Job Timeline — Standard NaNO₃ / Flour
Lumped-parameter ignition → burn → vent simulation. Hold over the charts to read instantaneous values.
- Depth
- 12,000 ft
- BHP
- 7,676 psi
- BHT
- 88 °F
r₀·(P/P_ref)^n → ideal-gas pressure rise in fixed effective volume → exponential vent with time constant τ. First-order; not a CFD. Use for relative comparison between formulations and confinement geometries.Multi-cluster stage
analytical stress shadow · Lorentzian decaySequentially fired perforation clusters along a lateral. Earlier clusters induce a local minimum-stress increase on later neighbors, derating their effective performance. The shadow kernel can be the simple Lorentzian heuristic or — when fracture geometry is solved below — a Sneddon (2-D plane-strain) elastic kernel with Olson (2004) finite-height 3-D decay.
Fracture Geometry
PKN regimePore-pressure ΔP and temperature ΔT at the fracture face shift σ_min via poro-/thermo-elastic Δσ_h. Width, net pressure and K_I/K_IC are re-solved against σ_min_eff.
- · §12.3 BHP drive = BHP − σ_min_eff = 4000 − 5069 = -1069 psi (below closure).
- · PKN selected: L > h ⇒ height-contained planar growth.
- · Toughness-dominated: net pressure exceeds elastic prediction.
- · Depletion Δσ_h = -2431 psi (poro -1149 + thermo -1282); σ_min_eff = 5069 psi.
- · §12.3 BHP drive = BHP − σ_min_eff = 4000 − 5069 = -1069 psi (below closure).
Depletion sensitivity sweep
w_avg and p_net,eff vs ΔP (pore pressure). Vertical line = current run value.
Click any cluster marker on the lateral to inspect its per-source stress contributions and effective performance.
σ₀·a²/(d²+a²). Effective performance η = η_base − k·Σ Δσ. Cluster efficiency = fraction firing within 90% of the lead cluster. For pre-job spacing screening; calibrate k against measured production logs before field decisions.