Effect of char gasification reaction order on bounding solutions for char combustion

The rate of oxidation and surface temperature of a char particle during combustion is determined by the combined action of reactions of carbon with oxygen and CO₂ at the surface and carbon monoxide with O₂ in the gas phase. Limiting values for the rates and temperature were determined by Amundson et al. assuming that the CO₂ and CCO₂ reactions were first order with respect to the gas reactant concentration. Results are presented here for the cases in which the CO₂ reaction is zeroth order and the CCO₂ reaction is both first and zero order to bound the reaction orders found in practice. Allowance for zeroth order kinetics is found to have a profound effect on the shape of the bounding solutions for burning rates and temperatures, most notably by showing that diffusion-limited combustion can occur at much lower temperatur than would be predicted using first order kinetics.     

The measurement of emulsion phase voidage in gas fluidized beds of fine powders

The results of two different experimental methods, X-ray absorption and bed collapse, for the determination of the emulsion-phase voidage of gas fluidized beds are compared. It is shown that good agreement exists between them over the range of gas velocities studied, but that possible differences in voidage in an axial direction are only revealed by the X-ray technique. The bed collapse method applied to a Geldart Group A powder confirms that there is little difference between the surface settling rates of a bubbling bed and of a uniformly expanded bed of the same voidage.     

Particle—particle interaction force in a dilute gas—solid system

An experiment to measure pressure drop and solids velocities in a dilute pneumatic conveying pipe has been designed and constructed. A model based on momentum balance over particles has been developed to translate pressure drop and solids velocities data into an expression for particle—particle interaction. A correlation for particle—particle interaction with the relative velocity of 7 to 16 m/s has been developed. This correlation describes our experimental data within the 20% deviation.     

The effect of pressure on the flow of gas in fluidized beds of fine particles

The division of gas flow between the bubble and dense phases of fluidized beds of six different types of Group A powders has been studied at pressures of up to 20 bar using surface collapse and X-ray absorption measurements. It was found that with these fine powders as pressure increases at constant volumetric gas flowrate so the size and hold-up of bubbles decrease while their frequency increases. Contrary to previous measurements the average bubb velocity appears to decrease with increasing pressure. The dominant mode of bubble break-up in all the powders was found to be division from the rear, contrast to that observed with Group B powders at atmospheric pressure. Interstitial phase voidage was found to increase with increasing pressure.The results are interpreted in terms of a model which assumes a difference between the voidages, and hence the gas flow, of powder in the wakes behind     

Fluidized bed char combustion kinetic models

The effect of the kinetics of the heterogeneous reaction between the char and oxygen, and the importance of the subsequent homogeneous oxidation of carbon monoxide oil the performance of an atmospheric fluidized bed combustor have been examined by a comparative analysis of three models. Numerical calculations illustrating the effect of operating variables such as bed temperature, fuel and sorbent particle feed size and excess air were performed for values of the parameters which are pertinent to the design of large scale utility boilers. It is found that the kinetic models predict existence of multiple steady states over a wide range of operating conditions and values of model parameters. The model predictions of combustion efficiency, carbon loading and CO concentrations are in qualitative agreement with experimental data reported in the literature.     

Effectiveness factor of a catalyst pellet in a trickle bed reactor: Limiting reactant in the gas phase

The influence of both internal and external wettings on the effectiveness factor of a partially wetted catalyst pellet in a trickle-bed reactor when the limiting reactant is in the gas phase is analyzed.A new parameter, not considered up to now, measuring the gas-liquid interfacial area inside and on the pellet surface, is introduced to study different forms of wetting.The reaction in the dry zone is also taken into account and its influence on the effectiveness factor for both the pores mouth and pores end dry is studied.An approximate analytical expression for the effectiveness factor, giving close results to the numerical solution, is proposed.     

Dissolution kinetics: The nature of the particle attack of layered silicates in HF

The dissolution of layered silicates by hydrofluoric acid was studied with the aid of a slurry reactor. The nature of particle dissolution was delineat by measurements of reaction rates and by the examination of partially dissolved particles using a scanning electron microscope. The rates of particle d per unit mass were modeled as a function of the fraction x dissolved by an equation of the form [-r?(x)]/[-r?(x = 0)] = (1 - x) ^n?1. For the three layer silicates the parameter n takes on a value of $\text{1}\text{2}$, reflecting radial attack at the unit cell edges. The reactive edge surface area is considerably smaller than the total wetted particle surface area. In contrast, the two layer kaolinite structure dissolves at both the layer edges and the planar faces, and the parameter n varies from 0 to 1 as the particle dissolution proceeds to completion. Comparison of the rates of dissolution on the basis of the actual reactive surface areas show that layered silicates having the same octahedral sheet dissolve at the same rate. It is concluded that attack is preferential at surfaces where the octahedral sheets are exposed.     

Dynamics of particle deposition in model fiber filters

Aerosol filtration in model filters composed of an array of identical parallel fibers with equal interfiber distance was studied through simulation and experimentation. The simulation was made using a stochastic model based on principles proposed earlier [7, 8]. The major modification is that particles impacting on collectors or already deposited particles may bounce off and escape collection if the impact velocity is great enough. Good agreement between simulation and experiment was observed, lending credence to the eventual application of the stochastic model as a basis for the study of deposition dynamics. Based on the simulation results and confirmed by experimental data, an empirical correlation relating the increase in collection efficiency with the degree of particle deposition was established.     

The cross-flow catalyst reactor. An alternative for liquid phase hydrogenations

Liquid phase hydrogenation of aqueous nitrobenzoic acid was performed in the presence of a palladium catalyst. The carrier of the catalyst was designed for cross-flow processing with the inflow of hydrogen in separate channels perpendicular to the inflow of the liquid phase. The catalyst consisted of a number of thin, porous plates, separated by corrugated planes. The two reactants thus penetrate the catalytical plates from different sides. The effectiveness factor was shown to be much higher than in corresponding hydrogenations in a trickle-bed. The properties of the cross-flow hydrogenation were discussed in connection with a mathematical model for reaction and mass transport in pores and channels of the cross-flow catalyst.     

Effect of particle size distribution on adsorption kinetics in stirred batch systems

The effect of different particle size distributions (PSD's) on kinetic behavior in stirred-batch adsorption systems was investigated by numerically modeling the uptake of p-nitrophenol from aqueous solution by granular activated carbon in a well-stirred batch type of environment. Four different Gaussian PSD'S, two different log-normal PSD's and one case of uniform particle size were studied. The model accounted for both external and internal mass transfer resistances, and for the highly nonlinear equilibrium relation which characterizes the p-nitrophenol/activated carbon system. All isotherm parameters and “base-case” kinetic parameters were experimentally determined values (from the literature). The kinetic parameter values were varied in some cases to assess their influence. Moreover, both infinite-bath and finite-bath situations were evaluated. The modeling results show that the different particle size distributions did not generally give kinetic behavior widely different from the uniform particle size case when an infinite bath was assumed. However, for the more realistic case of a finite bath, the different PSD's gave significantly more distinctive results, especially for fractional mass uptake values greater than about 0.7. It is concluded that, in finite bath experiments, the nature of the adsorbent PSD must be accounted for in interpreting data obtained at fractional mass uptake values greater than about 0.7, unless the adsorbent PSD is reasonably nar     

Estimation of the particle diffusivity in a liquid-solids fluidized bed based on a stochastic model

A simple method was developed for estimating the particle diffusivity or mixing coefficient in a liquid-solids fluidized bed from the variance (dispersion) of the number of particles in a given section of the bed during relaxation in the bed expansion. This variance was estimated from the pressure drop history above the location of the pressure sensor recorded continuously after the stepwise disturbance in the velocity of the fluidizing medium. The method has been verified by comparing the particle diffusivities obtained by the present method with the available data obtained by other methods.     

Temperature-dependent physical properties in physical gas absorption

A solution for interface temperature rise in physical gas absorption due to heat of solution was obtained by Danckwerts [1,2] with the limitation that the pertinent physical properties—diffusion coefficient, solubility of the gas and thermal conductivity of the liquid remained constant. This paper complements Danckwerts' contribution by considering the pertinent physical properties as temperature-dependent, the dependence being of the form:$\text{Q}\text{Qi}$ = exp [γ_Q(T ? T_i)]. Wagner [3] has obtained solutions for unsteady-state diffusion when the diffusion coefficient is similarly dependent on concentration. Wagner's solutions are adapted to provide a solution for the present problem. Two approximate solutions, one valid at high Lewis Number and the other when Lewis Number approaches unity are also presented. For the normal values of activation energies, Danckwerts' model is shown to be accurate when interfacial temperature rise is less than one percent of the absolute temperature of bulk liquid. The extent of departure from the Danckwerts' model is shown to depend on combinations of activation energies of the pertinent physical properties.     

Mass transfer with heterogeneous and first order homogeneous reaction using the film theory

The problem of mass transfer with both first order irreversible homogeneous and an arbitrary heterogeneous reaction has been analyzed using the film theory, subject to the assumption of a linear profile of reactant between the bulk phase and the heterogeneous reaction surface. The enhancement factor is shown to depend on the product of two dimensionless groups. One is analogous to the usual group arising from mass transfer and first order irreversible reaction, and the other is a Damköhler number which describes the transport of the reactant to and reaction on the surface. The result is discussed in the context of solubilization of an insoluble liquid amphiphile by an aqueous surfactant solution. A maximum in the flux enhancement is observed because of the resistances associated with transport of the reactant species to the reaction surface.     

Mixing and fast chemical reaction-VIII: Initial deformation of material elements in isotropic,homogeneous turbulence

The kinematics of the deformation of fluid elements, having a size on the order of the Kolmogoroff velocity microscale, are needed when describing fast reactions in turbulent fluids as competition between molecular diffusion and chemical reaction in shrinking laminae. Starting from the statistical theory of turbulent diffusion, a new kinematic relationship has been derived, which applies to short diffusion times. Comparisons with two previously used equations, valid for simple shear and a certain elongational flow, confirm the useful properties of the new equation. Its application to fast reac requires knowledge of the kinematic viscosity of the fluid, the rate of energy dissipation (e.g. by stirring) and the initial thickness of the laminae. parametric sensitivity of the predicted product distribution from fast, competitive, consecutive reactions with respect to the initial thickness, which on the order of the Kolmorgoroff scale, is relatively low.     

Mathematical modeling of combustion and gasification of a wet coal slab—II: Mode of combustion,steady state multiplicities and extinction

The previous one-dimensional steady state model for gasification of wet coal is extended to include both homogeneous and heterogeneous combustion. The conditions under which the flame separates from the coal surface are presented and it is shown that these conditions are functions of the properties of the coal and the ambient gas. It is also shown that for a given bulk gas temperature, there is a limiting bulk oxygen concentration for combustion. Above the limiting bulk gas oxygen concentration, two possible solutions were found: the flame located at the char surface (heterogeneous combustion) and the flame located in the ash layer or in the gas film (homogeneous combustion). The heterogeneous combustion is shown to be unstable while the homogeneous combustion, which has been observed experimentally, is shown to be stable. The global rates, the mode of combustion, the multiplicity of steady state solution and the flame extinction points are discussed as a function of ambient gas temperature, ash layer thickness, coal moisture content and film transport coefficients.     

The oxidation of Cu(I) by oxygen gas in concentrated NaCl solutions: A kinetic study

The oxidation of Cu(I) by oxygen gas in concentrated NaCl solutions was studied in a standard stirred reactor. Each test was carried out at constant pH and under stable hydrodynamic conditions. The effect of stirring speed, solution volume, temperature, pH, oxygen partial pressure, chloride and copper ion concentration of the solution were evaluated.The oxidation of Cu(I) followed linear kinetics up to 85% of the copper ions in the cupric state. The experimental results were interpreted by using the film theory of mass transfer with chemical reaction. In the linear range, the chemical reaction was found to be first order with respect to oxygen concentration. The kinetic constant is given. The flux equation was specific of a fast reaction regime and the overall reaction rate was independent of the mass transfer coefficient k_L up to a k_L-value of about 10^?2 cm/sec. A parallel study of the oxidation of SO₃^2? by oxygen gas was carried out in the same reactor. The effects of stirring speed and solution volume were similar for both systems.     

Solid particle mixing in a continously operated fluidized bed reactor

In a bench-scale fluidized bed reactor, 20cm in dia., residence time distribution of solid particles (d_p, = 137μm) were measured by the radionuclide technique (²⁴Na₂C0₃) in the absence and in the presence of the chemical reaction 2NaHCO₃→Na₂C0₃+C0₂+H₂O. The residence time distributions were evaluated by a backflow cascade model by nonlinear optimization. The radial and logitudinal concentration profile of NaHCO₃ in the emulsion phase of the reactor were measured during steady-state operation. The solid is well-mixed.The connection of the measured bubble properties with the longitudinal solid dispersion coefficient and the use of the Haines-King-Woodburn model allow