Bent-Sub Parameter Design for Slim-Hole Push-the-Bit Guided Coring Tools: Trade-Off Between Build-Up Capability and Structural Response

The bent sub is a main deflection component in the near-bit assembly of small-diameter push-the-bit guided coring tools, and its parameters affect build-up capability and local structural response. Existing studies mainly focus on conventional rotary steerable drilling systems, whereas slim-hole constraints, including narrow annular clearance and cross-sectional weakening induced by internal coring channels, remain insufficiently considered. To address this problem, a static bending model of the near-bit section was established based on Euler–Bernoulli beam theory. Channel-induced cross-sectional weakening was represented using the actual concentric annular geometry of the primary load-bearing outer tube, and the bent-sub initial curvature, dual push-the-bit loads, axial weight on bit, and borehole-wall contact and friction effects were incorporated. The build-up rate (BUR), maximum equivalent stress, and maximum curvature served as response indicators. A control-variable approach was used to analyze the bent-sub length Lb, bend angle γ, and distance from the bit Db. The results showed that Db had the strongest effect on BUR, and all parameters exhibited a trade-off between steering performance and structural safety. Increasing Lb from 0.30 m to 0.80 m reduced BUR from 12.65°/30 m to 9.79°/30 m, whereas increasing γ from 0.5° to 2.5° increased BUR from 4.12°/30 m to 10.70°/30 m. Considering structural constraints and normalized BUR retention, the recommended engineering ranges are Lb = 0.65–0.80 m, γ = 1.3°–1.9°, and Db = 0.50–0.70 m.