STANDARD HANDBOOK OF PETROLEUM & NATURAL GAS ...

888 Drilling and Well Completions
where A is the fluid cross-sectional area (in.2), The fluid cross-sectional area is
approximately
A -- 2ne:(n: - 1) (4- 159)
where er is the rotor rotation eccentricity (in.). The special case of a 1:2 lobe
profile motor has a fluid cross-sectional area of
A -- 2erdr (4-160)
where dr is the reference diameter of the motor (in.). The reference diameter is
dr = 2epS (4- 16 1)
For the 1:2 lobe profile motor, the reference diameter is approximately equal
to the diameter of the rotor shaft.
The instantaneous torque of the positive displacement motor M (ft-lb) is
M = 0.0133s Apq (4-1 62)
where Ap = differential pressure loss through the motor in psi
11 = total efficiency of the motor. The 1:2 lobe profile motors have efficiencies
around 0.80. The higher lobe profile motors have efficiencies
that are lower (Le., of the order of 0.70 or less)
The instantaneous speed of the positive displacement motor N (rpm) is
N=
231.016q
S
(4-163)
where q is the circulation flowrate (gal/min).
The positive displacement motor horsepower HP (hp) for any speed is
HP = - 9*P
1,714
(4-164)
The number of positive displacement motor chambers nc is
where L is the length of the actual motor section (in.).
The maximum torque Mma will be at the maximum differential pressure Apmm,
which is
M,, = 0.133s Ap,q (4-1 66)
The maximum horse power HPmu will also be at the maximum differential
pressure Ap, which is