The displacement of oil by anionic surfactant solutions in oil-wet horizontal capillary tubes is studied. The position of the oil-water interface is recorded with time. The surfactant solution used is a mixture of several different surfactants and co-solvents tailored to produce ultra-low interfacial tension (IFT) for the specific oil used in the study. The surfactant solution results in ultra-low IFT at optimum salinity and room temperature. Several experimental parameters including the capillary tube radius and surfactant solution viscosity are varied to study their effect on the interface speed. Two different models are used to predict the oil-water interface position with time. In the first model, it is assumed that the IFT is constant and ultra-low throughout the experiments. The second model involves change of wettability and IFT by adsorption of surfactant molecules to the oil-water interface and the solid surface. Comparing the predictions to the experimental results, it is observed that the second model provides a better match, especially for smaller capillary tubes. The model is then used to predict the imbibition rate for very small capillary tubes, which have equivalent permeability close to oil reservoirs. The results show that the oil displacement rate is limited by the rate of diffusion of surfactants to the interface.