Page 93 -

Mud Pumps 69

Combining Eqs. (3.1) and (3.3), the following relation is derived for the
maximum bit hydraulic horsepower criterion:
Δp d = 1 p p (3.4)
m + 1
Combining Eqs. (3.2) and (3.3), the following relation is derived for the
maximum jet impact force criterion:
Δp d = 2 p p (3.5)
m + 2
From which the expressions for the required pump pressure are
(3.6)
p p = ðm + 1ÞΔp d
and

p p = m + 2 Δp d (3.7)
2

for the maximum bit hydraulic horsepower criterion and the maximum
jet impact force criterion, respectively.

Illustrative Example 3.2
For the data in Illustrative Example 3.1 and the additional data given in
Figure 3.4, determine the minimum required pump pressure. Assume the
3
maximum mud weight of 12 ppg (1,440 kg/m ), the maximum plastic
viscosity of 15 cp (0.015 Pa-s), the maximum yield point of 10 lb/100 ft 2
(4.78 Pa), pipe wall roughness of 0.00025 in. (0.00635 mm), pressure drop at
the mud motor of 200 psi (1,379 kPa), and a mud flow rate of 300 gpm
3
(1.14 m /min).
Solution
This problem is solved using the spreadsheet program Pump Pressure.xls that is
attached to this book. To calculate the required pump pressure using Table 3.4,
(1) select a unit system, (2) update the data in the Input Data column, and
(3) click on the Solution button and obtain the result. The result is summarized
in Table 3.5 for the maximum bit hydraulic horsepower criterion. It indicates
that the required pressure is 3,461 psi (23.86 MPa).
(Continued )