1. Transport and Reaction: An Overview
Review of transport terms
Reactions:
radioactive decay
organic matter oxidation
mineral dissolution

2. Profiles of sediment composition represent
A: On short space / time scales, near the sediment surface:
Balance between:
** transport
… material added at sed. Surface, transported
downward by:
-- sediment burial
-- “mixing”
** reaction
B: Over longer time / space scales
All above
+ variable inputs over time

3. Solid phase transport:
[1] Mass accumulation & sedimentation rates
 ~ gsolid / cm2sed•yr …. mar
On short time scales: assume constant
w ~ cmsed / yr … sed rate
At any depth:
 = w s (1-) ~
At some depth,  becomes constant : = ∞ … Then
==> In general:

4. Example: Some porosity profiles from the central equatorial Pacific Ocean

5. Sediment mixing… “biodiffusion”
The diffusive flux: Fick’s first law
(and there may be nondiffusive transport processes, too)

6. Reaction terms
Take the general form,

7. Combine transport and reaction terms in mass balance
Consider a layer of sediment,
Change in C over time in the layer =
Net transport rate + Net reaction rate
Which leads to the simple case, with
steady state
constant ,s, DB

8. In order to make the equation useful, need 2 boundary conditions
[1] At x = 0
Require no net accumulation of material at x = 0
==> Flux, water column --> sed = transport away from swi
(need density, porosity terms since unit of F is amt / cm2sed/y
[2] At x = xmax (often, x --> ∞)
“no deeper reaction” condition
“no remaining reactant” condition

9. So far, we’ve examined a simple case… a solid phase component whose only reaction is radioactive decay
k -->  … radioactive decay constant
ƒ(solutes) = 1 … (no solute dependence)
C --> A … dpm/gsolid

10. And we solved 2 simple cases…
[1] Diffusive transport >> burial:
And the slope of the semi-log plot yields DB

11. Example: xs Pb-210 at a site on NW Atlantic contintental margin

12. [2] No diffusive transport -- only sediment burial
And slope of semi-log plot yields w

13. Example: C-14 vs. depth in a core from Buzzards Bay, MA
Below mixed layer:
Slope of radiocarbon
Age vs depth
--> w

14. More about F0
[1] !! Note: Don’t need to know F0 to calculate DB, w !!
[2] BUT -- it does contain useful information
Example: xs 230Th and “sediment focusing”
Example: xs 234Th … can be used in a similar way:
water column: 234U --> 234Th, which is removed by particle
scavenging
-- short time scale
-- variation in sed inventory reflects both
scavenging efficiency variation
sediment focusing

15. Example: xs 210Pb
Also used for information about sediment focusing
But: there are 2 sources of excess 210Pb to sediments:
(1) Deposition of xs210Pb from the atmosphere
-- 222Rn emanation from continental solis
-- rapid decay to 210Pb
-- 210Pb sorbs to aerosol particles
-- dry & wet deposition of aerosols
(2) Decay of 226Ra in water column;
226Ra --> 222Rn --> 210Pb,
removal of 210Pb by scavenging

16. The deposition of excess 210Pb from the atmosphere
(from Turekian et al.,
1977, Ann. Rev. Earth Planet.
Sci., 5: )

17. Calculating the flux of a radioisotope to the sediment-water interface from sedimentary data
Assume steady state over lifetime of tracer
(e.g., 234Th : <~ 4 months
e.g., 210Pb : <~ 100 years)
Then,
F0 = I
Where
How much does atmospheric deposition contribute to xs 210Pb Inv?
F0 ~ 0.7 dpm/cm2/y
 = y-1

18. Example: excess 210Pb inventories on continental shelf, NW Atlantic
Inv = 27 : balances atmos supply
Inv = 34 : balances total supply
(Bacon et al., 1992)

19. Reaction term for constituents other than radioactive isotopes Organic matter
Often, lump k x ƒ(solutes) together to get
Then, with simple diffusive mixing,
Looks a lot like the profile for a component undergoing
Radioactive decay…
In particular, G -->0 as x increases
Is that what’s observed??

20. Example: Organic carbon vs depth from a core taken in the eastern tropical Atlantic Ocean
Generally find a decrease
To a constant value
… divide inventory into
“reactive” and “nonreactive”
On Pb-210 time scale
Pb-210 mixed layer depth
But how to split organic matter
into pools of differing
reactivity??
Solution: “multi-G” model

21. A second problem with using solid phase organic C profiles to determine the organic C remineralization rate
Complex and difficult-to-quantify mixing processes!

22. So, maybe it makes sense to use solute profiles to define organic matter oxidation rates
Organic matter oxidation by O2:
And could use O2 vs depth or NO3- vs depth to quantify rate
Just as for solids, mass balancefor a solute in a sediment layer ==> change over time
Results from balance between net transport into the layer and net reaction in the layer
diffusive
transport
advective
transport
reaction

23. For O2, it has been convenient to use
R = P(x)
i.e., with no dependence on [O2], even though it’s a reactant
Can that be justified?
Devol (1978) DSR 25,
Cultured marine bacteria from low-O2 waters…
Found O2 consumption followed
Michaelis-Menten kinetics:
And found a
“Critical O2 Concentration” below
Which rate depended on [O2]
Of ~ 2.4 µmol/l

24. Example: a deep-sea O2 profile and a fit to it to derive the rate of O2 consumption vs depth, from which a rate of organic matter oxidation vs. depth could be derived
O2 consump vs depth stoichiometry of om --> C ox vs depth
But, ultimately, the reaction rate must depend on G, and must be linked to G -- then
!! -- the ki are 1st order rate constants with dimension
1/time, and give response time of sedimentary organic
Matter oxidation to changes in organic matter inputs

25. Another type of reaction
So far, 2 types:
1. Radioactive decay: R is simple and known ==> components
whose only reaction is radioactive decay can be used as
tracers of transport processes
2. Organic matter decomposition: Organic matter is unstable; reaction
occurs when organisms catalyze the process through respiration
**** rate varies with degree of decomposition
Now another reaction type:
3. Mineral dissolution / precipitation: Reaction may occur when the solution
bathing the mineral is either undersaturated (dissolution) or
supersaturated (precipitation) with respect to the mineral

26. Back to the general reaction rate term for a solid:
Defining ƒ(solutes):
Mineral equilibrium is defined by the solubility product
e.g. for calcite
Dissolution of calcite depends on 
** k may vary, just as for organic matter
** n is not well known, and may vary too
**  varies … it varies in a known way for pure calcite,
but the dissolving mineral may not always be the same!

27. How do we study the rate of calcite dissolution in sediments?
[1] Variations in %CaCO3 vs. depth do not provide much information
[2] So, look to solute distributions… which ones?
Can’t measure directly
-- can calculate from 2
among TCO2, Alkalinity, pH
Useful: but changes
Are small and hard to
measure

28. Example: Results from the Ceara Rise, western tropical Atlantic Ocean
Organic matter oxidation by O2, with no dissolution of CaCO3
∆TCO2 = ; ∆Alk = - 18
With CaCO3 dissolution:
∆Alk / ∆TCO2 ~ 1
Note: pore waters must be
Collected -- or concentrations
Measured -- using in situ
Techniques --
Data are hard to get!