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.

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.

Simulation of Gas-Water Two-Phase Flow in Tight Gas Reservoirs Considering the Gas Slip Effect

A mathematical model for the gas-water two-phase flow in tight gas reservoirs is elaborated.The model can account for the gas slip effect,stress sensitivity,and high-speed non-Darcy factors.The related equations are solved in the framework of a finite element method.The results are validated against those obtained by using the commercial software CMG(Computer Modeling Group software for advanced recovery process simulation).It is shown that the proposed method is reliable.It can capture the fracture rejection characteristics of tight gas reservoirs better than the CMG.A sensitivity analysis of various control factors(initial water saturation,reservoir parameters,and fracturing parameters)affecting the production in tight gas wells is conducted accordingly.Finally,a series of theoretical arguments are provided for a rational and effective development/exploitation of tight sandstone gas reservoirs.

Parametric study of gas−liquid two-phase flow field in horizontal stirred tank

Based on Fluent software,the gas−liquid two-phase flow in the horizontal stirred tank was simulated with SST k−ωturbulence model,Eulerian−Eulerian two-fluid model,and multi-reference flame method.The mixing process in the tank was calculated by tracer method.The results show that increasing the rotating speed or gas flow is conducive to a more uniform distribution of the gas phase and accelerates the mixing of the liquid phase.When the rotating speed exceeds 93 r/min,the relative power demand remains basically constant.The change in the inclination angle of the upper impeller has minimal effect on the gas phase distribution.When the inclination angle is 50°,the relative power demand reaches the maximum.An appropriate increase in the impeller distance from the bottom improves the gas holdup and gas phase distribution but increases the liquid phase mixing time.

SIMULATION OF GAS AND LIQUID TWO-PHASE FLOW THROUGH THE BLAST FURNACE DROPPING ZONE

A three-dimensional mathematical model,based on differential balances of mass and momentum,hasbeen developed to describe the two-phase flow of gas and liquid through the dropping zone of the blast fur-nace.Agreement between observed and calculated values verifies the validity of this model.On the basis of this model,various parameters for the surrounding of the dry zone of Blast FurnaceNo.I-BF of the Beijing Iron and Steel Company have been computed,from which a diagram for demar-cation of fluidization of coke and flooding of slag has been proposed.

Analysis of Maximum Liquid Carrying Capacity Based on Conventional Tubing Plunger Gas Lift

China’s unconventional gas fields have a large number of low-productivity and low-efficiency wells, many of whichare located in remote and environmentally harsh mountainous areas. To address the long-term stable productionof these gas wells, plunger-lift technology plays an important role. In order to fully understand and accurately graspthe drainage and gas production mechanisms of plunger-lift, a mechanical model of plunger-liquid column uplift inthe plunger-lift process was established, focusing on conventional plunger-lift systems and representative wellboreconfigurations in the Linxing region. The operating casing pressure of the plunger-lift process and the calculationmethod for the maximum daily fluid production rate based on the work regime with the highest fluid recovery ratewere determined. For the first time, the critical flow rate method was proposed as a constraint for the maximumliquid-carrying capacity of the plunger-lift, and liquid-carrying capacity charts for conventional plunger-lift withdifferent casing sizes were developed. The results showed that for 23/8 casing plunger-lift, with a well depth ofshallower than 808 m, the maximum drainage rate was 33 m3/d;for 27/8 casing plunger-lift, with a well depth ofshallower than 742 m, the maximum drainage rate was 50.15 m3/d;for 31/2 casing plunger-lift, with a well depthof shallower than 560 m, the maximum drainage rate was 75.14 m3/d. This research provides a foundation for thescientific selection of plunger-lift technology and serves as a decision-making reference for developing reasonableplunger-lift work regimes.

Simultaneous measurement of velocity profile and liquid film thickness in horizontal gas–liquid slug flow by using ultrasonic Doppler method

Horizontal gas-liquid two-phase flows widely exist in chemical engineering,oil/gas production and other important industrial processes.Slug flow pattern is the main form of horizontal gas-liquid flows and characterized by intermittent motion of film region and slug region.This work aims to develop the ultrasonic Doppler method to realize the simultaneous measurement of the velocity profile and liquid film thickness of slug flow.A single-frequency single-channel transducer is adopted in the design of the field-programmable gate array based ultrasonic Doppler system.A multiple echo repetition technology is used to improve the temporal-spatial resolution for the velocity profile.An experiment of horizontal gas-liquid two-phase flow is implemented in an acrylic pipe with an inner diameter of 20 mm.Considering the aerated characteristics of the liquid slug,slug flow is divided into low-aerated slug flow,high-aerated slug flow and pseudo slug flow.The temporal-spatial velocity distributions of the three kinds of slug flows are reconstructed by using the ultrasonic velocity profile measurement.The evolution characteristics of the average velocity profile in slug flows are investigated.A novel method is proposed to derive the liquid film thickness based on the instantaneous velocity profile.The liquid film thickness can be effectively measured by detecting the position and the size of the bubbles nearly below the elongated gas bubble.Compared with the time of flight method,the film thickness measured by the Doppler system shows a higher accuracy as a bubble layer occurs in the film region.The effect of the gas distribution on the film thickness is uncovered in three kinds of slug flows.

Numerical simulation of gas–liquid flow in the bubble column using Wray–Agarwal turbulence model coupled with population balance model

In this paper,an improved computational fluid dynamic(CFD)model for gas-liquid flow in bubble column was developed using the one-equation Wary-Agarwal(WA)turbulence model coupled with the population balance model(PBM).Through 18 orthogonal test cases,the optimal combination of interfacial force models,including drag force,lift force,turbulent dispersion force.The modified wall lubrication force model was proposed to improve the predictive ability for hydrodynamic behavior near the wall of the bubble column.The values simulated by optimized CFD model were in agreement with experimental data,and the errors were within±20%.In addition,the axial velocity,turbulent kinetic energy,bubble size distribution,and the dynamic characteristic of bubble plume were analyzed at different superficial gas velocities.This research work could provide a theoretical basis for the extension of the CFD-PBM coupled model to other multiphase reactors..

Gas liquid cylindrical cyclone flow regime identification using machine learning combined with experimental mechanism explanation

The flow regimes of GLCC with horizon inlet and a vertical pipe are investigated in experiments,and the velocities and pressure drops data labeled by the corresponding flow regimes are collected.Combined with the flow regimes data of other GLCC positions from other literatures in existence,the gas and liquid superficial velocities and pressure drops are used as the input of the machine learning algorithms respectively which are applied to identify the flow regimes.The choosing of input data types takes the availability of data for practical industry fields into consideration,and the twelve machine learning algorithms are chosen from the classical and popular algorithms in the area of classification,including the typical ensemble models,SVM,KNN,Bayesian Model and MLP.The results of flow regimes identification show that gas and liquid superficial velocities are the ideal type of input data for the flow regimes identification by machine learning.Most of the ensemble models can identify the flow regimes of GLCC by gas and liquid velocities with the accuracy of 0.99 and more.For the pressure drops as the input of each algorithm,it is not the suitable as gas and liquid velocities,and only XGBoost and Bagging Tree can identify the GLCC flow regimes accurately.The success and confusion of each algorithm are analyzed and explained based on the experimental phenomena of flow regimes evolution processes,the flow regimes map,and the principles of algorithms.The applicability and feasibility of each algorithm according to different types of data for GLCC flow regimes identification are proposed.

Quantitative research of the liquid film characteristics in upward vertical gas, oil and water flows

The study of liquid film characteristics in multiphase flow is a very important research topic, however,the characteristics of the liquid film around Taylor bubble structure in gas, oil and water three-phase flow are not clear. In the present study, a novel liquid film sensor is applied to measure the distributed signals of the liquid film in three-phase flow. Based on the liquid film signals, the liquid film characteristics including the structural characteristics and the nonlinear dynamics characteristics in three-phase flows are investigated for the first time. The structural characteristics including the proportion, the appearance frequency and the thickness of the liquid film are obtained and the influences of the liquid and gas superficial velocities and the oil content on them are investigated. To investigate the nonlinear dynamics characteristics of the liquid film with the changing flow conditions, the entropy analysis is introduced to successfully uncover and quantify the dynamic complexity of the liquid film behavior.

Liquid holdup measurement with double helix capacitance sensor in horizontal oil-water two-phase flow pipes

This paper presents the characteristics of a double helix capacitance sensor for measurement of the liquid holdup in horizontal oil–water two-phase flow. The finite element method is used to calculate the sensitivity field of the sensor in a pipe with 20 mm inner diameter and the effect of sensor geometry on the distribution of sensitivity field is presented. Then, a horizontal oil–water two-phase flow experiment is carried out to measure the response of the double helix capacitance sensor, in which a novel method is proposed to calibrate the liquid holdup based on three pairs of parallel-wire capacitance probes. The performance of the sensor is analyzed in terms of the flow structures detected by mini-conductance array probes.

Mechanism from particle compaction to fluidization of liquid–solid two-phase flow

A new model of particle yield stress including cohesive strength is proposed,which considers the friction and cohesive strength between particles.A calculation method for the fluidization process of liquid–solid two-phase flow in compact packing state is given,and the simulation and experimental studies of fluidization process are carried out by taking the sand–water two-phase flow in the jet dredging system as an example,and the calculation method is verified.

NUMERICAL MODELING OF TURBULENTEVAPORATING GAS-DROPLET TWO-PHASE FLOWS IN AN AFTERBURNER DIFFUSOR OF TURBO-FAN JET ENGINES

The two-dimensional turbulent evaporating gas-droplet two-phase flows in an afterburner diffusor of turbo-fan jet engines are simulated by the k-ε turbulence model and the particle trajectory model. Comparison of predicted gas velocity and temperature distributions with experimental results for the cases without liquid spray shows pretty good agreement. Gas-droplet two-phase flow predictions give plausible droplet trajectories, fuel-vapor concentration distribution, gas-phase velocity and temperature field in presence of liquid droplets. One run of computation with this method is made for a particular afterburner. The results indicate that the location of the atomizers is not favorable to flame stabilization and combustion efficiency. The proposed numerical modeling can also be adopted for optimization design and performance evaluation of afterburner combustors of turbo-fan jet engines.

Experimental analysis on adjusting performance of vapor-liquid two-phase flow controller

The vapor-liquid self-adjusting controller is an innovative automatic regulating valve.In order to ensure adjusted objects run safely and economically,the controller automatically adjusts the liquid flux to keep liquid level at a required level according to physical properties of vapor-liquid two-phase fluid.The adjusting mechanics,the controller’s performance and influencing factors of its stability have been analyzed in this paper.The theoretical analysis and successful applications have demonstrated this controller can keep the liquid level steady with good performance.The actual application in industry has shown that the controller can satisfactorily meet the requirement of industrial production and has wide application areas.

Application of time–frequency entropy from wake oscillation to gas–liquid flow pattern identification

Gas–liquid two-phase flow abounds in industrial processes and facilities. Identification of its flow pattern plays an essential role in the field of multiphase flow measurement. A bluff body was introduced in this study to recognize gas–liquid flow patterns by inducing fluid oscillation that enlarged differences between each flow pattern. Experiments with air–water mixtures were carried out in horizontal pipelines at ambient temperature and atmospheric pressure. Differential pressure signals from the bluff-body wake were obtained in bubble, bubble/plug transitional, plug, slug, and annular flows. Utilizing the adaptive ensemble empirical mode decomposition method and the Hilbert transform, the time–frequency entropy S of the differential pressure signals was obtained. By combining S and other flow parameters, such as the volumetric void fraction β, the dryness x, the ratio of density φ and the modified fluid coefficient ψ, a new flow pattern map was constructed which adopted S（1–x）φ and （1–β）ψ as the vertical and horizontal coordinates, respectively. The overall rate of classification of the map was verified to be 92.9% by the experimental data. It provides an effective and simple solution to the gas–liquid flow pattern identification problems.

Inter-layer interference for multi-layered tight gas reservoir in the absence and presence of movable water

Due to the dissimilarity among different producing layers,the influences of inter-layer interference on the production performance of a multi-layer gas reservoir are possible.However,systematic studies of inter-layer interference for tight gas reservoirs are really limited,especially for those reservoirs in the presence of water.In this work,five types of possible inter-layer interferences,including both absence and presence of water,are identified for commingled production of tight gas reservoirs.Subsequently,a series of reservoir-scale and pore-scale numerical simulations are conducted to quantify the degree of influence of each type of interference.Consistent field evidence from the Yan'an tight gas reservoir(Ordos Basin,China)is found to support the simulation results.Additionally,suggestions are proposed to mitigate the potential inter-layer interferences.The results indicate that,in the absence of water,commingled production is favorable in two situations:when there is a difference in physical properties and when there is a difference in the pressure system of each layer.For reservoirs with a multi-pressure system,the backflow phenomenon,which significantly influences the production performance,only occurs under extreme conditions(such as very low production rates or well shut-in periods).When water is introduced into the multi-layer system,inter-layer interference becomes nearly inevitable.Perforating both the gas-rich layer and water-rich layer for commingled production is not desirable,as it can trigger water invasion from the water-rich layer into the gas-rich layer.The gas-rich layer might also be interfered with by water from the neighboring unperforated water-rich layer,where the water might break the barrier(eg weak joint surface,cement in fractures)between the two layers and migrate into the gas-rich layer.Additionally,the gas-rich layer could possibly be interfered with by water that accumulates at the bottom of the wellbore due to gravitational differentiation during shut-in operations.

Experimental Investigation of Vibration Response of A Free-Hanging Flexible Riser Induced by Internal Gas-Liquid Slug Flow

The vibration response of a free-hanging flexible riser induced by internal gas-liquid slug flow was studied experimentally in a small-diameter tube model based on Froude number criterion. The flow regime in a curved riser model and the response displacements of the riser were simultaneously recorded by high speed cameras. The gas superficial velocity ranges from 0.1 m/s to 0.6 m/s while the liquid superficial velocity from 0.06 m/s to 0.3 m/s.Severe slugging type 3, unstable oscillation flow and relatively stable slug flow were observed in the considered flow rates. Severe slugging type 3 characterized by premature gas penetration occurs at relatively low flow rates. Both the cycle time and slug length become shorter as the gas flow rate increases. The pressure at the riser base undergoes a longer period and larger amplitude of fluctuation as compared with the other two flow regimes. Additionally, severe slugging leads to the most vigorous in-plane vibration. However, the responses in the vertical and horizontal directions are not synchronized. The vertical vibration is dominated by the second mode while the horizontal vibration is dominated by the first mode. Similar to the vortex-induced vibration, three branches are identified as initial branch, build-up branch and descending branch for the response versus the mixture velocity of gas-liquid flow.

Development of Liquid Slug Length in Gas-Liquid Slug Flow along Horizontal Pipeline: Experiment and Simulation

The liquid slug length distribution is crucial for designing the downstream processing system with mul-tiphase pipeline. Experiments were conducted in a 133m long horizontal test loop. The measurements were per-formed by conductivity probes to determine the liquid slug length distribution. The data covered both the slug and plug flow regimes. From experimental results, the mean liquid slug lengths were relatively insensitive to gas and liquid flow rates in the higher mixture velocity range. But in the lower mixture velocity range, the mean liquid slug length decreased and then increased with mixture velocity. It shows that the development length of slug flow was longer than x/D=1157. A slug tracking model was adapted to study the evolution of liquid slug length distribution in a horizontal pipeline. In the present model, the wake effect of elongated bubble and the pressure drop due to accel-eration are taken into account and random slug lengths are introduced at the entrance. The results of the model are compared with the measured slug length distributions of slug flow regime. It shows that the predicted mean and maximum slug lengths are in agreement with the experimental data at x/D=1157 and the form of the slug length distributions is also predicted well by the model.

Numerical investigation on flow process of liquid metals in melt delivery nozzle during gas atomization process for fine metal powder production

Based on volume of fluid(VoF)interface capturing method and shear-stress transport(SST)k-ω turbulence model,numerical simulation was performed to reveal the flow mechanism of metal melts in melt delivery nozzle(MDN)during gas atomization(GA)process.The experimental validation indicated that the numerical models could give a reasonable prediction on the melt flow process in the MDN.With the decrease of the MDN inner-diameter,the melt flow resistance increased for both molten aluminum and iron,especially achieving an order of 10^(2) kPa in the case of the MDN inner-diameter≤1 mm.Based on the conventional GA process,the positive pressure was imposed on the viscous aluminum alloy melt to overcome its flow resistance in the MDN,thus producing powders under different MDN inner-diameters.When the MDN inner-diameter was reduced from 4 to 2 mm,the yield of fine powder(<150μm)soared from 54.7%to 94.2%.The surface quality of powders has also been improved when using a smaller inner-diameter MDN.

Prediction of Flowing Bottomhole Pressures for Two-Phase Coalbed Methane Wells

A method is proposed to predict the flowing bottomhole pressures （FBHPs） for two-phase coalbed methane （CBM） wells. The mathematical models for both gas column pressure and two-phase fluid column pressure were developed based on the well liquid flow equation. FBHPs during the production were predicted by considering the effect of entrained liquid on gravitational gradients. Comparison of calculated BHPs by Cullender-Smith and proposed method was also studied. The results show that the proposed algorithm gives the desired accuracy of calculating BHPs in the low- productivity and low-pressure CBM wells. FBHP is resulted from the combined action of wellhead pressure, gas column pressure and fluid column pressure. Variation of kinetic energy term, compressibility and friction factors with depth increments and liquid holdup with velocity should be considered to simulate the real BHPs adequately. BHP is a function of depth of each column segment. The small errors of less than 1.5% between the calculated and measured values are obtained with each segment within 25 m. Adjusting BHPs can effectively increase production pressure drop, which is beneficial to CBM desorption and enhances reservoir productivity. The increment of pressure drop from 5.37 MPa2 to 8.66 MPa2 leads to an increase of CBM production from 3270 m3/d to 6700 m3/d and is attributed to a decrease in BHP from 2.25 MPa to 1.33 MPa.