Page 294 - Air and Gas Drilling Manual


fv 
2
+
dP = γ

(7-1)
mix 1
i  
 
gD
2
2
where P is fluid pressure (lb/ft , abs), dh Chapter 7: Reverse Circulation Models 7-3
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 i is the inside diameter of the drill string (ft),
2
g is the acceleration of gravity (32.2 ft/sec ).

Figure 7-1: Schematic of reverse circulation. P in is injection pressure into the top of the
annulus, P bca is pressure at bottom of casing in the annulus, P bdpa is pressure at bottom of
drill pipe in the annulus, P bdca is pressure at bottom of drill collars in the annulus, P bh is
bottomhole pressure in the annulus, P ai is pressure above drill bit inside the drill string,
P bdci is pressure at bottom of drill collars inside the drill string, P bdpi is pressure at bottom
of drill pipe inside the drill string, and P e is pressure at the exit at the top of the inside of
the drill string.

The first term on the right side of Equation 7-1 represents the incremental
pressure change due to the hydrostatic weight of the column of fluids (with entrained
rock cuttings) inside the drill string. The second term on the right side of Equation
7-1 represents the incremental pressure change due to the friction resistance to the
flowing fluids in the drill string.