Multi-scale characterization and identification of dilute solid particles impacting walls within an oil-conveying flow with an experimental evaluation by dual vibration sensors

https://doi.org/10.1016/j.cej.2021.129173Get rights and content

Highlights

  • A scale division method of particle-oil flow based on E/VMD analysis is proposed.

  • Macro-scale collision behaviors are identified by time-frequency plane in oil flow.

  • Collision behavior of IMFs is analyzed by energy, kurtosis, Hurst, entropy method.

  • Solid quantitative expression model is established from oil flow with good accuracy.

  • Best scale of particle characterization is meso- and micro-scale with SNR analysis.

Abstract

Although the characterization and identification of solid particle-wall collision behaviours within oil-conveying flows are important, these issues, which are closely associated with the optimization of particulate systems in the chemical and petroleum industries, are rarely discussed in the literature. In this work, a series of multi-scale vibration analysis methods were proposed for the quantitative characterization and identification of sand/glass features in an oil-conveying pipe flow. Dilute particles were identified within an oil-conveying flow in the 2-D time-frequency plane and then verified by the coherence method with dual sensors. The particle-wall collision features were analysed at multiple resolutions by empirical/variational mode decomposition (EMD/VMD) in combination with statistics for each intrinsic mode function (IMF) component. Corresponding verification experiments were performed, and good agreement was found between the test conditions (oil viscosity of 10–50 mPa·s, velocity of 1.8–3.0 m/s, and particle size of 160–270 μm) and multi-scale vibration energy (SE) responses at multiple bandwidths (the macro-scale bandwidths of 30–50 kHz and 40–50 kHz, meso-scale bandwidth of 45–50 kHz, and micro-scale bandwidth of 40–42 kHz). Particularly, a solid content model was established with variations in the oil viscosity h(μ), flow velocity G(v) and particle size p(s), expressed as Solidcontent=A·ps·[Gv·SE]Bhμ, and the model was verified for each scale. Moreover, considering the signal-to-noise ratio (SNR) performance, the best particle characterization scales were the meso-scale and micro-scale, with good error rates of 4.92% and 5.10%. Therefore, this study complements existing particle characterization methods and deepens the current understanding of particle-wall collisions in multi-phase flows.

Introduction

The characterization of solid particles in an oil-conveying flow based on particle–wall collision behaviour is an important process [1], [2]. The features of solid particles have played a role in the development of chemical and petroleum industrial technologies, such as fluidized beds [3], [4], [5], solid–liquid separators [6], and oil production [7], [8], [9]. In particular, particle–wall collisions are complex phenomena with many influencing factors [10]. As a result, the traditional characterization of particles from a liquid flow is tremendously difficult. Important production information is easily submerged in the background noise generated by solid particles continuously impacting the wall [11], and this collision behaviour poses an increasing threat to the reliability of the system and may induce erosion failure [12]. Therefore, obtaining further insight into a valid early particle multi-scale characterization method, based on which chemical and petroleum particulate systems could be optimized, is a highly attractive topic of ongoing research.

In recent decades, extensive efforts have been devoted to obtaining information on solid particles in liquid pipe-flow conveying systems by nonintrusive methods [13], [14], which advantageously avoid needlessly invading the production flow. Nevertheless, due to the complexity of the solid–liquid interface interaction behaviour [15], an accurate and convenient particle characterization method remains a global challenge [16], [17]. As a consequence, a growing number of researchers have recently attempted to achieve experimental and theoretical breakthroughs in multi-phase particulate flow based on the principles of sound and vibration, which are easy and safe to use in oilfields [18], [19]. A particle–wall collision generates elastic waves in particulate transportation systems. Then, these passive waves cause acoustic emission (AE) signals, acoustic signals, and vibration signals. Although the physical principles of these three signals are different, piezoelectric ceramics with different frequency response ranges are used for AE sensors [20], acoustic sensors [21], and vibration sensors [22], in which the piezoelectric effect produces the voltage signal caused by the passive elastic waves. Accordingly, the AE, acoustic and vibration methods have become important non-intrusive solid particle characterization methods.

The AE method has a superior ability to identify the rapid release of transient elastic waves from a multi-phase flow, typically at frequencies of 100 kHz to 1 MHz [23]. El-Alej et al. [24], [25] (2013,2014) identified the features of suspended solid particles in a slurry water flow from the test position of a horizontal pipeline and then qualitatively described the presence of water–sand droplets. Droubi et al. [26], [27] (2015,2016) obtained the AE energy of particle–wall impacts in a slurry air/water flow and established a statistical model of the relations between the energy and test conditions. Nsugbe et al. [28] (2017) used the AE method to estimate the distribution features of regular and irregular particles (150–250 μm) free falling in air with a time domain-based multiple-threshold method. Droubi et al. [29] (2018) investigated the static and oscillatory components of the AE impact energy of sand particles (212–710 μm) at different water flow speeds and improved the temporal sensitivity of the acquired AE signals. The AE method employed in the abovementioned studies focuses on characterizing the particle mass and size in gas and water particulate systems. Zhang et al. [30] (2019) quantitatively analysed the features of glass particles (0.4–1.2 mm) in a pneumatic conveying system using the AE method, and the relative error was within 12%. Lin et al. [31] (2020) detected the stratified fluidization of cohesive particles using the AE method with ten frequency scales. Zhang et al. [32] (2021) established a machine learning prediction model for the flow rate of polypropylene particles in a horizontal pneumatic conveying system using the AE method with an error of 8.4%. Therefore, the particle mass rate can also be quantitatively analysed in combination with traditional statistics and machine learning methods. The above studies lay a good foundation for particle characterization in highly complex multi-phase flows; however, in comparison with more complex non-Newtonian oil fluid particulate systems, multi-phase flows feature relatively particle–wall collisions, which greatly increases the difficulty of identification. Consequently, the characterization of solid particles in an oil flow still constitutes a substantial challenge when applying the AE method.

Numerous researchers have attempted to characterize particle information by analysing acoustic waves from particulate flows. For example, Rice et al. [33] (2015) developed an active acoustic dual-frequency concentration inversion method for particle concentration measurements. Stener et al. [34] (2016) used acoustic backscatter methods to obtain the velocity and concentration features of dense particles. Muramatsu et al. [35] (2017) detected dispersed particles with sub-millimetre and millimetre diameters in water by emitting radiation with a single-kHz band active acoustic method. Shen et al. [36] (2018) experimentally researched acoustic agglomeration with different particle size distributions and found the relation between the narrow size range and sound pressure level. Wang et al. [37] (2019) investigated acoustic sand signals from a water–gas pipe flow and uncovered five different particle–wall collision characteristic frequency bands. Yang et al. [38] (2020) analysed the interactions of dense polypropylene particles (1.5 mm) with the wall in a vertical pneumatic conveying flow and described the relation between the acoustic energy fraction of collision and the Janssen coefficient. Nevertheless, although the above active and passive acoustic methods are sensitive to the features of particles in a water flow, active acoustic methods depend strongly on the coupling of sensor parts and are limited by their ability to tolerate explosions in the field, whereas passive acoustic methods are restricted to the quantitative characterization of particles in a high-viscosity oil flow.

In addition, a growing number of researchers have focused on the identification and classification of particulate flows using vibration methods, which have the obvious advantages of convenience and low cost [39]. Xu et al. [40] (2016) revealed the multi-scale vibration behaviour of a millimetre-scale graphite tube containing a vapour-liquid–solid boiling flow at frequencies of 0–10 kHz. Ma et al. [41] (2017) investigated the behaviour of fluidized solid particles (1.3–3.5 mm) colliding with the wall of a graphite evaporator tube using vibration signal analysis at frequencies of 0–2.5 kHz. Hashemnia et al. [42] (2018) studied the effects of the vibration frequency and amplitude on the quality of fluidization of a vibrated dense granular flow. Wang et al. [43] (2019) experimentally evaluated the identification of sand particles (96–180 μm) in oil–water-gas multi-phase flows based on vibration signal analysis at a frequency of 20 kHz. Furthermore, Wang et al. [44] (2020) characterized the interactions between particles (96–550 μm) and the wall in a water pipe flow based on a multi-frequency viewing angle at a frequency of 50 kHz. These vibration methods are capable of the multi-scale identification of tiny solid particles at frequencies reaching 50 kHz. However, to date, no breakthroughs have been reported in the quantitative characterization of solid particles within high-viscosity oil-conveying flows. Additionally, the existing multi-scale methods are focused on the low-frequency band or manually select the frequency band and therefore lack the ability to mine the characteristics of the different scales that affect the particle–wall collision behaviour. As a result, these techniques lack self-adaptability and cannot analyse non-stationary random collision signals. By contrast, mode decomposition algorithms [45], [46] can be used to adaptively decompose and transform signals based on their intrinsic features at multiple resolutions and thus are more suitable for analysing non-stationary random signals than existing multi-scale methods.

Most previous theoretical and experimental studies have concentrated on the identification and characterization of solid particles in gas or water particulate systems with limited industrial applications or with only a qualitative characterization or multi-scale method in a narrow frequency band. In contrast, few investigations have focused on the mode-decomposed multi-scale characterization of the collision behaviour between particles (160–270 μm) and the wall in a complex non-Newtonian oil fluid particulate system using two vibration sensors. As a result, a real-time multi-scale quantitative characterization method was experimentally applied in this work to analyse the collision behaviour between dilute particles and the pipe wall in an oil-conveying flow. In addition, the effects of the fluid viscosity, flow velocity and particle size on the vibration energy of the collision behaviour were evaluated on multiple scales, thus improving the limitations of the existing methods.

Solid particles travelling within an oil flow strike the pipe wall at bends due to inertia, and the weak vibration responses generated from such collisions are easily masked by the strong background noise due to flow fluctuations [47]. Hence, differentiating these collision behaviours is a major challenge. In this paper, the multi-scale features of the collision behaviour between dilute particles and the pipe wall within an oil-conveying pipe flow were studied experimentally by employing two vibration sensors, as shown in Fig. 1(b). The initial particle–wall collision experiment in water provided a time- and frequency-analysis basis for the characterization inside an oil pipe flow, and the corresponding multi-scale features were evaluated by empirical mode decomposition (EMD) and statistical methods. The macro-scale features of the particle–wall collision behaviour were distinguished from the features of the oil-conveying flow in the time–frequency plane, and the findings were verified by coherence analysis. Furthermore, the meso-scale and micro-scale solid particles were characterized by variational mode decomposition (VMD) and statistical (normalized energy, kurtosis, Hurst, and entropy) methods. The effects of the oil viscosity, flow velocity and particle size on the vibration energy were investigated at the optimized scales by two sensors. Additionally, a quantitative particle content evaluation model was established based on several indoor evaluation tests. Finally, the proposed model was verified and evaluated by signal-to-noise ratio (SNR) analysis.

Section snippets

Experimental investigations

Two experiments were conducted to characterize the dilute solid particles within an oil-conveying pipe flow. The first experiment involves the initial particle–wall impingement in water, while the second experiment involves the particle–wall impingement inside an oil-conveying pipe flow.

Characterization of solid particle-oil two-phase pipe flows by time and frequency analyses

Solid particles travelling within an oil flow strike the pipe wall at bends due to inertia and then move forward as the liquid flows around the bend. The higher the fluid viscosity is, the weaker the inertia force of the particles being transported, and the particle–wall collision force in the outer region is consistently higher than that in the inner region in the bend [51]. The corresponding vibration response was generated from both the solid particle–wall interactions and the background

Multi-scale analyses of particle–wall impingement behaviours by the VMD method

Time-frequency and detailed frequency analyses have confirmed the particle collision characteristic frequencies to be within 30–50 kHz. Therefore, further empirical modal analysis was performed to characterize the particle–wall collision behaviour at multiple scales in the above frequency band. The time scales were self-adaptively decomposed by the EMD method across the whole frequency band of 0–50 kHz; therefore, the special VMD method was proposed for the multi-scale identification of

Multi-scale evaluation of the identified solid particles from two sensors

The two-sensor system is a redundant scheme with the advantage of being able to collect data from another sensor if one sensor fails. The system also enables the data to be verified and errors (such as poor sensitivity and failed installation) to be located. Typical digital bandpass filters for the multi-scale frequency bandwidths of 30–50 kHz and 40–50 kHz (the macro-scale bandwidths obtained by the time–frequency method), 40–42 kHz (the micro-scale bandwidth obtained by the VMD method) and

Solid particle quantitative characterization model

During the transport of particles within the solid particle-oil two-phase flow, particle–wall collision behaviours more easily occur near bends in the pipe. The detected vibration energy is affected by many flow parameters, such as the flow regime, fluid viscosity, operating pressure, flow velocity, pipe features (material, diameter, and schedule), particle features (size, shape, and density), and sensor-wall coupling type. In this paper, the flow regime, pressure, and pipe features were

Conclusions

In this paper, dispersed solid particles within an oil-conveying pipe flow were characterized at multiple scales based on the identified particle–wall collision vibration behaviours. A series of multi-scale methods was developed to identify and quantitatively characterize the solid particles inside the pipe flow using two sensors. Particle-wall collision experiments both within a water cylinder and within oil pipe flow were performed to evaluate the two-vibration sensor method. The preliminary

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This paper was supported by the Shandong Provincial Natural Science Foundation (ZR2017BEE060) and the Fundamental Research Funds for the Central Universities (17CX02011A).

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