A METHEMATICAL MODEL FOR 3D ANALYSIS OF GENERAL BOTTOMHOLE ASSEMBLY UNDER SMALL DEFLECTION AND ITS APPLICATION

With the progress of drilling technology, bottom hole assembly (BHA) has been developed rapidly to control well trajectory. Many new type of BHA such as steering motor assembly, dropping assembly with eccentric bend sub, dropping assembly with flexible joint have been developed upon common building, dropping and holding assemblies. A mathematical model is established which includes (1) differential equations;(2) boundary conditions at drill bit, stabilizer, bend angle, diameter change, tangent point and borehole wall;(3) lateral forces and deflection angles of bit. This model can work with common BHA, steering down hole motor assembly, BHA with off center bend and flexible joint. Under the small deflection assumption, the weighted residual method is employed to obtain the three-dimensional solution of the governing equations. The variations of building rates with the inclination of several BHAs are predicted and analyzed.