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54 Part I Liquid Drilling Systems

The hydraulic impact force is another indicator of the hole-cleaning
capacity of the drilling fluid. It is expressed as
p ffiffiffiffiffiffiffiffiffiffi
(2.89)
F j = 0:01823C d q ρΔp b
where
F j = bit hydraulic impact force, lb f or N

The constant 0.01823 becomes 1.4142 in SI units.

2.3.5 The Cuttings-Carrying Capacity of Mud
A minimum mud flow rate is required for carrying drill cuttings to the
surface. This minimum flow rate can be estimated based on the mini-
mum required mud velocity, which should be higher than the drill cut-
tings slip velocity. Unfortunately, because of the complex geometry and
boundary conditions involved, analytical expressions describing drill cut-
tings slip velocity have been obtained for only very idealized conditions.
For a drill cutting falling in a Newtonian fluid, its terminal slip velo-
city can be expressed as
v ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
!
ρ − 7:48ρ
u
u s f
d s
ν sl = 1:89 t (2.90)
f p 7:48ρ
f
where
v sl = cuttings slip velocity, ft/s or m/s
d s = equivalent cuttings diameter, in or m
3
ρ s = cuttings density, lb/ft or kg/m 3
3
ρ f = fluid density, ppg or kg/m
f p = particle friction factor, dimensionless
The constants 1.89 and 7.48 in U.S. units are 2.97 and 1 in SI units,
respectively.
The equivalent cuttings diameter depends on several factors, including
formation lithology, bit type, rate of penetration, and rotary speed at the
bit. It can be estimated on the basis of data from offset drilling. For a given
bit to drill a given formation of rock, the cuttings size can be reduced by
using a low rate of penetration and a high rotary speed. The following for-
mula gives an approximation of equivalent cutting diameter:
ROP
d s = 0:2 (2.91)
RPM