A transient one-dimensional model of mixing and segregation of liquids in pipes

A one-dimensional model is proposed for the prediction of transient two-phase flow of two immiscible liquids in pipes. The approach treats the liquid-liquid flow as being composed of two layers, each made up of either pure liquid or an emulsion of the two liquids. Each layer is treated as a single mixture where the relative slip between dispersed and continuous phases is determined from a driftflux model. Closure relations are proposed for the calculation of the entrainment rate of drops from one layer into the other, and for the reverse process of deposition of the dispersed phase drops. Closure relations are also used to evaluate the dispersed phase drop diameter, the mixture viscosity, and the phase inversion point. Phase inversion is catered to in an automatic way. Predictions obtained from the model are compared against experimental data for oil-water flow; in particular, dispersed phase fractions, pressure losses, and schematic flow regime maps are used to assess performance. The model reproduces with reasonable accuracy the experimental dispersed phase fraction trends and the changes in flow regime as functions of the flow parameters. Computed pressure losses at low mixture velocity are in good agreement with the experiments. Two factors influencing the results at high mixture velocities, secondary dispersion and drag reductions effects, are briefly discussed. © 2010 by Begell House, Inc.