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.

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.

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.

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.

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.

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.

Forced Convection Heat Transfer in Porous Structure: Effect of Morphology on Pressure Drop and Heat Transfer Coefficient

A light-weight structure with sufficient mechanical strength and heat transfer performance is increasingly required for some thermal management issues.The porous structure with the skeleton supporting the ambient stress and the pores holding the flowing fluid is considered very promising,attracting significant scientific and industrial interest over the past few decades.However,due to complicated morphology of the porous matrices and thereby various performance of the pressure drop and heat transfer coefficients (HTC),the comprehensive comparison and evaluation between different structures are largely unclear.In this work,recent researches on the efforts of forced convection heat transfer in light-weight porous structure are reviewed;special interest is placed in the open-cell foam,lattice-frame,structured packed bed,and wire-woven structures.Their experimental apparatus,morphological of the porous structures,effect of morphology on pressure drop and HTC,and further applications are discussed.The new method which measure morphology accurately should be paid more attention to develop more accuracy correlation.Also,the most research focused on low Reynolds number and existing structure,while very few researchers investigated the property of forced convection heat transfer in high velocity region and developed new porous structure.

Experimental investigation on the distribution uniformity and pressure drop of perforated plate distributors for the innovative spray-type packed bed thermal storage

As an innovative thermal energy technology,the spray-type packed bed has advantages of high efficiency and low cost.A liquid distributor is the key component for the spray-type packed bed for scattering heat-transfer liquid drops evenly.In this study,the distribution performance and pressure drop of the perforated plate distributors of different orifice diameters were studied experimentally.The experimental results indicate that orifice diameter has a greater effect on the distribution performance compared to flow rate.With an increase in flow rate,the flow pattern through the distributor changes from the uncovered drop to the covered drop and then to the jet flow.The covered drop pattern shows the best performance with a good distribution and a small pressure drop simultaneously,which is the design and optimization principle of the distributor for a spray-type packed bed.

Airside pressure drop characteristics of three analogous serpentine tube heat exchangers considering heat transfer for aero-engine cooling

This study explores the design,analysis,and air pressure drop assessment of three analogous air–fuel heat exchangers consisting of thin serpentine tube bundles intended for use in high Mach number aero-engines.In high speed flight,the compressor bleed air used to cool high temperature turbine blades and other hot components is too hot.Hence,aviation kerosene is applied to precool the compressor bleed air by means of novel air–fuel heat exchangers.Three light and compact heat exchangers including dozens of in-line thin serpentine tube bundles were designed and manufactured,with little difference existing in aspects of tube pitches and outer diameters among three heat exchangers.The fuel flows inside a series of parallel stainless serpentine tubes(outer diameter:2.2,1.8,1.4 mm with 0.2 mm thickness),while the air externally flows normal to tube bundles and countercurrent with fuel.Experimental studies were carried out to investigate the airside pressure drop characteristics on isothermal states with the variation of air mass flow rates and inlet temperatures.Non-isothermal measurements have also been performed to research the effect of heat transfer on pressure drops.The experimental results show that inlet temperatures have significant influence on pressure drops,and higher temperatures lead to higher pressure drops at the same mass flow rate.The hydraulic resistance coefficient decreases quickly with Reynolds number,and the descent rate slows down when Re>6000 for all three heat exchangers.Additionally,the pressure drop on heat transfer states is less than that on isothermal states for the same average temperatures.Moreover,the pressure drop through heat exchangers is greatly affected by attack angles and transverse pitches,and an asymmetric M-shaped velocity profile is generated in the crosssection of sector channels.

Pressure drop analysis on the positive half-cell of a cerium redox flow battery using computational fluid dynamics: mathematical and modelling aspects of porous media

Description of electrolyte fluid dynamics in the electrode compartments by mathematical models can be a powerful tool in the development of redox flow batteries(RFBs)and other electrochemical reactors.In order to determine their predictive capability,turbulent Reynolds-averaged Navier-Stokes(RANS)and free flow plus porous media(Brinkman)models were applied to compute local fluid velocities taking place in a rectangular channel electrochemical flow cell used as the positive half-cell of a cerium-based RFB for laboratory studies.Two different platinized titanium electrodes were considered,a plate plus a turbulence promoter and an expanded metal mesh.Calculated pressure drop was validated against experimental data obtained with typical cerium electrolytes.It was found that the pressure drop values were better described by the RANS approach,whereas the validity of Brinkman equations was strongly dependent on porosity and permeability values of the porous media.

Influence of the pressure drop and the air lock on the solid flux in a cross-flow moving bed

The gas-solid flow pattern in a rectangular cross-flow moving bed is simulated by the multiphase particle-in-cell(MP-PIC)model with the Barracuda software.The computed results are verified by the experimental data.In the bed,the actual solid flux generally equals the solid flow rates in the solid feed and discharge tubes.However,these two flow rates are greatly influenced by the air lock and the pressure drop in the solid feed and discharge tubes,namely,the negative and positive pressure gradients,respectively,rather than the traditional opinion that they are merely controlled by the valve openings.The pressure drops in these tubes are calculated by the proposed“common pressure pool with multiple outlets”(CPPMO)and the“common pressure pool”(CPP)methods.It is found that the local gas resistance dominates the pressure drop in the solid discharge tubes,while the gas frictional resistance determines the pressure drop in the solid feed tube.In addition,when the solid flow rate nearly tends to zero in the solid feed tube,the air lock forms.A solid flux equation is then given by considering both the air lock and the pressure drop factors in the cross-flow moving bed.

Assessment of pressure drop in conical spouted beds of biomass by artificial neural networks and comparison with empirical correlations

Pressure drop is an essential parameter in the operation of conical spouted beds(CSB)and depends on its geometric factors and materials used.Irregular materials,like biomass,are complex to treat and,unlike other gas–solid contact methods,CSB turn out to be a suitable technology for their treatment.Artificial neural networks were used in this study for the prediction of operating and peak pressure drops,and their performance has been compared with that of empirical correlations reported in the literature.Accordingly,a multi-layer perceptron network with backward propagation was used due to its ability to model non-linear multivariate systems.The fitting of the experimental data of both operating and peak pressure drop was significantly better than those reported in the literature,specifically in the case of the peak pressure drop,with R^(2) being 0.92.Therefore,artificial neural networks have been proven suitable for the prediction of pressure drop in CSB.

Computation of pressure drop for dilute gas-solid suspension across thin and thick orifices

The present work deals with the computation of the gas-solid two-phase flow pressure drop across thin and thick orifices for a vertically downward flow configuration at the higher limits of a dilute phase flow situation(0.01≤αs,in≤0.10).The Eulerian-Eulerian(two-fluid)model has been used in conjunction with the kinetic theory of granular flow with a four-way coupling approach.The validation of the solution process has been performed by comparing the computational result with the existing experimental data.It is observed that the two-phase flow pressure drop across the orifice increases with an increase in the thickness of the orifice,and the effect is more prominent at higher solid loading.The pressure drop is found to increase with an increase in the solid volume fraction.An increase in the Reynolds number or the area ratio increases the pressure drop.An increase in the size of the particles reduces the pressure drop across the orifice at both small and relatively large solid volume fractions.Finally,a two-phase multiplier has been proposed in terms of the relevant parameters,which can be useful to evaluate the gas-solid two-phase flow pressure drop across the orifice and can subsequently help to improve the system performance.

Two-Phase Flow Pressure Drop of Liquid Nitrogen Boiling in the Straight Section Downstream of U-Bend

The gas-liquid(two-phase) flow pressure drop of liquid nitrogen boiling in the straight section downstream of U-bend is investigated experimentally. The mass flux ranges from 32 to 280 kg/(m2· s). The inlet pressure of U-tube is from 140 to 272 kPa. And the curvature ratio is from 6.67 to 15. The tube wall including the U-bend is heated uniformly and the heat flux ranges from 0 to 22 kW/m2. The tube with higher inlet pressure has higher pressure drop in the downstream section of the bend. The bended degree of the U-bend influences the pressure drop in the downstream straight section of U-bend. A new correlation taking the effect of the secondary flow into account is proposed for the two-phase slip speed ratio. The pressure drop in the straight section downstream of U-bend calculated by the new correlation agrees well with experimental measurements.

The investigation of pressure drop in moving-beds

The pressure drop of a cross-flow moving-bed was investigated in a two-dimensional rectangular apparatus.The effects of the particle velocity,the superficial gas veloc-ity,the formation and development of cavity/raceway and voidage of particles on the pressure drop were investigated experimentally under the operational conditions of 0.09–1.35 m/s of the superficial gas velocity and 0.95–9.68 cm/min of the particle velocity.The experimental results show that the particle velocity has little influence on the pressure drop,while the phenomena of cavity and pinning occur when the cross-flow velocity is high enough.The development of a cavity or a raceway can result in three types of variations of pressure drop with time:stabilization,slight fluctuation and severe fluctuation.A cavity appears in a process cycle of‘formation-growing up-collapsing-fluidization’at a high gas velocity.On the basis of experimental results,a model for calculating the pressure drop after a cavity occurs and a dimensionless relationship of cavity size is developed,which gives a good qualitative account of the experimental data.

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.

ERRATUM TO “CHARACTERISTICS OF PRESSURE DROP AND CORRELATION OF FRICTION FACTORS FOR SINGLE-PHASE FLOW IN ROLLING HORIZONTAL PIPE”

This is the erratum to the article [zhang Jin-hong, Yan Chang-qi, Gao Pu-zhen, Journal of Hydrodynamics, 2009, 21(5)]. The Fig.5 is corrected.

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.