All three of these examples, and indeed any other example as well, show that as . This result is universal. The other limit for gives somewhat different results for the three cases considered, but they can all be approximated by using the form

(40) |

Since one of the implicit goals of the dynamic permeability analysis
is to determine a universal form for the function and thereby
determine a universal form for the dynamic permeability, it is
important to consider how these problems differ from each other.
The radius *R* is a measure of the particle size, but this size is not
easy to relate to the radius of the cylindrical pore in the third
case, or to the duct height in the second case. It would make more
sense to relate these quantities in some more general way since
the typical rock sample will not have any of these geometries.
Perhaps the obvious choice is to use itself, since we need
a pertinent measure of length squared, and that is exactly what
the low frequency permeability is.

In fact, if we first consider the form of (37) and take the point of view that the factor in the denominator determines a ``natural'' characteristic frequency for the problem given by

(41) |

(42) |

There are some exceptions to these rules but they are beyond our
present scope, so the reader is encouraged to see the paper by
Pride *et al.* (1993) for an extended discussion.

7/8/2003