Nonuniform Collective Dissolution of Bubbles in Regular Pore Networks

Abstract

Understanding the evolution of solute concentration gradients underpins the prediction of porous media processes limited by mass transfer. Here, we present the development of a mathematical model that describes the dissolution of spherical bubbles in two-dimensional regular pore networks. The model is solved numerically for lattices with up to 169 bubbles by evaluating the role of pore network connectivity, vacant lattice sites and the initial bubble size distribution. In dense lattices, diffusive shielding prolongs the average dissolution time of the lattice, and the strength of the phenomenon depends on the network connectivity. The extension of the final dissolution time relative to the unbounded (bulk) case follows the power-law function, $${B^k/\ell }$$ B k / ℓ , where the constant $$\ell$$ ℓ is the inter-bubble spacing, B is the number of bubbles, and the exponent k depends on the network connectivity. The solute concentration field is both the consequence and a factor affecting bubble dissolution or growth. The geometry of the pore network perturbs the inward propagation of the dissolution front and can generate vacant sites within the bubble lattice. This effect is enhanced by increasing the lattice size and decreasing the network connectivity, yielding strongly nonuniform solute concentration fields. Sparse bubble lattices experience decreased collective effects, but they feature a more complex evolution, because the solute concentration field is nonuniform from the outset.

Direct Pore-Scale Modeling of Foam Flow through Rough Fractures

“…In pore network modeling approaches, line segments represent transport between neighboring pores and the statistics of their connectivity reveal information about the rate-limiting conductance of large systems . The geometry of the pore space and physical processes are still simplified compared to their original complexity − and the simplification means that the foam changes due to local pore shape or surface roughness changes can be modeled only in an averaged sense. How to appropriately address the dependence of the trapped-gas saturation on various flow conditions in the foam model remains unexplored, especially during transient foam flow in a complex geometry based on three-dimensional (3D) X-ray microtomography images.…”