# Analysis of a well from a PI test

## Input(s)

P: Average Reservoir Pressure (psi)

q: Flow Rate (STB/day)

$$P_{w f}$$: Well Flowing Pressure (psi)

$$\mathrm{k}$$: Permeability $$(\mathrm{mD})$$

B: Volume Factor (RB/STB)

$$\mathrm{h}$$: Thickness of Reservoir ( $$\mathrm{ft}$$ )

$$\mu$$: Oil Viscosity $$(\mathrm{cP})$$

$$r_{e}$$: Drainage Radius (ft)

$$r_{w}$$: Wellbore Radius (ft)

## Output(s)

J: Productivity index (STB/day/psi)

$$k_{j}$$: Average Permeability $$(\mathrm{mD})$$

s: Skin Factor (dimensionless)

## Formula(s)

$\begin{gathered} J=\frac{q}{P-P_{w f}} \\ k_{j}=141.2 * J * B * \mu * \frac{\ln \left(\frac{r_{e}}{r_{w}}\right)-0.75}{h} \\ s=\left(\frac{k}{k_{j}}-1\right) *\left(\ln \left(\frac{r_{e}}{r_{w}}\right)-0.75\right) \end{gathered}$

## Reference(s)

Lee, J., Rollins, J. B., & Spivey, J. P. (2003). Pressure Transient Testing (Vol. 9). Richardson, Texas: Society of Petroleum Engineers, Page: 16.

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### Analysis of a flow test with smoothly varying rates

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