Catenary Well Profiles for Extended and Ultra-Extended Reach Wells

Abstract Extended-reach drilling (ERD) technology has rapidly developed during the past two decades and the drilling of ultraextended-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.