Production EngineeringHydraulic Fracturing

Wellbore Fracture Width - Acidizing Formula

W_w=L\left(\frac{\mu q_h}{EL^2}\right)^{0.25}

Wellbore Fracture Width - Acidizing calculates fracture width at the wellbore for hydraulic fracturing workflows in production engineering.

Calculate

How engineers use this formula

Use this formula when the listed inputs (q_h, mu, E, L) are known and the assumptions behind the cited hydraulic fracturing relationship match the engineering case being checked.

Assumptions

Input values are representative for the well, reservoir, fluid, or equipment case being evaluated.
The declared units match the field-unit constants used in the formula.
The cited formula applies to the selected petroleum engineering workflow.

Limitations

The calculation does not replace a full engineering model or operating procedure.
Accuracy depends on the source correlation, assumptions, input quality, and unit consistency.

Common mistakes

Mixing unit systems without converting the inputs.
Using default example values as field recommendations.
Applying the formula outside the source assumptions.

Default example

Using the default inputs, W_w equals 0.005373 m.

q_hm^2/s

0.1

mukg/(m s)

0.01

Ekg/(m s^2)

3000000000

Inputs

q_h

m^2/s

Injection Rate per Unit Fracture Height

mu

kg/(m s)

Fluid Viscosity

E

kg/(m s^2)

Young's Modulus

L

Fracture Length

Outputs

W_w

Fracture Width at the Wellbore

q_h

m^2/s

Injection Rate per Unit Fracture Height

mu

kg/(m s)

Fluid Viscosity

E

kg/(m s^2)

Young's Modulus

L

Fracture Length

Source and review

reviewed

Williams, B.B., Gidley, J.L. and Schechter, R.S. 1979. Acidizing Fundamentals. Henry L. Doherty Memorial Fund of AIME, Society of Petroleum Engineers of AIME, Page 29.

Source