Evaluation of frictional pressure drop correlations for air-water and air-oil two-phase flow in pipeline-riser system

Accurate prediction of the frictional pressure drop is important for the design and operation of subsea oil and gas transporting system considering the length of the pipeline. The applicability of the correlations to pipeline-riser flow needs evaluation since the flow condition in pipeline-riser is quite different from the original data where they were derived from. In the present study, a comprehensive evaluation of 24prevailing correlation in predicting frictional pressure drop is carried out based on experimentally measured data of air-water and air-oil two-phase flows in pipeline-riser. Experiments are performed in a system having different configuration of pipeline-riser with the inclination of the downcomer varied from-2°to-5°to investigated the effect of the elbow on the frictional pressure drop in the riser. The inlet gas velocity ranges from 0.03 to 6.2 m/s, and liquid velocity varies from 0.02 to 1.3 m/s. A total of885 experimental data points including 782 on air-water flows and 103 on air-oil flows are obtained and used to access the prediction ability of the correlations. Comparison of the predicted results with the measured data indicate that a majority of the investigated correlations under-predict the pressure drop on severe slugging. The result of this study highlights the requirement of new method considering the effect of pipe layout on the frictional pressure drop.

Pressure transient characteristics of non-uniform conductivity fractured wells in viscoelasticity polymer flooding based on oil-water two-phase flow

Polymer flooding in fractured wells has been extensively applied in oilfields to enhance oil recovery.In contrast to water,polymer solution exhibits non-Newtonian and nonlinear behavior such as effects of shear thinning and shear thickening,polymer convection,diffusion,adsorption retention,inaccessible pore volume and reduced effective permeability.Meanwhile,the flux density and fracture conductivity along the hydraulic fracture are generally non-uniform due to the effects of pressure distribution,formation damage,and proppant breakage.In this paper,we present an oil-water two-phase flow model that captures these complex non-Newtonian and nonlinear behavior,and non-uniform fracture characteristics in fractured polymer flooding.The hydraulic fracture is firstly divided into two parts:high-conductivity fracture near the wellbore and low-conductivity fracture in the far-wellbore section.A hybrid grid system,including perpendicular bisection(PEBI)and Cartesian grid,is applied to discrete the partial differential flow equations,and the local grid refinement method is applied in the near-wellbore region to accurately calculate the pressure distribution and shear rate of polymer solution.The combination of polymer behavior characterizations and numerical flow simulations are applied,resulting in the calculation for the distribution of water saturation,polymer concentration and reservoir pressure.Compared with the polymer flooding well with uniform fracture conductivity,this non-uniform fracture conductivity model exhibits the larger pressure difference,and the shorter bilinear flow period due to the decrease of fracture flow ability in the far-wellbore section.The field case of the fall-off test demonstrates that the proposed method characterizes fracture characteristics more accurately,and yields fracture half-lengths that better match engineering reality,enabling a quantitative segmented characterization of the near-wellbore section with high fracture conductivity and the far-wellbore section with low fracture conductivity.The novelty of this paper is the analysis of pressure performances caused by the fracture dynamics and polymer rheology,as well as an analysis method that derives formation and fracture parameters based on the pressure and its derivative curves.

Integrated numerical simulation of hydraulic fracturing and production in shale gas well considering gas-water two-phase flow

Based on the displacement discontinuity method and the discrete fracture unified pipe network model,a sequential iterative numerical method was used to build a fracturing-production integrated numerical model of shale gas well considering the two-phase flow of gas and water.The model accounts for the influence of natural fractures and matrix properties on the fracturing process and directly applies post-fracturing formation pressure and water saturation distribution to subsequent well shut-in and production simulation,allowing for a more accurate fracturing-production integrated simulation.The results show that the reservoir physical properties have great impacts on fracture propagation,and the reasonable prediction of formation pressure and reservoir fluid distribution after the fracturing is critical to accurately predict the gas and fluid production of the shale gas wells.Compared with the conventional method,the proposed model can more accurately simulate the water and gas production by considering the impact of fracturing on both matrix pressure and water saturation.The established model is applied to the integrated fracturing-production simulation of practical horizontal shale gas wells.The simulation results are in good agreement with the practical production data,thus verifying the accuracy of the model.

Identifying the enhancement mechanism of Al/MoO_(3) reactive multilayered films on the ignition ability of semiconductor bridge using a one-dimensional gas-solid two-phase flow model

Energetic Semiconductor bridge(ESCB)based on reactive multilayered films(RMFs)has a promising application in the miniature and intelligence of initiator and pyrotechnics device.Understanding the ignition enhancement mechanism of RMFs on semiconductor bridge(SCB)during the ignition process is crucial for the engineering and practical application of advanced initiator and pyrotechnics devices.In this study,a one-dimensional(1D)gas-solid two-phase flow ignition model was established to study the ignition process of ESCB to charge particles based on the reactivity of Al/MoO_(3) RMFs.In order to fully consider the coupled exothermic between the RMFs and the SCB plasma during the ignition process,the heat release of chemical reaction in RMFs was used as an internal heat source in this model.It is found that the exothermal reaction in RMFs improved the ignition performance of SCB.In the process of plasma rapid condensation with heat release,the product of RMFs enhanced the heat transfer process between the gas phase and the solid charge particle,which accelerated the expansion of hot plasma,and heated the solid charge particle as well as gas phase region with low temperature.In addition,it made up for pressure loss in the gas phase.During the plasma dissipation process,the exothermal chemical reaction in RMFs acted as the main heating source to heat the charge particle,making the surface temperature of the charge particle,gas pressure,and gas temperature rise continuously.This result may yield significant advantages in providing a universal ignition model for miniaturized ignition devices.

Numerical Simulation of Oil-Water Two-Phase Flow in Low Permeability Tight Reservoirs Based on Weighted Least Squares Meshless Method

In response to the complex characteristics of actual low-permeability tight reservoirs,this study develops a meshless-based numerical simulation method for oil-water two-phase flow in these reservoirs,considering complex boundary shapes.Utilizing radial basis function point interpolation,the method approximates shape functions for unknown functions within the nodal influence domain.The shape functions constructed by the aforementioned meshless interpolation method haveδ-function properties,which facilitate the handling of essential aspects like the controlled bottom-hole flow pressure in horizontal wells.Moreover,the meshless method offers greater flexibility and freedom compared to grid cell discretization,making it simpler to discretize complex geometries.A variational principle for the flow control equation group is introduced using a weighted least squares meshless method,and the pressure distribution is solved implicitly.Example results demonstrate that the computational outcomes of the meshless point cloud model,which has a relatively small degree of freedom,are in close agreement with those of the Discrete Fracture Model(DFM)employing refined grid partitioning,with pressure calculation accuracy exceeding 98.2%.Compared to high-resolution grid-based computational methods,the meshless method can achieve a better balance between computational efficiency and accuracy.Additionally,the impact of fracture half-length on the productivity of horizontal wells is discussed.The results indicate that increasing the fracture half-length is an effective strategy for enhancing production from the perspective of cumulative oil production.

Arbitrary High-Order Fully-Decoupled Numerical Schemes for Phase-Field Models of Two-Phase Incompressible Flows

Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.

Optimizing Two-Phase Flow Heat Transfer:DCS Hybrid Modeling and Automation in Coal-Fired Power Plant Boilers

In response to escalating challenges in energy conservation and emission reduction,this study delves into the complexities of heat transfer in two-phase flows and adjustments to combustion processes within coal-fired boilers.Utilizing a fusion of hybrid modeling and automation technologies,we develop soft measurement models for key combustion parameters,such as the net calorific value of coal,flue gas oxygen content,and fly ash carbon content,within theDistributedControl System(DCS).Validated with performance test data,thesemodels exhibit controlled root mean square error(RMSE)and maximum absolute error(MAXE)values,both within the range of 0.203.Integrated into their respective automatic control systems,thesemodels optimize two-phase flow heat transfer,finetune combustion conditions,and mitigate incomplete combustion.Furthermore,this paper conducts an in-depth exploration of the generationmechanismof nitrogen oxides(NOx)and low oxygen emission reduction technology in coal-fired boilers,demonstrating a substantial reduction in furnace exit NOx generation by 30%to 40%and the power supply coal consumption decreased by 1.62 g/(kW h).The research outcomes highlight the model’s rapid responsiveness,enabling prompt reflection of transient variations in various economic indicator parameters.This provides a more effective means for real-time monitoring of crucial variables in coal-fired boilers and facilitates timely combustion adjustments,underscoring notable achievements in boiler combustion.The research not only provides valuable and practical insights into the intricacies of two-phase flow heat transfer and heat exchange but also establishes a pioneering methodology for tackling industry challenges.

Numerical Solutions of the Classical and Modified Buckley-Leverett Equations Applied to Two-Phase Fluid Flow

Climate change is a reality. The burning of fossil fuels from oil, natural gas and coal is responsible for much of the pollution and the increase in the planet’s average temperature, which has raised discussions on the subject, given the emergencies related to climate. An energy transition to clean and renewable sources is necessary and urgent, but it will not be quick. In this sense, increasing the efficiency of oil extraction from existing sources is crucial, to avoid waste and the drilling of new wells. The purpose of this work was to add diffusive and dispersive terms to the Buckley-Leverett equation in order to incorporate extra phenomena in the temporal evolution between the water-oil and oil-water transitions in the pipeline. For this, the modified Buckley-Leverett equation was discretized via essentially weighted non-oscillatory schemes, coupled with a three-stage Runge-Kutta and a fourth-order centered finite difference methods. Then, computational simulations were performed and the results showed that new features emerge in the transitions, when compared to classical simulations. For instance, the dispersive term inhibits the diffusive term, adding oscillations, which indicates that the absorption of the fluid by the porous medium occurs in a non-homogeneous manner. Therefore, based on research such as this, decisions can be made regarding the replacement of the porous medium or the insertion of new components to delay the replacement.

A unified fractional flow framework for predicting the liquid holdup in two-phase pipe flows

Two-phase pipe flow occurs frequently in oil&gas industry,nuclear power plants,and CCUS.Reliable calculations of gas void fraction(or liquid holdup)play a central role in two-phase pipe flow models.In this paper we apply the fractional flow theory to multiphase flow in pipes and present a unified modeling framework for predicting the fluid phase volume fractions over a broad range of pipe flow conditions.Compared to existing methods and correlations,this new framework provides a simple,approximate,and efficient way to estimate the phase volume fraction in two-phase pipe flow without invoking flow patterns.Notably,existing correlations for estimating phase volume fraction can be transformed and expressed under this modeling framework.Different fractional flow models are applicable to different flow conditions,and they demonstrate good agreement against experimental data within 5%errors when compared with an experimental database comprising of 2754 data groups from 14literature sources,covering various pipe geometries,flow patterns,fluid properties and flow inclinations.The gas void fraction predicted by the framework developed in this work can be used as inputs to reliably model the hydraulic and thermal behaviors of two-phase pipe flows.

Simulation of Two-Phase Flowback Phenomena in Shale Gas Wells

The gas-water two-phaseflow occurring as a result of fracturingfluidflowback phenomena is known to impact significantly the productivity of shale gas well.In this work,this two-phaseflow has been simulated in the framework of a hybrid approach partially relying on the embedded discrete fracture model(EDFM).This model assumes the region outside the stimulated reservoir volume(SRV)as a single-medium while the SRV region itself is described using a double-medium strategy which can account for thefluid exchange between the matrix and the micro-fractures.The shale gas adsorption,desorption,diffusion,gas slippage effect,fracture stress sensitivity,and capillary imbibition have been considered.The shale gas production,pore pressure distribution and water saturation distribution in the reservoir have been simulated.The influences of hydraulic fracture geometry and nonorthogonal hydraulic fractures on gas production have been determined and discussed accordingly.The simulation results show that the daily gas production has an upward and downward trend due to the presence of a large amount of fracturingfluid in the reservoir around the hydraulic fracture.The smaller the angle between the hydraulic fracture and the wellbore,the faster the daily production of shale gas wells decreases,and the lower the cumulative production.Nonplanar fractures can increase the control volume of hydraulic fractures and improve the production of shale gas wells.

Ultrasonic method for measuring water holdup of low velocity and high-water-cut oil-water two-phase flow

Oil reservoirs with low permeability and porosity that are in the middle and late exploitation periods in China＇s onshore oil fields are mostly in the high-water-cut production stage.This stage is associated with severely non-uniform local-velocity flow profiles and dispersed-phase concentration（of oil droplets） in oil-water two-phase flow,which makes it difficult to measure water holdup in oil wells.In this study,we use an ultrasonic method based on a transmission-type sensor in oil-water two-phase flow to measure water holdup in lowvelocity and high water-cut conditions.First,we optimize the excitation frequency of the ultrasonic sensor by calculating the sensitivity of the ultrasonic field using the finite element method for multiphysics coupling.Then we calculate the change trend of sound pressure level attenuation ratio with the increase in oil holdup to verify the feasibility of the employed diameter for the ultrasonic sensor.Based on the results,we then investigate the effects of oildroplet diameter and distribution on the ultrasonic field.To further understand the measurement characteristics of the ultrasonic sensor,we perform a flow loop test on vertical upward oilwater two-phase flow and measure the responses of the optimized ultrasonic sensor.The results show that the ultrasonic sensor yields poor resolution for a dispersed oil slug in water flow（D OS/W flow）,but the resolution is favorable for dispersed oil in water flow（D O/W flow） and very fine dispersed oil in water flow（VFD O/W flow）.This research demonstrates the potential application of a pulsed-transmission ultrasonic method for measuring the fraction of individual components in oil-water two-phase flow with a low mixture velocity and high water cut.

LARGE-EDDY SIMULATION OF TWO-PHASE REACTING FLOW IN MODEL COMBUSTOR

The gas-droplet two-phase reacting flow in a model combustor with the V-gutter flame holder is studied by an Eulerian-Lagrangian large-eddy simulation (LES) approach. The k-equation subgrid-scale model is used to simulate the subgrid eddy viscosity, and the eddy-break-up (EBU) combustion subgrid-scale model is used to determine the chemical reaction rate. A two-step turbulent combustion subgrid-scale model is employed for calculating carbon monoxide CO concentration, and the NO subgrid-scale pollutant formation model for the evaluation of the rate of NO formation. The heat flux model is applied to the prediction of radiant heat transfer. The gas phase is solved with the SIMPLE algorithm and a hybrid scheme in the staggered grid system. The liquid phase equations are solved in a Lagrangian frame in reference of the particle-source-in-cell (PSIC) algorithm. From simulation results, the exchange of mass, moment and energy between gas and particle fields for the reacting flow in the afterburner with a V-gutter flame holder can be obtained. By the comparison of experimental and simulation results, profile temperature and pollutant of the outlet are quite in agreement with experimental data. Results show that the LES approach for predicting the two-phase instantaneous reacting flow and pollutant emissions in the afterburner is feasible.

Numerical simulation of two-phase flow field in underwater sealing device based on dynamic mesh

In order to speed underwater launch of minor-caliber weapons,a sealing device can be set in front of underwater muzzle to separate water,preventing the muzzle from water immersion.By establishing and simplifying the model of underwater weapon sealing device and unstructured mesh computing domain model based on computational fluid dynamics（CFD）,dynamic mesh and user defined function（UDF）,the N-S equation is solved and the numerical analysis and calculation of the complex two-phase flow inside the sealing device are carried out.The results show that the gas discharged from the sealing device is conducive to the formation of the projectile supercavity.When the projectile is launched at 5munder water,the shock wave before and after the projectile has impact on the box body up to 100 MPa,therefore the sealing device must be strong enough.The research results have the vital significance to the design of underwater weapon sealing device and the formation of the projectile supercavitation.

New numerical algorithm of gas-liquid two-phase flow considering characteristics of liquid metal during mold filling

A new program is developed for gas-liquid two-phase mold filling simulation in casting. The gas fluid, the superheated liquid metal and the liquid metal containing solid grains are assumed to be governed by Navier-Stokes equations and solved through Projection method. The Level set method is used to track the gas-liquid interface boundary. In order to demonstrate the correctness of this new program for simulation of gas-liquid two-phase mold filling in casting, a benchmark filling experiment is simulated （this benchmark test is designed by XU and the filling process is recorded by a 16-mm film camera）. The simulated results agree very well with the experimental results, showing that this new program can be used to properly predicate the gas-liquid two-phase mold filling simulation in casting.

Numerical simulation and analysis of solid-liquid two-phase threedimensional unsteady flow in centrifugal slurry pump

Based on RNG k-ε turbulence model and sliding grid technique, solid-liquid two-phase three-dimensional(3-D) unsteady turbulence of full passage in slurry pump was simulated by means of Fluent software. The effects of unsteady flow characteristics on solid-liquid two-phase flow and pump performance were researched under design condition. The results show that clocking effect has a significant influence on the flow in pump, and the fluctuation of flow velocity and pressure is obvious, particularly near the volute tongue, at the position of small sections of volute and within diffuser. Clocking effect has a more influence on liquid-phase than on solid-phase, and the wake-jet structure of relative velocity of solid-phase is less obvious than liquid-phase near the volute tongue and the impeller passage outlet. The fluctuation of relative velocity of solid-phase flow is 7.6% smaller than liquid-phase flow at the impeller outlet on circular path. Head and radial forces of the impeller are 8.1% and 85.7% of fluctuation, respectively. The results provide a theoretical basis for further research for turbulence, improving efficient, reducing the hydraulic losses and wear. Finally, field tests were carried out to verify the operation and wear of slurry pump.

4D-Flow MRI在肥厚型心肌病左室流出道血流评估中的价值探索

目的 探索四维血流(four-dimensional flow,4D-Flow)磁共振成像(magnetic resonance imaging,MRI)技术在左心室腔内应用的可行性。材料与方法 本研究为前瞻性、横断面研究,纳入2022年8月至2023年1月于我院接受心脏MRI检查的21例肥厚型心肌病患者,采用3.0 T MRI扫描仪进行二维血流(tow-dimensional flow,2D-Flow)及4D-Flow成像,收集患者一周内进行的超声心动图检查结果。采用组内相关系数(inter-class correlation coefficient,ICC)、变异系数(coefficients of variation,COV)及Bland-Altman分析比较2D-Flow、4D-Flow评估左室流出道峰值流速的可重复性及一致性,并通过Pearson相关性分析探究二者与超声心动图测量结果的关系。结果 2D-Flow和4D-Flow观察者内/观察者间的ICC分别为0.999/0.999和0.995/0.992,COV分别为0.5%/0.5%和2.4%/2.6%。4D-Flow与超声心动图的测量结果呈中度相关,相关系数r值为0.574(P=0.006),但一致性较差,ICC为0.375(P=0.013)。2D-Flow与4D-Flow和超声心动图间无显著的一致性及相关性。结论 4D-Flow技术能够可视化心腔内血流模式,对左室流出道峰值流速的测量具有高度可重复性,且与超声心动图的测量结果具有显著的一致性。

Design and Experimental Analyses of Small-flow High-head Centrifugal-vortex Pump for Gas-Liquid Two-phase Mixture

The design method of small-flow high-head centrifugal-vortex pump was presented. This pump, configured with inducer, complex-centrifugal impeller and open-vortex impeller, was put forward to deliver gas-liquid two-phase mixture. An HTB-5/60 type sample pump was developed and tested on a closed-loop test rig. Experimental studies on performance and cavitation tests for gas-liquid two-phase mixture were carried out compared with pure-water experimental results. Also the effect of gas phase on pump was analyzed and discussed. The experimental results show that performance and cavitation characteristics of the sample purnp deteriorates progressively with increasing volume fraction of gas. When the total capacity Qm is between 4.5 m^3·h^-1 and 6 m^3·h^-1 and the gas flow rate qg below 0.66 m^3·h^-1, or qg/Qm is lower than 15%, the characteristic curves are approximately parallel to those in pure water test, but the performance deteriorates sharply until an abrupt flow-cutting at a critical volume fraction of gas. This pump is found suitable for transporting gas-liquid two-phase mixture when working around rated capacity of 5 m^3·h^-1 with qglQm below 15%.

Computational Analysis of Centrifugal Pump Delivering Solid-liquid Two-phase Flow during Startup Period

The transient behavior of centrifugal pumps during transient operating periods, such as startup and stopping, has drawn more and more attention recently because of urgent needs in engineering. Up to now, almost all the existing studies on this behavior are limited to using water as working fluid. The study on the transient behavior related to solid-liquid two-phase flow has not been seen yet. In order to explore the transient characteristics of a high specific-speed centrifugal pump during startup period delivering the pure water and solid-liquid two-phase flow, the transient flows inside the pump are numerically simulated using the dynamic mesh method. The variable rotational speed and flow rate with time obtained from experiment are best fitted as the function of time, and are written into computational fluid dynamics （CFD） code-FLUENT by using a user defined function. The predicted heads are compared with experimental results when pumping pure water. The results show that the difference in the transient performance during startup period is very obvious between water and solid-liquid two-phase flow during the later stage of startup process. Moreover, the time for the solid-liquid two-phase flow to achieve a stable condition is longer than that for water. The solid-liquid two-phase flow results in a higher impeller shaft power, a larger dynamic reaction force, a more violent fluctuation in pressure and a reduced stable pressure rise comparing with water. The research may be useful to tmderstanding on the transient behavior of a centrifugal pump under a solid-liquid two-phase flow during startup period.

Flow Regime Identification of Gas-liquid Two-phase Flow Based on HHT

A new method to identify flow regime in two-phase flow was presented, based on signal processing of differential pressure using Hilbert Huang transform （HHT）. Signals obtained from a Venturi meter were decomposed into different intrinsic mode functions （IMFs） with HHT, then the energy fraction of each intrinsic mode and the mean value of residual function were calculated, from which the rules of flow regime identification were summarized. Experiments were carried out on two-phase flow in the horizontal tubes with 50mm and 40mm inner diameter, while water flowrate was in the range of 1.3m^3.h^-1 to 10.5m^3.h^-1, oil flowrate was from 4.2m^3.h^-1 to 7.0m^3.h^-1 and gas flowrate from 0 to 15m^3.h^-1. The results show that the proposed rules have high precision for single phase, bubbly, and slug, plug flow regirne identification, which are independent of not only properties of two-phase fluid. In addition, the method can meet the need of industrial application because of its simple calculation.

An improved large eddy simulation of two-phase flows in a pump impeller

An improved large eddy simulation using a dynamic second-order sub-grid-scale （SGS） stress model has been developed to model the governing equations of dense turbulent particle-liquid two-phase flows in a rotating coordinate system, and continuity is conserved by a mass-weighted method to solve the filtered governing equations. In the cur- rent second-order SGS model, the SGS stress is a function of both the resolved strain-rate and rotation-rate tensors, and the model parameters are obtained from the dimensional consistency and the invariants of the strain-rate and the rotation-rate tensors. In the numerical calculation, the finite volume method is used to discretize the governing equations with a staggered grid system. The SIMPLEC algorithm is applied for the solution of the discretized governing equations. Body- fitted coordinates are used to simulate the two-phase flows in complex geometries. Finally the second-order dynamic SGS model is successfully applied to simulate the dense turbu-lent particle-liquid two-phase flows in a centrifugal impeller. The predicted pressure and velocity distributions are in good agreement with experimental results.