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.     

Computation of the mass transfer coefficient of FCC particles in a thin bubbling fluidized bed using two- and three-dimensional CFD simulations

In this study, the standard kinetic theory based model with a modified drag correlation was successfully used to compute the mass transfer coefficients and the Sherwood numbers of FCC particles in a thin bubbling fluidized bed column using the additive diffusional and chemical reaction resistances concept. Also, the effects of the computational domain (two- or three-dimensional) and the reaction rate constant (low and high) are discussed.The computations show that the Sherwood numbers are in agreement with the measurement ranges for small particles in the fluidized bed system. The mass transfer coefficients and the Sherwood numbers are high near the inlet section, and decrease to a constant value with increasing height in the column. The two-dimensional computational domain simulations provide enough information to explain the phenomena inside a symmetrical system, but three-dimensional computational domain simulations are still needed for asymmetrical systems. Finally, the mass transfer coefficients and the Sherwood numbers increased with the larger reaction rate constant.     

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.     

Wall mass transfer in liquid-fluidized beds

Ionic mass transfer coefficients between the wall and a liquid fluidized bed of 0.043 inch lead glass spheres have been measured using the diffusion controlled reduction of ferricyanide ion at a nickel cathode. The coefficients obtained are correlated in terms of the dimensionless j factor and are compared with dissolution mass transfer results by this author and with a recent liquid fluidized bed heat transfer study⁽¹⁾ with these same particles. It is concluded that in the dissolution study either mechanical erosion or roughness effects or both were present. No analogy was found to exist between overall heat and mass transfer in a liquid fluidized bed in which there is a large difference between the Schmidt and Prandtl numbers because the dominant resistance is different for the two cases.     

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.     

Experimental validation of CFD simulations of a lab‐scale fluidized‐bed reactor with and without side‐gas injection

Fluidized‐bed reactors are widely used in the biofuel industry for combustion, pyrolysis, and gasification processes. In this work, a lab‐scale fluidized‐bed reactor without and with side‐gas injection and filled with 500–600 μm glass beads is simulated using the computational fluid dynamics (CFD) code Fluent 6.3, and the results are compared to experimental data obtained using pressure measurements and 3D X‐ray computed tomography. An initial grid‐dependence CFD study is carried out using 2D simulations, and it is shown that a 4‐mm grid resolution is sufficient to capture the time‐ and spatial‐averaged local gas holdup in the lab‐scale reactor. Full 3D simulations are then compared with the experimental data on 2D vertical slices through the fluidized bed. Both the experiments and CFD simulations without side‐gas injection show that in the cross section of the fluidized bed there are two large off‐center symmetric regions in which the gas holdup is larger than in the center of the fluidized bed. The 3D simulations using the Syamlal‐O'Brien and Gidaspow drag models predict well the local gas holdup variation throughout the entire fluidized bed when compared to the experimental data. In comparison, simulations with the Wen‐Yu drag model generally over predict the local gas holdup. The agreement between experiments and simulations with side‐gas injection is generally good, where the side‐gas injection simulates the immediate volatilization of biomass. However, the effect of the side‐gas injection extends further into the fluidized bed in the experiments as compared to the simulations. Overall the simulations under predict the gas dispersion rate above the side‐gas injector. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Kinetic theory based computation of PSRI riser: Part I—Estimate of mass transfer coefficient

The PSRI benchmark challenge problem one is modeled using kinetic theory based CFD with the energy minimization multi-scale (EMMS) drag law. These computations give a better comparison than the previous models to measured solids mass flux, solids density and pressure drop.The computer model was also used to calculate axial and radial normal Reynolds stresses, energy spectra, power spectra, granular temperatures, the FCC viscosity and axial and radial dispersion coefficients. The computed cluster sizes agreed with the published empirical correlations. Then, the mass transfer coefficients and the Sherwood numbers are estimated based on particle cluster sizes. The conventional Sherwood number is scaled with the particle cluster diameter. The Sherwood number is the order of 10^-2 and the mass transfer coefficient is the order of . This Sherwood number is two orders of magnitude smaller than the diffusion controlled limit of two based on particle diameter, in agreement with the experimental data for fluidization of fine particles.     

LIQUID-SOLID MASS TRANSFER IN A THREE PHASE DRAFT TUBE FLUIDIZED BED REACTOR

Liquid-solid mass transfer coefficients in a three phase draft tube fluidized bed reactor have been measured using spherical ion exchange particles. The particle diameters ranged from 655 to 1119μm and solids volume fractions of approximately 5 and 10% were employed in water at 28°C. The experimental data can be successfully correlated using a Reynolds number derived using Kolmogoroffs theory of isotropic turbulence, although it is doubtful whether isotropic turbulence actually prevails in the fluidized bed over the range of conditions employed. Comparison with correlations determined for bubble columns and gas-liquid fluidized beds is performed. A model which considers the draft tube reactor as comprising two distinct fluid mechanical regions is developed to explain the apparently lower values of mass transfer coefficients obtained in a draft tube as opposed to conventional fluidized bed reactor.     

A Tribute to the Late Professor Giulio Massarani 1937–2004

Spouted bed equipment has the potential of producing high-quality particulate materials with reduced energy consumption and environment impact. Particle-to-gas mass transfer was investigated in a spouted bed with a novel design of two rotating drums placed symmetrically in the apparatus to create air inlet openings of adjustable width, so that fluidization can be adapted to the requirements of each product and process. The mass transfer coefficients between particle surface and gas were derived from first-period drying experiments with porous, nonhygroscopic material by assuming perfect back-mixing or, alternatively, ideal plug flow of the gas. Respective Sherwood numbers were empirically correlated and found to be superior to the Sherwood numbers of conventional fluidized beds or conventional spouted beds.     

Heat Transfer from Immersed Vertical Cylinders in Gas‐Liquid and Gas‐Liquid‐Solid Fluidized Beds

The heat transfer coefficient, h, was measured using a cylindrical heater vertically immersed in liquid‐solid and gas‐liquid‐solid fluidized beds. The gas used was air and the liquids used were water and 0.7 and 1.5 wt‐% carboxymethylcellulose (CMC) aqueous solutions. The fluidized particles were sieved glass beads with 0.25, 0.5, 1.1, 2.6, and 5.2 mm average diameters. We tried to obtain unified dimensionless correlations for the cylinder surface‐to‐liquid heat transfer coefficients in the liquid‐solid and gas‐liquid‐solid fluidized beds. In the first approach, the heat transfer coefficients were successfully correlated in a unified formula in terms of a modified j_H‐factor and the modified liquid Reynolds number considering the effect of spatial expansion for the fluidized bed within an error of 36.1 %. In the second approach, the heat transfer coefficients were also correlated in a unified formula in terms of the dimensionless quantities, Nu/Pr^1/3, and the specific power group including energy dissipation rate per unit mass of liquid, E^1/3D^4/3/ν_l, within a smaller error of 24.7 %. It is also confirmed that a good analogy exists between the surface‐to‐liquid heat transfer and mass transfer on the immersed cylinder in the liquid‐solid and gas‐liquid‐solid fluidization systems.     

Particle‐scale simulation of the flow and heat transfer behaviors in fluidized bed with immersed tube

A kind of new modified computational fluid dynamics‐discrete element method (CFD‐DEM) method was founded by combining CFD based on unstructured mesh and DEM. The turbulent dense gas–solid two phase flow and the heat transfer in the equipment with complex geometry can be simulated by the programs based on the new method when the k‐ε turbulence model and the multiway coupling heat transfer model among particles, walls and gas were employed. The new CFD‐DEM coupling method that combining k‐ε turbulence model and heat transfer model, was employed to simulate the flow and the heat transfer behaviors in the fluidized bed with an immersed tube. The microscale mechanism of heat transfer in the fluidized bed was explored by the simulation results and the critical factors that influence the heat transfer between the tube and the bed were discussed. The profiles of average solids fraction and heat transfer coefficient between gas‐tube and particle‐tube around the tube were obtained and the influences of fluidization parameters such as gas velocity and particle diameter on the transfer coefficient were explored by simulations. The computational results agree well with the experiment, which shows that the new CFD‐DEM method is feasible and accurate for the simulation of complex gas–solid flow with heat transfer. And this will improve the farther simulation study of the gas–solid two phase flow with chemical reactions in the fluidized bed. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Mass transfer from a contaminated fluid sphere

The unsteady mass transfer from a contaminated fluid sphere moving in an unbounded fluid is examined numerically for unsteady‐state transfer. The effect of the interface contamination and the flow regime on the concentration profiles, inside and outside a fluid sphere, is investigated for different ranges of Reynolds number (0 < Re < 200) and Peclet number (0 < Pe < 10⁵), viscosity ratio between the dispersed phase and the continuous phase (0 < κ < 10), and the stagnant‐cap angle (0° < θ_cap < 180°). It was found that the stagnant‐cap angle significantly influences the mass transfer from the sphere to a surrounding medium. For all Peclet and Reynolds numbers and κ, the contamination reduces the mass transfer flux. The average Sherwood number increases with an increase of stagnant‐cap angle and reaches a maximum equal to the average one for a clean fluid sphere at low viscosity ratio and large Peclet numbers. A predictive equation for the Sherwood number is derived from these numerical results. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Combustion of single char particles in a turbulent fluidized bed

The combustion of single bituminous char particles (4-12 mm diameter) was studied in a turbulent fluidized bed operated at 1098 K using air as the fluidising medium. Results indicated that particles burn with constant density following a shrinking sphere model. Burning rates are much higher than those observed in a bubbling fluidized bed. The rate of transfer of oxygen to the particle surface is also higher than that observed in bubbling beds. A model is proposed to calculate the Sherwood numbers of the burning carbon particles. Experimental values of the Sherwood numbers agree well with those predicted from the model.     

Particle‐resolved direct numerical simulation of gas–solid dynamics in experimental fluidized beds

Particle‐resolved direct numerical simulations (PR‐DNS) of a simplified experimental shallow fluidized bed and a laboratory bubbling fluidized bed are performed by using immersed boundary method coupled with a soft‐sphere model. Detailed information on gas flow and individual particles’ motion are obtained and analyzed to study the gas–solid dynamics. For the shallow bed, the successful predictions of particle coherent oscillation and bed expansion and contraction indicate all scales of motion in the flow are well captured by the PD‐DNS. For the bubbling bed, the PR‐DNS predicted time averaged particle velocities show a better agreement with experimental measurements than those of the computational fluid dynamics coupled with discrete element models (CFD‐DEM), which further validates the predictive capability of the developed PR‐DNS. Analysis of the PR‐DNS drag force shows that the prevailing CFD‐DEM drag correlations underestimate the particle drag force in fluidized beds. The particle mobility effect on drag correlation needs further investigation. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1917–1932, 2016     

Dispersion and Mass Transfer Effects on the Performance of an Immobilized Lipase Packed Bed Reactor During the Hydrolysis of Rice Bran Oil

The performance of an immobilized packed bed reactor for the hydrolysis of rice bran oil has been investigated and can be well described by a dispersion model with an average standard deviation of 0.0388. Global mass transfer coefficients estimated using the model and experimental data ranged from 0.095‐0.482 min^?1, depending on substrate flow rates. A dimensionless mass transfer correlation between the Sherwood number and the Reynolds number was obtained as NSh = 3.96 ×NRe^2.07.     

A novel fluidized and induction heated microreactor for catalyst testing

The jiggled bed reactor (JBR) is a state‐of‐the‐art batch fluidized microreactor designed and developed to test catalysts for endothermic reactions. The solid particles in the microreactor are mechanically fluidized by agitating the reactor using a linear pneumatic actuator. An external induction field heats up vertical metal wires installed inside the reactor bed to generate heat rapidly and uniformly within the bed of solid particles, while eliminating hot spots and large temperature gradients. Image and signal processing techniques were utilized to investigate how the fluidization dynamics of the solid particles are affected by the amplitude and frequency of the vibrations, and the size distribution and the mass of the particles. The results show that the microreactor is very flexible: operating conditions can be optimized to successfully fluidize any type of catalyst. Heat‐transfer coefficients between heating surfaces and the bed are similar to the coefficients that could be obtained in a well‐bubbling fluidized bed. This confirms the excellent quality of the fluidization achieved with the new JBR. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3107–3122, 2014     

A model for collisional exchange in gas/liquid/solid fluidized beds

A new model is presented for numerical simulations of collisional transfer of mass, momentum and energy in gas/liquid/solid fluidized beds. The mathematical formulation uses a collision model similar to that of Bhatnagar, Gross, and Krook (BGK), in a particle distribution function transport equation, in order to approximate the rates at which collisions bring about local equilibration of particle velocities and the masses, compositions, and temperatures of liquid films on bed particles. The model is implemented in the framework of the computational-particle fluid dynamics (CPFD) numerical methodology, in which the particle phase is represented with computational parcels and the continuous phase is calculated on Eulerian finite-difference grid. Computational examples using the Barracuda^® code, a commercial CFD code owned by CPFD Software, LLC, show the ability of the model to calculate spray injection and subsequent liquid spreading in gas/solid flows.     

Bed-to-wall heat transfer characteristics in a circulating fluidized bed

The bed-to-wall heat transfer coefficients were measured in a circulating fluidized bed of FCC particles (d_p = 65 μm). The effects of gas velocity (1.0–4.0 m/s), solid circulation rate (10–50 kg/m²s) and particle suspension density (15–100 kg/m³) on the bed-to-wall heat transfer coefficient have been determined in a circulating fluidized bed (0.1 m-ID x 5.3 rn-high). The heat transfer coefficient strongly depends on particle suspension density, solid circulation rate, and gas velocity. The axial variation of heat transfer coefficients is a strong function of the axial solid holdup profile in the riser. The obtained heat transfer coefficient in terms of Nusselt number has been correlated with the pertinent dimensionless groups     

FROM SINGLE PARTICLE TO FLUID BED DRYING KINETICS

The concept of a normalized single particle drying curve has been integrated into a generic, heterogeneous fluid bed model in order to describe batch fluid bed drying. Drying curves have been measured for both single particles and fluid beds. Two different coarse-grained materials, aluminum silicate and a technical product, have been used. In general, fluid bed drying curves appear to be predictible on the basis of single particle data and with the help of the model. Dificulties may arise mainly with particles of low sphericity and a large initial moisture content. Model parameters are in the range indicated by general fluidization literature. However, Sherwood numbers for particle-to-fluid mass transfer in the- fluid bed are significantly lower than the values for single particles. This can hardly be attributed to bubbling and bypassing, since these effects have been explicitly accounted for in the model.