Hamdi Tchelepi (University of Stanford, USA). Direct Numerical Simulation of Multiphase Flow at the Pore Scale.

We discuss the shortcomings of Darcy-based formulations and constitutive relations for immiscible multiphase flow and transport in natural porous media, and we argue for a more rigorous connection between the Darcy-based representations and the underlying pore-scale dynamics. The focus is on problems associated with subsurface sequestration of CO2, especially in the long post-injection period. We then discuss the development of Direct Numerical Simulation (DNS) (i.e., Navier-Stokes equations) for two important problems: (1) the contact-line problem associated with immiscible two-phase flow, and (2) the dissolution dynamics associated with miscible flow in complex pore spaces. For the contact-line problem, we describe a level-set method coupled with a thin-film approximation. The applicability of the approach for low capillary numbers is demonstrated. We also discuss the influence of roughness on the propagation dynamics. For the dissolution problem, we describe a Darcy-Brinkman-Stokes (DBS) approach to represent the multiscale interactions. The approach is compared with experimental observations using micro-models. We then describe an upscaling strategy to translate the pore-scale results to an effective `Darcy-scale’ model. Finally, the remaining challenges and open questions associated with DNS of flow and transport at the pore scale are discussed.