Fluid—solid reactions limitations

Stable and radioactive tracers have been used extensively in catalysis to validate reaction networks, test for intermediates, confirm reaction orders, distinguish between intra- and inter-molecular mechanisms, establish rate limiting steps, docviment direct participation of surface atoms in fluid-solid reactions, etc. A unique feature of tracer studies is that Individual reaction steps can be followed in a complicated set of reactions without perturbing the chemical composition of the... 

Strictly speaking, the validity of the shrinking unreacted core model is limited to those fluid-solid reactions where the reactant solid is nonporous and the reaction occurs at a well-defined, sharp reaction interface. Because of the simplicity of the model it is tempting to attempt to apply it to reactions involving porous solids also, but this can lead to incorrect analyses of experimental data. In a porous solid the chemical reaction occurs over a diffuse zone rather than at a sharp interface, and the model can be made use of only in the case of diffusion-controlled reactions. 

Figure 2. Stationary concentration (reactant) and temperature profiles inside and around a porous catalyst pellet during an exo thermic, heterogeneous catalytic fluid-solid reaction (a) without transport influence, (b) limited only by intraparticle diffusion, (0 limited by lntcrphase and intraparticle diffusion, (d) limited only by interphase diffusion (dense pellet)...

XRD experiments can be carried out to characterize gas-solid reactions and, with some limitations, fluid-solid reactions more generally, as long as the fluid contributes little to the pathway of sight for the X-rays. Areas of recent investigation are catalytic gas-solid reactions, electrochemical processes, synthesis procedures involving precipitation and dissolution of solids, temperature-programmed reaction studies of crystallization, and oxidation and reduction of solids. This enumeration covers essentially all phases of the life of a catalyst. 

A fluid for our consideration here is either a liquid or a gas. Fluid-solid reactions can be kinetically limited by several steps [8] ... 

In the case of thermal decomposition of a mineral, there is only the solid B on the left-hand side of equation (5.26). These thermal decompositions can also be treated by the same rate limiting steps as given previously. Although the product layer is often porous, it can produce a slower rate of either heat conduction or diffusion than the boundary layer. As a result fluid-solid reactions occur at a sharply defined reaction interface, at a position r within the particle of size R. The mass flux associated with boundary layer mass transfer is given by... 

Fluid-solid reactions can be kinetically limited by several steps ... 

A heterogeneous catalytic reaction occurs at or very near the fluid-solid interface. The principles that govern heterogeneous catalytic reactions can be applied to both catalytic and noncatalytic fluid-solid reactions. These two other types of heterogeneous reactions involve gas-liquid and gas-Hquid-solid systems. Reactions between gases and liquids are usually mass-transfer limited. 

Conventionally, fluid-solid reactions are carried out in various types of reactors, such as packed beds, fluidized/slurry, and monolith reactors as summarized in Table 6.1 [1]. Packed bed reactors are relatively simple, easy to operate and suitable for reactions that require relatively large amounts of catalyst, as they provide a high volumetric catalyst fraction of about 60%. The characteristic feature of packed bed reactors is the pressure drop of the fluid flowing through the catalytic bed. To avoid excessive pressure drop the use of catalyst pellets of 2-6 mm is necessary. But, large porous particles lower the transformation rate through diffusion limitations in the porous network and may decrease product selectivity and yield as discussed in Chapter 2. 

In fluid-solid systems, the reaction takes place on the catalyst surface. Prior to this, the reactant molecules have first to reach the catalyst surface and, therefore, the rate of mass transfer is an important operational parameter (Figure 15.3). Two types of mass transfer need to be considered in fluid-solid reactions external and internal mass transfer. In particular, internal mass transfer limitations should be avoided, since they more often limit the performance of the reactor and more strongly influence the product selectivity. The internal mass transfer is characterized by an effectiveness factor, q, defined as the ratio of the observed reaction rate to that at constant concentration throughout the catalyst layer. To ensure an effectiveness factor of q > 0.95 in an isothermal catalyst layer, the following criterion must be fulfilled [16] ... 

When a solid acts as a catalyst for a reaction, reactant molecules are converted into product molecules at the fluid-solid interface. To use the catalyst efficiently, we must ensure that fresh reactant molecules are supplied and product molecules removed continuously. Otherwise, chemical equilibrium would be established in the fluid adjacent to the surface, and the desired reaction would proceed no further. Ordinarily, supply and removal of the species in question depend on two physical rate processes in series. These processes involve mass transfer between the bulk fluid and the external surface of the catalyst and transport from the external surface to the internal surfaces of the solid. The concept of effectiveness factors developed in Section 12.3 permits one to average the reaction rate over the pore structure to obtain an expression for the rate in terms of the reactant concentrations and temperatures prevailing at the exterior surface of the catalyst. In some instances, the external surface concentrations do not differ appreciably from those prevailing in the bulk fluid. In other cases, a significant concentration difference arises as a consequence of physical limitations on the rate at which reactant molecules can be transported from the bulk fluid to the exterior surface of the catalyst particle. Here, we discuss... 

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],... 

Internal recycle reactors are designed so that the relative velocity between the catalyst and the fluid phase is increased without increasing the overall feed and outlet flow rates. This facilitates the interphase heat and mass transfer rates. A typical internal flow recycle stirred reactor design proposed by Berty (1974, 1979) is shown in Fig. 18. This type of reactor is ideally suited for laboratory kinetic studies. The reactor, however, works better at higher pressure than at lower pressure. The other types of internal recycle reactors that can be effectively used for gas-liquid-solid reactions are those with a fixed bed of catalyst in a basket placed at the wall or at the center. Brown (1969) showed that imperfect mixing and heat and mass transfer effects are absent above a stirrer speed of about 2,000 rpm. Some important features of internal recycle reactors are listed in Table XII. The information on gas-liquid and liquid-solid mass transfer coefficients in these reactors is rather limited, and more work in this area is necessary. 

The greatest limitation to the widespread application of XRD of reacting materials is the creation of an appropriate reaction environment that allows the X-rays to penetrate the catalyst and the diffracted X-rays to escape to the detector system. In gas-solid reactions, the greatest challenges are in the provision of the correct gas-phase compositions of the reactants the addition of condensable components (notably steam and fluid hydrocarbons) presents the challenge of avoiding condensation on the cooling elements of heated cells and on the tubes or pipes in the feed supply and product analysis system. 

A major limitation of the present work is that it deals only with well-defined (and mostly unidirectional) flow fields and simple homogeneous and catalytic reactor models. In addition, it ignores the coupling between the flow field and the species and energy balances which may be due to physical property variations or dependence of transport coefficients on state variables. Thus, a major and useful extension of the present work is to consider two- or three-dimensional flow fields (through simplified Navier-Stokes or Reynolds averaged equations), include physical property variations and derive lowdimensional models for various types of multi-phase reactors such as gas-liquid, fluid-solid (with diffusion and reaction in the solid phase) and gas-liquid-solid reactors. 

The case of = 1 is a reasonable approximation for a great variety of cases while = 0 covers another common situation where the reaction rate is limited by the disengagement of molecules from the surface. The rate kRp, has its usual interpretation as moles formed per unit volume of reactor per unit time when A, is the surface area of the fluid-solid interface per unit volume of reactor. For single-particle experiments, Ai will be the surface area and will be in moles reacted per unit time. 

The above treatment assumes the only difliisional limitations are in the catalyst (one or two) grains, and not in the pellet as a whole—more general grain models are described in Chapter 4 in another application to fluid-solid heterogeneous reactions. Also, other extensknis have been provided by Gunn and Thomas [101]. 

This chapter has briefly described a series of models for gas-solid reactions. The literature contains several more and many more could be developed. It would be hard, if not impossible, to assess these models as to their respective merits since careful and detailed experimentation is seriously lagging behind. In the few cases in which it was possible to check the theoretical results with experimental data the lack of fit has mainly been ascribed to inaccuracies in the models. Insufficient attention has been devoted to the kinetic equations proper there is no reason for limiting the kinetics of the reaction between a fluid and the component of a solid to zero- or first-order expressions. 

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