A finite element simulation has been used in order to study the partition chromatography process of one species between an aqueous mobile phase and an organic stationary phase located at the bottom of a rectangular microchannel. The transient model incorporates convection--diffusion of the species in the water phase coupled to the diffusion in the stationary organic phase by the way of the partition kinetics at the interface. The time evolution of the injected species concentration is analyzed versus the velocity of the mobile phase, the detecting position and the thickness of the stationary phase. The comparison of simulation results with both experimental data and analytical model confirm its validity. These simulations show that thin channels can be used to measure log P of molecules from their retention time. Finally, we have shown how the sample velocity can be optimized for a given geometry of the channel and diffusion coefficient of the species.