| a | Ratio of the packing surface area to the reactor volume (m−1) |
| A(g) | Feed compound |
| CA | Concentration of species A (mol/m3) |
| Ci | Concentration of species i (mol/m3) |
| Ci,in | Initial concentration of species i |
| Ci,o | Inlet concentration of species i (mol/m3) |
| Ci,out | Concentration of species i at the outlet (mol/m3) |
| CR | Concentration of species R (mol/m3) |
| CS | Concentration of species S (mol/m3) |
| CP | Surface concentration of deactivated sites (mol/m2) |
| d | Reactor diameter (m) |
| DA | Dispersion coefficient for compound A (m2/s) |
| Di | Dispersion coefficient for compound i (m2/s) |
| DR | Dispersion coefficient for compound R (m2/s) |
| DS | Dispersion coefficient for compound S (m2/s) |
| i | Species A, R, S, or P. |
| k1 | Reaction rate coefficient of the first forward reaction (m2·s−1·mol−1) |
| k1r | Reaction rate coefficient of the first reverse reaction (m2·s−1·mol−1) |
| k2 | Reaction rate coefficient of the second forward reaction (s−1) |
| k2r | Reaction rate coefficient of the second reverse reaction (s−1) |
| k3 | Reaction rate coefficient of the third forward reaction (m2·s−1·mol−1) |
| k3r | Reaction rate coefficient of the third reverse reaction (s−1) |
| L | Reactor length (m) |
| m | Parameter in catalyst distribution equation |
| P(s) | Undesirable deactivating end product |
| R(g) | Desirable product |
| S(g) | Undesirable product |
| t | Time (s) |
| υ | Fluid velocity (m/s) |
| x | Location along the packed bed (m) |
| Z | Surface concentration of catalytic sites (mol/m2) |
| Z0 | Value of Z for uniform catalyst distribution (mol/m2) |