Development of a rock-bit interaction analytical model by considering the in-situ stresses for a bottom-hole element.

As can be seen, the current model’s trend of changes is such that when σ h < σ v , i.e., σ h = 80 MPa , increasing the well deviation angle up to 30° reduces the difference between the failure angle in the presented model and the model provided by Xin Ling, and, once again, this issue follows an increasing trend from 30° on.

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As can be seen, with the increase in the inclination of the well, the force required to break the rock first follows a decreasing trend, and then it increases, which is reasonable considering the change in vertical stress from the pressure of the fluid column to the stress caused by the weight of the overburdened rock, but this increase in the model presented by Xin Ling is such that the reduction of the cutting force that is required to break the rock eventually occurs up to the well inclination of about 10° and then the increasing trend becomes so intense that the order of the numbers changes sharply.

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