A supercritical vessel (30) for separating dissolved solids from a fluid solution includes a main body (40) defining a separation chamber (48) adapted to contain a fluid solution while the fluid solution is heated to a supercritical temperature so as to produce a supercritical fluid (58) from which dissolved solids precipitate. The vessel (30) further includes a fluid inlet (34) for receiving fluid solution, a fluid outlet (54) for discharging supercritical fluid (58), and a precipitate outlet (50) for discharging precipitated solids (60). The main body (40) is tilted at a tilt angle (Θ) relative to horizontal (P) such that the fluid inlet (34) is positioned vertically higher than the fluid outlet (54) and the precipitate outlet (50), so as to induce movement of the precipitated solids (60) in a downward direction toward the precipitate outlet (50). The fluid inlet (34) may be positioned proximate a first end (42) of the main body (40), and the fluid outlet (54) and precipitate outlet (50) may be positioned
