# 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.

An unhandled error has occurred. Reload 🗙