-
5500 meters. This
secondary maximum is related to bathymetry of the ocean, about 50% of the ocean surface
lying within this depth interval
(Menard & Smith 1966)
. Forty
-
two percent of aerobic
mineralization occurs within the depth zone 0
-
200 meters (Table 1, column 6). An

additional
30 percent occurs within the 200
-
2000 meter depth range and 28% occurs at locations with
water depths greater than 2000 meters. Similarly, of the total for both denitrification and
sulfate reduction occurring in ocean sediments, 63% and 64% res
pectively occurs within the
0
-
200 meter water depth range. Twenty
-
nine percent occurs in the depth range 200
-
2000
meters, for both denitrification and sulfate reduction. The remaining 8% (denitrification) and
7% (sulfate reduction) occurs at depths greater

than 2000 meters. These data clearly
demonstrate that benthic mineralization of organic matter primarily occurs within shallowest
depth zone of the oceans.

3.3.1.2

Contaminant Reactions

Mineralization of organic matter results in the release of many associated el
ements and
components. Some anthropogenic pollutants (PCBs, PAHs) are released in bottom waters by
decay of the organic carrier phase
(Baker, Eisenreich & Eadie 1991)
. From studies of surface
sediments in the deep
-
sea, it is well known that Copper (Cu), Iodine (I),

Bromine (Br),
Chromium (Cr), Cadmium (Cd), and Nickel (Ni) are released in this mineralization process
and returned to bottom water
(Boyle, Edmond & Sholkovitz 1977
;
Westerlund et al. 1986)
.
Upon release after decomposition of the organic carrier, many trace elements are scavenged

(adsorbed) again onto other phases (particle surface types) before being dispersed in the water
column
(Fischer et al. 1986)
. This in turn causes an enrichment of elements at the sediment
surface relative to sediments below. Thus, the concentration gradients across the sediment
-
water

interface must reflect the net effect of release by the organic carrier phase and
adsorption onto other phases.


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4.


Mathematical Approach

The general diagenetic equations for solutes and solids proposed by
Berner (1980)

are
usually simplified due to a lack of data. Assuming steady
-
state diagenisis, no density g
radient,
simple linear adsorptions/exchange that can be represented as an eddy


diffusion type mixing
of solids, the diagenetic equations for solutes and solids become:

For solids:

C
sed
R
C
K
x
C
D
x














)
1
(

= 0



(1)


For solutes:

0














c
b
R
S
x
S
D
x






(2)


where x is depth in the sediment, D
sed
is the bulk sediment diffusion coefficient, C is the
concentration of the solute,


is the sediment accumulation rate, K is the linear exchange
coefficient, D
b

is the eddy diffusion coefficient due to bioturbati
on, S is the concentration of
solid and

R represents the net of all “slow” processes not covered in the linear exchange
parameterization.

The variables for which values are needed to implement these diagenisis reactions in a
transport model are:

1. Bulk s
ediment diffusion coefficient
-

D
sed

(cm
2
/yr)

2. Sediment accumulation rate
-



(cm/yr)

3. Linear exchange coefficient
-

K (dimensionless)

4. Eddy diffusion coefficient due to bioturbation
-

D
b

(cm
2
/yr)

5. Slow reaction processes
-


R (mol/ cm
3
/yr)

How th
ese variables are handled in models is determined by the goals of a particular
modelling endevour and is also largely predicated on the region of interest. The values
proposed in this report assume a minimum of available data in any particular region of
in
terest.


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03

4.1.


Bulk Sediment Diffusion Coefficients (D
sed
)

Bulk sediment diffusion coefficients are usually estimated from free solution diffusion
coefficients corrected for temperature and salinity
(Li & Gregory 1974)

and sediment porosity
using relationships reported by
Ullman & Allen (1982)
.

Porosity is a term that is used to

describe the space existing between particle grains
deposited on the seabed through which water can flow. Porosity usually declines with depth
into the sediment
(Jahnke et al. 1986)

and is described by an equation of the form:













)
(
X
e

(x/coeff

)


(3)


where (

x
) is the porosity at depth (x) in the sediment; (


) is the porosity at infinite depth;

0

is the porosity at the sediment
-
water interface; and coeff


is determined from the
measured porosity versus depth profile in sediments.

The diffus
ion coefficient of a dissolved substance in the sediment at ambient temperature
T (

C) can be calculated from porosity (

) and sediment resistivity (F) as,


F
D
D
T
T
S








(4)

where D
T

is the diffusion coefficient in a free solution at temper
ature T in

C. Sediment
resistivity (F) relates to porosity as,

m
F
I








(5)

in which ‘m’ varies from 2.5
-
3. Setting m=3, the diffusion coefficient in the sediment is
calculated as:

2


T
T
S
D
D






(6)

The free solution dif
fusion coefficient at the ambient temperature (T) is calculated from the
zero
-
degree coefficient D
0
as,

aT
D
D
T


0





(7)



where ‘
a
’ is an ion
-
specific coefficient representing the temperature dependency of the
diffusio
n coefficient. Values for D
0
are available in
Li & Gregory (1974)
. Values for
a
can be
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approximated by linearly interpolating between the diffusion coefficient at 0


and at 18

C
(Appendix).


4.2.


Bulk Sedimentation Rate (



Sedimentation rates generally decrease with water
depth, although there is considerable
variability. At depths less than 100 m, sedimentation rates seem to be less predictable or at
least lower than expected based on empirical relationships derived for other parts of the ocean
(
Soetaert, Herman & Middelburg
1996)
. Considering water depths greater than 100 meters,
Soetaert, Herman & Middelburg (1996)

derived an empirical relationship of the form


548
.
1
982



D
w


(r
2

= 0.66, N=110)


(9)


This empirical relationship was derived by regressing sediment acc
umulation rate data from a
biogeochemical database of literature values versus water depth. The database covers a wide
range of oceanic conditions and was set up in the context of the European Union Ocean
Margin Exchange Program (OMEX). The database was co
mpiled specifically for use in
coupling global diagenetic models with ocean global circulation models.


4.3.


Linear Exchange Coefficient (K)
1

The uptake potential for chemical constituents on sediments is a function of the relative
influence of the chemic
al properties of the constituent, sediment characteristics and the
moderating influence of the oceanic environment. Many exchange reactions may occur at the
sediment
-
solute interface
(Børretzen & Salbu 1999)
. Reaction types as well as important
characteristics of particulate matte
r and water quality are summarized in Table 3. The
interdependencies among the variables shown in Table 3 help to explain why values of K



1

The reader is referred to the companion report by
Børretzen & Salbu (1999)

for additional
information on the assumptions and methods of this approach and descrip
tions of alternative
approaches.


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determined for individual elements often vary over several orders of magnitude
(Duursma &
Carroll 1996
;
Carroll et al. 1999
;
Carroll & Harms 1999
).



Table 3:
Reaction types and important characteristi
cs of particulate matter and water which
influence chemical exchanges between these media (from

Duursma & Carroll (1996)
).


Exchange Reactions

Particulate matter
characteristics

Water quality characteristics

Ion exchange

Colloids

pH

Colloid chemistry

Particulate OM
1

Dissolved OM
1

Particle aggregation/dis

Humic coatings

Salinity

Complexation

Clay mineralogy

Redox conditions

Precipitation

Grain size


Diffusion into pore spaces



Hydrolysis




O.M. = organic matter



Based on the linear exchange hypothesis, exchange coefficien
ts are typically reported as:








seawater
sed
sed
A
C
A
K




(10)

where A
sed

and A
seawater

are the concentration of a constituent on particles (ug/gsed) and
filtered seawater (ug/g seawater) respectively. This equation is based on the simplest model
for ion
adsorption to hydrous oxide surfaces, known as the surface complexation model
(Stumm, Huang & Jenkins 1970
;
Schindler 1975)
. To calculate K using equation 10, it is
assumed that (1) ion exchange between mono
-
valent chemical species is the primary reaction
mechanism, (2) surface reactions quickly reach an equilibrium

state and (3) reversible
exchange between particle surfaces and seawater occurs. When applied to natural particle
assemblages found in the ocean, the additional assumption is made that heterogeneous
particle assemblages may be treated as a single surface,

thereby obscuring the relative
importance of each component of the assemblage
(Balistrieri & Murray 1983; Balistrieri &
Murray 1984; Balistrieri & Murray 1986)
.

In oceanic systems where pH fluctuates narrowly around 8, the presence of surface oxides
of Manganese (Mn), Iron (Fe), Silicon (Si), and Aluminium
(Al) on particles is thought to
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dominate the rapid exchange process
(Balistrieri & Murray 1984; Li 1981)
. In addition, there
is ample evidence that colloids, including organic coatings, play a significant yet poorly
-
understood role in adsorption
(Balistrieri & Murray 1981
;
Davis 1984
;
Morel & Gschwend
1987
;
Dai & Martin 1995)
.

4.4.


Bioturbation coefficient (D
b
)

The simplest approach to modeling bioturbation is based on the assumption that the
bioturbation coefficient is constant in an up
per zone of the sediment column. Below this zone
of arbitrary thickness (x
b
) bioturbation declines rapidly to 0.


Thus, for
b
x
x



Db
x
= Db
0






(11)

below which (x>x
b
)



b
b
coeffD
x
x
x
e
Db
Db
/
0
*







(12)


This approach assumes the biodiffu
sion model of bioturbation (see section 3.2). As discussed
earlier, although alternative models have been proposed the biodiffusion approach is still the
most widely used procedure due to its ease of application and versatility. Based on the
empirical anal
ysis of
Boudreau (1998)
, the mean depth zone of biot
urbation is 9.8


4.5 cm. If
one assumes a value of 5 cm for the “constant mixed” layer and a value of 1 for the
exponential coefficient, bioturbation approaches zero at about 10 cm depth.

Middelburg, Soetaert & Herman (1997)

derived empirical relatio
nships based on all of the
data in the OMEX database for use in calibrating and parameterizing global diagenetic
models (Table 4). The values for Db differ if they are based on studies of the radionuclide Pb
-
210 and Th
-
234. The choice of which empirical re
lationship to use should be based on the
timescale of processes being modeled. Table 4 also provides an alternative empirical
relationship for sedimentation rate (

) that includes all data from the OMEX data base and is
not restricted to water depths great
er than 100 meters as is the case for equation 9. However,
as mentioned earlier, predictions within the depth zone <100 meters are uncertain due to the
high spatial and temporal variability associated with processes operating in marginal areas of
the ocean
.

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4.5.


Slow Reaction Processes (



Several boundary conditions must be established in order to simulate the reaction
processes associated with organic mineralization (Table 2). These include (1) the settling flux
of labile organic matter, (2) degradabi
lity of organic matter, as well as (3) rates of aerobic
mineralization. Depending on the level of detail of the processes to be simulated, only some
of the other mineralization processes described in Table 2 are typically included in sediment
diagenetic mo
dels. As a result, the rate of metabolic activity will depend not only on the
degradability of the organic matter but also on the availability of the oxidant utilized. In
addition, the presence of some oxidants may inhibit other metabolic pathways. A var
iety of
approaches may be used to model these limitation and inhibition functions depending on the
overall structure of the sediment model. These must therefore be chosen for models on a case
by case basis. A useful example of how these functions may be ma
thematically described is
given in
Middelburg, Soetaert & Herman (1997)

(Appendix).


Table 4:
Summary of predictive empirical relationships (from
Middelburg, Soetaert &
Herman (1997)
).

Predictive relationship: variable=10
(a+bZ)*
CF

Variable



a

b

s
2

CF

R
2

N

p



-
0.87478367

-
0.00043512

0.455993

3.3

0.615

220

0.0000

F
b

-
0.84672973

-
0.00061506

0.561665

4.4

0.686

105

0.0000

D
b
(
210
Pb)

0.76241122

-
0.00039724

0.622614

5.2

0.432

132

0.0000

D
b
(
234
Th)

1.75398833

-
0.00007505

0.0367395

1.1

0.241

11

0.12

F
c

-
0.50860503

0.00038900

0.211673

1.8

0.690

80

0.0000

AEROBIC

-
0.82693415

-
0.00030493

0.229916

1.8

0.584

35

0.0000

DEN

-
0.95644723

-
0.00052040

0.524713

4.0

0.635

38

0.0000

SRR

-
0.72144197

-
0.00054697

0.250458

1.9

0.764

49

0.0000


Z:water depth (m)


:se
diment accumulation rate (cm year
-
1
)

F
b
:organic carbon burial rate (mmol C cm
-
2
year
-
1
)

D
b
: bioturbation rate based on
210
Pb (cm
2
year
-
1
)

D
b:
bioturbation rate based on

234
Th (cm
2
year
-
1
)

F
c:

mineralization rate (mmol C cm
-
2
year
-
1
)

AEROBIC:aerobic m
ineralization (mmol C cm
-
2
year
-
1
)

DEN: denitrification (mmol C cm
-
2
year
-
1
)

SRR: sulfate reduction rate (mmol C cm
-
2
year
-
1
)

CF=exp(2.65s
2
), p= significance level



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Empirical relationships have further been established for a number of other important
react
ion processes (Table 4). These relationships are also useful for setting boundary
conditions for some of the reactions controlling sediment organic matter oxidation. The
individual processes were outlined previously in section 3.3.1 and empirical relations
hips are
given in Table 4.

5.

Discussion


Natural processes operating in the sedimentary environment and methods of incorporating
these processes into transport models have been described in the previous sections of this
report. For purposes of modeling co
ntaminant distributions, the implementation of diagenetic
reactions into contaminant transport models can be considered as a three step process.




Sediment accumulationation and Bioturbation



Sediment Biochemical Reactions



Contaminant Reactions


5.1

Sediment Ac
cumulation and Bioturbation

The simplest approach is to assume that sediments are inert and therefore any
contaminants adsorbed to particles deposited on the seabed will remain adsorbed for all time.
Then the only variables of interest are the sediment acc
umulation rate and bioturbation rate.
These variables control (1) the rate of supply of particle
-
associated contaminants (sediment
accumulation rate) and (2) the concentration of particle
-
associated contaminants at the seabed
surface (bioturbation rate). T
he geographic distribution of values for these variables has been
empirically derived (Table 4) and can be implemented as described previously in Section 4.1.
Based on the sedimentation and bioturbation rates, the concentration of contaminants can be
simpl
y determined based on the principle of conservation of mass.


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5.2

Sediment Biochemical Reactions

To be able to model changes in contaminant concentrations in porewater and sediments
and hence to determine the dynamic equilibrium between sediments and over
lying waters,
one must be able to simulate the full sequence of diagenetic reactions associated with the
breakdown of organic matter at the seabed. There have been a number of marine transport
models developed incorporating some aspects of these processes.

Many models are restricted
to a few biochemical reactions, typically for specific types of sediments, e.g. deep
-
sea
sediments
( R
abouille & Gaillard 1991; Heggie et al. 1987; Goloway & Bender 1982; Jahnke,
Emerson & Murray 1982;)
. More recently, a numerical model of sedimentary diagenetic
processes was developed by
Soetaert, Herman & Middelburg (199
6)
. This model includes
oxic and anoxic mineralization. The model accounts for depth
-
dependent bioturbation and
porosity profiles and can be used to calculate steady
-
state and transition conditions. The
model is particularly versatile because it is applic
able from the shelf to abyssal ocean depths.
It reproduces the cycling of carbon, oxygen, nitrate, ammonium, and other reduced
substances. Furthermore, important boundary conditions (e.g. oxygen concentration and
carbon mineralization rate) are given for t
he model. A similar approach could be
implemented as a coupled module to the current transport models under development in the
Transport Program. The approach relies heavily on empirical relationships for setting
boundary values and is limited to the water

depth zone >100 meters. In shallower areas
sediment and organic carbon supplies to the seabed may be decoupled from water depth so
that empirical relationships are less useful. Nonetheless, the approach represents a valuable
starting point for incorporati
ng diagenetic equations into marine transport models. The paper
by
Soetaert, Herman & Middelburg (1996)

describing this approach is provided as an
appendix to this report.

5.3

Contaminant Reactions

While some contaminants are highly insoluble, they may still un
dergo release to solution,
adsorption, diffusion, and other processes, and thus require complex expressions to explain
their distribution in sediments. But if the kinetics of such reactions are reasonably well
-
known, as is the case, for example, for certai
n radionuclides, it is possible to construct
diagenetic equations for such contaminants of the same form as equations 1 and 2. Due to the
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interdependency of many contaminant transformation processes on the processes described in
the previous section, conta
minant diagenetic equations should be developed for individual
contaminants and implemented into the models after the implementation of sediment
biochemical reactions. Modules for individual contaminants can be added once the basic
biochemical reaction com
puter module is operational. Thus the number of contaminants
included can be slowly increased over time in accordance with the specific goals of individual
modelling activities.

6.


Recommendations

The approach described in 1 (Sediment Accumulation and Biot
urbation) is very simple
and can be implemented immediately into currently operating contaminant transport models.
Used in conjunction with information provided in the complementary report, ‘Geochemical
Models for Sediment
-
Seawater Interactions,’ the initi
al storage of contaminants in sediments
may be estimated fully by this approach. For those models that currently do not contain any
sediment biochemical reactions and wish to do so, this report and the work of
Soetaert,
Herman & Middelburg (1996)

provide a g
ood starting point. Once the process of carbon
mineralization as outlined in
Soetaert, Herman & Middelburg (1996)
, has been implemented
into the model, then a variety of modules for simulating distributions with water depth and
fluxes at the sediment
-
water
interface may be developed for individual contaminants. The
contaminant modules will be based on the same principles as for the other constituents (i.e.
based the development of diagenetic equations for the contaminants of interest according to
equations 1

and 2).

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Akvaplan
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24

www.akvaplan.niva.no

Rapport
APN
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414.1672.0
03


8.

Appendix


Soetaert, K., P.M.J. Herman & J.J. Middelburg 1996. A model

of early diagenetic processes
from the shelf to abyssal depths.
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Geochimica et Cosmochimica Acta

60(6): 1019
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1040.