Gas-solid reaction models

G. Uhde, U. Hoffmann, Noncatalytic Gas-Solid Reactions Modelling of Simultaneous Reaction and Formation of Surface with a Nonisothermal Crackling Core Model, Chem. 

Figure 5.10 Representation of the unreacted-core gas/solid reaction model for a particle of unchanging size. As reaction time progresses from left to right in the figure, the reaction surface recedes into the particle, the unreacted core shrinks, and the ash layer (containing the reaction product) increases in thickness.

Hastaoglu M. A. Hassam M. S. (1995) Application of a general gas-solid reaction model to flash pyrolysis of wood in a circulating fluidized bed. Fuel, 74, 697-703. 

Here the reactor equation is general and independent of the rate equation, which depends on the gas-solid reaction model used. It can also be adapted to other reactors with appropriate modifications. However, these involve unacceptable assumptions for the fluid-bed model. 

The more important basic gas-solid reaction models and their extensions are described in Section... 

Therefore, the simplest non-catal3dic gas-solid reaction model with unchanged diameter is introduced here, i.e., the shrinking core model (SCM). Figure 5.3 is the schematic diagram of SCM. It is commonly considered that SCM reasonably describes real particle behavior during reaction process and gives a simple conversion expression. 

The value of tire heat transfer coefficient of die gas is dependent on die rate of flow of the gas, and on whether the gas is in streamline or turbulent flow. This factor depends on the flow rate of tire gas and on physical properties of the gas, namely the density and viscosity. In the application of models of chemical reactors in which gas-solid reactions are caiTied out, it is useful to define a dimensionless number criterion which can be used to determine the state of flow of the gas no matter what the physical dimensions of the reactor and its solid content. Such a criterion which is used is the Reynolds number of the gas. For example, the characteristic length in tire definition of this number when a gas is flowing along a mbe is the diameter of the tube. The value of the Reynolds number when the gas is in streamline, or linear flow, is less than about 2000, and above this number the gas is in mrbulent flow. For the flow... 

The above rate equations were originally largely developed from studies of gas—solid reactions and assume that particles of the solid reactant are completely covered by a coherent layer of product. Various applications of these models to kinetic studies of solid—solid interactions have been given. 

Similar to the case of gas-solid reactions, we represent the stoichiometry of a gas-liquid reaction in a model or generic sense by... 

In the use of the shrinking-core model for a gas-solid reaction, what information could be... 

A kinetics study was performed to examine the rate-controlling steps in a gas-solid reaction governed by the shrinking-core model ... 

The performance of a reactor for a gas-solid reaction (A(g) + bB(s) -> products) is to be analyzed based on the following model solids in BMF, uniform gas composition, and no overhead loss of solid as a result of entrainment. Calculate the fractional conversion of B (fB) based on the following information and assumptions T = 800 K, pA = 2 bar the particles are cylindrical with a radius of 0.5 mm from a batch-reactor study, the time for 100% conversion of 2-mm particles is 40 min at 600 K and pA = 1 bar. Compare results for /b assuming (a) gas-film (mass-transfer) control (b) surface-reaction control and (c) ash-layer diffusion control. The solid flow rate is 1000 kg min-1, and the solid holdup (WB) in the reactor is 20,000 kg. Assume also that the SCM is valid, and the surface reaction is first-order with respect to A. 

The gas-solid reaction rate is modeled by the nonlinear expression... 

Fig. 4. Gas—solid reaction (shrinking core model), that...

Figure 7-4 Slurry reactor (left) for well-mixed gas-solid reactions and fluidized bed reactor (center) for liquid-solid reactions. At the right is shown a riser reactor in which the catalyst is carried with the reactants and separated and returned to the reactor. The slurry reactor is generally mixed and is described by the CSTR model, while the fluidized bed is described by the PFTR or CSTR models.

Most of the gas-solid reactions that have been studied appear to proceed by the shrinking core reaction mode. In the simplest type of unreacted core model it is assumed that there is a non-porous unreacted solid with the reaction taking place in an infinitely thin zone separating the core from a completely reacted product as shown in Fig. 3.36 for a spherical particle. Considering a reaction between a gaseous reactant A and a solid B and assuming that a coherent porous solid product is formed, five consecutive steps may be distinguished in the overall process ... 

In the new edition, the material on Chemical Reactor Design has been re-arranged into four chapters. The first covers General Principles (as in the earlier editions) and the second deals with Flow Characteristics and Modelling in Reactors. Chapter 3 now includes material on Catalytic Reactions (from the former Chapter 2) together with non-catalytic gas-solids reactions, and Chapter 4 covers other multiphase reactor systems. Dr J. C. Lee has contributed the material in Chapters 1, 2 and 4 and that on non-catalytic reactions in Chapter 3, and Professor W. J. Thomas has covered catalytic reactions in that Chapter. 

The observation that, at high pressures, the combustion parameters become nearly independent of gas pressure (a phenomena typical for solid-solid systems) is very important and can lead to significant simplications in the modeling of these gas-solid reactions. 

Phase transformations in heterogeneous catalysis have been described recently by topochemical kinetic models [111-115]. These models were taken from solid chemistry, where they had been developed for "gas-solid reactions. The products of such reactions are solids. When gas is in contact with the initial solid, the reaction rate is negligible. But as nucleates of the phase... 

The limitation of such a model to first-order reaction rates is not as restricting as it seems. In fact, many reactions might at least be considered as of pseudo -first order, which means that they behave macroscopically like first-order reactions. This is the case for diluted fluids and for non-catalytic gas/solid reactions such as the so-called shrinking core or shrinking particle model. Other examples are electrochemical reactions [106],... 

The mathematical models of the reacting polydispersed particles usually have stiff ordinary differential equations. Stiffness arises from the effect of particle sizes on the thermal transients of the particles and from the strong temperature dependence of the reactions like combustion and devolatilization. The computation time for the numerical solution using commercially available stiff ODE solvers may take excessive time for some systems. A model that uses K discrete size cuts and N gas-solid reactions will have K(N + 1) differential equations. As an alternative to the numerical solution of these equations an iterative finite difference method was developed and tested on the pyrolysis model of polydispersed coal particles in a transport reactor. The resulting 160 differential equations were solved in less than 30 seconds on a CDC Cyber 73. This is compared to more than 10 hours on the same machine using a commercially available stiff solver which is based on Gear s method. 

In the modeling of solid fuel conversion reactors differential equations arise for the description of particle temperatures and gas-solid reactions among others. These equations are coupled and they must be solved simultaneously. Because of the usually wide range of particle sizes the time constants for thermal transients of solids differ considerably. This causes stiffness in the differential equation model. Depending on the type of the gas-solid reactions stiffness may also be introduced by the variation of reaction rates with individual reaction type and with temperature. 

Keywords gas-solid reaction, metals, thermal analysis, mathematical modeling... 

Prasannan, P. C. A model for gas-solid reactions with structure changes in the presence of inert solids, Chem. Eng. Sci., 40, 1251 (1985). 

Yu, H. C, and Sotirchos, S. A generalized pore model of noncatalystic gas-solid reaction exhibiting pore closure, AIChE J., 33, 782 (1987). 

In some cases, adsorption of analyte can be followed by a chemical reaction. The Langmuir-Hinshelwood (LH) and power-law models have been used successfully in describing the kinetics of a broad range of gas-solid reaction systems [105,106]. The LH model, developed to describe interactions between dissimilar adsorbates in the context of heterogeneous catalysis [107], assumes that gas adsorption follows a Langmuir isotherm and that the adsorbates are sufficiently mobile so that they equilibrate with one another on the surface on a time scale that is rapid compared to desorpticm. The power-law model assumes a Fre-undlich adsorption isotherm. Bodi models assume that the surface reaction is first-order with respect to the reactant gas, and that surface coverage asymptotically approaches a mmiolayer widi increasing gas concentration. 

The LH model assumes that the adsorption process is at equilibrium and that the chemical reaction at the surface is the rate-limiting step. The LH expression for the rate, r, of an irreversible gas/solid reaction is... 

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