Kinetic theory based computation of PSRI riser: Part II—Computation of mass transfer coefficient with chemical reaction

The design of circulating fluidized bed systems requires the knowledge of mass transfer coefficients or Sherwood numbers. A literature review shows that these parameters in fluidized beds differ up to seven orders of magnitude.To understand the phenomena, a kinetic theory based computation was used to simulate the PSRI challenge problem I data for flow of FCC particles in a riser, with an addition of an ozone decomposition reaction. The mass transfer coefficients and the Sherwood numbers were computed using the concept of additive resistances. The Sherwood number is of the order of 4 × 10⁻³ and the mass transfer coefficient is of the order of 2 × 10⁻³ m/s, in agreement with the measured data for fluidization of small particles and the estimated values from the particle cluster diameter in part one of this paper. The Sherwood number is high near the inlet section, then decreases to a constant value with the height of the riser. The Sherwood number also varies slightly with the reaction rate constant. The conventionally computed Sherwood number measures the radial distribution of concentration caused by the fluidized bed hydrodynamics, not the diffusional resistance between the bulk and the particle surface concentration. Hence, the extremely low literature Sherwood numbers for fluidization of fine particles do not necessarily imply very poor mass transfer.     

Mass transfer around freely moving active particles in the dense phase of a gas fluidized bed of inert particles

The mass transfer coefficient around freely moving active particles under bubbling/slugging fluidized bed conditions was measured in a lab-scale reactor. The technique used for the measurements consisted in the oxidation reaction of carbon monoxide at over one or few Pt catalyst spheres immersed in an inert bed of sand. It was shown that this technique is simple and accurate, and allows to overcome most of the difficulties and uncertainties associated with other available techniques. The experimental campaign was carried out by varying the fluidization velocity (0.15-0.90 m/s), the active particle size (1.0-10.0 mm) and the inert particle size (0.1-1.4 mm). Results were analyzed in terms of the particle Sherwood number. Experimental data showed that Sh is not influenced by the fluidization velocity and by a change of regime from bubbling to slugging, whereas it increases with a square root dependence with the minimum fluidization velocity and with the active particle size. These results strongly suggest that the active particles only reside in the dense phase and never enter the bubble/slug phase. Data were excellently fitted by a Frössling-type correlation:

Sh=2.0·ε_mf+K·(Re_mf/ε_mf)^1/2·Sc^1/3     

Simulation of bubbling fluidized bed of fine particles using CFD

Computational fluid dynamics (CFD) simulation for bubbling fluidized bed of fine particles was carried out. The reliability and accuracy of CFD simulation was investigated by comparison with experimental data. The experimental facility of the fluidized bed was 6 cm in diameter and 70 cm in height and an agitator of pitched-blade turbine type was installed to prevent severe agglomeration of fine particles. Phosphor particles were employed as the bed material. Particle size was 22 μm and particle density was 3,938 kg/m³. CFD simulation was carried by two-fluid module which was composed of viscosity input model and fan model. CFD simulation and experiment were carried out by changing the fluidizing gas velocity and agitation velocity. The results showed that CFD simulation results in this study showed good agreement with experimental data. From results of CFD simulation, it was observed that the agitation prevents agglomeration of fine particles in a fluidized bed.     

EMMS-based Eulerian simulation on the hydrodynamics of a bubbling fluidized bed with FCC particles

Although great progress has been made in modeling the bubbling fluidization of Geldart B and D particles using standard Eulerian approach, recent studies have shown that suitable sub-grid scale models should be introduced to improve the simulation on the hydrodynamics of Geldart A particles. In this study, the flow structures inside a bubbling fluidized bed of FCC particles are simulated in an Eulerian approach employing the energy minimization multi-scale (EMMS) model (Chemical Engineering Science, 2008, 63: 1553-1571) as the sub-grid scale model for effective inter-phase drag force, using an implicit cluster diameter expression. It was shown that the experimentally found axial and radial solid concentration profiles and radial particle velocity profiles can be well reproduced.     

Computation and measurements of mass transfer and dispersion coefficients in fluidized beds

Conventional design of circulating fluidized beds requires the knowledge of dispersion and mass transfer coefficients, expressed in dimensionless forms as Sherwood numbers. However, these are known to vary by five or more orders of magnitude. Furthermore, the Sherwood numbers for fine particles reported in the literature are several orders of magnitude lower than the Sherwood number of two for diffusion to a single particle. We have shown that by replacing the particle diameter in the conventional Sherwood number with cluster or bubble diameter, the modified Sherwood number is again of the order of two.We have also shown that the kinetic theory based computational fluid dynamics codes correctly compute the dispersion and mass transfer coefficients. Hence, the kinetic theory based computational fluid dynamics codes can be used for fluidized bed reactor design without any such inputs.     

CFD modeling and validation of the turbulent fluidized bed of FCC particles

An experimental and computational study is presented on the hydrodynamic characteristics of FCC particles in a turbulent fluidized bed. Based on the Eulerian/Eulerian model, a computational fluid dynamics (CFD) model incorporating a modified gas‐solid drag model has been presented, and the model parameters are examined by using a commercial CFD software package (FLUENT 6.2.16). Relative to other drag models, the modified one gives a reasonable hydrodynamic prediction in comparison with experimental data. The hydrodynamics show more sensitive to the coefficient of restitution than to the flow models and kinetics theories. Experimental and numerical results indicate that there exist two different coexisting regions in the turbulent fluidized bed: a bottom dense, bubbling region and a dilute, dispersed flow region. At low‐gas velocity, solid‐volume fractions show high near the wall region, and low in the center of the bed. Increasing gas velocity aggravates the turbulent disorder in the turbulent fluidized bed, resulting in an irregularity of the radial particle concentration profile. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

An extended DEM–CFD model for char combustion in a bubbling fluidized bed combustor of inert sand

This paper proposes a transient three-phase numerical model for the simulation of multiphase flow, heat and mass transfer and combustion in a bubbling fluidized bed of inert sand. The gas phase is treated as a continuum and solved using the computational fluid dynamics (CFD) approach; the solid particles are treated as two discrete phases with different reactivity characteristics and solved on the individual particle scale using an extended discrete element model (DEM). A new char combustion submodel considering sand inhibitory effects is also developed to describe char particle combustion behavior in the fluidized bed. Two conditions, i.e. a single larger graphite particle and a batch of smaller graphite particles, are used to test the prediction capability of the model. The model is validated by comparing the predicted results with the previous measured results and conclusions in the literature in terms of bed hydrodynamics, individual particle temperature, char residence time and concentrations of the products. The effects of bed temperature, oxygen concentration and superficial velocity on char combustion behavior are also examined through model simulation. The results indicate that the proposed model provides a proximal approach to elucidate multiphase flow and combustion mechanisms in fluidized bed combustors.     

The bubbling behavior of cohesive particles in the 2D fluidized beds

The present work focuses on a fully statistical analysis of bubbling behavior in the two-dimensional (2D) fluidized beds with cohesive particles. Various significant bubble properties such as bubble size, rising velocity, aspect ratio, bed expansion and bubble hold-up, etc., were investigated. An equation for bubble diameter is developed, , and the observed bubbles are generally smaller than the ones generated in the beds with A or B type powders. Both the average bubble size and rising velocity initially increase with the elevation above the distributor and keep constant beyond certain heights. The bubbles exhibit oblong with the most density aspect ratio (β) equal to 0.7. In addition, the bubble rising velocity coefficient ranges from 0.8 to 1.5. Two core-annular flows form in the large diameter, shallow fluidized bed used in this experiment.     

Heat and mass transfer characteristics in a gas-slurry-solid fluidized bed

The gas-slurry-solid fluidized bed is a unique operation where the upward flow of a liquid-solid suspension contacts with the concurrent up-flow of a gas, supporting a bed of coarser particles in a fluidized state. In the present study we measured the gas holdup, the coarse particle holdup, the cylinder-to-slurry heat transfer coefficient, and the cylinder-to-liquid mass transfer coefficient at controlled slurry concentrations. The slurry particles were sieved glass beads of 0.1 mm average diameter and their volumetric fraction was varied at 0, 0.01, 0.05 or 0.1. The slurry and the gas velocities were varied up to about 12 and 15 cm/s, respectively. The coarse particles fluidized were sieved glass beads of average diameters of 3.6 and 5.2 mm. The individual phase-holdup values were measured and served for use in correlating the heat and mass transfer coefficients. The heat and mass transfer coefficients in the slurry flow, gas-slurry transport bed, slurry-solid fluidized bed and gas-slurry-solid fluidized bed operations can be correlated well by dimensionless equations of a unified formula in terms of the Nusselt (Sherwood) number, the Prandtl (Schmidt) number and the specific power group including the energy dissipation rate per unit mass of slurry, with different numerical constants and exponent values, respectively, to the heat and mass transfer coefficients. The presence of an analogy between the heat and mass transfer from the vertically immersed cylinder in these slurry flow, gas-slurry transport bed and gas-slurry-solid fluidized bed systems is suggested.     

New predictive correlation for mass transfer coefficient in structured packed extraction columns

Developments in the area of packed columns, particularly structured packed columns, are ongoing, specifically in the area of liquid–liquid extractions in different industries. In the present study, mass transfer coefficients have been obtained experimentally in a structured packed extraction column to develop a new correlation for prediction of continuous phase Sherwood number. The experiments were carried out for toluene/acetic acid/water and n-butyl acetate/acetic acid/water systems with counter current flow in different heights of column. A new dimensionless parameter, d₃₂/h, is introduced in proposed equation. This number considers the effect of column height (h) and mean drop diameter (d₃₂) jointly. The main advantage of this approach is that the principal effect of column height is considered in correlation without which the experimental data could not be fitted with a acceptable accuracy.     

CFD simulation of solids residence time distribution in a multi-compartment fluidized bed

The present work focuses on a numerical investigation of the solids residence time distribution(RTD)and the fluidized structure of a multi-compartment fluidized bed,in which the flow pattern is proved to be close to plug flow by using computational fluid dynamics(CFD)simulations.With the fluidizing gas velocity or the bed outlet height rising,the solids flow out of bed more quickly with a wider spread of residence time and a larger RTD variance(σ2).It is just the heterogeneous fluidized structure that being more prominent with the bed height increasing induces the widely non-uniform RTD.The division of the individual internal circulation into double ones improves the flow pattern to be close to plug flow.     

CFD simulations of wall mass transfer for Taylor flow in circular capillaries

Computational fluid dynamics is used to investigate the mass transfer from the liquid phase to the channel wall for Taylor flow of bubbles rising in circular capillaries. The separate influences of the Taylor bubble rise velocity, unit cell length, gas holdup, and liquid diffusivity on mass transfer were investigated for capillaries of 1.5, 2 and 3 mm diameter. A correlation is proposed for estimation of the wall mass transfer coefficient and this correlation has been tested against published experimental data.     

Effects of temperature on local two-phase flow structure in bubbling and turbulent fluidized beds of FCC particles

A novel high temperature optical fiber probe has been developed to study the effects of bed temperature on the local two-phase flow structure in a pilot scale fluidized bed of the FCC particles with bed temperatures ranging from 25°C to 420°C, covering both the bubbling and turbulent fluidization regimes. The results show that fluidization is enhanced and fluctuations of the local two-phase flow structure become more intense with increasing bed temperature. At constant superficial gas velocities, the averaged local particle concentration, the dense phase fraction and particle concentration in the dense phase decrease with increasing bed temperature, whereas both the frequency of the dilute/dense phase cycle and the ratio of the dilute phase duration to the dense phase duration increase. In addition, the effects of temperature on the dilute phase depend on superficial gas velocity. The conventional two-phase models fail to predict these changes of the local flow structure with temperature, which may be explained by the fact that the role of interparticle forces is neglected at different bed temperatures. Indeed, fluidization behaviors of the FCC particles tested increasingly shift from typical Geldart A towards B with increasing temperature due to a decrease of the interparticle attractive forces and a simultaneous increase of interparticle repulsive forces.     

CFD simulations of mass transfer from Taylor bubbles rising in circular capillaries

Computational Fluid Dynamics (CFD) is used to investigate mass transfer from Taylor bubbles to the liquid phase in circular capillaries. The liquid phase volumetric mass transfer coefficient k_La was determined from CFD simulations of Taylor bubbles in upflow, using periodic boundary conditions. The separate influences of the bubble rise velocity, unit cell length, film thickness, film length, and liquid diffusivity on k_La were investigated for capillaries of 1.5, 2 and diameter. The mass transfer from the Taylor bubble is the sum of the contributions of the two bubble caps, and the film surrounding the bubble. The Higbie penetration model is used to describe the mass transfer from the two hemispherical caps. The unsteady-state diffusion model of Pigford is used to describe the mass transfer to the downward flowing liquid film. The developed model for k_La is in good agreement with the CFD simulated values, and provides a practical method for estimating mass transfer coefficients in monolith reactors.     

Gas and liquid phase mass transfer within KATAPAK-S structures studied using CFD simulations

The gas phase mass transfer in the empty channels, and the liquid phase mass transfer within the catalyst-packed channels, of the criss-crossing sandwich structures of KATAPAK-S have been studied using computational fluid dynamics. Due to the “upheaval” caused by the flow splitting at the cross-overs, the mass transfer coefficient is significantly larger than that for fully developed flow in a single tube.     

Convective heat transfer coefficient for the side-wall in a fixed bed

Fixed beds are widely used in the chemical and process industry due to their relatively simple yet effective performance. Determining the radial heat transfer at the wall in a fixed bed is crucial to predict the performance of columns. Heat transfer parameters often need to be obtained experimentally. Various Nusselt ${\mathrm{Nu}}_w$ versus Reynolds ${Re}_p$ correlations in literature show considerable scatter and discrepancies. The tube-to-particle diameter ratio $\frac{D_{\mathrm{t}}}{D_{\mathrm{p}}}$ and boundary conditions on the particle surface have been understood to affect heat transfer near the wall by virtue of influence on the near-wall porosity and mixing. In this work, a fixed bed consisting of mono-disperse particles is generated via gravity-forced sedimentation modelling utilizing the discrete element method for a $\frac{D_{\mathrm{t}}}{D_{\mathrm{p}}}$ ratio of 3.3. The system is meshed and imported in a computational fluid dynamics (CFD) solver. Fluid inlet velocity is varied to get ${Re}_p\in \left[1,1500\right]$ corresponding to the laminar and turbulent flow regimes. The particles are treated as boundaries with Dirichlet, Neumann, and Robin boundary conditions applied for the closure of energy balance. Another set of simulations is run with particles modelled as solids with varying thermal conductivities ($k_s/k_f$). The heat flux and volume-averaged fluid temperature calculated during post-processing are used to determine the wall heat transfer coefficient and, subsequently, the wall Nu number. Fifteen ${\mathrm{Nu}}_w$ versus ${Re}_p$ correlations are compiled and analyzed. A new semi-empirical correlation for the wall Nusselt number has been developed for a fixed bed packed with monodisperse spheres for $\frac{D_t}{D_p}=3.3$ and results compared with data published in literature. Additionally, the impact of buoyancy effect on the wall Nusselt number has been studied.     

Experimental mass transfer coefficients in a pilot plant multistage column extractor

The volumetric overall mass transfer coefficients in a multistage column have been measured using axial dispersion model for toluene–acetone–water system. The effect of operating parameters on the volumetric overall mass transfer coefficients has been investigated for both mass transfer directions. The results show that the mass transfer performance is strongly dependent on rotor speed and mass transfer direction, although only slightly dependent on phase flow rates. In addition, empirical correlations to predict the overall mass transfer coefficients have been developed. The proposed correlations based on dimensionless numbers can be considered as a useful tool for the possible scale up of the multistage column extractor.     

Heat transfer between FCC catalyst and an electrically heated horizontal cylinder in a circulating fluidized bed

The heat transfer coefficient between a suspension of FCC particles and a horizontal cylindrical heat transfer probe inserted into the riser or the standpipe of a CFB has been quantified. With the heat transfer probe located in the riser 4.75 meters above the L-valve, and solids mass flux varied between 0 to 100 kg/(m²·s), the heat transfer coefficient ranged from 70 W/(m²·K) to 475 W/(m²·K). On a plot of heat transfer coefficient versus solids mass flux, three zones have been identified, which correspond to the difference in the flow structure of the solids around the heat transfer probe as the solids mass flux increases. Also, measurements were taken of the radial solids flux in two orthogonal directions using an isokinetic sampling system. The data shows the asymmetry due to the perturbations introduced by the heat transfer probe. Finally, the heat transfer in the downcomer was investigated. It has been found that the magnitude of the heat transfer coefficient in the downcomer is dominated by the solids flux; variation in gas bypassing in the standpipe has little effect. Results obtained by traversing the heat transfer probe across the diameter of the standpipe suggest that the heat transfer coefficient is nearly independent of radial position within the standpipe.     

CFD modeling of pervaporative mass transfer in the boundary layer

Modeling mass transfer in the liquid boundary layer accounting for concentration polarization in pervaporation (PV) is particularly challenging since there is no practical way of experimentally determining solute concentration at the membrane surface. We have developed a computational fluid dynamics (CFD) approach to describe not only velocity distribution but also concentration profile in the liquid boundary layer of a slit membrane channel. The satisfactoriness of the numerical methodology used in CFD for obtaining concentration profiles were verified using a classic diffusion problem with its known analytical solution. The overall mass transfer coefficients from the numerical study were also compared with those from the experiment.     

A multiscale mass transfer model for gas-solid riser flows: Part II—Sub-grid simulation of ozone decomposition

This article is to test the EMMS-based multiscale mass transfer model through computational fluid dynamics (CFD) simulation of ozone decomposition in a circulating fluidized bed (CFB) reactor. Three modeling approaches, namely types A, B and C, are classified according to their drag coefficient closure and mass transfer equations. Simulation results show that the routine approach (type C) with assumption of homogeneous flow and concentration overestimates the ozone conversion rate, introduction of structure-dependent drag force will improve the model prediction (type B), while the best fit to experimental data is obtained by the multiscale mass transfer approach (type A), which takes into account the sub-grid heterogeneity of both flow and concentration. In general, multiscale behavior of mass transfer is more distinct especially for the dense riser flow. The fair agreement between our new model with literature data suggests a fresh paradigm for the CFB related reaction simulation.