In the 12/7/2013 posting, two effectiveness factor methods were mentioned for the pellet model... (1) intrapellet effectiveness factor and (2) overall effectiveness factor that includes the gradients in composition and temperature across the film surrounding the pellet. The first method is used with known values of the catalyst surface variables, and the second method is used with known values of the bulk fluid variables. Since the second method incorporates many of the same parameters used in the first method, the discussion in this posting will be valid for both methods.
The "presumed advantage" of this method
The concept is to apply a correction factor, i.e. effectiveness factor, to the reaction rates that are computed using the bulk variables, when the integrated rates within the catalyst are actually needed. This effectiveness factor is to be computed as a function of the reaction network, reaction rates, and transport parameters. However, due to Problem 4 below, this "advantage" is never fully realized.
Problem 1: Transport parameters
The problems associated with the effective internal diffusivity and thermal conductivity described in the previous posting apply to this method also.
Problem 2: Multiple reactions
Nearly all theoretical developments for effectiveness factor relationships are based on single reactions. I may be wrong, but I think the effectiveness factor concept breaks down for multiple reactions.
Problem 3: Complex kinetics
Analytical expressions for effectiveness factors are available for special cases such as single reactions that are n th order in a single reactant, or isothermal pellets. However, Hougen-Watson type rate expressions and expressions with multiple reactants do not in general have analytical expressions. The effectiveness factor plots for such reactions (e.g. Carberry, Ch. 9) are produced by numerical integration of the material and energy balances for the pellet and film. Thus, we are back to the method in the 12/13/2013 posting.
Problem 4: The non-observable "observable"
Many effectiveness factor relationships are in terms of an "observable" dimensionless reaction rate. This development can be very useful in calculating the effectiveness factor based on a measured (observed) rate in a laboratory reactor. However, in a reactor design model, the "observable" rate for the pellet is not known. Only the rate based on the bulk fluid variables is known prior to computation of the effectiveness factor.
Problem 5: Iterations required
As a result of Problem 4, iteration is required to obtain the effectiveness factor and the true reaction rate in a reactor design model. If the reaction case has an analytical expression for the effectiveness factor, these iterations will not require repeated solution of the intrapellet ODEs.
Conclusion: Effectiveness factors are overrated
I have nine books that deal with reactors, kinetic analysis, and reactor modeling and they all include discussions of effectiveness factors. This puzzles me because I have never found them particularly useful for the reasons above. Is there a reason for the attention they receive?
A possible use for effectiveness factors in special cases is for examination of the significance of resistances in laboratory data. However, for the film resistance, the gradients can be easily computed without using effectiveness factors.
There is one use for effectiveness factors. They can be used in plots to demonstrate the effects of catalyst activity, temperature, and mass and heat transfer parameters on the reaction rate. I have benefitted from these plots, as you will discover in the next posting. Thus, for me, effectiveness factors are a useful tool for demonstrating concepts in a reactor engineering course or book, but they are not useful for reactor modeling. In some cases, the authors of the books I mentioned agree with my position and they recommend the approach in the next posting. However, that is not often the case.
I would be interested in hearing from practicing engineers that use effectiveness factors in their modeling approach. Maybe I have something to learn. You can leave a comment on the blog or send a private message using the contact form on this website.
Carberry, J.J., Chemical and Catalytic Reaction Engineering, Dover (2001)