Drag bit/rock interface laws for the transition between two layers

This paper extends bit/rock interface laws for drag (PDC) bits, originally formulated for homogeneous rocks, to the transition between two rock layers with distinct mechanical properties. It formulates a set of relations between the weight-on-bit, the torque-on-bit, the depth-of-cut per bit revolution, and the engagement parameter of the bit in the lower rock layer. This model enables us to extend the 2D E−S diagram for the homogeneous case to a 3D E−S diagram for the transitional case, where the third dimension is related to the engagement parameter. Moreover, this model is used to derive an expression for the drilling efficiency for the transitional phase. Examples are provided for describing the 3D E−S diagram and drilling efficiency under the condition of quasi-stationary drilling (i.e., constant angular velocity, constant weight-on-bit). These examples show that the drilling efficiency depends nonlinearly on the bit engagement between the two rock layers. This intrinsic dependency is closely related to the bit shape.