The Claus process is used extensively in the industry to recover elementary sulfur from hydrogen sulfide present in gases from refineries and natural gases. It involves thermal oxidation of hydrogen sulfide and its reaction with sulfur dioxide to form sulfur and water vapor. In this study, we used a computational fluid dynamics (CFD) tool to build a three-dimensional finite-element model that describes the detailed flow fields and chemical reactions for two different industrial cases. The first case consisted of three Claus industrial reactors in series (R1A, R1B and R1C) and the second case consists of two Claus industrial reactors in series (R2A and R2B), each having one inlet and one outlet with different operating temperatures and feed concentrations. The flow behavior and the outlet compositions of the partially packed Claus reactors at temperature range of 458-570 K, with varying SO2 and H2S feed concentrations are presented and discussed. We present two sets of empirical kinetic rate equations, both of which, give good agreement with the available industrial data. (C) 2016 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.