Pressure Drop Model Research Articles

Identifying the performance and losses of a scroll compressor with vapour injection and R1234ze(E)

This work investigates a vapour injection scroll compressor integrated in a heat pump using the refrigerant R1234ze(E). The water-to-water heat pump was tested under a wide temperature range at the evaporator and condenser sides. The test results revealed that the performance is significantly reduced for lifts of over 30 K with the coefficient of performance being even below 2 and the maximum 2nd law efficiency was just 28%. In order to enlighten the reasons behind such significant compressor underperformance, a semi-empirical model has been extended to include vapour injection, and a new improved modelling approach for the suction pressure drop was developed and implemented considering both the turbulent and laminar inlet flow regimes. Once the accuracy of the developed semi-empirical model was verified, the model was then adjusted to account for the R1234ze(E) operation, by fine-tuning its parameters based on the test data. The main loss mechanism identified is the high suction pressure drop, due to the high friction factor, with the inlet refrigerant flow possibly being laminar instead of turbulent. This resulted in a significant reduction of the mass flow rate and volumetric efficiency, while the standard model for suction pressure drop was not able to capture this effect.

Influence of Vertical Downward Annulus Eccentricity on Steam-Water Two-Phase Flow Pressure Drop

Concentric dual-tubing steam injection technique is one of the main methods to improve heavy oil recovery efficiency. From field data, it was discovered that hot fluid at high temperature and pressure caused steam injection casing to have elongation strain and “necking” eccentric buckling, and the eccentricity change affected the accurate prediction of steam-water two-phase flow pressure drop in the steam injection casing. This paper established a coupling model for the steam-water two-phase flow pressure drop in vertical downward eccentric annulus and the wellbore heat transfer and developed a mathematical model calculation program, to validate the accuracy of calculating the liquid holdup and pressure gradient of fully eccentric annulus. This revealed the influential law of eccentricity on the annulus steam-water two-phase pressure, dryness, and enthalpy value. The results indicated that when the eccentricity e increased from 0 to 1, the saturation pressure of steam at annulus wellbore bottom increased by 0.265 MPa, and the dryness and enthalpy value decreased by 8.54 × 10−3 and 11.22 kJ kg−1, respectively. Compared to the concentric layout, the eccentrically arranged steam injection inner tube cannot promote the wet steam dryness at annulus wellbore bottom.

Study on Calculation Method for Wellbore Pressure in Gas Wells with Large Liquid Production

In order to solve the inaccuracy in the calculation of the wellbore pressure distribution caused by large liquid production in the Donghai gas field, the gas–liquid production conditions of the Donghai gas field were simulated with indoor experiments, and the flow patterns for different pipe diameters, different inclinations, and different flow patterns were systematically analyzed using a flow pattern discrimination method, liquid holdup calculation method, and pressure drop calculation method. Using the experimental data, the division methods for different flow patterns were screened. Finally, based on the fact that the change trend for the flow patterns was consistent, the Kaya–Sarica–Brill method was selected to establish the flow pattern discrimination formula. According to the calculation method for the Mukherjee and Brill (M–B) liquid holdup, the M–B model was re-established according to a 75 mm pipe diameter and 60 mm pipe diameter using the instantaneous liquid holdup measured in the laboratory. Through the comparison and analysis of the measured data and the calculated data for the Beggs and Brill (B–B_ pressure drop model under the same working conditions, it was found that when the B–B model was applied to different angles and different gas–liquid ratios, the error decreased with an increase in the angle and increased with a decrease in the gas–liquid ratio. After verifying the correlation of different dimensionless numbers that can characterize the gas–liquid ratio, it was considered that the introduction of the Reynolds number into the original model could greatly improve the accuracy of the calculation, so a new pressure drop calculation model was established. The new pressure drop calculation model takes into account the two parameters of the well deviation angle and gas–liquid ratio. The accuracy was greatly improved, as verified by field measurements in four wells.

Additively manufactured multiplexed inertial coalescence filters

Multiphase flows often pose a significant challenge to the efficient and reliable design of thermofluidic systems. This paper describes multiplexed inertial coalescence filters composed of parallel helical pathways, designed to capture fine droplets (<40 µm) through inertial separation while maintaining a low pressure drop (<400 Pa). Filtration efficiencies for 7 µm and 30 µm droplets were characterized for varying flow conditions, with complete capture observed above a threshold flow rate. Models for filtration efficiency and pressure drop were developed and validated against experimental results to allow system design and optimization, enabled by the tunable additive manufacturing approach used to fabricate the filters. Filter quality factor was computed for varying droplet sizes, showcasing exceptional quality factor when compared to state-of-the-art filters documented in the literature. This multiplexed inertial coalescence filtration approach could find use in dehumidification systems, fog harvesting, chemical reactors, and microgravity droplet capture.

Characterization of a convection-based support microstructure through a flow resistance parameter.

Modern convection-based supports differ substantially in pore size, porosity, and microstructure topology. Due to such variability, it is challenging to evaluate the contribution of a particular microstructure topology on flow resistance. We demonstrated that the flow resistance parameter ( ) introduced decades ago can be used as a criterion to evaluate the effect of microstructure topology on a pressure drop when the pore size is used as a characteristic support dimension. Furthermore, the value of simple cubic packing was calculated over the entire range of open porosity and compared to the values determined for pressure drop models derived for particular convection-based supports and experimental values of various convection-based supports from the literature. It was shown that different convection-based supports become clustered into distinct groups when plotted according to their and open porosity values, allowing their discrimination.

Adiabatic two-phase pressure drop of carbon dioxide in different channel orientations

Adiabatic pressure drop measurements of two-phase Carbon Dioxide (CO2) have been carried out in horizontal, vertical upward and downward direction with a dedicated test facility at the European Organization for Nuclear Research (CERN). A database of more than 1100 measurements, consisting of 512 data points in horizontal and 295 data points for each vertical up- and downflow respectively, has been compiled within this study. The experiments cover saturation temperatures from -25°C⩽Tsat⩽+5°C, mass velocities from 100kgm-2s-1⩽G⩽450kgm-2s-1 and are carried out in test sections with an inner diameter of 8 mm. The analysis of the pressure drop signals reveals that pressure fluctuations are increasing around the slug flow regime and the oscillation effects get magnified in vertical direction. The measurements in horizontal direction are compared to 18 frictional pressure drop models. For the comparison of the vertical data, 21 void fraction correlations accounting for the static head have been combined with the frictional models. The data sets of the horizontal and vertical upflow measurements are well predicted by several pressure drop models with an acceptable statistical significance. However, the prediction models perform less accurately for vertical downflow and it has been found that the static head is not well described by the void fraction correlations. In particular at low mass velocities, the effects of phase separation due to dominant buoyancy forces are not well incorporated by the void fraction models considered. In addition to the comparison of the entire data sets, subdivided analyses accounting for the flow patterns are provided within the present work.

A new pseudo 3D hydraulic fracture propagation model for sandstone reservoirs considering fracture penetrating height

Due to the thin layers in sandstone reservoir, the fractures are likely to break through the target horizon and extend to the interlayer. Therefore, it is necessary to control the fracture height according to the penetrated height diameters. However, currently available 2D (PKN and KGD) and pseudo 3D (P3D) hydraulic fracturing models are unable to simulate the height of fractures penetrating through the sandstone reservoir. Address this issue, we coupling the wedge-shaped fracture model (pressure drop model in fractures), penetrating fracture propagation model, PKN model and Carter fluid loss model, we established a new P3D hydraulic fracture propagation model applicable to sandstone reservoir, and use new model simulate the effects of factors, e.g. injection ratio, filtration coefficient, stress difference between reservoir and its adjoining bed, fracture toughness of interlayer, Young’s modulus of interlayer and Poisson’s ratio of interlayer, on fracture propagation. A negative correlation is found between fracture height, fracture toughness of interlayer, stress difference between reservoir and its adjoining bed and filtration coefficient, while fracture length and width increase as these factors increase; fracture height is positively correlated with injection ratio, Young’s modulus and Poisson’s ratio of reservoir rock, while fracture length and width decrease with the increase of these factors. The simulation results are well consistent with the previous studies, which verifies the accuracy and superiority of the established model, this model can effectively simulate the propagation of hydraulic fractures in sandstone reservoir.

Mechanistic modeling and measurement of foamed gas flow resistance in fractures

Geologic heterogeneity is one of the important factors controlling migration and distribution of nonaqueous phase liquids in the subsurface. Heterogeneity, such as fractures, complicates the effectiveness of environmental remediation, and uncharacterized aquifer heterogeneity causes significant uncertainties in the removal of nonaqueous phase liquids. Foaming an injection gas is an effective method to alleviate the challenges in accessing heterogeneous media during remediation processes because foam is nonNewtonian and redirects gas and liquid flow. Foamed gas may also assist in increasing the storage of carbon dioxide in saline formations. This paper investigates foam flow behavior in microscale fractures and develops a mechanistic transient foam flow model using the population balance method. Microscale experiments in fractures with apertures of 25 and 88 μm are used to validate the model for pressure drop, gas saturation, and bubble texture. Key differences related to modeling foam in fractures are the potential for continuously varying gas–liquid curvature in fractures and the relationship of this curvature to apparent foam viscosity. Incorporation of a local foam flow resistance factor is important to representing flow physics accurately. Hence, the results of this study provide foundational understanding for upscaling foam rheology in different sized fractures to ensure successful operations in soil/aquifer remediation and CO2 storage in saline formations.

Investigation on thermal performance of water-cooled Li-ion cell and module with tree-shaped channel cold plate

The performance of lithium-ion batteries shows high susceptibility to temperature. A well-designed thermal management system can improve the service life and safety of the battery pack. In this study, we developed a novel cooling plate with the inherent advantages of low flow resistance. To highlight the performance advantages of the cooling plate, it was compared with a previous tree-shaped cooling plate as well as the U-turn cooling plate used by Chevrolet. Furthermore, combining Kriging interpolation with Latin hypercube sampling test, three prediction models of pressure drop, maximum temperature, and standard deviation of the surface temperature of the novel cooling plate were established to investigate the influence of structural parameters and boundary conditions on the performance of the novel cooling plate. To verify the accuracy of the prediction models, 10 sets of test combinations were constructed through the uniform test design. Finally, a prismatic battery module was created using the battery design studio (BDS) and STAR-CCM+. The effect of cooling water temperature and battery discharge rate on the thermal performance of the battery module was investigated. The results indicated that the novel cooling plate exhibited slightly better heat dissipation with only a 1/3 pressure drop than the other two cooling plates. The Kriging models were in good agreement with the simulation results, which demonstrated the excellent prediction abilities of the Kriging models. The lower temperature but larger temperature difference was achieved in the battery module by reducing the cooling water temperature. The novel cooling plate could maintain the maximum temperature of the battery module, maximum cell-to-cell temperature difference, and maximum temperature gradient within the cell below 40 °C, 1 °C, and 5 °C, respectively.

Performance and pressure drop ofCO2absorption into task‐specific and halide‐free ionic liquids in a microchannel

AbstractThe gas–liquid two‐phase flow pattern, absorption rate and pressure drop of CO2absorbed into the aqueous solution of the task‐specific ionic liquids (1‐aminopropyl‐3‐methylimidazole tetrafluoroborate [Apmim][BF4] and 1‐hydroxyethyl‐3‐methylimidazole tetrafluoroborate [OHemim][BF4]) and halide‐free ionic liquid 1‐butyl‐3‐methylimidazolium methylsulfate [Bmim][CH3SO4] were investigated in a microreactor. The absorption mechanism of the three ionic liquids was analyzed employing the13C NMR spectroscopy. The [Apmim][BF4] was found to have the best ability of CO2capture compared with the other two ionic liquids, as chemical absorption occurred between [Apmim][BF4] and CO2, while only physical absorption took place between [OHemim][BF4]/[Bmim][CH3SO4] and CO2. The sequence of CO2absorption rate in three ionic liquids aqueous solutions is: [Apmim][BF4] &gt; [Bmim][CH3SO4] &gt; [OHemim][BF4]. Furthermore, the effects of gas–liquid flow rate and ionic liquids concentration on CO2absorption rate and pressure drop were studied, the pressure drop models based on various flow patterns were proposed.

Condensation heat transfer of R1234ze(E) and its A1 mixtures in small diameter channels

R1234ze(E) has emerged in the recent years as low Global Warming Potential substitute for R134a in refrigeration and air-conditioning systems. As a drawback, R1234ze(E) is classified as a mildly flammable fluid (A2L class) and, in the search for non-flammable alternatives to R134a, hydrofluorocarbon/hydrofluoroolefin binary mixtures can be considered. In the present work, condensation tests are performed with R1234ze(E) and non-flammable binary mixtures R450A (R1234ze(E)/R134a at 58.0/42.0% by mass) and R515B (R1234ze(E)/R227ea at 91.1/8.9% by mass) inside two channels with inner diameter equal to 3.38 mm and 0.96 mm. R515B is an azeotropic mixture whereas R450A is a near-azeotropic blend (temperature glide 0.6 K at 40 °C). Heat transfer coefficients are measured at 40 °C saturation temperature and mass flux from 40 kg m−2 s−1 to 600 kg m−2 s−1. Flow pattern visualizations are recorded by a high-speed camera in the 3.38 mm inner diameter tube. Two-phase pressure gradients are measured in the 0.96 mm test section at mass flux equal to 200 and 400 kg m−2 s−1. The prediction accuracy of condensation heat transfer and two-phase pressure drop models is assessed against the experimental results. A comparative study between the tested fluids and R134a, accounting for both the heat transfer coefficients and the two-phase pressure drops, is performed.

Structured ZoneFlow™-Bayonet steam reforming reactor for reduced firing and steam export: Pressure drop and heat transfer modelling and evaluation of the reactor performance

The ZoneFlow™ reactor is an annular structured reactor that offers lower pressure drop and significantly better heat transfer than standard pellets used in Steam Methane Reforming. The annular ZoneFlow™ reactor is particularly suited for use in a bayonet configuration. The produced syngas then returns via the central tube, the so-called bayonet, allowing counter-current heat exchange between the return gas and the gas reacting in the ZoneFlow™ reactor. As such, the heat supplied by the furnace can be maximally used for the reactions and steam export can be reduced. To intensify the heat transfer between the gas in the bayonet and in the annulus, an insert is installed inside the bayonet, forming a second annulus that forces the gas to flow close to the bayonet wall at high velocity. In the present work, the pressure drop and heat transfer resulting from various bayonet configurations are experimentally measured at commercial scale reactor dimensions and air flow rates equivalent to commercial conditions. Correlations for the friction factors and the heat transfer coefficients are derived from the data. The correlations are then used to simulate a commercial scale ZoneFlow™-bayonet reactor and optimize the design.

Sub-channel analysis of lead–bismuth fast reactor fuel assembly with wire spacers for China initiative accelerator driven system

The lead bismuth eutectic (LBE) cooled fast reactor fuel assemblies in China Initiative Accelerator Driven subcritical System (CiADS) are supported by wire spacers, and the sub-channel code is a significant analysis method to evaluate the thermal–hydraulic behavior of fuel assemblies. In this study, a sub-channel analysis code for LBE coolant is developed, in which the pressure drop model, turbulent mixing model, and heat transfer model based on LBE are added and applied. Besides, the heat transfer experience of the 61-pin fuel assembly and other sub-channel codes are chosen to verify. Finally, the full-scale simulation of CiADS fuel assembly is calculated. The results show that the thermal–hydraulic parameters of CiADS meet the design criterion. The optimized range of pitch to diameter ratio is 1.133–1.145 according to the thermal–hydraulic analysis. It is recommended to use 37-pin bundle for the numerical simulation simplification of full-scale rod bundles.

Modeling and experiment of pressure drop on valve section of hydraulic oscillator

The article at hand focuses on the pressure drop at the hydraulic oscillator valve section. The flow path of the valve section is simplified through the hydraulic oscillator working principle and the valve structure. Further, based on the kinematic model of the positive displacement motor (PDM) and the moving valve, the flow area calculation model between valve sections was deduced. Next, using the simplified valve section flow path, said path is divided into four stages, and the analytical model of pressure drop was established by applying the fluid mechanic theory. Aiming to verify the analytical model, the transient finite element model, and the test bench were set up. Finally, three methods were used to calculate the pressure drop within the 1.3-inch and 1.4-inch stationary valves corresponding to the same input parameters. The results have shown that pressure drops obtained by all the methods are in good agreement; the maximum error between the analytical and experimental results was 7.6 %. Additional comparisons were made between the analytical and finite element model (FEM) results at various flow rates. In that case, the maximum error between the two methods was 7.05 %. Thus, the model can be used to further study the hydraulic oscillator mechanisms and provide a useful reference for both the design and optimization.

A new method of pressure drop modelling in sandstone rocks

Production capacity of any hydrocarbon reservoir is the most important question that needs to be answered. This depends on both the obtainable drawdown between the well and reservoir and the petrophysical properties (pore size distribution, wettability properties, saturations etc.) of the porous rock material. Permeability, introduced by Darcy is the parameter describing restrictions present during fluid flow in porous media. Although this method is the one currently accepted and implemented in the industry it has a major flaw because it considers flow in the geometric (total) rather than the effective volume, where it truly develops. During this study a new approach of flow restriction modelling was found, where flow restrictions, measured from sandstone plug samples were compared with the theoretic flow volumes which are equal to the total pore volumes, constructed of steel capillaries of equal diameter. Results show that flow restrictions of incompressible fluids in sandstone can be demonstrated by the new model.

Two-Phase Flow Pressure Drop Modelling in Horizontal Pipes with Different Diameters

Two-Phase Flow Pressure Drop Modelling in Horizontal Pipes with Different Diameters

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 horizontal wells and understanding the oil-water exchange law of shale reservoir after fracturing.

Saturated flow boiling inside conventional and mini/micro channels: A new general model for frictional pressure drop using genetic programming

• A new general model for FPD during saturated boiling was proposed using GP. • 6021 experimental data samples from 42 published sources were analyzed. • Present model showed favor outcomes for different flow regimes and channel sizes. • The accuracy of previous models was considerably lower than the present one. • The new model presented favor physical trends at different operating conditions. This study presents a general explicit model for estimating the saturated flow boiling frictional pressure drop (FPD) in conventional (macro) and mini/micro channels heat exchangers. An extensive database including 6021 experimental data samples has been gathered from 42 published sources, covering a broad range of fluids, channel diameters and operating parameters. The new model is based on the separated model suggested by Lockhart and Martinelli (1949) for two-phase flow. Thus, the two-phase multiplier, ϕ l o 2 has been estimated using the intelligent approach of genetic programming (GP). The presented model predicts the mentioned database with a reasonable value of average absolute relative deviation (AARD) of 21.34%. Moreover, 74.85% of predicted data have an error of lower than 30% of the experimental values. The entire database is compared with ten well-known two-phase pressure drop correlations for the evaluation of previous models. But all of them showed a total AARD of more than 27%. The GP model shows good accuracy for both conventional and mini/micro channels and different flow regimes, including low and high Reynolds numbers. In addition, it is applicable for estimating the boiling FPD in different operating conditions. Based on 752 additional data from 4 independent sources, the new model provides the best predictions for estimating the FPD in conventional and mini/micro channels.

Numerical Simulation of Low-Pressure Drop Static Mixers for Mixing Enhancement

Static mixers (SM), also generally known as inline mixers, form a newly developing industry trend. They have no moving parts, hence have lower energy consumption, lower installation cost, and very low maintenance cost, and are thus an attractive alternative to the conventional agitators. Modifications were made in the design to reduce pressure drop and increase the mixing intensity across the mixer and increase the application of inline mixers in the industries. Three hybrid geometries (different combinations of Kenics and LPD) of static mixers were constructed and simulated using computational fluid dynamics (CFD) tools. Kenics is an excellent radial mixing device, and low-pressure drop (LPD) an excellent axial mixing device. The key design parameter to modify LPD was the slope angle of elliptical plates which affects the mixer performance. Different slope angles from 90o to 120o were simulated. Kenics was modified for different aspect ratios, and the edge of Kenics was curved. Pressure drop, thermal, and Discrete Phase Model (DPM) analysis were performed on these three different classifications of hybrid geometries. The most promising geometry to emerge based on the low-pressure drop and good mixing efficiency both was the curved edge Kenics. Keen-sighted these results, further analysis was performed on curved edge Kenics after the modification of blend radius. It was concluded that for a lower Reynold number, the curved edge with a higher blend radius dominates all other mixers. Result validation was done by comparing the trends and sensitivity of process variables with the established results and standards.

Modeling and Optimization of Gas-Solid Fluidization of Binary Mixtures using Box-Behnken Experimental Design

The influence of different factors on the fluidization of a binary mixture of red mud and aluminum was investigated. A new model was developed for predicting pressure drop through the solid bed using experimental data of other work. Statistical analysis based on response surface methodology has been used to develop correlations for bed pressure drop with three independent factors, minimum fluidization velocity (Umf), red mud to aluminum ratio (R/A), and static head (Hs). The design of experiments offers a best alternative to study the effect of factors and their response with the minimum number of experiments. The hydrodynamic characteristics of fluidization, bed pressure drop, superficial gas velocity (Umf), red mud to aluminum ratio (R/A), and initial static bed height (Hs) were modeled and optimized. ANOVA has been used to analyze the system parameters on bed pressure drop. A model of bed pressure drop was found to have a correlation coefficient of 0.98. The measured values of bed pressure drop from RSM were found to match the experimental values very well.