Extended-reach drilling (ERD) technology has rapidly developed during the past two decades and the drilling of ultra-extended-reach (u-ERD) wells to extend their reach to greater depths requires improved models. Wellbore friction is an important issue for ultra-long wells, and optimizing the well path design is an effective means of reducing torque and drag.

This paper presents the dimensionless mathematical model and provides a new method for planning a catenary well profile. The new mathematical model of a catenary well path does not involve hyperbolic functions and uses an exact mathematical solution. The method of explicit solution avoids a trial-and-error procedure and provides excellent maneuverability of planning requirements.

Conversely, bit-walk is a natural tendency of the drill bit to drift sideways while drilling. To reduce azimuth correction frequencies and wellbore tortuosity, effective well path planning and design should account for bit-walk effects. This paper presents a newly developed a 3D mathematical model of the catenary well path and the method for planning bit-walk catenary paths to fit the bit-walk rate by a given rock layer. This paper analyzes the compositive relation of inclination units and azimuth units, provides a method to divide the catenary well profile into many shorter intervals for calculation, discusses the characteristics of planning bit-walk paths, and presents the constraint equations and solutions for ERD wells.

The results show that the essential elements of planning a 2D or 3D catenary profile include determining the position of the catenary section, parameters, such as starting and ending inclinations, and length of the succeeding hold-up section. The model and methods provided use an exact mathematical solution and results. The planned catenary well path completely fits the predetermined bit-walk rates and is absolutely smooth from the wellhead to the given target.


ERD wells not only provide solutions for restricted reservoir production, but also help to eliminate additional platforms. ERD techniques and technologies have rapidly evolved, and step-out wells have incrementally increased since 1993 when the ERD program began accessing offshore reserves under Poole Harbor from land-based wellsites (Robertson et al. 2005). Wytch Farm was at the forefront of extended reach drilling. In 1997, Well M11 broke the 10 km departure milestone to set a new world record. In 2000, Well M16 established another world record at 10,727 m and a measured depth of 11,278 m (Robertson et al. 2005; Meader et al. 2000). Mason and Judzis (1998) indicated that it is possible to drill and complete u-ERD wells in the future.

The comprehensive use of various techniques and technologies is critical to the success of ERD programs. This paper focuses on the models and methods of effectively planning a catenary profile. The catenary profile was first introduced to the oil and gas industry by McClendon and Anders (1985). Early attempts have not had the expected effect because of the constraint of techniques and technologies. Du and Zhang (1987) illustrated two field cases using catenary trajectories drilled in China. Han (1987, 1997) and Liu (2007) discussed the methods for planning a catenary profile. However, most of the ERD well design research has focused on the selection of profile types to reduce well friction and emphasized the analysis of torque and drag (Payne et al. 1994; Aadnoy and Andersen 1998; Aadnoy et al. 2006). Moreover, all of the presented methods focus on planning 2D catenary profiles and do not present a method for planning a 3D catenary profile.

Drilling deviation is the result of rock removal under the complex action of the bit. The "rock-bit interaction" model, which is the kernel of the theoretical analysis of the fundamental problems, is used to predict and control the deviation tendencies of a drill bit. The use of a rock-bit interaction model requires a reliable 3D bottomhole assembly (BHA) analysis program to generate the bit force and bit axis directions. The industry has performed a great deal of research that focuses on the selection and/or design of BHAs and bits (Lubinski and Woods 1953; Walker and Freedman 1977; Millheim et al. 1978; Millheim et al. 1978; Bai 1982; Ma and Azar 1986; Ho 1987; Chen et al. 2008), but provides few published works about how to use the bit-walk tendency to successfully drill a well.

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