Page 653 - Air and Gas Drilling Manual

Chapter 12: Directional Drilling Operations 12-17
12.4.3 Equations for Radius and Slant (or Horizontal) Drilling
Direct circulation equations have been developed for air or gas drilling
operations that can be used to model the radius segment and the horizontal (or slant)
segment of a directionally drilled borehole [6]. These equations have been developed
using the basic equations given in Chapter 6, namely, Equations 6-57 (annulus flow)
and 6-72 (inside drill string flow).
The equations that model the radius and straight sections of a directional
borehole neglect the column weight of the air or gas in these borehole segments.
Annulus Flow
The equation for the pressure at the bottom of the radius segment, P , in the
br
annulus is
 2 aR  05 .
a
P =   P tr 2 + 2 a b T av L e T av   (12-2)
br
a
a
   
2
where P is the pressure at the top of the radius segment (lb/ft abs),
tr
R is the radius of the curved segment (ft).
The values of a and b are given by Equations 6-55 and 6-56, respectively. The
a
a
arc length of the curved segment, L, is
L = θ m R (12-3)
where θ is the maximum angle the borehole axis makes with vertical (radians).
m
The equation for the pressure at the bottom of the horizontal segment, P , in
ex
the annulus is
ex [
P = P en 2 + 2 a b T av ] 05 . (12-4)
L
a
a
2
where P is the pressure at the entrance to the horizontal segment (lb/ft abs),
en
L is the length of the horizontal segment (ft).
Inside Drill String Flow
The equation for the pressure at the top of the radius segment, P , inside the
tr
drill string is
 2 aR  05 .
i
P tr =   P br 2 + 2 a b T av L e T av   (12-5)
i
i
   
2
where P is the pressure at the bottom of the radius segment (lb/ft abs). The
br
values of a and b are given by Equations 6-70 and 6-71, respectively.
i i