Note:

Formula Explanation: This formula calculates the volume of a hydraulic fracture using the PKN model. It helps in designing and monitoring hydraulic fracturing operations for oil, gas, and geothermal applications.

Parameters:

• ( x_f ) (Fracture Half-Length in ft): The distance from the center of the fracture to the tip.
• ( h_f ) (Fracture Height in ft): The vertical height of the fracture.
• ( \overline{w}_m) (Average Fracture Width in ft): The average width of the fracture.

Real-Life Applications:

• Oil & Gas Industry: Determines fracture volume for efficient hydrocarbon extraction.
• Geothermal Energy: Helps in designing heat extraction fractures.
• Mining & Rock Mechanics: Optimizes underground rock fracturing.

Conclusion:

Using this calculation, engineers can design effective fractures to maximize resource extraction while ensuring environmental and structural safety.