An inverse dispersed multiphase flow model for liquid production rate determination S. Guet a, * , O.M.H. Rodriguez a , R.V.A. Oliemans a , N. Brauner b a Kramers Laboratorium, J.M. Burgers Centre for Fluid Mechanics, Delft University of Technology, Prins Bernhardlaan 6, 2628 BW Delft, The Netherlands b School of Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel Received 9 August 2005; received in revised form 19 January 2006 Abstract The aim of this study is to develop a model for the determination of the superficial velocities in horizontal and slightly inclined oil–water pipe flow conditions by using pressure gradient and mixture density information. In this article an inverse model is suggested for a dispersion of oil in water and of water in oil. This approach permits to select dispersed flow conditions from a set of experimental data, and uses a new hybrid model for the effective viscosity. A set of 310 oil–water experimental data points collected on an experimental set-up of length L = 15 m and diameter D = 8.28 cm at various (slight) orientations is used to validate the inverse method. The comparison between model reconstructions and measured flow velocities show a reasonable agreement. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Liquid–liquid flow; Inverse model; Dispersed regime; Effective viscosity; Drop size 1. Introduction In the oil industry, very often a number of pipes are connected via T-junctions in under-sea or under ground configurations. These pipelines are producing from different oil reservoirs with different intake pres- sure and water cut conditions. Current technologies have shown that pressure and mixture density determina- tion are possible on these pipelines by using piezo-electric and gamma-ray measurement techniques. However, the in situ determination of the oil and water flow rate remains an important issue, since available flow rate measurement techniques would be difficult to install in such situations. In the present research project we want to develop a method for computing the oil and water superficial velocities based on pressure gradient and 0301-9322/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmultiphaseflow.2006.01.008 * Corresponding author. Present address: Institut Franc ¸ais du Pe ´trole, 3-4 Avenue de Bois-Pre ´au, 92500 Rueil Malmaison, France. E-mail addresses: s.c.l.guet@wbmt.tudelft.nl, sebastien.guet@ifp.fr (S. Guet). International Journal of Multiphase Flow 32 (2006) 553–567 www.elsevier.com/locate/ijmulflow