A study of test data for a number of Alberta gas wells has revealed that flow during such tests is seldom in the "fully developed" turbulence region. Because computer programs used to calculate pressure profiles usually assume "fully developed" turbulent flow, they tend to underestimate the friction factor, and as a. result the pressure drop due to friction, in such wells. In order to avoid such bias, a subroutine, which generates the Moody friction factor chart, is present and recommended for use in computer calculation.
THE CALCULATION of bottom-hole pressures or pressure profiles in flowing gas wells may be effected by various methods.(1–3) Despite the differences between these methods, they have one thing in common they all require the estimation or calculation of a friction factor.
(Equation in full paper.)
Although these approximate methods are handy and appropriate to desk calculation, the modern practice of calculating pressure profiles by means of high-speed computers has made such approximations unnecessary and in some instances inappropriate. For example, one may set up a simple subroutine for calculating friction factors, using the expressions employed by Moody, as is indicated in Figure 1. Such a program will permit the use of absolute roughness values other than 0＿0006 in., and will do away with approximation error.
Because the Colebrook equation approaches the von Karman expression asymptotically, the point at which one changes from the former to the latter depends on the percentage error one is willing to accept at that point. Thus, if one is willing to accept a 1% error at the change-over point one should select the point Re=1600 d/E. On the other hand, one may use Re=3200 d/E for a 0.5% maximum error, as suggested by Moody, or Re = 16,000 d/E when the maximum permissible difference is 0.1 %＿ If, however, one is willing to incur the added cost of iteration in the region where f is essentially insensitive to further changes in Re, he may use the Colebrook equation for all values of Re greater than 4000. This is, in fact, the method that was employed by Aziz, Govier and Fogarasi(8).
The subroutine shown in Figure 1 was tested against the Cullender – Binckley and Cullender-Smith methods at 12 points, as shown in Tables 1 and 2. This comparison showed that:
friction factor remains reasonably constant over the length of the well, thereby verifying the common assumption that such is the case;
flow in gas wells, of the type found in Alberta, is not usually in the fully developed turbulent region;
the Cullender-Binckley method provides a reasonable estimate of friction factor in the transition region, whereas the Cullender-Smith method consistently underestimates the friction factor when turbulence is not fully developed.
In addition, the comparison showed that the cost of application of the subroutine exceeds that of the Cullender-Smith method by less than 2 cents per hundred factors calculated.
This subroutine was also compared to that proposed by Aziz-Govier-Fogarasi.