## Petroleum Engineering Equations & Formulas

#### Fluid Flow near the Wellbore

The difference between the following wellbore pressure (P_{wf}) and the average reservoir pressure (
P) is the pressure drawdown (ΔP_{DD}).

Pressure drawdown ΔP_{DD}= P - P_{wf}[psi] or [bar] Where: P is Reservoir pressure P_{wf}is Flowing wellbore pressure

The relationship between the floarate (Q) towards the well and the pressure drawdown is approximately linear, and is defined by the productivity index (PI)

Productivity Index PI = Q/ΔP_{DD}[bbl/d/psi] or [m^{3}/d/bar]

The flowrate of oil into the wellbore is also influenced by the reservoir properties of permeability(k)
and the reservoir thickness(h), by the oil properties viscosity(μ) and formation volume factor
(B_{o}) and by any change in the resistance to flow near the wellbore whch is represented
bu the dimensionless term called skin (S). For semi-steady state flow behaviour abd radial inflow for
the oil into a vertical wellbore is represented by equation 3:

### $$ \Delta P_{DD} = \overline{P} - P_{wf}\;\;\; [psi]\;or\;[bar] $$

Where:

- $\Delta P_{DD}$ is the pressure drawdown
- $\overline{P}$ is the average reservoir pressure
- $P_{wf}$ is the flowing wellbore pressure

### $$ PI = \frac{Q}{\Delta P_{DD}} \;\;\;[bbl/d/psi]\;or\;[m^{3}/d/bar] $$

Where:

- $PI$ is the productivity index
- $Q$ is the flowrate
- $\Delta P_{DD}$ is the pressure drawdown