Experimentally Validated Nonlinear Delayed Differential Approach to Model Borehole Propagation for Directional Drilling

Jiamin Xu

Abstract:

This paper presents the development and validation of a nonlinear delay differential equa-
tion (DDE) model for borehole propagation in the inclination plane. Most importantly, built
upon a quasi-linear model, the nonlinear approach incorporates information pertaining to
the floating stabilizers and bit tilt saturation by formulating a linear complementarity
problem. As a result, the outputs of the nonlinear model were in better agreement with
the field data when compared with the quasi-linear model. The maximum modeling error
of the nonlinear DDE is less than 1 deg over a drilled depth of 600 feet.