Wellbore Genius

PKN early-time diagnostic Method

Downhole wellbore pressure and fluid-temperature evolution from the earliest resolvable time window of a height-contained PKN fracture. Compares the Nordgren analytical solution (t^(1/5) net-pressure growth) against the Newton-runner numerical kernel so the early-time formulation gap is visible on-page — not hidden inside an aggregate residual.

Inputs

Field units — converted internally to SI.

Injection rate [bpm]

Plane-strain modulus E' [Mpsi]

Viscosity μ [cP]

Fracture height h_f [ft]

Reservoir pressure [psi]

Reservoir temperature [°F]

Injection temperature [°F]

Thermal τ (Newton cooling) [s]

Hydrostatic / STP (optional)

TVD to perfs [ft]

Wellbore fluid density [ppg]

Pipe friction Δp [psi]

t_min [s]

t_max [s]

Samples [—]

Hydrostatic / surface treating pressure

p_stp = p_bhp − ρ·g·TVD + Δp_pipe. Optimal surface treating pressure to deliver the analytical BHP at each sample.

Hydrostatic p_hyd

4364 psi

Pipe friction Δp

0 psi

STP @ t_min (analytical)

1665 psi

STP @ t_max (analytical)

1719 psi

Wellbore pressure [psi]

Absolute BHP = p_res + p_net; log-time x-axis; net pressure follows Sneddon p_net = E'·w_w/(2·h_f).

med |Δp_net|/max = 31.77%

max = 596.21%

Wellbore fluid temperature [°F]

Lumped Newton-cooling proxy T_w(t) = T_res + (T_inj−T_res)·exp(−t/τ). Not an energy-balance solution — advisory only.

Advisory proxy