A Mechanistic Model for Multiphase Flow in Pipes
Authors: Petalas N. , Aziz K. 
Published: March 2010

Abstract
Mechanistic models for multiphase flow calculations can improve our ability to predict pressure drop and holdup in pipes, especially in situations that cannot easily be modeled in a laboratory and for which reliable empirical correlations are not available. In this paper, a new mechanistic model, applicable to all pipe geometries and fluid properties, is presented. New empirical correlations are proposed for liquid/wall and liquid/gas interfacial friction in stratified flow, for the liquid fraction entrained and the interfacial friction in annular-mist flow, and for the distribution coefficient used in the determination of holdup in intermittent flow.

Introduction
Empirical models often prove inadequate in that they are limited by the range of data on which they were based and, generally, cannot be used with confidence in all types of fluids and conditions encountered in oil and gas fields. Furthermore, many such models exhibit large discontinuities(1) at the flow pattern transitions and this can lead to convergence problems when these models are used for the simultaneous simulation of petroleum reservoirs and associated production facilities. Mechanistic models, on the other hand, are based on fundamental laws and thus can offer more accurate modeling of the geometric and fluid property variations.
All of the models presented in the literature are either incomplete(2,3), in that they only consider flow pattern determination, or are limited in their applicability to only some pipe inclinations(4,5). A preliminary version(6)of the model proposed here that overcomes these limitations was presented in 1996.
For most of the flow patterns observed, one or more empirical closure relationships are required even when a mechanistic approach is used. Where correlations available in the literature are inadequate for use in such models, new correlations must be developed. In order to be able to achieve this, access to reliable experimental data is important.
A large amount of experimental data has been collected through the use of a Multiphase Flow Database(7) developed at Stanford University. The database presently contains over 20,000 laboratory measurements and approximately 1,800 measurements from actual wells. Based on subsets of these data, the previously proposed model(6) included a detailed investigation of the annular mist flow regime and new correlations for the liquid fraction entrained and for interfacial friction. This model has since been refined based on additional investigations of the stratified and intermittent flow regimes, and is the subject of this paper.

Flow Pattern Determination
The procedure for flow pattern determination begins with the assumption that a particular flow pattern exists and is followed by an examination of various criteria that establish the stability of the flow regime. If the regime is shown to be unstable, a new flow pattern is assumed and the procedure is repeated. Figure 1 shows flow pattern transitions based on the superficial velocities of the phases where the stability criteria (transition boundaries S1, S2, etc.) considered in this model are sketched. The procedure for flow pattern determination is illustrated in Figure 3, where it is seen that the examination of the dispersed bubble flow regime is the first to be considered.