A method is proposed to simulate reactive flow, fully taking into account the effect of the reactions on the flow. Operator splitting is used to separate the computation of convection and reaction. A fast solver for mildly stiff ordinary differential equations and parallelization of the reaction term evaluation have been implemented to reduce the CPU time. The proposed method is applied to the steady-state, two-phase gas-solid simulation of a Fluid Catalytic Cracking riser reactor. A relatively simple kinetic model with four lumped components is used to demonstrate the feasibility of the method. The results show that the method is able to handle reactive flow with significant feedback of the reactions on the flow. (C) 2009 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.