Geertsma's model for porosity/transit-time relationship
Input(s)
\(\mathrm{K}_{\mathrm{b}}\): Bulk Modulus Constant for Formation (dimensionless)
\(\sigma_{\mathrm{b}}\): Bulk Density \(\left(\mathrm{kg} / \mathrm{m}^{3}\right)\)
\(\mu_{\mathrm{b}}\): Poisson Ratio for Formation (dimensionless)
\(\mathrm{K}_{\mathrm{ma}}\): Bulk Modulus Constant for Matrix (dimensionless)
\(\sigma_{\text {ma }}\): Matrix Density \(\left(\mathrm{kg} / \mathrm{m}^{3}\right)\)
\(\mu_{\mathrm{ma}}\): Poisson (dimensionless)
Output(s)
\(\mathrm{V}_{\mathrm{b}}\): Acoustic Velocity in Bulk Formation \((\mathrm{m} / \mathrm{s})\)
\(\mathrm{V}_{\mathrm{ma}}\): Acoustic Velocity in Matrix (m/s)
Formula(s)
\[
\begin{gathered}
\mathrm{V}_{\mathrm{b}}=\left(\left(3 * \frac{\mathrm{K}_{\mathrm{b}}}{\sigma_{\mathrm{b}}}\right) *\left(\frac{1-\mu_{\mathrm{b}}}{1+\mu_{\mathrm{b}}}\right)\right)^{0.5} \\
\mathrm{~V}_{\mathrm{ma}}=\left(\left(3 * \frac{\mathrm{K}_{\mathrm{ma}}}{\sigma_{\mathrm{ma}}}\right) *\left(\frac{1-\mu_{\mathrm{ma}}}{1+\mu_{\mathrm{ma}}}\right)\right)^{0.5}
\end{gathered}
\]
Reference(s)
Bassiouni, Z., 1994, Theory, Measurement, and Interpretation of Well Logs. SPE Textbook Series Vol. 4. Chapter 3, Page: 55.