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.

Buckling Properties of Water-Drop-Shaped Pressure Hulls with Various Shape Indices Under Hydrostatic External Pressure

The water-drop-shaped pressure hull has a good streamline,which has good application prospect in the underwater observatory.Therefore,this study conducted analytical,experimental and numerical investigation of the buckling properties of water-drop-shaped pressure hulls under hydrostatic pressure.A water-drop experiment was conducted to design water-drop-shaped pressure hulls with various shape indices.The critical loads for the water-drop-shaped pressure hulls were resolved by using Mushtari’s formula.Several numerical simulations including linear buckling analysis and nonlinear buckling analysis including eigenmode imperfections were performed.The results indicated that the critical loads resolved by Mushtari's formula were in good agreement with the linear buckling loads from the numerical simulations.This formula can be extended to estimate the buckling capacity of water-drop-shaped pressure hulls.In addition,three groups of pressure hulls were fabricated by using stereolithography,a rapid prototyping technique.Subsequently,three groups of the pressure hulls were subjected to ultrasonic measurements,optical scanning,hydrostatic testing and numerical analysis.The experimental results were consistent with the numerical results.The results indicate that the sharp end of the water-drop-shaped pressure hulls exhibited instability compared with the blunt end.This paper provides a new solution to the limitations of experimental studies on the water-drop-shaped pressure hulls as well as a new configuration and evaluation method for underwater observatories.

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.

Flow pattern and pressure drop of gas-liquid two-phase swirl flow in a horizontal pipe

The gas-liquid two-phase swirl flow can increase the gas-liquid two-phase contact area and enhance the heat and mass transfer efficiency between gas and liquid.The swirl flow has important practical application value for promoting gas hydrate formation and ensuring the flow safe of natural gas hydrate slurry.The experimental section was made of plexiglass pipe and the experimental medium was air and water.The flow pattern of the gas-liquid two-phase swirl flow in the horizontal pipe was divided,according to a high-definition camera and the overall characteristics of the gas-liquid interface.The flow pattern map of the gas-liquid two-phase swirl flow in a horizontal pipe was studied.The influence of the flow velocity and vane parameters on pressure drop was investigated.Two types of gas-liquid two-phase swirl flow pressure drop models was established.The homogeneous-phase and split-phase pressure drop models have good prediction on swirl bubble flow,swirl dispersed flow,swirl annular flow and swirl stratified flow,and the predictive error band is not more than 20%.

Measurement and Correlation of Pressure Drop for Gas-Liquid Two-phase Flow in Rectangular Microchannels

The pressure drop of gas-liquid two-phase flow in microchannel is of fundamental importance in heat and mass transfer processes. In this work,the pressure drop of gas-liquid two-phase flow in horizontal rectangular cross-section microchannels was measured by a pressure differential transducer system. Water,ethanol and n-propanol were used as liquid phase to study the effects of capillary number on pressure drop;air was used as the gas phase. Four microchannels with various dimensions of 100 μm× 200 μm,100 μm× 400 μm,100 μm× 800 μm and 100 μm× 2000 μm(depth × width) were used for determining the influence of configuration on the pressure drop. Experimental results showed that in micro-scale,the capillary number also affected the pressure drop remarkably,and in spite of only one-fold difference in aspect ratio,the variation of pressure drop reached up to near three times under the same experimental conditions. Taking the effects of aspect ratio and surface tension into account,a modi-fied correlation for Chisholm parameter C in the Chisholm model was proposed for predicting the frictional multi-plier,and the predicted values by the proposed correlation showed a satisfactory agreement with experimental data.

Pressure Drop of Liquid–Solid Two-Phase Flow in the Vertical Tube Bundle of a Cold-Model Circulating Fluidized Bed Evaporator

A cold-model vertical multi-tube circulating fluidized bed evaporator was designed and built to conduct a visualization study on the pressure drop of a liquid–solid two-phase flow and the corresponding particle distribution.Water and polyformaldehyde particle(POM)were used as the liquid and solid phases,respectively.The effects of operating parameters such as the amount of added particles,circulating flow rate,and particle size were systematically investigated.The results showed that the addition of the particles increased the pressure drop in the vertical tube bundle.The maximum pressure drop ratios were 18.65%,21.15%,18.00%,and 21.15%within the experimental range of the amount of added particles for POM1,POM2,POM3,and POM4,respectively.The pressure drop ratio basically decreased with the increase in the circulating flow rate but fluctuated with the increase in the amount of added particles and particle size.The difference in pressure drop ratio decreased with the increase in the circulating flow rate.As the amount of added particles increased,the difference in pressure drop ratio fluctuated at low circulating flow rate but basically decreased at high circulating flow rate.The pressure drop in the vertical tube bundle accounted for about 70%of the overall pressure drop in the up-flow heating chamber and was the main component of the overall pressure within the experimental range.Three-dimensional phase diagrams were established to display the variation ranges of the pressure drop and pressure drop ratio in the vertical tube bundle corresponding to the operating parameters.The research results can provide some reference for the application of the fluidized bed heat transfer technology in the industry.

Numerical analysis of the two-phase pressure drop and liquid distribution in single-screw expander prototype

In this paper, the numerical simulations have been carried out to evaluate the two-phase pressure drop and liquid distribution in screw channel. The numerical models are validated against the present experimental data with statistical accuracy. The effects of pitch circle diameter(PCD), inlet velocity and inlet sectional liquid holdup on the pressure drop and liquid distribution characteristics in the screw channel are illustrated. It is found that decreasing the PCD and increasing the inlet sectional liquid holdup can increase the liquid holdup on the outer side in screw channel. The PCD and the inlet sectional liquid holdup need to be considered in evaluating the two-phase frictional pressure drop per unit length in the screw channel. The PCD has an effect on the development of the average pressure in the various cross sections, and the inlet sectional liquid holdup has no visible impact on the changing process of the pressure drop in the screw channel. The correlation developed predicts the two-phase frictional pressure drop in the screw channel with great statistical accuracy.

A Pressure-Drop Model for Oil-Gas Two-Phase Flow in Horizontal Pipes

The accurate prediction of the pressure distribution of highly viscous fluids in wellbores and pipelines is of great significance for heavy oil production and transportation.The flow behavior of high-viscosity fluids is quite different with respect to that of low-viscosity fluids.Currently,the performances of existing pressure-drop models seem to be relatively limited when they are applied to high-viscosity fluids.In this study,a gas-liquid two-phase flow experiment has been carried out using a 60 mm ID horizontal pipe with air and white oil.The experimental results indicate that viscosity exerts a significant influence on the liquid holdup and pressure drop.At the same gas and liquid volume,both the liquid holdup and pressure drop increase with an increase in the viscosity.Combining two existing models,a modified pressure drop method is developed,which is applicable to horizontal pipes for different viscosities and does not depend on the flow pattern.This new method displays a high accuracy in predicting the new experimental data presented here and other published data in literature.

Pressure drop of the film-enlarged tube bundles in air-water two-phase cross flow in evaporative air cooler

An experiment was carried out to investigate the relation of the maximum velocity of air passing through narrowest passage, mass flux of spray water in one square meter in one hour and the pressure drop of tube bundles. Twelve equations were obtained for the relation. The results show that the pressure drop of the tube bundles increases with increase of the maximum velocity of air and the mass flux of spray water. Comparing the pressure drop of the bare tube bundles with that of the film-enhanced tube bundles, it is found that the pressure drop of the film-enhanced tube bundles is lower about 11% and the surface roughness of the film-enhanced plates is a main factor that influences the pressure drop. The data and method obtained in the paper can be used to compute the pressure drop of the film-enhanced tube bundles and is helpful for selection of fan.

Experimental study on steam-water two-phase flow frictional pressure drops in helical coils

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In Tube Condensation:Changing the Pressure Drop into a Temperature Difference for a Wire-on-Tube Heat Exchanger

A theoretical study based on the Penalty factor(PF)method by Cavallini et al.is conducted to show that the pressure drop occurring in a wire-on-tube heat exchanger can be converted into a temperature difference for two types of refrigerants R-134a and R-600a typically used for charging refrigerators and freezers.The following conditions are considered:stratified or stratified-wavyflow condensation occurring inside the smooth tube of a wire-on-tube condenser with diameter 3.25,4.83,and 6.299 mm,condensation temperatures 35℃,45℃,and 54.4℃ and cover refrigerant massflow rate spanning the interval from 1 to 7 kg/hr.The results show that the PF variation is not linear with vapor quality and attains a maximum when the vapor quality is 0.2 and 0.18 for the R-134a and R-600a refrigerants,respectively.The PF increases with the refrigerant massflow rate if the inner diameter and saturation temperature constant,and it decreases on increasing the inner diameter to 6.299 mm for constant refrigerant massflow rate and saturation temperature.The PF for R-600a is higher than that for R-134a due to the lower saturation pressure in thefirst case.Furthermore,a stratifiedflow produces higher PF in comparison to the annularflow due to the effect of the surface tension.

Pressure drop of structured packing in pilot column and comparison to common correlations

Packed columns are widely used in the chemical industry such as absorption,stripping,distillation,and extraction in the production of e.g.organic chemicals,and pharmaceuticals.Pressure loss and pressure drop correlations are of special interest when it comes to the hydrodynamic properties of a column.The pressure loss across the column is of interest in the design phase when the size of the blower to drive the gas stream through the column has to be decided.The loading point and flooding point are also influenced by the pressure loss and the area of operation is determined from these points.This work examines four different correlations on pressure drop.The correlations are(i)Ergun’s equation(1952),(ii)an improved version of Ergun’s equation by Stichlmair,Bravo,and Fair(1989),(iii)an equation developed by Billet and Schultes(1999),and(iv)an equation by Rocha,Bravo,and Fair(1993).The complexity of the correlations is increasing in the mentioned order,Ergun’s equation being the simplest one.This study investigates if the more complicated correlations give better predictions to pressure drop in packed columns.This is determined by comparing the correlations to experimental data for pressure drop in a packed column with 8.2 m of structured packing using water as the liquid and atmospheric air as the gas.Seven experiments were carried out for determining the pressure drop in the column with liquid flows varying from 0 to 500 kg·h^(-1).At constant liquid flow,the gas flow was varied from approximately 10 to 70 kg·h^(-1).The pressure drop across the non-wetted column was best described by the correlation by Rocha et al.while the pressure drop for liquid flows from 100 to 500 kg·h^(-1)was,in general,best described by Stichlmair’s equation.For an irrigated column,the highest deviation was a predicted pressure drop 69.6%lower than measured.The best prediction was 0.1%higher than the measured.This study shows,surprisingly,that for a system of water and atmospheric air,complicated correlations on pressure drop determination do not provide better estimates than simple equations.

Multi-criteria comparative analysis of the pressure drop on coal gangue fly-ash slurry at different parts along an L-shaped pipeline

Disposing of coal gangue and fly-ash on the surface is a risky method with tremendous potential catastrophic consequences for the environment.Backfill mining is a promising practice for turning those hazardous wastes into functional backfill materi-als.Unfortunately,how to efficiently deliver the slurry to the desired places remains under-researched.To address this issue,the computational fluid dynamics software Fluent was used in the current study in addition to a laboratory rheological test to simulate the impact of various parameters on the evolution of pressure at a particular section of the pipeline.Furthermore,the response surface method was employed to investigate how the various components and their corresponding influencing weights interact to affect the pressure drop.This study demonstrates that the pressure drop of the slurry is highly influenced by slurry concentration,speed,and pipe diameter.While conveying speed is the main component in the bend section,pipe diameter takes over in the horizontal and vertical pipe sections.

Influence of Wellbore Trajectory on Pressure Drop and Fluid Discharge

An experimental analysis has been conducted to study the process of fluid accumulation for different borehole trajectories.More specifically,five heel angles have been experimentally realized to simulate the borehole trajectory of the sloping section of the formation.The fluid-carrying capacity,pressure drop and fluid discharge volatility have been investigated for these conditions and,accordingly,the relationship between heel angle and wellbore pressure drop fluid-carrying capacity has been determined.The results show that while the reasonable roll angle can increase the pressure loss in the wellbore,it is beneficial to drainage.In terms of pressure loss and liquid-carrying capacity,when the heeling angle is 50°,the latter is increased while the former becomes very high,which indicates that when drilling and completing wells on site,a 50°roll angle should be avoided.It is found that the main reason for the increase of the total pressure drop in the wellbore is the increase of the local pressure loss in the inclined section.From the perspective of drainage stability,when there is heeling in the inclined section of the horizontal well,the fluctuation of the wellbore drainage tends to be enhanced.Through the comparison of the Beggs-Brill(B-B)and Mukherjee-Brill liquid holdup methods,it is found that B-B method better predicts liquid holdup.A new method for calculating the pressure drop in the inclined section in the presence of lateral inclination is obtained by taking into account the pressure drop in the curved section.Through comparison with experimental data,it is found that the error is within 20%,and the prediction accuracy is high.

Pump-stopping pressure drop model considering transient leak-off of fracture network

By introducing the coupling flow expressions of main fracture-matrix, secondary fracture-matrix and main fracture-secondary fracture into the traditional main fracture material balance equation, the “main fracture-secondary fracture-matrix” leak-off coupling flow model is established. The pressure-dependent fracture width equation and the wellbore injection volume equation are coupled to solve the pressure-rate continuity problem. The simulation and calculation of the bottomhole pressure drop and fracture network closure after the pump stopping in slickwater volumetric fracturing treatment are realized. The research results show that the log-log curve of pump-stopping bottomhole pressure drop derivative presents five characteristic slope segments, reflecting four dominant stages, i.e. inter-fracture crossflow, fracture network leak-off, fracture network closure and residual leak-off, after pump shutdown. At the initial time of pump shutdown for volumetric fracturing treatment of horizontal well, the crossflow between main and secondary fractures is obvious, and then the leak-off becomes dominant. The leak-off of main and secondary fractures shows a non-uniform decreasing trend. Specifically, the leak-off of main fractures is slow, while that of secondary fractures is fast;the fracture network as a whole presents the leak-off law of fast first, then slow, until close to zero. The influence of fracture network conductivity on the shape of pressure decline curve is relatively weaker than that of fracture network size. The fracture network conductivity is positively correlated with leak-off volume and fracture closure. The secondary fracture size is positively correlated with leakoff volume and closure of the secondary fracture, but negatively correlated with closure of the main fracture. Field data validation proves that the proposed model and simulation results can effectively reflect the closure characteristics of the fracture network, and the interpretation results are reliable and can reflect the non-uniform stimulation performance of each fracturing stage of an actual horizontal well.

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.

Numerical Simulation and Experimental Analysis of the Influence of Asymmetric Pressure Conditions on the Splitting of a Gas-Liquid Two-Phase Flow at a T-Junction

Dedicated experiments and numerical simulations have been conducted to investigate the splitting characteristics of a gas-liquid two phase flow at a T junction.The experiments were carried out for different gas-liquid velocities.The flow rates in the two branches were measured accurately to determine how the two considered phases distribute in the two outlets.The experimental results have shown that when the two outlet pressures are asymmetric,the two-phase flow always tends to flow into the outlet which has a lower pressure.As the inlet liquid velocity increases,however,the two-phase flow gradually tends to split evenly.Compared with the experiment results,the pressure difference between the two outlets can be determined more accurately by means of numerical simulation.The trends of experimental results and simulations are in very good agreement.

A lattice Boltzmann exploration of two-phase displacement in 2D porous media under various pressure boundary conditions

While experimental designs developed in recent decades have contributed to research on dynamic nonequilibrium effects in transient two-phase flow in porous media,this problem has been seldom investigated using direct numerical simulation(DNS).Only a few studies have sought to numerically solve Navier—Stokes equations with level-set(LS)or volume-of-fluid(VoF)methods,each of which has constraints in terms of meniscus dynamics for various flow velocities in the control volume(CV)domain.The Shan—Chen multiphase multicomponent lattice Boltzmann method(SC-LBM)has a fundamental mechanism to separate immiscible fluid phases in the density domain without these limitations.Therefore,this study applied it to explore two-phase displacement in a single representative elementary volume(REV)of two-dimensional(2D)porous media.As a continuation of a previous investigation into one-step inflow/outflow in 2D porous media,this work seeks to identify dynamic nonequilibrium effects on capillary pressure—saturation relationship(P_(c)—S)for quasi-steady-state flow and multistep inflow/outflow under various pressure boundary conditions.The simulation outcomes show that P_(c),S and specific interfacial area(a_(nw))had multistep-wise dynamic effects corresponding to the multistep-wise pressure boundary conditions.With finer adjustments to the increase in pressure over more steps,dynamic nonequilibrium effects were significantly alleviated and even finally disappeared to achieve quasisteady-state inflow/outflow conditions.Furthermore,triangular wave-formed pressure boundary conditions were applied in different periods to investigate dynamic nonequilibrium effects for hysteretical Pc—S.The results showed overshoot and undershoot of P_(c)to S in loops of the nonequilibrium hysteresis.In addition,the flow regimes of multistep-wise dynamic effects were analyzed in terms of Reynolds and capillary numbers(Re and Ca).The analysis of REV-scale flow regimes showed higher Re(1<Re<10)for more significant dynamic nonequilibrium effects.This indicates that inertia is critical for transient twophase flow in porous media under dynamic nonequilibrium conditions.

Gas-Liquid Two-Phase Axial Backmixing Through Structured Packing at Elevated Pressure

An experimental study of the extent of axial backmixing in both gas and liquid phases was conducted in a 150 mm ID column packed with Mellapak 250Y corrugated structured packing. The column was operated at pressures ranging from 0.3 MPa to 2.0MPa with nitrogen and water flowing countercurrently through the packing. The amount of axial backmixing was experimentally evaluated by the pulse response techniques using hydrogen in gas phase and an aqueous solution of NaCl in liquid phase as inert tracers. The response of the tracer was monitored by means of thermal conductivity in the gas phase and electrical conductance in the liquid phase. The experimentally determined residence time distribution (RTD) curves were interpreted in terms of the diffusion-type modei. The results indicated that the axial backmixing in the gas increased notably with gas flowrate and slightly with operating pressure and liquid flowrate. The liquid-phase axial backmixing was an increasing function of both gas and liquid flowrates and insensitive to pressure. Various correlations were developed for reproducing the experimental mixing data. The agreement between experimental and correlated data appeared to be acceptable and within ±20% of difference.