## 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:

ρ_{b}= ρ_{fl}Φ + ρ_{ma}(1-Φ) Where: ρ_{b}: is the formation bulk density (read from the density log) ρ_{ma}: is the matrix density ρ_{fl}: is the fluid density

Porosity (Φ) is:

Φ = (ρ_{ma}- ρ_{b}) / (ρ_{ma}- ρ_{fl})

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

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