Assisting Directional Drilling by Calculating a Safe Operating Envelope

Nowadays, complex 3D trajectories are executed with a succession of circular arcs (CAs). Although they have constant curvature, their tool face is not constant. Consequently, directional drillers must adjust the tool face regularly to reach the target entry within its tolerances. This paper investigates the use of the constant curvature and constant tool face (CTC in short) curve as an alternative to the CA to assist the directional drilling work to reach the target entry within its boundaries. The problem is addressed by calculating a safe operating envelope (SOE) to reach the boundaries of the target entry and provide a tolerance window for the curvature and tool face to support directional drilling decisions. The target entry tolerance is discretized as a polygon. From the current bit position and its direction, the possible choices of curvatures and tool faces are obtained to reach the edges of the target entry shape. The SOE can be calculated with the CA or with the CTC curve. It is, therefore, possible to compare the advantages and disadvantages of both types of curves to attain the target entry and stay within its boundaries. The CA is shorter than the CTC curve. However, it requires adjusting the tool face during the navigation, which is not the case with the CTC curve. As a result, the directional driller can control the bottomhole assembly (BHA) direction such that the well lands within the target entry limits by using set points for tool face and curvature inside the calculated SOE. Furthermore, a new way to represent the SOE is introduced. It makes use of a 3D cylindrical representation where the curvature is mapped as the height of a cylinder, while the tool face corresponds to the azimuth in the cylindrical coordinate system, and the length is linked to the radial distance. This provides a visual aid to understand the SOE. Moreover, this visualization helps to appreciate the relationship between the initial bit location and direction in the construction of the SOE and how the margins increase in a particular manner as the bit approaches the target entry polygon. The CTC curve is the natural one followed by directional positive displacement motors (PDMs) or rotary steerable systems (RSS). Potentially, the CTC curve may be a more straightforward solution to automated directional drilling control because it is easier to be followed by both PDM and RSS.