Intrapellet diffusion coefficients

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... 

Notice that the molar density of key-limiting reactant A on the external surface of the catalytic pellet is always used as the characteristic quantity to make the molar density of component i dimensionless in all the species mass balances. effective is the effective intrapellet diffusion coefficient of species i. If there is only one chemical reaction, or one rate-limiting step in a multiple reaction sequence, that is characterized by nth-order irreversible kinetics, then the rate constant in the numerator of the Damkohler numbers is the same for each A -. Hence, kj is written as k , which signifies that has units of (volume/mole)" /time for... 

Effectiveness factor is given vs. the intrapellet Damkohler number for different molecular sizes of reactant B. This effect is considered by changing the effective intrapellet diffusion coefficient of reactant B, which affects Sb-... 

The delta parameters defined above are consistent with the following ranking in molecular size for the two reactants and one product C > A2 > B. Effective diffusion coefficients and intrapellet Damkohler numbers are species specific because pore diffusion in the gas phase varies inversely with the square root of molecular weight. Hence, larger molecules have smaller diffusivities, larger delta parameters, and larger intrapellet Damkohler numbers. Investigate the sensitivity of E vs. A to ... 

Now, consider the realistic situation where there are j chemical reactions between i species in a mixtme. It is possible to construct a Damkohler number for reaction j that is species specific. This is necessary because the effective pore diffusion coefficient within a catalytic pellet is a function of the molecular size of species i. Hence, if reaction j is described by nth-order irreversible chemical kinetics, then the intrapellet Damkohler number of component i, based on the jih chemical... 

Notice that the molar density of key-limiting reactant A on the external surface of the catalytic pellet is always used as the characteristic quantity to make the molar density of component i dimensionless in all the component mass balances. This chapter focuses on explicit numerical calculations for the effective diffusion coefficient of species i within the internal pores of a catalytic pellet. This information is required before one can evaluate the intrapellet Damkohler number and calculate a numerical value for the effectiveness factor. Hence, 50, effective is called the effective intrapellet diffusion coefficient for species i. When 50, effective appears in the denominator of Ajj, the dimensionless scaling factor is called the intrapellet Damkohler number for species i in reaction j. When the reactor design focuses on the entire packed catalytic tubular reactor in Chapter 22, it will be necessary to calcnlate interpellet axial dispersion coefficients and interpellet Damkohler nnmbers. When there is only one chemical reaction that is characterized by nth-order irreversible kinetics and subscript j is not required, the rate constant in the nnmerator of equation (21-2) is written as instead of kj, which signifies that k has nnits of (volume/mole)"" per time for pseudo-volumetric kinetics. Recall from equation (19-6) on page 493 that second-order kinetic rate constants for a volnmetric rate law based on molar densities in the gas phase adjacent to the internal catalytic surface can be written as... 

INTRAPELLET DIFFUSION COEFFICIENTS AND DAMKOHLER NUMBERS is in Kelvin, then the Knudsen diffnsion coefficient for gas i in cm /s is... 

The parallel-pore model provides an in-depth description of the void volume fraction and tortuosity factor Tor based on averages over the distribution in size and orientation, respectively, of catalytic pores that are modeled as straight cylinders. These catalyst-dependent strncture factors provide the final tools that are required to calculate the effective intrapellet diffusion coefficients for reactants and prodncts, as well as intrapellet Damkohler numbers. The following conditions are invoked ... 

The void area fraction in (21-76) is based on the fractional area in a plane at constant x that is available for diffusion into catalysts with rectangular symmetry. A rather sophisticated treatment of the effect of g 6) on tortuosity is described by Dullien (1992, pp. 311-312). The tortuosity of a porous medium is a fundamental property of the streamlines or lines of flux within the individual capillaries. Tortuosity measures the deviation of the fluid from the macroscopic flow direction at every point in a porous medium. If all pores have the same constant cross-sectional area, then tortuosity is a symmetric second-rank tensor. For isotropic porous media, the trace of the tortuosity tensor is the important quantity that appears in the expression for the effective intrapellet diffusion coefficient. Consequently, Tor 3 represents this average value (i.e., trace of the tortuosity tensor) for isotropically oriented cylindrical pores with constant cross-sectional area. Hence,... 

Generate expressions for the effective intrapellet diffusion coefficient of component A in catalytic pellets when (a) all pores have radii below 50 A, and (b) aU pores have radii that are larger than 1 (im (i.e., 10 A). All pores can be described by straight cylindrical tubes at an angle of inclination of 45° with respect to the thinnest dimension of flat-slab catalysts. The gas mixture contains two components, A and B. 

Step 5. Enter the net intrapellet diffusion coefficient of reactant gas A in units... 

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. 

The temperature dependence of the effective intrapellet diffusion coefficient conforms to the assumption that ordinary molecular diffusion provides the dominant resistance to mass transfer in the pores, relative to Knudsen diffusion. This is valid when the pore diameter is larger than 1 tim. Gas-phase diffusivities are approximately proportional to the three-halves power of absolute temperature. Hence,... 

Effect of the enthalpy change for exothermic chemical reaction on the effectiveness factor when the temperature dependence of effective intrapellet diffusion coefficients is neglected in the mass transfer equation. 

It might be possible to neglect the external gas phase resistance to mass transfer relative to intrapellet diffusional resistance through a tortuous pathway. An increase in the gas stream flow rate reduces the external mass transfer resistance further. Remember that diffusion coefficients and mass transfer coefficients increase as one progresses from solids to liquids to gases. Hence, gas-phase mass transfer resistances are small, but the intrapellet gas-phase diffusional resistances should be significant, particularly when the intrapellet Damkohler number is quite large. In contrast, thermal conductivities and heat transfer coefficients increase... 

---