The regimes of fluid displacement from a formation consisting of interleaving layers of different permeability are studied within the framework of the cross-sectional problem of flow through a porous medium. The method for evaluating the efficiency of displacement from layers is developed by modeling the flow in an equivalent homogeneous porous medium within assuming a large number of layers. It is shown that the displacement process is characterized by five similarity criteria and those values for the equivalent formation and individual layers are different. Therefore, different regimes of fluid displacement are realized in an equivalent medium and in separate permeable layers. The effect of capillary pressure and fluids viscosities on the sweep efficiency is investigated. The results of the present study may be useful in the oil and gas industry in estimating the efficiency of various field development methods.
Andreeva et al. (2025) studied this question.