Page 158 - Air and gas Drilling Field Guide 3rd Edition

6.2 General Derivation 149

(6-8)
P g ¼ P pl
T g ¼ T pl ; (6-9)
2
where p pl is the pipeline pressure (psia, N/cm abs), P pl is the pipeline pressure
2
2
(lb/ft abs, N/m abs), t pl is the pipeline temperature ( F, C), and T pl is the abso-

lute pipeline temperature ( R, K).

Substituting Equations (6-8) and (6-9) into Equation (5-11), the specific weight
of the gas from a pipeline can be obtained. This is
P g S g P pl S g
g ¼ ¼ : (6-10)
g
R e T g R e T pl
In this equation, S g would be the specific gravity of the pipeline natural gas (e.g.,
usually between 0.65 and 0.85).
Substituting the result from Equation (6-10) into Equation (6-7) gives the weight
rate of flow of gas from a pipeline, where Q g is thevolumetricflowrateofnatural
gas from thepipeline at pressurep pl and temperature t pl . Note that the volumetric flow
3
rate in a pipeline is usually given by flow meters in either scfm or standard m /sec
regardless of surface elevation location. This value must be converted to obtain the
actual volumetric flow rate at p pl and t pl (see Appendix A). As discussed in Chapter
5, care must be taken to determine which set of standard conditions are being used
3
to define the “scfm or standard m /sec.” Chapter 5 gives a summary of the most
common standard condition specifications used throughout the industrialized world.

6.2.2 Three-Phase Flow in the Annulus
This general solution for three-phase flow is valid for aerated (gasified) drilling
fluids where the three phases in the annulus are gas, incompressible fluid, and
solids (cuttings).
The weight rate of flow of incompressible drilling fluid (usually drilling mud),
_ w m , into the well is
Q m ; (6-11)
m
_ w m ¼ g
where _ w m is the weight rate of flow of drilling mud (lb/sec, N/sec), g m is the spe-
3 3
cific weight of the drilling mud (lb/ft , N/m ), and Q m is the volumetric flow rate
3 3
of drilling mud (ft /sec, m /sec).
The weight rates of flow _ w g and _ w m entering the well through the top of the
drill string and flow to the bottom of the string and exit into the annulus through
the openings in the drill bit (open orifices or the bit nozzles). After passing
through the drill bit, the fluids entrain the rock cuttings generated by the drill
bit as the bit is advanced. The entrained weight rate of flow of the solids, _ w s ; is
p 2
_ w s ¼ D g ð2:7Þ k; (6-12)
w
h
4
where _ w s is the weight rate of flow of solid rock cuttings (lb/sec, N/sec), D h
is the diameter of the drilled hole (i.e., the bit diameter) (ft, m), g w is the