Horizontal Drilling & Coiled-Tubing Mechanics, Dawson-Paslay (1984) & Helical Lockup
Dawson-Paslay Sinusoidal & Helical Pipe Buckling Formula
Calculate Lateral Gravity Wall Support (N/m), Dawson-Paslay Sinusoidal Buckling Load Fsin (kN), Chen-Lin-Cheatham Helical Lockup Load Fhel (kN), and Helical Lockup Ratio (%).
Drillpipe buckles MORE easily in an 18° upper build washed-out hole than in a 78° horizontal lateral—because continuous low-side gravity support w_e·sin(theta) braces deviated pipe!
In vertical wells (`theta -> 0°`), Arthur Lubinski (`1950`) showed slender drillpipe buckles under just a few kilonewtons of compression; yet **Raymond Dawson and Paul R. Paslay (`1984`)** proved that inclining a wellbore to Angle `theta` (`deg` from vertical) lays Buoyed Linear Pipe Weight `w_e` (`N/m`) continuously along the low side of the hole (`Radial Annular Clearance r_c = (D_{hole} - OD_{pipe}) / 2` mm -> `r_c / 1,000` m), supplying **Restoring Gravity Support `w_{lat} = w_e * sin(theta)`** (`N/m`)! Across Pipe Bending Rigidity `E * I` (`kN·m²`), **Onset of Snaking Sinusoidal Buckling rises to `F_{sin} = (2 * sqrt((E * I * 1,000 * w_{lat}) / (r_c / 1,000))) / 1,000`** (`kN`), while **Y.C. Chen, Y.H. Lin & J.B. Cheatham (`1990`)** showed full **3D Spiral Helical Buckling initiates at `F_{hel} = sqrt(2) * F_{sin}`** (`kN`)—above which capstan wall friction grows exponentially into **Helical Lockup** where surface slack-off weight never reaches the bit!
Verify on `5`-inch Drillpipe (`E * I = 1,420` kN·m²) Sliding in an `8.5`-inch Near-Horizontal Lateral—Flexural_Rigidity `E * I` = 1,420 kN·m² (B2), Buoyed_Weight `w_e` = 245 N/m (B3), Hole_Inclination `theta` = 78.0° (B4), Radial_Clearance `r_c` = 48.0 mm (B5), and Applied_Axial_Compression = 135 kN (B6): Low-Side Gravity Support equals `239.65` N/m (E2), Dawson-Paslay Sinusoidal Onset `F_{sin}` equals **`168.40` kN** (E3), Helical Buckling Load `F_{hel}` equals **`238.15` kN** (E4), keeping string compression straight at **`56.7%` of `F_{hel}`** (E5)!
| Dawson-Paslay / Chen-Cheatham Buckling KPI (EI=1,420 kN·m², we=245 N/m, WOB=135 kN) | Formula | Verified Output |
|---|---|---|
| Low-Side Gravity Support (N/m) | Buoyed_Weight_N_m * SIN(Inclination_rad) | 239.65 N/m @ 78° (75.71 N/m @ 18° build!) |
| Sinusoidal Buckling Fsin (kN) | 2 * SQRT(EI_Nm2 * w_lat / rc_m) / 1000 | 168.40 kN straight (72.42 kN snaking!) |
| Helical Buckling Fhel (kN) | SQRT(2) * Sinusoidal_Fsin_kN | 238.15 kN (102.41 kN @ washed-out build!) |
| Compression vs Helical Fhel (%) | (Applied_Compression_kN / Helical_Fhel_kN) * 100 | 56.7% STRAIGHT (131.8% HELICAL LOCKUP!) |
Dawson-Paslay (1984) Sinusoidal & Sqrt(2) Helical Buckling Threshold Formula
Validate `Flexural_Rigidity EI` in `[5, 25,000]` kN·m², `Buoyed_Weight w_e` in `[10, 2,000]` N/m, `Inclination theta` in `[2, 90]`°, `Radial_Clearance r_c` in `[3, 300]` mm, and `Compression >= 0` kN!
=LET(ei_k, B2, we_n, B3, in_d, B4, rc_m, B5, wb_k, B6, wl_n, we_n * SIN((in_d * PI()) / 180), fh_k, SQRT(2) * ((2 * SQRT(((ei_k * 1000) * wl_n) / (rc_m / 1000))) / 1000), IF(OR(ei_k < 5, ei_k > 25000, we_n < 10, we_n > 2000, in_d < 2, in_d > 90, rc_m < 3, rc_m > 300, wb_k < 0), "Invalid Buckling Input", ROUND((wb_k / fh_k) * 100, 1)))Upper `18°` Build Section in `12.25"` Washed-Out Hole (`r_c = 82` mm) Helical Corkscrew Check
Check that same `135` kN compressive load passing through an upper `B4 = 18.0°` tangent inside a wider `B5 = 82.0` mm radial clearance: Low-Side Support E2 drops `3.2x` to `75.71` N/m while wider `r_c` slashes `F_{sin}` E3 to `72.42` kN and **`F_{hel}` E4 to `102.41` kN**—putting the upper pipe into **`131.8%` Helical Corkscrew Buckling** (E5)!
=IF(ISTEXT(E5), E5, LET(wl_n, B3 * SIN((B4 * PI()) / 180), fs_k, (2 * SQRT(((B2 * 1000) * wl_n) / (B5 / 1000))) / 1000, ROUND(SQRT(2) * fs_k, 2)))Try the example
Use the original values or change them to test your understanding.