Geomechanics and FracturingNaturally Fractured Reservoirs

Warren-Root Interporosity Flow Coefficient Formula

\lambda=\alpha r_w^2\frac{k_m}{k_f}

Warren-Root Interporosity Flow Coefficient calculates interporosity flow coefficient for naturally fractured reservoirs workflows in geomechanics and fracturing.

Calculate

How engineers use this formula

Use this formula when the listed inputs (alpha, r_w, k_m, k_f) 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, lambda_ip equals 0.000065 dimensionless.

alpha1/ft^2

0.6

r_wft

0.33

k_mmD

k_fmD

1000

Inputs

alpha

1/ft^2

Matrix Block Shape Factor

r_w

Wellbore Radius

k_m

Matrix Permeability

k_f

Fracture Permeability

Outputs

lambda_ip

dimensionless

Interporosity Flow Coefficient

alpha

1/ft^2

Matrix Block Shape Factor

r_w

Wellbore Radius

k_m

Matrix Permeability

k_f

Fracture Permeability

Source and review

reviewed

Warren, J.E. and Root, P.J. 1963. The Behavior of Naturally Fractured Reservoirs; summarized in Water 2024, 16(8), 1072.

Source