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Mud Pumps 77

The constant 0.0068 in U.S. units is 1:57 × 10 − 9 in SI units.
The pumped volume per stroke is
2
q S = e v d l (3.15)
5,912

where
q S = pumped volume per stroke, bbl or m 3

The constant 5,912 in U.S. units is 0.6069 in SI units.
The input horsepower needed from the prime mover is expressed as

2 2
pð2d − d ÞlN
HP = 1 2 (3.16)
252,101e m
The constant 252,101 in U.S. units is 2:8 × 10 10 in SI units.

Illustrative Example 3.4
Two identical pumps are considered for drilling the well shown in Illustrative
Example 3.2. These pumps are the TSC WF700 triplex pumps, each having a
stroke length of 8.5 in. (0.216 m). Table 3.6 provides the pump specification
data given by the manufacturer.
The pump can run at the maximum speed of 150 spm with piston dia-
meters from 4 in. to 7 in. (0.108 m to 0.178 m). Assuming that the volumetric
efficiency and mechanical efficiency are 0.95 and 0.9, respectively, if the flow
3
rate of 350 gpm (1.325 m /min) is desired with 4.5-in. (0.114 m) liners, what is
the required pump speed? What is the total input horsepower needed from
the prime movers?
Solution
Equation (3.11) gives

N = q T
2
0:01e v d l
= 350/2
2
0:01ð0:95Þð4:5Þ ð8:5Þ
= 107 spm
(Continued )