Multiphase Science and Technology A Quarterly

ISSN for PRINT: 0276-1459

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2002, Volume14

Issue 4

82 pages

Issue price - $140.00

D. Biberg
Scandpower Petroleum Technology, P.O.Box 113, Gåsevikvn. 2-4 N-2027 Kjeller, Norway

The analytic solution for two-phase laminar stratified pipe flow has been examined by a large number of workers over the years. The immediate solution of the boundary value problem yields the velocity field in terms of holdup and pressure drop. The corresponding shear stress is determined by formal differentiation and the flow rates by integration. This work is concerned with inverting the equations, yielding the solution for holdup and pressure drop for given flow rates - i.e. the more relevant formulation in most cases. The corresponding expressions for the mean wall and interfacial shear stress are given special attention. Two-phase symmetry is emphasized by writing the separate equations for the phases f = g or l into a single generic expression for phase f. The pipe geometry specific effects are emphasized by comparison with the corresponding but less complex channel flow case. The wall shear stress is demonstrated to be given by a linear combination of a single phase free surface flow term and a two-phase interfacial drag term, accounting for the presence of the opposite phase. The effective diameter in the free surface flow term is in surprisingly close agreement with the corresponding hydraulic diameter. The mean interfacial shear stress is symmetric and proportional to a slip velocity resembling the mean velocity difference between the phases, as in channel flow. It is demonstrated to have a direct influence on the frictional pressure drop, not found in channel flow. Symmetry in the holdup equation links the holdup solution in an upwardly inclined pipe to a corresponding void fraction solution in a downwardly inclined pipe for a certain set of inverted parameters. The holdup equation is single valued in horizontal and friction dominated flows (which includes equal density flows). There may be three distinct solutions in the transition from gravity to friction dominated concurrent flow in inclined pipes. The multivaluedness occurs for low flow rates of the more dense fluid in upwardly inclined pipes and for low flow rates of the less dense fluid in downwardly inclined pipes. Local backflow of the more dense and less dense fluids may occur in up and downwardly pipes respectively and may lead to the phenomenon of negative mean wall shear stress for positive net flow rates. Counter current flows are sustained by differences in the fluid densities in inclined pipes. The holdup equation may either have two solutions or no solution in this case.

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