The use of accelerometers in conventional surveying techniques is well known. The use of magnetometers or gyroscopes in combination with one or more accelerometers to determine direction is also known. Deployments of such sensor sets are well known to determine borehole characteristics such as inclination, azimuth, positions in space, gravity toolface, magnetic toolface, and magnetic azimuth (i.e., an azimuth value determined from magnetic field measurements). While magnetometers and gyroscopes may provide valuable information to the surveyor, their use in borehole surveying, and in particular measurement while drilling (MWD) applications, tends to be limited by various factors. For example, magnetic interference, such as from magnetic steel or ferrous minerals in formations or ore bodies, tends to cause errors in the azimuth values obtained from a magnetometer. Motors, stabilizers, and bits used in directional drilling applications are typically permanently magnetized during magnetic particle inspection processes, and thus magnetometer readings obtained low in the bottom hole assembly (BHA) are often unreliable. Gyroscopes are sensitive to high temperature and vibration and thus tend to be difficult to utilize in drilling applications. Gyroscopes also require a relatively long time interval (as compared to accelerometers and magnetometers) to obtain accurate readings. Furthermore, at low angles of inclination (i.e., near vertical); it becomes very difficult to obtain accurate azimuth values from gyroscopes.
U.S. Pat. No. 6,480,119 to McElhinney and commonly assigned U.S. Pat. No. 7,080,460 to Illfelder disclose techniques for determining borehole azimuth via tri-axial accelerometer measurements made at first and second longitudinal positions on a drill string. Using gravity as a primary reference, the disclosed methods make use of the inherent bending of the structure between the accelerometer sets in order to calculate a change in borehole azimuth between the first and second positions. The disclosed methods assume that the tri-axial accelerometer sets are spaced by a known distance via a rigid structure, such as a drill collar, that prevents relative rotation between the sets. Gravity based methods for determining borehole azimuth, including the McElhinney and Illfelder methods, as well as exemplary embodiments of the present invention, are referred to herein as Gravity MWD.
While the Gravity MWD techniques disclosed by McElhinney and Illfelder are known to be commercially serviceable, there is yet room for further improvement. For example, the physical constraint that the accelerometer sets be rotationally fixed relative to one another imposes a constraint on the structure of the BHA. It would be highly advantageous to extend Gravity MWD methods to eliminate this constraint and thereby allow relative rotation between the first and second accelerometer sets.
The Illfelder patent further discloses that the change in borehole azimuth can be determined from borehole inclination and gravity toolface measurements using numerical root finding algorithms, graphical methods, and/or look-up tables. Such methods are readily available and easily utilized at the surface, e.g., via a conventional PC using software routines available in MathCad® and/or Mathematica®. However, it is difficult to apply such numerical and/or graphical methods using on-board, downhole processors due to their limited processing power. This is particularly so in smaller diameter tools which require physically smaller processors (which therefore typically have lower processing power). Furthermore, surface processing tends to be disadvantageous in that it requires transmission of multiple high resolution (e.g., 12 bit) gravity measurement values or inclination and tool face angles to the surface. Such downhole to surface transmission is often accomplished via bandwidth limited mud pulse telemetry techniques.
Therefore there also exists a need for a simplified method for determining the change in borehole azimuth, preferably including calculations that can be readily achieved using a low-processing-power downhole processor.