Mathematical model and design methods of parabola well paths

Well-path planning is the prerequisite for operators to drill directional or horizontal wells successfully.The deformation of a bottom drilling string accords with the mechanics model of parabola,and the drilled wellbore trajectory almost approximates to parabola,thus it is reasonable to plan well paths using parabola model in theory.The essential of planning a parabola well path was to determine the shape and position of the parabola section.The characteristic parameter of a parabola,P,describes its shape,and the parameters,such as starting inclination,ending inclination,length of the succeeding hold-up section,locate the position of the parabola section in the well path profile.The author systematically discussed the mechanical and mathematical models of a parabola well path,analyzed the characteristic parameters and known data of a parabola profile,and presented two methods for planning the parabola profile(iterative calculation and explicit solution).With the same requirements,the two methods educed the same planned results and certify each other.The method of explicit solution,avoiding a trial-and-error procedure and iterative calculations,provided excellent maneuverability of planning requirements,and it was convenient for oil field application.Optimally planning parabola profiles could reduce the drag and torque of a pipe string in favor of decreasing the wear and tear quantity of drilling string and casing,improve the status of the forces applied on them,lighten their fatigue failure and reduce the probability of creating key ways.Accordingly,operators could apply higher WOB and drill continuously,which was propitious to increasing penetration rate.