The use of an efficiency factor to make pipe equations match physical reality is not a new concept - it's been around as long as there have been flow equations. It fell into some disrepute and was deemed unnecessary by some when sound theoretical equations for pipe flow began to replace the older empirical ones. Efficiency, however, is of more use that just fixing bad equations since it also is useful in adjusting specific pipes for problems and considering operational issues. A previous paper, A Tutorial on Pipe Flow Equations, presented at the 2001 PSIG meeting as a replacement paper in the wake of 9/11 but not published with the proceedings since it was too late, ended with the thought that pipeline efficiency was a valuable tool in calibrating gas models, more so than that of pipe roughness. Since then, I have received much verbal support from people within the industry but continue to hear comments that pipe roughness should be used as "the" tuning parameter. This paper builds on the original paper to explore the concept of pipe efficiency, its effect on flow equations, and its value as a calibration tool. Along the way some concepts regarding system design in the face of load variance within a day are also presented. Also some considerations with using the Panhandle equations that have been lost over time are mentioned.
The flow of natural gas through pipes is well known in the literature and will not be re-derived here. For more details, please refer to the earlier papers referenced in the bibliography, particularly the excellent detailed derivation in the one by Susan Gibson from the 1981 PSIG conference.
As stated above, all of the "practical" equations make some simplifying assumption about the variance of friction factor with flow ranging from constant values to explicit exponential functions. This gives rise to the fact that these equations are only valid within some range of conditions and must be corrected as conditions change. For example, my experience with the Weymouth equation has shown that at typical diameters around 20" and appropriate flows, efficiencies of 106% are often required to make the equation match observed data in a truly steady-state case. Since the forms based on the Moody Diagram surmount these problems, the remainder of this discussion, except for the following comments regarding the Panhandle equations, will deal only with the Colebrook-White equation, although its conclusions are equally valid for the GERG equation and its explicit forms. Therefore, this component of efficiency, e1, will be considered to be 100% or 1.00 since the equation should not need correcting. For those still using the Panhandle equations, either "A", "B", or some variant thereof, there is a further consideration that seems to have been lost in antiquity.
