How is the productivity index calculated?

How is the productivity index calculated?

• A. q divided by the difference between the surface pressure and the wellbore pressure
• B. The well flow rate q multiplied by the drop in pressure from the average reservoir pressure to the flowing wellbore pressure
• C. The well flow rate q divided by the drop in pressure from the surface pressure to the reservoir pressure
• D. Well flow rate q, divided by the drop in pressure from the average reservoir pressure to the flowing wellbore pressure pwf

Answer: (D)

Productivity index describes how much fluid a well produces for each unit of pressure difference driving the flow from the reservoir to the well. It is defined as J = q / (p_r,avg − p_wf), where q is the flow rate, p_r,avg is the average reservoir pressure around the well, and p_wf is the flowing wellbore pressure. The denominator represents the pressure drop that pushes fluid toward the well; a larger drop for the same q means a higher driving force, but the productivity index itself measures how efficiently that force translates into flow. The chosen option uses this exact drop—between the average reservoir pressure and the flowing wellbore pressure—and divides the rate by it, which is the correct form. The other formulations mix surface pressures or use multiplication, which do not reflect the standard definition or yield the wrong units.

Productivity index describes how much fluid a well produces for each unit of pressure difference driving the flow from the reservoir to the well. It is defined as J = q / (p_r,avg − p_wf), where q is the flow rate, p_r,avg is the average reservoir pressure around the well, and p_wf is the flowing wellbore pressure. The denominator represents the pressure drop that pushes fluid toward the well; a larger drop for the same q means a higher driving force, but the productivity index itself measures how efficiently that force translates into flow. The chosen option uses this exact drop—between the average reservoir pressure and the flowing wellbore pressure—and divides the rate by it, which is the correct form. The other formulations mix surface pressures or use multiplication, which do not reflect the standard definition or yield the wrong units.