We present the results of the numerical investigation of the Soret-induced convection in a ternary liquid mixture consisting of dodecane, isobutylbenzene and tetralin, taken in equal portions. The mixture is placed into a square porous cavity with rigid impermeable boundaries heated from below. The lateral boundaries are adiabatic. The problem under consideration is a model of natural hydrocarbon reservoir with porous medium, and the components of mixture are representatives of the main groups of chemical compounds comprising oil. Due to the thermodiffusion effect, dodecane and isobutylbenzene as the lighter components of this mixture with positive separation ratios are accumulated in the warmer domain of the cavity, and the heavy component, tetralin, is accumulated in the colder domain, which may lead to the development of convection. The calculations are performed for the parameters of porous medium close to the real parameters of oil fields and temperature gradient that correspond to geothermal gradient. They provide data on the temporal evolution of the characteristics of the flow and component separation. We also analyze the onset and development of single-vortex and two-vortex instability modes with the growth of the Rayleigh number Rapor. It is found that at a certain value of the supercriticality, the stationary flow regime is replaced by the oscillatory regime. At even higher values of the Rayleigh number, the chaotic oscillations take place. The transitions between single-vortex and two-vortex flows are also observed. For porosity equal to 0.1, the two oscillatory regimes at different oscillation amplitudes are excited. With the porosity growth, the region of the existence of the oscillatory regimes becomes narrower.