To find ρb:

To find Φ:

## Petroleum Engineering Equations & Formulas

#### Porosity

Reservoir porosity can be measured directly from core samples or indirectly using logs. Logging is the most common method employed. The formation density log is the main tool for ensuring porosity. The tool is constructed so that medium energy gamma rays are directed from a radioactive source into the formation. These rays react with the formation by a process know as Compton scattering. Gamma rays lose energy each time they collide with an electron. The number of gamma rays reaching detectors in the tool is inversely proportional to the number of electrons in the formation which is related to the formation bulk density. A low gamma count implies a high electron (and bulk) density and therefore a low porosity

The bulk density measured by the logging tool is the weighted average of the rock matrix and fluid densities so that:

       ρb = ρflΦ + ρma(1-Φ)

Where:

ρb : is the formation bulk density (read from the density log)

ρma: is the matrix density

ρfl: is the fluid density



Porosity (Φ) is:

       Φ = (ρma - ρb) / (ρma - ρfl)



### $$\rho_{b} = \rho_{fl}\Phi + \rho_{ma}(1-\Phi)$$

The formula can be rearranged to give the porosity %($\Phi$)

### $$\Phi = \frac{\rho_{ma} - \rho_{b}}{\rho_{ma} - \rho_{fl}}$$

Where:

• $\rho_{b}$   is the formation bulk density
• $\Phi$    is the porosity (%)
• $\rho_{ma}$ is the matrix density
• $\rho_{fl}$   is the fluid density