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The accurate prediction of build rate of rotary steerable system (RSS) is the prerequisite for the precise control of wellbore trajectory and optimal design of the steerable tool. Push-the-bit RSS refers to a steerable drilling system that controls well trajectory through adjustment of stretch length of pushing block. Based on this feature, a three-dimensional mechanical model of push-the-bit RSS is established on the basis of the conventional steerable tool mechanical model while considering pushing force. Meanwhile, the effects of bit cutting performance and formation anisotropy are considered. Next, the lateral force method, inclination trend angle method, and ultimate build rate method based on zero lateral force are analyzed and a new ultimate build rate method based on zero lateral drilling penetration is built. A conversion coefficient is introduced to reflect the ratio of actual build rate to theoretical build rate. At last, the new model is applied to a case study. The new method is superior to other previous methods, because the effects of bit-rock interaction and actual drilling process are sufficiently considered. The influence mechanism of build rate includes “leverage effect,” “pendulum effect,” and “pushing effect.” The build rate of steerable tool is a comprehensive outcome of various effects, of which the “pushing effect” plays a dominant role. With the increase of weight on bit (WOB), the proportion of “leverage effect” increases, while the proportion of “pushing effect” decreases, and therefore the build rate decreases.

In order to reveal the rock breaking mechanism of the rotary-percussive drilling, considering the coupling effect of the static pressure, impact force and rotary cutting and using the finite element methods (FEM), a three-dimensional (3D) insert-rock mutual action model is established. We use a Mohr-Coulomb type material model to describe when and how rock fails, and a triangular wave to replace the stress wave. Using the finite element analysis software (ANSYS), the 3D contact analysis of the insert and rock under percussion and rotary-percussion is carried out respectively. Considering the inclined plane angle (α) of the bit end face as 0° (vertical impaction), 20°, 25°, 30°, 35°, 40° and 45° (inclined impaction), the stresses of the insert with percussive drilling and rotary-percussive drilling are calculated respectively. The results show that: the torsional shear stress causes volume breaking, tensile stress accelerates the crack extension and volume rock breaking, while the compressive stress contributes as a secondary factor for the rock breaking, 30°, 35° and 40° are the preferred angle for the flat bit with single inclined plane, and the combination angle of 20°-40° is preferred for the flat bit with double inclined planes. The results of the 3D contact analysis are further calibrated with a series of field applications and research results.