Abstract

The trajectory of a wellpath is a tortuous space curve with permanent changes in directions and curvatures. A usage of steerable directional drilling tools in nowadays drilling practices even more forces the bit apart from its natural tendencies of running a smooth course - enforcing a highly curved shape of the well. Although this is well known all to the author's knowledge existing wellpath computation methods are based on piecewise approximating the wellpath with constant curvature linear, circular and helical curves and arcs.

A new proposed trajectory computation method gives up these old paradigms and introduces a new approach to accurately calculate the spatial course of a wellpath while maintaining its realistic shape from standard wellbore survey measured depth, inclination and azimuth data. In detail the discussed algorithm is founded on fundamental differential geometry practices in synergy with piecewise spline-curve approximation techniques. This limits the common problems of spline-curve approximations. The result is a highly accurate wellpath description with proven curvature continuity in any position along its course.

The proposed new method is a further step in more accurate wellbore trajectory and dogleg severity computation - especially for complex shaped and extended reach wells. The proposed model's accuracy and reliability is proven and verified with a complex shaped, 11.3 km synthetic wellbore example (with known results) followed by extended-reach and complex shaped field case studies.

Introduction

Since the early time of directional drilling, accurate wellpath surveys are considered as an absolute requirement for correlating bottom-hole locations with geological properties and possible assessments of property rights in jurisdictional disputes. With an increasing number of offshore drilling activities and wellpath extensions, accurate directional wellpath surveys are needed to avoid interference and collision with existing wells drilled from slots as well as to ensure reaching desired targets with a defined accuracy.

Wellbore survey measurements are usually performed at a number of discrete survey stations along the wellpath. The principal measured components are the wellpath length, earth gravity field and either the local magnetic field or a rotation vector. Instrumental performance model convert and correct these raw data measurements to direction, Azimuth f, describing the horizontal deviation angle from geometrical north, and Inclination ?, describing the deviation angle from the vertical. Together with the Measured Depth or Along-Hole Depth s it makes up a three-component measurement vector. The spatial course of the well finally is calculated by piece-wise integration of assumed curves between two survey stations.

Standard Wellpath Computation Methods.

The first model, considering the wellpath as series of straight-line segments between survey station points, was the tangential method. Although very simple to calculate, this method caused sizable errors, as it did not account for previous inclination and direction angles. This drawback was improved by the average angle (or angle averaging) method, considering the average of the angles of two neighboring survey stations.

Several modifications of the straight-line models (secant, triangular and trapezoidal) tried to come closer to the realistic shape of a wellpath in order to increase computation accuracy.

In succession, advanced models were created to remove the abrupt change of direction in the survey stations of the computed path. The circular arc method1 and minimum-curvature method2 represented the wellpath as a succession of circular arcs. Although two consecutive circular arc segments have a common tangent in their node point, they differ in radii of curvatures while also lying in general in different planes.

Standard Wellpath Computation Methods.

The first model, considering the wellpath as series of straight-line segments between survey station points, was the tangential method. Although very simple to calculate, this method caused sizable errors, as it did not account for previous inclination and direction angles. This drawback was improved by the average angle (or angle averaging) method, considering the average of the angles of two neighboring survey stations.

Several modifications of the straight-line models (secant, triangular and trapezoidal) tried to come closer to the realistic shape of a wellpath in order to increase computation accuracy.

In succession, advanced models were created to remove the abrupt change of direction in the survey stations of the computed path. The circular arc method1 and minimum-curvature method2 represented the wellpath as a succession of circular arcs. Although two consecutive circular arc segments have a common tangent in their node point, they differ in radii of curvatures while also lying in general in different planes.

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