Interpellet Damkohler number

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... 

The interpeUet Damkohler number is a ratio of two mass transfer rate processes the rate of chemical reaction relative to the rate of mass transfer via interpellet... 

When the intrapellet Damkohler number for reactant A is large enough and the catalyst operates in the diffusion-limited regime, the effectiveness factor is inversely proportional to the Damkohler number (i.e., Aa, intrapeiiet)- Under these conditions, together with a large mass transfer Peclet number which minimizes effects due to interpellet axial dispersion, the following scaling law is valid ... 

At seven different values of the interpellet Damkohler number for which real and ideal packed catalytic tubular reactor performance is summarized in Table 22-2, it is possible to identify a critical value of the mass transfer Peclet number (Re Sc)cnticai, above which the effects of interpellet axial dispersion are insignificant for second-order irreversible chemical kinetics. For example, if ideal performance is justified when the outlet conversion of reactants under real and ideal conditions differs by less than 0.5%,... 

TABLE 22-3 Effect of the Interpellet Damkohler Number on the Critical Value of the Mass Transfer Peclet Number for Second-Order Irreversible Chemical Kinetics in Packed Catalytic Thbular Reactors"... 

Based on this requirement, one obtains the correlation shown in Table 22-4 between the interpellet Damkohler number and the critical value of the mass transfer Peclet number for ideal response. For interpellet Damkohler numbers between 100 and 500 [i.e., 100 < (1 interpellet) ( A, intrapeIlet) A, interpellet — ... 

TABLE 22-5 Effect of the Interpellet Damkohler Number on the Zeroth- and First-Order Coefficients in a Linear Empirical Correlation Between Real and Ideal Outlet Conversions", Given by Equation (22-67)... 

Step 6. Calculate the interpellet Damkohler number, based on axial dispersion, which appears in the mass balance with convection, diffusion, and chemical reaction. 

Interpellet Damkohler number, A interpeiiet Interpellet porosity, inteipeUet = 0.5... 

Answer The mass transfer Peclet number scales as Lpfr, and the interpellet Damkohler number scales as Lpp,. Therefore, PeMi = 150 and A mterpeiiet = 60. The other three dimensionless numbers are unaffected when the reactor length is doubled. 

The important dimensionless parameter that determines the significance of external mass transfer resistance for nth-order irreversible chemical kinetics in packed catalytic tubular reactors was introduced in equation (30-63) as a = iS(CA.iniet)" Simple algebraic manipulation allows one to relate a to the interpellet Damkohler number, the effectiveness factor, the mass transfer Peclet number, and a few other dimensionless parameters. For example, let the coefficient of the chemical reaction term in the dimensionless mass transfer equation be defined as follows ... 

The numerator of a contains S Papphn, surface(CA, iniet)" which also appears in the numerator of the interpellet Damkohler number, as defined by equation (22-7) ... 

Figure 30-1 Effect of the mass transfer Peclet number and Pesimpie on dimensionless reactant molar density in the exit stream of a non-ideal packed catalytic tubular reactor with first-order irreversible chemical kinetics and significant external mass transfer resistance. The product of the interpellet Damkohler number, the effectiveness factor, and the catalyst filling factor is 1.

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... 

Use the following data to analyze the performance of a packed catalytic tubular reactor that contains porous spherical pellets. The heterogeneous kinetic rate law is pseudo-first-order and irreversible such that / surface, with units of moles per area per time, is expressed in terms of the partial pressure of reactant A, only (i.e., surface = i.siufacePA), and ki, surface has dimensions of moles per area per time per atmosphere, ki, surface is not a pseudo-volumetric kinetic rate constant. Remember that the kinetic rate constant in both the intrapellet and interpellet Damkohler numbers must correspond to a pseudo-volumetric rate of reaction, where the rate law is expressed in terms of molar densities, not partial pressures. 

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