Nonlinear dynamical analysis of large diameter vertical upward oil–gas–water three-phase flow pattern characteristics Z.Y. Wang, N.D. Jin n , Z.K. Gao, Y.B. Zong, T. Wang School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China article info Article history: Received 17 September 2009 Received in revised form 21 June 2010 Accepted 22 June 2010 Available online 30 June 2010 Keywords: Oil–gas–water three-phase flow Flow pattern Conductance fluctuating signal Nonlinear dynamical characteristics Chaotic attractor morphology Complexity measure abstract Based on two kinds of signals measured from mini-conductance probe array and vertical multi- electrode array (VMEA) conductance sensor, we study oil–gas–water three-phase flow in a vertical upward 125 mm ID pipe. Using the ratio of oil flowrate to total liquid flowrate (f o ) and the superficial gas velocity (U sg ), we draw the six different flow pattern maps under four total mixture liquid flowrates. In addition, we indicate that: (a) the increase of f o makes oil in water type slug flow occur at lower U sg ; (b) for large diameter pipe and low flow velocity, the phase inversion of liquids occurs at about f o ¼0.9 and the increase of U sg makes the phase inversion of liquids move to low f o . Furthermore, we investigate the nonlinear dynamical characteristics of five water continuous phase flow patterns in terms of chaotic attractor morphological description and complexity measures (Lempel–Ziv complexity and approx- imate entropy), and find that: (a) the chaotic attractor morphological characteristics can identify three- phase flow patterns; (b) the combination of Lempel–Ziv complexity and approximate entropy can serve as a unique classification criterion of three-phase flow patterns. In this regard, the nonlinear analysis of conductance fluctuating signals can give an effective indicator to understand and identify the oil–gas– water three-phase flow pattern characteristics. & 2010 Elsevier Ltd. All rights reserved. 1. Introduction Oil–gas–water three-phase flow widely exists in the oil well production and oil–gas transportation. Flow pattern indicates how the phases are distributed and mixed due to the physical nature of the system. In addition, the pressure gradient, momentum loss, rate of back mixing and pipe vibration all vary greatly with the flow patterns. Identifying three-phase flow patterns is crucial to many industrial problems such as pipeline installation, optimal design of artificial lift production device and downhole flowmeter, and interpretation of well logging data. Hence, it is quite important to discern different three-phase flow patterns. But due to the complex interfacial interaction between phases, the identification of oil–gas–water three-phase flow pattern is still an unsolved problem. In early studies of oil–gas–water three-phase flow, Tek (1961) treated the two immiscible liquids as an equivalent single phase and predicted the pressure loss with an empirical correlation. Shean (1976) did the flow loop test in vertical upward Nujol- water and Nujol-water–air flows. Pleshko and Sharma (1990) predicted the flow pattern transition by using the model of gas– liquid two-phase flow (Taitel et al., 1980), but the result indicated that the two-phase models were unsuitable for the prediction of three-phase flow pattern transitions. Guo et al. (1991) conducted three-phase flow experiment in a 125 mm ID pipe and divided flow patterns into bubble flow and slug flow by visual method, they subdivided the bubble flow into two typical patterns, which were the distinguishable and undistinguishable oil droplet and air bubble. Chen (1991) investigated three-phase flow characteristics in vertical upward pipe and classified the flow patterns on oil in water or water in oil type flow. Woods et al. (1998) conducted three-phase flow experiment in a 26 mm ID perspex pipe; they concluded the nine flow patterns based on the water dominated and oil dominated and proposed flow pattern map. More recently, Oddie et al. (2003) carried out oil–gas–water three-phase flow loop test, and they treated the oil–water flow as a homogeneous with no slippage between phases. In addition, other impact factors, such as, the properties of pipe material, pipe geometry, liquid viscosity and surface tension, played an important role in the flow pattern transition (Chupin and Nydal, 2003; Furukawa Fukano, 2001; Hewitt, 2005;Wegmann et al., 2007). Recently, some progress have been made in applying the nonlinear analysis method mainly based on Fractal and Chaos theory (Daw and Halow, 1993; Fan et al., 1990; Fraguio et al., 2007; Jin et al., 2001; Kikuchi et al., 1996, Kikuchi and Tsutsumi, 2001; Wu et al., 2001; Yano et al., 1999). Nevertheless, these proposed algorithms are relatively complicated and time-con- suming, and often dependent on the selected specific parameters Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ces Chemical Engineering Science 0009-2509/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2010.06.026 n Corresponding author. Tel./fax: + 86 22 27407641. E-mail address: ndjin@tju.edu.cn (N.D. Jin). Chemical Engineering Science 65 (2010) 5226–5236