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52 Part I Liquid Drilling Systems

Illustrative Example 2.9 (Continued )
total borehole pressure will be lower than the formation pore gradient. Assume
that the casing is fully opened and laminar flow in the annulus.
Casing depth: 6,400 ft (1,951 m)
Pore gradient: 0.78 psi/ft
Hole diameter: 14¾ in
Mud weight: 15.5 ppg
Plastic viscosity: 37 cp
Yield point: 6 lb/100 ft 2
Pipe velocity: 110 ft/min
Solution
" 2 2 4 #
v m = − 110 × 4×10:75 ×ð14:75 − 10:75Þ − 3×10:75
2
2
2
2
60 4×10:75 ×ð14:75 − 10:75Þ ×ð14:75 − 10:75 Þ+6×10:75 4
= 0:0718ft/s
k = 0:275× 10:75 +0:25 = 0:45
14:75
v e = 0:0718+0:45× 110 = 0:90ft/s
60
Use the annular flow pressure loss equation for the laminar flow:
" #
Δp f = 37 × 0:90 + 6 × 6,400 = 61 psi
2
200 × ð14:75 − 10:75Þ
1,000 × ð14:75 − 10:75Þ
EMW = 15:5 − 61 = 15:32 ppg
0:052 × 6,400
The equivalent mud weight of the pore gradient (EMW P )is
EMW P = 0:78 = 15 ppg < 15:32 ppg
0:052
Therefore, the borehole will be safe while running the casing at this depth.

2.3.4 Pressure Drop at the Bit
The purpose of installing jet nozzles on a bit is to improve the cleaning
action of the drilling fluid at the bottom of the hole. Because of the
small diameter of bit nozzles, fluids reach high velocities inside the nozzle.
This velocity is called nozzle velocity and is expressed as
q
v n = 0:32086 (2.85)
A T