Drilling Model for Soft-Formation Bits
Authors: Warren Tommy M. 
Published: December 2007

Summary
A new laboratory-derived drilling model for fullscale soft-formation bits that relates weight on bit (WOB), rotary speed, bit size, bit type, and rock strength to penetration rate is presented in this paper. The model was developed from tests with 6- to 12 1/4 in. (15.24- to 31.11-cm) bits on a research drilling rig that has adequate WOB, rotary speed, torque, and hydraulic capacity to test the bits under realistic running conditions. It shows a definite improvement in relating these variables to penetration rate over any of the other published penetration rate models. The rock strength as determined from drilling tests in various rocks was correlated with the rock mechanics properties of these same rocks. Shear strength correlated well with the rock strength that was calculated from drilling tests.

Introduction
There have been numerous drilling models presented in the literature over the years to relate the various mechanical factors involved in the drilling process to the penetration rate. The model published by Galle and Woods is the model for soft-formation bits that has been used most frequently. This model is inadequate as discussed by Randall and Estes. The basic problem with the model is that it cannot be applied in a practical situation without violating the assumptions from which it was developed. In addition, the model does not reflect properly the effect on penetration rate of changing WOB and rotary speed when all other conditions remain constant, as shown in Fig. 1.The "perfect cleaning" model proposed by Maurer from studies of single-tooth impacts is not applicable to most soft-formation drilling situations. Fig. 1 shows the penetration rate response to WOB that would be predicted by his model. He attributes the deviation of field data from his model to inadequate hole cleaning. Our data indicate that deviation from his model will occur under all reasonable hydraulic conditions for soft formations. One of the latest models to be proposed was that of Cunningham. His model also fails to match the experimental data as shown in Fig. 1.Because of the inadequacies of the existing models, a research effort was undertaken to develop a new model for soft-formation bits that would reflect the specific drilling characteristics for each bit type. The model was developed based on the premise that the effect of mechanical conditions such as WOB, rotary speed, bit size, bit type, and rock strength on penetration rate could be determined in the laboratory with full-scale bits. This model then could be coupled with a generalized model that would correct for the effects of mud properties, hydraulics, differential pressure, etc., that would occur under normal drilling conditions. The principles used in this mud and hydraulics model have been discussed by Lummus.

Experimental Measurement of Bit Performance
Experimental data were taken in the laboratory on the performance of IADC Series 1 bits. The data were collected with a large-scale drilling rig shown schematically in Fig. 2. This rig is capable of testing 6- to 12 1/4-in. (15.24- to 31.12-cm) bits under WOB, rotary speed, and hydraulic conditions similar to that experienced in the field.Each bit was tested in Bedford limestone rocks with some additional tests performed in Carthage marble. Water was used as the drilling fluid for most of the tests with the hydraulic conditions of flow rate per inch of bit diameter and jet velocity kept constant.
JPT
P. 963^