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Well Control & Drilling Operations, Burkhardt (1961) Pipe-Tripping Surge & Swab Hydraulics

Burkhardt Wellbore Surge & Swab Tripping Pressure Formula

Calculate Burkhardt Effective Annular Fluid Velocity Veff (m/s), Laminar Annular Surge/Swab Pressure Change (kPa), Running-In Surge EMW (SG), and Pulling-Out Swab EMW (SG).

Over-65% of oilfield gas blowouts start NOT while drilling, but when pulling drillpipe too fast swabs bottomhole pressure below pore pressure!

Running a plugged/float-valved drillstring (`Collar/Pipe OD D_p` mm) into an open borehole (`Hole ID D_h` mm) at **Hoist Tripping Speed `V_p`** (`m/s`) acts like a leaky hydraulic piston! **J. A. Burkhardt (`1961`, `SPE-1546`)** proved that total upward mud shear combines `1)` **Closed-End Volumetric Displacement `V_p * (D_p^2 / (D_h^2 - D_p^2))`** PLUS `2)` **Viscous Wall-Clinging Drag `K * V_p`** (`Clinging Constant K ~= 0.45` for annular `D_p / D_h ~ 0.6–0.7`), driving **Effective Annular Mud Velocity `V_{eff} = V_p * ((D_p^2 / (D_h^2 - D_p^2)) + K)`** (`m/s`)! Across Radial Slot Clearance `H_{slot} = (D_h - D_p) / 2,000` (`m`), Mud Viscosity `mu` (`mPa·s`), and String Length `L` (`m` vertical), laminar slot shear generates **`Delta_P_{trip} = ((12 * (mu / 1,000) * V_{eff}) / H_{slot}^2) * (L / 1,000)`** (`kPa`), spiking bottomhole **Running-In-Hole Surge `EMW_{surge} = SG_{mud} + Delta_P / (9.80665 * L)`** (`fracture/lost-circulation risk!`) and dropping **Pulling-Out-of-Hole Swab `EMW_{swab} = SG_{mud} - Delta_P / (9.80665 * L)`** (`swabbed gas-kick risk!`)!

Verify on a Controlled `0.45` m/s (`~20` s per `9` m single) Trip with `5"` (`127.0` mm) Pipe in an `8.5"` (`215.9` mm) Hole—Pipe_OD `D_p` = 127.0 mm (B2), Hole_ID `D_h` = 215.9 mm (B3), Burkhardt_Clinging `K` = 0.45 (B4), Hoist_Trip_Speed `V_p` = 0.45 m/s (B5), Plastic_Viscosity `mu` = 28.0 mPa·s (B6), String_TVD `L` = 2,800 m (B7), and Static_Mud `SG` = 1.340 (B8): `V_{eff}` equals `0.441` m/s (E2), Trip Pressure equals a gentle `209.8` kPa (`30` psi, E3), keeping Surge `EMW` at `1.348` SG (E4) and Swab `EMW` safely overbalanced at `1.332` SG (E5)!

Burkhardt Surge/Swab KPI (Dp=127 mm, K=0.45, TVD=2,800 m, Static Mud=1.340 SG)FormulaVerified Output
Effective Fluid Velocity Veff (m/s)Vp * ((Dp^2 / (Dh^2 - Dp^2)) + Cling_K)0.441 m/s (2.247 m/s fast pull in slim hole!)
Surge / Swab Friction dP (kPa)((12 * (mu/1000) * Veff) / ((Dh-Dp)/2000)^2)*L/1000209.8 kPa (5,489.5 kPa = 796 psi swab!)
Running-In Surge EMW (SG)Static_SG + Trip_dP_kPa / (9.80665 * TVD_m)1.348 SG (1.540 SG lost-returns fracture!)
Pulling-Out Swab EMW (SG)Static_SG - Trip_dP_kPa / (9.80665 * TVD_m)1.332 SG (1.140 SG SWABBED GAS KICK!)

Burkhardt (1961) Closed-End Piston Displacement + Clinging Drag Formula

Validate `Pipe_OD >= 50` mm, `Hole_ID >= Pipe_OD + 25` mm, `Clinging_Factor K` in `[0.30, 0.55]`, `Trip_Speed V_p` in `(0, 3.0]` m/s, `Viscosity mu` in `[1, 150]` mPa·s, `TVD >= 100` m, and `Static_Mud_SG` in `[0.85, 2.50]`!

=LET(dp_m, B2, dh_m, B3, kc_f, B4, vp_s, B5, mu_c, B6, lv_m, B7, sg_m, B8, ve_s, vp_s * (((dp_m ^ 2) / ((dh_m ^ 2) - (dp_m ^ 2))) + kc_f), hs_m, (dh_m - dp_m) / 2000, pt_k, ((12 * (mu_c / 1000) * ve_s) / (hs_m ^ 2)) * (lv_m / 1000), IF(OR(dp_m < 50, dh_m < dp_m + 25, kc_f < 0.3, kc_f > 0.55, vp_s <= 0, vp_s > 3, mu_c < 1, mu_c > 150, lv_m < 100, sg_m < 0.85, sg_m > 2.5), "Invalid Trip Input", ROUND(sg_m - (pt_k / (9.80665 * lv_m)), 3)))

Fast Hoisting Across Tight BHA/Slim Hole (`D_h = 171.5` mm, `V_p = 1.35` m/s, `mu = 36` cP) Swab-Kick Check

Yank `5"` collars out of a `6.75"` (`B3 = 171.5` mm) slim hole or balled-up stabilizer at `B5 = 1.35` m/s in `36` cP mud (`B6 = 36`): `V_{eff}` E2 surges `5.1x` to `2.247` m/s, Swab Suction E3 spikes `26x` to **`5,489.5` kPa**, and Bottomhole Swab `EMW` E5 plunges `-0.200` SG down to **`1.140` SG**—sucking formation gas straight into the stairwell!

=IF(ISTEXT(E5), E5, LET(ve_s, B5 * (((B2 ^ 2) / ((B3 ^ 2) - (B2 ^ 2))) + B4), hs_m, (B3 - B2) / 2000, ROUND(((12 * (B6 / 1000) * ve_s) / (hs_m ^ 2)) * (B7 / 1000), 1)))

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