Porosity intrapellet

The effective diffusivity Dn decreases rapidly as carbon number increases. The readsorption rate constant kr n depends on the intrinsic chemistry of the catalytic site and on experimental conditions but not on chain size. The rest of the equation contains only structural catalyst properties pellet size (L), porosity (e), active site density (0), and pore radius (Rp). High values of the Damkohler number lead to transport-enhanced a-olefin readsorption and chain initiation. The structural parameters in the Damkohler number account for two phenomena that control the extent of an intrapellet secondary reaction the intrapellet residence time of a-olefins and the number of readsorption sites (0) that they encounter as they diffuse through a catalyst particle. For example, high site densities can compensate for low catalyst surface areas, small pellets, and large pores by increasing the probability of readsorption even at short residence times. This is the case, for example, for unsupported Ru, Co, and Fe powders. 

Higher intrapellet residence times increase the contribution of chain initiation by a-olefins to chain growth pathways. This intrapellet delay, caused by the slow diffusion of large hydrocarbons, leads to non-Flory carbon number distributions and to increasingly paraffinic long hydrocarbon chains during FT synthesis. But intrapellet residence time also depends on the effective diameter and on the physical structure (porosity and tortuosity) of the support pellets. The severity of transport restrictions and the probability that a-olefins initiate a surface chain as they diffuse out of a pellet also de-... 

The probability of readsorption increases as the intrinsic readsorption reactivity of a-olefins (k,) increases and as their effective residence time within catalyst pores and bed interstices increases. The Thiele modulus [Eq. (15)] contains a parameter that contains only structural properties of the support material ( <>, pellet radius Fp, pore radius 4>, porosity) and the density of Ru or Co sites (0m) on the support surface. A similar dimensional analysis of Eqs. (l9)-(24), which describe reactant transport during FT synthesis, shows that a similar structural parameter governs intrapellet concentration gradients of CO and H2 [Eq. (25)]. In this case, the first term in the Thiele modulus (i/>co) reflects the reactive and diffusive properties of CO and H2 and the second term ( ) accounts for the effect of catalyst structure on reactant transport limitations. Not surprisingly, this second term is... 

Most important, heterogeneous surface-catalyzed chemical reaction rates are written in pseudo-homogeneous (i.e., volumetric) form and they are included in the mass transfer equation instead of the boundary conditions. Details of the porosity and tortuosity of a catalytic pellet are included in the effective diffusion coefficient used to calculate the intrapellet Damkohler number. The parameters (i.e., internal surface area per unit mass of catalyst) and Papp (i.e., apparent pellet density, which includes the internal void volume), whose product has units of inverse length, allow one to express the kinetic rate laws in pseudo-volumetric form, as required by the mass transfer equation. Hence, the mass balance for homogeneous diffusion and multiple pseudo-volumetric chemical reactions in one catalytic pellet is... 

Evaluating SmPapp Based on Average Pore Radii and Intrapellet Porosity... 

ESTIMATING TORTUOSITY FACTORS AND INTRAPELLET POROSITY BASED ON THE DISTRIBUTION IN ORIENTATION AND SIZE OF CATALYTIC PORES VIA THE PARALLEL-PORE MODEL... 

However, the void area fraction is equivalent to the void volume fraction, based on equation (21-76) and the definition of intrapellet porosity Sp at the bottom of p. 555. Effectiveness factor calculations in catalytic pellets require an analysis of one-dimensional pseudo-homogeneous diffusion and chemical reaction in a coordinate system that exploits the symmetry of the macroscopic boundary of a single pellet. For catalysts with rectangular symmetry as described above, one needs an expression for the average diffusional flux of reactants in the thinnest dimension, which corresponds to the x direction. Hence, the quantity of interest at the local level of description is which represents the local... 

The intrapellet porosity or void volume fraction Sp is given by an average over the radial part of the distfibution function h(r). l en all cylindrical pores are oriented parallel to the x direction (i.e., perpendicular to the external surface), the angular part of the distribution function is spiked at 6> = 0, which implies that... 

Consider the synthesis of methanol from carbon monoxide and hydrogen within the internal pores of catalysts with cylindrical symmetry. The radius of each catalytic pellet is 1 mm, the average intrapellet pore radius is 40 A, the intrapellet porosity is 0.50, the intrapellet tortuosity factor is 2, and the gas-phase molar density of carbon monoxide in the vicinity of the external surface of the catalytic pellet is 3 x 10 g-mol/cm. A reasonable Hougen-Watson kinetic rate law is based on the fact that the slowest step in the mechanism is irreversible chemical reaction that requires five active sites on the catalytic surface, due to the postulate that both hydrogen molecules must dissociate and adsorb spontaneously (see Section 22-3.1). Do not linearize the rate law. In units of g-mol/cm -min-atm, the forward kinetic rate constant is... 

Step 3. Enter the intrapellet porosity of a single pellet, which is dimensionless ... 

Step 11. Make the kinetic rate constant psendo-volumetric with units of inverse seconds. The product of and Papparent is equivalent to twice the intrapellet porosity divided by the average pore radius. Hence, fei, pseudo =... 

The appropriate diffusion coefficient of reactant A2 must be modified by intrapellet porosity and tortuosity factors which summarize the internal pore structure of each catalytic pellet. For spherical catalysts, the peUet radius R is taken as the characteristic length L. 

Intrapellet Damkohler number of reactant A Aa, intrapeUet = 5 Interpellet porosity of the packed bed mteipeUet = 0.50 Time constant for zeroth-order irreversible chemical reaction o) = 1 minute... 

Average pore radius average = 40 A (i.e.,1 A = 10" cm) Intrapellet porosity of each catalytic pellet p, mtrapeiiet = 0.50 Tortuosity factor Tor = 2... 

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