Correlation For Mass Transfer Coefficient Research Articles

Experimental study of interfacial mass transfer from single CO2 bubbles ascending in stagnant water

The study focuses on the interfacial mass transfer from single CO2 bubbles with initial diameter in the range of 0.7−3.0 mm in a vertical column with stagnant deionized water. The objective is to enhance the understanding of the intricate phenomena involved in interfacial mass transfer by examining the individual effects of the liquid-side mass transfer coefficient and the bubble size. The liquid-side mass transfer coefficient is found in this study to be influenced by both the initial bubble diameter and on the bubble age, i.e., the time the bubble is exposed to the liquid influences the obtained liquid-side mass transfer coefficient. Existing literature suggests that bubbles of diameter <2−3 mm behave as rigid spheres with immobile interface and reduced internal gas circulation, which negatively impact the interfacial mass transfer. The results obtained from this study show that the maximum value of the liquid-side mass transfer coefficient is obtained for bubbles of diameter 2.1−2.3 mm. For bubbles with a mean diameter ≤1.4 mm, the mean liquid-side mass transfer coefficient decreases with decreasing mean bubble diameter. A Lagrangian model description is used with various correlations for the liquid-side mass transfer coefficients to perform numerical simulations of the change in bubble volume during the bubble rise. The existing correlations for the liquid-side mass transfer coefficient give very different simulation results and fail to accurately capture the transient evolution of the bubble as it exposes to the mass transfer phenomenon and hydrostatic pressure gradient. The correlation for the liquid-side mass transfer coefficient proposed by Clift et al. (1978) is modified in this work, and the experimentally obtained data are well predicted by the new modified correlation.

Intensifying the extraction of rare earth elements by a mini-channel counter-current extractor

Developing new extraction processes is essential for the effective separation of rare earths. Liquid-liquid counter-current extraction of rare earth elements was conducted in innovatively developed mini-channel extractors with a diameter of 4 ∼ 6 mm. 30 % saponified P507/sulfonated kerosene was used as extractant to form monodispersed droplets and flowed upward in the vertical mini-channel by buoyancy. LaCl3 solution (La2O3 + HCl solution) was used as the continuous phase and flowed downward by gravity. The influence of the superficial velocity of organic phase, superficial velocity of aqueous phase, the diameter and length of mini-channel on the extraction yield, volumetric mass transfer coefficient and theoretical stages were studied. The volumetric mass transfer coefficients were in the range of 0.07 × 10−3 ∼ 5.46 × 10−3 s−1. It is much higher than that in co-current mini-channel and traditional extractors. An empirical correlation of volumetric mass transfer coefficients was established with a prediction error of ± 20 %. The strong relative movement of two phases and the maximal driving force of mass transfer give the counter-current mini-channel extractor an excellent mass transfer performance. When the mini-channel length was greater than 250 mm, the number of extraction stages was larger than one. The research results provide guidance for the design of novel extractors and the improvement of rare earth elements extraction.

Experimental Investigation into the Heat and Mass Transfer in an Indirect Contact Closed Circuit Cooling Tower

The heat and mass transfer coefficients of the indirect contact closed circuit cooling tower, ICCCCT, were investigated experimentally. Different experiments were conducted involving the controlling parameters such as air velocity, spray water to air mass flow rate ratio, spray water flow rate, ambient air wet bulb temperature and the provided heat load to investigate their effects on the performance of the ICCCCT. Also the effect of using packing on the performance of the ICCCCT was investigated. It was noticed that these parameters affect the tower performance and the use of packing materials is a good approach to enhance the performance for different operational conditions. Correlations for mass and heat transfer coefficients are presented. The results showed a good agreement with other published works. Correlations are showed that the spray heat transfer coefficient is a function flow rates of spray water and air as well as spray water temperature while mass transfer coefficient is a function of spray water and air flow rates only.

Mathematical Modelling and CFD Simulation for Oxygen Removal in a Multi-Function Gas-Liquid Contactor

This paper presents and compares the mathematical models and computational fluid dynamics (CFD) models for degassing of oxygen from water in a laboratory-scale multi-function gas-liquid contactor under various operating conditions. The optimum correlations of the overall volumetric liquid-phase mass transfer coefficient (kLa) are determined by the mathematical models of specific contactors. Both the continuous-reactor model and semi-batch model can evaluate the degassing efficiency with relative errors within ±13%. Similarly, CFD models agree with experimental data with relative errors of ±10% or less. Overall, the mathematical models are deemed easy to use in engineering practice to assist the selection of efficient contactors and determine their optimum operation parameters. The CFD models have a wider applicability, and directly provide the local mass transfer details, making it appropriate for harsh industrial scenarios where empirical correlations for important quantities are unavailable. Combining these two types of models can effectively guide the design, optimization, and operation of the high-throughput degassing system.

Experimental investigation on volumetric heat transfer coefficient during intermittent spray drying of mannitol solution

The paper presents a detailed experimental investigation on volumetric heat transfer during intermittent spray drying of a 20% w/w of mannitol solution in a custom-made spray dryer. Unlike the conventional intermittent drying process, which achieves intermittency by pulsating the properties of the carrier gas medium, the present works achieve intermittency by pulsating the nozzle spray. The estimated volumetric heat transfer coefficient varies between 0.8 and 2 kW/m3K, and the volumetric mass transfer coefficient is between 0.6 and 2.5 s−1. The correlation for heat and mass transfer coefficients is evolved that relates the heat and mass transfer coefficient with the flow properties and thermophysical properties of both the carrier gas and the precursor fluid in terms of Ohnesorge number and Nusselt number. The investigation uses response surface analysis to analyze the effect of Reynolds number of air and Ohnesorge number of precursors on the volumetric heat transfer coefficient. The results show that a decrease in Reynolds number for a wide range and Ohnesorge number causes the volumetric heat transfer coefficient to increase.

A Correlation of Overall Mass Transfer Coefficient of Water Transport in a Hollow-Fiber Membrane Module via an Artificial Neural Network Approach.

Water transport in a hollow-fiber membrane depends on mass convection around the tube, mass convection inside the tube, and water diffusion through the membrane tube. The performance of water transport is then explained by the overall mass transfer coefficient in hollow-fiber membranes. This study presents the prediction of overall mass transfer coefficients of water transport in a hollow-fiber membrane module by an artificial neural network (ANN) that is used for a humidifier of a vehicular fuel cell system. The input variables of ANN are collected from water transport experiments of the hollow-fiber membrane module that is composed of inlet flow rates, inlet relative humidity, system pressures, and operating temperatures. The experimental mass transfer coefficients are the targets of the training model, which are determined via the effectiveness analysis. When unknown data are applied to the ANN model, the correlation of the overall mass transfer coefficient predicts precise results with R = 0.99 (correlation coefficient). The ANN model shows good prediction capability of water transport in membrane humidifiers.

Heat and mass transfer characteristics during spray drying of Na2Fe0.6Mn0.4PO4F/C cathode material for Na-ion batteries

The paper presents a detailed experimental investigation on heat and mass transfer characteristics during the synthesis of Na2Fe0.6Mn0.4PO4F/C using intermittent spray drying. The drying process is carried out in a custom-made spray dryer. The novelty of the work is the study of the effect of intermittency on the spray drying process heat and mass transfer characteristics using a volumetric approach. The nozzle orifice diameter, spray duration, and spray pressure are operating parameters of the process that are varied between 0.2 and 0.4 mm at 10 and 40 sand 4 and 7 bar. An increase in nozzle orifice diameter and pumping pressure improves the heat transfer significantly; however, an increase in spray time diminishes the heat transfer. Under considered operating conditions, the volumetric heat transfer coefficient varied between 1.5 and 3.5 kW/m3K. The volumetric mass transfer coefficient ranges between 2.5 and 5.0 s−1. Based on the study, correlations for heat and mass transfer coefficients have been developed that relate the thermophysical properties of both the carrier gas and the precursor fluid in terms of Ohnesorge number and Reynolds number.

Cascade deep air dehumidification with integrated direct-contact cooling and liquid desiccant absorption

Deep dehumidification of the feed air is expected for the energy saving and stable operation of the air compression process in large-scale industries. Liquid desiccant-based dehumidification technology provides an alternative solution mainly featuring the continuous operation and low regeneration temperature, but the conventional systems still face a challenge to achieve the deep air dehumidification at high air-to-solution flow ratios, especially under high humidity conditions. Based on the cascade matching of driving forces, this study first presents a cascade deep air dehumidification system integrating a direct-contact cooling module (DCCD) and multi-stage internally-cooled liquid desiccant module (MILDD). In particular, the DCCD uses a novel internal matrix structure where the moist air is in direct contact with the cooling water with low hygroscopic. To evaluate the proposed system, a complete thermodynamic model is developed based on the newly-fitted general empirical correlation for mass transfer coefficient between the moist air and cooling water. The numerical model is validated against the initial experiment of the DCCD–MILDD test bench with a mean relative discrepancy of 6%–9%. The supplied air states and energy performance of the cascade system are evaluated at low humidity and high humidity conditions. The cooling water utilization is further improved by two series-looping schemes of cooling water allocation. Numerical results show that the DCCD–MILDD cascade system can achieve deep air dehumidification with the outlet air humidity ratio lower than 6.2 g/kg and the air-to-solution flow ratios over 4.0 even at high humidity conditions. This attributes to an improvement of the coefficient of performance and exergy efficiency, respectively 1.90 and 0.57. This work may provide an effective design of the liquid desiccant-based deep air dehumidification systems applied to the large-scale air compression process.

Comparison of Intergroup Mass Transfer Coefficient Correlations in Two-Group IATE for Subcooled Boiling Flow

The interfacial area concentration (IAC) is of vital importance in determining the interfacial transfer terms of mass, momentum, and energy between phases in the two-fluid model. The two-group (2-G) interfacial area transport equation (IATE) dynamically models the IAC evolution of large and small bubbles, and the intergroup transfer bookkeeps the mass transferring between two groups. Different intergroup mass transfer coefficient correlations are employed in the 2-G IATE model, which include one old correlation and three new correlations previously developed by the authors. The two-group IATE is benchmarked with subcooled boiling experimental dataset. The group-1 interfacial area concentration results show that the three modified correlations improve the physically incorrect prediction by the old correlation. With the modified correlations, the 2-G IATE is foundationally capable of predicting the group-1 interfacial area concentration in subcooled boiling flow.

Mechanism study on magnitude of mass transfer coefficients in liquid desiccant dehumidification and regeneration

• Mass transfer coefficients of regeneration are much lower than dehumidification. • Lower mass transfer coefficients of regeneration are decided by transfer direction. • Water release has a huge free energy barrier but water absorption has not. • Correlations considering parameters of aqueous solution show higher accuracy. Liquid desiccant systems have attracted extensive attention due to huge energy-saving and environmental potential. Mass transfer coefficients are key parameters for system design and performance evaluation. Contrast experiments between liquid desiccant dehumidification and regeneration were conducted here to investigate the magnitude of mass transfer coefficients by using LiBr aqueous solutions. Mass transfer coefficients of dehumidification were found to be much higher than regeneration even under the condition that the mass transfer driving force and inlet parameters except solution temperatures were kept the same. To obtain microscopic explanation, free energy curves of water transport were simulated by molecular dynamics based on umbrella sampling. Results show that large energy obstacle should be overcome for water moving into air, which is unnecessary for water transported into aqueous solution. Lower mass transfer coefficients of regeneration should be attributed to the mass transfer direction rather than higher solution temperatures of regeneration than dehumidification. Dimensionless correlations of mass transfer coefficients using water diffusivity in LiBr aqueous solution and correlations using surface tensions show better prediction performance than dimensionless correlations using water diffusivity in air. This study discloses changing mechanism of mass transfer coefficients and helps develop correlations with high accuracy.

Numerical investigation on interfacial characteristics of steam bubble condensation in subcooled water

Numerous direct-contact condensation (DCC) and boiling issues are numerically investigated with the Lee model under an assumed constant mass transfer coefficient through trial and error. A new mass transfer coefficient correlation is proposed, and the accuracy of the correlation is confirmed via comparison to Kim and Park’ experimental results from steam bubble injected vertically into a flow channel with diameter of 4.9 mm and subcooled temperature of 12 K in this work. The established correlation reveals that a fixed mass transfer coefficient value throughout the whole bubble condensation process is unreasonable and may cause solution divergence. Moreover, values of the mass transfer rate and velocity at the steam-water interface are explicitly derived at several moments. The results demonstrate that the mass transfer rate causes velocity fluctuations at the steam-water interface, and these velocity fluctuations promote bubble deformation, which in turn affects the condensation mass transfer rate.

Experimental analysis and rate-based stage modeling of multicomponent distillation in a Rotating Packed Bed

Rotating Packed Beds (RPBs) offer increased flexibility and the potential of significant size-reductions for distillation processes through mass transfer intensification. This may be of interest for example for retrofits or off-shore applications. However, validated models for process design of multicomponent distillation in RPBs are not available up to now. To bridge this gap, distillation of binary and ternary mixtures at total reflux was experimentally investigated in an RPB test rig. Depending on the flowrate and rotational speed, up to 10 theoretical stages were achieved in the investigated RPB, corresponding to an HETP (height equivalent of a theoretical plate) of as low as 17mm at the best operating point. With increasing centrifugal acceleration, separation efficiency increased at first, but decreased again at high centrifugal accelerations. Using the rate-based stage approach, a correlation for gas-side volumetric mass transfer coefficient in the RPB is developed. It is capable of reproducing the observed maximum of separation efficiency. Coefficients are fitted for this correlation, based on results obtained from distillation of ethanol/n-propanol. The model is validated using data obtained from distillation of ethanol/water and ethanol/n-propanol/water. Overall volumetric mass transfer coefficients and numbers of theoretical stages are described for most of the data within ±30%.

Experimental Study and Correlation for Mass Transfer Coefficient in the Pilot Plant Multistage Column with the Presence of Molybdenum

In the present work, multistage extraction column performance for reactive separation of molybdenum from the leach aqueous phase by using D2EHPA and TBP in kerosene was investigated by using axial diffusion model. Initially, the values of initial pH and extractant concentration were optimized on the batch experiments. The variation of volumetric overall mass transfer coefficients based on continuous phase at various operating conditions was obtained. By considering the chemical reaction conditions, the experimental data indicate that the volumetric overall mass transfer coefficients increase with an enhancement in rotor speed and continuous and dispersed phase flow rates. According to the sensitivity analysis, the rotor speed and flow rate of dispersed phase have more influence on column performance. Also, the continuous flow rate has little effect on volumetric overall mass transfer coefficients. After the steady-state condition was established, the concentration profile for the extraction of molybdenum along the column was obtained. The experimental data were studied and compared with the previous models. A new model based on dimensionless numbers was derived from the evaluation of overall mass transfer coefficients with consideration of the reactive extraction system.

Correlations for Concentration Polarization and Pressure Drop in Spacer-Filled RO Membrane Modules Based on CFD Simulations.

Empirical correlations for mass transfer coefficient and friction factor are often used in process models for reverse osmosis (RO) membrane systems. These usually involve four dimensionless groups, namely Reynolds number (Re), Sherwood number (Sh), friction factor (f), and Schmidt number (Sc), with the associated coefficients and exponents being obtained by fitting to experimental data. However, the range of geometric and operating conditions covered by the experiments is often limited. In this study, new dimensionless correlations for concentration polarization (CP) modulus and friction factor are presented, which are obtained by dimensional analysis and using simulation data from computational fluid dynamics (CFD). Two-dimensional CFD simulations are performed on three configurations of spacer-filled channels with 76 combinations of operating and geometric conditions for each configuration, covering a broad range of conditions encountered in RO membrane systems. Results obtained with the new correlations are compared with those from existing correlations in the literature. There is good consistency in the predicted CP with mean discrepancies less than 6%, but larger discrepancies for pressure gradient are found among the various friction factor correlations. Furthermore, the new correlations are implemented in a process model with six spiral wound modules in series and the predicted recovery, pressure drop, and specific energy consumption are compared with a reference case obtained by ROSA (Reverse Osmosis System Analysis, The Dow Chemical Company). Differences in predicted recovery and pressure drop are up to 5% and 83%, respectively, highlighting the need for careful selection of correlations when using predictive models in process design. Compared to existing mass transfer correlations, a distinct advantage of our correlations for CP modulus is that they can be directly used to estimate the impact of permeate flux on CP at a membrane surface without having to resort to the film theory.

Synergistic effect of functionalized ionic liquid and alkanolamines mixed solution on enhancing the mass transfer of CO2 absorption in microchannel

A novel hybrid absorbent by combining functionalized ionic liquid (IL) 1-(3-aminopropyl)-3-methylimidazolium tetrafluoroborate [Apmim][BF4] with alkanolamines (monoethanolamine (MEA) and N, N-diethylethanolamine (DEEA)) was proposed for CO2 capture. By means of a high-speed camera, the capacity and mass transfer performance of CO2 absorption into the hybrid absorbent were investigated experimentally in microchannel over a wide range of concentration ratios (IL: amine) at the room temperature and atmosphere pressure. Three flow patterns were observed: Taylor-bubbly flow, Taylor flow and Taylor-annular flow. The results show that the CO2 loading and mass transfer coefficient of alkanolamine solution could be improved remarkably by the addition of an appropriate amount of [Apmim][BF4]. The molar ratio 3:2 of IL to amine was found to be optimal for CO2 loading and mass transfer. Furthermore, the influences of gas and liquid flow rates on mass transfer were studied, and a new predicting correlation for CO2 volumetric mass transfer coefficient was proposed.

Dissolution reaction kinetics and mass transfer during aqueous choline chloride pre-treatment of oak wood

Lignocellulosic biomass processing employing ionic liquids is of recent research interest for the biorefinery industry. The data on biomass dissolution kinetics in ionic liquids is important for designing scale-up pre-treatment reactor design. In this study, the reaction mechanism and kinetics of oak wood dissolution in aqueous choline chloride was investigated. In an extended effort, a correlation of dimensionless numbers was developed for the estimation the mass transfer coefficient. The analyses suggested that oak wood dissolution in choline chloride occurred in two stages. The diffusion of ionic liquid through the product layer was the dominating rate-controlling step in the first stage of dissolution followed by the surface chemical reaction in the second stage. The diffusivity of choline chloride into the oak wood matrix was ranging between 2.96E−14 and 2.84E−13 m2/s. The activation energy of the diffusion controlled stage and surface chemical reaction controlled stage was approximately 24.2 and 40.3 kJ mol−1, respectively. The proposed mathematical correlation for mass transfer coefficient fitted well with the experimental mass transfer coefficient values.

Bubble diameter distribution and intergroup mass transfer coefficient in flows with phase change

The intergroup mass transfer term is investigated in the multigroup two-fluid model. Past intergroup mass transfer modeling is thoroughly reviewed, highlighting the limited applicability to phase-change flows due to the closure need of the intergroup mass transfer coefficient. The intergroup mass transfer coefficient is dependent on the bubble diameter distribution. The backward transform method, which is used to transform chord length distribution data to a bubble diameter distribution, is improved with a new regularization strategy which can better reduce the inherent instability of the inverse problem. Experimental data from phase-change flows are processed with the modified backward transform method to evaluate the bubble distribution and to determine the intergroup mass transfer coefficient. Analytical correlations for the intergroup mass transfer coefficient are developed, employing the Nukiyama-Tanasawa distribution function and the Rosin-Rammler distribution function. The benchmark with the experimental data demonstrates that the new correlations for the intergroup mass transfer coefficient are accurate over a wide range of two-phase flow conditions. In addition, a new empirical correlation for the intergroup mass transfer coefficient is developed from a regression of the experimental data.

Distributed parameter system modeling approach for the characterization of a high flux hollow fiber forward osmosis (HFFO) membrane

In this work, the performance of a commercially available Aquaporin incorporated axial flow Hollow Fiber Forward Osmosis (HFFO) membrane is studied for NaCl – Water system. The mathematical model developed for the FO experimental setup includes the model for the HFFO module, dynamic feed, and draw tanks, respectively. The HFFO module's model has been developed using the solution-diffusion (SD) mechanism, concentration polarization phenomenon, the momentum, solute, and solvent mass balance equations across the module. The model equations are solved to predict the following experimental measurements: concentrations, volume changes over time of both feed (FS), and draw solutions (DS). The membrane transport properties (A, B), structural parameter (S), and coefficients of mass transfer coefficient correlation (α, β) are estimated by minimizing the error between the model output and the experimental results of NaCl – water system. The estimated values of the membrane transport parameters are as follows: water permeability coefficient (A) = 0.914 LMH/bar, a salt permeability coefficient (B) = 0.34 LMH, and structural parameter (S) 194.79 μm. Based on the simulation results, an optimization strategy is developed to obtain the maximum permeate at minimum specific energy consumption (SEC) at various draw solution concentrations.

Evaporation due to infrared heating and natural convection

The results obtained from a drying experiment using infrared heating are compared to those obtained from an analytical model based on correlations for the mass transfer coefficients, which are commonly used to obtain evaporation rates for drying applications. It was shown that the mass transfer coefficients calculated by natural convection correlations are approximately ten times lower than those measured under infrared (IR) exposure. In an attempt to explain this discrepancy, which has been also observed in other studies and explained on the basis of thermal radiation effects, optical properties of the solvent are presented and the implications of the IR and near infrared (NIR) spectrum on the thermal radiation effects and ensuing evaporation rates are discussed. The results show that the correlation for mass transfer coefficient has to take into account the IR radiation temperature and the surface emissivity. This study provides important evaporation data on mass flux and mass transfer coefficients, which cannot be predicted using traditional correlations, for the design of IR assisted drying systems.

The influence of plate corrugations geometry scale factor on performance of plate heat exchanger as condenser of vapour from its mixture with noncondensing gas

The condensation of steam from a steam-air mixture is studied experimentally at three samples of Plate Heat Exchanger (PHE) channel. For three test samples corrugations are similar but differ in scale with the height 5, 7.5 and 10 mm. The results of tests are compared to calculations with one dimensional mathematical model of the process. The identification of correlations for local heat and mass transfer coefficients, as also friction factor in condensing two-phase flow, is made by comparison of computed results with tests data. The correlations for condensing two-phase flow are based on single-phase correlations for considered channels. For mass transfer coefficients, the best results are obtained using a stagnant film model for accounting transverse mass flux influence. For the prediction of pressure losses in two-phase condensing flow, the correlation with Lockhart-Martinelli parameters is used for zones of low liquid flow rates. For other channelzones are proposed its combination with an equation based on a dispersed annular model of flow structure. The presented equations can be used for calculation of heat and mass transfer intensity and pressure losses in two-phase condensing flow when designing PHE for condensation of steam from its mixture with air by local process parameters.