Fluid-Particle Reactions Kinetics

This chapter treats the class of heterogeneous reactions in which a gas or liquid contacts a solid, reacts with it, and transforms it into product. Such reactions may be represented by 

A(fluid) + 6B(solid) fluid products solid products 

As shown in Fig. 25.1, solid particles remain unchanged in size during reaction when they contain large amounts of impurities which remain as a nonflaking ash or if they form a firm product material by the reactions of Eq. 2 or Eq. 3. Particles shrink in size during reaction when a flaking ash or product material is formed or when pure B is used in the reaction of Eq. 1. 

Fluid-solid reactions are numerous and of great industrial importance. Those in which the solid does not appreciably change in size during reaction are as follows. 

The roasting (or oxidation) of sulfide ores to yield the metal oxides. For example, in the preparation of zinc oxide the sulfide ore is mined, crushed, separated from the gangue by flotation, and then roasted in a reactor to form hard white zinc oxide particles according to the reaction 

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Chapter 23 Fluid-Fluid Reactions Kinetics /523 Chapter 24 Fluid-Fluid Reactions Design /540 Chapter 25 Fluid-Particle Reactions Kinetics /566 Chapter 26 Fluid-Particle Reactions Design /589... 

The three-dimensional voidage distribution provides the basic correlation for building a reactor model for fast fluidization, given data on particle-fluid transfer coefficients and intrinsic particle reaction kinetics. 

Thermodynamics Hendrick C. Van Ness, Michael M. Abbott Heat and Mass Transfer James G. Knudsen, Hoyt C. Hottel, Adel F. Sarofim, Phillip C. Wankat, Kent S. Knaebel Fluid and Particle Dynamics Janies N. Tilton Reaction Kinetics Stanley M. Walas... 

FIG. 16-9 General scheme of adsorbent particles in a packed bed showing the locations of mass transfer and dispersive mechanisms. Numerals correspond to mimhered paragraphs in the text 1, pore diffusion 2, solid diffusion 3, reaction kinetics at phase boundary 4, external mass transfer 5, fluid mixing. 

Permissible gas velocities are usually set by entrainment, and for a given throughput the vessel diameter is thus determined. The amount of catalyst or other bed particles is set by reaction kinetics and the bubble-solids contacting expected. Very often there is a scale-up debit involved in fluid bed reactors. As mentioned earlier, small reactors... 

In a fixed-bed catalytic reactor for a fluid-solid reaction, the solid catalyst is present as a bed of relatively small individual particles, randomly oriented and fixed in position. The fluid moves by convective flow through the spaces between the particles. There may also be diffusive flow or transport within the particles, as described in Chapter 8. The relevant kinetics of such reactions are treated in Section 8.5. The fluid may be either a gas or liquid, but we concentrate primarily on catalyzed gas-phase reactions, more common in this situation. We also focus on steady-state operation, thus ignoring any implications of catalyst deactivation with time (Section 8.6). The importance of fixed-bed catalytic reactors can be appreciated from their use in the manufacture of such large-tonnage products as sulfuric acid, ammonia, and methanol (see Figures 1.4,11.5, and 11.6, respectively). 

In addition to flow, thermal, and bed arrangements, an important design consideration is the amount of catalyst required (W), and its possible distribution over two or more stages. This is a measure of the size of the reactor. The depth (L) and diameter (D) of each stage must also be determined. In addition to the usual tools provided by kinetics, and material and energy balances, we must take into account matters peculiar to individual particles, collections of particles, and fluid-particle interactions, as well as any matters peculiar to the nature of the reaction, such as reversibility. Process design aspects of catalytic reactors are described by Lywood (1996). 

The kinetics and rate-controlling steps of a fluid-solid reaction are deduced by noting how the progressive conversion of particles is influenced by particle size and operating temperature. This information can be obtained in various ways, depending on the facilities available and the materials at hand. The following observations are a guide to experimentation and to the interpretation of experimental data. 

As expected, the fluid bed system looks most attractive when the reaction is severely diffusion limited. Here the required reactor volume is only 20-30% of that required by a fixed bed of 1/8-inch particles. However, reducing the particle size in a fixed bed from 1/8 to 1/16 inch would accomplish a similar reduction. As a result, we can conclude that from a reaction kinetics viewpoint a reaction must be limited severely by pore diffusion before the extra reactor volume required for small particles in fluidized beds is offset by their increased activity. Few residuum reactions are presently hindered to this extent. 

Fluid-solid reactions include thermal decomposition of minerals, roasting (oxidation) of sulfide ores, reduction of metal oxides with hydrogen, nitridation of metals, and carburization of metals. Each t3 e of reaction will be discussed finm the thermodynamic point of view. Then reaction kinetics for all of the various rate determining steps in fluid-sohd reactions will be discussed for two general models shrinking core and shrinking particle. 

Tank reactors for solid-catalyzed gaseous or liquid reactions are seen much less frequently than tubular reactors because of the difficulty in separating the phases and in agitating a fluid phase in the presence of solid particles. One type of CSTR used to study catalytic reactions is the spinning basket reactor, which has the catalyst embedded in the blades of the spinning agitator. Another is the Berty reactor, which uses an internal recycle stream to achieve perfectly mixed behavior." These reactors (see Chapter 5) are frequently used in industry to evaluate reaction mechanisms and determine reaction kinetics. 

The nanoparticle-fluid interfacial energy values may be substantially different in fluids other than deionized water. Furthermore, interfacial energies may decrease more for one polymorph than another in some solutions. This could significantly perturb size-temperature-pressure phase relations. The solution will also affect reaction kinetics because, under hydrothermal conditions, mass transfer can occur via the liquid, an electric double layer will develop around each nanoparticle, substances can be adsorbed onto surfaces, and nanoparticles may dissolve. The effects of particle size on reaction kinetics are considered below. 

N R number of reaction units see Eq. (54) r equilibrium parameter s column-capacity parameter for fixed-bed operation, based on reaction-kinetics calculation t solution-capacity parameter for fixed-bed operation, based on reaction-kinetics calculation x ratio of fluid-phase concentration of a component to that of all components, c/C0 (xa, etc.) y ratio of particle-phase concentration of a component to total for solid at saturation with the feed, q/Q... 

The analysis of many technological processes involving dissolution, extraction, vaporization, combustion, chemical transformations in dispersions, sedimentation of colloids, etc. are based on the solution of the problem of mass exchange between particles, drops, or bubbles and the ambient medium. For example, in industry one often deals with processes of extraction from drops or bubbles or with heterogeneous transformations on the surface of catalyst particles suspended in a fluid. The rate of extraction and the intensity of a catalytic process to a large extent are determined by the value of the total diffusion flux of a reactant to the surface of particles of the disperse phase, which, in turn, depends on the character of flow and the particle shape, the influence of neighboring particles, the kinetics of the surface chemical reaction, and some other factors. 

Statement of the problem. In the preceding chapters we considered processes of mass transfer to surfaces of particles and drops for the case of an infinite rate of chemical reaction (adsorption or dissolution.) Along with the cases considered in the preceding chapters, finite-rate surface chemical reactions (see Section 3.1) are of importance in applications. Here the concentration on the surfaces is a priori unknown and must be determined in the course of the solution. Let us consider a laminar fluid flow with velocity U past a spherical particle (drop or bubble) of radius a. Let R be the radial coordinate relative to the center of the particle. We assume that the concentration is uniform remote from the particle and is equal to C. Next, the rate of chemical reaction on the surface is given by Ws = KSFS(C), where Ks is the surface reaction rate constant and the function F% is defined by the reaction kinetics and satisfies the condition Fs(0) = 0. 

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