A Versatile Gyro Inclinometer, Adaptive to the Borehole Trajectory, Based on a Uniaxial Angular Rate Sensor

Introduction. An approach to designing a gyroscopic inclinometer (GI) based on a single uniaxial angular rate sensor (ARS) is developed. It is argued that such an ARS should be considered a modification of a longitudinal GI scheme, preserving the well-known disadvantages of its performance characteristics. The latter include a lack of adaptability to the trajectory, i.e., commensurability of GI errors at different zenith angles. This work sets out to develop a scheme with one ARS in order to achieve a multiple increase in the accuracy of azimuth measurements for vertical and adjacent-to-the-vertical boreholes when the GI is operated in continuous mode.

Aim. To make a GI based on a uniaxial angular velocity sensor more adaptive to the borehole trajectory thought its design modification and a comparative analysis of errors.

Materials and methods. Algorithms for ideal operation of the proposed scheme in continuous mode are synthesized based on matrix transformations of coordinates and Euler equations. The properties of orientation errors are examined using linearization methods, integral calculus, fundamentals of the calculus of variations, and the theory of linear differential equations.

Results. The adaptivity of the modified GI scheme to the borehole trajectory was achieved by means of a structurally provided deviation of the ARS sensitivity axis by a certain angle of non-orthogonality to the GI longitudinal axis. When designing a GI based on the developed approach, it is possible to realize the value of this angle of 20°. For this angle, the increase in the compassing error does not exceed the uncertainty of the ARS drift statistical characteristics, while achieving an effective level of adaptivity to the borehole trajectory in continuous mode.

Conclusion. The developed scheme makes it possible to significantly reduce the influence of the ARS drift on the accuracy of azimuth calculation in the transitional zenith angles area (from vertical to directional boreholes) in comparison with the well-known longitudinal scheme, thereby maintaining an increased initial azimuth accuracy during movement in the initial alignment at the wellhead.

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