Page 299 - Air and Gas Drilling Manual

7-8 Air and Gas Drilling Manual

P  

T
g
av
Q =
Q


(7-21)
 
g
P  

T 
g
The three-phase flow of gas, incompressible fluid, and rock cuttings up the
inside of the drill string can be described by a mixed specific weight term which is a
function of its position inside the drill string. This mixed specific weight, γ mix, is
w ˙
γ = t (7-22)
 P g   T av 
mix
    Q + Q m
g
 P   T g 
In the derivation of Equation 7-22 the volume of the solids (the rock cuttings) is
assumed to be small and negligible relative to the volumes of the gas and the
incompressible fluid in the mixture.
The velocity of this mixture changes as a function of its position inside the drill
string. The velocity, V, of the three-phase flow inside the drill string is
Q + Q
V = m (7-23)
π
D i 2
4
where D i is the inside diameter of the drill string (ft),
Substituting Equation 7-21 into Equation 7-23 yields
 P   T av 
g
 
  P   T   Q + Q m
g
V = g (7-24)
π
D i 2
4
Substituting Equations 7-22 and 7-24 into Equation 7-1 yields
 
 
 w ˙ 
dP =  t 
  P   T av  
g
     Q + Q m 
g
   P   T   
g