Partially miscible fluids often exhibit complex behavior. While previous studies have focused on the phase characteristics, the coupled phase equilibrium and transport processes under near-critical/supercritical conditions are not well studied. Here, the binary/ternary phase equilibria of light oil (maltenes)-heavy oil (asphaltenes)-water mixtures, are examined at 25 MPa and 640-660 K. Within this temperature range, three regimes exist in the ternary phase diagram. Next, the mixing of a two-component oil droplet under near-critical/supercritical water is studied numerically. In the simulations, the evolution and final distribution of the oils in the different phases depend on the temperature. The number of distinct zones in space and oil concentration in each zone are consistent with the phase diagram, while the separation process is driven by the heat and mass transfer from the bulk water phase to the oil droplet. The transport of the heavier oil exhibits the so-called "uphill diffusion".