Page 282 - Air and Gas Drilling Manual
P. 282
The flow down the annulus is three phase flow (gas, fluid, and solids). The exit
pressure for stable foam drilling operations is the back pressure, P bp, upstream of the
valve in the flow line from the annulus. Equation 6-26 becomes
∫ P bh dP = ∫ H dh Chapter 6: Direct Circulation Models 6-27
(6-88)
P
P bp B () 0
a
2
where P bp is the back pressure on the annulus (lb/ft , abs), and
w ˙
B () = t
P
a
P T av
g
Q + Q f
g
P T
g
2
P g T av
P Q g + Q f
T
1 + f π g
2 ( h − ) ( D 2 − )
2
D
gD
D
p
4 h p
where the total weight rate of flow, ˙ w , in the annulus from the bottom of the well
t
to the surface is (see Equation 6-13)
˙ w = ˙ w + ˙ w + ˙ w
t g f s
The Fanning friction factor f given in the above equation is determined by the
standard fluid mechanics empirical expressions relating the friction factor to the
Reynolds number, diameter (or hydraulic diameter), and absolute pipe roughness. In
general, the values for Reynolds number, diameter, and absolute pipe roughness are
known. The classic expression for the Reynolds number is
D
( D h − ) V
p
N = (6-89)
ν
R
There are three flow conditions that can exist in the annulus. These are laminar,
transitional, and turbulent flow conditions.
The empirical expression for the Fanning friction factor for laminar flow
conditions is