Note:

This formula calculates the fold of increase, measuring how much the well's productivity improves after hydraulic fracturing. A higher fold of increase indicates a more effective fracturing process. The equation compares the productivity of a fractured well against a non-fractured well.

Explanation of Parameters:

• r_e (Drainage Radius): The area from which the well extracts fluids. A larger value means a wider reservoir.
• r_w (Wellbore Radius): The radius of the drilled well, affecting fluid inflow to the wellbore.
• S_f (Skin Factor): Represents flow resistance near the well. A high S_f indicates formation damage.

Why Do Some Inputs Give Unexpected Results?

• If r_e = r_w, then ln(re / rw) = ln(1) = 0, making the formula divide by zero.
• This leads to a result of zero, which is not meaningful in this context.
• For valid results, r_e must be greater than r_w.

Valid Input Guidelines:

• r_e > r_w: Drainage radius should always be larger than wellbore radius for a meaningful calculation.
• r_w > 0: Wellbore radius must be greater than zero, as a well cannot have zero size.
• S_f: Can be any real number, but extreme values may distort results.

Real-Life Applications:

• Petroleum Industry: Determines how effective hydraulic fracturing is in increasing oil and gas production.
• Environmental Engineering: Evaluates underground water extraction efficiency.
• Geothermal Energy: Assesses the impact of well stimulation on geothermal reservoirs.
• Mining Operations: Helps optimize fluid extraction from rock formations.

Condition	Feedback Message
re = rw	Drainage radius must be greater than wellbore radius for valid calculations.
rw ≤ 0	Wellbore radius cannot be zero or negative.
Fold of Increase = 1	No improvement in productivity. Check input values!
Fold of Increase > 1	Productivity increased successfully! Effective fracturing.

Conclusion:

The fold of increase helps engineers understand how effective fracturing is in enhancing well productivity. Lower values indicate minimal improvement, while higher values show significant enhancement. Accurate input values ensure reliable calculations and real-world applicability.