Bottomhole assembly analysis by finite difference differential method

This paper presents a three‐dimensional finite difference differential method for bottomhole assembly (BHA) analysis under static loads. The analysis is required to optimize the BHA configurations for drilling directional boreholes in the petroleum industry. The optimization of BHA configurations ensures the controlled cruising of the drill bit to drill the hole along a planned trajectory. The model incorporates the contact response between drillstring and wellbore wall, the upper tangent point problem, stabilizer configurations, bent sub model and other considerations for numerical solutions. The overall formulations are presented in a matrix format within convenient coordinate systems developing a transformation matrix. Key solution algorithms for computer programming are then described in detail. One analytical solution for beams under weight and torque is used to verify the method. Also the analytical solutions of three other simple BHA configurations are used for verification. The verified method is then applied in a series of parametric investigations to characterize the responses of typical BHAs. The BHA responses studied include the side force at bit and lateral deformation of the assembly along its length with varying weights on bit and hole inclination angles for typical building, dropping and holding assemblies. BHAs with bent sub are analyzed with various tool face angles and bent angles. The effect of wellbore curvature on side forces is also demonstrated. Copyright © 2007 John Wiley & Sons, Ltd.