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Nonlinear Darcy flow dynamics during ganglia stranding and mobilization in heterogeneous porous domains

Giotis Andreas, Dollari A., Kainourgiakis Μ.Ε., Salin D., Talon L.

Πλήρης Εγγραφή

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Περίληψη

We study the steady-state displacement of nonwetting liquid ganglia during immiscible two-phase flows in realistic, stochastically reconstructed porous domains, focusing primarily on the nonlinear Darcian regime that arises when capillary to viscous (or gravity) forces become comparable at the pore scale. During this process, the ganglia undergo a continuous cycle of dynamic coalescence and fragmentation, resulting in two populations (a mobile and a stranded one) with distinct structural and rheological features, that continuously exchange mass between them under “stationary” flow conditions. We use a lattice Boltzmann model for the explicit solution of flow and interfacial dynamics at the pore scale driven by a constant body force field (i.e., gravity), and a periodic clustering algorithm for the identification and classification of mobile and stranded ganglia. Our simulation results reveal that an increase in the applied Bond number (Bo) leads to a gradual mobilization of the initially stranded ganglia population, resulting in a power-law scaling with an exponent being a strong function of the nonwetting-phase saturation. The linear Darcian scaling for the nonwetting phase is progressively restored at high Bo, while the wetting phase appears to maintain a linear Darcian scaling over the entire range of Bo values. We show that the mobilization process is characterized by a critical Bo, which is independent of saturation, above which new flow paths are created, in a similar fashion as a yield-stress fluid flows in a porous medium. Our results also offer a unique insight on the distinct structural characteristics of the mobile and stranded populations (e.g., ganglia size and length), as well as on their velocity and orientation with respect to their size.

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