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Towards the deterministic modelling of immiscible flows in porous media: Mesoscale simulations and Experimental verification

Final Report Summary - REAL PORE FLOWS (Towards the deterministic modelling of immiscible flows in porous media: mesoscale simulations and experimental verification)

The REAL PORE FLOWS project focused on the study of pore scale transport phenomena during the isothermal evaporation of volatile hydrocarbons from porous media, as well as the dynamics of non-aqueous phase liquids (NAPLs) during immiscible flows. This was achieved through an integrated approach combining targeted experiments and state-of-the-art modelling tools.

In the case of drying, we performed a series of experiments with glass bead packings saturated by liquid pentane / hexane or heptane in predominantly two-dimensional (2D) glass cells under environmental conditions to study the dynamics of the drying process and identify the major transport mechanisms. Our experimental setup allowed for the monitoring of the bulk liquid and gas phase distribution patterns, as well as the liquid films that form at the pore walls after the invasion of the bulk gas phase.

We were thus able to classify the drying pore space into three distinct regions:

- a far-field completely-wet region, where the pore space is saturated by the bulk liquid hexane;
- a completely dry region, close to side of the medium open to the ambient environment, that contains only hexane vapours; and
- an intermediate region, located between the first two, that is partially saturated by liquid hexane in the form of liquid films at the walls of the pores and by hexane vapours in the central part of the pore space.

Based on our experimental results, we proposed a pore network model that accounts for all major transport mechanisms within the porous medium coupled with mass transfer by diffusion through a mass boundary layer over the external surface of the medium. We showed that in the limit of a gravity-stabilised percolation front (interface between the completely wet and film regions) the medium can be treated as a 1D continuum where analytical solutions to the governing equations are derived. We are thus able to obtain results for the drying rates, the critical saturation and the extent of the film region with respect to the various dimensionless numbers that describe the process; the Bond number, a film-based capillary number and the dimensionless extent of the mass boundary layer.

In the case of NAPLs undergoing immiscible displacement through a permeable porous medium at high capillary numbers, we proposed a convenient lattice Boltzmann algorithm for the solution of the flow problem in stochastically reconstructed porous domains. In a typical configuration, the non-wetting phase flows through the porous medium in the form of blobs under the combined action of capillary, viscous and gravity forces. We found that the process is governed by the dynamical coalescence and breaking up of blobs, that result in two interacting populations of mobile and stranded blobs, that continuously exchange mass between them.

At steady state, when the rates of blob breaking up and coalescing become equal, both populations follow a log-normal size distribution with an average size and cumulative volume that depends strongly on the applied Bond number. At higher Bo numbers, the ratio of mobile to stranded blob saturation increases significantly, as gravity forces overcome capillarity as fluid-fluid interfaces move through pore bodies, and the breaking rate increases, leading to a smaller average blob sizes. Our simulations showed that the transition between single and 2-phase flow occurs when a critical value of the Bond number is applied, and then the mobile blob volume increases non-linearly with Bo until viscous forces become dominant in the system.

Three flow regimes are identified; a single phase Darcy-type regime at low Bond numbers, an non-Darcy 2-phase flow regime at intermediate values of Bo, where the Capillary number scales as Ca Bo2, and a Darcy type 2-phase regime at higher values of Bo. These results are in reasonable agreement with recent experimental and theoretical works.