... deflection. The mathematical models include (1) differential equations; (2) boundary conditions of drill bit, stabilizer, diameter change, tangent point, and bore hole wall; (3) methods for calculating lateral forces and deflection angles of the bit; and (4) models for determining navigation ability...

.... The method of solution approximates straight tapered stress joints with one, whose cross sectional moment of inertia varies parabolically along the stress joint. This approximation leads to the classic Euler type differential equation, which can be solved directly giving a closed form solution...

...: A. K. Wojtanowicz. 01 July 2001 01 May 2002 20 11 2002 oil technology modelling water control engineering differential equations interface phenomena Many wells producing oil or gas from mature reservoirs worldwide currently have a high ratio of produced water...

.... 03 November 2000 07 June 2001 pipe flow transients motion control gases liquids simulation differential equations fluid dynamics mass transfer Pigs are normally utilized in different stages of the pipeline life to perform operations such as dewatering, cleaning...