Buoyancy in WCSB Drilling and Well Engineering: Archimedes Force on Tubular Strings, Hook Load Calculation, and the Effect of Mud Weight on Drill String Weight, Casing Running Loads, and Packer Setting Force in Alberta Wells

Key Takeaways

• Buoyancy factor derivation and its application to WCSB drill string hookload calculation and weight indicator interpretation: The buoyancy factor is derived from Archimedes' principle applied to a closed tubular: any object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object's volume. For drill pipe, the displaced fluid volume equals the steel cross-sectional area × pipe length. The buoyancy factor BF = (density_steel - density_fluid) / density_steel simplifies to BF = 1 - density_fluid/density_steel. At WCSB typical water-based mud weights of 1.40-1.65 sg, BF = 0.79-0.82; at oil-based mud weights of 1.80-2.20 sg used for deep WCSB Montney and Foothills HPHT wells, BF = 0.72-0.77. These BF values are applied to the in-air weight of each string component: drill collars (steel, ~2.2 kg/m per cm2 of cross-section), heavy-weight drill pipe, and regular drill pipe each have their in-air weight per meter reduced by the BF to get the buoyed weight per meter, which is then summed over the total depth to give the total buoyed string weight and the expected weight indicator reading when the bit is off-bottom. Overpull is defined as the increase in hookload above the rotating-off-bottom weight indicator reading, and the allowable overpull for stuck-pipe freeing operations in WCSB Montney wells is typically 150,000-300,000 N above the buoyed hanging weight, staying within 80% of the derrick rated capacity and the pipe body tensile yield strength.
• Buoyancy effect on casing running weight and the risk of casing collapse from excessive running speed in heavy WCSB mud systems: When running 5-1/2-inch production casing in a WCSB Montney horizontal well with 1.85-sg OBM, the buoyed weight of the casing string (50 kg/m in-air × 0.764 BF × 4,200 m TVD = approximately 159,000 N compared to 208,000 N in-air) represents the static hanging weight at the surface when the casing is stationary. During running in hole, the apparent weight decreases further due to drag (buoyed weight minus friction), meaning the driller must monitor the downward force imparted to the casing when slacking off, which in a highly inclined WCSB well can be much less than the buoyed hanging weight because drag in the lateral and build sections absorbs most of the string weight. If the driller attempts to force the casing to bottom by applying weight in excess of the available push from the buoyed string above the deviated section, the casing may buckle in the high-inclination section (sinusoidal buckling when F_buckling = -EI × (pi/L)^2, where L is the casing contact interval), which for 5-1/2-inch N-80 casing in a 35-degree inclination section occurs at approximately 85-120 kN of compressive force, well within the range achievable by over-applying weight in a WCSB horizontal well with insufficient drag.
• Packer setting force calculation incorporating buoyancy in WCSB Cardium and Mannville well completions: Mechanical packers used in WCSB Cardium and Mannville oil completions are set by compressing the packer element using the weight of the tubing string above: the driller sets down weight until the gauge shows the required setting force (typically 20-50 kN for a mechanical packer in a 2.875-inch tubing string). The available setting weight from the tubing string above is the buoyed weight of the tubing from surface to the packer depth: W_setting = w_tubing × buoyancy_factor × TVD_packer. For WCSB Cardium completions at 1,800 m TVD with 2.875-inch 8.7 lb/ft EUE tubing (12.9 kg/m) and 1.07-sg brine completion fluid: BF = 1 - (1,070/7,850) = 0.864, W_setting = 12.9 × 0.864 × 1,800 = 20,079 N. At a packer setting requirement of 20 kN, the available setting weight exactly meets the requirement at this depth, meaning that for deeper WCSB Cardium wells (above 2,200 m TVD) or with heavier completion fluid, additional weight is available and the packer sets with positive margin; for shallower wells (below 1,200 m TVD in light completion fluid), insufficient tubing weight is available and a coiled tubing or wireline setting system is required instead of the conventional set-down-weight procedure.
• Buoyancy in heavy-wall WCSB conductor pipe and surface casing running: monitoring floatation versus sinking during casing running operations: When running large-diameter surface casing (16-inch or 20-inch OD, wall thickness 15-20 mm) in WCSB shallow formations where the annular mud weight is low (1.03-1.10 sg for fresh water with light cuttings load), the steel volume of the large-diameter casing is relatively small compared to the casing internal volume, and the casing string may float if it is air-filled and the annular mud provides sufficient upward buoyant force on the outside of the string. A floating casing string creates a hazardous condition at the rig floor: the driller must apply downward force to run the string to bottom, and if the casing is accidentally dropped or control is lost, it can shoot upward from the wellhead. WCSB surface casing running procedures address this by filling the casing with mud (float shoe or auto-fill float equipment opens immediately) so that the internal fluid pressure eliminates the net upward buoyant force. For 20-inch conductor pipe (steel cross-sectional area approximately 0.0093 m2 per meter), the buoyant force from mud on the outside (1.05 sg) minus the weight of mud on the inside (approximately balanced) equals the submerged weight of the steel, which for 20-inch conductor at 1.0-1.1 sg annular mud gives a net downward force of only 50-80 N/m — barely enough to prevent floating in sections where annular cuttings cause momentary upward fluid velocity surges.
• Buoyancy correction in WCSB directional drilling torque-and-drag modeling for horizontal well completions with high drag loads: In the torque-and-drag (T&D) model for WCSB Montney and Cardium horizontal wells, buoyancy is applied at each individual element of the string (each pipe joint modeled as a segment with its local mud-weight-corrected effective weight) rather than as a simple sum of the total string weight times a single buoyancy factor, because in deviated wells the string contacts the wellbore wall and the normal contact force at each contact point is a function of the local effective weight component perpendicular to the wellbore axis — not the vertical weight. At 90-degree inclination in the WCSB horizontal lateral, the component of buoyed string weight perpendicular to the borehole is essentially zero (the string rests on the low side of the hole but vertical gravity is zero in the horizontal plane), so buoyancy does not directly reduce the lateral contact force; however, in the build section (30-90 degrees), buoyancy reduces the total string weight and thereby reduces the axial tension in the vertical section, which in turn reduces the available weight transfer to the lateral for sliding mode directional drilling. WCSB T&D models therefore require accurate mud-weight input at each depth point (accounting for ECD variations during drilling) to correctly predict hookload, surface torque, and the available weight-on-bit in the lateral section for efficient slide drilling with a positive-displacement motor.