Numerical simulations of transient porous media thermohaline convection including phase separation into a high-density, high-salinity brine phase and a low-density, low-salinity vapor phase at pressures and temperatures well above the critical point of pure H2O are presented. Using a novel finite element--finite volume (FEFV) solution technique and a new equation of state for the binary NaCl-H2O system, convection of a NaCl-H2O fluid in an open top square box of 4 ¿ 4 km is studied at geologically realistic pressure p, temperature T, and salinity X conditions. In the simulations, the basal temperature and salinity are varied systematically from 200 to 600¿C and from 3.2 to 40 or 60 wt % NaCl, for permeabilities of 10-15 or 10-14 m2 and hydrostatic pressure conditions. Resulting flow patterns are diffusive, steady convective, or oscillatory. Single-phase thermohaline convection occurs at temperatures below 400¿C. Between 400 and 450¿C, phase separation can occur during the buoyant rise of heat and salt if the permeability is high or the salinity low. Above 450¿C, the fluid at the basal boundary is a vapor phase coexisting with a brine phase. In this case, convection is dominated by heat and salt transport during the buoyant rise of vapor. Convection sets in almost instantaneously at these conditions. Above 570¿C, a nearly pure H2O vapor phase coexists with solid salt at the basal boundary. Convection is driven exclusively by the applied temperature gradient. Since fluid properties change by highly nonlinear functions of p, T, and X, parameters such as the Rayleigh number and buoyancy ratio, which are classically used to quantify the different regimes of thermohaline convection, are not meaningful in this context. This implies that parametric studies that make use of the Boussinesq approximation and assume incompressibility are not representative of thermohaline convection in geologic environments. We use the concept of a local Rayleigh number and a fluxibility parameter to provide a better insight into the onset and evolution of thermohaline convective systems.