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DYNAMIC PERMEABILITY AND TORTUOSITY

Now we will return to the expression (9) and make the following two definitions: First, the dynamic tortuosity is given by
   \begin{eqnarray}
\alpha(\omega) \equiv \phi q(\omega)/ \rho_f =
\alpha + iF(\xi)\eta\phi/\kappa_0\omega
 \end{eqnarray} (30)
and, second, the inverse of the dynamic permeability is given by
   \begin{eqnarray}
{{1}\over{\kappa(\omega)}} \equiv
{{\omega q(\omega)}\over{i \eta\rho_f}}.
 \end{eqnarray} (31)
This second expression can also be rewritten as
   \begin{eqnarray}
\kappa(\omega) = {{\kappa_0}\over{F(\xi) - i\kappa_0\alpha\omega/\eta\phi}}.
 \end{eqnarray} (32)
The motivations for both definitions can be seen in their limiting values:
\begin{eqnarray}
\alpha(\infty) = \alpha \qquad\hbox{and}\qquad
\kappa(0) = \kappa_0.
 \end{eqnarray} (33)
These results follow once it is recognized that the dynamic viscosity factor $F(\xi)$ has unity as its the limit when $\omega \to 0$ and, although it can have differing numerical factors, it always goes like $(-i \omega/\omega_0)^{1/2}$ for large $\omega \to \infty$. We will give some examples of this behavior in the next section.


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Next: ANALYTICAL EXAMPLES OF THE Up: Berryman: Dynamic permeability Previous: Another Interpretation of as
Stanford Exploration Project
7/8/2003