A new model for thermal volatilization of solid particles undergoing fast pyrolysis

A new model is proposed for representing the thermal volatilization of solid particles under the conditions of fast pyrolysis. The solid, initially at low temperature, is suddenly immersed into a high-temperature medium where it decomposes to gaseous products, the external surface of the particle being exposed to a high heat flux from the medium. As heat penetrates into the solid by conduction, the decomposition reaction occurs at a rate which increases with temperature. Equations for simultaneous heat and mass balances are derived and numerically solved, yielding the internal temperature profile and the rate of shrinkage of the particle, from which the time for total consumption is easily deduced. It is shown that the regime of volatilization depends on two parameters: a thermal Thiele and a thermal Biot modulus. The ablation regime is achieved if both M and B are large (⪢ 100). In this regime, the shrinking velocity is constant and the reaction takes place only in a thin layer at the solid surface.     

A contact‐point based approach for the analysis of reactions among solid particles

The contact‐point framework, 1 which replaces the picture of continuous contact between the reactants by contact at a finite number of points, has been proposed as a rational one for treating reactions among particulate solids. However, available models suffer from various drawbacks, the main one being that they do not show the right asymptotic behavior for large number of contact points. A model is presented here, that corrects these deficiencies. The results show that the contact‐point model approaches particle‐continuum behavior whenever the number of contact points exceeds 500. The model predictions have been compared with some data from our previous work on calcia‐alumina system in the temperature range 1,150–1,300°C. The model fits the data well, with the fitted values of diffusivity (of calcia through alumina) being of the order of 10^?16 m²/s. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

The crackling core model for the reaction of solid particles

A one parameter model is here proposed to represent the reaction of an initially nonporous solid with gas. It views that cracks form at the pellet surface and penetrate into the interior. As a result the virgin core shrinks leaving behind a grainy structure which then reacts away according to the shrinking core model.Simple conversion-time expressions are obtained, methods of comparison with data are suggested, and a good fit is shown to reported iron ore reduction data.     

Reactions of solid particles with nonuinform distribution of solid reactant: The volume reaction model

The effect of non-uniform solid reactant distribution on conversion of solid particles in gas-solid reactions is analyzed based on the volume reaction model. Certain special features of such systems are pointed out. The possibility of ash layer formation in the kinetically controlled regime is discussed. Conditions leading to single or double ash layer formation, both at the center and surface of the particle, in the intermediate regime of diffusion with simultaneous reaction are described. Detailed mathematical equations which are useful for calculation of the conversion-time relationship for particles with non-uniform solid reactant distribution are presented. Comparison is made to reaction of uniform particles and differences in required reaction time for desired conversion are outlined.     

A model of the coagulation process with solid particles and flocs in a turbulent flow

A mathematical model was developed on the basis of population balances to predict the floc size distribution in a coagulating suspension. The coagulation process is performed in a stirred tank reactor with a turbulent flow field. In the population model the influence of the different local energy charges inside the reactor is taken into account. Moreover two sorts of particles are distinguished, i.e. the originally present and completely dispersed primary particles and the flocs. Contrary to the primary particles the flocs can be disrupted due to pressure and shear forces as they are mechanically not very stable. This different behaviour requires separate population balances for the two sorts of particles. The model parameters that are necessary are adapted to one single experiment.For the steady state the results represent different floc size distributions dependent on the solid concentration and the energy charge. Moreover it is shown that the assumption of an ideally mixed reactor that is often used cannot be maintained to be always true for the prediction of the resulting floc size distribution. The calculation results achieved are validated by image processing measurements of coagulating quartz particles in an aqueous suspension.     

A model for mixing with fast chemical reactions

A previously published model of an unmixed spherical eddy containing an immobile reactant surrounded by a restricted volume of well mixed fluid has been improved by allowing all of the reactants and products to diffuse equally both within the eddy and in the surrounding fluid. The predicted development of the concentration profiles for a competitive consecutive second order reaction scheme is illustrated and shown to be physically reasonable. The final comparison with published experimental data confirms that the model is capable of predicting the results without the necessity of fitting any parameter values other than choosing the Kolmogoroff microscale for the diameter of the eddies.     

Modeling of multi gas—solid reactions: A transient model

A rigorous multicomponent multi gas-solid reaction model is developed. It is based on the particle — pellet model and considers the transient nature of the system, inter- and intra-particle heat and mass transfer and the variation of structural parameters with reaction. The model equations describing the structural changes along with property evaluation schemes are formulated for a general multicomponent system. Simulation results are compared with experimental data for carbon gasification and the reduction of a nickel oxide/hematite mixture. The match between model and experiment was found satisfactory. Both concentration and temperature profiles and other parameters are examined.     

Gas-solid reactions: Experimental evaluation of the zone model

Zinc sulfide pellets sintered at 1200°C, 1000°C, 800°C and 600°C were partially oxidized in a single pellet reactor. Sulfur profiles of these samples were measured using Auger electron spectroscopy (AES) and electron probe microanalysis (EPMA). These profiles showed the coexistence of three zones: ash layer, reaction zone, and unreacted core. The zone thickness was found to be approximately the same for samples of comparable porosities. The effective diffusivities of sintered zinc sulfide pellets calculated by using the values of zone thickness measured in the present study compare well with the literature values reported from kinetic studies.     

Gas‐solid catalytic reactions with an extended DSMC model

An algorithm of diffusive gas transport in porous solids based on random collisions of molecules (DSMC) is extended to include basic heterogeneous reaction mechanisms (adsorption, coadsorption, desorption, and reaction of gas species on the surface of the solid). With this model, we study the catalytic oxidation of CO inside highly porous nanoparticle layers in the transition regime using kinetic parameters from Pd(111) surfaces at ultra high vacuum conditions. Investigation of the reaction at different temperatures reveals a clear transition between a kinetic limit (low temperatures) and a diffusion limit (high temperatures). At high temperatures and under steady‐state conditions, the porous layer shows three distinct regions with different reaction rates (reactor poisoning, an effective reaction region, and a region with CO depletion), whose extends are determined by CO concentration and mass‐transport limitation. We expect that similar investigations help optimizing the structure of gas sensor elements based on nanoparticle layers fabricated with flame spray pyrolysis. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2092–2103, 2015     

A technique for solution of the equations for fluid—solid reactions with diffusion

The kinetic equations for several types of models for fluid—solid heterogeneous non-catalytic reactions with diffusional limitations have a similar mathematical structure. These coupled nonlinear partial differential equations possess very few analytical solutions, and are even difficult to solve numerically because of the “wave-like” nature of the concentration profiles. A transformation has been formulated that reduces these problems to a single, nonlinear diffusion-reaction equation in a new variable. Then, the multitude of results available for this type of problem can be used. With pseudo-steady-state conditions, the conversion of solid becomes analogous to an “effectiveness factor” in the transformed variable. For slab geometry, especially simple results are obtained, leading to analytical or semi-analytical results.     

A structural model for gas—solid reactions with a moving boundary—IV. Langmuir—Hinshelwood kinetics

The Langmuir—Hinshelwood type of kinetic expression has been incorporated into the “general structural model” for the reaction of a porous solid with a gas. Thus the system occupies the domain between the asymptotes corresponding to first-order and zeroth-order kinetics.The effect of the form of the rate expression is found to be the largest in the intermediate regime where both chemical reaction and diffusion play important roles in determining the overall rate. A “gas—solid reaction modulus” generalized for the Langmuir—Hinshelwood type of rate expression was developed to define the regimes of the different controlling mechanisms.     

Application of the zone model to multiple noncatalytic fluid-solid reactions

The effect of intraparticle diffusion on the multiple gas-solid reactions occurring in a porous solid reactant is analyzed by the zone reaction model. In parallel reactions for gases and a consecutive reaction for the solid, the solutions of transient concentration profiles of two solid reactants are given by classifying three zones, viz. Reaction zone and reaction-diffusion zone and diffusion zone in the course of the reaction progression. As an example, the simultaneous reduction-sulfidation of porous iron oxide sorbent in the desuifurization from low BTU coal gases is analyzed by the present model. The Thiele modulus of the reaction governs the behavior of the moving boundary between the reaction zone and the diffusion zone. When the Thiele modulus tends to be infinite, the present model is consistent with the solutions based on the unreacted shrinking core model.     

A kinetic model for curing reactions of epoxides with amines

Curing reactions of epoxy resins are accelerated by added hydrogen-bond donor solvent and hydroxyl groups produced during the course of polymerization. A kinetic model comprising several different polycondensation and polyaddition reactions that occur simultaneously is developed. The concept of diffusion controlled reactions is employed to describe the change of reaction rate constants with conversion after the formation of an infinite crosslinking network. Good agreement is obtained between the model predictions and experimental data available in the literature.     

CFB密相区大颗粒横向扩散系数的CPFD模拟

运用一种离散单元法（DEM）计算颗粒流体力学（CPFD）对尺寸为900 mm×100 mm×1200 mm的准三维流化床的密相区大颗粒扩散行为进行研究。模拟之前,依照前人实验研究对CPFD方法进行验证,模拟结果与实验结果符合较好,证明了CPFD方法模拟的有效性。模拟中通过注入示踪粒子的方法来研究大颗粒在密相区中的横向扩散系数,研究了流化风速、颗粒直径对颗粒横向扩散系数的影响。模拟结果显示,气泡是引起密相区内颗粒混合的主要因素;随着流化风速增加,颗粒横向扩散系数变大;随着颗粒直径增大,颗粒横向扩散系数减小。     

A geometrical model for coalescing aerosol particles

Geometrical relationships for two unequal-sized coalescing aerosol particles in the entire coalescing process are obtained by considering the coalescing process at the point where the neck size equals the diameter of the small particle and under the assumption that each particle is in the shape of a spherical cap. Comparisons on the shrinkage length have been made between present model and the Yadha and Helble [(2004). Modeling the coalescence of heterogenous amorphous particles. Journal of Aerosol Science, 35, 665–681] geometrical model. Excess surface area of titania nanoparticles sintering at different temperatures has also been compared between predictions from the present model, the Koch and Friedlander [(1990). The effect of particle coalescence on the surface area of a coagulating aerosol. Journal of Colloid and Interface Science, 140, 419–427] model, and the literature data. The results show that the present model gives reasonable predictions based on an overall solid-state diffusion mechanism at the start and the volume solid-state diffusion mechanism at later stages of the coalescing process.     

Surface diffusion of strongly adsorbing vapors in activated carbon by a differential permeation method

Conventional methods to determine surface diffusion of adsorbed molecules are proven to be inadequate for strongly adsorbing vapors on activated carbon. Knudsen diffusion permeability (B_k) for strongly adsorbing vapors cannot be directly estimated from that of inert gases such as helium. In this paper three models are considered to elucidate the mechanism of surface diffusion in activated carbon. The transport mechanism in all three models is a combination of Knudsen diffusion, viscous flow and surface diffusion. The collision reflection factor f (which is the fraction of molecules undergoing collision to the solid surface over reflection from the surface) of the Knudsen diffusivity is assumed to be a function of loading. It was found to be 1.79 in the limit of zero loading, and decreases as loading increases. The surface diffusion permeability increases sharply at very low pressures and then starts to decrease after it has reached a maximum (B_μm) at a threshold pressure. The initial rapid increase in the total permeability is mainly attributed to surface diffusion. Interestingly the B_μms for all adsorbates appear at the same volumetric adsorbed phase concentration, suggesting that the volume of adsorbed molecules may play an important role in the “surface” diffusion mechanism in activated carbon.