A generalized model for spontaneous imbibition in a horizontal, multi-layered porous medium

Spontaneous imbibition of a wetting fluid in a homogeneous porous medium follows Washburn's diffusive law. For heterogeneous porous media, the imbibition phenomenon deviates from the diffusive dynamics. A Washburn-like model, developed in the past predicts the imbibition in a three-layered porous medium. In this work, we use experiments to establish the applicability of the model for a horizontal three-layered porous medium. The model is dependent on a scaling law to determine the relative positions of the fronts in the layers. In a multi-layered porous medium, the scaling law cannot predict the relative front advancements. We use a five layered porous medium to develop a strategy and generalize the model for multi-layered porous medium. We show that, the layering pattern, capillary pressure and permeability contrasts among the layers impacts the imbibition behavior significantly and leads to different travel times of the fronts of the invading fluid in the layers.