STANDARD HANDBOOK OF PETROLEUM & NATURAL GAS ...

948 Drilling and Well Completions
8. Compute the velocity of the pressure wave in the drillpipes.
9. Compute the amplitude of a pressure wave at surface of a wave generated
at bottom with an amplitude of 200 psi at frequencies of 0.2, 6, 12 and
24 Hz.
Pressure loss in pipe (turbulent flow) is
dP =
dL y0.75
Po=
1800. d’.25
(4-1 87)
Pressure loss in annulus (turbulent flow) is
dP =
dL y0.75
1396 (d, - d,
Class
(4-188)
where dP = pressure loss in psi
dL = pipe or annulus length in ft
y = fluid specific weight in lb/gal
v = fluid velocity in ft/s
d = ID pipe diameter in in.
d, = OD pipe diameter in in.
d, = external annulus diameter in in.
p = fluid viscosity in cp
Solution
1. Bottomhole pressure, no flow: 6,240 psi
2. Drillpipe pressure loss: 1,076 psi
3. Annulus pressure loss: 113 psi
4. Bit nozzle pressure loss: 1,055 psi
5. Pump pressure: 2,244 psi
6. Graph (see Figure 4-256)
7. Wave velocity in free mud: 4,294 ft/s
8. Wave velocity in drill pipes: 4,064 ft/s
9. Wave amplitude at surface (Equations 4-184 and 4-185):
0.2 Hz, L = 86,744 ft, 178 psi
6 Hz, L = 15,837 ft, 106 psi
12 Hz, L = 11,198 ft, 81 psi
24 Hz, L = 7,918 ft, 56 psi
Example 10: Mud Pulse Telemetry-Pulse
Veloclty and Attenuation
Assume a well 10,000-ft deep, mud weight of 12 lb/gal, mud viscosity of
12 cp, 4+in drillpipes (3.640 in. ID), mud flowrate of 400 gal/min, steel Young
modulus of 30 x lo6 psi, and steel Poisson ratio of 0.3.
1. Compute the pressure at bottom inside the drill collars:
a. with no flow and no surface pressure,
b. with no flow and 2,500 psi surface pressure,
c. while pumping 400 gal/min with 2,500 psi at surface.