In situ Adaptive Tabulation algorithm is applied to efficiently solve the chemical substep in the context of the simulation of heterogeneous reactors. A numerical strategyspecifically conceived for unsteady simulation of catalytic deviceshas been developed and interfaced, in the context of the operator splitting technique, with the solution of the chemical substep, which requires 70-90% of the total computational time. The algorithm performances have been illustrated by considering a single channel of a honeycomb reactor operating the catalytic partial oxidation of methane and a methane steam reforming packed bed reactor. The application of in situ adaptive tabulation resulted in a speed-up of the chemical substep up to approximate to 500 times with an overall speed-up of approximate to 5-15 times for the whole simulation. Such reduction of the computation effort is key to make affordable fundamental computational fluid dynamics simulations of chemical reactors at a level of complexity relevant to technological applications. (c) 2016 American Institute of Chemical Engineers AIChE J, 63: 95-104, 2017