Systems Modeling and Design of Automated-Directional-Drilling Systems

Abstract

Summary A tractable analytical technique has been devised for gaining insight into the directional performance of a wide range of drilling systems. The software for simulating the directional behavior of drilling tools has reached a high level of technical sophistication. However, this has not rendered the analytical path redundant. The role of the computer is vital to both approaches. In the former, it is the immense number-crunching power, and in the latter, it is an ability to search for an explanation of what the mathematical forms actually mean. The technique used will be accessible to engineers with a general understanding of circuit analysis or control. The lateral borehole-propagation response of a wide class of directional-drilling systems is derived as a simple delay-differential equation. The “delayed” part of the expression is determined by the contact points of the bottomhole assembly (BHA) with the borehole. With this insight, a succinct and intuitive method for constructing the transfer-function response of a drilling system's directional tendency consequent upon the influence of gravity, weight on bit (WOB), and active steering actuator influences will be explored. The analytical approach gives manageable algebraic forms for a tool's dogleg capability and leads to simple graphical techniques for determining whether the trajectory will be smooth or spiraled. The directional capability of passive BHAs to build, drop, or hold is considered first as a springboard to analyze today's rotary-steerable systems (RSSs), wherein the strength of the steering actuation overshadows the BHA's inherent gravity-induced directional tendency. This leads to an understanding of how closing the loop around a directional-drilling system will affect the performance of a wider automated-steering system.