Mathematical Problems in Engineering

Volume 2016 (2016), Article ID 2879524, 10 pages

http://dx.doi.org/10.1155/2016/2879524

## Time Irreversibility from Time Series for Analyzing Oil-in-Water Flow Transition

^{1}College of Electronic Information and Automation, Tianjin University of Science and Technology, Tianjin 300222, China^{2}School of Computer Science & Software Engineering, Tianjin Polytechnic University, Tianjin 300387, China

Received 31 December 2015; Revised 20 February 2016; Accepted 7 March 2016

Academic Editor: Konstantinos Karamanos

Copyright © 2016 Du Meng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

We first experimentally collect conductance fluctuation signals of oil-in-water two-phase flow in a vertical pipe. Then we detect the flow pattern asymmetry character from the collected signals with multidimensional time irreversibility and multiscale time irreversibility index. Moreover, we propose a novel criterion, that is, AMSI (average of multiscale time irreversibility), to quantitatively investigate the oil-in-water two-phase flow pattern dynamics. The results show that AMSI is sensitive to the flow pattern evolution that can be used to predict the flow pattern transition and bubble coalescence.

#### 1. Introduction

Oil-in-water two-phase flow widely exists in petroleum industry such as crude oil production and transportation. Due to the existence of fluid turbulence and phase interfacial interaction, the mixed fluid often exhibits complex behaviors. In particular, under very low mixture velocity, the existence of bubble coalescence phenomenon leads to more complex fluid dynamics. In this regard, characterizing the oil-in-water two-phase flow structure and dynamics is still quite a challenging problem which is helpful for the flow parameters measurement and pipe pressure drop prediction.

Study on oil-in-water two-phase flow dates back to the 1960s, and early researchers’ main focus is on the flow pattern observation and definition. Govier et al. [1] first define the dispersed oil phase in 1.04-inch inner diameter pipe as oil bubble and slug. Then Flores et al. [2] redefine the dispersed oil phase as three different flow patterns, that is, slug flow, bubble flow, and dispersed bubble. This definition for dispersed oil phase is more elaborate that has been approved by several researchers [3, 4]. Recently, researchers are more concerned about oil-in-water two-phase flow under certain flow conditions, such as two-phase flow in bend pipe [5], two-phase flow in microchannels [6], and high-viscosity oil-water two-phase flow [7]. In addition, more advanced experimental methods are adopted to explore the oil bubble characteristics. The methods such as miniprobe detection [8], high speed photography [9], microwave measurement [10], process tomography [11], and PIV technology [12] have been applied to study the characteristics of oil-in-water two-phase flow.

In recent years, characterizing complex systems from time series has attracted much attention [13, 14]. These signals are time series that are collected to reflect the conductance or pressure fluctuations of the mixed fluid. Note that adopting different signal processing methods would reveal different aspects of flow characteristics. For example, time-frequency method [15] focuses on revealing the motion behaviors of dispersed phase, wavelet analysis [16] and Hilbert-Huang transform method [17] mainly reflect the multiscale and polymorphism dynamics, and nonlinear information analysis techniques [18] are advanced in complex fluid dynamic indication. It is worth noting that complex network has been proved to be an effective tool to characterize the system dynamics [19–21], and the fluid dynamic can also be revealed with mapping the fluctuating signals to networks [22–26]. In general, the flow dynamics revealed from experiment fluctuation signals are less affected by flow condition such as flow rate, pipe diameter, and pipe direction; these methods have attracted many researchers’ attention in recent years.

It is a remarkable fact that under low mixture velocity the oil-in-water two-phase flow exhibits quite complex dynamics. First, the fluid exhibits spatial asymmetry structure due to the bubble coalescence. How to characterize this fluid asymmetry is still a difficult problem. In addition, how to effectively characterize the flow pattern transition phenomenon, for example, from slug flow to bubble flow, is still unsolved. Therefore, developing a reliable tool to characterize the oil-in-water two-phase flow dynamics and flow pattern evolution character is quite a necessary issue. Recently, time irreversibility index has been proved to be a powerful tool to detect system dynamics and quantify the existence of system disequilibrium [27]. If the statistical properties of a time series are invariant with respect to time reversal, we can say that this time series is reversal. Otherwise it is time irreversible. Till now, many indexes have been proposed to quantify the time series irreversibility of a complex system, such as multiscale time irreversibility [27–31], symbolic time series irreversibility [32], time irreversibility extracted from Poincaré plot [33–35], complex network time irreversibility [36, 37], and time irreversibility in high dimensional space [38, 39]. The scientific and engineering applications of time series irreversibility also involve many fields including financial system [40, 41], human heart rate [42–44], human brain [45], and seismicity [46]. Employing the time irreversibility index to analyze the two-phase flow fluctuating signals can effectively reveal the flow pattern formation, coalescence, and evolution characteristics. Also, the time irreversibility index can be an indicator for the flow pattern transition phenomenon, for example, from slug to bubble.

In this paper, we first carry out low flow rate oil-water two-phase flow experiment in vertical 20 mm inner diameter Plexiglass pipe and the conductance fluctuation time series which reflect the oil-in-water two-phase flow characteristics have been collected. Then we investigate the time irreversibility of the collected fluctuation series. Note that the dimension of an oil-water two-phase system is typically 5 or more [47]; we use Casali’s multiple testing strategy [38] to detect the oil bubble flow time irreversibility. Multiscale analysis method has also been employed to the time irreversibility detection, considering that oil-water two-phase flow dynamics can be revealed more clearly under different scales [48–50]. Moreover, we propose a novel criterion, that is, average of multiscale time irreversibility (AMSI) to quantitatively characterize the two-phase flow system time irreversibility. The results suggest that AMSI can be a sensitive indication to predict the flow pattern transition phenomenon.

#### 2. Experiments and Data Acquisition

##### 2.1. Experimental Setup

We carried out the low flow rate oil-water two-phase flow experiment in a vertical 20 mm inner diameter Plexiglass pipe. As shown in Figure 1, the oil-water two-phase flow loop consists of a water tank, an oil tank, a mix tank, two peristaltic metering pumps, and testing pipes. During the experiment, the two phases, that is, oil and water, are first pumped out from the tanks, respectively, and mixed in the horizontal pipe section. Then the mixed fluid flows into the vertical test pipe, on which the measurement facility and sensor are installed. After the flow parameters and fluctuation measurement are done, the mixed fluid is drained into the mix tank to separate. The peristaltic pumps we used in the experiment are high precision metering pump, which can ensure precision of inlet flow rate and phase fraction.