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56 Part I Liquid Drilling Systems

Table 2.4 Computer Program Cuttings Slip Velocity.xls
Input Data U.S. Units SI Units
Particle diameter 0.25 in
Particle spherity 0.8
Drilling fluid viscosity 6 cp
Drilling fluid density 12 ppg
Cuttings specific gravity 2.7
Solution
2
A′ = 2:2954 − 2:2626 ψ + 4:4395 ψ − 2:9825 ψ 3 = 1.7996
2
B′ = −0:4193−1:9014ψ +3:3416ψ −2:0409ψ 3 = –0.8467
2
C′ = 0:1117 + 0:0553 ψ − 0:1468 ψ + 0:1145 ψ 3 = 0.1206
f
N ReP = 928ρ v sl d s = 240
μ

2
= 2.9350
^
f p = 10 A′ + B′logðN ReP Þ + C′½logðN ReP ފ
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ρ − 7:48ρ

ν sl = 1:89 d s s f = 0.5166 ft/s = 0.157 m/s
f p 7:48ρ f
1986). This critical diameter is directly proportional to the gel strength
of the fluid. Multiple correlations have been developed to estimate the
cuttings slip velocity in non-Newtonian fluids. These correlations are
documented by Chien (1971), Moore (1986), and Walker and Mayes
(1975). However, Eq. (2.90) gives conservative estimates for the cuttings
terminal slip velocity in non-Newtonian fluids.
The minimum required mud velocity should be higher than the drill
cuttings slip velocity by an additional amount called transport velocity—that is,

(2.97)
v min = v sl + v tr
where

v min = minimum required mud velocity, ft/s or m/s
v tr = transport velocity, ft/s or m/s
The required transport velocity depends on the rate of penetration
and the maximum allowable cuttings concentration in the annular space.
The following equation was proposed by Guo and Ghalambor (2002) for
the required transport velocity:
2
πd ROP
v tr = b (2.98)
4C p A 3,600