PKN Hydraulic Fracture Geometry & Propagation Calculator

Model 2D fracture propagation where fracture length is much greater than height (L >> h), calculating wellbore dynamic width, tip net pressure, and half-length.

Treatment & Formation Parameters

Slurry Injection Rate Q_i (bbl/min):

Pumping Duration t_p (min):

Fracture Height h_f (ft): Confined between bounding stress barriers

Plane-Strain Modulus E' (psi): E' = E / (1 - ν²)

Apparent Slurry Viscosity μ (cP):

Fluid Efficiency η (% retained in frac): Leakoff consumes (100 - η)%

PKN Fracture Geometry Dimensions

Fracture Half-Length x_f:

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Max Wellbore Width w_0:

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Average Fracture Width w_avg:

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Net Wellbore Pressure P_net:

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Total Injected Slurry Volume:

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Created Fracture Volume:

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Frequently Asked Questions

When is the PKN model preferred over the KGD model?

Use the PKN model whenever the fracture half-length exceeds its height (xf / hf > 2 or 3) and height is strictly bounded by stress barriers. Use KGD (Khristianovic-Geertsma-de Klerk) for short, unconfined, or radial fractures where length is comparable to height.

What is the plane-strain modulus E'?

The plane-strain Young’s modulus accounts for lateral constraint in the rock matrix: E' = E / (1 - ν²), where E is static Young’s modulus and ν is Poisson’s ratio (typically 0.20 to 0.28 for sandstone/shale).