Abstract: A process involves placing a solid sample imbibed or saturated with a first fluid (for example water) in a closed chamber; injecting, via pressure means, another liquid under pressure at a first end of the chamber to drain or expel the first liquid from the sample; and sweeping an opposite end of the chamber with a low pressure liquid, circulated by pumping means, which carries or discharges the drained first liquid outside the chamber. A device for conducting the process includes measuring means for determining the pressure and saturation variations of the sample at at least one point of the length of the sample in the chamber, the amount of fluid discharged from the chamber, and the electrical resistivity of the sample. A progressive variation of the flow of the liquid injected allows complete draining and imbibition cycles to be performed while setting up capillary pressure variation curves and calculating relative permeabilities, without touching the sample.