A 2-D pore-network model of the drying of single-component liquids in porous media

The drying of liquid-saturated porous media is typically approached using macroscopic continuum models involving phenomenological coefficients. Insight on these coefficients can be obtained by a more fundamental study at the pore- and pore-network levels. In this paper, we present a model based on a pore-network representation of porous media that accounts for various processes at the pore-scale. These include mass transfer by advection and diffusion in the gas phase, viscous flow in liquid and gas phases and capillary effects at the gas–liquid menisci in the pore throats. We consider isothermal drying in a rectilinear horizontal geometry, with no-flow conditions in all but one boundary, at which a purge gas is injected at a constant rate. The problem is mainly characterized by two dimensionless parameters, a diffusion-based capillary number, Ca , and a Peclet number, Pe , in addition to the various geometrical parameters of the pore network. Results on the evolution of the liquid saturation, the trapped liquid islands and the drying rate are obtained as a function of time and the dimensionless parameters. The importance of trapped liquid islands on screening mass transfer to the continuous liquid cluster is emphasized. For fixed parameter values, the drying front does not in general obey invasion percolation rules. However, as drying progresses, and depending on the relative magnitude of the capillary and Peclet numbers, a transition to a percolation-controlled problem occurs. Effects of capillarity and mass transfer on saturation profiles and drying rates are discussed. The results are then used to discuss upscaling to continuum models.