Particle with a Porous Product Layer

For particles with a porous product layer, the interfacial area, tipA, is constant during the reaction  

The expressions for the ratio between the interfadal area and reactor volume (op) and the gas holdup (ec) are inserted into the balance Equation 8.110, and we obtain 

For a general system containing N components in the gas phase, the coupled system of N + I differential equations, Equations 8.110 and 8.18, is solved. The flux N, and the surface concentration c are given in Equations 8.50 and 8.51, respectively. The coupled differential equations must be solved numerically using the tools and methods introduced, for instance, in Appendix 2. For first-order reactions, however, a simplified procedure is possible. 

For a first-order reaction, with the reaction kinetics 

Inserting the expression for the flux Na into the balance equation. Equation 8.112, yields 

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Equation 8.18 relates the particle radius to the surface reaction rate in a general way. The surface concentration, c , is highly dependent on the conditions on the reactive surface. Let us now consider two extreme cases a particle with a porous product layer (ash layer model) and the shrinking particle model. 

A particle with a porous product layer is divided into three zones the gas film around the product layer, the porous product layer, and the unreacted solid material. The structure of the particle is shown in Figure 8.2. The gas-phase component A diffuses through the gas film and product layer to the interface, where chemical reactions occur. The gas-phase product, P, has the opposite transport route. The molar flux of A is denoted as Na, and the positive transport direction is given in Figure 8.2. 

Examples of the development of concentration profiles in packed beds are shown in Figure 8.6 [4 ]. This figure is valid for particles with a porous product layer. The development of a reaction zone moving from the inlet toward the outlet is a typical behavior of packed beds. At the reactor inlet, the particles have reacted completely, whereas the particles close to the outlet are totally unreacted. 

The concentration of A, C g, in the bulk of the gas reactant A is assumed to remain unchanged with time as reactant A is present in excess quantity. Thus, the conversion of solid to product occurs in a constant gas environment. The solid particle is non-porous. So the reaction would occur only on the outer surface of the solid particle. However, the converted solid particle is assumed to be porous. Thus, on complete conversion of B present on the outer layer of a solid particle, a porous product layer would be formed. Reactant A would diffuse through this porous product layer (called ash layer) and react with reactant B present on the surface of the unreacted spherical core lying beneath the product layer. Thus, at any point of time, the spherical particle will have an unreacted core of radius surrounded by a product layer as shown in Figure 4.3. 

It should be noted that in the case of the reaction of a fluid with a nonporous solid, the chemical reaction step and the mass transport step are connected in series. This makes the analysis much simpler as compared to the case of a porous solid. In reactions of nonporous particles there can essentially be two cases one which shows absence of a solid product layer, and the other which shows its presence. 

For a gas-solid reaction with a gaseous product, the non-porous particle shrinks (r = Tp for t = 0 and r = rc for t > 0) and thus so also does the external surface. The rate of transport of the gaseous reactant A through the boundary layer, Eq. (4.6.1), equals the reaction rate, Eq. (4.6.3) ... 

For a description of the rate of such a process a reasoning similar to that of dissolving porous particles can be used see section 5,43,3. Assume that as the solid reactant is consumed at the pore walls, it is constantly replaced by a porous layer of product. As a B-layer widi original thickness A6 is converted, it becomes a porous P-layer with thickness (l+co )A5. A volumetric balance can be coupled with the rate equation ... 

SynChropak size exclusion supports are composed of spherical uniformly porous silica that has been derivatized with a suitable layer. SynChropak GPC supports are available in six pore diameters ranging from 50 to 4000 A and particle diameters from 5 to 10 /zm. SynChropak CATSEC supports are available in four pore diameters. Table 10.1 details the physical characteristics of the product lines. 

Ilford is calling the microporous layer "nanoporous" since the particle and pore size in the layer they produce is weU below the micron level, with typical 20 nanometer particles while, practically, no particles are larger then 70 nanometers. The mineral oxides used in the porous products are surface treated in a proprietary process to balance physical properties such as brittleness and gloss with imaging properties such as color brilliance, layer transparency, and permanence. 

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... 

Shrinking Core with an Ash Layer This occurs when one of the reaction products forms a porous layer (ash, oxide, etc.). As the reaction proceeds, a layer of ash is formed in the section of the particle that has reacted, externally to a shrinking core of the sohd reactant. The fluid reactant diffuses through the ash layer, and the reaction occurs at the surface of a shrinking core until the core is consumed completely. 

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