MATHEMATICAL-MODELING OF DIFFUSION AND REACTION FOR GAS-SOLID CATALYTIC-SYSTEMS WITH COMPLEX-REACTION NETWORKS - NEGATIVE EFFECTIVENESS FACTORS

The concept of effectiveness factor (eta) as a measure of diffusional limitations for gas-solid catalytic reactions has gone a long way since the time of Thiele. Multiple steady states giving rise to multiple values of (eta) for the same bulk conditions, and eta values greater than unity have been widely reported in the literature in the last three decades. In this paper an interesting phenomenon associated with the effectiveness factors (eta) for industrial gas-solid catalytic reactions is reported, that is the possible occurrence of negative values of eta for certain intermediate components. This physically means that diffusional resistance can also reverse the direction of the net production or consumption of intermediate components in consecutive and/or reversible reaction networks. It is shown both numerically and analytically that the results represent real physical phenomenon and not artefacts resulting from numerical problems or model simplifications. Two industrially important reactions are considered, namely, the steam reforming of natural gas which is a highly endothermic reaction and the partial oxidation of O-xylene to phthalic anhydride which is a highly exothermic reaction.