In a deasphalting process wherein the deasphalted oil is separated from the deasphalting solvent, the invention consists of performing said separation in at least two separate steps, differing by their temperatures, and of recovering heat from the deasphalted oil. The oil to be deasphalted (26) passes through an extractor (1), then through heat recuperators (3) and (4). The oil-solvent separation is achieved in two steps (5) and (11), under supercritical conditions, at different temperatures. The process has the particular advantage of saving power since external heat is provided (10) to only part of the charge.
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