Geomechanics and FracturingNaturally Fractured Reservoirs

Single-Fracture Flow Rate from Cubic Law Formula

Q=\frac{Wb_h^3\Delta p}{12\mu L}

Single-Fracture Flow Rate from Cubic Law calculates single-fracture flow rate for naturally fractured reservoirs workflows in geomechanics and fracturing.

Calculate

How engineers use this formula

Use this formula when the listed inputs (W_m, b_h_mm, DeltaP_Pa, mu_Pa_s, L_m) are known and the assumptions behind the cited naturally fractured reservoirs 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, Q_m3_s equals 0.000208 m3/s.

W_mm

b_h_mmmm

0.5

DeltaP_PaPa

100000

mu_Pa_sPa s

0.001

L_mm

Inputs

W_m

Fracture Width

b_h_mm

Hydraulic Fracture Aperture

DeltaP_Pa

Pressure Difference Across Fracture Length

mu_Pa_s

Pa s

Fluid Dynamic Viscosity

L_m

Fracture Flow Length

Outputs

Q_m3_s

m3/s

Single-Fracture Flow Rate

W_m

Fracture Width

b_h_mm

Hydraulic Fracture Aperture

DeltaP_Pa

Pressure Difference Across Fracture Length

mu_Pa_s

Pa s

Fluid Dynamic Viscosity

L_m

Fracture Flow Length

Source and review

reviewed

CubicLawPermeability, OpenGeoSys

OpenGeoSys documentation. CubicLawPermeability property.

Source