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76 Part I Liquid Drilling Systems

3.5.1 Triplex Pumps
Geometrical analysis allows for the following equation to be derived for
triplex pumps (Guo et al., 2007):
2
q T = 0:01e v d lN (3.11)
where
3
q T = flow rate of triplex pump, gpm or m /min
e v = volumetric efficiency, dimensionless
d = piston diameter, in or m
l = stroke length, in or m
N = pumping speed, spm

The constant 0.01 in U.S. units is 2.3066 in SI units.
The pumped volume per stroke is
2
q S = e v d l (3.12)
4,118
where

q S = pumped volume per stroke, bbl or m 3
The constant 4,118 in U.S. units is 0.4201 in SI units.
The input horsepower needed from the prime mover is expressed as
2
pd lN
HP = (3.13)
168,067e m
where
HP = pump horsepower, hp
e m = pump mechanical efficiency, dimensionless

The constant 168,067 in U.S. units is 18.98 in SI units.

3.5.2 Duplex Pumps
Geometrical analysis allows for the following equation to be derived for
duplex pumps (Guo et al., 2007):
2
2
q D = 0:0068e v ð2d − d ÞlN (3.14)
1 2
where
3
q D = flow rate of duplex pump, gpm or m /min
d 1 = piston diameter, in or mm
d 2 = rod diameter, in or mm