There are number of effects that distinguish multi-component gas diffusion from binary diffusion. According to the analysis of existing works, convective instability occurs in some systems with significantly different diffusion coefficients and specific geometric and thermophysical properties. By analyzing the stability of the system, it is possible to determine the parameters that can cause transition from diffusive state to convective one. However, this method does not allow to consider the dynamics of the process to characterize the development of convective flows in three-component systems and to assess the influence of the diffusion channel size on the occurrence of concentration gravitational convection. The paper considers the application of mathematical model implementing the method of splitting by physical parameters to describe the occurrence of convective flows. The concentration fields of gas with the highest molecular mass at different moments of time are numerically calculated.