A unified correlation for predicting slug liquid holdup in viscous two-phase flow for pipe inclination from horizontal to vertical

Abstract

This study presents new measured slug liquid holdup data for liquid viscosity ranging from 200 to 800 mPa s. The experiments were conducted using two different large pipe diameters (0.08 and 0.1 m) and pipe inclination angles of 0°, 30°, 60° and 90° from horizontal. To our best knowledge, most of the existing experimental data were limited to either vertical or horizontal flow and mostly performed using small pipe diameters. Based on the measured data, a new unified empirical correlation is developed to predict slug liquid holdup for viscous two-phase flow in horizontal, vertical and inclined pipes. The proposed correlation is simple and fully consistent with the trends of published experimental data. This study also investigates in details the performance of the existing liquid holdup correlations using different flow conditions. The investigation reveals several discrepancies associated with these correlations. Based on statistical analysis, the proposed correlation performs best as compared to the existing correlations using both the present measured data and data from three independent sources. Keywords Slug liquid holdup • Two-phase flow • High liquid viscosity • Inclined flow List of symbols A, C Constants d Pipe diameter (m) g Acceleration gravity (m/s 2) N Dimensionless number H Slug liquid holdup N f Inverse viscosity number N Re Reynolds number T Temperature (°C) V Velocity (m/s) Greek letters ɛ Residual error ɸ Correlation independent parameter σ Surface tension (N/m) µ Viscosity (kg/m s) (Pa s) ρ Density (kg/m 3) Δρ Density difference (kg/m 3) θ Inclination angle from horizontal (°)

Investigating the Characteristics of Two-Phase Flow Using Electrical Capacitance Tomography (ECT) for Three Pipe Orientations

“…Bestion (1990) proposed a correlation to predict high liqui slug flow patterns [38,39]. Similar correlations to predict high liquid holdup als Kore et al (2011) with ɛ(L) higher than 0.8 and Al-Safran et al, (2015) with ɛ(L) high and high viscosity oil for horizontal pipe [40][41][42]. Some of the cited correlat combined effect of the viscous and the inertial forces [33,35,36,[40][41][42], whil proposed by Spedding and Chen (1984), Hamersma and Hart (1987), Bestion (1 have no viscosity as a variable.…”

“…The proposed model is validated by two independent measuring techniques which is rarely available in the literature. It also was validated (L) higher than 0.6 using air and high viscosity oil for horizontal pipe [40][41][42]. Some of the cited correlations depend on the combined effect of the viscous and the inertial forces [33,35,36,[40][41][42], while other correlations proposed by Spedding and Chen (1984), Hamersma and Hart (1987), Bestion (1990) and Ishii (1977) have no viscosity as a variable.…”

“…It also was validated (L) higher than 0.6 using air and high viscosity oil for horizontal pipe [40][41][42]. Some of the cited correlations depend on the combined effect of the viscous and the inertial forces [33,35,36,[40][41][42], while other correlations proposed by Spedding and Chen (1984), Hamersma and Hart (1987), Bestion (1990) and Ishii (1977) have no viscosity as a variable. Their proposed correlations are influenced by the gas-liquid velocity ratios and the inertial forces [32][33][34][37][38][39].…”

“…The between ɛ(L) values higher than 0.2 (for air/heavy oil for horizontal , air/water, and air/oil for horizontal and upward inclinations), 0) proposed a correlation to predict high liquid holdup values for r correlations to predict high liquid holdup also were proposed by han 0.8 and Al-Safran et al, (2015) with ɛ(L) higher than 0.6 using air ontal pipe [40][41][42]. Some of the cited correlations depend on the and the inertial forces [33,35,36,[40][41][42], while other correlations (1984), Hamersma and Hart (1987), Bestion (1990) and Ishii (1977) heir proposed correlations are influenced by the gas-liquid velocity 34,[37][38][39]. similarity between different experimental setups, dimensionless ber (Re) is usually used; also it is used to scale between multiphase es operating on a gas-liquid multiphase flow system are the inertial on between these two forces are inherent in a Reynold number (Re) odel is proposed which is based on the relation between the liquid the two phases (i.e., the liquid and the gas).…”

“…The holdup in a multiphase system (i.e., gas-liquid, liquid-liquid or gas-solid) is affected by many factors including gas/liquid/solid superficial velocities, liquid/gas/solid densities and viscosities, the conduit dimension and inclinations [25,[32][33][34][35][36][37][38][39][40][41][42][43][50][51][52][53]. Concerning a gas-liquid multiphase flow in a pipe, the holdup is a function of the following factors [43]:…”