Simulation of Multi-Phase Flow Using a Dual Model

We first introduce a dual model of pore spaces that consists of two parts related by duality: a decomposition of the pore space into contractible pore bodies and a pore network that is homotopy equivalent to the pore space. The dual model can be constructed from synthetic pore spaces or 3D images of real pore spaces. It is well-suited to simulate multi-phase flow since, by duality, the elements of the pore network can be equipped with geometric attributes that describe the geometry of the dual pore bodies and pore throats. We then derive rules for multi-phase flow on the pore scale that are based on the geometric attributes of the pore bodies and pore throats. Specifically, we use pore-morphology-based modeling and Lattice-Boltzmann modeling to derive and verify these rules. Finally, the pore network is used to upscale multi-phase flow from the pore scale to the porous medium scale. We also compare our results with experimental data.