To find Ct

To find Rt

To find Sw

## Petroleum Engineering Equations & Formulas

#### Hydrocarbon Saturation

       Ct = SwnΦm Cw

Where:

Ct: is the conductivity

Cw: is the pore water conductivity

Sw: 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:

       Rt = Sw-nΦ-mRw

Where:

Rt: is the formation resistivity (ohm.m)

Sw: is the water saturation (fraction)

Φ : is porosity(fraction)

Rw: 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:


Sw = n√((Rw)/(ΦmRt))

and hydrocarbon saturation (fraction)

Sh= 1 - Sw



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

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)