File last modified 27 November 1996
18.2 Physical and Biological Diagenetic Processes
There are three key physical/biological processes that must be addressed when modeling sediment profiles: advection, diffusion, and bioturbation. Keep in mind that you don't necessarily need to address them all at once.
Advection is the flow of solids or pore water with respect to the frame of reference, i.e. the seawater-sediment interface. Compaction is the loss of water from a sediment layer due to compression of the overlying sediments. These two concepts taken together lead to the idea of porosity, which is defined as:
This is not quite the same thing as total porosity, but for recently buried sediments it is close enough. Total porosity includes those isolated pockets of water in the sediment through which water cannot flow. In the types of sediments that we will be talking about here these extra voids are very small and can be ignored.
Another concept that needs to be defined is rate of deposition, which is equal to 
only if the
sedimentation rate is constant and compaction is absent or steady state. We can suppose that:
that is, non-constant deposition. If there has been compaction, we can write:
here s= the rate of deposition, or put another way, the thickness of an annual layer. At the surface
the two can be set equal to each other, 
, but it is still difficult to evaluate (18.2.3)
because ds/dt has to be evaluated for the same sediment layer at two different times. So we generally
make the constant sedimentation rate and steady state compaction assumption and finding the rate of
deposition becomes a matter of correcting 
for the effects of steady state compaction. This can be
written as:
which is the rate of sedimentation in mass per unit area per unit time and
is the average density of
the solids in the sediment.
In pore water the process of molecular diffusion operates, but with some additional complications due to the presence of the solids. Let's consider how "having to go around" the sediment solids can effect Fick's Laws. In an aqueous environment we write:
for Fick's first and second laws. But while I'm at it I want to show you two other geometries that occur frequently in sediments that you may, someday, find handy. In spherical geometries Fick's second law becomes:
and in cylindrical geometries it is:
Now in sediments corrections must also be made not only for geometry but also for electrical effects:
where Zi is the valence of i, T is the absolute temperature, R is the gas constant, mi is the mobility of ion i at infinite dilution, E is the electrical potential, and F is Faraday's constant. To correct for electrical effects we need one more piece of information, electroneutrality:
Now electrical effects may be appreciable, but more important are the effects of tortuosity. Tortuosity is brought about by the tortuous path ions must follow when diffusing through the pore fluids due to the presence of the solids. The ions are not free to diffuse in any direction, they collide with the particles and we must compensate for this. Tortuosity is defined as:
where 
represents the actual path length the ion must travel over a sediment depth of dz. Since
and the diffusion coefficient in sediments is expressed as:
here Ds refers to the whole sediment diffusion coefficient. Unfortunately 
is difficult to
evaluate/measure, typically then, we use the following relationships:
where F is the formation factor which is given by the ratio of the whole sediment resistivity to the pore waters resistivity. If n equals 2 in the above formulation it is called Archie's Law and it seems to work well for sands and sandstones. Using Ds with Fick's laws becomes:
It should be noted here that so far we have been talking about the pore water concentration C, as we shall see, these equations can be made to look more like the ones we're used to by recasting them in terms of the whole sediment.
Bioturbation refers to the mixing activities of benthic organisms. Some of these creatures influence can reached several tens of centimeters beneath the seawater-sediment interface. Some times their influence isn't due to actual movement of sediment solids, some creatures regularly flush their burrows with seawater and this effect is called irrigation.
Because each organism is unique in its impact on the sediment environment, all bio-mixing processes are generally lumped together and described as a random mixing process, much like diffusion. For solids:
where 
equals the mass of solid per volume of total sediment and DB is the biodiffusional
coefficient. For pore waters:
where in this case the I stands for irrigation. Keep in mind that bioturbation can also affect the porosity.
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