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Mud Hydraulics Fundamentals 55

where
ROP = rate of penetration, ft/hr or m/hr
RPM = rotary speed of bit, rpm

The constant 0.2 in U.S. units is 0.0167 in SI units.
The particle friction factor f is a function of the Reynolds number
N Re and particle sphericity ψ. The sphericity is defined as the surface area
of a sphere containing the same volume as the particle divided by the
surface area of the particle. A conservative value for cuttings sphericity is
0.8. Engineering charts are available for finding the values of the friction
factor (Bourgoyne et al., 1986). Fang et al. (2008) developed the follow-
ing correlation to replace the charts:

2
^ (2.92)
f p = 10 A′ + B′ logðN ReP Þ + C′½logðN ReP ފ
where
2
A′ = 2:2954 − 2:2626 ψ + 4:4395 ψ − 2:9825 ψ 3 (2.93)
B′ = −0:4193 − 1:9014 ψ + 3:3416 ψ − 2:0409 ψ 3 (2.94)
2

C′ = 0:1117 + 0:0553 ψ − 0:1468 ψ + 0:1145 ψ 3 (2.95)
2
where the particle Reynolds number is defined as

f
N ReP = 928ρ v sl d s (2.96)
μ
where
μ = viscosity of Newtonian fluid, cp or Pa-s

The constant 928 in U.S. units is 1 in SI units.
Because the slip velocity is implicitly involved in Eqs. (2.90) and
(2.92), the slip velocity can only be solved numerically (trial and error).
A computer program called Cuttings Slip Velocity.xls is attached to this
book for easy calculations. To calculate the particle slip velocity using
Table 2.4, (1) select a unit system, (2) update the data in the Input Data
column, and (3) click the Solution button and obtain the result.
In non-Newtonian fluids, an analytical solution for cuttings terminal
slip velocity has not been developed. For Bingham plastic fluids, there is
a critical (minimum) cuttings diameter for it to slip (Bourgoyne et al.,