STANDARD HANDBOOK OF PETROLEUM & NATURAL GAS ...

MWD and LWD 935
The calculation of the amplitude of pressure variation at bottom can be done
assuming that the restriction behaves as a choke. The pressure loss can be
estimated using the relations
Q' y 144
AP =
2.g,.c2.A~
(4-180)
where AP = pressure loss in psi
Q = flowrate in ft5/s
y = fluid specific weight in lb/ft3
c = coefficient assumed to be one
A,, = cross-sectional area of the restriction in
g, = acceleration of gravity (32.2 ft/s2)
When using a mud motor, the AP due to the restriction must be added to
the AP due to the motor and the bit nozzles.
The mud motor pressure loss is given by
(4-1 8 1)
where AP = pressure loss in psi
W = motor power in HP
q = motor efficiency
Q = mud flowrate in gal/min
Formula 4-180 will apply to the bit nozzle pressure loss.
Transmission by Negative Pulses. Drilling with a nozzle bit or with a downhole
motor introduces a differential pressure between the inside and the outside
of drill collars. This differential pressure can be changed by opening a valve
and creating a communication between the inside of the drill string and the
annular space. In this way, negative pulses are created that can be used to
transmit digital data in the same way as positive pulses. Halliburton and other
companies are marketing devices using this transmission principle.
Equation 4-180 can be used to calculate the pressure change inside the drill
collars by changing the cross-sectional area A,, from bit nozzles only to bit nozzles
plus the pulser nozzle.
Continuous-Wave Transmission. Anadrill, a subsidiary of Schlumberger,
markets a tool which produces a 12-Hz sinusoidal wave downhole. Ten-bit words
representing data are transmitted by changing or maintaining the phase of the
wave at regular intervals (0.66 s). A 180' phase change represents a 1, and phase
maintenance represents a 0.
Figure 4-247 shows a sketch of principle of the system and of the phase-shiftkeying
technique. Frames of data are transmitted in a sequence. Each frame
contains 16 words, and each word has 10 bits. Some important parameters may
be repeated in the same frame, for example, in Figure 2-248, the torque Tp,
the resistivity R and the gamma ray GR, are repeated four times. The weight
on bit WOB is repeated twice, and the alternator voltage Val, one time. Note
that a synchronization pulse train starts the frame.