1. Drilling Engineering Prepared by: Tan Nguyen Drilling Engineering - PE 311 Modeling of Drilling Drill Bits

2. Drilling Engineering Prepared by: Tan Nguyen Modeling of Drill Bits Rollercone bits have been used extensively in the drilling industry and among its various types; the three-cone rolling cutter bit is by far the most widely used all over the two Cunningham (1960) showed that the drilling rate of a roller-cone bit is proportional to the rotary speed of the bit at the atmospheric pressure for a wide range of RPM and WOB as expressed below: R = K*W a *N where R = drilling rate, ft/hr ; W = weight on bit, klbf ; N = rotary speed ; and K, a = constants of proportionality Modeling of Roller Cone Bit

3. Drilling Engineering Prepared by: Tan Nguyen Modeling of Drill Bits Cunningham’s model did not integrate the effect of other drilling parameters: bit diameter, rock strength, etc. Maurer (1962) proposed his model for the perfect hole cleaning condition Modeling of Roller Cone Bit

4. Drilling Engineering Prepared by: Tan Nguyen Modeling of Drill Bits Bingham (1965) suggested the correlation based on limited laboratory data K is the constant accounting for the rock strength a is the WOB exponent Modeling of Roller Cone Bit

5. Drilling Engineering Prepared by: Tan Nguyen Modeling of Drill Bits Bourgoyne and Young (1973) suggested a drilling rate model considering the effect of several drilling variables on rate of penetration. In this model, the effect of the parameters such as WOB, RPM, bit tooth wear and others were assumed to be independent of one another. Modeling of Roller Cone Bit

6. Drilling Engineering Prepared by: Tan Nguyen Modeling of Drill Bits Modeling of Roller Cone Bit

7. Drilling Engineering Prepared by: Tan Nguyen Modeling of Drill Bits Warren (1981) introduced an equation to calculate the ROP for roller cone bits that integrated the effects of the mechanical conditions such as RPM, WOB, rock strength, bit type and size through the verification with full-scale experimental data. He developed his model using dimensional analysis and generalized response curves for the best fit using laboratory data. The results have revealed that the generated rock volume by a single tooth is proportional to tooth force squared and inversely proportional to rock strength squared. His model was later modified by Hareland (1994) for taking into account the bit wear and chip hold down effects as presented below: Modeling of Roller Cone Bit

8. Drilling Engineering Prepared by: Tan Nguyen Modeling of Drill Bits Modeling of Roller Cone Bit

9. Drilling Engineering Prepared by: Tan Nguyen Modeling of Drill Bits In the above model, the chip hold down function characterizes the resultant force on the cuttings after they are generated by the bit and its integrated effect on ROP. Also, the wear function shows the effect of the bit wear on rate of penetration as presented below: ΔBG represents the bit wear as a function of WOB, RPM, confined rock strength and formation abrasiveness. The constant Cc which is called “bit wear coefficient” Modeling of Roller Cone Bit

10. Drilling Engineering Prepared by: Tan Nguyen Modeling of Drill Bits Warren and Sinor (1986) proposed a single PDC cutter model to predict some parameters such as cutter forces, cutter temperature and cutter wear. Their model was developed based on a thorough geometrical relationships which was tested and verified using different sets of 30 laboratory data. Modeling of PDC

11. Drilling Engineering Prepared by: Tan Nguyen Modeling of Drill Bits Another model was developed by Kuru and Wojtanowsicz (1988) for assessing the PDC bits’ performance using single cutter force analysis. The effect of the friction between the PDC cutters and the rock was considered in their study which made it different than the previous approaches and capable of predicting ROP, bit torque as well as the bit life. Modeling of PDC

12. Drilling Engineering Prepared by: Tan Nguyen Modeling of Drill Bits Hareland and Rampersad (1994) developed a model for predicting formation drillability of drag bits. It was derived based on the conservation of mass where the rate of cutting removal in front of the cutters is equivalent to the rate of penetration. The effect of the operational parameters was integrated on rate of penetration with proper consideration of geometrical relationship and rock failure criteria as shown below. Modeling of PDC

13. Drilling Engineering Prepared by: Tan Nguyen Modeling of Drill Bits Finally, the most recent ROP model for the PDC bits was developed by Motahari et al. (2008) which claimed to be working accurately in drilling performance Modeling of PDC

14. Drilling Engineering Prepared by: Tan Nguyen Modeling of Drill Bits Modeling of PDC