are near the bottom of the range used by Saffer and Bekins (1998) relationship, and can
be represented by a line with the relationship, log (k) = -20.15 + 5.39n (Figure 3-4).
Modeling Methods
Theoretical Background
As sediments are loaded, the sediment column beneath will compact if the pore
fluid can escape at a rate comparable to the loading rate. However, if the permeability of
the sediment column is low, dewatering will be inhibited, excess pore pressures will
build, and compaction will be prevented. Darcy's Law expresses the relationship
between pore pressures, sediment properties, and fluid velocities. For constant density
saturated flow, Darcy's Law can be written in terms of the hydraulic head (Voss, 1984).
v =K Vh (4a)
P
where h = -- + h (4b)
Pfg
where v is pore fluid velocity [L T-], Kis hydraulic conductivity [L T-], n is porosity, h
is hydraulic head [L], pfis fluid density [M L-3], g is gravitational acceleration [L T-2],
and hz is elevation head [L]. Hydraulic conductivity is defined by K=kpfg /, where k is
intrinsic permeability [L2] and p is dynamic viscosity [M L-1 T-1]. Intrinsic permeability
is a function of the porous medium while fluid density and viscosity depend on the
properties of the fluid and may change with temperature, salinity, and to a lesser extent
with pressure.
Combining the mass conservation of fluid with Darcy's law (Eq. 4a), the following
equation can be written for diffusion of head in porous media for saturated fluid flow.
?h
V(KVh) = S + Q (5)
-at