Process and device for separating liquid from a multiphase mixture

A process for separating liquid from a multiphase mixture contained in a vessel and comprising solid particles and at least one liquid phase forming together at least one suspension, and a gas phase flowing upwards through the suspension such that a gas-lift effect occurs inside the vessel, in which at least part of the multiphase mixture, optionally at least partially degassed, is circulated through at least one cross-flow filter located outside the vessel, therefore separating said part of the multiphase mixture into a filtered liquid and a concentrate, wherein said part of the multiphase mixture circulates through the cross-flow filter using the natural recirculation provided by the gas-lift effect occurring inside the vessel, and wherein the tangential velocity of said multiphase mixture, continuously impoverished in filtered liquid, along a filter medium is of from 400 to 2000 times the trans-medium velocity of the filtered liquid through the filter medium.