Page 287 - Air and Gas Drilling Manual

6-32 Air and Gas Drilling Manual
where e is the absolute roughness of the annulus surface (ft). In general, Equation 6-
105 is valid for values of Reynolds numbers from 2,000 to 4,000.
The empirical expression for the Fanning friction factor for turbulent flow
conditions is known as the von Karman equation. This empirical expression is
  2
 
 1 
f =   (6-106)
  D  
i
+ 1 14


 2 log. 
e 

 
In general, Equation 6-106 is valid for values of Reynolds numbers greater than
4,000.
For follow-on calculations for flow in the drill string the absolute roughness for
commercial pipe, e p = 0.00015 ft, will be used for the inside surfaces of the drill
pipe and drill collars.
Equation 6-102 together with Equations 6-103 through 6-106 can be used in
sequential trial and error integration steps starting at the bottom of the inside of the
drill string (with the known pressure above the drill bit inside the drill string) and
continuing for each subsequent change in drill string cross-sectional area until the
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, University of Tulsa, January 1999.
5. Lapedes, D. H., McGraw-Hill Encyclopedia of the Geological Sciences, McGraw-
Hill, 1978.
6. Gatlin, C., Petroleum Engineering: Drilling and Well Completions, Prentice-
Hall, 1960.

7. Bourgoyne, A. T., Millheim, K. K., Chenevert, M. E., and Young, F. S.,
Applied Drilling Engineering, SPE, First Printing, 1986.

8. Guo, B., Hareland, G., and Rajtar, J., “Computer Simulation Predicts