This paper describes the application of a directional-drilling model to the phenomenon of wellbore spiraling and compares its predictions with field data. The spiraling tendency of a bottomhole assembly (BHA) is determined from a stability analysis of the delay differential equations (DDEs) that govern the propagation of a borehole. These propagation equations are derived from a novel mathematical model, constructed by combining a bit/rock-interaction law, which relates the force and moment acting on the bit to its penetrations per revolution through the rock; kinematic relationships, which link the bit motion to the local borehole geometry; and a model for the BHA, which expresses the force and moment at the bit as a function of the external loads and the deflection imposed by the stabilizers. Spatial delays, associated with the positions of the stabilizers, account for the feedback of the borehole geometry as the stabilizers interact with the wellbore. The analytical form of the propagation equations makes it possible to perform 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 reduced downhole weight on bit (WOB) that depends on the actual downhole WOB, the state of wear of the bit, 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, a function of the lateral-steering resistance of the bit, the active weight, and properties of the BHA, relative to a critical value that depends only on the BHA configuration. 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 estimated 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 wear flats. This ability means that the model can be used to optimize BHA designs and determine critical WOB levels, both of which will mitigate the creation of spiraled holes.
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