Claims
- 1. A method of optimizing bit rate of penetration while drilling, which comprises the steps of:
- collecting bit rate of penetration and weight on bit data at selected times during drilling;
- averaging collected bit rates of penetration and weights on bit over selected time intervals to obtain an average bit rate of penetration BIT.sub.-- ROP(t) and an average weight on bit BIT.sub.-- WT(t) for each time interval t;
- lagging said average bit rates of penetration to obtain a first lagged bit rate of penetration BIT.sub.-- ROP(t-1) for each time interval (t-1) and a second lagged bit rate of penetration BIT.sub.-- ROP(t-2) for each time interval (t-2);
- performing a multiple linear regression with average bit rate of penetration BIT.sub.-- ROP(t) as the response variable and first lagged bit rate of penetration BIT.sub.-- ROP(t-1), second lagged bit rate of penetration BIT.sub.-- ROP(t-2), and average weight on bit BIT.sub.-- WT(t) as the explanatory variables over a selected time period while drilling, to obtain a mathematical model of the drilling environment during said selected time period, said mathematical model being an equation of the form BIT.sub.-- ROP(t)=.alpha.+.beta..sub.1 BIT.sub.-- ROP(t-1)+.beta..sub.2 BIT.sub.-- ROP(t-2)+.beta..sub.3 BIT.sub.-- WT(t); and,
- using said mathematical model to select a weight on bit to achieve a desired bit rate penetration.
- 2. The method as claimed in claim 1, including the step of cleaning said average bit rates of penetration and average weights on bit to remove zeros and outliers prior to said lagging step.
- 3. The method as claimed in claim 1, including the step of testing said mathematical model for significance prior to said using step.
- 4. The method as claimed in claim 3, wherein said step of testing said mathematical model includes the step of:
- determining if bit weight coefficient .beta..sub.3 is greater than zero.
- 5. The method as claimed in claim 3, wherein said step of testing said mathematical model includes the step of:
- determining if bit weight coefficient .beta..sub.3 is statistically significant.
- 6. The method as claimed in claim 3, wherein said step of testing said mathematical model includes the step of:
- determining if said mathematical model is well-fitted to said average bit rates of penetration and average weights on bit over said selected time period.
- 7. The method as claimed in claim 6, including the step of maintaining weight on bit at said computed weight on bit.
- 8. The method as claimed in claim 7, including the step of maintaining said feasible weight on bit.
- 9. The method as claimed in claim 8, including the step of computing a confidence interval for said predicted bit rate of penetration.
- 10. The method as claimed in claim 6, including the step of determining if said computed weight on bit is feasible.
- 11. The method as claimed in claim 3, including the step of:
- building a new mathematical model if said mathematical model is not significant.
- 12. The method as claimed in claim 1, wherein said step of using said mathematical model includes the step of:
- computing a weight on bit necessary to achieve a desired bit rate of penetration based upon said mathematical model.
- 13. The method as claimed in claim 12, including the step computing a feasible rate of penetration based upon said mathematical model and a feasible weight on bit.
- 14. The method as claimed in claim 1, wherein said step of using said mathematical model includes the step of:
- computing a weight on bit necessary to achieve a maximum feasible bit rate of penetration based upon said mathematical model.
- 15. The method as claimed in claim 14, including the step of:
- testing if an observed bit rate of penetration is within said confidence interval.
- 16. The method as claimed in claim 1, including the step of:
- forecasting a predicted bit rate of penetration based upon said mathematical model.
- 17. The method as claimed in claim 16, including the step of:
- using said mathematical model as long as observed bit rate of penetration are within said confidence interval.
- 18. The method as claimed in claim 16, including the step of:
- building a new mathematical model whenever two successive observed bit rates of penetration are outside said confidence interval.
CROSS-REFERENCE TO RELATED APPLICATION
This Application claims the benefit of U.S. Provisional Application Ser. No. 60/059,794, filed Sep. 23, 1997.
US Referenced Citations (21)