Porosity and Permeability in Bioturbated Sediments - Trace Fossils as Indicators of Sedimentary Environments - page 816

1
P

K harmonic ¼ :

n

d i
k i d

i¼ 1

Finally, if the porous medium is not layered (i.e., it is homogeneous), the effec-
tive homogeneous permeability is isotropic and is best estimated by the volume-
weighted geometric mean of the measured permeabilities ( Warren et al., 1961 ):

X

n

In ð K i Þ d i

In ð k geometric Þ¼ :

d

i ¼ 1

Gingras et al. (1999) explored the concept of applying arithmetic and harmonic
means to estimate the bulk permeability of bioturbated media. By developing a
set of empirical and numerically modeled solutions to bulk permeability, they
showed that, under conditions of low burrow connectivity, bulk permeability
could best be characterized using the harmonic mean. As burrow networks
became increasingly interconnected, a modified arithmetic mean could be used,
particularly for the estimation of k v . The geometric mean is broadly applied in
transitional situations where the permeable burrow structures were only locally
connected (this is further explored in La Croix et al., 2012 ). For these studies,
the above equations were modified such that the weighted volume (i.e., d i / d )
represents the proportional volume occupied by burrows, which is proportional
to burrowing intensity.

3.2 Bioturbation Intensity and Connectivity
Higher intensities of bioturbation contribute to a higher effective permeability
in two ways: (1) by increasing the amount of permeable flow medium present,
and (2) by providing continuous flow paths through burrow interpenetration.
Gingras et al. (1999) conducted a sensitivity analysis of flow responses in a
numerical model with varying burrowing volumes (1%, 2%, 10%, 25%, and
50%). Because burrows possess at least a partial vertical component, changes
in burrow abundance have an effect on both the bulk k h and k v . Generally, ver-
tical permeability is semilogarithmically enhanced by increases in burrow den-
sity ( Gingras et al., 1999; Weaver and Schultheiss, 1983 ).
As noted above, burrow interpenetrations increase in number with bioturba-
tion intensity; exceptions to this generalization might include monospecific
assemblages such as Skolithos piperock, wherein, due to the burrowmorphology,
interpenetrations are rare. Using a range of recognized burrow morphologies and
populating a three-dimensional model using various Monte Carlo simulations,
La Croix et al. (2012) produced randomly generated bioturbate flow media.
They observed that between levels of 20% and 30% bioturbation (by volume),
continuous flow paths were formed across the modeled flowmedium. Above this
degree of bioturbation, the geometric and arithmetic means of permeability can be
used to characterize the bulk permeability of a flow medium.