Wellbore Genius
Wellbore Genius
Performance modeling
v1.0Solver: OK
Analytical verification
Closed-form KGD, PKN, radial, Carter, and Theis cases the kernel must match every build — independent of history matching. Each row renders the equation, assumptions, validity bounds, and the L2 / L∞ relative error vs the textbook solution. Thresholds: ok ≤ 5%, watch ≤ 15%, fail otherwise.
Rollup: OK (≤ 5%)
How to use: the default rows score the analytical engine against itself (trivially OK). To stress-test the bands, dial a perturbation % per case to simulate solver drift; the verdict will flip through OK → WATCH → FAIL at 5% and 15%. Real solver hookup runs in CI via
bun test verification/.KGD plane-strain (Geertsma & de Klerk 1969)
JPT Dec 1969 pp. 1571-1581
OK (≤ 5%)
Equation
x_f = 0.539 · (E'·q³ / µ·h³)^(1/6) · t^(2/3) ; w_w = 2.36 · (µ·q·x_f² / E'·h)^(1/4)
Assumptions
- Plane-strain (KGD) geometry — fixed height
- Newtonian fluid, zero leak-off
- Single, planar bi-wing fracture
- Linear elastic, homogeneous rock
Validity: Valid when fracture length >> height and viscous dissipation dominates toughness. Fails outside Newtonian regime or with significant Carter leak-off.
L∞ rel error
0.000%
L2 rel error
0.000%
| Field | Simulated | Expected (analytical) | Rel error |
|---|---|---|---|
| halfLengthFt | 1210.7557 | 1210.7557 | 0.000% |
| widthAtWellboreIn | 0.4682 | 0.4682 | 0.000% |
Show raw simulated payload
{
"halfLengthFt": 1210.7557495072708,
"widthAtWellboreIn": 0.4681648852714756
}PKN viscosity-dominated (Nordgren 1972)
SPE-3009
OK (≤ 5%)
Equation
x_f = 0.524 · (E'·q³ / µ·h⁴)^(1/5) · t^(4/5) ; w_w = 3.04 · (µ·q·x_f / E')^(1/4)
Assumptions
- Vertical plane-strain (PKN) geometry — fixed height
- Newtonian fluid, zero leak-off
- Elliptical cross-section, slow-growth (decoupled tip)
- Linear elastic, homogeneous rock
Validity: Valid for length-dominated growth when height is well-contained by stress barriers. Breaks down for radial / unconfined geometry.
L∞ rel error
0.000%
L2 rel error
0.000%
| Field | Simulated | Expected (analytical) | Rel error |
|---|---|---|---|
| halfLengthFt | 2193.2726 | 2193.2726 | 0.000% |
| widthAtWellboreIn | 0.3751 | 0.3751 | 0.000% |
Show raw simulated payload
{
"halfLengthFt": 2193.272618677552,
"widthAtWellboreIn": 0.37506393102058033
}Radial K-vertex (Savitski-Detournay 2002)
IJSS 39 pp.6311
OK (≤ 5%)
Equation
R(t) = 0.8546 · (E'·q·t / K')^(2/5) ; w₀ = 0.6537 · (K'⁴·t / E'⁴·q)^(1/5)
Assumptions
- Penny-shaped radial geometry (no height confinement)
- Toughness-dominated K-vertex regime
- Constant injection, zero leak-off
- Linear elastic homogeneous medium
Validity: Valid when dimensionless toughness K_m ≫ 1. In viscous regime use the M-vertex / MK universal asymptote instead.
L∞ rel error
0.000%
L2 rel error
0.000%
| Field | Simulated | Expected (analytical) | Rel error |
|---|---|---|---|
| halfLengthFt | 1550.3392 | 1550.3392 | 0.000% |
| widthAtWellboreIn | 0.0159 | 0.0159 | 0.000% |
Show raw simulated payload
{
"halfLengthFt": 1550.3391860618278,
"widthAtWellboreIn": 0.015949917637991078
}References: Geertsma & de Klerk, JPT 1969; Nordgren, SPE-3009 1972; Savitski & Detournay, IJSS 39 (2002); Howard & Fast, Hydraulic Fracturing Monograph 1957/1970; Theis, EOS Trans. AGU 1935.