A new approach was developed for modeling the dogleg severity (DLS) of curved wellbores during directional drilling. The approach is based on superimposing a modified three-point contact method with beam bending effects. The conventional three-point contact method provides a quick prediction of the DLS capability of mud motors. However, it is limited with respect to imposing a predetermined location of the three contact points and ignoring the weight on bit (WOB) and hole inclination effects. Moreover, hole enlargement is not considered in a three-point contact method, which can significantly influence the borehole curvature or DLS because of the change in stabilizer/borehole contact. The new bottomhole assembly (BHA) contact/bending method presented in this paper involves a twostage solution method. First, a modified three-point contact method is used that assumes a certain number and location of borehole contact points along the lower end of the BHA. This method calculates a preliminary value of the DLS without the loading effects. Subsequently, the effects resulting from WOB and hole inclination are considered to cause bending effects to the lower end of the BHA. These bending effects result in a change to the bend angle of the drill bit, which is used to correct the bend angle initially defined in the modified three-point contact method to obtain a final DLS solution. In addition, the hole enlargement attributable to the formation properties is considered to change the BHA-borehole contact points, thus influencing the achievable DLS range. This superposition approach, between the BHA-borehole contact and bending, results in DLS predictions for slick motors and stabilized directional drilling tools at various WOB and hole inclinations. The contact-bending superposition (CBS) method is verified by using mud motor field survey data and is compared to the conventional three-point contact method. The CBS results show good correlation with field survey data. A greater rate of change in DLS is observed with slickbore assemblies, wherein the WOB and hole-inclination is more pronounced than stabilized assemblies. The CBS method and results demonstrate that a three-point contact approach with rigid BHA assumption is not sufficient to describe DLS. The bending effects are important considerations, particularly for assemblies with flex collars near the first stabilization point. This new method provides a simple calculation of DLS for directional drilling tools. It is also useful when the time-consuming numerical models must be avoided, particularly at the conceptual design level, or when an efficient means of analyzing the DLS limitation of an existing tool is necessary.
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