Analysis and interpretation of residence time distribution experimental curves in FM01-LC reactor using axial dispersion and plug dispersion exchange models with closed-closed boundary conditions

The liquid phase mixing flow pattern at low (20 < Re < 120) and intermediate liquid flow rate (120 < Re < 400) was studied by means of residence time distribution (RTD) experimental curve in an up-flow Filter Press electrochemical reactor (FM01-LC) bench scale. For this purpose, a plastic turbulence promoter was used with stainless-steel and platinised titanium structural meshes as electrodes in channel configuration. To visualize and determine the mixing flow pattern in the liquid phase, the stimulus-response technique was employed using dextran blue (D_M = 1.058 × 10⁻¹¹ m² s⁻¹, 25 °C, in water) as model tracer. A theoretical analysis and approximation RTD experimental curves with axial dispersion model (ADM) and plug dispersion exchange model (PDE), with “closed-closed vessel” boundary conditions were used in order to establish a better approximation of the axial dispersion, stagnant zones, channelling and by-pass (preference flow) effects present at low and intermediate Re. RTD curves show that the liquid flow pattern in the FM01-LC deviates considerably from axial dispersion model at low Re, where the FM01-LC exhibits large channelling, stagnant zones, and dead zone. The PDE model represents fairly this deviation from ideal flow (less dead zone).     

Liquid backmixing in oscillatory flow through a periodically constricted meso-tube

This paper deals with the measurement and modelling of axial liquid dispersion in a 4.5 mm internal diameter tube provided with smooth-periodic constrictions (meso-tube) in steady and oscillatory flow conditions. The residence time distribution (RTD) in the meso-tube was monitored for a range of fluid oscillation frequency (f) and amplitude (x₀) at laminar flow. The RTD response was modelled with three hydrodynamic models: (i) tanks-in-series, (ii) tanks-in-series with backflow and (iii) plug flow with axial dispersion. The steady flow through the meso-tube at flow rates up to 21.30 ml/min resulted in broad RTDs, mainly due to the parabolic velocity profile. The use of fluid oscillations allowed a fine-control of the axial liquid dispersion in the meso-tube due to generation of secondary flow in the regions between the constrictions. The axial dispersion coefficient D was reduced by up to 13-fold in comparison with the steady flow situation. Values of x₀ ≤ 1 mm and f = 10 Hz generally resulted in a maximum reduction in axial dispersion through, therefore maximum improvements in RTD. The tanks-in-series model was generally not capable of predicting RTDs in the meso-tube. The potential of this platform for the continuous, sustainable production of added-value products is herein demonstrated.     

Solids mixing behavior in a nano-agglomerate fluidized bed

The nano-particles mixing behavior in a nano-agglomerate fluidized bed (NAFB) using R972, a kind of nano-SiO₂ powder, was investigated by the nano-particle coated phosphors tracer method. The axial and radial solids dispersion coefficients in this system were two orders of magnitude lower than those in fluid catalytic cracking (FCC) catalyst systems. The axial solids dispersion coefficient increased with increasing superficial gas velocities, and ranged between 9.1 × 10^− 4 and 2.6 × 10^− 3 m²/s. There was a step increase in the axial solids dispersion coefficient between the particulate fluidization regime and bubbling and turbulent fluidization regimes. As the superficial gas velocity increased, the radial solids dispersion coefficient increased gradually, from 1.2 × 10^− 4 to 4.5 × 10^− 4 m²/s. The much smaller D_a and D_r, compared to regular fluidized systems, is mainly due to the reduced density difference between the fluidized particles and fluidizing medium. To validate this, the solids dispersion coefficients in the NABF were compared with literature values for liquid-solid particulate systems in the particulate fluidization regime and FCC systems in the bubbling and turbulent fluidization regimes. The density difference between the fluidized particles and fluidizing medium and kinetic viscosity of the fluidizing medium, and other hydrodynamic factors like the superficial velocity of the fluidizing medium and the average diameters of the fluidized particles, were the key factors in the solids mixing in the fluidized beds. Empirical correlations are given to describe the results.     

Liquid phase axial mixing in bubble columns operated at high pressures

Liquid phase axial mixing was measured in a 100 mm i.d. bubble column operated in the pressure range of 0.1-0.5 MPa. Water, ethanol and 1-butanol were used as the liquid phase and nitrogen as the gas phase. The temperature and superficial gas velocity were varied in the range of 298-323 K and 0.01-0.21 m/s, respectively. The axial dispersion coefficient increased with an increase in the gas density due to pressure. The temperature had surprisingly a small effect. A CFD model was developed for the prediction of flow pattern in terms of mean velocity and eddy diffusivity profiles. The model was further extended for the prediction of residence time distribution and hence the axial dispersion coefficient (D_L). The predictions of axial dispersion coefficient agree favorably with all the experimental data collected in this work as well as published in the literature. The model was extended for different gas-liquid systems. The predicted values of axial dispersion coefficient were found to agree very well with all the experimental data.     

Experimental, kinetic and 2-D reactor modeling for simulation of the production of hydrogen by the catalytic reforming of concentrated crude ethanol (CRCCE) over a Ni-based commercial catalyst in a packed-bed tubular reactor

Mechanistic kinetic models were formulated based on Langmuir-Hinshelwood-Hougen-Watson and Eley-Rideal approaches to describe the kinetics of hydrogen production by the catalytic reforming of concentrated crude ethanol over a Ni-based commercial catalyst at atmospheric pressure, temperature range of 673-863 K, ratio of weight of catalyst to the molar rate of crude ethanol 3472-34722 kg cat s/kmol crude in a stainless steel packed bed tubular microreactor. One of the models yielded an excellent degree of correlation, and was selected for the simulation of the reforming process which used a pseudo-homogeneous numerical model consisting of coupled material and energy balance equations with reaction. The model was solved using finite elements method without neglecting the axial dispersion term. The crude ethanol conversion predicted by the model was in good agreement with the experimental data (AAD%=4.28). Also, the predicted concentration and temperature profiles for the process in the radial direction indicate that the assumption of plug flow isothermal behavior is justified within certain reactor configurations. However, the axial dispersion term still contributed to the results, and thus, cannot be neglected.     

Liquid-phase axial mixing study in a mobile bed contactor with low density particles

Axial mixing of the liquid phase in a 0.15 m ID mobile bed contactor has been studied for spherical, cork and irregular-shaped particles of densities 53, 183 and 112 kg m^?3, respectively, using the air-water system. The range of gas and liquid flow rates covered were from 0.5 to 5 m s^?1 and from 0.011 to 0.044 m s^?1, respectively. The experimental breakthrough curves were interpreted by means of the axial dispersion model. Correlations for the Peclet number and axial dispersion coefficient have been proposed. The results indicate that near plug flow of the liquid phase could be achieved with higher static bed heights if the congregation of particles at the wall could be avoided.     

Longitudinal dispersion of solid particles in fluid beds with horizontal baffles

The axial pressure profiles, allowable gas velocities and temperature distributions are measured for the fluidization of air—FCC cracking catalyst systems in 12- and 19-cm-diam. eight-stage fluid beds equipped with seven horizontal baffles. From these measurements, gas bubble holdup, apparent longitudinal dispersion and intermixing velocity of solid particles through the baffles are studied as functions of baffle design. It is shown that the gas bubble holdup increases, the operational range of gas flow decreases and the flow pattern of solid particles approaches plug flow with decreasing free area of baffles.     

Extraction of dioxouranium(VI) in small channels using ionic liquids

The extraction behaviour of dioxouranium(VI) from nitric acid solutions with tributylphosphate (TBP) dissolved (30%, v/v) in room temperature ionic liquids (viz. 1-butyl-3-methylimidazolium bis{(trifluoromethyl)sulfonyl}amide, [C₄mim][NTf₂], 1-decyl-3-methylimidazolium bis{(trifluoromethyl)sulfonyl}amide, [C₁₀mim][NTf₂], and trihexyltetradecylphosphonium bis{(trifluoromethyl)sulfonyl}amide, [P_6 6 6 14][NTf₂]) was investigated. The experiments were performed in a capillary (0.5 mm internal diameter) made of Teflon, operated in the plug flow regime. The effects of ionic liquid type, initial nitric acid concentration, and residence time on dioxouranium(VI) extraction were studied. UV–vis spectroscopy was used for the determination of the dioxouranium(VI) concentration in the ionic liquid phase. For increasing [HNO₃]_aq,init, the %extraction decreased and then increased for [C₄mim][NTf₂], while for the other two ionic liquids it increased. The %extraction also increased with residence time in the channel. Overall mass transfer coefficients were about 0.2 s^–1 in all TBP/ionic liquid systems at the initial nitric acid concentration of 3 M when a 10 cm capillary was used.     

Heat transfer study in a pilot-plant scale bubble column

The effects of superficial gas velocity on heat transfer coefficient and its time-averaged radial profiles along the bed height have been investigated in a pilot-plant scale bubble column of 0.44 m diameter using air-water system. Notable differences were observed in heat transfer coefficients along the bed axial locations particularly between the sparger (Z/D = 0.28) and the fully developed flow (Z/D = 4.8) regions. In the fully developed flow region larger heat transfer coefficient values were obtained compared to those in the sparger region. About 14-22% increase in heat transfer coefficients measured in the fully developed flow region has been observed compared to those measured in the distributor region when the superficial gas velocity increases from 0.05 to 0.45 m/s. The heat transfer coefficients in the column center for all the conditions studied are about 9-13% larger than those near the wall region. It has been noted that in the fully developed flow region, the axial variation of the heat transfer coefficients was not significant.     

Limiting withdrawal rate and maximum film thickness during dip-coating of titania sols onto a Si substrate

The article highlights new insights into production of thin titania films widely used as catalyst support in many modern reactors including capillary microreactors, microstructured fixed-bed reactors and falling film microreactors. Dip-coating of a titania sol onto a Si substrate has been studied in the range of the sol viscosities of 1.5-2.5 mPa s and the sol withdrawal rates of 0.2-18 mm/s. Different viscosities of sols were created by addition of desired amounts of nitric acid to the synthesis mixture of titanium isopropoxide and Pluronic F127 in ethanol which allowed to control the rate of the condensation reactions. Uniform mesoporous titania coatings were obtained at the solvent withdrawal rates below 10 mm/s at sol viscosities in the range from 1.6 mPa s to 2.5 mPa s. There exists a limiting withdrawal rate corresponding to a capillary number of ca. 0.01 beyond which uniform titania films cannot be obtained. Below the limiting withdrawal rate, the coating thickness is a power function of the sol viscosity and withdrawal rate, both with an exponent of 2/3. The limiting withdrawal rate increases as the solvent evaporation rate increases and it decreases as the sol viscosity increases.     

Axial dispersion characteristics in three phase fluidized beds

Axial dispersion coefficients in three-phase fluidized beds have been measured in a 0.152 m-ID x 1.8 m high column by the two points measuring technique with the axially dispersed plug flow model. The effects of liquid velocity (0.05–0.13 m/s), gas velocity (0.02–0.16 m/s) and particle size (3-8 mm) on the axial dispersion coefficient at the different axial positions (0.06–0.46 m) in the bed have been determined. The axial dispersion coefficient increases with increasing gas velocity but it decreases with an increase in particle size and exhibits a maximum value with an increase in the axial position from the distributor. The axial dispersion coefficients in terms of the Peclet number have been correlated in terms of the ratio of fluid velocities, the ratio of the panicle size to column diameter, and the dimensionless axial position in the bed based on the isotropic turbulence theory.     

Numerical study of particle dispersion in the wake of gas-particle flows past a circular cylinder using discrete vortex method

A numerical investigation on the particle dispersion in the wake of particle-laden gas flows past a circular cylinder at Reynolds number of 10⁵ is presented. In the numerical method, the Discrete Vortex Method with the diffusion velocity model is employed to calculate the unsteady gas flow fields and a Lagrangian approach is applied to track individual particles. A dispersion function is defined to represent the dispersion scale of the particle. The distributions of gas velocities and vortex blobs, the trajectories and dispersion functions as well as distributions for particles with various Stokes numbers ranging from 0.01 to 1000 are obtained. The numerical results show that: (1) very small sized particles with St = 0.01 can distribute both in the vortex core and around the vortex periphery, whereas intermediate sized particles with St = 1.0, 10 are distributed around the vortex periphery, and very large sized particles with St = 1000 do not feel the gas flow; (2) only at small Stokes number (St = 0.01, 0.1) the particles do not impact with the cylinder; (3) the particle's dispersion intensity decreases precipitously as St is increased from 0.01 to 10.     

Measurement of residence time distribution in microfluidic systems

We present a method for measuring the residence time distribution (RTD) in microfluidic systems. A piezoelectrically actuated sample injector releases approximately 100 nl of tracer liquid into a microchannel of rectangular cross section. The spreading of the tracer pulse in pressure-driven microflows is monitored with fluorescence microscopy measurements. Residence time distributions are determined for single-phase liquid and segmented gas-liquid microflows, with the RTD being significantly narrower for the latter case. The selected flow conditions are relevant to synthesis in microreactors with residence times up to several minutes.     

Hydrodynamics of three-phase fluidized bed systems examined by statistical, fractal, chaos and wavelet analysis methods

Hydrodynamic studies were conducted in gas-liquid-solid systems (0.1 m ID, 2 m high) of 3.0 mm glass beads and of 2.1 mm polypropylene low-density particles, with particles densities of 2471 and 1290 kg/m³, respectively. Simultaneous measurement of differential pressure and bubble conductivity probe signals sampled at 500 Hz for 60 s enabled the investigation of the change in flow structure in relation to the flow regime transitions. Superficial gas velocities ranged between 0.010 and 0.052 m/s for polypropylene particles, and extended to 0.12 m/s for glass beads, while the superficial liquid velocities covered the ranges of 0.0007-0.045 m/s for polypropylene particles, and ranged up to 0.056 m/s for glass beads.Spectral analysis of the pressure fluctuations revealed a transition from dispersed to coalesced bubbling flow with decreasing liquid velocity for a given superficial gas velocity. The use of a conductivity probe facilitated characterization of the local flow structure in terms of bubble movement. The measurements were extensively analyzed using fractals and chaos, power spectra frequency analysis and wavelet decomposition in addition to the standard statistical analyses. The coefficient of variation of the bubble probe signals was found to be the most effective in deducing the transition velocity between coalesced and dispersed bubbling flow regimes, while wavelet energy confirmed the similarity in the distribution between two axial positions once operated in the dispersed flow regime. Comparison of the flow structure between glass beads and polypropylene particles showed that both the minimum liquid fluidization velocity and the transition velocity between the bubble flow regimes were much higher for the glass beads than for the lighter polypropylene particles. Furthermore, the standard deviations of the decomposed bubble probe signals through wavelet transformation successfully highlighted the difference between the two systems of particles.     

Ideality analysis and general laws of bubble swarm microflow for large-scale gas-liquid microreaction processes

The flow ideality of bubbly microflow remains unclear even though it is vital for the design of microreactors, especially the ideality of bubble swarm microflow for large-scale gas-liquid microreaction processes. This work is the first time to report the ideality analysis of the microbubble swarm in a relatively large microchannel. The bubble swarm microflow has undergone two conditions: quasi-homogeneous plug flow and liquid phase/gas-liquid quasi-homogeneous phase two-phase laminar flow. Both the deviations of void fraction and bubble velocity from the ideal plug flow can divide into two parts, and the two transition points simultaneously happen at the velocity ratio of 1.25. There exists a critical capillary number to maintain the quasi-homogeneous plug flow, which could be regarded as the general laws for the design of gas-liquid microreactors. Finally, a novel model is developed to predict the bubble velocity. This work could be very helpful for the large-scale gas-liquid microreactors design.     

Residence Time Distribution of a Capillary Microreactor Used for Pharmaceutical Synthesis

The main drivers for application of small-scale reactors in the pharmaceutical industry are the possibility of rapid synthesis and screening of novel drugs as well as the readiness of the scale-up. The characterization of fluid flow pattern was performed through step-up and step-down residence time distribution experiments using a tracer at six different flow rates. Four single-parameter models were considered for representing deviations from ideal plug flow and ideal laminar flow in tubes. The model that provided the best results was the axial dispersion model and the Peclet and Reynolds numbers could be well correlated. Obtained Peclet values from 44 to 244 were close to Pe > 100, in which axial dispersion can be neglected and the reactor can be considered as plug flow reactor.     

Axial dispersion with chemical reaction in packed bed reactors

Data on axial dispersion in packed beds is presented. The effect of axial dispersion on first and second order reactions in packed beds in the near plug flow region is predicted from transient response with no reaction.     

The experimental observation and modelling of microdroplet formation within a plastic microcapillary array

This paper reports an experimental study of the formation of a two-phase liquid mixture in a circular capillary tube of 0.74 mm diameter. Organic liquid, the continuous phase, flowed through the capillary. Aqueous liquid, the dispersed phase, was injected through a hypodermic entering the side of the capillary and a stream of aqueous droplets was formed in the flowing organic liquid. The observed droplet diameters depended strongly on the ratio of the flow-rates between the dispersed and continuous phases: droplet diameters ranged between 480 and 64 μm. A simple model gave good predictions, matching the data and showing how the droplet diameter is dependant on the flow rates of the two phases. The flow geometry was similar to the T-junction configuration used for emulsion formation in microfluidic devices and was fabricated from an extruded plastic capillary array termed a microcapillary film (MCF).     

Influences of various vortex structures on the dispersion and deposition of small ash particles

Numerical simulations were conducted to study the influences of various vortex structures on the dispersion and deposition processes of 1 μm to 10 μm diameter fly ash particles on the rear side surface of a boiler tube. Turbulent gas flow was simulated with detached eddy simulation (DES) method and vortex structures in the wakes were modeled. Results suggested that the motions of particles in the near wake region were controlled by different vortex structures, and the impact efficiency and deposit concentration on the rear side surface induced by the vortices varied considerably at different velocities. The results of volume percentages distribution of the deposited particles with various diameters simulated were in good agreement with the experimental data.