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.

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.

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.

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.

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.

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.

Effect of perforation density distribution on production of perforated horizontal wellbore

To address the issue of horizontal well production affected by the distribution of perforation density in the wellbore,a numerical model for simulating two-phase flow in a horizontal well is established under two perforation density distribution conditions(i.e.increasing the perforation density at inlet and outlet sections respectively).The simulation results are compared with experimental results to verify the reliability of the numerical simulation method.The behaviors of the total pressure drop,superficial velocity of air-water two-phase flow,void fraction,liquid film thickness,air production and liquid production that occur with various flow patterns are investigated under two perforation density distribution conditions based on the numerical model.The total pressure drop,superficial velocity of the mixture and void fraction increase with the air flow rate when the water flow rate is constant.The liquid film thickness decreases when the air flow rate increases.The liquid and air productions increase when the perforation density increases at the inlet section compared with increasing the perforation density at the outlet section of the perforated horizontal wellbore.It is noted that the air production increases with the air flow rate.Liquid production increases with the bubble flow and begins to decrease at the transition point of the slug-stratified flow,then increases through the stratified wave flow.The normalized liquid flux is higher when the perforation density increases at the inlet section,and increases with the radial air flow rate.

Effect of the Particle Packing Configuration on Fixed Bed Performance

Fixed-bed reactors are generally considered the optimal choice for numerous multi-phase catalytic reactions due to their excellent performance and stability.However,conventional fixed beds often encounter challenges related to inadequate mass transfer and a high pressure drop caused by the non-uniform void fraction distribution.To enhance the overall performance of fixed beds,the impact of different packing configurations on performance was investigated.Experimental and simulation methods were used to investigate the fluid flow and mass transfer performances of various packed beds under different flow rates.It was found that structured beds exhibited a significantly lower pressure drop per unit length than conventional packed beds.Furthermore,the packing configurations had a critical role in improving the overall performance of fixed beds.Specifically,structured packed beds,particularly the H-2 packing configuration,effectively reduced the pressure drop per unit length and improved the mass transfer efficiency.The H-2 packing configuration consisted of two parallel strips of particles in each layer,with strips arranged perpendicularly between adjacent layers,and the spacing between the strips varied from layer to layer.

A Calculation of Steady Pressure Drop and an Analysis of HT-7U CICC

Under the condition of steady state, the pressure drop of coolant is mainly caused by friction along the cable. In the CICC (cable-in-conduit-conductor), helium flow within the conductor consists of two parallel interconnected tubes. The velocity distribution has some differece between the central channel and conductor space. The region of Reynolds number is from 103 to 106. This paper describes the calculation of pressure drop of HT-7U CICC at various mass flows. It is assumed that the coolant flows in two parallel, rough tubes during the calculation.

Effect of Radial Resistance Gap on the Pressure Drop of a Compact Annular-Radial-Orifice Flow Magnetorheological Valve

A compact annular-radial-orifice flow magnetorheological(MR)valve was developed to investigate the effects of radial resistance gap on pressure drop.The fluid flow paths of this proposed MR valve consist of a single annular flow channel,a single radial flow channel and an orifice flow channel through structure design.The finite element modelling and simulation analysis of the MR valve was carried out using ANSYS/Emag software to investigate the changes of the magnetic flux density and yield stress along the fluid flow paths under the four different radial resistance gaps.Moreover,the experimental tests were also conducted to evaluate the pressure drop,showing that the proposed MR valve has significantly improved its pressure drop at 0.5 mm width of the radial resistance gap when the annular resistance gap is fixed at 1 mm.

Analysis of MHD Pressure Drop in Liquid LiPb Flow in Chinese ITER DFLL-TBM with Insulating Coating

Magnetohydrodynamic （MHD） pressure drop in the Chinese Dual Functional Liquid Lithium-lead Test Blanket Module （DFLL-TBM） proposed for ITER is discussed in this paper. Electrical insulation between the coolant channel surfaces and the liquid metal is required to reduce the MHD pressure drop to a manageable level. Insulation can be provided by a thin insulating coating, such as Al2O3, which can also serve as a tritium barrier layer, at the channel surfaces in contact with LiPb. The coating＇s effectiveness for reducing the MHD pressure drop is analysed through three-dimensional numerical simulation. A MHD-based commercial computational fluid dynamic （CFD） software FLUENT is used to simulate the LiPb flow. The effect on the MHD pressure drop due to cracks or faults in the coating layer is also considered. The insulating performance requirement for the coating material in DFLL-TBM design is proposed according to the analysis.

A pressure drop model of post-fracturing shut-in considering the effect of fracturing-fluid imbibition and oil replacement

Since the production regime of shut-in after fracturing is generally adopted for wells in shale oil reservoir,a shut-in pressure drop model coupling wellbore-fracture network-reservoir oil-water two-phase flow has been proposed.The model takes into account the effects of wellbore afterflow,fracture network channeling,and matrix imbibition and oil exchange after stop of pumping.The simulated log-log curve of pressure-drop derivative by the model presents W-shape,reflecting the oil-water displacement law between wellbore,fracture network and matrix,and is divided into eight main control flow stages according to the soaking time.In the initial stage of pressure drop,the afterflow dominates;in the early stage,the pressure drop is controlled by the cross-flow and leakoff of the fracture system,and the fractures close gradually;in the middle stage of pressure drop,matrix imbibition and oil exchange take dominance,and the fracturing fluid loss basically balances with oil replaced from matrix;the late stage of pressure drop is the reservoir boundary control stage,and the leakoff rate of fracturing-fluid and oil exchange rate decrease synchronously till zero.Finally,the fracture network parameters such as half-length of main fracture,main fracture conductivity and secondary fracture density were inversed by fitting the pressure drop data of five wells in Jimsar shale oil reservoir,and the water imbibition volume of matrix and the oil replacement volume in fracture were calculated by this model.The study results provide a theoretical basis for comprehensively evaluating the fracturing effect of shale oil hori-zontal wells and understanding the oil-water exchange law of shale reservoir after fracturing.

Preliminary Analysis of Liquid Metal MHD Pressure Drop in the Blanket for the FDS

Preliminary analysis and calculation of liquid metal Li17Pb83 magnetohydrodynamic (MHD) pressure drop in the blanket for the FDS have been presented to evaluate the significance of MHD effects on the thermal-hydraulic design of the blanket. To decrease the liquid metal MHD pressure drop, Al2O3 is applied as an electronically insulated coating onto the inner surface of the ducts. The requirement for the insulated coating to reduce the additional leakage pressure drop caused by coating imperfections has been analyzed. Finally, the total liquid metal MHD pressure drop and magnetic pump power in the FDS blanket have been given.

Experimental study on prediction model of wet gas pressure drop across single-orifice plate in horizontal pipes in the low gas phase Froude number region

The pressure drop prediction of wet gas across single-orifice plate in horizontal pipes had been solved satisfactorily under an annular-mist flow in the upstream of orifice plates.However,this pressure drop prediction is still not clearly determined when the upstream is in an intermittent flow or stratified flow,which is corresponding to a region of low FrG(gas phase Froude number)in the flow pattern map of wet gases.In this study,the wet gas pressure drop across a single-orifice plate was experimentally investigated in the low FrG region.By the experiment,the flow pattern transition in the downstream of single-orifice plates,as well as the effects of FrG and FrL(liquid phase Froude number)on UG(gas phase multiplier),were determined and compared when the upstream is in the flow pattern transition and the stratified flow region,respectively.Prediction performances were examined on the available pressure drop models.It was found that no model could be capable of jointly predicting the wet gas pressure drop in the low FrG region with an acceptable accuracy.With a new method of correlating FrG and FrL simultaneously,new correlations were proposed for the low FrG region.Among which the modified Chisholm model shows the best prediction accuracies,with the prediction deviations of UG being within 7%and 3%when the upstream is in flow pattern transition and stratified flow region,respectively.

Heat Transfer Characteristics and Pressure Drop in a Horizontal Circulating Fluidized Bed Evaporator

A vapor-liquid-solid horizontal circulating fluidized bed evaporation setup was constructed to study the thermal-exchange properties and pressure change.The influences of the operating variables,including the amount of added particles,heat flux,and circulating flow velocity,were systematically inspected using resistance temperature detectors and pressure sensors.The results showed that the heat transfer eff ect was improved with the increase in the amount of added particles,circulating flow velocity,and particle diameter,but decreased with increasing heat flux.The pressure drop fluctuated with the increase in operating parameters,except circulating flow velocity.The enhancing factor reached up to 71.5%.The enhancing fac-tor initially increased and then decreased with the increase in the amount of added particles and circulating flow velocity,fluctuated with increasing particle diameter,and decreased with increasing heat flux.Phase diagrams showing the variation ranges of the operation variables for the enhancing factor were constructed.

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.

Expansion of Application Range of Component Restricting Pressure Change Caused by Oil Temperature Change

One of the advantages of an oil-hydraulic system is that the system keeps the value of oil pressure when the pressurized oil is enclosed in a container.However,when the pressurized oil is enclosed in a head or a rod end chamber of an actuator by a check valve or a shut-off valve,the value of the oil pressure deceases gradually by the leakage from the check valve or the shut-off valve.Then,it is necessary to employ non-leakage valve which is expensive or to control the pressure by using a valve or a pump control.In pressure control,energy to compensate pressure is required.From the view point of cost reducing or especially energy saving,it seems to be desirable to develop a component which prevents this pressure drop without energy consumption.Authors had developed a component restricting pressure change caused by oil temperature change.This component has simple mechanism and hardly needs energy.In this study,the possibility of the component to prevent pressure drop due to leakage is investigated experimentally.Consequently,it makes clear that the component is effective to prevent pressure drop by leakage and the enclosed pressure decreases only about 3%in 3 min and about 7%in 60 min when the target enclosed pressure is 3.5 MPa.

Viscous behavior of 1-hexyl-methylimidazolium bis(trifluoromethylsulfonyl)imide/titanium dioxide/polyethylene glycol

Viscous behavior is important for the process design, especially for the non-Newtonian fluid. In this study, the viscous behaviors of slurry, i.e., 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)im ide([Hmim][NTf_(2)])/titanium dioxide(TiO_(2))-polyethylene glycol(PEG200), were determined experimentally and systematically. The pressure drop was estimated when [Hmim][NTf_(2)]/TiO_(2)-PEG200 was used as the solvent in the absorption/desorption towers. The results show that the slurry belongs to the non-Newtonian fluid with shear-thinning behavior. High temperature and low solid content are beneficial to reduce the viscosity of [Hmim][NTf_(2)]/TiO_(2)-PEG200, and the presence of [Hmim][NTf_(2)] can effectively reduce the viscosity of the slurry. In addition, high temperature is preferable for reducing the pressure drop, and the pressure drop of slurry with the solid content value of 8.0%(mass) can reduce by 28.0%when the temperature increases from 313 to 333 K.

Simulation of gas–liquid two-phase flow in a flow-focusing microchannel with the lattice Boltzmann method

A lattice Boltzmann method for gas–liquid two-phase flow involving non-Newtonian fluids is developed. Bubble formation in a flow-focusing microchannel is simulated by the method. The influences of flow rate ratio, surface tension,wetting properties, and rheological characteristics of the fluid on the two-phase flow are analyzed. The results indicate that the flow pattern transfers from slug flow to dry-plug flow with a sufficiently small capillary number. Due to the presence of three-phase contact lines, the contact angle has a more significant effect on the dry-plug flow pattern than on the slug flow pattern. The deformation of the front and rear meniscus of a bubble in the shear-thinning fluid can be explained by the variation of the capillary number. The reduced viscosity and increased contact angle are beneficial for the drag reduction in a microchannel. It also demonstrates the effectiveness of the current method to simulate the gas–liquid two-phase flow in a microchannel.

Optimal Concentration of the Bubble Drainage Agent in Foam Drainage Gas Recovery Applications

Foam drainage is theflow of liquid through the interstitial spaces between bubbles driven by capillarity and grav-ity and resisted by viscous damping.The so-called foam drainage gas recovery technology is a technique tradi-tionally used to mitigate the serious bottom-hole liquid loading in the middle and late stages of gas well production.In this context,determining the optimal concentration of the bubble drainage agent is generally cru-cial for the proper application of this method.In this study,a combination of indoor experiments and theoretical analysis have been used to determine the pressure drop related to the foam-carrying capacity in a representative gasfield.Dynamic and static experiments were designed with a bubble drainage agent concentration varying in the range 0.3%–0.6%.Using thefield formation water data,the optimal soaking agent concentration was obtained and pressure drop test experiments on the foam carrying capacity were conducted accordingly.These tests have revealed that the optimal foam displacement agent concentration is 0.5%,and the foam quality at the optimum concentration is between 0.78–0.98.A theoretical method for calculating the pressure drop at the optimum soak-away concentration based on experimental data has also been introduced.The error of the proposed method is within 15%compared to the experimental measured value,demonstrating that it is highly accurate and simple.