ΔPDD:

PI:

Q:

## Petroleum Engineering Equations & Formulas

#### Fluid Flow near the Wellbore

The difference between the following wellbore pressure (Pwf) and the average reservoir pressure ( P) is the pressure drawdown (ΔPDD).

       Pressure drawdown ΔPDD = P - Pwf [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/ΔPDD [bbl/d/psi] or [m3/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 (Bo) 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