New assessment of friction factor correlations for power law fluids in turbulent pipe flow: A statistical approach

Abstract

A new statistical approach to assessing the friction factor correlations was presented. Fourteen correlations, published from 1959 to 2003, were collected to calculate friction factors for power law fluids in turbulent pipe flow. A series of Fanning friction factors, f, were computed from these equations. Then the relations between the calculated values of f and Re_MR (Metzner-Reed Reynolds number) were analyzed, when the rheological behavior index, n, was given. To verify the foregoing analysis result, in addition, the relations between the calculated values of f and n were analyzed, when Re_MR was given. The f value calculated from each equation was compared with each mean value of all the f values from the 14 equations, when each combination (n, Re_MR) (n ranging from 0.4 to 1.4 and Re_MR from 4 000 to 100 000) was set. The comparison results were surveyed in the relative deviation table of the calculated f values. It shows that the overall mean relative deviation (OMRD) of the Dodge-Metzner correlation is the minimum, 1.5%. Therefore, the Dodge-Metzner correlation is recommended for predicting the friction factors for the turbulent pipe flow of power law fluids.

Keywords

friction factor / turbulence / power law fluids / hydraulic analysis / fluid mechanics

References

[1] DodgeD. W., MetznerA. B.. Turbulent flow of non-Newtonian systems[J]. AICHE Journal, 1959, 5(2): 189-204

[2] HEYWOOD N I. Pipeline design for non-newtonian fluids[J]. Transactions of the Institute of Chemical Engineering Symposium, 1984(6): 33–45.

[3] HanksRichard W., RicksBrad L.. Transitional and Turbulent Pipeflow of Pseudoplastic Fluids. Journal of Hydronautics, 1975, 9(1): 39-44

[4] DarbyR.. Hydrodynamics of slurries and suspensions. Encyclopedia of Fluid Mechanics, Vol.5 (Slurry Flow Technology) [M], 1986, Houston, Gulf Pub Co

[5] DarbyR.. Laminar and turbulent pipe flows of non-Newtonian fluids. Encyclopedia of Fluid Mechanics, Vol.7 (Rheology and Non-Newtonian Flows)[M], 1988, Houston, Gulf Pub Co

[6] SzilasA. P.. Flow mechanics and production, Part A In: Production and Transport of Oil and Gas. Developments in Petroleum Science[M], 19852nd edAmsterdam, Elsevier Science Pub Co

[7] BobokE.. Fluid Mechanics for Petroleum Engineers. Developments in Petroleum Science[M], 1993, Amsterdam, Elsevier Science Pub Co

[8] KAWASE Y, SHENOY A V, WAKABAYASHI K. Friction and heat and mass transfer for turbulent pseudoplastic non-Newtonian fluids flowing in rough pipes[J]. Canadian Journal of Chemical Engineering, 1994(72): 798–804.

[9] DesoukyS. M., El-EmamN. A.. A generalized pipeline design correlation for pseudoplastic fluids[J]. Journal of Canadian Petroleum Technology, 1990, 29(5): 48-54

[10] HemeidaA. M.. Friction factor for yieldless fluids in turbulent pipe flow[J]. Journal of Canadian Petroleum Technology, 1993, 32(1): 32-35

[11] El-EmamN., KamelA. H., El-ShafeiM., et al. . New equation calculates friction factor for turbulent flow of non-Newtonian fluids[J]. Oil & Gas Journal, 2003, 101(36): 74-83

[12] GovierG. W., AzizK.The Flow of Complex Mixtures in Pipes[M], 1972, New York, Van Nostrand Reinhood Co

[13] GongJ., YanD. F.. Comparison of the friction factor methods for non-Newtonian fluids in pipe flow[J]. Petroleum Planning & Engineering, 1994, 5(3): 28-32