Characterization of Oil-Water Two-phase Flow Patterns in Vertical Upward Flow Pipes Based on Fractal and Chaotic Time Series Analysis
Authors: Jin Ningde , Wang Weiwei , Xingbin Liu , Shuxiang Tian 
Published: December 2007

Abstract
Characterization of oil-water two-phase flow patterns in vertical upward oil-water two-phase flow having an inner diameter 18mm are elucidated based on fractal and chaotic time series fluctuation signals analysis. For 60.5% Kw 91% and 10(m3/d) Qt 60(m 3/d), the local fractal dimensions and correlation dimensions of chaotic attractors range from 1.006 to 1.631 and 4.30 to 6.77, respectively. For the same water cut, the local fractal dimensions decrease, and the correlation dimensions of chaotic attractor increase with increasing total flowrates. Although the distributions of dispersed oil phase tend to be homogeneous with increasing total flowrates, the flow statuses of dispersed oil phase tend to be more turbulent.
For water cut 51% or 51.5% and 20(m3/d) Qt 60(m3/d), the local fractal dimensions and correlation dimensions of chaotic attractors range from 1.17 to 1.758 and 5.46 to 7.05, respectively. Both dimensions show irregular sudden changes with total flowrate variations, which corresponds to happenings of transitional flow pattern. The feasibility of the irregular sudden changes in both dimensions is verified with a complex power spectrum of the fluctuation signals and a flow pattern map proposed by our previous study.
The calculated maximum Lyapunov exponents from the time series signals prove that oil-water two-phase flow in vertical upward pipes is a chaotic system.

Introduction
As most oil fields go into mature stage in China, the oil-water two-phase flow in wellbores is often encountered. A reliable Prediction of characteristics of oil-water two-phase flow is required so that production logging data can be interpreted accurately. In fact, The research results of oil-water two-phase flow patterns are less than those of gas-liquid two-phase flow and until now the opinions for the flow patterns identification criterion are still not coincident perfectly.
Early, Govier et al. (1961) have studied oil-water two-phase flow patterns in vertical upward pipes. Four flow patterns (bubble flow, slug flow, froth flow, mist flow) in pipes having inner diameter of 1.04 inches were proposed. The flow map established by Govier et al. is still an important source in estimate of oil-water two-phase flow patterns in vertical upward pipes.
The Schlumberger (1973) recommended that the water phase becomes dispersed for water holdup less than 0.25~0.30 and oil phase becomes dispersed for water holdup larger than 0.30. Vigneaux et al. (1988) proposed that the water holdup is range from 0.20 to 0.30 for transitional flow pattern in vertical upward oil-water two-phase flow. Zavaeh et al (1988) confirmed the existence of water- and oil-external regions for 18.4 centimeter diameter vertical pipes and no slug or churn flow patterns appeared.
Recently, Flores et al. (1997) presented a comprehensive study of oil-water flow patterns in vertical and deviated pipes. A mechanism model of flow patterns transition was proposed. Their study also shows that while the behavior of oil-water flow has many similarities with gas-liquid flow, important differences remain.