Measurement of oil fraction in oil-water dispersed flow with swept-frequency ultrasound attenuation method

Highlights

• A swept-frequency ultrasound attenuation method based on droplet size estimation is proposed to measure oil fraction.

• An ultrasonic attenuation model considering the absorption and scattering attenuation is established.

• A chirp-based detection method is developed to quickly measure the ultrasonic attenuation of multiple frequencies.

• Trust region algorithm combined with Gaussian QPSO is proposed for inversion calculation of phase fraction.

Abstract

It is very meaningful to measure the oil fraction of oil-water dispersed flow in pipelines. Traditional single-frequency ultrasonic methods measure the oil fraction by treating the dispersed flow with an average droplet size, which ignores the influence of the droplet size distribution and limits the measurement accuracy. Therefore, a swept-frequency ultrasound attenuation method based on droplet size distribution is proposed for the measurement of oil fraction. According to the characteristics of similar physical parameters and large droplet size of oil-water two phases, the Bouguer-Lambert-Beer's Law and McClements model are combined to predict ultrasonic attenuation in the oil-water dispersed flow, considering the attenuation effects of absorption and scattering. Due to the time-varying characteristic of the oil-water two-phase flow state, the chirp-based detection method is proposed to quickly measure the ultrasonic attenuation of multiple frequencies. For the nonlinear problem of ultrasonic attenuation response, trust region algorithm combined with Gaussian quantum particle swarm optimization is proposed for inversion calculation of oil fraction. Finally, the effectiveness of the ultrasonic attenuation mechanism model and inversion algorithm is verified by simulation and numerical calculation, and the experiments are carried out in the test device for liquid-liquid two-phase flow. The experimental results show that the proposed method can measure the oil fraction of oil-water dispersed flow with an average error less than 1.67% and a maximum error less than 3.57%.

Introduction

When the oil field enters the middle and later stage of exploitation, the water content of crude oil increases significantly, usually between 70% and 80%, even to 90%. Accurate measurement for oil fraction of the oil-water dispersed flow is of great significance for predicting remaining productivity, ensuring the safety of oil production and transportation, and studying the flow characteristics of two-phase flow in the petroleum industry (Salim et al., 2008). However, due to the similar physical properties of oil-water two-phase and the unstable and random flow characteristics of the oil-water flow process, it is difficult to measure the oil fraction accurately (Angeli and Hewitt, 2000).

At present, the main measurement methods for phase fraction of the dispersed flow are quick closing valve method (Oddie et al., 2003), sedimentation method (Yoshida et al., 2001), radiation method (Kastengren et al., 2017), electrical method (Yan et al., 2017), optical-based diffraction and scattering measurement method (Dumouchel et al., 2009) and ultrasonic method (Su et al., 2017). The quick closing valve method and the sedimentation method are only used for off-line measurement conditions due to the measuring principle. The radiation method has high requirements for safety protection and measurement conditions, which makes it not suitable for use in industrial sites. Although the electrical method is simple in structure and fast in measurement, it needs to take the flow pattern or phase distribution as a priori information, which is very sensitive to the phase distribution state and flow pattern. Optical-based diffraction and scattering measurement methods can realize on-line measurement, but they are limited by light penetration. Ultrasonic method not only requires a lower measurement environment and conditions than optical method, but also has the advantage of non-invasive.

The ultrasonic attenuation obtained by ultrasonic transmission of the dispersion flow contains abundant fluid information, which can be used to measure the phase fraction. Yang carried out an experimental study on the particle concentration measurement of micron glass bead-glycerol suspension and aqueous polystyrene suspension with ultrasonic attenuation spectroscopy (Yang et al., 2016). Inoue studied the effect of temperature on ultrasonic attenuation and used attenuation spectroscopy to detect the particle size distribution of micron-sized gel particles dispersed in water (Inoue et al., 2018). Huang used Monte Carlo method to establish the characterization model of sub-micron particle size in the dispersion system, and predicted the ultrasonic attenuation of different particle size distribution by numerical calculation (Huang et al., 2019). Through the above research, it can be known that the particle size distribution is obtained by using multi-frequency attenuation information, so that the phase fraction of the dispersion system can be measured more accurately than the methods based on average particle size (Su et al., 2017, 2018). However, most studies are mainly focused on the dispersed flow with small particle size and large difference in physical parameters, while there is a lack of research on the dispersed flow with large particle size and similar physical parameters.

For different dispersion systems, the commonly used models of ultrasonic attenuation mechanism are the ECAH (Epstein-Carhart-Allegra-Hawley) model (Allegra and Hawley, 1971; Epstein and Carhart, 1953), BLBL (Bouguer-Lambert-Beer's Law) model (Riebel and Löffler, 1989), McClements model (McClements et al., 1998), HT (Harker & Temple) model (Harker and Temple, 1988) and so on. ECAH model is suitable to solve the dispersion flow with small particle size, where the wave length is far larger than the particle size, because it mainly considers the attenuation effect including the visco-inertial and thermal interaction of the dispersions. Waterman and Lloyd et al. improved the ECAH model by considering multiple scattering respectively (Lloyd and Berry, 1967; Waterman and Truell, 1961). The theory of ECAH model is complex, and it requires many physical parameters of the measured fluid, so it is difficult to be applied in practice. McClements and Povey et al. studied the simplified theoretical model of ultrasonic attenuation for dispersed systems with small density difference between dispersed and continuous phases considering the heat loss effect (McClements et al., 1998; Povey, 1997). Y. Hemar et al. considered the effect of the thermal wave overlap around the dispersed phase and established Core-Shell model (Hemar et al., 1997), but Core-Shell model is more complex than ECAH model, and it is also difficult to be applied in practice. A coupled phase model, including HT model and other related models (Dukhin and Goetz, 1996; Harker and Temple, 1988) was established to explain the ultrasonic attenuation based on hydrodynamics. Although the coupled phase model is a relatively mature theory, it is mainly suitable for dispersion systems with high density difference between two phases. Most of the above models are suitable for dispersed systems with small size of dispersed phase. For dispersed systems with large dispersed phase size, Rieble established a BLBL model (Riebel and Löffler, 1989) to explain the ultrasonic attenuation, which considered the acoustic energy loss caused by scattering. According to the characteristics of the oil-water dispersed flow with large droplet size and similar physical parameters, the BLBL scattering model combined with McClements absorption model is developed for prediction of ultrasonic attenuation in this paper.

The inversion problem of oil fraction based on ultrasonic attenuation model can be transformed into the solution of Fredholm integral equation of the first kind, which is an ill-posed problem. The commonly used inversion algorithms are regularization methods, such as L₁-norm regularization (Xu et al., 2012), Tikhonov (Ayme-Bellegarda and Habashy, 1992), truncated singular value decomposition (TSVD) (Zhang et al., 2019). The regularization algorithms are vulnerable to the impact of regularization parameter selection, which directly affect the accuracy of the inversion results; At the same time, the algorithms are linear inversion theories, which are not suitable for inversion calculation of oil fraction due to the nonlinear response of ultrasonic attenuation. In fact, the major goal of phase fraction inversion is to find an optimal value of a function of several variables, which can explain the observations of ultrasonic attenuation. Thus, the inversion problem can be transformed into a mathematical optimization problem. Therefore, trust region (TR) algorithm (Chen et al., 2018) combined with Gaussian quantum particle swarm optimization (GQPSO) (Tharwat and Hassanien, 2019) is proposed for inversion calculation of oil fraction in this paper. The function form of the problem to be optimized is close to the quadratic function in a small neighborhood. The TR method uses the quadratic model to approximate the original objective function, which can simply replace the linear search and solve the problem of the indefiniteness of Hessian matrix. However, the inversion result of the TR algorithm depends on the selection of the initial value. If the deviation between the initial value and the optimal value is too large, it is difficult to obtain the optimal value in the iterative process. Therefore, GQPSO is adopted to get the value which is close to the optimal value. Then, the result of GQPSO is used as the initial value of TR algorithm to get final inversion results.

According to the characteristics of the oil-water dispersed flow with large droplet size and similar physical parameters, the multi-frequency ultrasound attenuation method is proposed for the oil-water dispersed flow to measure the oil fraction in this paper. The BLBL model combined with McClements model is developed for prediction of ultrasonic attenuation based on the droplet size distribution; And the TR algorithm combined with GQPSO is proposed for inversion calculation of oil fraction based on the measured attenuation.

The remainder of this paper is organized as follows. Section 2 establishes the attenuation prediction model for the ultrasonic propagation in the dispersed flow, and details the inversion algorithm for the oil fraction. Section 3 presents relevant simulations, numerical analysis and experimental results demonstrating the effectiveness of the proposed method. Finally, Section 4 discusses conclusions and future extensions of this work.