“…The study of multiphase flow in porous rocks is related to a broad field with important challenges [ Bruce and Klute , ; Richards , ; Sahimi , ; Singh , ; Washburn , ]. The investigation of water imbibition in porous rocks is important in a variety of contexts, including the recovery of hydrocarbons from ultralow permeability reservoirs [ Akin and Kovscek , ; Karpyn et al ., ; Li and Horne , , ], the disposal of nuclear waste [ Hunt and Tompson , ; Sahimi , ; Tompson et al ., ], the sequestration of CO 2 [ Doster et al ., ; Herring et al ., ], the environmental remediation [ Faybishenko et al ., ], and the protection of buildings and groundwater [ Birdsell et al ., ; Cheng et al ., ; Hall and Hoff , ]. Several nondestructive techniques [ Roels et al ., ], including nuclear magnetic resonance (NMR) or magnetic resonance imaging (MRI) [ Carpenter et al ., ; Leech et al ., ; Pohlmeier et al ., ] and Îł ray attenuation [ Ferguson and Gardner , ; Nielsen , ; Nizovtsev et al ., ], have been applied to probe distributions of water saturation and to study the dynamics of liquid transport in porous materials.…”