Instrumentation and Signal Processing for the Verification of Directional Drilling

This paper presents the development of a new instrument and signal processing algorithm that enables the measurement of the trajectories of underground holes during directional drilling. It uses gyroscopes and accelerometers to determine when the drill string is stationary and at these locations to determine the local orientation of the trajectory with respect to Earth's gravity. Hierarchical indexing of the multivariate time-series data has been implemented to ensure high numerical efficiency. The statistical behavior of the sensors is characterized to ensure the correct application of least squares approximation to the reconstruction process. A differential geometric approach is taken to the curve reconstruction from local gradients. The instrument was tested on a full-scale drilling rig performing directional drilling. The goal is to acquire test data under fully realistic operational conditions and to ensure that the sensors withstand the harsh drilling conditions. The signal processing methods are demonstrated on the data acquired during the real drilling process; yielding the trajectory of the test holes.