Convective Heat and Mass Transfer Modeling in Gas‐Fluidized Beds

This review examines selected mechanistic and empirical models reported in the literature to predict convective heat and mass transfer coefficients in gas‐fluidized beds. The role of hydrodynamics in heat and mass transfer is briefly outlined before embarking on the modeling approaches. Both bed to wall and interphase heat transfer, are considered. In bed to wall heat transfer, the main focus of the review is the modeling of particle convective components, based on surface renewal. The concepts of transient and local heat transfer models are also discussed briefly. In the case of mass transfer, only interphase transfer is considered. Emphasis is placed on models based on combustion where mass transfer is seen to occur from a few active particles contained in a fluidized bed of inert particles.     

Modeling Gas‐Solid Reactions in the Bed of a Rotary Kiln

When dealing with gas‐solid reactions in rotary kilns, it is necessary to realize that the total particle surface within the granular bed can be much larger than the outer surface of the bed. Depending on the reaction conditions this inner surface can contribute considerably to the chemical conversion in the kiln. In this paper, a model is presented, which describes the reaction within the bed for the case of bed movement according to the cascade mode. In this case, gas is drawn into the rotating bed together with the particles. As a key quantity, an effectiveness factor η of the bed is defined. It is the ratio of the actual conversion to the conversion that would occur if the concentration of the reacting component remained unchanged throughout the bed, i.e. at its entrance concentration. An evaluation for reactions of order mshows this factor to be more than 25 % when the Damköhler number is smaller than 2. It approaches 100 % as the Damköhler number approaches 0. The Damköhler number used in this paper contains the void fraction of the particle bed in its denominator.     

Drying Kinetics in a Vertical Gas‐Solid System

A one‐dimensional steady‐state two‐fluid model has been developed to demonstrate the drying kinetics in the vertical up‐flow gas‐solid system. The model takes into account mass, momentum, and heat transfer between the continuous and dispersed phases. A set of non‐linear differential equations have been solved numerically for the velocity, moisture content, and temperature of both the continuous and dispersed phases along the dryer length. The effect of operating parameters on drying kinetics has been critically examined and the model simulations are compared with the data reported in the literature.     

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.     

Hydrodynamics and Mass Transfer in Gas‐Liquid‐Solid Circulating Fluidized Beds

Although extensive work has been performed on the hydrodynamics and gas‐liquid mass transfer in conventional three‐phase fluidized beds, relevant documented reports on gas‐liquid‐solid circulating fluidized beds (GLSCFBs) are scarce. In this work, the radial distribution of gas and solid holdups were investigated at two axial positions in a GLSCFB. The results show that gas bubbles and solid particles distribute uniformly in the axial direction but non‐uniformly in the radial direction. The radial non‐uniformity demonstrates a strong factor on the gas‐liquid mass transfer coefficients. A local mass transfer model is proposed to describe the gas‐liquid mass transfer at various radial positions. The local mass transfer coefficients appear to be symmetric about the central line of the riser with a lower value in the wall region. The effects of gas flow rates, particle circulating rates and liquid velocities on gas‐liquid mass transfer have also been investigated.     

Modeling the Heat and Mass Transfer in Microwave Drying of White Oak

A 2D comprehensive heat and mass transfer model was developed to simulate the free liquid, vapor, and bound water movement in microwave drying of white oak specimens. The experimental and model results showed that, for white oak, moisture movement was easily impeded and high gradient of internal vapor pressure occurred. The internal vapor pressure was affected by sample dimension (length and thickness). At the same input power density, the internal pressure generated in the core increased with the sample length and thickness. However, as compared with sample length, sample thickness has less effect on the pressure gradient because of the high ratio of permeability between longitudinal and transverse directions.     

Mass Transfer Coefficients in Mechanically Agitated Gas‐Liquid Contactors

There are a large number of correlations given in literature for the prediction of volume‐related liquid‐side mass transfer coefficients in mechanically agitated gas‐liquid contactors. Significant disagreement can be observed concerning the proposed correlations, so that no single correlation exists representing all of the mass transfer data given in the literature. The observed differences can mainly be ascribed to the differences in the geometry of the system, the range of operational conditions and the measurement method used. On the basis of a comparative study of mass transfer phenomena in agitated Newtonian and non‐Newtonian aerated liquids, a critical discussion of the literature results is presented in this review article, so that final conclusions can be drawn for the k_Lα values in the different single‐ and multiple‐impeller agitated systems studied in the literature.     

Effect of Operating Parameters on Gas‐Solid Hydrodynamics and Heat Transfer in a Spouted Bed

Through a combined computational fluid dynamics and discrete element method approach, the effect of the operating parameters on the hydrodynamics and heat‐transfer properties of gas‐solid two‐phase flows in a spouted bed are extensively investigated. Considering the high velocity in the fountain region, gas turbulence is resolved by employing the large‐eddy simulation. The rolling friction model is adopted for more precise predictions of solid behavior near the wall. Subsequently, the gas‐solid flow patterns, gas‐solid velocities, and temperature evolution are investigated. Moreover, different operating conditions and geometry configurations are evaluated with respect to heat‐transfer performance. The results provide a fundamental understanding of heat‐transfer mechanisms in spouted beds.     

Gas‐Liquid Mass Transfer Characteristics in a Rotating‐Drum Bioreactor

The oxygen volumetric mass transfer coefficient is a key parameter to characterize the performance of aerobic bioreactors. A novel rotating‐drum bioreactor (RDB) fitted with a sparger as proposed in a previous work has demonstrated its excellent gas‐liquid mass transfer performance. To provide primary information on the design and scale‐up of the novel RDB, effects of reactor configuration including the number and width of lifters and operation conditions such as rotational speed, aeration rate, and solid volume fraction on mass transfer performance were systematically investigated in a new medium‐sized RDB. Compared with the stirred bioreactor and traditional RDBs, this new RDB exhibits better mass transfer performance. Taking both operational and reactor configuration parameters into consideration, an empirical correlation to predict the volumetric mass transfer coefficient in this type of RDBs was proposed which is valuable for its design and scale‐up.     

Heat Transfer in the Downer and the Riser of a Circulating Fluidized Bed – A Comparative Study

The characteristics of heat transfer were studied in both a gas‐solids concurrent downflow fluidized bed (downer) and a gas‐solids concurrent upflow fluidized bed (riser) with FCC particles. The radial and axial distribution profiles of the heat transfer coefficient between a suspended surface and the gas‐solids flow suspension were obtained using a miniature heat transfer probe, under different operating conditions. Comprising the results of the heat transfer in the downer and the riser shows that there exists some significant distinction between the heat transfer processes in the two reactors. The characteristics of heat transfer in both cases are closely related to their hydrodynamics and the distinct flow structures determinate the different heat transfer behaviors. The results also indicate that the operating conditions present some different effects in the two beds.     

Reactor Modeling of Gas‐Phase Polymerization of Ethylene

A model is developed for evaluating the performance of industrial‐scale gas‐phase polyethylene production reactors. This model is able to predict the properties of the produced polymer for both linear low‐density and high‐density polyethylene grades. A pseudo‐homogeneous state was assumed in the fluidized bed reactor based on negligible heat and mass transfer resistances between the bubble and emulsion phases. The nonideal flow pattern in the fluidized bed reactor was described by the tanks‐in‐series model based on the information obtained in the literature. The kinetic model used in this work allows to predict the properties of the produced polymer. The presented model was compared with the actual data in terms of melt index and density and it was shown that there is a good agreement between the actual and calculated properties of the polymer. New correlations were developed to predict the melt index and density of polyethylene based on the operating conditions of the reactor and composition of the reactants in feed.     

Critical Bed Height for Solid Circulation in a Compartmented Gas‐Fluidized Bed

The influence of design and operating parameters on minimum upstream bed height required for steady solid circulation across a compartmented gas‐fluidized bed has been studied. The partition plate in the compartmented bed is fitted with two pairs of V‐valve and riser with orifices in them. Silica sand of three different sizes, viz., 490 μm, 325 μm and 250 μm, has been used and the range of the aeration rate tested covers 1–3U_mf through the bed, 5–60U_mf through the V‐valve and 0–60U_mf through the riser. A model incorporating pressure balance across the circulation loop has been developed to analyze the experimental findings. Studies show the existence of a unique critical bed height for a given set of fluidization velocities through the bed, V‐valve, riser and the size of the solids.     

Gas‐Liquid Mass Transfer Rates and Impeller Power Consumptions for Industrial Vessel Design

Volumetric mass transfer coefficients (k_La) and power input (P) are often the key parameters in the design of gas‐liquid contactors. However, due to the limitations of most measurement methods, there is a lack of reliable data for predicting k_La for non‐coalescent batches under high energy dissipation rates. Accurate k_La and P correlations are proposed. The reliability of the correlations is ensured by using experimental data from a wide range of process conditions conducted in multiple‐impeller vessels of both laboratory scale and pilot scale, and including both non‐coalescent and coalescent batches. Applying the proposed correlations, the scale‐up and optimization of industrial vessels can be performed more accurately.     

Modeling of Electrochemistry and Heat/Mass Transfer in a Tubular Solid Oxide Steam Electrolyzer for Hydrogen Production

A finite‐volume based mathematical model has been developed for modeling hydrogen production by a tubular cell of solid oxide steam electrolyzer (SOSE), taking into account the electrochemical reactions and heat/mass transfer effects. The model is composed of three systems of nonlinear equations that govern the electric current density, energy balance in the solid SOSE cell, and energy balance in the flow of steam and hydrogen. The simulated hydrogen production rate proportional to the applied potential agreed well with the experimental measurements published in the literature. The intermediate modeling results indicated that the activation effect dominate the overall cell overpotential due to low exchange current density through the SOSE cell electrodes. Thus, higher electrode activity was identified as an important factor for enhancing cell performance. Parametric modeling analyses were conducted to gain better understanding of the SOSE characteristics. It was found that low‐temperature gas intake would cause a high temperature gradient in the tubular cell material at the inlet, possibly leading to a thermal expansion problem. The risk could be reduced by increasing the gas inlet temperature. It was also found that energy‐efficient SOSE hydrogen production can be achieved by reducing the hydrogen content in the steam intake and regulating the steam intake flow rate to an optimum that minimizes the overall electrical and thermal requirements. More parametric modeling results are discussed in this paper. The tubular SOSE cell model developed in this study can easily be expanded to accomplish tubular SOSE stack analysis for comprehensive system design optimization.     

Improving Gas‐Liquid Mass Transfer in Bubble Columns by Applying Low‐Frequency Vibrations

We show that application of low‐frequency vibrations, in the 50–200 Hz range, to the liquid phase of an air‐water bubble column causes significantly smaller bubbles to be generated at the distributor plate. For bubble column operation in the homogeneous flow regime, measurements of the volumetric mass transfer coefficient using the oxygen absorption technique show that the increase in the k_La values ranges from 50–100 % depending on the flow rate. It is concluded that application of low‐frequency vibration has the potential of improving the performance of bubble columns.     

Gas‐Liquid Mass Transfer in Fibrous Bed Reactor with Counter‐Current Liquid Recycle

In this work, the gas‐liquid mass transfer in a lab‐scale fibrous bed reactor with liquid recycle was studied. The volumetric gas‐liquid mass transfer coefficient, k_La, is determined over a range of the superficial liquid velocity (0.0042–0.0126 m.s^–1), gas velocity (0.006–0.021 m.s^–1), surface tension (35–72 mN/m), and viscosity (1–6 mPa.s). Increasing fluid velocities and viscosity, and decreasing interfacial tension, the volumetric oxygen transfer coefficient increased. In contrast to the case of co‐current flow, the effect of gas superficial velocity was found to be more significant than the liquid superficial velocity. This behavior is explained by variation of the coalescing gas fraction and the reduction in bubble size. A correlation for k_La is proposed. The predicted values deviate within ± 15 % from the experimental values, thus, implying that the equation can be used to predict gas‐liquid mass transfer rates in fibrous bed recycle bioreactors.     

Effect of Ethylene Glycol on the CO2/Water Gas‐Liquid Mass Transfer Process

The effect caused by the presence of ethylene glycol on the gas‐liquid mass transfer velocity of CO₂ in a aqueous phase has been studied. In this study two different gas‐liquid contactors have been used, a bubbling stirred reactor and a flat surface stirred vessel. The first contactor, gas phase, was introduced using a porous bubbling plate. The influence of operational variables, stirring rate, gas flow rate and ethylene glycol concentration were studied. The experiments were carried out at 298.15 K using a semicontinuous regime. The final aim was to obtain empirical equations that allow the calculation of the mass transfer velocity for this system a priori.     

Coupled Mass and Heat Transfer between a Cone and a Power‐Law Fluid

Coupled mass and heat transfer between a cone and a non‐Newtonian fluid was studied when the concentration level of the solute in the solvent is finite (finite dilution of solute approximation). Convective heat and mass transfer between a laminar flow and a stationary cone and between a rotating cone and a quiescent fluid is investigated. Solutions of both problems are found in the form of the dependencies of Sherwood number vs. Reynolds and Schmidt numbers. Coupled thermal effects during dissolution and solute concentration level effect on the rate of mass transfer are investigated. It is found that the rate of mass transfer between a cone and a non‐Newtonian fluid increases with the increase of the solute concentration level. The suggested approach is valid for high Peclet and Schmidt numbers. Isothermal and nonisothermal cases of dissolution are considered whereby the latter is described by the coupled equations of mass and heat transfer. It is shown that for positive dimensionless heat of dissolution, K > 0, thermal effects cause the increase of the mass transfer rate in comparison with the isothermal case. On the contrary, for K < 0 thermal effects cause the decrease of the mass transfer rate in comparison with the isothermal case. The latter effect becomes more pronounced with the increase of the concentration level of the solute in a solvent.     

Determination of Mass Transfer Parameters by Means of Chemical Absorption

The paper presents an explicit equation for the enhancement factor of a fast irreversible second‐order reaction. The equation makes it possible to determine the effective interfacial area and the liquid‐phase mass‐transfer coefficient of this reaction regime. With the help of a new plot as described in this paper, the Danckwerts plot, and the method for determining the interfacial area by means of a pseudo‐first‐order reaction the paper discusses a novel method for characterizing the reaction regime of experimental data.