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.

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.

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.

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.

Numerical study of pressure drop for a new fibrous media model

An open-source computational fluid dynamics（CFD）code named OpenFOAM is used to validate the flow field characteristics（flow patterns and pressure drop）around a single cylinder.Results show that OpenFOAM is suitable for simulating the low Reynolds number flow and Shaw＇s analytical expression is one of the solutions to Stokes＇ paradox.Experiments are performed on fibrous media and OpenFOAM simulation is carried out using the Tronville-Rivers two-dimensional random fiber model in terms of the characteristics of pressure drop.It is shown that the Kuwabara model predicts the pressure drop of fibrous filter media more accurately than the Happel model,and the experimental pressure drop is between simulated pressure drops with both non-slip and full-slip boundaries on fiber surfaces.

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.

Prediction of Pressure Drop of Slurry Flow in Pipeline by Hybrid Support Vector Regression and Genetic Algorithm Model

This paper describes a robust support vector regression （SVR） methodology, which can offer superior performance for important process engineering problems. The method incorporates hybrid support vector regression and genetic algorithm technique （SVR-GA） for efficient tuning of SVR meta-parameters. The algorithm has been applied for prediction of pressure drop of solid liquid slurry flow. A comparison with selected correlations in the lit- erature showed that the developed SVR correlation noticeably improved the prediction of pressure drop over a wide range of operating conditions, physical properties, and pipe diameters.

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%.

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.

Research on Pressure Drop Performance of the Packing-Flotation Column

A packing-flotation column was proposed to optimize the flotation environment A research system was es- tablished using a 100 mm diameter cyclonic micro-bubble flotation column to study fluid properties. Dry-plate and wet- plate pressure drops were studied and the corresponding pressure drop equations developed. The results show that the dry-plate pressure drop of the packing cyclonic micro-bubble flotation column is 10–15 times less than that of the chemical tower, which is principally shown in its relatively small resistance coefficient, ξ ≈0.0207. The wet-plate pressure drop is 2–3 times higher than that of the chemical tower, which is largely caused by the separation materials and characteristics of the equipment. With flotation, the greater the pressure drop, the better the flotation environment.

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.

Experimental investigation on boiling heat transfer and pressure drop of R245fa in a horizontal micro-fin tube

An experimental investigation on the boiling heat transfer and frictional pressure drop of R245fa in a 7 mm horizontal micro-fin tube was performed.The results show that in terms of flow boiling heat transfer characteristics,boiling heat transfer coefficient(HTC)increases with mass velocity of R245fa,while it decreases with the increment of saturation temperature and heat flux.With the increase of vapor quality,HTC has a maximum and the corresponding vapor quality is about 0.4,which varies with the operating conditions.When vapor quality is larger than the transition point,HTC can be promoted more remarkably at higher mass velocity or lower saturation temperature.Among the four selected correlations,KANDLIKAR correlation matches with 91.6%of experimental data within the deviation range of±25%,and the absolute mean deviation is 11.2%.Also,in terms of frictional pressure drop characteristics of flow boiling,the results of this study show that frictional pressure drop increases with mass velocity and heat flux of R245fa,while it decreases with the increment of saturation temperature.MULLER-STEINHAGEN-HECK correlation shows the best prediction accuracy for frictional pressure drop among the four widely used correlations.It covers 84.1%of experimental data within the deviation range of±20%,and the absolute mean deviation is 10.1%.

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.

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.

Experimental Study on Heat Transfer and Pressure Drop of Micro-Sized Tube Heat Exchanger

A micro-sized tube heat exchanger(MTHE) was fabricated, and its performance in heat transfer and pressure drop was experimentally studied. The single-phase forced convection heat transfer correlation on the sides of the MTHE tubes was proposed and compared with previous experimental data in the Reynolds number range of 500—1 800. The average deviation of the correlation in calculating the Nusselt number was about 6.59%. The entrance effect in the thermal entrance region was discussed. In the same range of Reynolds number, the pressure drop and friction coefficient were found to be considerably higher than those predicted by the conventional correlations. The product of friction factor and Reynolds number was also a constant, but much higher than the conventional.

Pressure Drop Measurements on Distillation Columns

Pressure drops are of major importance for distillation/absorption columns. This paper mainly discusses how to correctly measure, interpret and use pressure drop data. The possible causes of incorrect pressure drop measurements are studied including the effects of pressure tap dimensions, locations, and vapor condensation etc. The effect of the static head of vapor on the pressure drop data and column pressures is evaluated. Variations of sectional pressure drops along the column are investigated based on the experimental data obtained from commercial size distillation columns at Fractionation Research, Inc. （FRI）. For a packed column, it is found that the spacing between the liquid distributor and the top of the bed affects the overall pressure drop measurements, which is confirmed by a fundamental fluid dynamics analysis.

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.

Effect of nozzle geometry on pressure drop in submerged gas injection

Submerged gas injection into liquid leads to complex multiphase flow, in which nozzle geometries are crucial important for the operational expenditure in terms of pressure drop. The influence of the nozzle geometry on pressure drop between nozzle inlet and outlet has been experimentally studied for different gas flow rates and bath depths. Nozzles with circular, gear-like and four-leaf cross-sectional shape have been studied. The results indicate that, besides the hydraulic diameter of the outlet, the orifice area and the perimeter of the nozzle tip also play significant roles. For the same superficial gas velocity, the average pressure drop from the four-leaf-shaped geometry is the least. The influence of bath depth was found negligible. A correlation for the modified Euler number considering the pressure drop is proposed depending on nozzle geometric parameter and on the modified Froude number with the hydraulic diameter of the nozzle do as characteristic length.