An Amott cell is usually done for this. The expelled phase is then collected at the top of the cell and the volume is measured as corresponding to imbibed volume. If you need mass, just apply the density. If you consider gas, then the procedure can be done in a similar way if the system is pressurized and density changes are negligible. You could likely also just keep track of the liquid phase which is of negligible compressibility.
Pål Østebø Andersen thanks for the suggestion. The plan however is to conduct spontaneous imbibition experiments on rock samples (shale) using water. the rock will be immersed in water and its mass will be measured at specified times until such a time when there is no more increase in the mass of the rock. The problem is how to measure the mass of the rock at different times without having to take out the core from the water, as taking it out could affect the results. The experiment will be repeated also under confined pressure.
Such a method could be Nuclear Magnetic Resonance. The NMR signal from the point of view of relaxation can be characterized by the time of spin-spin relaxation T2. Of course, all the water will give a signal. But here at the water that went into the core the value of T2 will be much less than that of the water of volume.
Obviously, the population of the components of water in the core, you can find a lot of water in the core. The signal level is proportional to the mass of the hydrogen-containing liquid. Therefore, registering an increase in the level of the signal in the core, we can tell how much it has collected fluid. To go from signal level to mass, you need to additionally do a calibration.
D.s. Ivanov NMR method is a top notch approach. Please can you give more light on how to convert signal to mass as regards to the imbibition experiment?