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Mud Hydraulics Fundamentals 57

where
d b = bit diameter, in or m
C p = cuttings concentration, volume fraction
2
A = annulus cross-sectional area at the depth of interest, in or m 2
For directional well drilling, the minimum required mud velocity for
drilling the inclined hole sections is usually considered to be 1.8 times
the minimum required mud velocity for drilling the vertical holes. For
horizontal well drilling, the minimum required mud velocity for drilling
the horizontal hole sections is usually considered to be 1.5 times the
minimum required mud velocity for drilling the vertical holes.
Finally, the minimum required mud flow rate in the extreme well-
bore geometry can be calculated using
q min = 3:1167v min A (2.99)

where
3
q min = minimum required mud rate, gpm or m /min
The constant 3.1167 in U.S. units is 60 in SI units.

SUMMARY

This chapter presented fundamentals for mud hydraulics. Drilling
muds are characterized on the basis of their rheological properties. Pres-
sure loss in a conduit depends on fluid properties, flow regime, conduit
geometry, and flow rate. The cuttings-carrying capacity of drilling mud is
controlled by cutting size and fluid properties.

REFERENCES
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Bourgoyne Jr., A.T., Millheim, K.K., Chenevert, M.E., Young Jr., F.S., 1986. Applied
Drilling Engineering. SPE Textbook Series, Dallas.
Burkhardt, J.A., 1961. Wellbore pressure surges produced by pipe movement. Trans.
AIME 222, 595–605.
Chen, N.H., 1979. An explicit equation for friction factor in pipe. Ind. Eng. Chem. Fund.
18, 296.
Chien, S.F., 1971. Annular velocity for rotary drilling operations. Proceedings of the 5th SPE
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