Page 410 - Air and Gas Drilling Manual

9-14 Air and Gas Drilling Manual
Assuming laminar flow conditions, the effective absolute viscosity of the drilling
mud is equal to the plastic viscosity. Therefore, the effective absolute viscosity is
lb sec
.
0 0006267
e1 mp 2
ft
The approximate average diameter of the rock cuttings particle in consistent units is
.
0 198
D c
12
D c 0 0165 ft
.
Substituting the above values for, s , m, e1, and D c into Equation 9-3a yields
the terminal velocity for laminar flow conditions. Equation 9-3a gives
168 5 . 75 0 .
.
V t1 0 0333 0 0165) 2
( .
0 0006267
.
V t1 1 353 ft/sec
.
Using Equation 9-1, the total velocity of the fluid is
.
V 0 417 1 353
.
m1
.
V m1 1 770 ft/sec
The above total velocity of the fluid must be the minimum average velocity of
the incompressible fluid in the borehole annulus section where the cross-sectional
area is the largest. In this illustrative example, the largest cross-sectional area of the
annulus is in the cased section of the well where the inside diameter of the casing is
8.017 inch and the outside of the diameter of the drill pipe is 4.50 inch. Thus, this
annulus cross-sectional area, A a, is
2 2
.
.
8 017 450
A a
4 12 12
A 0 240 ft 2
.
a
The volumetric flow rate in the above annulus section is
Q a1 (. 1 770)
0 240) (
.