Page 312 - Air and Gas Drilling Manual

dP
P ai
(7-67)
()
i
where ∫ P at BP = ∫ 0 H dh Chapter 7: Reverse Circulation Models 7-21
 
 
 w ˙ 
BP() =  t 
i
  P   T av  
g
     Q + Q m 
g
   P   T   
g
   2 
    P g   T av  
    P     Q g + Q m  
  T

1 + f  π g   

 2gD i  D 2  
  4 i  
      

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, 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
DV
i
N = (7-68)
R ν
There are three flow conditions that can exist inside the drill string. These are
laminar, transitional, and turbulent flow conditions.
The empirical expression for the Fanning friction factor for laminar flow
conditions is
f = 64 (7-69)
N
R
This equation can be solved directly once the Reynolds number is known. In
general, Equation 7-69 is valid for values for Reynolds numbers from 0 to 2,000.
The empirical expression for the Fanning friction factor for transitional flow
conditions is known as the Colebrook equation. the Fanning friction factor cannot
be determined directly and must be solved by trial and error. This empirical
expression is