A Mechanistic Slug Liquid Holdup Model for Wide Ranges of Liquid Viscosity and Pipe Inclination Angle
Authors: Wang Shufan , Pereyra Eduardo , Sarica Cem , Zhang Hong-Quan 
Published: May 2013

Abstract
Slug liquid holdup is one of the most important parameters of slug flow. It is closely related to the average liquid holdup and pressure gradient of slug flow in wells and pipelines. Barnea and Brauner (1985) and Zhang et al. (2003a) mechanistic models are based on the turbulent nature of liquid slugs, which is typical for low viscosity oils. However, for high viscosity oil slug flow, the liquid slug is laminar due to low slug Reynolds number. In this study, a slug liquid holdup mechanistic model is developed for low and high viscosity oil slug flows. The model is based on two shear mixings including shear between the slug front and pipe wall, and shear between the slug body and liquid film. The equations are solved based on slug flow characteristics which can be calculated by solving the continuity and momentum equations of slug flow. A data bank consisting of 418 slug liquid holdup measurements is used to validate the model. In the data bank, liquid viscosity ranges from 0.0016 to 0.589 Pa·s (1.6 to 589 cP). Pipe inclination angle is from −30? to upward vertical. Pipe inner diameter (ID) varies from 5.08 to 10 cm. Statistical evaluations are also conducted against predictions of other models. Significant improvement is observed in the performance of the new model.

Introduction
Heavy oil constitutes a major portion of the world's total oil reserve. It is discovered and produced around the world and has become one of the most important future hydrocarbon resources with ever increasing world energy demand and depletion of conventional oils. However, heavy oil possesses very high viscosity which poses many challenges for its production and transportation.
Accurate pressure gradient and liquid holdup predictions of high-viscosity oil multiphase pipe flows are imperative for heavy oil production and transportation. Most of the current multiphase flow experimental studies, correlation and model developments were conducted using low-viscosity conventional oils or other liquids. However, high-viscosity oil multiphase flow behaves very differently than low-viscosity oil multiphase flow. Significant discrepancies were observed in model comparisons.
Slug flow is a dominant flow pattern in high-viscosity oil/gas pipe flow. In two-phase slug flow, liquid slugs and gas pockets propagate alternatively in the pipe. Liquid slugs without gas entrainment are rare under normal pipeline operating conditions. Instead, gas bubbles are often entrained in the liquid slugs. The liquid volume fraction in the slug body is known as the slug liquid holdup. The slugs can carry different amount of entrained gas, which primarily depends on flow rates, fluid properties, and pipe diameter. A slug unit consists of the slug body and a liquid film zone. The fast moving aerated slug body over rides the slow moving liquid film ahead of it. The slug scoops the liquid film and accelerates it to the velocity of the slug (mixture velocity). Liquid is shed from the tail of the slug to a trailing film. Slug liquid holdup is an important parameter for slug flow modeling. Most of the pressure drop in slug flow occurs in the slug body. The frictional pressure drop is greater in the slug body than in the film region. The liquid film acceleration also causes significant pressure drop in the mixing zone at the slug front. Thus the overall pressure gradient depends greatly on the slug liquid holdup and slug length.