77
In the following Section 3.2, the laws of
diffusion and the particularities of their
application to sediment pore waters will be
treated in more detail. In this context, the problem
of steady state and non-steady state situations
will have to be covered, since the simple examples
described above have anticipated steady state
situations. Moreover, as a further simplification,
the examples of this section have by necessity
neglected advection, bioirrigation, and bioturbation. These processes will be discussed in detail
in Section 3.6. Section 3.7 will then cover the investigations of the sediment’s solid phase and
thereby disclose the result of one or the other
process of early diagenesis.
3.2
Calculation of Diffusive
Fluxes and Diagenetic
Reaction Rates
3.2.1
Steady State and
Non-Steady State Situations
In the preceding section and especially in all the
following chapters, one pair of terms will assume
extraordinary importance for describing and
understanding biogeochemical processes: the
steady state and non-steady state situation.
Let us first consider the steady state situation
as its description is more straight forward in a
model concept. In Figure 3.2c a concentration
profile is shown in which a substance is continually consumed at a specific rate of reaction and
within a reactive layer. At the same time, a constant
concentration is prevalent in the bottom water
above the sediment surface, an infinite reservoir as
compared to the consumption in the sediment. It
follows therefore that a constant concentration
gradient exists between the sediment surface and
the reactive layer, and thus everywhere the same
diffusive flux. Such a concentration gradient is
referred to as being in steady state. It remains in
this condition as long as its determining factors -
turn-over rates in the reactive layer, concentration
at the sea-floor, dimension and properties of the
space between the reactive layer and sediment
surface - are not changed.
Any change of the conditions that is liable to
exert any kind of influence on the concentration
profile, terminates the steady state situation. A
non-steady state emerges, which is a time-dependent situation occurring in the pore water. If the
system remains unperturbed in the changed
situation for a sufficient length of time, a new
steady state situation can become established,
different from the first and reflecting the novel
configuration of conditions.
Strictly speaking, there are no real steadystate situations in nature. Even the sun had
begun to shine at a certain time, the earth and,
upon her, the oceans have come into existence at
a certain time, and all things must pass sooner or
later. Hence, the term referring to the steady-state
condition also depends on the particular stretch
of time which is under study, as well as on the
dimension of the system, and, not least, on the
accuracy of the measurements with which we
examine the parameters that describe the system.
Fig. 3.3 Calculated non-steady state concentration profiles in pore water of a young sediment. It was assumed
that the concentration of ‘1’ has been previously
constant in the pore water of the sediment as well as in
the supernatant bottom water for a long period of time,
so that a steady state situation was prevalent. Then the
concentration of bottom water changed shortly to ‘9’.
The concentration profiles a to e are non-steady states
after 2 and up to 48 hours. The calculation of such nonsteady state concentration profiles can be performed , for
example, with the aid of the model program CoTAM
(Hamer and Sieger 1994) or CoTReM (cf. Chap. 15).
3.2
Calculation of Diffusive Fluxes and Diagenetic Reaction Rates
In the following Section 3.2, the laws of
diffusion and the particularities of their
application to sediment pore waters will be
treated in more detail. In this context, the problem
of steady state and non-steady state situations
will have to be covered, since the simple examples
described above have anticipated steady state
situations. Moreover, as a further simplification,
the examples of this section have by necessity
neglected advection, bioirrigation, and bioturbation. These processes will be discussed in detail
in Section 3.6. Section 3.7 will then cover the investigations of the sediment’s solid phase and
thereby disclose the result of one or the other
process of early diagenesis.
3.2
Calculation of Diffusive
Fluxes and Diagenetic
Reaction Rates
3.2.1
Steady State and
Non-Steady State Situations
In the preceding section and especially in all the
following chapters, one pair of terms will assume
extraordinary importance for describing and
understanding biogeochemical processes: the
steady state and non-steady state situation.
Let us first consider the steady state situation
as its description is more straight forward in a
model concept. In Figure 3.2c a concentration
profile is shown in which a substance is continually consumed at a specific rate of reaction and
within a reactive layer. At the same time, a constant
concentration is prevalent in the bottom water
above the sediment surface, an infinite reservoir as
compared to the consumption in the sediment. It
follows therefore that a constant concentration
gradient exists between the sediment surface and
the reactive layer, and thus everywhere the same
diffusive flux. Such a concentration gradient is
referred to as being in steady state. It remains in
this condition as long as its determining factors -
turn-over rates in the reactive layer, concentration
at the sea-floor, dimension and properties of the
space between the reactive layer and sediment
surface - are not changed.
Any change of the conditions that is liable to
exert any kind of influence on the concentration
profile, terminates the steady state situation. A
non-steady state emerges, which is a time-dependent situation occurring in the pore water. If the
system remains unperturbed in the changed
situation for a sufficient length of time, a new
steady state situation can become established,
different from the first and reflecting the novel
configuration of conditions.
Strictly speaking, there are no real steadystate situations in nature. Even the sun had
begun to shine at a certain time, the earth and,
upon her, the oceans have come into existence at
a certain time, and all things must pass sooner or
later. Hence, the term referring to the steady-state
condition also depends on the particular stretch
of time which is under study, as well as on the
dimension of the system, and, not least, on the
accuracy of the measurements with which we
examine the parameters that describe the system.
Fig. 3.3 Calculated non-steady state concentration profiles in pore water of a young sediment. It was assumed
that the concentration of ‘1’ has been previously
constant in the pore water of the sediment as well as in
the supernatant bottom water for a long period of time,
so that a steady state situation was prevalent. Then the
concentration of bottom water changed shortly to ‘9’.
The concentration profiles a to e are non-steady states
after 2 and up to 48 hours. The calculation of such nonsteady state concentration profiles can be performed , for
example, with the aid of the model program CoTAM
(Hamer and Sieger 1994) or CoTReM (cf. Chap. 15).
3.2
Calculation of Diffusive Fluxes and Diagenetic Reaction Rates