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
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
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.