Page 258 - Air and Gas Drilling Manual

Chapter 6: Direct Circulation Models 6-3


+
dP = γ
h (
1

mix
gD −
2

2 fV 2 D p)     dh (6-1)
where P is fluid pressure (lb/ft , abs),
h is the reference depth (ft),
H is the total depth (ft)
γ mix is the specific weight of the mixture of air (or other gas) , incompressible
3
fluid, and the rock cuttings (lb/ft ),
f is the Fanning friction factor,
V is the average velocity in the annulus (ft/sec),
D h is the inside diameter of the borehole (ft),
D p is the outside diameter of the drill pipe (ft),
2
g is the acceleration of gravity (32.2 ft/sec ).

Figure 6-1: Schematic of direct circulation. P in is the injection pressure into the top of
the drill string, P bdpi is pressure at bottom of drill pipe inside the drill string, P bdci is
pressure at bottom of drill collars inside the drill string, P ai is pressure above drill bit
inside the drill string, P bdca is pressure at bottom of drill collars in the annulus, P bh is
bottomhole pressure in the annulus, P bdpa is pressure at bottom of drill pipe in the
annulus, P bca is pressure at the bottom of casing in the annulus, and P e is pressure at the
top of the annulus.
The first term on the right side of Equation 6-1 represents the incremental
pressure change due to the hydrostatic weight of the column of fluid (with entrained
rock cuttings) in the annulus. The second term on the right side of Equation 6-1
represents the incremental increase pressure change due to the friction loss of the
flowing fluid mixture.