Chemical systems often exhibit dynamics in different time scales owing to fast and slow reactions. Thus deriving models suitable for computation with standard numerical methods is challenging. In this tutorial we present a systematic approach for modeling chemical reaction systems including (known) slow reactions and fast reactions that can be assumed at equilibrium. The presented approach consists of the following steps: (i) identifying an independent set of reactions; (ii) writing the Overall mass balance; (iii) writing a species balance for each species; (iv) writing the species transformation rates as a function of the net reaction rates; (v) introducing a constitutive equation for each reaction (either kinetic rate or equilibrium condition); (vi) performing index reduction of the differential-algebraic-equation (DAE) system. The resulting reduced system can be readily solved with standard DAE integrators. We discuss the number of initial conditions to be specified and illustrate the method through simple examples: methane reforming, Michaelis-Menten reaction and hydrogen-deuterium exchange. (C) 2016 Elsevier Ltd. All rights reserved.