Three-phase Flow Research Articles

Bubble rising and interaction in ternary fluid flow: a phase field study.

Bubble-droplet interaction is essential in the gas-flotation technique employed in wastewater treatment. However, due to the limitations of experimental methods, the details of the fluid flow involved have not been fully understood. Therefore, a phase field model for a three-phase flow was developed to study the rise of a single bubble and bubble-droplet interactions. The fluid-fluid interfaces are tracked by the Cahn-Hilliard equation, which is coupled with the Navier-Stokes equations with an equivalent volumetric force substituted for interfacial tensions. The model was discretized using an explicit finite difference method on a half staggered grid, and the pressure velocity coupling was tackled using the projection method. The in-house code was written in Fortran and run with the help of OpenMP, a shared memory parallelism. The model was validated against experiments with gratifying agreement achieved. Bubble-droplet interaction was simulated in two distinct situations: the first features a gas bubble crossing the interface between two other phases, and the second features a gas bubble chasing from behind an oil droplet in a surrounding fluid of the third phase.

Pressure relaxation in some multiphase flow models

We consider in this paper multiphase flow models involving two, three or four fields, in total mechanical and thermodynamical disequilibrium. Thus several pressure fields arise, and we precisely focus here on the pressure relaxation process, while restricting to four distinct multiphase flow models. The first two models only involve immiscible compressible components, while the last two hybrid models involve both miscible and immiscible components. It is shown that some -weak- restrictions may occur on pressure gaps, which are unlikely to appear in practice. Evenmore, three-phase flow models may involve a non-monotone behaviour in the return to pressure equilibrium.

Capillary washboarding during slow drainage of a frictional fluid.

Numerous natural and industrial processes involve the mixed displacement of liquids, gases and granular materials through confining structures. However, understanding such three-phase flows remains a formidable challenge, despite their tremendous economic and environmental impact. To unveil the complex interplay of capillary and granular stresses in such flows, we consider here a model configuration where a frictional fluid (an immersed sedimented granular layer) is slowly drained out of a horizontal capillary. Analyzing how liquid/air menisci displace particles from such granular beds, we reveal various drainage patterns, notably the periodic formation of dunes, analogous to road washboard instability. Considering the competitive role of friction and capillarity, a 2D theoretical approach supported by numerical simulations of a meniscus bulldozing a front of particles provides quantitative criteria for the emergence of those dunes. A key element is the strong increase of the frictional forces, as the bulldozed particles accumulate and bend the meniscus horizontally. Interestingly, this frictional enhancement with the attack angle is also crucial in small-legged animals' locomotion over granular media.

Machine Learning and Data-Driven Modeling to Discover the Bed Expansion Ratio Correlation for Gas–Liquid–Solid Three-Phase Flows

Machine Learning and Data-Driven Modeling to Discover the Bed Expansion Ratio Correlation for Gas–Liquid–Solid Three-Phase Flows

A mixture of probabilistic predictable feature analysis for multi-mode dynamic process monitoring

In modern industrial processes, the demand for safety and reliability is increasingly prioritized, spawning quantities of related research on process monitoring models. It is significant for process monitoring to consider multi-mode operating conditions simultaneously. This work proposes an efficient method based on multi-mode probabilistic predictable feature analysis (MPPFA) for complex industrial process monitoring. A strategy combining deep auto-encoder (DAE) and Gaussian mixture model (GMM) is first designed to extract low-dimensional features and identify possible running modes. In line with the obtained features, original training samples are classified into corresponding Gaussian distributions with reasonable probabilities. Further, local PPFA models are established based on the separated training batches. Five monitoring statistics, including TP2, SPEP, and DIP for PPFAs, TD2 and SPED for DAE, are defined to detect abnormalities. The proposed method is first applied to a three-phase flow facility, and its superiority over comparison methods has been verified. The effectiveness of the proposed method is further demonstrated through an experiment on a practical coal pulverising system.

Application of Three-Phase Power Flow Analysis to the Nigerian Distribution Networks

Single-phase power flow analysis is used to study most distribution networks in Nigeria. The use of single-phase-power flow analysis assumes that the network is balanced and that the conductor phases act identically. However, Nigerian distribution networks are highly imbalanced because of untransposed lines, irregularly distributed loads in conductor phases, mismatched conductor sizes, and spacing. Consequently, single-phase modeling of the networks fails to reflect actual network behavior, resulting in an incorrect power flow solution. This research presents the three-phase modeling of radial distribution networks for a three-phase-power flow study of Nigerian distribution networks. Olusanya's 54-bus and Ajinde's 62-bus distribution networks in Nigeria were evaluated, both of which were very imbalanced. Without making any assumptions about the network components, these two distribution networks were properly modeled. Each network's three-phase power flow study was carried out in the MATLAB environment. The power flow solutions for each network demonstrated unevenness in the voltage profile for each network phase, as well as inequality in the real and reactive power losses in each phase, indicating that the deployed three-phase-power flow analysis properly mirrored the underlying network characteristics. Therefore, applying three-phase power flow analysis to distribution networks is critical for proper assessment of distribution network performance.

A local–global transformer for distributed monitoring of multi-unit nonlinear processes

Nonlinear modeling of modern industrial processes with multi-unit, large-scale characteristics is very challenging. Centralized modeling involving all process variables at a time may neglect local behaviors. And most local–global modeling methods tend to ignore the correlation between units. To preserve the intra-unit information and inter-unit correlation, this paper proposes a local–global transformer (LGT) for distributed process monitoring. First, the local representation of each unit is extracted based on feedforward neural networks (FNN). Considering that the units have a fixed order in the process, the designed orthogonal positional encoding (OPE) is added to the local representation to obtain the token of each unit, which also enhances the local behaviors. Then the attention mechanism in the transformer can adaptively adjust the attention to different units and learn the inter-unit correlation from the tokens to extract global features. Finally, the distributed monitoring framework and the variable contribution rate are combined to achieve fault detection and location. The proposed LGT demonstrates the feasibility through a numerical simulation. Extensive experimental results on Tennessee Eastman (TE) process and three-phase flow (TPF) process show the superiority of LGT. The source code of LGT can be found in https://github.com/YiQian-137/Local--global-transformer.

Low-Coordinated Pd Site within Amorphous Palladium Selenide for Active, Selective, and Stable H2 O2 Electrosynthesis.

The development of high-performance catalysts with high activity, selectivity, and stability are essential for the practical applications of H2 O2 electrosynthesis technology, but it is still formidably challenging. It is reported that the low-coordinated structure of Pd sites in amorphous PdSe2 nanoparticles (a-PdSe2 NPs) can significantly boost the electrocatalytic synthesis of H2 O2 . Detailed investigations and theoretical calculations reveal that the disordered arrangement of Pd atoms in a-PdSe2 NPs can promote the activity, while the Pd sites with low-coordinated environment can optimize the adsorption toward oxygenated intermediate and suppress the cleavage of O-O bond, leading to a significant enhancement in both the H2 O2 selectivity and productivity. Impressively, a-PdSe2 NPs/C exhibits high H2 O2 selectivity over 90% in different pH electrolytes. H2 O2 productivities with ≈3245.7, 1725.5, and 2242.1mmol gPd -1 h-1 in 0.1m KOH, 0.1m HClO4 , and 0.1m Na2 SO4 can be achieved, respectively, in an H-cell electrolyzer, being a pH-universal catalyst for H2 O2 electrochemical synthesis. Furthermore, the produced H2 O2 can reach 1081.8ppm in a three-phase flow cell reactor after 2h enrichment in 0.1m Na2 SO4 , showing the great potential of a-PdSe2 NPs/C for practical H2 O2 electrosynthesis.

Discrimination method of low-current grounding fault of primary and secondary integrated equipment under three-phase asymmetric harmonic power flow calculation

In order to realize the accurate judgment of the ground fault and improve the fault discrimination effect, this paper proposes a low-current ground fault discrimination method for the primary and secondary fusion complete sets of equipment under the calculation of three-phase asymmetric harmonic power flow. The three-phase asymmetric harmonic power flow calculation is carried out, the ground fault line selection model is constructed according to the calculation results, and the faulted line is obtained by the zero-sequence active component method and the zero-sequence reactive power component method; the wavelet packet transform method is used to extract the transient zero-sequence power direction, and use it as a line selection criterion to identify whether a ground fault occurs. The amplitude characteristic enhancement value of each section is obtained by calculation. According to the distribution characteristics of the zero-sequence current amplitude of the faulted feeder, the corresponding section is selected as the fault section, and the mutation logic array is used in the determined fault section to realize the low-current grounding fault judgment. The experimental results show that the method has high judgment accuracy in practical application, and the highest value is 98.5 %, which indicates that the method can accurately judge the fault line and determine whether ground fault occurs.

Hydrodynamic characteristics of liquid–liquid–liquid three-phase flow in a confined microchannel

Numerical simulations have been performed to reveal the hydrodynamic characteristics of liquid–liquid–liquid three-phase flow in a confined microchannel via a VOF-CSF model. Further the effects of outer phase flowrate, dimensions, the viscosities of all three phases as well as the interfacial tensions of both inner and outer interfaces are systematically investigated. It is found that the shear stress and pressure gradient together determine the formation and disappearance of vortices inside the compound droplets. The internal fluid velocity of compound droplets is significantly altered by the flowrate and viscosity, while the effect of interfacial tension can be ignored. As for the vorticity distribution inside the compound droplets, it exhibits a positive correlation with the capillary number of outer phase. Besides, a prediction correlation for the average velocity of compound droplets with several dimensionless numbers is also established with good precision. The results obtained in this study could provide meaningful theoretical guidance for rational design and regulation of transport behaviors with liquid–liquid–liquid three-phase flow in a confined microchannel.

In-line measurement of multiphase flow viscosity

The transportation modes depend entirely on the viscosity of the oil. To date, none of the viscometric methods are able to provide measurements to meet all the requirements of oil flow, features of main oil pipelines, and trends in the oil industry, such as decarbonization and digitalization. The method of inline viscosity measurement of multiphase flow through a metal pipeline can be based on direct gamma ray measurement. It is stipulated by the ability of gamma-radiation to penetrate through the pipeline material without destroying it, as well as by the ability to work with flows containing free gas and the high capability to be introduced into automatic control systems. The authors consider the physical forces acting on the gas inclusions in the oil flow. They determine the physical dependence between the parameters determined by the radioisotope method and the viscosity of oil in the three-phase flow. These studies show good agreement with the work of other scientists. The prospect of further research will be to clarify the mathematical model of gas-oil flow, to increase the accuracy by reducing the number of assumptions made.

Pore-scale study of three-phase reactive transport processes in porous media

Coupled three-phase flow and reactive transport processes are widely encountered in many scientific and engineering problems. In the present study, a pore-scale model based on the lattice Boltzmann method is developed to simulate coupled three-phase flow and reactive transport processes. The model is validated by contact angle test of droplets on a curved surface and confined reactive mass transport in a three-phase system. The pore-scale model validated is then employed to study the three-phase reactive transport in channels and porous media. The evolution of the three-phase distribution, the concentration field, and the contact line length are discussed in detail. For a two-channel structure, the result shows that as the viscosity ratio increases, the phase with higher viscosity is more difficult to be displaced. Moreover, as the surface tension force between two certain phases increases, the third phase tends to form a film between the two phases, thus suppressing the reactive transport between the two phases. Finally, pore-scale simulation results of three-phase flow in a two-dimensional porous medium show that as viscosity of the phase to be displaced increases, the recovery rate of the displaced phase decreases, and the displacing phase tends to follow the mechanism of viscous fingering. Finally, while the viscosity of the displaced phase can be reduced due to the existence of the species, the recovery rate does not necessarily increase and sometimes even reduces due to the combined bypass and lubrication effects.

Experimental study of the critical sand starting velocity of gas-water-sand flow in an inclined pipe

The purpose of this paper is to study the critical sand starting velocity and transformation law of flow pattern based on gas–water–sand three-phase flow in an inclined pipe. Firstly, the indoor simulation experiment system of gas–water–sand three-phase flow was used to test the conversion law of flow pattern based upon the different gas void fraction. Secondly, the influence of slug bubbles on sand migration was investigated according to distinctive hole deviation angles, gas void fraction and sand concentration. Finally, the critical sand starting velocity was tested based on dissimilar hole deviation angles, gas void fraction, sand concentration and sand particle size, and then the influence of the above-mentioned key parameters on the sand starting velocity was debated based on the force analysis of the sand particles. The experimental results illustrated that when the gas void fraction was less than 5%, it was bubbly flow. When it increased from 5% to 30%, the bubbly flow and slug flow coexisted. When it was between 30% and 50%, the slug flow and agitated flow coexisted. When it reached 50%, it was agitated flow. Providing that the hole deviation angle was 90°, the phenomenon of overall migration and wave-like migration on the surface of sand bed was observed. On the contrary, the phenomenon of rolling and jumping migration was recognized. The critical sand starting velocity was positively correlated with the hole deviation angle and sand particle size, but negatively associated with the gas void fraction and sand concentration. This research can provide a certain reference for sand-starting production in the field of petroleum engineering.

A new calculation method and model of hydrate slurry flow of the multiphase pipeline in deep water gas field

The transportation environment of multiphase pipelines in deepwater gas fields is likely to cause the problem of hydrate flow safety. Aiming at the gas-liquid-solid three-phase flow problem containing hydrate, a hydrate slurry flow model for a multiphase pipeline in a deep-water gas field was developed based on the two-fluid model coupled with the population balance equation, and a mesh was carried out for the axial distance of pipeline and size difference of hydrate particles to obtain a transient solution. The multiphase flow characteristics of the pipeline are simulated upon engineering scale, the transient flow characteristics of gas and liquid phases, the aggregation and fragmentation characteristics of hydrate particles, and the coupling interaction between them were studied, which lays the foundation for further research on the characteristics of hydrate particle deposition and blockage based on particle size distribution. This study provides support for the safety of hydrate flow in multiphase pipelines in deepwater gas fields.

Development of resolved CFD–DEM coupling model for three-phase flows with non-spherical particles

In this work, a resolved CFD–DEM coupling model for gas–liquid-solid three-phase flows with non-spherical particles is developed where the shape of the particle is implicitly captured by a superquadric function. Both gas–liquid and fluid–solid interfaces are smoothly represented with a specified thickness so that the interface thicknesses and CFD cell size are independent of each other. Several sensitivity studies are carried out and criteria for mesh- and thickness-independent results are proposed. It is confirmed that the proposed model can properly predict the hydrodynamic and capillary forces acting on particles with a wide range of shapes and contact angles. Finally, the model proposed is applied to perform several virtual experiments of typical chemical engineering processes: a liquid–solid fluidised bed and bubbly flow with various particle shapes. It is found that particle shape can have a significant impact on the fluid-particle interactions and resultant particle movement, leading to segregation and preferential alignment.

Numerical Simulation of Phase Transitions in Porous Media with Three-Phase Flows Considering Steam Injection into the Oil Reservoir

This study focuses on the analysis of an approach to the simulation of the phase transition in porous media when hot steam is injected into the oil reservoir. The reservoir is assumed to consist of a porous medium with homogeneous thermal properties. Its porous space is filled with a three-phase mixture of steam, water, and oil. The problem is considered in a non-stationary and non-isothermal formulation. Each phase is considered to be incompressible, with constant thermal properties, except for the dynamic viscosity of oil, which depends on the temperature. The 1D mathematical model of filtration, taking into account the phase transition, consists of continuity, Darcy, and energy equations. Steam injection and oil production in the model are conducted via vertical or horizontal wells. In the case of horizontal wells, the influence of gravity is also taken into account. The Lee model is used to simulate the phase transition between steam and water. The convective terms in the balance equations are calculated without accounting for artificial diffusion. Spatial discretization of the 1D domain is carried out using the finite volume method, and time discretization is implemented using the inverse (implicit) Euler scheme. The proposed model is analyzed in terms of the accuracy of the phase transition simulation for various sets of independent phases and combinations of continuity equations. In addition, we study the sensitivity of the model to the selected independent phases, to the time step and spatial mesh parameters, and to the intensity of the phase transition. The obtained results allow us to formulate recommendations for simulations of the phase transition using the Lee model.

Sand settling in a three-phase flow inside a horizontal separator

Sand particles in multiphase flows have been a major problem in the oil and gas industry, with many recent reports of failures in equipment due to erosion from solid particles. Horizontal separators have proven to be one of the most effective methods for sand removal especially the design developed by Specialized Desanders Inc., this study will analyze the sand separation in a three-phase flow from two angles. First, by applying multiphase numerical analysis using Star CCM+ software. Experimental testing with the three-phase flow (air, water, and sand) was performed and compared to the numerical results. Both the experimental and the simulation results have shown that 99% of sand has settled within 54% of the Desander length. Second, an analytical model was also performed to analyze the forces acting on the sand particles ( d = 150 µm and 300 µm) in a simplified matter to solve particle equations of motion in each phase the particle transits. The analytical model showed both particle sizes did not reach terminal velocity in the gas phase. Both particles reached terminal velocity in the liquid phase, the particles trajectories become linear until it hits the bottom of the separator. These sand trajectories give an insight into where to expect the sand particle to settle inside the Desander. Both methods are very useful and insightful for future analysis and design optimization when the properties of the fluid change with the change of the operating condition.

Analysis of the flow pattern and periodicity of gas–liquid–liquid three-phase flow in a countercurrent mixer-settler

In contrast to the concurrent mixer-settler, the interaction between the mixing and settling chambers have to be taken into account in the simulation of the countercurrent mixer-settler, and no work has been reported for this equipment. In this work, a three-phase flow model based on the Eulerian multiphase model, coupled with a sliding mesh model is proposed for a countercurrent mixer-settler. Based on this, the dispersed phase distribution, flow pattern, and pressure distribution are investigated, which can help to fill the gap in the operation mechanism. In addition, the velocity vector distribution at the phase port shows an intriguing phenomenon that two types of vectors with opposite directions are distributed on the left and right sides of the same plane, which indicates that the material exchange in the mixing and settling chambers is simultaneous. Analysis of this variation at this location by a fast Fourier transform (FFT) method reveals that it is mainly influenced by the mixing chamber and is consistent with the main period of the outlet flow fluctuations. Therefore, by monitoring the fluctuation of the outlet flow and then analyzing it by the FFT method, the state of the whole tank can be determined, which makes it promising for the design of control systems for countercurrent mixer-settlers.

Using OPF-Based Operating Envelopes to Facilitate Residential DER Services

The proliferation of residential distributed energy resources (DER), such as solar PV and batteries, is creating opportunities for DER owners to provide system-level services through aggregators. However, if this aggregated response is not adequately managed by distribution companies, the simultaneous active power exports (or imports) can result in voltages and currents well beyond the limits of their networks. But the big barrier is that, often, distribution companies cannot directly manage DER or aggregators. This work proposes the use of operating envelopes—time-varying, meter-level export/import limits that a distribution company issues to aggregators—to ensure network integrity while facilitating residential DER services. The operating envelopes are calculated using a linearised, three-phase optimal power flow (OPF) technique that also exploits controllable network assets (e.g., on-load tap changers). Using a realistic Australian MV-LV network with 4,600+ residential customers, results show that network integrity can be ensured without the need for distribution companies to directly control DER. Furthermore, existing on-load tap changers create additional voltage headroom and, thus, larger operating envelopes (and potential services). Given that distribution companies do not know the ultimate exports/imports of customers providing services, a probabilistic testing of the operating envelopes confirms that they are adequate for most plausible scenarios.

Resilient Distribution Networks by Microgrid Formation Using Deep Reinforcement Learning

Resilience becomes vital for power grids facing the increasingly frequent extreme weather events. Microgrid formation is a promising way to achieve resilient distribution networks (RDN) when the utility power is unavailable. This paper proposes a RDN-oriented microgrid formation (RoMF) method based on the deep reinforcement learning (DRL) technique, which integrates the OpenDSS as an interaction object and searches for optimal control policies in a model-free fashion. Specifically, we formulate the microgrid formation problem as a Markov decision process, taking into account complex factors such as unbalanced three-phase power flow and microgrid operation constraints. Next, a simulator-based RoMF environment is constructed and integrated into the OpenAI Gym, providing a standard agent-environment interface for applying DRL algorithms. Then, the deep Q-network is used to search for optimal microgrid formation strategies, and an offline-training and online-application framework of the DRL-based RoMF is given. Finally, extensive numerical results validate the effectiveness of our proposed method.