Actual 3D Shape of Wellbore Trajectory: An Objective Description for Complex Steered Wells

Abstract

Abstract All conventional methods for calculating the trajectory of a wellbore involve assumptions. Most calculations assume that segments of the trajectory can be approximated as straight lines, polygonal lines, cylindrical helixes, circular arcs, or combination of these approximations. Conventional methods calculate the course coordinates of a well survey interval according to the predetermined shape for the trajectory. But, what does the real shape of a trajectory in each surveyed interval really look like? Why? What parameters play decisive roles in determining the true shape of a surveyed interval? Is it reasonable to assume that every survey interval has the same kind of approximate shape? Until now, the drilling industry has not found satisfactory solutions to these questions. This paper presents the results of research about the true shape of a wellbore trajectory relative to its survey stations. It also provides a universal equation for a wellbore trajectory in a surveyed interval and presents an objective approach for describing and calculating a wellbore trajectory in space. The new method does not assume that the shape of wellbore trajectory is a set of typical approximations. The study shows that the wellbore curvature and torsion at survey stations determine the shape of the wellbore trajectory at subsequent intervals, and that 3D coordinates of wellbore trajectory in a local coordinate system are linear, quadratic, and cubic functions vs. curve length, respectively. The new method yields a continuous wellbore trajectory. Extensive simulations have been carried out and are reviewed in this paper. The paper compares the results predicted by mathematical simulation using the new method with actual, observed trajectories and describes the results from other methods to show the accuracy of the new, improved method. The new method shows excellent precision in calculation and reliability. This study has also proved that the minimum curvature method and the natural curve method, the most commonly used methods, are related to the new method. Introduction Originally, the oil and gas industry was focused on drilling vertical wells. The concept of inclination angle arose when engineers realized that a drilled wellbore trajectory was not a plumb line. Then the concept of azimuth angle came into being when they further understood that a drilled trajectory can deviate from a vertical plane. In fact, a wellbore trajectory is a continuous and smooth curve in space, which bends and turns simultaneously. Therefore, a reasonable method of survey calculation must be on the basis of a 3D wellbore trajectory model. Survey calculation is the fundamental, necessary work of quantitatively monitoring and controlling wellbore trajectories. The industry has recognized the importance of survey calculation for more than 50 years and has widely applied the research results in the field. Inclinometers can only give parameters from separate survey stations and cannot give the real profile of a wellbore trajectory. Therefore, every method of survey calculation is based on some assumptions mostly that the segments are: straight lines, polygonal lines, cylinder helixes, or circular arcs (Callas et al, 1979). These methods are simple, but they are not sufficiently accurate or precise for out of the ordinary wells such as extended-reach wells and multiple-target wells. The earliest method of survey calculation is the tangential method. It is no longer used because it shows considerable error. In 1950's, the industry (Edison, 1957; Walstrom et al, 1972) provided the average angle method and balanced tangential method to calculate a drilled trajectory. The average angle method assumes the wellbore trajectory in each survey interval as a linear section, and the inclination and azimuth angles of the straight section are the average values of those at the two survey stations, respectively. The balanced tangential method assumes the wellbore trajectory as a polygonal line. The method divides each survey interval into halves in length, and the inclination and azimuth angles of each straight section are consistent with those at the adjacent survey stations.