Session: 11-03-01 Data Science Applications in Drilling

Submission Number: 157430

Borehole Trajectory Modeling Using Circular Arcs, Constant Curvature and Toolface, and Sections With Constant Build-Up and Turn Rates 

Wellbore trajectories are often represented by numerous survey stations, either because they reflect the measurement data or because they were generated by a planning-stage algorithm using generative algorithms. The number of points in a trajectory can become very large, particularly when continuous inclinations and azimuths, as provided by rotary steerable systems (RSS), are considered. Such fine discretization of trajectories is not always practical, especially for tasks like torque and drag or hydraulic calculations. In these cases, a smoother representation of the wellbore would be more beneficial, offering a form better suited for hydro-mechanical analyses.

To smooth a finely discretized trajectory, a series of sections is identified that can represent the original trajectory within an acceptable distance tolerance. One possible section type is the circular arc, which forms the basis of the minimum curvature survey calculation method. Another relevant section type is the constant curvature and constant toolface section, which accurately describes the natural behavior of RSS and the trajectories drilled by directional positive displacement motors (PDMs) in oriented mode. A third section type is the constant build-up rate and turn rate curve, which effectively represents the natural behavior of a plain rotary assembly or a bottom hole assembly (BHA) using a directional PDM in rotating mode. All three section types are utilized to smooth the well path. The method leverages specific mathematical properties of these curve types to achieve the best fit with the original trajectory.

The process of segmenting a trajectory into a series of sections is both fast and controllable in terms of accuracy. By minimizing the number of sections and selecting the most suitable of the three section types to fit the longest possible segments of the well path, the method enables the reconstruction of the originally intended well path after drilling. Additionally, it can generate a smooth well path for automatically generated trajectories during the planning stage for instance using a generative algorithm. The difference between the smoothed trajectory and the original one also provides a more accurate estimate of the wellbore's tortuosity.

With a well path represented by a limited number of sections, it becomes possible to use long steps in hydro-mechanical calculations. This enables fast yet relatively accurate evaluations, facilitating efficient engineering analyses. Rapid hydro-mechanical evaluations also create opportunities for stochastic approaches to estimate the accuracy of predictions made with an hydro-mechanical model.

Presenting Author: Eric Cayeux NORCE

Presenting Author Biography: Eric Cayeux is chief scientist for the drilling and well modelling group at NORCE. After an 18 years career in the industry working with the development of expert system solutions for directional drilling and multi-disciplinary (geophysics, geology, reservoir engineering and drilling) well planning applications, he joined NORCE in 2004, where he worked with drilling automation, real-time drilling diagnostic and drilling simulators. The last decade, he has more focused on basic research and mathematical modelling of the drilling process. Cayeux holds an M.Sc. degree in civil engineering from Ecole Nationale des Travaux Publics de l’Etat, Lyon, France, an M.Sc. degree in software engineering from the University of Nice, France, and a Dr. Philos. degree in petroleum engineering from the University of Stavanger, Norway.