Analytical parity scoreboard
Closed-form solutions from analyticalFractureBenchmarks.ts — the reference values our numerical kernels must reproduce. PKN and KGD use the same constants and one-wing rate (q = q_total/2) as the analytical verification page, so both pages agree for the same inputs. Rock: E = 30.0 GPa, ν = 0.22, E' = 31.53 GPa.
Reference cases
| Benchmark | Quantity | Value | Formula | Reference |
|---|---|---|---|---|
Sneddon 1946 plane-strain slit | Max aperture w₀ (Δp=500 psi, a=200 ft) | 0.0875 ft | w₀ = 4·p·a / E' | Sneddon (1946) Proc. R. Soc. A |
Sneddon 1946 penny crack | Max aperture w₀ (Δp=500 psi, R=200 ft) | 0.0557 ft | w₀ = 8·p·R / (π·E') | Sneddon (1946) Proc. R. Soc. A |
PKN (Nordgren 1972) | Half-length L(1 hr) | 6212.7710 ft | L = 0.524·[E'·q³/(μ·h⁴)]^(1/5)·t^(4/5), q = q_total/2 | Nordgren, JPT 1972 |
PKN (Perkins-Kern) | Wellbore width w_w(1 hr) | 0.0220 ft | w_w = 3.04·[μ·q·L/E']^(1/4), q = q_total/2 | Nordgren, JPT 1972 (Perkins-Kern geometry) |
KGD plug-flow | Half-length L(1 hr) | 2883.2600 ft | L = 0.539·[E'·q³/(μ·h³)]^(1/6)·t^(2/3), q = q_total/2 | Geertsma-de Klerk, JPT 1969 |
Nordgren radial | Radius R(1 hr) | 980.2133 ft | R = 0.548·[E'·q³/μ]^(1/9)·t^(4/9) | Nordgren, JPT 1972 (radial) |
Rice near-tip asymptotic | Aperture at 1 ft from tip (K_I=1500 psi·√ft) | 0.0010 ft | w(r) = (K_I/E')·√(32r/π) | Rice (1968) — Fracture Vol II, Ch 3 |
Growth cases use q = 60 bpm into one wing, μ = 5 cP, h = 100 ft, t = 1 hr and no leak-off, so the lengths are the no-loss upper bound for those inputs, not a field half-length. These are the reference values the numerical kernels are compared against.