Abstract
This paper describes the application of a directional drilling model to wellbore spiraling and compares it to field data. In this paper, the spiraling tendency of a Bottom Hole Assembly (BHA) is determined from a stability analysis of the delay differential equations that govern the propagation of a borehole. These propagation equations are derived from a novel mathematical model, constructed by combining (1) a bit/rock interaction law, which relates the forces acting on the bit to the penetrations of the bit in the rock per revolution; (2) kinematical relationships, which link the bit motion to the local borehole geometry; and (3) a model for the BHA, which expresses the forces and moments at the bit from the external loads and the deflections imposed by the stabilizers. Spatial delays associated with the positions of the stabilizers account for the feedback of the borehole as the stabilizers interact with the wellbore.
The analytical form of the propagation equations makes it possible to carry out a stability analysis and determine whether borehole spiraling is expected. The coefficients of the propagation equations embody the characteristics of a particular drilling system; these include the BHA configuration, bit properties, and the active weight, Wa, a calculated reduced weight on bit that depends on the actual Weight On Bit (WOB), the cutter wearflats, and the rock strength. If the bit trajectory is unstable, then any perturbation in the borehole geometry is amplified gradually, eventually leading to the generation of a spiraled hole.
The stability of the bit trajectory essentially is controlled by the magnitude of a dimensionless group relative to a critical value that depends on the BHA configuration. This group is a function of the lateral steering resistance of the bit, the bit wear, the rock strength, and the WOB. Thus, a BHA can be either stable or unstable depending on the selected bit, its state of wear, and the WOB.
Predictions of the stability analysis are compared with field data from spiral holes pertaining to eight sections from four wells drilled with different bit types and BHA configurations. The paper shows that the propensity of a BHA to spiral can be predicted by the model by assuming reasonable values for parameters such as the lateral steering resistance and the part of the WOB transmitted by the cutter wearflats. This comparison suggests that the model can be used to optimize BHA designs and critical WOB levels that will mitigate the creation of spiral holes.
