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164     CHAPTER 6 Direct Circulation Models




                          Equations (6-70), (6-71), (6-75), and (6-76) can be used in sequential calculation
                          steps starting at the bottom of the inside of the drill string and continuing for
                          each subsequent change in the cross-sectional area in the drill string until the sur-
                          face injection pressure is determined.





                          REFERENCES
                           1. Daugherty, R. L., Franzini, J. B., and Finnemore, E. J., Fluid Mechanics with Engineering
                             Applications, Eighth Edition, McGraw-Hill, 1985.
                           2. Brown, K. E., and Beggs, H. D., The Technology of Artificial Lift Methods, Vol. 1, PennWell
                             Books, 1977.
                           3. Brown, K. E., et al, The Technology of Artificial Lift Methods, Vol. 2a, PennWell Books, 1980.
                           4. Personal communications with Stefan Miska, Department of Petroleum Engineering, Uni-
                             versity of Tulsa, January 1999.
                           5. Lapedes, D. H., McGraw-Hill Encyclopedia of the Geological Sciences, McGraw-Hill, 1978.
                           6. Kaminski, D. A., and Jensen, M. K., Introduction to Thermal and Fluid Engineering, Wiley
                             and Sons, 2005.
                           7. Guo, B., Hareland, G., and Rajtar, J., “Computer Simulation Predicts Unfavorable Mud Rate and
                             Optimum Air Injection Rate for Aerated Mud Drilling,” SPE Paper 26892, Presented at the SPE
                             Eastern Regional Conference and Exhibition, Pittsburgh, Pennsylvania, November 2–4, 1993.
                           8. Gatlin, C., Petroleum Engineering: Drilling and Well Completions, Prentice-Hall, 1960.
                           9. Bourgoyne, A. T., Millheim, K. K., Chenevert, M. E., and Young, F. S., Applied Drilling
                             Engineering, SPE, First Printing, 1986.
                          10. Beyer, A. H., Millhone, R. S., and Foote, R. W., “Flow Behavior of Foam as a Well Circulating
                             Fluid,” SPE Paper 3986, Presented at the SPE 47th Annual Fall Meeting, San Antonio, Texas,
                             October 8–11, 1972.
                          11. Underbalanced Drilling Manual, Gas Research Institute, GRI Reference No. GRI-97/0236,
                             1997.
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