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A three-dimensional model with the laminar flow of an incompressible viscous gas at a steady-state is developed to simulate a urea-SCR system by the SIMPLE algorithm. A porous medium coated by a metal-oxide-based catalyst is considered in this study. The flow field and chemical reactions inside the reactor are calculated simultaneously by a porous medium approach. In a urea-SCR modeling, the gas transport properties exist as parameters in each of the conservation equations. The evaluations of density, diffusion coefficients, viscosities, thermal conductivities and specific heats are required to select the most suitable gas transport properties in a numerical modeling of a multi-component gaseous mixture and chemically reacting flow.