Axial and lateral dispersion of fine particles in a binary-solid riser

Axial and lateral mixing of fine particles in a binary-solid riser have been investigated using a phosphor tracer method. The measured bimodal residence time distribution (RTD) demonstrated two types of axial dispersions of the fines: the dispersion of discrete particles and that of clusters. A proposed one-dimensional, bimodal dispersion model describes the bimodal RTDs very well. The axial Peclet number of the fines is not sensitive to the fraction of coarse particles, gas velocity and solids circulation rate. Lateral solids dispersion was determined by measuring the solids RTD at different radii using a point source tracer injection. A two-dimensional dispersion model describes the measured RTDs satisfactorily. Lateral solids mixing decreased as coarse particles were added into the riser. Correlations of the axial and lateral Peclet numbers obtained fit the experimental data well.     

双颗粒提升管中细颗粒的混合行为研究(Ⅱ)──弥散颗粒的轴径向混合行为

利用磷光颗粒示踪技术,使用点源示踪的方法在不同的径向位置测得反映颗粒径向扩散行为的停留时间分布曲线,并对弥散细颗粒的径向混合行为进行了分析．提出二维扩散模型描述所测量的停留时间分布曲线特征．实验发现弥散细颗粒的径向扩散Peclet数随粗颗粒加入量的增加而增加,随细颗粒浓度的增大而增大,而几乎不随气速变化．给出了一个与实验数据吻合较好并可适用于单颗粒提升管的关联式．     

双颗粒提升管中细颗粒的混合行为研究(Ⅱ)──弥散颗粒的轴径向混合行为

利用磷光颗粒示踪技术，使用点源示踪的方法在不同的径向位置测得反映颗粒径向扩散行为的停留时间分布曲线，并对弥散细颗粒的径向混合行为进行了分析．提出二维扩散模型描述所测量的停留时间分布曲线特征．实验发现弥散细颗粒的径向扩散Peclet数随粗颗粒加入量的增加而增加，随细颗粒浓度的增大而增大，而几乎不随气速变化．给出了一个与实验数据吻合较好并可适用于单颗粒提升管的关联式．     

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.     

Radial gas mixing characteristics in a downer reactor

In a downer reactor (0.1 m-I.D.x3.5 m-high), the effects of gas velocity (1.6-4.5 m/s), solids circulation rate (0–40kg/m²s) and particle size (84, 164 Μm) on the gas mixing coefficient have been determined. The radial dispersion coefficient(D _r ) decreases and the radial Peclet number (Pe_r) increases as gas velocity increases. At lower gas velocities, D_r in the bed of particles is lower than that of gas flow only, but the reverse trend is observed at higher gas velocities. Gas mixing in the reactor of smaller particle size varies significantly with gas velocity, whereas gas mixing varies smoothly in the reactor of larger particle size. At lower gas velocities, D_r increases with increasing solids circulation rate (G_s), however, D_r decreases with increasing G_s at higher gas velocities. Based on the obtained D_r values, the downer reactor is found to be a good gas-solids contacting reactor having good radial gas mixing.     

Axial gas dispersion in a fluidized bed of polyethylene particles

Gas mixing behavior was investigated in a residence time distribution experiment in a bubbling fluidized bed of 0.07 m ID and 0.80 m high. Linear low density polyethylene (LLDPE) particles having a mean diameter of 772 Μm and a particle size range of 200-1,500 Μm were employed as the bed material. The stimulus-response technique with CO₂ as a tracer gas was performed for the RTD study. The effects of gas velocity, aspect ratio (H₀/D) and scale-up on the axial gas dispersion were determined from the unsteady-state dispersion model, and the residence time distributions of gas in the fluidized bed were compared with the ideal reactors. It was found that axial dispersion depends on the gas velocity and aspect ratio of the bed. The dimensionless dispersion coefficient was correlated with Reynolds number and aspect ratio.     

Residence time distribution and liquid holdup in Kenics KMX static mixer with hydrogenated nitrile butadiene rubber solution and hydrogen gas system

A Kenics^® KMX static mixer that has curved-open blade internal structure was investigated to study its hydrodynamic performance related to residence time distribution and liquid holdup in a gas/liquid system. The static mixer reactor had 24 mixing elements arranged in line along the length of the reactor such that the angle between two neighboring elements is 90°. The length of the reactor was 0.98 m with an internal diameter of 3.8 cm and was operated cocurrently with vertical upflow. The fluids used were hydrogen (gas phase), monochlorobenzene (liquid phase) and hydrogenated nitrile butadiene rubber solution (liquid phase). In all the experiments, the polymer solution was maintained as a continuous phase while hydrogen gas was in the dispersed phase. All experiments were conducted in the laminar flow regime with the liquid side hydraulic Reynolds number in the range of 0.04-0.36 and the gas side hydraulic Reynolds number in the range of 3-18. Different polymer concentrations and different operating conditions with respect to gas/liquid flow rates were used to study the corresponding effects on the hydrodynamic parameters such as Peclet number (Pe) and the liquid holdup (ε_L). Empirical correlations were obtained for the axial dispersion coefficient (D_a) and liquid holdup in liquid system alone and for the gas/liquid system separately. It was observed that the Peclet number decreased with the introduction of gas in to the reactor while in the liquid system alone, an increase in viscosity decreased the Peclet number. The liquid holdup was empirically correlated as a function of the physical properties of the fluids used in addition to the operating flow rates.     

Concentration profiles of solids suspended in a stirred tank

The solids concentration profiles in a slurry mixing tank with mechanical agitation have been measured by using a photo-electric method. The concentration profile has been explained by the sedimentation-dispersion model in which the slurry flow in a stirred tank with a flat-disk turbine or a marine propeller is assumed to be dominated mainly by the upflow. The model parameters, modified Peclet numbers, Pe_s in terms of the falling velocity of the solid particles and Pe_f in terms of the liquid flow velocity, have been markedly influenced by the amount of the solids suspended. The Peclet number Pe_s is proportional to the solids concentration in the stirred tank under the present experimental conditions, while the parameter ratio Pe_f/Pe_s, which coincides with the ratio of the liquid flow velocity to the falling velocity of the solid particles, approaches a constant value as the concentration of solid particles is increased to 20vol.% or more.     

Nonlocal dispersion in porous media: Nonmechanical effects

Nonmechanical dispersion mechanisms at high Peclet number in porous media give rise to persistent transients that cannot be predicted by a local Fickian macrotransport equation. Instead, a nonlocal macrotransport equation is derived, which relates the average mass flux to a convolution integral in space and time between the average concentration gradient and a spatial- and temporal-wavelength-dependent effective diffusivity. The nonlocal diffusivity is derived from the fundamental microstructural transport processes. The transient effects arising due to stagnant and recirculating regions in the medium and due to a diffusive boundary layer near solid surfaces are shown to affect the residence-time distribution (RTD) of media whose overall length to microscale size ratio L/a is not large compared to Pe and Pe^1/3, respectively. Here, the Peclet number, Pe = Ua/D, is based on the average velocity through the medium U, the microstructural length scale a and the molecular diffusivity D in the medium. The nonlocal dispersion theory allows a calculation of the full form of the RTDs, which may be bimodal and generally exhibit long-time tails in media of short to moderate length. Experimental measurements of transient dispersion in consolidated media are shown to be in agreement with the theoretical prediction of dispersion due to the diffusive boundary layers near solid surfaces.     

Axial mixing of liquid in a turbulent-bed contactor

The axial dispersion of liquid in a 12-in. turbulent-bed contactor has been investigated for three packing sizes: ½-in., 1-in. and 1½-in. The gas and liquid flow rates were varied from 500 to 2700 lb./(hr.)(sq. ft.) and from 1500 to 11,000 lb./(hr.)(sq. ft.) respectively. The transient response technique using KCl solution as the tracer was employed for this purpose. The experimentally determined residence-time distribution curves were interpreted by means of a one-dimensional dispersion model. The axial dispersion coefficient, D_L, was found to increase with increasing gas flow rate, liquid flow rate, or packing size. In terms of Peclet number (N_Pe = ū d_p/D_L), the present data showed that N_Pe was dependent on Reynolds number (N, = d_p ū ρ/μ), Gallileo number (N_Ga = d_p³ ρ³ g/μ²), and reduced gas mass velocity (Δ = (G-G_mf)/G_mf), but the ratio of the Peclet number for a turbulent contactor to the Peclet number for a fixed-bed contactor, N_Pe/N_Peo, depended only on Δ, and the diameter ratio d_p/d_t. A correlation of N_Pe/N_Peθo with Δ and d_p/d_t is presented.     

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.     

Axial dispersion in metal foams and streamwise-periodic porous media

We present a study on the axial dispersion in metal foams and laser sintered reactors. Commercially available metal foams of 20 and 30 ppi are compared to a designed streamwise-periodic structure in terms of axial dispersion coefficients and pressure drops. Therefore tracer pulse experiments were performed and post processed by means of a deconvolution method. The Peclet number Pe_p based on the pore size is ranging from 5×10⁴ to 8×10⁵ which is attributed to the increased velocities due to the high porosity of the material compared to fixed bed reactors. The attained dispersion coefficients ranging from 1.3×10⁻⁴ to demonstrate the trend of packed beds and common packing materials and increase monotone with the Peclet number Pe_p. The pressure drop versus the interstitial bulk velocity follows the Forchheimer equation and can be described by the conventional Ergun model for all investigated porous media. The parameters obtained correspond to values found in literature. The results of this study show the high potential of foam reactors for catalyst driven reactions. They provide the same or even a higher surface area per volume of catalyst bed while inducing a much smaller pressure drop than corresponding fixed beds.     

Radial gas mixing in a fluidized bed using response surface methodology

Radial gas mixing in a fluidized bed was studied using response surface methodology (RSM), which enables effect examinations of parameters with a moderate number of experiments. All experiments were conducted in a 0.29-m ID fluidized-bed cold model. The gas dispersion process within the bed is described using the dispersed plug flow model. Pure carbon dioxide was used as the tracer gas, continuously injected into the center of the bed by a point source. The downstream radial tracer concentration profile was measured using a gas chromatograph.The radial gas dispersion coefficient, D_r, was well correlated with operating parameters and the particle and gas properties: (U−U_mf)/U_mf, H_s/d_b, φ_d, and Ar, with a determination coefficient R² of 0.966. Effect test indicates that the dimensionless characteristic velocity, (U−U_mf)/U_mf, has the most significant influence on D_r, while the static bed height to bed diameter ratio, H_s/d_b, is less remarkable. The interactions of (U−U_mf)/U_mf with the distributor open-area ratio, φ_d, and with the Archimedes number, Ar, both play important roles. An evolutive response surface model was proposed to describe the radial gas mixing in the bubbling/slugging fluidization regimes.     

Solids mixing in a fluidized bed riser

The solids mixing in a riser with a height of 10 m and 0.186 m inner diameter was investigated by using pneumatic phosphor tracer technique. Considering the shielding effect of the bed material on the light emitted from the phosphor tracer particle, a modified method for the phosphor tracer measurement is proposed. And then the curves of particle residence time distribution were obtained. The experimental results show that the particle diffusion mechanism can be explained by the dispersions of dispersed particles and particle clusters in the axial direction, and as well the core-annulus nonuniform distribution of the solids fraction in the radial direction of the riser. Moreover, based on the experimental results, a two-dimensional dispersion model was established to predict the solids axial and radial diffusion. Furthermore, the effects of superficial gas velocity and solids circulating flux on the axial and radial Peclet number of the particles were discussed; two empirical correlation formulas about the axial and the radial Peclet numbers were given; the calculated values agree well with the experimental results.     

Overall map and correlation of dispersion data for flow through granular packed beds

Measured values of the coefficients of transverse and longitudinal dispersion (D_T and D_L, respectively) are reported for liquid flow through granular packed beds. Measurements of D_T were made for 50<Sc<1950 and 300<Pe_m<10⁵, working with water at temperatures between 278 and 373 K, and values of D_L were measured for Sc≅750 and 1<Pe_m<45, working with water at 293 K; nearly two hundred new data points are reported.The data obtained, together with data from other sources, both for gas and liquid flow, are reported in plots of Pe_T vs Pe_m and Pe_L vs. Pe_m, in order to stress the influence of Sc on dispersion and elucidate the difference between liquid and gas behaviour.Empirical correlations are presented for the prediction of the dispersion coefficients (D_T and D_L) over the entire range of practical values of Sc and Pe_m, and they are shown to give the dispersion coefficients with very good accuracy.     

Liquid phase mixing in turbulent bed contactor

Axial mixing of the liquid phase in turbulent bed contactor (TBC) is studied through residence time distribution (RTD) experiments over a large range of variables such as flow rate of gas and liquid phases, static bed heights, diameter and density of particles and number of stages in presence of downcomer using air water system. Since all the liquid exits only through the downcomer, it enables the correct estimation of exit concentration of the tracer. The experimental RTD curves are satisfactorily compared with the axial dispersion model. The Peclet numbers evaluated by axial dispersion model and the Peclet numbers reported in the literature are used to propose a unified correlation in terms of operating and geometric parameters. Correlation is also developed for predicting the axial dispersion coefficient. It was observed in the present study that almost plug flow conditions can be achieved in multistage TBC.     

Solids concentration simulation of different size particles in a cyclone separator

To deepen our knowledge of the flow in cyclones, the solids concentrations of different size particles in a scroll cyclone separator were numerically simulated by using the Lagrange approach on the platform of commercial CFD software package, FLUENT 6.1. The numerical calculations visualize that there exists a spiral dust strand near the cyclone wall and a dust ring beneath the cyclone top plate. There are two regions in the radial solids concentration distribution, with which the solids concentration is low in the inner region (r/R(dimensionless radial position) ≤ 0.75) and increases greatly in the outer region (r/R > 0.75). Large particles generally have higher concentration in the wall region and small particles have higher concentration in inner vortex region. The axial distribution of the solids concentration in the inner vortex region (r/R ≤ 0.3) shows that serious fine particle re-entrainment exists within the height of 0.5 D (cyclone diameter) above the dust discharge port. We study the effect of solids particle on the gas flow field by two-way couple. The concepts of back-mixing rate, first escaping rate and second escaping rate are proposed for quantifying the local flow phenomena.     

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.