Page 281 - Air and Gas Drilling Manual

6-26 Air and Gas Drilling Manual
In general, Equation 6-87 is valid for values of Reynolds numbers from 2,000 to
4,000.
The empirical expression for the Fanning friction factor for turbulent flow
conditions is known as the von Karman equation. This empirical expression is
  2
 
 1 
f =   (6-86)
  D  
i

+ 1 14

 2 log. 
e 

 
In general, Equation 6-86 is valid for values of Reynolds numbers greater than 4,000.
For follow-on calculations for flow in the drill string the absolute roughness for
commercial pipe, e p = 0.00015 ft, will be used for the inside surfaces of the drill
pipe and drill collars.
Equation 6-82 together with Equations 6-83 through 6-86 can be used in
sequential trial and error integration steps starting at the bottom of the inside of the
drill string (with the known pressure above the drill bit inside the drill string) and
continuing for each subsequent change in drill string cross-sectional area until the
injection pressure is determined.
6.5 Stable Foam Drilling Model
Stable foam drilling is a special case of the general derivation given in
Subsection 6.2.1. In stable foam drilling operations, the mixture of gas (usually air
or nitrogen) and water (with a surfactant) are specified (foam quality) at the top and,
therefore, throughout the annulus. Foam quality, Γ, is defined as
Q g
Γ = (6-87)
Q g + Q f
3
where Q g is the volumetric flow rate of gas (ft /sec),
3
Q f is the volumetric flow rate of the incompressible fluid (ft /sec).
The control of the foam quality at the top allows the foam quality at the bottom
of the annulus to be calculated. This control is accomplished by placing a valve on
the flow line from the annulus. Upstream of the valve is a pressure gauge and by
maintaining a specified back pressure upstream of the valve the foam quality at this
position can be determined. Knowing the foam quality at this position (and the
other flow characteristics of the circulating system), the foam quality at any position
in the annulus (particularly at the bottom of the annulus) can be determined. The
foam quality at the bottom of the annulus must be maintained at approximately 0.60
or greater [9]. If the foam quality at this position drops much below this level, the
foam will collapse and the flow will be in three separate phases. To maintain the
bottomhole foam quality in the annulus at a value of approximately 0.60 or greater,
the foam quality upstream of the back pressure valve is usually in the range 0.90 to
0.98.