In many industrial installations, a gas and a liquid can flow together. For instance, in the oil and gas industry (Kiran et al., 2020) or in chemical reactors (Wang et al., 2021), where several types of fluids are encountered. Moreover, a phase change caused by evaporation or condensation may induce the appearance of a second one in a pipe. Such phenomena occur mainly in petroleum and gas production and in nuclear reactors (Sassi et al., 2020).
It is important to identify and control the flow pattern for a better design and control of the industrial devices (Raeiszadeh et al., 2018). Under certain conditions, the liquid and gas phases may flow alternately and irregularly as elongated bubble (also called gas pocket or gas slug) and bulk of liquid regions filling the entire pipe as liquid slug (Mohmmed et al., 2021, Liu et al., 2022), resulting in the intermittence of flow parameters such as pressure, void fraction, flow rates of both phases, heat and mass coefficients, etc. This flow regime, called intermittent flow, represents a destructive flow pattern (Saini et al., 2022; Adouni et al., 2022), which makes it challenging for the engineers. Indeed, the alternating flow of the two structures causes several industrial problems such as instability of heat and mass exchange in chemical reactors and liquid overflow in upstream installations. To date, the exact nature of the intermittent flows is not yet well known (Mohmmed et al., 2021). Subdividing the intermittent regime into sub-regimes may be a way to better understand and comprehend this type of flow, especially from the aspect of fluid-structure interaction (Arabi et al., 2020d). Based on the shape of the elongated bubble/liquid slug interface and the aeration of the slugs, Thaker and Banerjee (2015, 2016a) proposed to classify the intermittent flow into three sub-regimes:
-
Plug flow (Fig. 1.a): In this flow sub-regime, the liquid slugs are free from gas bubbles. The elongated bubble has a staircase shape tail with a hydraulic jump followed by a long tail.
-
Less Aerated Slug flow (LAS flow) (Fig. 1.b): The transition from plug flow to slug flow is accompanied by the presence of gas bubbles inside the liquid slugs. In LAS flow, the liquid slugs transport small quantities of gas bubbles. The elongated bubbles end by a simple hydraulic jump without a presence of the long tail.
-
Highly Aerated Slug flow (HAS flow) (Fig. 1.c): Comparatively to LAS flow, the liquid slugs in the case of HAS flow carried out large quantities of gas bubbles. The presence of eddies due to the secondary flow represents also a criterion used to differentiate the HAS flow from LAS flow.
Our group has obtained interesting results using this classification approach in series of recent works. Indeed, it was found that the slug frequency (Arabi et al., 2020), the pressure drop (Arabi et al., 2021c) and the behaviour of the flow structures crossing a sudden expansion (Arabi et al., 2021d), depend on the nature of the sub-regime. Despite these results, the investigations carried out using these sub-regimes classification are still scarce, as indicated by the limited number of existing flow pattern maps, showing the zones of the existence of these sub-regimes (Thaker and Banerjee, 2016; Dinaryanto et al., 2018; Humami et al., 2018).
As mentioned earlier, this approach to classify sub-regimes, as well as flow regimes (Arabi et al., 2022), is based on visual observations. This technique of identifying and distinguishing between regimes and sub-regimes is restricted to transparent pipes. As recently reminded by Arabi et al. (2022), various devices for measuring different flow parameters such as static pressure (Drahoš et al., 1987; Luo et al, 2010; Hanafizadeh et al., 2016), differential pressure between two points in the pipe (pressure drop) (Luo et al., 2010; Arabi et al., 2018), void fraction (Kong et al., 2018; Bouyahiaoui et al., 2020), liquid holdup (Deendarlianto et al., 2019; Arellano et al., 2020), velocity (Wang et al., 2020; Xu et al., 2020) and temperature (Guo et al., 2020) have been used to characterize the flows and in particular to identify the flow regimes. Temporal fluctuations of flow parameters in two-phase flows (except for the case of smooth stratified flow) do not allow considering the averaged parameters as reliable data. Excluding the fluctuating components of these parameters does not reflect the physical reality of the phenomena (Wang and Shoji, 2002), especially in case of intermittent flows where fluctuations are the most important. The analysis of time series signal fluctuations is done either through signal visualization (Weismann et al., 1979; Dinaryanto et al., 2018; Arabi et al., 2018; Ma et al., 2020), or by using statistical tools, notably statistical moments (Kadji et al., 2009; Zeghloul et al., 2017) and the Probability Density Function (PDF) (Drahos̆ and C̆ermák, 1989; Amani et al., 2020). It should be observed that frequency analysis has also been used (Wang and Shoji, 2002; Arabi et al., 2018). Utilization of more sophisticated analysis techniques was also reported in the literature (see for instance the reviews carried out recently by Saini and Banerjee (2021) and Wijayanta et al. (2022)). The PDF obtained from void fraction or liquid holdup series is frequently used as a tool to identify the regimes (Costigan and Whalley, 1997; Parsi et al., 2017; Abdulkadir et al., 2020a, 2020b). Indeed, each regime has its own PDF shape. The transitions between the regimes can also be detected by an abrupt change in some parameters’ values (Bertola, 2003). Ye and Guo (2013) have extracted different statistical parameters and principal components from pressure signals in order to propose a tool for identifying the flow patterns in pipeline-riser systems. By applying different feature space, which designates the plot of the collected data using the calculated parameters as coordinates, the authors have found that the data of each regime are clustered in separate region. It is important to note that the feature space is not widely used to study two-phase flow in straight pipe. Abdulkadir et al. (2018) used it by plotting the mixture velocity versus the measured mean void fraction values. The authors reported that this feature space can be used as a flow pattern map for both horizontal and vertical pipes. By plotting the slug frequency data using the gas based Strouhal number as function of the mixture Froude number, Arabi et al. (2020) proposed this feature space as a tool to distinguish between the sub-regimes of the intermittent flow.
Among the most common flow monitoring devices in the industry, the absolute and differential pressure transducer have several advantages: robust, easy to use, non-intrusive and inexpensive (Arabi et al., 2020; Wu et al., 2022). Weismann et al. (1979) used pressure drop signals between two points in a pipe for the flow regimes identification in horizontal configuration. They observed that the signal for each flow regime is characterized by its own signature. The signal is smooth for the stratified regime, and contains low amplitude peaks for the wavy flow. For the slug regime, the signal is composed of large peaks with high amplitudes, indicative of the passage of slugs. Indeed, the differential pressure values oscillate with the frequency of liquid slug (Kim and Kim, 2022). The absolute pressure sensor can also be used to detect the passage of liquid slugs (Lin and Hanratty, 1987a; Saini and Banerjee, 2021; Thaker et al., 2021). Wambsganss et al. (1994) plotted the static pressure Root Mean Square (RMS) parameter as function of the mass quality. The authors found that such representation can predict the plug-bubble/slug flow and slug/annular flow transitions well.
By applying the PDF on absolute and differential pressure signals collected from a 50 mm ID horizontal pipe, Luo et al. (2010) found that the PDF of the pressure drop signals had a unimodal profile in case of slug flow while those obtained from the absolute pressure drop signals could have a unimodal or bimodal distribution. They also found that an increase in phasic superficial velocity leads to an increase in the maximum pressure drop, in the maximum pressure and the dispersion of the values collected with the two kinds of signals. It should be noted that the authors observed that the peaks, indicative of the passage of the slugs, were more pronounced in case of differential pressure signals than those obtained with the absolute pressure sensor. This is due to the fact that the former type of sensor filters out the original fluctuations from outside the interval between the two points connected to the pressure sensors (Arabi et al., 2020). Wang et al. (2019) were able to correlate the fluctuations of the pressure drop signals with the void fraction for the bubbly, plug and slug flow regimes. The authors applied the Extreme-Point Symmetric Mode Decomposition (ESMD) components on differential pressure signals collected across a venturi placed on a 40 mm ID horizontal pipe.
Regarding the studies on time series analysis carried out with the sub-regimes of the intermittent flow, Dinaryanto et al. (2018) analyzed the fluctuations of the absolute pressure signals collected on a 16 mm pipe. In the slug and plug flow (which is a transition between plug and LAS flow (Thaker and Banerjee, 2015; Arabi et al., 2021a)), the pressure signals are characterized by small and low fluctuations. The values given by the signals as well as the fluctuations are larger in case of LAS flow. The HAS flow is characterized by the largest static pressure values and the largest fluctuations. In this study, the authors studied qualitatively the pressure signals for each sub-regime. No quantitative criteria were proposed to distinguish between the sub-regimes. Saini and Banerjee (2021) explained that absolute pressure signals cannot be used as a means of distinguishing between plug, LAS and HAS flows. They proposed to apply the recurrence analysis to these signals. This method is based on the reconstructed phase space trajectory representing non-linear signals from the system in d-dimensional space. From signals obtained using air-water and 25 mm ID pipe, the authors have reported that the recurrence plot and quantification parameters change as the flow transits from one to another sub-regime.
Despite the interesting results obtained by Saini and Banerjee (2021) using the above-mentioned quantitative method, the level of complexity of the latter makes it difficult to be applied on an industrial scale. The present study investigates the fluctuations of the differential pressure time series using simple statistical parameters, such as PDF and statistical moments. The aim of this paper is to propose simple and objective tools to identify and distinct between the sub-regimes of the intermittent flow. The originality of this work resides also in the use of feature space using the parameters obtained from calculated statistical moments and PDF. This paper is a continuation of our works on plug, LAS and HAS flow sub-regimes observed in a 30 mm ID pipe (Arabi, 2019; Arabi et al., 2020b, 2021b, 2021c).