Further On the Calculation of Friction Factors For Use In Flowing Gas Wells

Abstract

Abstract A comparison of two computer subroutines to calculate friction factors from the Moody(2) chart has been made. The comparison shows that, contrary to the claim of Dranchuk and Abou-Kassem(1), their method and that of Aziz et al.(5) give identical results in the partially-rough-wall and the fully-rough-wall turbulence regions. The transition from the former to the latter is predicted to occur at slightly different Reynolds numbers in the two methods because of the choice by Dranchuk and Abou-Kassem of an arbitrary transition criterion. Both routines are suitable for computer calculation of friction factors, but the Aziz et al. method is more efficient, requiring fewer iterations. IN A RECENT TECHNICAL NOTE, Dranchuk and Abou Kassem(l) recommend the use of the Moody chart(2) instead of approximate relationships to determine friction factors in pressure-drop calculations for flowing gas wells. Without doubt, fundamental equations with a properly chosen friction factor based on the correct reynolds number and the best estimate of the relative roughness will yield more accurate pressure-drop predictions than equations incorporating approximations for the friction factor(3). (Equation in full paper) Dranchuk and Abou-Kassem compare Darcy-Weisbach friction factors calculated by their own and the Aziz et al. method and arrive at the following conclusions: The Aziz-Govier-Fogarasi method:generates Fanning friction factors;yields values which are higher than Colebrook at low values of Re and lower than Colebrook at high values of Re;yields values which are higher than Moody at low values of Re and lower than Moody at high values of Re when flow is in the transition zone) but higher than Moody at low values of Re and lower than Moody for high values of Re when flow is fully turbulent;cannot generate values for smooth pipe." These conclusions seem unwarranted. Table 1 shows a comparison of Darcy-Weisbach friction factors calculated by the two methods for a wide range of relative roughnesses and Reynolds numbers. The comparison shows that:the friction factors are exactly the same in the PRW and FRW regions, as they should be, because both routines use the same equations;a slight difference (half a per cent or less) at the transition from PRW to FRW turbulence due to the difference in the transition criterion chosen by Dranchuk and Abou-Kassem and the assymptotic approach used in the Aziz et al. routine;the Aziz et al. routine is more efficient, requiring fewer iterations. (Table in full paper) Keeping in mind that Moody indicated that his chart would predict friction factors with no better than 10 per cent accuracy, the small differences are insignificant. The friction factors, for practical purposes, are the same. Finally, the Aziz et al. method was not intended for the calculation of friction factors in smooth pipes. It was designed only to deal with the practical problem of estimating pressure drops in actual gas wells, which may always be expected