Natural Gas Technology - Measurement of Resistance to Flow of Fluids in Natural Gas Wells

Before this paper was presented, the terms "f" and "v1/f in flow equations had been called "friction coefficient" and "friction factor," respectively. However, many authors have used the names for the terms interchangeably, with the result that considerable confusion has existed in the literature on flow of fluids. In an effort to establish a clear and concise terminology for these terms, the authors have designated f as "resistance coefficient" and dm as "transmission factor." Transmission factors for the flow strings of gas wells were determined by tests on wells in six fields of Oklahoma, Texas, and Louisiana. Data were collected on 14 gas wells while gas was flowing through 1 1/4, 2, 21/2, and 3-in. tubing and 51/2 and 7-in. casing. The transmission factors developed from these data were found to follow the resistance equation published by Nikuradse1 for turbulent flow in "rough" pipes with an average absolute roughness of 0.000,65 in. This average absolute roughness is believed to be representative generally of the flow strings of gas wells with the exception of those that have been exposed to corrosion or other conditions causing undue roughness. Also, use of an absolute roughness of 0.000,65 in. probably will result in transmission factors that are more representative of gas-well conditions than those in common use today, provided that the transmission factors are calculated by the methods outlined in this report. The authors believe that use of these transmission factors will permit calculation of more accurate subsurface pressures in gas wells than those in use today. Engineers use transmission factors in flow equations to compute subsurface pressures in flowing gas wells from measured wellhead pressures. These subsurface pressures are necessary for determining the productivity of gas wells from "back-pressure" tests. The methods of calculating pressures in flowing gas wells, as outlined by Rawlins and Schellhardt2 in Bureau of Mines Monograph 7, are based on the transmission factors in the well-known Weymouth formula" Natural gas engineers have realized that errors introduced by using transmission factors as given by the Weymouth formula are relatively unimportant in testing low-capacity gas wells; but they also know that such factors are important considerations in testing large-capacity wells. Accordingly, the research described in this report was undertaken to fulfill the need for more accurate means of calculating subsurface pressures in gas wells. This report is part of the Bureau's study of the flow of natural gas through pipe and commercial pipelines. Several of the conclusions regarding flow in the flow strings of gas wells were influenced by the results of the study of flow in horizontal pipelines. These instances are mentioned in the text of this report. METHODS OF COMPUTING TRANSMISSION FACTORS Methods and procedures for computing transmission factors for turbulent flow in circular pipes from test data taken on gas wells have been derived and explained in detail in a paper by Smith4. As these methods were used to calculate the transmission factors presented in this report, a summary is included. Starting with