Interpellet axial dispersion

Internodal pathways, 5 80 Interparticle forces, 77 800-801 Interpellet axial dispersion, 25 281-283, 288... 

Nonideal tubular reactor models, inclusion of interpellet axial dispersion in,... 

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... 

DIFFERENTIAL FORM OF THE DESIGN EQUATION FOR IDEAL PACKED CATALYTIC TUBULAR REACTORS WITHOUT INTERPELLET AXIAL DISPERSION... 

If there is only one chemical reaction on the internal catalytic surface, then vai = — 1 and subscript j is not required for all quantities that are specific to the yth chemical reaction. When the mass transfer Peclet number which accounts for interpellet axial dispersion in packed beds is large, residence-time distribution effects are insignificant and axial diffusion can be neglected in the plug-flow mass balance given by equation (22-11). Under these conditions, reactor performance can be predicted from a simplified one-dimensional model. The differential design equation is... 

The rate of convective mass transfer relative to the rate of mass transfer via interpellet axial dispersion is eqnivalent to the ratio of the diffusion time constant relative to the residence time for convective mass transfer. The interpellet Damkohler nnmber for reactant A is... 

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 ... 

NON-IDEAL REACTORS WITH INTERPELLET AXIAL DISPERSION... 

Convergence is obtained when the appropriate guess for d p./di at the reactor inlet predicts the correct Danckwerts condition in the exit stream, within acceptable tolerance. To determine the range of mass transfer Peclet numbers where residence-time distribution effects via interpellet axial dispersion are important, it is necessary to compare plug-flow tubular reactor simulations with and without axial dispersion. The solution to the non-ideal problem, described by equation (22-61) and the definition of Axial Grad, at the reactor outlet is I/a( = 1, RTD). The performance of the ideal plug-flow tubular reactor without interpellet axial dispersion is described by... 

It is possible to avoid some of the instabilities associated with guessing the dimensionless axial concentration gradient at the inlet to a non-ideal tubular reactor by solving the one-dimensional mass transfer equation backwards from outlet to inlet. In practice, it is necessary to introduce a new dimensionless independent spatial variable which increases as one travels backward through the packed catalytic tubular reactor. This stipulation is required by conventional ODE solvers. Hence, if = 1 — f, then the two coupled ODEs which represent the mass balance with convection, interpellet axial dispersion, and nth-order irreversible chemical reaction are rewritten as follows ... 

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%,... 

Interpellet axial dispersion does not affect reactor performance when the mass transfer Peclet number is above (Re-Sc)critical. 

This is an unprecedented novel idea that allows one to compare 4 a( = 1, RTD) and = 1. ideal) when both boundary conditions for the non-ideal PFR with interpellet axial dispersion are the same as those for the ideal PFR. In both cases, T a = 1 at the inlet to the reactor (i.e., = 0). The shategy is as follows ... 

Use this boundary condition (i.e., T a = 1 at C = 0) to solve the mass balance without interpellet axial dispersion for the ideal plug-flow reactor. 

Problem. Think about the overall strategy that must be implemented to account for the effect of interpellet axial dispersion on ihe outlet concentration of reactant A when Langmuir-Hinshelwood kinetics and Hougen-Watson models are operative in a packed catalytic tubular reactor. Residence-time distribution effects are important at small mass transfer Peclet numbers. 

MASS TRANSFER PECLET NUMBERS BASED ON INTERPELLET AXIAL DISPERSION IN PACKED CATALYTIC TUBULAR REACTORS... 

Results from the previous section in this chapter illustrate how and when interpellet axial dispersion plays an important role in the design of packed catalytic tubular reactors. When diffusion is important, more sophisticated numerical techniques are required to solve second-order ODEs with split boundary conditions to predict non-ideal reactor performance. Tubular reactor performance is nonideal when the mass transfer Peclet number is small enough such that interpellet axial dispersion cannot be neglected. The objectives of this section are to understand the correlations for effective axial dispersion coefficients in packed beds and porous media and calculate the mass transfer Peclet number based on axial dispersion. Before one can make predictions about the ideal vs. non-ideal performance of tubular reactors, steady-state mass balances with and without axial dispersion must be solved and the reactant concentration profiles from both solutions must be compared. If the difference between these profiles with and without interpellet axial dispersion is indistinguishable, then the reactor operates ideally. 

The following strategy should be used to calculate the interpellet axial dispersion coefficient and the mass transfer Peclet number in packed catalytic tubular reactors (see Dullien, 1992, Chap. 6). Initially, one should calculate a simplified mass transfer Peclet number (i.e., Pesimpie) based on the equivalent diameter of the catalytic pellets, equivalent, the average interstitial fluid velocity through the packed bed, (Uj>intetstitiai, and the ordinary molecular diffusion coefficient of reactant A, a, ordinary-... 

ISOTHERMAL DESIGN OF HETEROGENEOUS PACKED CATALYTIC REACTORS is the mass transfer Peclet number which accounts for interpellet axial dispersion ... 

Gas chromatography is a separation technique based on the fact that different components in the mixture exhibit different average residence times due to interactions with the porons packing material. These interactions can be classified as intrapellet diffusion and the column operates similar to a packed catalytic tubular reactor. The important mass transfer mechanisms are convection and diffusion. Hence, it is important to calculate the mass transfer Peclet number that represents an order-of-magnitude ratio of these two mass transfer rate processes. Intrapellet diffusion governs residence times, and interpellet axial dispersion affects the degree to which the output curve is broadened. For axial dispersion in packed columns and packed catalytic tubular reactors. 

Step 4. Use the experimental correlation to calculate the interpellet axial dispersion coefficient. 

Step 15. Determine the experimental correlation coefficient for interpellet axial dispersion via a conditional IF statement ... 

Draw a block diagram that illustrates the computer logic required to design a packed catalytic tubular reactor. Your logic should be flexible enough to account for interpellet axial dispersion, if necessary. Do not include any eqnations. 

Answer When the chemical kinetics are first-order and irreversible (i.e., n 1), with no complications from interpellet axial dispersion, the final conversion of reactants to products in an ideal PFR is... 

Consider Taylor dispersion of a tracer in packed beds, mass transfer Peclet numbers based on interpellet axial dispersion coefQcients, and the resolution of a chromatograph to explain how the performance of a chromatographic separation device depends on the length of the packed column if all other design parameters, particularly the size of the packing material, remain constant. 

Peclet numbers, where interpellet axial dispersion is negligible, the equations of interest are... 

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