Gas–Liquid Transport in Ducts
2.2.8 Application of the Angle-Dependent Flow-Pattern Map
The flow-pattern map in its most generalized form is incorporated in computer codes for the design of two-phase gas-pipelines and well tubing. With such a code, one can generate a map in which, for a fixed
101
10−3 10−2 10−1 100
Densimetric gas Froude number (dimensionless)
= 0°
10−1 100 101
10−2 Densimetric liquid Froude number (dimensionless)
Dispersed
FIGURE 2.19 Flow-pattern map for horizontal flow:θ 0°.
10−1 100 101
10−2 Densimetric liquid Froude number (dimensionless)
Densimetric gas Froude number (dimensionless)
FIGURE 2.20 Flow-pattern map for upward flow:θ0.5°.
inclination θ, the occurrence of flow patterns is given in terms of the densimetric Froude numbers for liq-uid and gas, FL and FG, respectively. It should be realized that, strictly speaking, eight groups are involved (for instance: FL, FG, ρG/ρL, ReSL, ReSG, Ku, k/D, and θ). Therefore, using only three groups is not a sound basis for a more general flow-pattern map. Generally speaking, maps obtained in this way should be applied only to those cases for which the detailed computer runs have been carried out. However, for the more important transitions (stratified to nonstratified and annular to nonannular), for liquids that are not too viscous (ReSL0), the pipe inclination and the Froude numbers appear to be among the more important groups in the current flow-pattern map if the Kelvin–Helmholtz instability approach by Dukler and Taitel is chosen. If the more general approach to this instability is selected, the density ratio ρG/ρL comes into the picture as an important group as well.
Taking as an example a 4-in. pipe with gas–oil flowing at 150 bar, Figures 2.19–2.26 give an overview of the occurrence of two-phase flow patterns at various pipe inclinations from 90 to 90°. The most
Densimetric gas Froude number (dimensionless) 10−1
100 101
10−2
101
10−3 10−2 10−1 100
Densimetric liquid Froude number (dimensionless)
Intermittent Annular
entrained Dispersed
bubble
= +5° Stratified wavy
entrained +
+
+
+ + + + + +
FIGURE 2.21 Flow-pattern map for upward flow:θ5°.
= + 50°
Densimetric liquid Froude number (dimensionless)
101
10−3 10−2 10−1 100
Densimetric gas Froude number (dimensionless) 10−1
100 101
10−2
Annular entrained Intermittent
Dispersed bubble +
+
+
+ + + + +
+
FIGURE 2.22 Flow-pattern map for upward flow:θ 50°.
significant changes with inclination can be seen for stratified flow. The stratified regime largely disappears at even small upward inclinations, while the regime becomes more extended for downward flow. At ver-tical downward flow, however, no stratified flow exists.
= +90°
Densimetric liquid Froude number (dimensionless)
101
10−3 10−2 10−1 100
Densimetric gas Froude number (dimensionless) 10−1
100 101
10−2
Annular entrained Intermittent
Dispersed bubble +
+
+
+ + + + + +
FIGURE 2.23 Flow-pattern map for upward flow:θ90°.
Densimetric gas Froude number (dimensionless)
= −5°
101
10−3 10−2 10−1 100
10−1 100 101
10−2 Densimetric liquid Froude number (dimensionless)
Intermittent
Intermittent annular
Stratified wavy entrained Stratified
wavy Dispersed
bubble
+ + + +
++ + + +
FIGURE 2.24 Flow-pattern map for downward flow:θ5°.
Nomenclature
A Area
c Phase velocity of dynamic wave
C Shedding parameter
Co Distribution parameter
D Pipe diameter
= − 50°
10−1 100 101
10−2
101
10−3 10−2 10−1 100
Densimetric gas Froude number (dimensionless) Densimetric liquid Froude number (dimensionless)
Intermittent
Annular entrained Stratified
wavy entrained Stratified
wavy
Dispersed bubble +
+
+
++ + + + +
FIGURE 2.25 Flow-pattern map for downward flow:θ50°.
Densimetric gas Froude number (dimensionless)
= −90°
Densimetric liquid Froude number (dimensionless)
101
10−3 10−2 10−1 100
10−1 100 101
10−2
Annular entrained
Intermittent
Annular Dispersed bubble +
+
+
+ + + + +
+
FIGURE 2.26 Flow-pattern map for downward flow:θ90°.
E Entrainment fraction
Eo Eötvös number
f Fanning friction factor Fr m Froude number of mixture FL Liquid Froude number g Acceleration due to gravity G Mass flux per unit area
h Height
k Wave vector
Ku Kutateladze number
l Length
M Momentum flux
NL Dimensionless liquid velocity
p Pressure
P Perimeter
Re Reynolds number
us Superficial velocity vs Slug frequency
x Distance
X Lockhart-Martinelli parameter Greek Symbols
α Phase holdup γ Top angle θ Inclination angle λ Volume fraction µ Viscosity ρ Density σ Surface tension τ Shear stress
Φ Two-phase flow multiplier ω Frequency
Subscripts
G Gas
h Homogeneous i Interface L Liquid m Mixture
w Wall
References
Andreussi, P., Private communication, 1988.
Andreussi, P. and Bendiksen, K., An investigation of void fraction in liquid slugs for horizontal and inclined gas /liquid pipe flow, Int. J. Multiphase Flow, 15, 937–946, 1989.
Barnea, D., A unified model for predicting flow pattern transitions for the whole range of pipe inclina-tions, Int. J. Multiphase Flow, 13, 1–12, 1987.
Barnea, D., Shoham, O., and Taitel, Y., Flow pattern transition for down ward inclined two-phase flow:
horizontal to vertical, Chem. Eng. Sci., 37, 735–740, 1982a.
Barnea, D., Shoham, O., and Taitel, Y., Flow pattern transition for vertical downward two-phase flow, Chem. Eng. Sci., 37, 741–746, 1982b.
Barnea, D., Shoham, O., and Taitel, Y., Gas–liquid flow in inclined tubes: flow pattern transitions for upward flow, Chem. Eng. Sci., 40, 131–136, 1985.
Barnea, D. and Taitel, Y., Structural and interfacial stability of multiple solutions for stratified flow, Int. J.
Multiphase Flow, 18, 821–830, 1992.
Cheremisinoff, N.P. and Davis, E.J., Stratified turbulent–turbulent gas/liquid flow, AIChE J., 25, 48–56, 1979.
Chisholm, D., A theoretical basis for the Lockhart–Martinelli correlation for two-phase flow, Int. J. Heat Mass Transfer, 10, 1767–1778, 1967.
Churchill, S.W., Friction-factor equation spans all fluid-flow regimes, Chem. Eng., 7, 91, 1977.
Cohen, L.S. and Hanratty, T.J., Effect of waves at a gas/liquid interface on turbulent air flow, J. Fluid Mech., 31, 467–479, 1968.
Colebrook, C.F., Turbulent flow in pipes with particular reference to the transition region between the smooth and rough pipe laws, J. Inst. Civil Eng., 11, 133, 1939.
Collins, R., de Moraes, F.F., Davidson, J.F., and Harrison, D., The motion of a large gas bubble rising through liquid flowing in a tube, J. Fluid Mech., 89, 497–514, 1978.
Crowley, C.J. and Rathe, P.H., Assessment of mechanistic two-phase analysis methods for gas/condensate pipelines, PSIG Annual Meeting, Toronto, October, 20–21, 1988.
Dukler, A.E. and Hubbard, M.G., Model for gas–liquid flow in horizontal and near-horizontal tubes, Ind.
Eng. Chem. Fundam., 14, 337–347, 1975.
Dukler, A.E. and Taitel, Y., Flow pattern transitions in gas–liquid systems. Measurements and modelling, in Multiphase Science and Technology, Vol. II, G.F. Hewitt, J.M. Delhaye, and N. Zuber, Eds., Hemisphere, Washington, DC, 1986.
Fernandes, R.C., Experimental and Theoretical Studies of Isothermal Upward Gas–Liquid Flows in Vertical Tubes, Ph.D. thesis, University of Houston, 1981.
Ferschneider, G., Lagière, M., Bourgeois, T., and Fitremann, J.M., How to calculate two-phase flow of gas and oil in pipelines, Pipe Line Industry, 63, 33–39, 1985.
Hewitt, G.F. and Lahey, R.T., Proceedings Third International Workshop on Two-Phase Flow Fundamentals, June 15–19, London, UK, 1992.
Heywood, N.I. and Richardson, J.F., Slug flow of air/water mixtures in a horizontal pipe: determination of liquid hold-up by γ-ray absorption, Chem. Eng. Sci., 34, 17–30, 1979.
Hinze, J.O., Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes, AIChE J., 1, 289–295, 1955.
Hoogendoorn, C.J., Gas/liquid flow in horizontal pipes, Chem. Eng. Sci., 9, 205–216, 1959.
Ishii, M. and Grolmes, M.A., Inception criteria for droplet entrainment in two-phase concurrent film flow, AIChE J., 21, 308–318, 1975.
Lockhart, R.W. and Martinelli, R.C., Proposed correlation of data for isothermal two-phase, two-compo-nent flow in pipes, Chem. Eng. Prog., 45, 39–45, 1949.
Miya, M., Woodmansee, D.E., and Hanratty, T.J., A model for roll waves in gas/liquid flow, Chem. Eng.
Sci., 26, 1915–1931, 1971.
Moody, L.F., Friction factors for pipe flow, Trans. ASME, 671, 1944.
Moissis, R. and Griffith, P., Entrance effects in a two-phase slug flow; J. Heat Transfer, 82, 29–39, 1962.
Oliemans, R.V.A., Liquid Hold-Up during Two-Phase Slug Flow in Inclined Pipes, KSLA Internal Report, 1976.
Oliemans, R.V.A., Modelling of gas/condensate flow in horizontal and inclined pipes, Paper presented at 1987 ETCE Conference, Dallas, February 15–19, ASME, PD. Vol. 6, pp. 73–81.
Oliemans, R.V.A., Pots, B.F.M., and Trompé, N., Modelling of annular dispersed two-phase flow in verti-cal pipes, Int. J. Multiphase Flow, 12, 711–732, 1986.
Pan, P. and Hanratty, T.J., Correlation of entrainment for annular flow in horizontal pipes, Int. J. Multiphase Flow 28, 385–408, 2002.
Pots, B.F.M., An Omni-Angle Flow Pattern Map for Gas/Liquid Two-Phase Flow in Pipes, Internal Shell Report, 1985.
Pots, B.F.M., Oliemans, R.V.A., and Trompé, N., The KSLA Method for Gas/Liquid Two-Phase Pipe Flow Calculations, KSLA internal report, 1988.
Richter, H.J., Flooding in tubes and annuli, Int. J. Multiphase Flow, 7, 647–658, 1981.
Shoham, O. and Taitel, Y., Stratified turbulent–turbulent gas/liquid flow in horizontal and inclined pipes, AIChE J., 30, 377–385, 1984.
Taitel, Y. and Dukler, A.E., A model for predicting flow regime transitions in horizontal and near-hori-zontal gas–liquid flow, AIChE J., 22, 47–55, 1976.
Taitel, Y., Barnea, D., and Dukler, A.E., Modelling flow pattern transitions for steady upward gas–liquid flow in vertical tubes, AIChE J., 26, 345–354, 1980.
Ullmann, A., Zamir, M., Gat, S., and Brauner, N., Multi-holdups in co-current stratified flow in inclined tubes, Int. J. Multiphase Flow, 29, 1565–1581, 2003.
Vassiliadou, E. and Schellekens, C., Liquid Loaded Gas Wells. Physical Mechanisms Related to Unstable Flow, KSLA Internal Report, 1988.
Wallis, G.B., One-Dimensional Two-Phase Flow, McGraw-Hill, New York, 1969.
Whalley, P.B., Boiling, Condensation, and Gas/Liquid Flow, Clarendon Press, Oxford, 1987.
Wu, H.L., Pots, B.F.M., Hollenberg, J.F., and Meerhoff, R., Flow pattern transitions in two gas/condensate flow at high pressure in an 8-inch horizontal pipe, Proceedings of the 3rd International Conference on Multiphase Flow, The Hague, The Netherlands, May, 18–20, 13–21, 1987.
Zuber, N. and Findlay, J.A., Average volumetric concentration in two-phase flow systems, J. Heat Transfer, 87, 453–468, 1965.
Zukoski, E.E., Influence of viscosity, surface tension, and inclination angle on motion of long bubbles in closed tubes, J. Fluid Mech., 25, 821–837, 1966.