PKN Fracture Geometry Calculator
Calculate fracture half-length, width, net pressure, and fluid efficiency using the Perkins-Kern-Nordgren model. Replace your frac design software.
Input Parameters
E' = E / (1 − ν²) | ww = 2.5 × [(μQ Lf)/E']0.25 × hf0.25
Pnet = E' × ww / (2 × hf) | Vfrac = π/4 × wavg × hf × 2Lf
Fracture Half-Length
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Max Width (wellbore)
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Avg Width
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Net Pressure
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Fracture Volume
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Fluid Efficiency
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Fracture Width vs Distance from Wellbore
How this was calculated
PKN Model: The Perkins-Kern-Nordgren (PKN) model assumes a vertically confined fracture with an elliptical cross-section. Height is fixed; length and width evolve with time.
Plane strain modulus: E' = E / (1 - v^2)
Width at wellbore: w_w = 2.5 * [(mu * Q * Lf) / E']^0.25 * hf^0.25. Converted to consistent units (cgs) internally.
Iterative solve: Fracture half-length is solved iteratively using material balance: total volume pumped = fracture volume + fluid lost to formation.
Assumptions: Newtonian fluid, constant height, no proppant effects, Carter leak-off model, 2D geometry. For more accurate results, use a 3D planar or fully-3D simulator.
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Book a free strategy call →Understanding the PKN Fracture Model
The PKN (Perkins-Kern-Nordgren) model is one of the two classical 2D models for hydraulic fracture geometry, alongside the KGD model. In the PKN model, the fracture is assumed to have a fixed height equal to the pay zone thickness, with an elliptical cross-section perpendicular to the direction of propagation. The fracture width is maximum at the wellbore and decreases toward the tip.
The PKN model is most applicable when fracture length is significantly greater than fracture height (Lf >> hf), which is common in many tight-gas and unconventional completions. The net treating pressure increases with time in a PKN fracture, unlike the KGD model where it decreases. This difference has important implications for treatment design and pressure interpretation.
Key design outputs include: fracture half-length (how far the fracture extends from the wellbore), maximum and average width (which determines proppant placement), net pressure (critical for staying below screenout conditions), and fluid efficiency (the fraction of pumped volume that creates fracture volume vs. leaking off into the formation).
All calculations run entirely in your browser. Built by Groundwork Analytics, an AI and engineering company building digital tools for the energy industry. Get in touch or email info@petropt.com.