Diamond Drilling Model Verified in Field and Laboratory Tests
Authors: Peterson J.L. 
Published: December 2007

A simple, theoretical blade-type approach to the mechanical aspects of how a diamond bit drills has been developed. The technique is incorporated into a mathematical model that yields a bit-design philosophy essential to the understanding of diamond-bit mechanical philosophy essential to the understanding of diamond-bit mechanical design variables.

Introduction
For more than 25 years, most diamond bits have been used in the oil field without the purchaser understanding how they drilled or the significance of the design variables. In many cases, it appears that the industry has learned what bit type drilled best by a trial-and-error procedure. To gain an understanding of the effect of the procedure. To gain an understanding of the effect of the mechanical design variables, a simplified model was developed and verified by laboratory and field tests. Through proper application of the model, bit penetration rate can be improved up to 25 percent while penetration rate can be improved up to 25 percent while lowering the bit cost and over-all drilling cost per foot.

The Model
The model describes the mechanical aspects of any diamond bit. Because of the complexity of the hydraulic component of diamond drilling, no attempt was made to use equations to describe the cleaning effects. The equations developed assume "perfect cleaning;" however, that condition is not necessary to apply the model.
In developing a universal model for understanding the mechanical aspects of bit design, all equations are based on a flat-bottom bit with round, surface-so diamonds.
The bit is modeled to be a combination of several "equivalent blades," where each makes a series of cuts in a stair-step fashion as the bit rotates. Fig. 1 shows the bottom of a bit with enough stones in each quadrant for their combined cutting action to make a uniform depth of cut from the center of the hole to the gauge section, forming an equivalent blade. The lower section of Fig. 1 shows an expanded cross-section of the gauge of the hole with the position of the four blades at various times during one rotation. For the four-blade bit, there are four diamonds that pass over the same point in each revolution. Therefore, the bit advance per revolution is four times the depth of cut of each blade. After traveling 90 degrees at a given depth of penetration, the diamonds reach the section removed by the preceding blade and then repeat the process by advancing into the formation. From a practical standpoint, however, the actual advance of each diamond is better represented by a spiral. Similarly, the diamonds on a particular blade would be laid out on a helix rather than being located within a given quadrant.
The diamonds can penetrate the formation if the load applied to each diamond divided by the projected surface area of the diamond in contact with the formation exceeds the formation resistance. Fig. 2 shows a diamond drilling, while Fig. 3 shows the projected area in contact with the formation. When drilling. only Side 1 is in contact with the formation; however, both Sides 1 and 2 are in contact initially.
Adjacent-blade diamonds work together to make a uniform depth of cut, as illustrated in Fig. 4 for the case of maximum diamond penetration. The number of diamonds working together at each radius provides redundancy that is equal to the number of equivalent blades in the bit.
JPT
P. 213