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A simple capillary model of free spontaneous imbibition and waterflood is introduced and used to interpret the ‘complete’ capillary number CA for immiscible displacement in porous media. The ‘complete’ capillary number is applied to characterize saturation profile histories obtained in sandpacks. Its value is equal to 1 in free spontaneous imbibition, and in a waterflood it is equal to the ratio of the water injection rate to the initial rate of free spontaneous imbibition. In situ saturation profiles in waterfloods in sandpacks at 1:1 viscosity ratio were determined by light transmission measurement. For CA ≪ 1 capillary forces controlled and the saturation rose practically uniformly along the entire length of the model from the initial connate water saturation to the final value, corresponding to residual oil saturation. For CA ≫ 1 viscous forces controlled and there was a step change in saturation from the connate water to the residual oil value, advancing as a piston. At intermediate values of CA the saturation profiles were S-shaped curves. The saturation profile histories in two packs of different lengths of the same sand were identical, within experimental error, at the same values of CA in the two packs, if plotted against normalized distance coordinates. The saturation profile histories measured in packs of the same length of two very different sands A and B were found to be similar for values of CA in the ratio (CA)B/(CA)A ≈ 5, for all values of CA.