Prediction of imbibition from grain-scale interface movement

Processes in porous media governed by capillary forces, such as drainage or imbibition of wetting phase, are of great importance in different branches of soil science, petroleum engineering and hydrology. In this work we describe a new way of modeling imbibition by considering the movement and merger of interfaces at the pore level. The model is based upon a physically consistent dynamic criterion for the imbibition of a single pore originally proposed by Melrose. The approach can be applied to any porous medium whose grain-scale geometry is well characterized, such as stochastic reconstructions and 3D microtomographic images. Here we illustrate it in a simple but physically representative porous medium, the “ideal soil” (a dense random packing of equal spheres). The spatial location of each sphere is accurately known. Delaunay tessellation of the sphere centers defines the location and geometry of each pore throat in the packing. We simulate imbibition as a quasi-static displacement, so that at any stage of the simulation the geometry of menisci in pore throats and of pendular rings at grain contacts can be determined from the Young–Laplace equation. This approach provides a natural and mechanistic way to account for different values of contact angle and different initial conditions (for example, different drainage endpoints). Predicted capillary pressure curves are consistent with experimental data presented in the literature. This provides strong (though indirect) support for the physically consistent dynamic criterion for the imbibition of a single pore. We illustrate two important and non-trivial consequences of the criterion that also agree with experiments: its implications when wettability (value of contact angle) of the medium varies, and its consistency with the Mayer–Stowe–Princen criterion for drainage at the level of individual pores. We then explore novel features of the criterion. For example, the percolation threshold for imbibition is a manifestation of two kinds of accessibility of the wetting phase, rather than one. Another feature is the strong coupling between the criterion and the spatial correlation of pore-level geometric features, which significantly affects the topology and connectivity of the wetting phase.