There is an epidemic of papers being published that appear to ignore the effect of the molar change in a gas phase reactor. I've tried to determine if there is some common factor among the papers with this error. So far the only thing I've noticed is that most of the publications have not appeared in peer reviewed journals. However, several were graduate research papers which are reviewed by the supervising professor.
The molar change in a fixed bed reactor may be ignored under any of the following conditions:
This error is probably common because reaction rates are usually defined in terms of concentrations or partial pressures. I think this leads some modelers to assume that the mass balance should be in terms of concentrations also. Concentrations may be used, but the velocity has to be adjusted for the extent of reaction(s) and molar change. None of the papers in question mention a variable velocity even though their reaction system involves molar change.
I prefer to use mass fractions as the dependent variables in the mass balances. As I show in my book, this changes the mass balance so the mass flux may be used. Since the mass flux remains constant throughout the reactor, there is no need to explicitly adjust a velocity for molar change. The conversion between mass fractions and molar concentrations is conveniently made within the reaction rate function. The changing weight fraction affects the fluid molecular weight and the fluid density in response to the molar change.
If you see this error in a paper, usually as an error of omission, you need to be cautious in accepting the conclusions in the paper (see Gauglitz, P.A., and E.E. Petersen. “Molar Expansion in Nonisothermal Packed-bed Chemical Reactors.” Chemical Engineering Science 41, no. 4 (January 1986): 757–764. doi:10.1016/0009-2509(86)87155-X).