Production EngineeringHydraulic Fracturing

Fracture-Fluid Invasion Velocity - Acidizing Formula

v_N=0.0374\sqrt{\frac{k\phi\Delta P_v}{\mu t}}

Fracture-Fluid Invasion Velocity - Acidizing calculates fluid loss velocity for hydraulic fracturing workflows in production engineering.

Calculate

How engineers use this formula

Use this formula when the listed inputs (DeltaP_v, mu, phi_pct, k, t) 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, v_N equals 0.482832 ft/min.

DeltaP_vpsi

1000

mucP

phi_pct%

kDarcy

0.5

tmin

Inputs

DeltaP_v

psi

Pressure Difference Between Fracture Wall and Fluid Interface

mu

Viscosity

phi_pct

Porosity

k

Darcy

Permeability

t

min

Time

Outputs

v_N

ft/min

Fluid Loss Velocity

DeltaP_v

psi

Pressure Difference Between Fracture Wall and Fluid Interface

t

min

Time

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 41.

Source