Gas Solid Reaction (Julian Szekely, James W. Evans, Hong Yong Sohn) is a good reference for gas solid reaction. In the section of chemical reaction control, that I have attached here, the equation converted to dimensionless form to calculate equation X according to t.
for calculate this equation, I must convert it to dimensionless form or there is another solution too?
A(g) + bB(s) ___> cC(g)
The section that you cite is standard reaction models, I recommend Levenspiel's text for a better approach. However, the issue with gas / solid reactions is always to calculate the diffusion component, the reaction step and internal pore diffusion. Two phase models are never easily analysed and I would not use dimensional analysis forms as they reduce the visibility of the stages. Large particles react initially under diffusion control then pore transport and reaction rates become important. Simultaneously, the temperature of the reacting particle alters. There are many papers and texts to examine!
You've taken a standard approach to a gas-solid reaction. Gasification is much more complex involving equilibrium reactions, the CHONS composition of the material to be gasified, taking account of tar formation, char formation and the gasification temperature. You need to look at papers on gasification to understand the overall process. Countless papers and reports on this topic and if you look even some free Gibbs free energy models for the basic reactions. I developed a Gibbs Free Energy model taking into account the gasification agent (O2, CO2, H2O, N2), its composition and temperature, tar formation and composition of the tars and char formation in the elemental balance and several reactions to model the final equilibrium gas composition. It takes time to set this sort of model up, but its more accurate.
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