Full Morphology Method¶
The Full Morphology Method (FMM) simulates pressure-driven fluid displacement using morphological operations.
The method assumes: - zero capillary number, - strong wettability of the displaced fluid, - immiscible fluids, - a quasi-static process,
such that equilibrium is achieved between consecutive iterations.
The saturation map is generated by sphere intrusion. It is based on the simplified Young–Laplace equation, which assumes cylindrical throats. This equation relates the capillary pressure to the invaded radius:
where $gamma$ is the interfacial tension, $theta$ is the contact angle, and $R$ is the invaded radius.
For a given radius, the algorithm consists of three main steps: erosion, connectivity check and dilation. During the erosion step, voxels within the pore space whose Euclidean Distance Transform (EDT) is greater than or equal to the current radius are identified. These voxels represent candidate sphere centers that the injected fluid can occupy.
From this set, the connectivity check retains only the voxels that are connected to the inlet. This step prevents invasion from occurring within isolated regions in the interior of the domain, ensuring that the displacement process remains physically consistent.
Finally, dilation is applied to this filtered set of sphere centers. Voxels located within a distance equal to the radius from these centers are relabeled as invaded, completing the algorithm for the given radius.
This process can be repeated for a set of decreasing radii, which gives the relation between saturation and pressure. The Young-Laplace equation translates this relation into $P_c$-saturation data, resulting in a capillary curve or MICP (mercury injection capillary curve) depending on the protocol adopted, as described below.
Protocols
The algorithm employed in this routine is adapted from ZABOT and has two protocols: drainage and micp.
The drainage protocol simulates an incompressible displacement with intrusion from a single face, chosen by the user. Because the displaced fluid is incompressible, regions of trapped fluid may remain within the pore space.
Protocol micp invades the sample from all faces, and the displaced fluid is set as compressible. As a result, all pores connected to the exterior are filled with a sufficiently small radius. This protocol mimics a porosimetry experiment, in which mercury is injected in a porous media under vacuum conditions.