A multicomponent one-dimensional dynamic mathematical model for the reacting slurry systems with a change in gas flow rate due to the chemical reaction is developed. A change in gas flow rate caused by the chemical reaction is modeled using the overall gas mass balance. Thus, all relevant chemical species are included in the model. Linear first-order reaction kinetics is considered. The gas phase is modeled using the two-bubble class hydrodynamic model. The interaction between small and large bubbles is included as the cross-flow. Suspension of liquid and solids is assumed to form a pseudo slurry phase. Back-mixing in all of the three considered phases, small bubbles, large bubbles and slurry, is accounted for using the axial dispersion model (ADM). Energy balance of the slurry phase is also included in the model. The developed general reacting slurry system model is used to simulate the performance of the Fischer-Tropsch (FT) slurry bubble column (SBC) reactor. Performance of the developed ADM based model is compared with the reactor scale models in which the reactor back-mixing is represented using some combination of the two limiting ideal reactor models of, complete stirred or plug flow. (C) 2003 Elsevier Science B.V. All rights reserved.