Page 273 - Air and Gas Drilling Manual

6-18 Air and Gas Drilling Manual
2

f
 R
=
p)
h (
b

S 
π
a
 
gD −
D
2
2
  2 D ( w ˙ h 2 g 2 − D p) 2 (6-53)
4
In the above form, both sides of Equation 6-51 can be integrated. Using the
constants in Equations 6-52 and 6-53 the solution to Equation 6-51 is
ln P ( 2 + b T av) = a h (6-54)
1 P bh a H
2
2 a T av 0
P at
Evaluating Equation 6-54 at the limits and rearranging the results gives
 P 2 + b T  2 a
2
ln  bh a av  = a H (6-55)
2
  P at 2 + b T   T av
a
av
Raising both sides of Equation 6-55 to the natural exponent, e, gives
a
P 2 + b T 2 2 aH
bh a av = e T av (6-56)
P 2 + b T 2
at a av
Equation 6-59 can be rearranged and a solution obtained for P bh. This yields
 2 aH  05 .
a
−
2
P bh =   P ( at 2 + bT av) ebT av 2   (6-57)
T av
a
a
   
The flow of gas to the well must be sufficient to carry solid rock cuttings from
the bottom of the annulus to the surface. Therefore, it is assumed that the flow
condition in both the annulus and the inside of the drill string is turbulent. The
empirical von Karman relationship for determining the Fanning friction factor for the
annulus is
  2
 
f =   D − 1   (6-58)
D 

 2 log. 
p
h
+ 1 14
   e   
 
For follow-on calculations for flow in the annulus the absolute roughness for
commercial pipe, e p = 0.00015 ft, will be used for the outside surfaces of the drill