We performed Direct Numerical Simulation (DNS) of an exothermic gas-phase reaction under laminar flow condition in a 2-D packed bed reactor with random distribution of cylindrical particles of 2.9 mm diameter. The reaction used in this work is of Arrhenius type between Ethylene and Oxygen with Ethylene Oxide as a product. The gas flows into the reactor as a mixture of Ethylene and Oxygen. The simulations show that there is a region in the reactor with high reaction rate where basically all heat is produced. There is a large temperature gradient in this region in the radial direction and in the other parts of the reactor there is no temperature gradient in the radial direction. There is not a big convection term in the radial direction in the modeled packed bed. This rather small convection in the radial direction is the result of the arrangement of the particles. CFD simulations provide useful data on the flow field and radial convective term inside the packed beds which can be used for the improvement and further optimization on the design and operation of the packed bed reactors. (C) 2013 Elsevier Ltd. All rights reserved.