Which expression correctly represents the denominator in the productivity index?

Which expression correctly represents the denominator in the productivity index?

• A. The average reservoir pressure
• B. The wellbore pressure pwf
• C. The product of flow rate and pressure differential
• D. The drop in pressure from the average reservoir pressure to the flowing wellbore pressure pwf

Answer: (D)

The key idea is that the denominator in the productivity index represents the pressure drop driving production. In the productivity index, the production rate is divided by the difference between the average reservoir pressure and the flowing wellbore pressure, written as p_r minus p_wf. This pressure drop is what propels fluids from the reservoir into the well, so it must appear as the denominator to relate how much production you get per unit driving pressure. Using just the average reservoir pressure would omit the necessary pressure difference that drives flow. Multiplying flow rate by a pressure differential yields a quantity with different units (not a simple pressure drop) and doesn’t represent the driving force in the index. The option that describes the drop in pressure from the average reservoir pressure to the flowing wellbore pressure pwf accurately captures the driving force behind production.

The key idea is that the denominator in the productivity index represents the pressure drop driving production. In the productivity index, the production rate is divided by the difference between the average reservoir pressure and the flowing wellbore pressure, written as p_r minus p_wf. This pressure drop is what propels fluids from the reservoir into the well, so it must appear as the denominator to relate how much production you get per unit driving pressure.

Using just the average reservoir pressure would omit the necessary pressure difference that drives flow. Multiplying flow rate by a pressure differential yields a quantity with different units (not a simple pressure drop) and doesn’t represent the driving force in the index. The option that describes the drop in pressure from the average reservoir pressure to the flowing wellbore pressure pwf accurately captures the driving force behind production.