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

Abstract This paper presents the development and validation of a nonlinear delay differential equation (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 a 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 degrees over a drilled depth of 600 feet.