Laminar flow reactors are frequently used to experimentally study an isolated elementary reaction step as well as chemical kinetic mechanisms of many coupled reactions. This classical method is effective in measuring kinetic rate parameters when the effects of mass diffusion and wall surface reactions can be neglected or accurately assessed. We perform a series of two-dimensional direct numerical simulations to investigate issues related to the operation of this classical apparatus. By utilizing a well-established gas phase kinetic mechanism for moist CO oxidation and a commonly used sub-model for multi-component diffusive transport, we investigate a virtual elementary kinetic experiment. In particular, we extract data from the simulations and evaluate the rate parameters of the reaction CO + OH reversible arrow CO2 + H as one would in an actual experiment. We show that under appropriate operating conditions, the desired elementary reaction rate parameters can be recovered accurately with minimal efforts in analyzing the experimental data. We also demonstrate that two-dimensional simulations can be useful in refining the operating conditions of an experiment to minimize uncertainties in the determined rate parameters. Numerical results confirm that operating conditions that differ from the classical "plug flow" condition can yield more accurate results. Finally, we investigate laminar reactor operating conditions typical of those used in the literature to study reacting systems of many coupled elementary reactions. Using the same CO oxidation mechanism as an example, we show that for oxidation experiments conducted at one atmospheric pressure, the coupling between transport and chemical kinetics results in a highly two-dimensional reacting flow field. Interpreting these results on a one-dimensional basis can lead to significant inaccuracies in the evaluated rate parameters.