Simulating imbibition process using interacting capillary bundle model with corner flow: The role of capillary morphology

Interacting capillary bundle model has been much attended for modeling of imbibition process, however, how the tube morphology controls the front displacement is not well discussed in the available literature, especially when corner flow of wetting phase is considered. Tubes with non-circular cross-sections were used for simulating imbibition process performed on drained bundle of tubes. Different combinations of the interacting tubes with equilateral triangular, square, and circular cross sections were used in the bundle model to explore the role of capillary morphology. The evolution of displacement front, as well as transient water saturation profiles along the model, were obtained for oil-water two phase system. The results showed that the position of displacement front is controlled by the shape factor of tubes. The cylindrical capillaries present the highest front velocity while the equilateral triangular tubes indicate the lowest one, and the square tubes falls in between. It has been observed when the water injection rate is low, the displacement interfaces in the cylindrical model may advance slower than those of in non-circular tubes, especially at early times. The gravity force was also considered in a vertical interacting bundle model, which has been rarely attended in previous studies, and it is found that the behavior of dimensionless differences between front positions in presence and absence of gravity forces versus dimensionless time is linear. Results of this work help to better understand the role of tube morphology on displacement efficiency in imbibition process when wetting phase is present in the corner of drained angular tubes.