Porosity catalyst pellet

The term porosity refers to the fraction of the medium that contains the voids. When a fluid is passed over the medium, the fraction of the medium (i.e., the pores) that contributes to the flow is referred to as the effective porosity of the media. In a general sense, porous media are classified as either unconsolidated and consolidated and/or as ordered and random. Examples of unconsolidated media are sand, glass beads, catalyst pellets, column packing materials, soil, gravel and packing such as charcoal. 

In order to compare the micro-channel and the fixed-bed reactor, the design and operation parameters should be adjusted in such a way that certain key quantities are the same for both reactors. One of those key quantities is the porosity s, defined as the void fraction in the reactor volume, i.e. the fraction of space which is not occupied by catalyst pellets or channel walls. The second quantity is the specific... 

The porosity of the catalyst pellet (8p) is defined as the void fraction. 

The catalyst activity depends not only on the chemical composition but also on the diffusion properties of the catalyst material and on the size and shape of the catalyst pellets because transport limitations through the gas boundary layer around the pellets and through the porous material reduce the overall reaction rate. The influence of gas film restrictions, which depends on the pellet size and gas velocity, is usually low in sulphuric acid converters. The effective diffusivity in the catalyst depends on the porosity, the pore size distribution, and the tortuosity of the pore system. It may be improved in the design of the carrier by e.g. increasing the porosity or the pore size, but usually such improvements will also lead to a reduction of mechanical strength. The effect of transport restrictions is normally expressed as an effectiveness factor q defined as the ratio between observed reaction rate for a catalyst pellet and the intrinsic reaction rate, i.e. the hypothetical reaction rate if bulk or surface conditions (temperature, pressure, concentrations) prevailed throughout the pellet [11], For particles with the same intrinsic reaction rate and the same pore system, the surface effectiveness factor only depends on an equivalent particle diameter given by... 

The pore volume j)er unit mass, Vg, (a measure of the catalyst pellet porosity) is also a parameter which is important and is implicitly contained in eqn. (14). Since the product of the particle density, Pp, and specific pore volume, V, represents the porosity, then Pp is inversely proportional to Fg. Therefore, when the rate is controlled by bulk diffusion, it is proportional not simply to the square root of the specific surface area, but to the product of Sg and Vg. If Knudsen diffusion controls the reaction rate, then the overall rate is directly proportional to Vg, since the effective Knudsen diffusivity is proportional to the ratio of the porosity and the particle density. 

One approach to describe the kinetics of such systems involves the use of various resistances to reaction. If we consider an irreversible gas-phase reaction A — B that occurs in the presence of a solid catalyst pellet, we can postulate seven different steps required to accomplish the chemical transformation. First, we have to move the reactant A from the bulk gas to the surface of the catalyst particle. Solid catalyst particles are often manufactured out of aluminas or other similar materials that have large internal surface areas where the active metal sites (gold, platinum, palladium, etc.) are located. The porosity of the catalyst typically means that the interior of a pellet contains much more surface area for reaction than what is found only on the exterior of the pellet itself. Hence, the gaseous reactant A must diffuse from the surface through the pores of the catalyst pellet. At some point, the gaseous reactant reaches an active site, where it must be adsorbed onto the surface. The chemical transformation of reactant into product occurs on this active site. The product B must desorb from the active site back to the gas phase. The product B must diffuse from inside the catalyst pore back to the surface. Finally, the product molecule must be moved from the surface to the bulk gas fluid. 

The following results refer to a bed 0.91 m deep containing spherical catalyst pellets of diameter 1.52 mm, with porosity 0.4 due to pores of diameter 75 A and tortuosity factor 3.5. 

Figure 5 shows the dependence of the effectiveness factor on the Thiele modulus for the different pellet shapes. At small values of 4> the effectiveness factor approaches unity in all cases. Here, the chemical reaction constitutes the rate determining step—the corresponding concentration profiles over the pellet cross-section arc flat (sec Fig. 4). This situation may occur at low catalyst activity (k is small), large pore size and high porosity (Dc is large), and/or small catalyst pellets (R is small, i.c. in fluidized bed reactors R is typically around 50 /im).

In this equation ep is the porosity of the catalyst pellet and yp the tortuosity of the catalyst pores as discussed in Chapter 3 (the rest of the symbols are as defined before). From this formula it follows that the effective diffusion coefficient depends on both the gas composition and the pressure. Since we know the pressure as a function of the concentration, Equation 7.74 provides the effective diffusion coefficient as a function of the concentration. If we define... 

A significant increase in catalytic activity as compared to the limiting values, shown in Figure 8.1, can be achieved by the use of bidisperse porous structures. Such catalyst pellets are formed by compressing, extruding or in some other manner compacting finely powdered mkroporous material into a pellet. Ideally the micropores are due to the porosity in the individual microparticles of catalyst. The macropores result from voids between the microparticles, after pelletization or extrusion. In such catalysts, most of the catalytic surface is contained in the micropores, since S llre. The bidisperse structure is illustrated in Figure 8.2 compared to monodisperse particle. 

The general approach for modelling catalyst deactivation is schematically organised in Figure 2. The central part are the mass balances of reactants, intermediates, and metal deposits. In these mass balances, coefficients are present to describe reaction kinetics (reaction rate constant), mass transfer (diffusion coefficient), and catalyst porous texture (accessible porosity and effective transport properties). The mass balances together with the initial and boundary conditions define the catalyst deactivation model. The boundary conditions are determined by the axial position in the reactor. Simulations result in metal deposition profiles in catalyst pellets and catalyst life-time predictions. 

Now consider a catalyst pellet with a random network of zig-zag pores. The surface of the pellet is composed of both solid material and pores. The flux equation derived earlier must be modified to account for the fact that the flux, N, is based only on the area of a pore. A parameter called the porosity of the pellet, or Bp, is defined as the ratio of void volume within the pellet to the total pellet volume (void -f solid). The flux can be expressed in moles of A diffusing per unit pellet surface area (containing both solids and pores) by using 8 as... 

The porosity (i ) and tortuosity (t ) of the flat plate catalyst pellet are then used to calculate the ejfective diffusivities associated with each component according to ... 

The irreversible, first-order reaction of gaseous A lo B occurs in spherical catalyst pellets with a radius of 2 mm. For this problem, the molecular diffusivity of A is 1.2 X 10" cm s and the Knudsen diffusivity is 9 X 10 " cm s. The intrinsic first-order rate constant determined from detailed laboratory measurements was found to be 5.0 s . The concentration of A in the surrounding gas is 0.01 mol L . Assume the porosity and the tortuosity of the pellets are 0.5 and 4, respectively. 

The benefits of nonuniform activity distributions (site density) or diffusive properties (porosity, tortuosity) within pellets on the rate of catalytic reactions were first suggested theoretically by Kasaoka and Sakata (Ml). This proposal followed the pioneering experimental work of Maatman and Prater (142). Models of nonuniform catalyst pellets were later extended to more general pellet geometries and activity profiles (143), and applied to specific catalytic reactions, such as SO2 and naphthalene oxidation (144-146). Previous experimental and theoretical studies were recently discussed in an excellent review by Lee and Aris (147). Proposed applications in Fischer-Tropsch synthesis catalysis have also been recently reported (50-55,148), but the general concepts have been widely discussed and broadly applied in automotive exhaust and selective hydrogenation catalysis (142,147,149). 

Particulate catalyst can be arranged in arrays of any geometric configuration. In such arrays, three levels of porosity (TLP) can be distinguished. The fraction of the reaction zone that is free to the gas flow is the first level of porosity. The void fraction within arrays is the second level of porosity. The fraction of pores within the catalyst pellets is referred as the third level of porosity. Parallel-passage and lateral-flow reactors... 

The square root of the coefficient of ip", i.e., Thiele modulus ulus. The Thiele modulus, +, will always contain a subscript (e.g., n) which will distinguish this symbol from symbol for porosity, cf), defined in Chapter 4, which has no subscript. The quantity is a measure of the ratio of a surface reaction rate to a rate of diffusion through the catalyst pellet ... 

It follows from Equations 2 and 2a that at a critical value of X, which equals B/(AG/G) Hdcp approaches zero - the disappearance of DCP takes place in spite of CF actively proceeding. For some types of NiC the critical values of A, are practically accessible. At this and greater X values the catalyst pellet can be heated from ambient temperature up to T , without any deformation. As an example, the data obtained during the cyclic treatment of the promoted Ni/a-AljOj high porosity catalyst at A, = 2.5 K/min are presented in Figure 9. 

In materials science applications of NMR imaging the geometry of the object can often be chosen at liberty. For example, cylindrical samples can be used for studies of porosity by diffusion and flow in rocks and catalyst pellets [Maj2], and investigations of deterioration in polymers and elastomers. Furthermore, many biological samples show radial or close... 

Macro- and micropore volumes and porosities for bidisperse catalyst pellets are calculated by the same methods as used for monodisperse pore systems. Example 8-5 illustrates the procedure. 

The Parallel-pore Model Wheeler proposed a model, based on the first three of these properties, to represent the monodisperse pore-size distribution in a catalyst pellet. From p and Vg the porosity e is obtained from Eq. (8-16). Then a mean pore radius d is evaluated by writing equations for the total pore volume and total pore surface in a pellet. The result, developed as Eq. (8-26), is... 

Poisoning of catalyst 42, 398, 400 Pontryagin maximum principle 276, 286-290 Pore diffusion 54 Porosity 19, 96, 300 Porous catalyst pellet 15, 139, 192-260, 436-448 structure 15 Prandtl number 299 Pre-exponential (frequency) factor 62,... 

For non-porous catalyst pellets the reactants are chemisorbed on their external surface. However, for porous pellets the main surface area is distributed inside the pores of the catalyst pellets and the reactant molecules diffuse through these pores in order to reach the internal surface of these pellets. This process is usually called intraparticle diffusion of reactant molecules. The molecules are then chemisorbed on the internal surface of the catalyst pellets. The diffusion through the pores is usually described by Fickian diffusion models together with effective diffusivities that include porosity and tortuosity. Tortuosity accounts for the complex porous structure of the pellet. A more rigorous formulation for multicomponent systems is through the use of Stefan-Maxwell equations for multicomponent diffusion. Chemisorption is described through the net rate of adsorption (reaction with active sites) and desorption. Equilibrium adsorption isotherms are usually used to relate the gas phase concentrations to the solid surface concentrations. 

Experimentally, it is difficult to separate the effects of F and z on the effective diffusivity. Often, empirical values of the product Ft are reported as the tortuosity. This is particularly true in the literature of transport/reac-tion in porous catalyst pellets. For the large variety of catalysts, the tortuosity —equal to /h(SK in Equation 4-42—ranges from 1 to 10 [103]. Although it has been difficult to correlate these tortuosity values with experimentally determined pore structure parameters, the tortuosity almost always decreases with increasing porosity. 

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