## Petroleum Engineering Equations & Formulas

#### Hydrocarbon Saturation

C_{t}= S_{w}^{n}Φ^{m}C_{w}Where: C_{t}: is the conductivity C_{w}: is the pore water conductivity S_{w}: is the water saturation^{n}: is the saturation exponent^{m}: is the cementation exponent

In pratice logging tools are often used to measure the resistivity of the formation rather than the conductivity and therefore the above equation is more commonly inverted and expressed as:

R_{t}= S_{w}^{-n}Φ^{-m}R_{w}Where: R_{t}: is the formation resistivity (ohm.m) S_{w}: is the water saturation (fraction) Φ : is porosity(fraction) R_{w}: is the water resistivity (ohm.m) m : is the cementation exponent n : is the saturation exponent

In a large ange of reservoirs the saturation and cememntation exponents can be taken as m=n=2. The remaining unknown is the water saturation and the equation can be rearranged so that:

S_{w}=^{n}√((R_{w})/(Φ^{m}R_{t})) and hydrocarbon saturation (fraction) S_{h}= 1 - S_{w}

### $$ C_{t} = S_{w}^{n}\Phi^{m}C_{w} $$

Where:

- $\rho_{b}$ is the formation bulk density
- $\rho_{ma}$ is the matrix density
- $\rho_{f}$ is the fluid density

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

### $$ R_{t} = S_{w}^{-n}\Phi^{-m}R_{w} $$

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

### $$ S_{w} = \sqrt[n]\frac{R_{w}}{\Phi^{m}R_{t}} $$

and hydrocarbon saturation (fraction)