3D PDC Bit Model Predicts Higher Cutter Loads

Abstract

Summary Historically, PDC bit modeling has incorporated the assumption that cutter forces are constant for a full revolution of the bit. This assumption places considerable limits on the model's ability to simulate drilling in nonhomogeneous rock and in cases where the bit whirls. Recent studies have shown that cutter damage caused by impact loading is a primary cause of PDC bit failure. These impacts may be caused by both bit whirl and drilling through nonhomogeneous rock. The 3D model presented provides the capability to evaluate cutter loading for both conditions. It shows that the cutter loads for common drilling situations may be as much as 10 times greater than those calculated with previously available 2D models. Introduction Ashmore et al.1 began PDC bit modeling at Sandi Natl. Laboratories to develop a PDC bit for geothermal drilling. Several researchers continued the work over a number of years, and Glowka2 summarized this work. Warren and Sinor3 and Sinor and Warren4 developed a similar PDC bit model based on actual bit measurements, and their results compared model predictions with laboratory data for several bit designs. The models mentioned above use a 3D description of the bit and a 2D description of the bottomhole geometry. The 3D detail of the bit is needed to define the cutter geometry adequately, but, because it is assumed that the area of cut for any cutter on the bit is constant for a full revolution of the bit, the bottomhole geometry is described adequately with just two dimensionless. The 2D geometry results in the model being much simpler and computationally faster than if a 3D rock geometry were used. The constant-area-of-cut assumption allows the force calculations for each cutter to be made only as it passes a fixed radial rock plane, which results in a constant force on any cutter for a full rotation of the bit. The 2D model is used primarily to evaluate steady-state bit performance in homogeneous rock but also can be applied with reasonable accuracy to cases where a bit drills across a bed boundary perpendicular to the bit axis. Brett et al.5 presented results that show that damage to PDC bits by cutter breakage owing to impact loading is much more significant than previously thought. They describe a mechanism called bit whirl that causes the bottomhole pattern for a PDC bit to be lobed and that may lead to impact damage of the PDC cutters. When this occurs, the 2D model cannot be used to calculate the cutter loads. In fact, the steady-state cutter loads predicted by the 2D model are much lower than the loads required to break cutters. The 2D model cannot be used for modeling bed boundaries that are not perpendicular to the bit axis, nor can it be used to model the effect of drilling nonhomogeneous formations, such as concretions or pyrite and chert nodules. These three deficiencies in modeling real drilling phenomena (which can cause impact loading of cutters) provided the impetus for the development of the 3D model discussed below. Model Description The PDC bit model discussed in this paper is a 3D kinematic model derived from the basic 2D model Warren and Sinor3 presented. It can predict cutter loading for nonhomogeneous formation drilling and any arbitrary bit motion although it is not a full dynamic model in the sense of predicting when bit whirl will begin. In the earlier work, the bit geometry was already 3D; thus, it required no modification. Because many features of the 3D model, such as the cutter-force model, are the same as in the 2D model, only the differences between the models are discussed in this paper. The Appendix in Ref. 3 gives a description of the bit geometry, 2D bottomhole geometry, cutter-force model, and cutter-integration technique. For the model described here, the formation geometry is handled in a similar way as in the 2D technique except that multiple rock planes are used instead of tracking the formation surface on a single radial plane. The multiple planes provide nearly continuous rock elements parallel to the bit axis at discrete radial and circumferential locations in a cylindrical coordinate system. These planes typically are located at 5° increments around the borehole with 0.006-in. radial grid spacing on each plane. This results in approximately 600 elements/in.2 near the gauge of an 8 1/2-in. bit. As each cutter passes a plane, any formation that extends above the cutter edge is removed. The total rock volume removed, the cutter parameters, and rock strength are then used to calculate the force on the cutter. These forces are recalculated each time the cutter crosses one of the radial formation planes. The weight on bit (WOB), torque, and bit imbalance force are updated each time an individual cutter force is modified. The formation properties can be defined independently for any area along the rock planes. This allows tilted formation boundaries and nodules (roughly spherical inclusions) to be incorporated into the formation description. Typically, properties are assigned to different formations by defining their respective boundaries in the cylindrical coordinate system. For bed boundaries, equations of a plane are used; for inclusions, equations of a sphere are used. Proper formation characteristics for each cut are determined by whether the spatial coordinates of the cutter edge fall within the locus of points that defines the first or second set of formation properties. The 2D model allows the bit to be rotated around any fixed point on the bit; however, much more complicated bit motion is required to simulate bit whirl and produce the lobed bottomhole patterns Brett et al.5 described. Lobed bottomhole patterns are created when the center of rotation continuously changes as the bit rotates. To provide the flexibility needed to predict cutter forces for a whirling bit, the model was developed with a very general bit-motion algorithm that calculates individual cutter trajectories and displacements. The equations Brett et al.5 presented were used to define and prescribe the bit motion for the whirl examples presented below. Originally, the model was designed to run at a constant rate of penetration (ROP) because of the simplicity in determining the cutter forces. However, field practice for running PDC bits is to control the WOB normally rather than to run at constant ROP. This means that, when formation discontinuities are encountered, the ROP changes instead of the force on the bit changing. To simulate constant WOB drilling, an iterative procedure was developed to find the ROP that provides the desired WOB. The cutter forces for each revolution are temporarily stored and summed to determine the average WOB for that revolution. If the desired WOB is not obtained, the bit is moved back to the position it was in before the last revolution, the penetration per revolution is adjusted, the rock is restored to its prior geometry, and the bit is rotated again. This results in a constant penetration per revolution during any complete bit revolution, although it may vary from one revolution to the next. Hence, the average WOB for each successive revolution is constant, but the instantaneous WOB within a revolution may vary.