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.

Numerical Simulations of Wave Impact Forces on the Open-Type Sea Access Road Using A Two-Phase SPH Model

A numerical study based on a two-dimensional two-phase SPH(Smoothed Particle Hydrodynamics)model to analyze the action of water waves on open-type sea access roads is presented.The study is a continuation of the analyses presented by Chen et al.(2022),in which the sea access roads are semi-immersed.In this new configuration,the sea access roads are placed above the still water level,therefore the presence of the air phase becomes a relevant issue in the determination of the wave forces acting on the structures.Indeed,the comparison of wave forces on the open-type sea access roads obtained from the single and two-phase SPH models with the experimental results shows that the latter are in much better agreement.So in the numerical simulations,a two-phaseδ-SPH model is adopted to investigate the dynamical problems.Based on the numerical results,the maximum horizontal and uplifting wave forces acting on the sea access roads are analyzed by considering different wave conditions and geometries of the structures.In particular,the presence of the girder is analyzed and the differences in the wave forces due to the air cushion effects which are created below the structure are highlighted.

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 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.

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.

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.

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.

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.

Assessment of Low Global Warming Potential Refrigerants for Waste Heat Recovery in Data Center with On-Chip Two-Phase Cooling Loop

Data centers(DCs)are highly energy-intensive facilities,where about 30%–50%of the power consumed is attributable to the cooling of information technology equipment.This makes liquid cooling,especially in twophase mode,as an alternative to air cooling for the microprocessors in servers of interest.The need to meet the increased power density of server racks in high-performance DCs,along with the push towards lower global warming potential(GWP)refrigerants due to environmental concerns,has motivated research on the selection of two-phase heat transfer fluids for cooling servers while simultaneously recovering waste heat.With this regard,a heat pump-assisted absorption chiller(HPAAC)system for recovering waste heat in DCs with an on-chip twophase cooling loop driven by the compressor is proposed in the present paper and the low GWP hydrofluoroolefin refrigerants,including R1224yd(Z),R1233zd(E),R1234yf,R1234ze(E),R1234ze(Z),R1243zf and R1336mzz(Z),are evaluated and compared against R245fa as server coolant.For theHPAAC system,beginning with the development of energy and economic models,the performance is analyzed through both a parametric study and optimization using the coefficient of performance(COP),energy saving ratio(ESR),payback period(PBP)and net present value(NPV)as thermo-economic indicators.Using a standard vapor compression cooling system as a benchmark,the results indicate that with the evaporation temperature between 50℃and 70℃and the subcooling degree ranging from5℃to 15°C,R1233zd(E)with moderate compressor suction pressure and pressure ratio is the best refrigerant for the HPAAC systemwhile R1234yf performs the worst.More importantly,R1233zd(E)is also superior to R245fa based on thermo-economic performance,especially under work conditions with relatively lower evaporation temperature as well as subcooling degree.Under the given working conditions,the overall COP,ESR,NPV,and PBP of R1233zd(E)HPAAC with optimum subcooling degree range from4.99 to 11.27,25.53 to 64.59,1.13 to 4.10×10^(7) CNY and 5.77 to 2.22 years,respectively.Besides,the thermo-economic performance of R1233zd(E)HPAAC under optimum working conditions in terms of subcooling degree varying with the evaporation temperature is also investigated.

A Note on an Order Level Inventory Model with Varying Two-Phased Demand and Time-Proportional Deterioration

The main purpose of this paper is to generalize the effect of two-phased demand and variable deterioration within the EOQ (Economic Order Quantity) framework. The rate of deterioration is a linear function of time. The two-phased demand function states the constant function for a certain period and the quadratic function of time for the rest part of the cycle time. No shortages as well as partial backlogging are allowed to occur. The mathematical expressions are derived for determining the optimal cycle time, order quantity and total cost function. An easy-to-use working procedure is provided to calculate the above quantities. A couple of numerical examples are cited to explain the theoretical results and sensitivity analysis of some selected examples is carried out.

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.

Numerical modeling and parametric sensitivity analysis of heat transfer and two-phase oil and water flow characteristics in horizontal and inclined flowlines using OpenFOAM

Estimating the oil-water temperatures in flowlines is challenging especially in deepwater and ultra-deepwater offshore applications where issues of flow assurance and dramatic heat transfer are likely to occur due to the temperature difference between the fluids and the surroundings. Heat transfer analysis is very important for the prediction and prevention of deposits in oil and water flowlines, which could impede the flow and give rise to huge financial losses. Therefore, a 3D mathematical model of oil-water Newtonian flow under non-isothermal conditions is established to explore the complex mechanisms of the two-phase oil-water transportation and heat transfer in different flowline inclinations. In this work, a non-isothermal two-phase flow model is first modified and then implemented in the InterFoam solver by introducing the energy equation using OpenFOAM® code. The Low Reynolds Number (LRN) k-ε turbulence model is utilized to resolve the turbulence phenomena within the oil and water mixtures. The flow patterns and the local heat transfer coefficients (HTC) for two-phase oil-water flow at different flowlines inclinations (0°, +4°, +7°) are validated by the experimental literature results and the relative errors are also compared. Global sensitivity analysis is then conducted to determine the effect of the different parameters on the performance of the produced two-phase hydrocarbon systems for effective subsea fluid transportation. Thereafter, HTC and flow patterns for oil-water flows at downward inclinations of 4°, and 7° can be predicted by the models. The velocity distribution, pressure gradient, liquid holdup, and temperature variation at the flowline cross-sections are simulated and analyzed in detail. Consequently, the numerical model can be generally applied to compute the global properties of the fluid and other operating parameters that are beneficial in the management of two-phase oil-water transportation.

A two-phase type-curve method with multiscale fluid transport mechanisms in hydraulically fractured shale reservoirs

The quantitative understanding of hydraulic fracture(HF)properties guides accurate production forecasts and reserve estimation.Type curve is a powerful technique to characterize HF and reservoir properties from flowback and long-term production data.However,two-phase flow of water and hydrocarbon after an HF stimulation together with the complex transport mechanisms in shale nanopores exacerbate the nonlinearity of the transport equation,causing errors in type-curve analysis.Accordingly,we propose a new two-phase type-curve method to estimate HF properties,such as HF volume and permeability of fracture,through the analysis of flowback data of multi-fractured shale wells.The proposed type curve is based on a semianalytical solution that couples the two-phase flow from the matrix with the flow in HF by incorporating matrix influx,slippage effect,stress dependence,and the spatial variation of fluid properties in inorganic and organic pores.For the first time,multiple fluid transport mechanisms are considered into two-phase type-curve analysis for shale reservoirs.We analyze the flowback data from a multi-fractured horizontal well in a shale gas reservoir to verify the field application of the proposed method.The results show that the fracture properties calculated by the type-curve method are in good agreement with the long-time production data.

Pore-Scale Investigation of Coupled Two-Phase and Reactive Transport in the Cathode Electrode of Proton Exchange Membrane Fuel Cells

A three-dimensional multicomponent multiphase lattice Boltzmann model(LBM)is established to model the coupled two-phase and reactive transport phenomena in the cathode electrode of proton exchange membrane fuel cells.The gas diff usion layer(GDL)and microporous layer(MPL)are stochastically reconstructed with the inside dynamic distribution of oxygen and liquid water resolved,and the catalyst layer is simplifi ed as a superthin layer to address the electrochemical reaction,which provides a clear description of the fl ooding eff ect on mass transport and performance.Diff erent kinds of electrodes are reconstructed to determine the optimum porosity and structure design of the GDL and MPL by comparing the transport resistance and per-formance under the fl ooding condition.The simulation results show that gradient porosity GDL helps to increase the reactive area and average concentration under fl ooding.The presence of the MPL ensures the oxygen transport space and reaction area because liquid water cannot transport through micropores.Moreover,the MPL helps in the uniform distribution of oxygen for an effi cient in-plane transport capacity.Crack and perforation structures can accelerate the water transport in the assembly.The systematic perforation design yields the best performance under fl ooding by separating the transport of liquid water and oxygen.

Numerical Simulation of a Two-Phase Flow with Low Permeability anda Start-Up Pressure Gradient

A new numerical model for low-permeability reservoirs is developed.The model incorporates the nonlinear characteristics of oil-water two-phase flows while taking into account the initiation pressure gradient.Related numerical solutions are obtained using a finite difference method.The correctness of the method is demonstrated using a two-dimensional inhomogeneous low permeability example.Then,the differences in the cumulative oil and water production are investigated for different starting water saturations.It is shown that when the initial water saturation grows,the water content of the block continues to rise and the cumulative oil production gradually decreases.

Study on two-phase cloud dispersion from liquefied CO_(2) release

The knowledge of two-phase cloud dispersion mechanism from HLG(hazardous liquefied gas) release is the prerequisite for accurate assessment and precise rescue of such accidents. In this paper, an experiment of two-phase cloud dispersion from liquefied CO_(2) hole release is performed. The source terms, such as vapour mass fraction, release velocity and mean droplet diameter, are calculated based on thermodynamic theory. Taking phase transition of CO_(2) droplets to gas into account, CFD(computational fluid dynamics) model for two-phase cloud dispersion is established. The predicted cloud temperatures at the downstream agree well with the experimental data, with the maximum relative error of 5.8% and average relative error of 2.3%. The consequence distances in the downstream direction and in the crosswise direction calculated through two-phase model are larger than those through single-phase model,with the relative differences of 57.8% and 53.6% respectively. CO_(2) concentration calculated by twophase model is smaller in the vicinity of release hole, and larger beyond 0.135 m downstream. A smaller leakage rate results in a lower CO_(2) concentration and a higher cloud temperature.

Characterisation and separation of infectious bursal disease virus-like particles using aqueous two-phase systems

Infectious bursal disease(IBD)causes considerable economic losses in the commercial poultry industry worldwide.The principal way to control IBD virus(IBDV),the causative agent of IBD,is still through vaccination programs.Virus-like particles(VLPs)are recognised as a safe and potent recombinant vaccine platform.This research work explores the characterisation and separation of infectious bursal disease virus-like particles(IBD-VLPs)from crude feedstock.Various characteristics were studied with highperformance size-exclusion chromatography(HP-SEC),sodium dodecyl sulphate–polyacrylamide gel electrophoresis(SDS-PAGE)and transmission electron microscopy(TEM)analyses.Subsequently,the separation of IBD-VLPs using polyethylene glycol(PEG)/sodium citrate-based aqueous two-phase systems(ATPSs)was conducted and optimised.Moreover,a scale-up study of the best ATPS constituted of 15%PEG 6000,11%sodium citrate and 10%crude feedstock was performed to compare the separation performance of IBD-VLPs with and without centrifugation-assisted.The results indicated that the optimised ATPS with centrifugation-assisted for both 5 g and 50 g systems showed good recovery of IBDVLPs of>97%in the interphase between the PEG-rich top and salt-rich bottom phases.These optimised systems also showed high removal efficiencies of impurities of>95%.The results demonstrated that aqueous two-phase extraction could be a promising technology for efficient VLPs separation.

Performance analyses of two-phase closed thermosyphons for road embankments in the high-latitude permafrost regions

Two-phase closed thermosyphons(TPCTs)are widely used in infrastructure constructions in permafrost regions.Due to different climatic conditions,the effectiveness of TPCT will also be different,especially in the extremely cold region of the Da Xing'anling Mountains.In this study,a series of three-dimensional finite element TPCT embankment models were established based on the ZhanglingMohe highway TPCT test section in Da Xing'anling Mountains,and the thermal characteristics and the cooling effect of the TPCTs were analyzed.The results indicated that the TPCTs installed in the northeastern high-latitude regions is effective in cooling and stabilizing the embankment.The working cycle of the TPCTs is nearly 7 months,and the cooling range of the TPCTs can reach 3 m in this region.However,due to the extremely low temperature,the TPCT generates a large radial gradient in the permafrost layer.Meanwhile,by changing the climate conditions,the same type of TPCT embankment located in the Da Xing'anling Mountains,the Xiao Xing'anling Mountains,and the Qinghai-Tibet Plateau permafrost regions were simulated.Based on the comparison of the climate differences between the Qinghai-Tibet Plateau and Northeast China,the differences in the effectiveness of TPCTs were studied.Finally,the limitations of using existing TPCTs in high-latitude permafrost regions of China were discussed and the potential improvements of the TPCT in cold regions were presented.

Comprehensive modeling of frictional pressure drop during carbon dioxide two-phase flow inside channels using intelligent and conventional methods

Environmentally friendly nature of CO_(2),associated with its safety and high efficiency,has made it a widely used working fluid in heat exchangers.Since CO_(2)has strange thermophysical features,specific models are required to estimate its two-phase characteristics,particularly frictional pressure drop(FPD).Herein,a widespread dataset,comprising 1195 experimental samples for two-phase FPD of CO_(2)was adopted from 10 sources to fulfill this requirement.The literature correlations failed to provide satisfactory precisions and exhibited the average absolute relative errors(AAREs)between 29.29% and 67.69% from the analyzed data.By inspiring the theoretical method of Lockhart and Martinelli,three intelligent FPD models were presented,among which the Gaussian process regression approach surpassed the others with AARE and R^(2)values of 5.48% and 98.80%,respectively in the test stage.A novel simple correlation was also derived based on the least square fitting method,which yielded opportune predictions with AARE of 19.76% for all data.The truthfulness of the newly proposed models was assessed through a variety of statistical and visual analyses,and the results affirmed their high reliability over a broad range of conditions,channel sizes and flow patterns.Furthermore,the novel models performed favorably in describing the physical attitudes corresponding to two-phase FPD of CO_(2).Eventually,the importance of operating factors in controlling the FPD was discussed through a sensitivity analysis.