Interphase Mass Transfer Rates Research Articles

Performance evaluation and optimization of a suspension-type reactor for use in heterogeneous catalytic ozonation

Packed fixed-bed reactors are traditionally used for heterogeneous catalytic ozonation. However, a high solid-to-liquid requirement, poor ozone dissolution, ineffective utilization of catalyst surface area, and production of large amounts of catalyst waste impede application of such reactors. In this study, we designed a suspension catalytic ozonation reactor and compared the performance of this reactor with that of a traditional fixed-bed catalytic ozonation reactor employing oxalic acid (OA) as the target contaminant. Our results showed that total O3 dissolved into the suspension reactor (117–134 mg.L−1) was much higher compared to that measured in the fixed-bed reactor (53 mg.L−1) due to a higher O3(g) interphase mass transfer rate in the suspension reactor. In accordance with the higher O3(g) interphase mass transfer, we observed a much higher proportional OA removal (32 %) compared to that achieved in the fixed-bed reactor (10%) employing an Fe-oxide catalyst supported on Al2O3 (Fe-oxide@Al2O3) in both reactors. Use of a double-layered Cu-Al hydroxide (Cu-Al LDHs) catalyst in the suspension reactor further enhanced the performance with nearly 90 % OA removal observed. Given the superior performance of the suspension reactor, we investigated the impact of operating conditions (catalyst dosage, hydraulic retention time and ozone dosage) employing Cu-Al LDHs as the catalyst. We also developed a mathematical kinetic model to describe the performance of the suspension reactor and, through use of the kinetic model, showed that O3(g) interphase transfer rate was the rate-limiting step in OA removal. Thus, improvement in ozone gas diffuser design is required to improve the performance of the suspension reactor. Overall, the present study demonstrated that suspension reactors were more effective than fixed-bed reactors for oxidation of surface-active organic compounds such as OA due to the higher ozone interphase mass transfer rate and effective utilization of the catalyst surface area that can be achieved. As such, further research on suspension reactor design and development of catalysts suitable for use in suspension reactors should facilitate large-scale application of catalytic ozonation processes by the wastewater treatment industry.

Numerical Study of the Influence of the Type of Gas on Drag Reduction by Microbubble Injection

In this work, a novel numerical method for studying the influence of gas types on drag reduction by microbubble injection is presented. Aimed at the microbubble drag reduction (MBDR) process for different types of gases, the mass transfer velocity of different types of gases in the gas–liquid phase is defined by writing a user-defined function (UDF), which reflected the influence of gas solubility on the drag reduction rate. An Eulerian multiphase flow model and the Realizable k−ε turbulence model are used for numerical calculation. The population balance model is used to describe the coalescence and breakup phenomena of the microbubble groups. Henry’s theorem is used to calculate the equilibrium concentration of the microbubble mixed flow. The interphase mass transfer rate of the microbubble injection process for different types of gases is studied by using permeation theory. The local mass fraction of the mixed flow is solved by the component transport equation. It is found that the larger the solubility of the gas, the lower the efficiency of MBDR. When the volume flow rate of the same type of gas is the same but the injection speed is different, the larger the solubility of the gas is, the greater the difference in the drag reduction ratio.

Kinetics of Fixed Bed Sorption Processes

Adsorption and ion exchange are examples of fixed-bed sorption processes that show transient behavior. This means that differential equations are needed to design them. As a result, numerical methods are commonly utilized to solve these equations. The solution frequently used in analytical methods is called the Thomas solution. Thomas gave a complete solution that adds a nonlinear equilibrium relationship that depends on second-order reaction kinetics. A computational approach was devised to solve the Thomas model. The Thomas model's validity was established by conducting three distinct sets of experiments. The first entails the adsorption of acetic acid from the air through the utilization of activated carbon. Following this, zeolite-5A adsorbs trichloroethylene (TCE) from the air. Finally, activated carbon is employed for the purpose of adsorbing o-cresol from aqueous solutions. A study was done to estimate phase equilibria and interphase mass transfer rates. To find the kinetic mass-transfer coefficient (K) for gases, the phase coefficients for mass transfer in the fluid phase ( ) and the pore phase ( ) were added together. The estimation of (K) for liquid was performed using the mass transfer coefficient for the solid phase and togather. The results suggest that the adsorption of acetic acid from air on activated carbon gives a good agreement with the Thomas model. The other sets of data demonstrate a disparity due to the underlying assumptions inherent in the Thomas model.

Numerical study on the effect of longitudinal vortex generator on semi-dry desulfurization process in 3D spouted beds

A longitudinal vortex generator was introduced into spouted beds to improve the heat and mass transfer rates in a semi-dry desulfurization process. The flue gas desulfurization processes in a 3D conventional spouted bed (CSB) and a spouted bed with a longitudinal vortex (LVSB) were simulated and verified experimentally. The simulation results show that the generator can strengthen the gas-particle-slurry contact in the spouting and annular areas. The average interphase slip velocities of the gas-particle and gas–liquid in the LVSB were 26.6 and 26.5 % higher than that in the CSB. The generator also increased the liquid temperature and interphase mass transfer rates in the spouted beds. The simulated desulfurization efficiencies of the CSB and LVSB were 77.75 and 80.85 %, respectively, which indicate the addition of a generator is beneficial for promoting the semi-dry desulfurization process.

Carbon capture in laval nozzles with different bicubic parametric curves and translation of witoszynski curves

This work investigates the influence of convergent curve of supersonic nozzle on the carbon separation process. The CFD model based on nucleation and growth theory, second-order upwind scheme and density-based solution method are employed to predict the CO2 supersonic separation process in the nozzle. The effects of bicubic parametric curve and translation of Witoszynski curve on flow characteristics and spontaneous condensation characteristics are illustrated. The results show that the mixed gas accelerates and deviates from the equilibrium state in the Laval nozzle, and nucleation occurs when the supersaturation is greater than 1.81. After nucleation, gas enters the droplet growth stage, during which mass and heat transfer are carried out between gas and liquid phase, and the droplet radius increases continuously. With the increase of the parameter xm in the bicubic parametric curve equation and the axis shift quantity yh in the translation of Witoszynski curve equation, the flow parameters in the nozzle change more violently, the nucleation location moves to the nozzle exit, and the interphase mass transfer rate and liquid fraction decrease in varying degrees.

Design and development of a new static mixing bioreactor for enzymatic bioprocess: Application in biodiesel production

Mass transfer efficiency plays an important role in enzymatic biological processes, especially for non-aqueous biocatalytic processes. In these processes, low interphase mass transfer rates result in relatively long reaction residence time in traditional batch reactors. Therefore, the design and development of new bioreactors is crucial. In this study, a novel static mixing bioreactor was designed and applied to enzymatically catalyzed biodiesel production, which is a typical interfacial reaction system. In order to achieve good mixing effect and low pressure drop, the structure of bioreactor, including unit configuration, aspect ratio and rotation angle was designed and optimized by computational fluid dynamics. The realizable k-epsilon model was used, it was proved to be grid independent with 833678 hexahedral unstructured grids that were adopted to improve the structure for material mixing. After modification of the reactor, the final optimized structure is an R-R configuration with an aspect ratio of 1.5 and a rotation angle of 150°. Based on the above improved bioreactor, the process conditions for enzymatic production of biodiesel were optimized. The optimized reaction conditions were as follows: the length of the static mixer was 30 cm, the material flow rate was 1.77 m/s, the reaction temperature was 40 °C, the amount of methanol added was 3 times, and molar ratio of 3.4 alcohol to oil and 10% lipase dose were used. Under the optimal conditions, the yield of biodiesel in 1.5 h could reach 81.28%, and it could still be above 70% after 12 times of repeated use of lipase. Under the same reaction conditions, the reaction time for the static mixer to reach the same conversion rate (81.28%) was 1/3 of that of the stirred reactor, confirming the excellent mass transfer performance of the static mixer bioreactor.

A new efficiency relaxation model for rigorous stage number optimization of distillation columns

Determining the optimal state number in distillation column design is a mixed-integer nonlinear programming (MINLP) problem, which is difficult to solve. One strategy to solve this problem is relaxing integer stage numbers into continuous variables and solving an easier nonlinear programming (NLP) problem. However, the existing relaxation model often converges to non-integer stage numbers or poor local optima in practical applications, which motivates this paper to develop a new relaxation model. The proposed relaxation model employs an interpolation function to relax the discrete decision on the existence of a stage by varying interphase mass and heat transfer rate between zero and equilibrium state. By adjusting a shape parameter in the interpolation function, the interpolation function shape and its penalty extent of non-integer stage can be manipulated. The results of three distillation column optimization cases show that the proposed model can effectively avoid converges to non-integer stage numbers or poor optima.

Numerical investigation of the non-condensable gas effect on predicting the cavitation performance of a centrifugal pump

Improving the prediction accuracy of cavitation performance of pumps is a research hotspot. The non-condensable gas effect has been included in some existing cavitation models. However, the amount of the non-condensable gas in water still needs discussing since it will affect the vaporization process. In this paper, Zwart-Gerber-Belamri model was used to calculate the cavitation performance of a three-blade centrifugal pump with water temperature of 10 °C and a corresponding cavitation experiment was carried out to verify the numerical model. Numerical results respectively with five volume fractions of the non-condensable gas were analyzed. Compared to the recommended default value, the head drop curve obtained with a much lower volume fraction of the non-condensable gas agrees better with the experimental result. Comparison and analysis of the cavitation patterns as well as the flow field indicates that the default volume fraction of the non-condensable gas which was proposed at 25 °C overestimates the interphase mass transfer rate at 10 °C Reasonably setting the volume fraction of non-condensable gas in the cavitation model will achieve more accurate cavitation pattern, and then the head drop curve of pump can be predicted more precisely.

Analysis of Ozonation Processes Using Coupled Modeling of Fluid Dynamics, Mass Transfer, and Chemical Reaction Kinetics.

The efficacy of oxidation of recalcitrant organic contaminants in municipal and industrial wastewaters by ozonation is influenced by chemical reaction kinetics and hydrodynamics within a reactor. A 3D computational fluid dynamics (CFD) model incorporating both multiphase flow and reaction kinetics describing ozone decay, hydroxyl radical (•OH) generation, and organic oxidation was developed to simulate the performance of continuous flow ozonation reactors. Formate was selected as the target organic in this study due to its well-understood oxidation pathway. Simulation results revealed that the dissolved ozone concentration in the reactor is controlled by rates of O3(g) interphase transfer and ozone self-decay. Simulations of the effect of various operating conditions showed that the reaction stoichiometric constraints between formate and ozone were reached; however, complete utilization of gas phase ozone was hard to achieve due to the low ozone interphase mass transfer rate. Increasing the O3(g) concentration leads to an increase in the formate removal rate by ∼5% due to an enhancement in the rate of O3(g) interphase mass transfer. The CFD model adequately describes the mass transfer occurring in the two-phase flow system and confirms that O3(g) interphase mass transfer is the rate-limiting step in contaminant degradation. The model can be used to optimize the ozone reactor design for improved contaminant degradation and ozonation efficiency.

Wellbore multiphase flow behaviors during gas invasion in deepwater downhole dual-gradient drilling based on oil-based drilling fluid

Knowledge of wellbore multiphase flow characteristics is important for early gas invasion identification and treatment, especially in oil-based drilling fluid. The wellbore multiphase flow law in downhole dual-gradient drilling (DDGD) is more complex than that in conventional single-gradient drilling. There was no relevant literature report at present. In this paper, considering the synergistic feedback relationship of multiphase flow, interphase mass transfer, and wellbore temperature, a fully transient wellbore multiphase flow model was established based on oil-based drilling fluid in deepwater DDGD. The model also coupled the variable temperature–mass flows caused by the dynamic transfer of hollow glass balls and formation gas. The bubble interface mass transfer theory was adopted to describe the interphase mass transfer rate. The model was verified through the experimental measurement data. The calculated results indicated that the dynamic transfer of hollow glass balls varied the wellbore pressure gradient and flow rate in DDGD, resulting in a sudden decrease in gas fraction and gas solubility along the flow direction at the separator. Additionally, the transient interphase mass transfer and wellbore temperature had large impact on the wellbore multiphase flow behaviors. Moreover, the model based on bubble interface mass transfer theory could more accurately characterize the development of the wellbore multiphase flow. This research could provide a certain theoretical basis for the detection and treatment of gas invasion in deepwater DDGD.

The coupled model of transient non-equilibrium interphase mass transfer rate of sliding bubble and two-phase flow in variable gradient drilling

The aim of this research is to investigate the influence of key parameters of variable gradient drilling by injecting hollow-glass spheres (Referred to as HGS, it is a low-density and micron-sized hollow glass sphere) on the interphase mass transfer rate of the surface boundary layer of the sliding bubble in the annulus and the flow law of the two-phase flow in the wellbore after the gas intrusion occurred. Firstly, the key parameters of variable-gradient drilling, such as HGS volume fraction, HGS density, the depth of the filter separator, were coupled with the model of non-equilibrium interphase mass transfer rate and the mathematical model of two-phase flow to establish a new two-phase flow model of transient non-equilibrium interphase mass transfer for variable-gradient drilling. Secondly, the existing classic model and measured data were used for comparative analysis with the model in this paper, and then the accuracy of the model in this paper was verified. Thirdly, based on the on-site data, the numerical calculations and sensitivity analysis were carried out using the model in this paper. Finally, a comparative analysis of the interphase mass transfer rate was performed under equilibrium and non-equilibrium conditions. In addition, the influence on non-equilibrium interphase mass transfer rate of surface boundary layer of the bubble, bottom hole pressure, overflow rate and overflow rate exerted by different separator positions, HGS volume fraction, HGS density, and pumping rate was studied. The results indicated that the interphase mass transfer rate under the non-equilibrium condition was lower than that under the equilibrium condition when the both were at the same well depth or at the same circulation time. The interphase mass transfer rate enhanced with the increase of pumping rate, the depth of filter separator and HGS density, but decreased with the increase of HGS volume fraction. The bottom-hole pressure was negatively correlated with the depth of the filter separator and the volume fraction of HGS, on the contrary, it was positively correlated with the HGS density. Similarly, the gas void fraction, overflow rate and overflow were positively correlated with the depth of filter separator and HGS volume fraction, but negatively correlated with the HGS density. This research can provide a certain theoretical reference for variable gradient drilling.

Numerical simulation on constituent separation and mass transfer of binary zeotropic mixtures in a branching T-junction

The study of constituent separation in T-junction is important to realize the operation of the constituent adjustable system. This paper presents a numerical simulation on the constituent separation and mass transfer of R134a and R600a in T-junction. The multiphase flow model of volume of fluid (VOF) is adopted, and the interphase mass transfer of R134a and R600a is achieved by adding source terms in governing equations. The quality at inlet varies from 0.51 to 0.92. The mass flow rate at inlet and flow rate weighting of branch outlet are 10 g⋅s−1 and 0.3, respectively. Results show that the error of numerical simulation with mass transfer is lower than that of numerical simulation without mass transfer. When the quality at inlet is 0.81, the error of numerical simulation with mass transfer can be reduced by 50.07% compared with the numerical simulation without mass transfer. The higher the quality at inlet, the higher the separation efficiency of R134a when the quality at inlet is less than 0.81. When the quality at inlet is 0.81, the separation efficiency of R134a in the numerical simulation with mass transfer is the largest, whose value is 1.47%. Most of the flow patterns are annular flow. The pressure and flow pattern have an important influence on the constituent separation and the interphase mass transfer rate. A correlation with 10% error band of interphase mass transfer for annular flow in T-junction is proposed.

Numerical study of the hydrofoil cavitation flow with thermodynamic effects

High-temperature water exhibits evident thermodynamic effects during cavitation, which influences the cavitation flow and generates complex flow characteristics. To reveal the mechanism of thermodynamic effects on the cavitation flow in high-temperature water, a flow around NACA 0015 hydrofoil was simulated. Based on the existing isothermal cavitation model, the thermodynamic effects were considered by correcting evaporation and condensation source terms and coupling physical parameters with temperature. Numerical results obtained from the thermodynamic effect cavitation model agree well with the available experiments. A comparative analysis of performance characteristics, cavitation shape, and interphase mass transfer rate was performed. The thermodynamic effects on the cavitation flow of hydrofoil under different temperature were presented. The existence of the thermodynamic effects lowers the local temperature of the cavitation, reduces the vapor phase volume fraction of the cavitation area, and inhibits the development of cavitation. Moreover, a novel entropy production analysis was conducted to reveal the thermodynamic effects on the energy loss. The difference of local entropy production rate in the cavitation flow with and without thermodynamic effects was revealed. The analyses show that the existence of the thermodynamic effects reduces the energy loss owing to the reduction of the dissipation loss caused by the velocity gradient. When the thermodynamic effects are considered, the energy loss caused by the temperature gradient shows an increase; however, the proportion of this loss is still small.

Experimental and numerical study of non-equilibrium dissolution and exsolution behavior of CO2 in a heavy oil system utilizing Hele-Shaw-like visual cell

A novel methodology utilizing high-pressure Hele-Shaw-like visual cell has been developed to study solvent dissolution and exsolution behavior of a CO2-heavy oil system. The experimental setup overcomes the visualization shortcomings of traditional apparatuses such as a hardly-visual cylindrical PVT cell, or non-visual transfer cylinders. Experimentally, a heavy oil sample (viscosity at 1500cP at de-gassed state) was used to conduct solvent dissolution and exsolution tests. CO2 diffusion tests have been conducted by pressure decay method. At the end of each diffusion stage, pressure depletion tests were subsequently conducted on the CO2-heavy oil system to study foamy oil stability under different pressure depletion schemes. The effect of various factors on the foamy oil volumetric behavior have been investigated, including the effect of initial solution GOR, continuous pressure depletion rate, immediate pressure drawdown level and solvent-heavy oil contact time. A MATLAB-controlled reservoir simulator was developed for numerical validation. For solvent dissolution tests, CO2 diffusion coefficient in oil (intra-phase mass transfer) was optimized and achieved by history matching the pressure decay curves. Results showed that, diffusion coefficients increased from 6.198 × 10−9 to 25.333 × 10−9m2/s when pressure increased from 1555 to 3320 kPa. Solvent exsolution behavior was simulated through defining multiple kinetic reactions. Kinetic reaction rate frequency factors (RRFs), which indicated the rate of multi-component inter-phase mass transfer, were achieved by history matching foamy oil volume under multiple operational schemes. Comparing RRFs, foamy oil stability was found to be increasing under higher initial GOR, pressure depletion rate and pressure drawdown as well as for longer solvent-heavy oil contact time.

The effect of interfacial mass transfer of slip-rising gas bubbles on two-phase flow in the vertical wellbore/pipeline

During drilling or oil recovery, it is common that the formation trap gas invades the vertical wellbore/pipeline to cause the gas-liquid two-phase flow, which brings challenges and dangers to wellbore/pipeline pressure control. In this paper, coupling the interfacial mass transfer theory of slip-rising bubbles based on bubble hydraulics to the gas-liquid two-phase flow theory, a new transient non-isothermal gas-liquid two-phase flow model in the vertical wellbore/pipeline was developed. In this model, the effects of flow regime and heat transfer on the mass transfer rate were considered. The proposed model was validated using the measured experiment data and field data. Using this model, the effect of interfacial mass transfer of slip-rising bubbles on the evolution of gas-liquid two-phase flow in a special gas kick scenario was analyzed. The simulation results indicated that the mass transfer rate between oil dispersion and invasion gas was relatively slow, which made the gas not instantaneously dissolved in the oil dispersion or not instantly saturated the oil dispersion. Under the same gas invasion rate, the fraction and mass of free gas calculated by this model were always larger than those obtained by Yin's model, resulting in a faster of the bottomhole pressure reduction rate and pit gain increase rate. Additionally, increasing the gas concentration and flow rate could promote the interphase mass transfer rate, while increasing the temperature would inhibit it. This model could characterize the wellbore/pipeline gas-liquid two-phase flow with interphase mass transfer in more detail and accurately.

Numerical simulation of particle growth process in a polysilicon fluidized bed reactor

An Eulerian–Eulerian model coupled with a population balance model (PBM) is adopted to investigate the growth process of polysilicon particles in a polysilicon fluidized bed reactor. A novel particle growth model, considering the effect of interphase velocity difference, is proposed and incorporated into PBM. The interphase mass transfer rate and particle growth rate are obtained based on the modified PBM. The effects of operating velocity and silane mole fraction on the particle growth rate and deposition efficiency are also analyzed. The results show that silicon fines scavenging occurs in the solid phase, especially in central and near-wall regions. Moreover, the increases of operating velocity and silane mole fraction lead to the decrease in the deposition efficiency.

Intra-NAPL diffusion and dissolution of a MGP NAPL exposed to persulfate in a flow-through system.

Intra-NAPL diffusion is a critical process that can influence NAPL/water mass transfer. A series of physical model experiments was performed to investigate the role of intra-NAPL diffusion on the transient dissolution of a complex multicomponent NAPL subjected to persulfate treatment. To support these observations, a diffusion-based model was developed and calibrated using the experimental data. The experimental results indicated that while persulfate was able to completely degrade dissolved phase components, mass loss after ∼410 pore volumes of persulfate flushing was less than the no-treatment system. Intra-NAPL diffusion limitations were not observed in the physical model experiments. A comparison of experimental and simulated results indicated that processes related to persulfate/NAPL interactions restricted mass transfer, and yielded multicomponent mass transfer rate coefficients that were ∼30% of those estimated from an equivalent water-flushing experiment. Simulation results showed that a combination of NAPL composition and geometry, and interphase mass transfer rate can yield intra-NAPL diffusion limitations. Remedial technologies that rely on the aggressive flushing of reagents into NAPL zones may give rise to intra-NAPL diffusion limitations, which will directly affect treatment efficiency.

Micro-reactor mixing unit interspacing for fast liquid-liquid reactions leading to a generalized scale-up methodology

The effect of geometrical arrangements of a residence time channel (RTC) positioned in between LL-Rhombus static mixing elements on interphase mass transfer rates is investigated. Four variations of a micro-reactor plate are tested with four immiscible aqueous-organic systems: water coupled with n-butanol, n-hexanol, methyl tert-butyl ether and toluene. The alkaline hydrolysis of 4-nitrophenyl acetate is used to determine the overall volumetric mass transfer coefficient (Kda). For all solvent pairs, the micro-reactor without a RTC has the greatest Kda at a given flow rate due to a greater energy dissipation rate (ɛ) and the fact that drops can re-coalesce leading to reduced advective transfer in the RTC pending the flow regime. An increase in flow rate results in a rise in conversion up to a maximum, after which viscous dissipation impedes further turbulent breakdown of the droplets as they near the Kolmogorov length scale. When the resulting flow is finely dispersed, interphase mass transfer rates no longer depend on reactor geometry but was correlated to the solvent system and rate of energy dissipated. The negative impact of operating at greater ɛ values than at maximum conversion is shown via the required pressure loss to achieve a certain conversion or residence time. Lastly, relevant to production rates in the fine chemical and pharmaceutical industry, an algorithm for scaling a generic mass transfer-limited liquid-liquid reaction at identified optimal operating conditions is presented.

The role of intra-NAPL diffusion on mass transfer from MGP residuals

An experimental and computational study was performed to investigate the role of multi-component intra-NAPL diffusion on NAPL-water mass transfer. Molecular weight and the NAPL component concentrations were determined to be the most important parameters affecting intra-NAPL diffusion coefficients. Four NAPLs with different viscosities but the same quantified mass were simulated. For a spherical NAPL body, a combination of NAPL properties and interphase mass transfer rate can result in internal diffusion limitations. When the main intra-NAPL diffusion coefficients are in the range of self-diffusion coefficients (10−5 to 10−6 cm2/s), dissolution is not limited by internal diffusion except for high mass transfer rate coefficients (>180 cm/day). For a complex and relatively high viscous NAPL (>50 g/(cm s)), smaller intra-NAPL diffusion coefficients (<10−8) are expected and even low mass transfer rate coefficients (~6 cm/day) can result in diffusion-limited dissolution.

Separation performance investigation of packed distillation columns using simple NEQ approach based on packing multicomponent efficiencies and effective mass transfer coefficients

A simple non-equilibrium modeling approach is proposed to simulate multicomponent distillation process in packed columns. The real behavior of the column is simply considered by the evaluation of interphase mass transfer rate based on the overall mass transfer coefficient. Two distinct methods are used to calculate this overall coefficient including the effective mass transfer coefficient method and the packing efficiency method. The modelling procedure consists of an iterative segment-wise algorithm implemented in a MATLAB home-code. For verification, the obtained composition profiles from a structured and a random packed column are compared with reported experimental data. Comparisons show that the packing efficiency-based model could acceptably predict the experimental profiles with an average relative deviation of 18% and 25% for structured and random packed columns, respectively. This confirms that our simple non-equilibrium approach is a reliable and robust model for the performance evaluation of packed columns.