Abstract
The project began with a review of the open literature, to discover the state of the art of horizontal drilling technology. Investigation revealed that there is significant effort being expended, by elements of the private sector, to discover workable methods for the trajectory control of horizontal drilling equipment. While there appears to be some academic interest in formulating the problem, there has been no report of any experimental endeavor to explore the possibility of providing closed-loop feedback control for horizontal drilling. An effort was next initiated to develop a mechanistic model of the downhole drilling dynamics of a drill string, including essential tools such as the bit, mud motor, and collars. The spinning, flexible tub model included a steering capability that was presumed to provide wall forces (lateral), which in turn could provide build-drop rate adjustment while drilling. The modeling analysis effort produced a semianalytic, closed-form solution of the three-dimensional combined bending-torsion boundary value problem. That solution provided the basis of a quasi-state drilling process model that provided a basis for an iterative, real- time closed-loop control of the system. The controller was designed to provide minimum variance tracking of a prescribed trajectory. Quadratic penalties were also imposed on doglegging. A spin-rate- dependent rate of progress was incorporated, and an estimator (observer) was proposed to verify bottomhole tide forces and to detect varying lithography downhole.
