Oil displacement from water-wet fractured reservoirs by spontaneous imbibition leads to the entrapment of a considerable fraction of oil. Understanding the entrapment phenomenon and mechanism is significant for designing recovery processes. In this study, experiments of pure co-current spontaneous imbibition are conducted with packed columns. The packed columns are filled with either glass beads or quartz sands and saturated completely with oil or gas. The geometry of the glass bead is regular with a narrow size distribution. In contrast, the geometry of the quartz sand is irregular with a wide size distribution. In experiments, one end of the packed column is in contact with brine and the other end is in contact with oil or gas. Both the oil/gas production and the advancing distance of the imbibition front versus imbibition time are measured. The relative permeability to brine behind the imbibition front and the capillary pressure at the imbibition front are estimated as well. For glass-bead-packed columns, the magnitude of entrapment and the relative permeability to brine behind the imbibition front have no significant variation with the increase in oil/gas viscosity. However, for quartz-sand-packed columns, the magnitude of entrapment increases rapidly and the relative permeability decreases rapidly with the increase in oil/gas viscosity. The reason for this behavior is the difference in the pore size distribution of the packed columns. The capillary pressure at the imbibition front estimated by the piston-like model is always smaller than that measured under restricted counter-current imbibition. This work will help us better understand the process of the spontaneous imbibition, which is significant for the oil/gas recovery in fractured reservoirs.