New developments in surface roughness measurements, characterization, and modeling fluid flow in pipe

Abstract The purpose of this paper is to present petroleum and chemical engineers with a simple means of measuring or estimating the absolute surface roughness, ϵ, and relative roughness, ϵ/D, for internally coated pipes. Our research thrust is to develop new relative roughness charts along with corresponding mathematical equations for internally coated pipes. An integral part of the frictional pressure drop due to fluid flow in pipes involves the determination of absolute surface roughness and relative roughness. An accurate determination of the pressure drop due to fluid flow in oil and gas wells is required for optimizing oil and gas production design calculations. Some of these calculations include developing tubing programs to maximize well deliverability, wellbore flow performance, sizing surface flow lines, and designing artificial lift installations. Previous multiphase fluid flow laboratory and field tests, during the past 50 years, provided correlations for calculating pressure gradients in tubulars [Chem. Eng. Prog. 45(1) (1949) 39; Hetsroni, G., 1982. Handbook of Multiphase Systems, Hemisphere/McGraw Hill, 1174 pp.; Brown, K.E., 1984. The Technology of Artificial Methods, vol. 4, Penn Well Publishing, Tulsa, OK, 447 pp.; Tengesdal, J.O., 1998. Predictions of Flow Patterns, Pressure Drop, and Liquid Holdup in Vertical Upward Two-Phase Flow. MSc Thesis, The University of Tulsa, Tulsa, OK; Farshad, F., Garber, J.D., Polaki, V., 2000. Comprehensive model for predicting corrosion rates in gas wells containing CO2. Soc. Pet. Eng. Prod. Facil. 15(3), 183–190]. All the multiphase fluid flow correlations, used in production operations to calculate these pressure gradients and flow regimes, stem from the general energy balance equation and involves the determination of friction pressure losses. Still today, these friction losses only are being evaluated by practicing engineers using the Darcy–Weisbach equation, which involves the Moody friction factor, f [Szilas, A.P., 1975. Production and Transport of Oil and Gas. Elsevier Sci. Publ., Amsterdam, p. 630; Economides, M.J., Hill, D.A., Ehlig-Economides, C., 1994. Petroleum Production Systems, Prentice Hall, Englewood Cliffs, NJ, 611 pp.]. Moody [Trans. AME 66 (1944) 671] prepared a relative roughness chart for a number of common piping materials. This initial relative roughness correlation was based on experiments on pipes artificially roughened with sand grains. At that time, internally coated pipes were not invented. Hence, Moody did not provide the relative roughness for internally coated pipes. In addition, Moody did not perform a regression analysis of the data to generate functional forms of equations by relating roughness, ϵ/D, as a function of internal pipe diameter, D. Currently, internally coated pipes are being utilized worldwide in oil field production systems. Consequently, new absolute surface roughness and relative roughness values of internally coated pipes are needed to properly model the hydrodynamics [Brown, K.E., 1984. The Technology of Artificial Methods, vol. 4, Penn Well Publishing, Tulsa, OK, 447 pp.]. The new relative roughness plots developed for internally coated pipes are presented and show that the correlation fits between the commercial steel and drawn tubing in the Moody chart.