Direct Calculation of Unsteady-State Weymouth Equations for Gas Volumetric Flow Rate with Different Friction Factors in Horizontal and Inclined Pipes

Abayomi O. Olatunde, Tunde A. Adeosun, Mohammed A. Usman, Olabisi M. Odunlami, Moses A. Olowofoyeku, Testy E. Ekakitie, Atanda M. Mohammed

Department of Chemical Engineering, Lagos State Polytechnic, Lagos, Nigeria.
Department of Chemical Engineering, University of Lagos, Lagos, Nigeria.
Department of Civil Engineering, Yaba College of Technology, Yaba, Nigeria.
Department of Mathematics, Yaba College of Technology, Yaba, Nigeria.

DOI: 10.4236/eng.2012.44027                

Abstract

Direct calculations of unsteady-state Weymouth equations for gas volumetric flow rate occur more frequently in the design and operation analysis of natural gas systems. Most of the existing gas pipelines design procedures are based on a particular friction factor and steady-state flow analysis. This paper examined the behavior of different friction factors and the need to develop model analysis capable of calculating unsteady-state gas flow rate in horizontal and inclined pipes. The results show different variation in flow rate with Panhandle A and Panhandle B attaining stability in accurate time with initial unsteadiness at the instance of flow. Chen and Jain friction factors have opposition to flow with high flow rate: The prediction also reveals that Colebrook-White degenerated to Nikuradse friction factor at high Reynolds number. The horizontal and inclined flow equations are considerably enhanced on the usage of different friction factors with the aid of Matlab to handle these calculations.

Keywords

Unsteady-State; Flow Rate; Friction Factor; Stability; Variations; Unsteadiness

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	T. R. Weymouth, “Problems in Natural Gas Engineering,” Transactions of the ASME, Vol. 34, 1912, p. 185.
[2]	J. A. Ferguson, “Gas Flow in Long Pipelines,” Chemical Engineer-ing, Vol. 56, No. 11, 2002, pp. 112-135.
[3]	M. A. Stoner, “Steady-State Analysis of Gas Production, Transmission and Distribution Systems,” Fall Meeting of the Society of Petroleum Engineers of AIME, Denver, 28 September-1 October 1969, 8 Pages.
[4]	D. W. Schroeder, “A Tutorial on Pipe Flow Equa-tions,” 33rd Annual Meeting Pipeline Simulation Interest Group (PSIG), Salt Lake City, 17-19 October 2001.
[5]	J. Zhou and M. A. Adewumi, “Gas Pipeline Network Analysis Using an Analytic Steady-State Flow Equation,” Eastern Re-gional Meeting, Pittsburgh, 9-11 November 1998, 13 Pages.
[6]	L. Ouyang and K. Aziz, “Steady-State Gas Flow in Pipes,” Journal of Petroleum Science and Engineering, Vol. 14, No. 3-4, 1996, pp. 137-158. doi:10.1016/0920-4105(95)00042-9.
[7]	R. N. Maddox and P. Zhou, “Use of Steady-State Equations for Transient Flow Cal-culations,” 15th Annual Meeting Pipeline Simulation Interest Group (PSIG), Detroit, 27-28 October 1983.
[8]	G. A. Rhoads, “Which Flow Equation—Does It Matter?” 15th An-nual Meeting Pipeline Simulation Interest Group (PSIG), De-troit, 27-28 October 1983.
[9]	T. A. Adeosun, A. O. Olatunde and A. Okwananke, “Development of Unsteady-State Equa-tions for the Flow of Gas through Pipelines,” Journal of Ad-vances and Applications in Fluid Mechanics, Vol. 7, No. 1, 2010, pp. 45-60.
[10]	S. Tian and M. A. Adewumi, “Develop-ment of Analytical Design Equation for Gas Pipelines,” SPE Production & Facilities, Vol. 9, No. 2, 1994, pp. 100-106.
[11]	T. A. Adeosun, A. O. Olatunde, J. O. Adero-hunmu and T. O. Ogunjare, “Development of Unsteady-State Weymouth Equations for Gas Volumetric Flow Rate in Hori-zontal and Inclined Pipes,” Journal of Natural Gas Science and Engineering, Vol. 1, No. 1, 2009, pp. 113-117. doi:10.1016/j.jngse.2009.09.001
[12]	D. L. Katz and R. L. Lee, “Natural Gas Engineering Production and Storage,” McGraw-Hill Publishing Co., New York, 1990.
[13]	C. U. Ikoku, “Natural Gas Production Engineering," John Wiley and Sons Publishing Co, New York, 1984.
[14]	P. U. Ohirihian, “Direct Calculation of the Gas Volumetric Flow Rate in Hori-zontal and Inclined Pipes,” Paper SPE 37394, 2002.