Numerical simulation on the multiphase flow and reoxidation of the molten steel in a two-strand tundish during ladle change

A 3D mathematical model was proposed to investigate the molten steel–slag–air multiphase flow in a two-strand slab continuous casting(CC)tundish during ladle change.The study focused on the exposure of the molten steel and the subsequent reoxidation occurrence.The exposure of the molten steel was calculated using the coupled realizable k–εmodel and volume of fluid(VOF)model.The diffusion of dissolved oxygen was determined by solving the user-defined scalar(UDS)equation.Moreover,the user-defined function(UDF)was used to describe the source term in the UDS equation and determine the oxidation rate and oxidation position.The effect of the refilling speed on the molten steel exposure and dissolved oxygen content was also discussed.Increasing the refilling speed during ladle change reduced the refilling time and the exposure duration of the molten steel.However,the elevated refilling speed enlarged the slag eyes and increased the average dissolved oxygen content within the tundish,thereby exacerbating the reoxidation phenomenon.In addition,the time required for the molten steel with a high dissolved oxygen content to exit the tundish varied with the refilling speed.When the inlet speed was 3.0 m·s^(-1)during ladle change,the molten steel with a high dissolved oxygen content exited the outlet in a short period,reaching a maximum dissolved oxygen content of 0.000525wt%.Conversely,when the inlet speed was 1.8 m·s^(-1),the maximum dissolved oxygen content was 0.000382wt%.The refilling speed during the ladle change process must be appropriately decreased to minimize reoxidation effects and enhance the steel product quality.

A transient production prediction method for tight condensate gas wells with multiphase flow

Considering the phase behaviors in condensate gas reservoirs and the oil-gas two-phase linear flow and boundary-dominated flow in the reservoir,a method for predicting the relationship between oil saturation and pressure in the full-path of tight condensate gas well is proposed,and a model for predicting the transient production from tight condensate gas wells with multiphase flow is established.The research indicates that the relationship curve between condensate oil saturation and pressure is crucial for calculating the pseudo-pressure.In the early stage of production or in areas far from the wellbore with high reservoir pressure,the condensate oil saturation can be calculated using early-stage production dynamic data through material balance models.In the late stage of production or in areas close to the wellbore with low reservoir pressure,the condensate oil saturation can be calculated using the data of constant composition expansion test.In the middle stages of production or when reservoir pressure is at an intermediate level,the data obtained from the previous two stages can be interpolated to form a complete full-path relationship curve between oil saturation and pressure.Through simulation and field application,the new method is verified to be reliable and practical.It can be applied for prediction of middle-stage and late-stage production of tight condensate gas wells and assessment of single-well recoverable reserves.

A new interacting capillary bundle model on the multiphase flow in micropores of tight rocks

Surfactants are widely used in the fracturing fluid to enhance the imbibition and thus the oil recovery rate. However, current numerical models cannot capture the physics behind capillary imbibition during the wettability alteration by surfactants. Although the interacting capillary bundle(ICB) model shows potential in characterizing imbibition rates in different pores during wettability alteration, the existing ICB models neglect the influence of wettability and viscosity ratio on the imbibition behavior, making it difficult to accurately describe the oil-water imbibition behavior within the porous media. In this work,a new ICB mathematical model is established by introducing pressure balance without assuming the position of the leading front to comprehensively describe the imbibition behavior in a porous medium under different conditions, including gas-liquid spontaneous imbibition and oil-water imbibition.When the pore size distribution of a tight rock is known, this new model can predict the changes of water saturation during the displacement process in the tight rock, and also determine the imbibition rate in pores of different sizes. The water saturation profiles obtained from the new model are validated against the waterflooding simulation results from the CMG, while the imbibition rates calculated by the model are validated against the experimental observations of gas-liquid spontaneous imbibition. The good match above indicates the newly proposed model can show the water saturation profile at a macroscopic scale while capture the underlying physics of the multiphase flow in a porous medium at a microscopic scale. Simulation results obtained from this model indicate that both wettability and viscosity ratio can affect the sequence of fluid imbibition into pores of different sizes during the multiphase flow, where less-viscous wetting fluid is preferentially imbibed into larger pores while more-viscous wetting fluid tends to be imbibed into smaller pores. Furthermore, this model provides an avenue to calculate the imbibition rate in pores of different sizes during wettability alteration and capture the non-Darcy effect in micro-and nano-scale pores.

A semi-analytical rate-transient analysis model for light oil reservoirs exhibiting reservoir heterogeneity and multiphase flow

Rate-transient analysis(RTA)has been widely applied to extract estimates of reservoir/hydraulic fracture properties.However,the majority of RTA techniques can lead to misdiagnosis of reservoir/fracture information when the reservoir exhibits reservoir heterogeneity and multiphase flow simultaneously.This work proposes a practical-yet-rigorous method to decouple the effects of reservoir heterogeneity and multiphase flow during TLF,and improve the evaluation of reservoir/fracture properties.A new,general,semi-analytical model is proposed that explicitly accounts for multiphase flow,fractalbased reservoir heterogeneity,anomalous diffusion,and pressure-dependent fluid properties.This is achieved by introducing a new Boltzmann-type transformation,the exponent of which includes reservoir heterogeneity and anomalous diffusion.In order to decouple the effects of reservoir heterogeneity and multiphase flow during TLF,the modified Boltzmann variable allows the conversion of three partial differential equations(PDE's)(i.e.,oil,gas and water diffusion equations)into ordinary differential equations(ODE's)that are easily solved using the Runge-Kutta(RK)method.A modified time-power-law plot is also proposed to estimate the reservoir and fracture properties,recognizing that the classical square-root-of-time-plot is no longer valid when various reservoir complexities are exhibited simultaneously.Using the slope of the straight line on the modified time-power-law plot,the linear flow parameter can be estimated with more confidence.Moreover,because of the new Boltzmann-type transformation,reservoir and fracture properties can be derived more efficiently without the need for defining complex pseudo-variable transformations.Using the new semi-analytical model,the effects of multiphase flow,reservoir heterogeneity and anomalous diffusion on rate-decline behavior are evaluated.For the case of approximately constant flowing pressure,multiphase flow impacts initial oil rate,which is a function of oil relative permeability and well flowing pressure.However,multiphase flow has a minor effect on the oil production decline exponent.Reservoir heterogeneity/anomalous diffusion affect both the initial oil production rate and production decline exponent.The production decline exponent constant is a function of reservoir heterogeneity/anomalous diffusion only.The practical significance of this work is the advancement of RTA techniques to allow for more complex reservoir scenarios,leading to more accurate production forecasting and better-informed capital planning.

Exploration of the coupled lattice Boltzmann model based on a multiphase field model:A study of the solid-liquid-gas interaction mechanism in the solidification process

A multiphase field model coupled with a lattice Boltzmann(PF-LBM)model is proposed to simulate the distribution mechanism of bubbles and solutes at the solid-liquid interface,the interaction between dendrites and bubbles,and the effects of different temperatures,anisotropic strengths and tilting angles on the solidified organization of the SCN-0.24wt.%butanedinitrile alloy during the solidification process.The model adopts a multiphase field model to simulate the growth of dendrites,calculates the growth motions of dendrites based on the interfacial solute equilibrium;and adopts a lattice Boltzmann model(LBM)based on the Shan-Chen multiphase flow to simulate the growth and motions of bubbles in the liquid phase,which includes the interaction between solid-liquid-gas phases.The simulation results show that during the directional growth of columnar dendrites,bubbles first precipitate out slowly at the very bottom of the dendrites,and then rise up due to the different solid-liquid densities and pressure differences.The bubbles will interact with the dendrite in the process of flow migration,such as extrusion,overflow,fusion and disappearance.In the case of wide gaps in the dendrite channels,bubbles will fuse to form larger irregular bubbles,and in the case of dense channels,bubbles will deform due to the extrusion of dendrites.In the simulated region,as the dendrites converge and diverge,the bubbles precipitate out of the dendrites by compression and diffusion,which also causes physical phenomena such as fusion and spillage of the bubbles.These results reveal the physical mechanisms of bubble nucleation,growth and kinematic evolution during solidification and interaction with dendrite growth.

Effect of gas blowing nozzle angle on multiphase flow and mass transfer during RH refining process

A three-dimensional mathematical model was developed to investigate the effect of gas blowing nozzle angles on multiphase flow,circulation flow rate,and mixing time during Ruhrstahl-Heraeus(RH) refining process.Also,a water model with a geometric scale of 1:4 from an industrial RH furnace of 260 t was built up,and measurements were carried out to validate the mathematical model.The results show that,with a conventional gas blowing nozzle and the total gas flow rate of 40 L·min^(-1),the mixing time predicted by the mathematical model agrees well with the measured values.The deviations between the model predictions and the measured values are in the range of about 1.3%–7.3% at the selected three monitoring locations,where the mixing time was defined as the required time when the dimensionless concentration is within 3% deviation from the bath averaged value.In addition,the circulation flow rate was 9 kg·s^(-1).When the gas blowing nozzle was horizontally rotated by either 30° or 45°,the circulation flow rate was found to be increased by about 15% compared to a conventional nozzle,due to the rotational flow formed in the up-snorkel.Furthermore,the mixing time at the monitoring point 1,2,and 3 was shortened by around 21.3%,28.2%,and 12.3%,respectively.With the nozzle angle of 30° and 45°,the averaged residence time of 128 bubbles in liquid was increased by around 33.3%.

Numerical simulation study on multiphase flow pattern of hydrate slurry

The research on the multiphase flow characteristics of hydrate slurry is the key to implementing the risk prevention and control technology of hydrate slurry in deep-water oil and gas mixed transportation system.This paper established a geometric model based on the high-pressure hydrate slurry experimental loop.The model was used to carry out simulation research on the flow characteristics of gas-liquid-solid three-phase flow.The specific research is as follows:Firstly,the effects of factors such as slurry flow velocity,hydrate particle density,hydrate particle size,and hydrate volume fraction on the stratified smooth flow were specifically studied.Orthogonal test obtained particle size has the most influence on the particle concentration distribution.The slurry flow velocity is gradually increased based on stratified smooth flow.Various flow patterns were observed and their characteristics were analyzed.Secondly,increasing the slurry velocity to 2 m/s could achieve the slurry flow pattern of partial hydrate in the pipeline transition from stratified smooth flow to wavy flow.When the flow rate increases to 3 m/s,a violent wave forms throughout the entire loop.Based on wave flow,as the velocity increased to 4 m/s,and the flow pattern changed to slug flow.When the particle concentration was below 10%,the increase of the concentration would aggravate the slug flow trend;if the particle concentration was above 10%,the increase of the concentration would weaken the slug flow trend,the increase of particle density and liquid viscosity would weaken the tendency of slug flow.The relationship between the pressure drop gradients of several different flow patterns is:slug flow>wave flow>stratified smooth flow.

Experimental verification of mathematical model for multiphase flow in air-agitated seed precipitation tank

In order to check the validity of the mathematical model for analyzing the flow field in the air-agitated seed precipitation tank,a scaled down experimental apparatus was designed and the colored tracer and KCl tracer were added in the apparatus to follow the real flow line.Virtue tracers were considered in the mathematical model and the algorithm of tracers was built.The comparison of the results between the experiment and numerical calculation shows that the time of the tracer flows out of stirring tube are 40 s in the experiment and 42 s in numerical calculated result.The transient diffusion process and the solution residence time of the numerical calculation are in good agreement with the experimental results,which indicates that the mathematical model is reliable and can be used to predict the flow field of the air-agitated seed precipitation tank.

A developed transient gas-liquid-solid flow model with hydrate phase transition for solid fluidization exploitation of marine natural gas hydrate reservoirs

The multiphase flow characteristic is one of the most concerning problems during solid fluidization exploitation of marine natural gas hydrate reservoirs.In this research,a new transient gas-liquid-solid multiphase flow model with hydrate phase transition was developed.Meanwhile,this model considered the coupling relationship among convective heat transfer,hydrate dynamic decomposition,and multi-phase flow.The model can simulate the change of flow pattern from solid-liquid to gas-liquid-solid flow,and describe the distribution character of volume fraction of phase,wellbore temperature and pressure,and hydrate decomposition rate during transportation.The simulation results indicate that the hydrate decomposition region in the wellbore gradually expands,but the hydrate decomposition rate gradually decreases during the solid fluidization exploitation of hydrate.When mining time lasts for 4 h,and the bottom hole pressure decreases by about 0.4 MPa.Increasing NaCl concentration in seawater helps expand hydrate decomposition regions and improves the wellbore hydrate decomposition rate.When the Nacl mass fraction in seawater reaches 15%,it will raise the hydrate decomposition regions to the whole wellbore.In addition,the higher the wellhead backpressure,the lower the decomposition area and decomposition rate of hydrate in the wellbore.When wellhead backpressure reaches 2 MPa,the volume fraction of gas near the wellhead will reduce to about 12%.This work is expected to provide a theoretical basis for the development of marine hydrate reservoirs.

Uncertainty analysis of flow rate measurement for multiphase flow using CFD

The venturi meter has an advantage in its use,because it can measure flow without being much affected by the type of the measured fluid or flow conditions.Hence,it has excellent versatility and is being widely applied in many industries.The flow of a liquid containing air is a representative example of a multiphase flow and exhibits complex flow characteristics.In particular,the greater the gas volume fraction（GVF）,the more inhomogeneous the flow becomes.As a result,using a venturi meter to measure the rate of a flow that has a high GVF generates an error.In this study,the cause of the error occurred in measuring the flow rate for the multiphase flow when using the venturi meter for analysis by CFD.To ensure the reliability of this study,the accuracy of the multiphase flow models for numerical analysis was verified through comparison between the calculated results of numerical analysis and the experimental data.As a result,the Grace model,which is a multiphase flow model established by an experiment with water and air,was confirmed to have the highest reliability.Finally,the characteristics of the internal flow Held about the multiphase flow analysis result generated by applying the Grace model were analyzed to find the cause of the uncertainty occurring when measuring the flow rate of the multiphase flow using the venturi meter.A phase separation phenomenon occurred due to a density difference of water and air inside the venturi,and flow inhomogeneity happened according to the flow velocity difference of each phase.It was confirmed that this flow inhomogeneity increased as the GVF increased due to the uncertainty of the flow measurement.

Annular multiphase flow behavior during deep water drilling and the effect of hydrate phase transition

It is very important to understand the annular multiphase flow behavior and the effect of hydrate phase transition during deep water drilling. The basic hydrodynamic models, including mass, momentum, and energy conservation equations, were established for annular flow with gas hydrate phase transition during gas kick. The behavior of annular multiphase flow with hydrate phase transition was investigated by analyzing the hydrate-forming region, the gas fraction in the fluid flowing in the annulus, pit gain, bottom hole pressure, and shut-in casing pressure. The simulation shows that it is possible to move the hydrate-forming region away from sea floor by increasing the circulation rate. The decrease in gas volume fraction in the annulus due to hydrate formation reduces pit gain, which can delay the detection of well kick and increase the risk of hydrate plugging in lines. Caution is needed when a well is monitored for gas kick at a relatively low gas production rate, because the possibility of hydrate presence is much greater than that at a relatively high production rate. The shut-in casing pressure cannot reflect the gas kick due to hydrate formation, which increases with time.

Lagrangian-based investigation of multiphase flows by finite-timeLyapunov exponents

Multiphase flows are ubiquitous in our daily life and engineering applications. It is important to investigate the flow structures to predict their dynamical behaviors ef- fectively. Lagrangian coherent structures （LCS） defined by the ridges of the finite-time Lyapunov exponent （FTLE） is utilized in this study to elucidate the multiphase interactions in gaseous jets injected into water and time-dependent turbu- lent cavitation under the framework of Navier-Stokes flow computations. For the gaseous jets injected into water, the highlighted phenomena of the jet transportation can be observed by the LCS method, including expansion, bulge, necking/breaking, and back-attack. Besides, the observation of the LCS reveals that the back-attack phenomenon arises from the fact that the injected gas has difficulties to move toward downstream re- gion after the necking/breaking. For the turbulent cavitating flow, the ridge of the FTLE field can form a LCS to capture the front and boundary of the re-entraint jet when the ad- verse pressure gradient is strong enough. It represents a bar- rier between particles trapped inside the circulation region and those moving downstream. The results indicate that the FFLE field has the potential to identify the structures of mul- tiphase flows, and the LCS can capture the interface/barrier or the vortex/circulation region.

Multiphase Flow and Wear in the Cutting Head of Ultra-high Pressure Abrasive Water Jet

Abrasive water jet cutting technology is widely applied in the materials processing today and attracts great attention from scholars, but many phenomena concerned are not well understood, especially in the internal jet flow of the cutting head at the condition of ultra-high pressure. The multiphase flow in the cutting head is numerically simulated to study the abrasive motion mechanism and wear inside the cutting head at the pressure beyond 300 MPa. Visible predictions of the particles trajectories and wear rate in the cutting head are presented. The influences of the abrasive physical properties, size of the jewel orifice and the operating pressure on the trajectories are discussed. Based on the simulation, a wear experiment is carried out under the corresponding pressures. The simulation and experimental results show that the flow in the mixing chamber is composed of the jet core zone and the disturbance zone, both affect the particles trajectories. The mixing efficiency drops with the increase of the abrasive granularity. The abrasive density determines the response of particles to the effects of different flow zones, the abrasive with medium density gives the best general performance. Increasing the operating pressure or using the jewel with a smaller orifice improves the coherency of p articles trajectories but increases the wear rate of the jewel holder at the same time. Walls of the jewel holder, the entrance of the mixing chamber and the convergence part of the mixing tube are subject to wear out. The computational and experimental results give a qualitative consistency which proves that this numerical method can provide a reliable and visible cognition of the flow characteristics of ultra-high pressure abrasive water jet. The investigation is benefit for improving the machining properties of water jet cutting systems and the optimization design of the cutting head.

Pore-scale study of the pressure-sensitive effect of sandstone and its influence on multiphase flows

The pressure-sensitive effect on the pore structure of sandstone was investigated using X-ray computed micro-tomography and QEMSCAN quantitative mineral analysis. In a physical simulation study, we extracted the pore network model from digital cores at different confining pressures and evaluated the effect of pressure sensitivity on the multiphase displacement process. In both the pore network model and QEMSCAN scanning, the pore structure was observed to be damaged under a high confining pressure. Due to their different scales, the pores and throats exhibited inhomogeneous changes; further, the throats exhibited a significant variation compared to that exhibited by the pores. Meanwhile, the heterogeneity of the pore structure under the two aforementioned activities was aggravated by the elastic-plastic deformation of the pore structure.The pressure-sensitive effect increased the proportion of mineral particles, such as quartz(the main component of the core skeleton), and reduced the proportion of clay minerals. The clay minerals were originally attached to the pore walls or interspersed in the pores; however, as the pressure increased, the clay minerals accumulated in the pores resulting in blockage of the pores. While simulating the multiphase displacement process, increasing the confining pressure was observed to severely restrict the flowability of oil and water. This study promises to improve the efficiency of reservoir development in terms of oil and gas exploitation.

DIRECT NUMERICAL SIMULATIONS OF MULTIPHASE FLOWS

Direct numerical simulations have recently emerged as a viable tool to study finite Reynolds number multiphase flows. The approach parallels direct numerical simulations of turbulent flows, but the unsteady motion of a deformable phase boundary adds considerable complexity. Here, a front tracking method that has been used to study several multiphase flow problems is described. The Navier Stokes equations are solved by a finite difference/front tracking technique that allows the inclusion of fully deformable interfaces and surface tension, in addition to inertial and viscous effects. A parallel version of the method makes it possible to use large grids and resolve flows containing a few hundred bubbles.

A pseudopotential-based multiple-relaxation-time lattice Boltzmann model for multicomponent/multiphase flows

In this paper, a pseudopotential-based multiplerelaxation-time lattice Boltzmann model is proposed for multicomponent/multiphase flow systems. Unlike previous models in the literature, the present model not only enables the study of multicomponent flows with different molecular weights, different viscosities and different Schmidt numbers, but also ensures that the distribution function of each component evolves on the same square lattice without invoking ad- ditional interpolations. Furthermore, the Chapman-Enskog analysis shows that the present model results in the correct hydrodynamic equations, and satisfies the indifferentiability principle. The numerical validation exercises further demonstrate that the favorable performance of the present model.

Advances in Studies on Turbulent Dispersed Multiphase Flows

Dispersed multiphase flows,including gas-particle(gas-solid),gas-spray,liquid-particle(liquid-solid) ,liquid-bubble,and bubble-liquid-particle flows,are widely encountered in power,chemical and metallurgical,aeronautical and astronautical,transportation,hydraulic and nuclear engineering. In this paper,advances and re-search needs in fundamental studies of dispersed multiphase flows,including the particle/droplet/bubble dynamics,particle-particle,droplet-droplet and bubble-bubble interactions,gas-particle and bubble-liquid turbulence interac-tions,particle-wall interaction,numerical simulation of dispersed multiphase flows,including Reynolds-averaged modeling(RANS modeling),large-eddy simulation(LES) and direct numerical simulation(DNS) are reviewed. The research results obtained by the present author are also included in this review.

Multiphase Flow Simulations through Tarbela Dam Spillways and Tunnels

Tarbela dam is one of the largest earth filled dam in the world used for power generation and irrigation purposes. Like all reservoirs the sediments inflow in the Tarbela reservoir has resulted in reduction in water storage capacity and is also causing damage to the tunnels, power generating units and ultimately to the plant equipment. This numerical study was performed to predict the flow patterns and characteristics in Tarbela dam. Tunnel 3 and 4 inlets;originally on the bed level were raised in the 3-D model and meshed. Analysis was performed using multiphase flow (water and air) for maximum inflow in the reservoir, i.e., considering summer season and discharging water through different locations, i.e., tunnels and spillways. Pressure, velocities, flow rate and free surface height results obtained were found in good agreement with the analytical and existing results where available. Results show uneven discharge through each gate due to maximum velocity near exits and overall stagnant phenomena of water within the reservoir. Maximum velocity was observed along the spillways outlet. Strong vortex motion was observed near the spillways outlet and tunnel inlets. New design of Tunnel 3 and 4 were suggested to WAPDA in order to decrease the sediment inflow and improvements in design of the spillways were suggested.

Characterization of multiphase gas–solid flow and accuracy of turbulence models for lower stage cyclones used in suspension preheaters

This study involved the analysis and characterization of the multiphase flow phenomenon inside the lower stage cyclone separator used in the clinker burning process.The analysis was performed using both CFD and experimental research methods.Very few studies are devoted to such types of cyclone separators,which in addition to their basic functions are also responsible for the technological process.Due to the atypical working conditions of these cyclone separators,they are characterized with a complex geometry,which significantly differs from that of the traditional separators.Furthermore,the evaluation of the accuracy and level of reliability of the two models of turbulence closure—k-e RNG and RSM(RANS),and the LES.The results obtained led to the conclusion that for the lower stage cyclone separators,the LES model proved to be the most accurate(both in the case of forecasting the separation efficiency and pressure drop).The performance parameter(in particular the separation efficiency)values obtained for the RSM model were also characterized by high accuracy.The k-e RNG model was characterized by significantly larger deviations.

Volumetric fraction measurement in oil-water-gas multiphase flow with dual energy gamma-ray system

Volumetric fraction distribution measurement is a constituent part of process tomography system in oil-water-gas multiphase flow. With the technological development of nuclear radial inspection, dual-energy γ-ray techniques make it possible to investigate the concentration of the different components on the cross-section of oil-water-gas multiphase pipe-flow. The dual-energy gamma-ray technique is based on materials attenuation coefficients measurement comprised of two radioactive isotopes of 241Am and 241Cs which have emission energies at 59.5 keV and 662 keV in this project. Nuclear instruments and data acquisition system were designed to measure the material’s attenuation dose rate and a number of static tests were conducted at the Multiphase Laboratory, Institute of Mechanics, Chinese Academy of Sciences. Three phases of oil-water-gas media were inves- tigated for their possible use to simulate different media volumetric fraction distributions in experimental vessels. Attenuation intensities were measured, and the arithmetic of linear attenuation coefficients and the equations of volumetric fractions were studied. Investigation of an unexpected measurement error from attenuation equations revealed that a modified arithmetic was involved and finally the system achieved acceptable accuracy in experimental research.