Wetting front dynamics in an isotropic porous medium

Abstract

A new approach to the modelling of wetting fronts in porous media on the Darcy scale is developed, based on considering the types (modes) of motion the menisci go through on the pore scale. This approach is illustrated using a simple model case of imbibition of a viscous incompressible liquid into an isotropic porous matrix with two modes of motion for the menisci, the wetting mode and the threshold mode. The latter makes it necessary to introduce an essentially new technique of conjugate problems that allows one to link threshold phenomena on the pore scale with the motion on the Darcy scale. The developed approach (a) makes room for incorporating the actual physics of wetting on the pore scale, (b) brings in the physics associated with pore-scale thresholds, which determine when sections of the wetting front will be brought to a halt (pinned), and, importantly, (c) provides a regular framework for constructing models of increasing complexity.

Mechanism of anomalously increased oil displacement with aqueous viscoelastic polymer solutions

“…In either trapping scenario, it should be expected that fluctuations in the aqueous flow field will give rise to additional stress fluctuations which, if large enough, will initiate either displacement of menisci though constrictions or movement of contact lines [23]. Those displacements or movements cause trapped phase mobilisation, and hence oil desaturation, at lower capillary numbers than expected through consideration of the steady state pressure gradient generated by steady viscoelastic flow alone.…”

Darcy's law for two‐dimensional flows: Singularities at corners and a new class of models

“…14 Although the porous medium here occupies only a half-space, the flow entering it normally to its boundary has to turn around as this boundary is a streamline, so that in the porous medium one effectively has a flow round a corner. One has a similar situation once the wetting front propagating through a porous medium fragment as one section of it is brought to a halt, for example, as a result of it being stuck in the threshold mode of motion, 15 while the neighboring section continues to move ( Figure 1b). Then, on the Darcy scale, the advancing fluid appears to have a flow domain with a corner with the angle of 3p=2.…”

“…The situation becomes serious when what matters is not an integral but the values of the velocity. This happens, such as when one deals with two-phase flows where in the boundary conditions at the liquid-fluid interface 15,17 involve the velocity itself and not its integral. Then, the singularity in the velocity distribution becomes a major obstacle for the realistic modelling of the propagation of liquid-fluid interfaces in the situations where the flow becomes essentially two-dimensional.…”

“…Now, considering a bent channel of width a with the radius of curvature R of its centerline (Figure 2). Then after simple calculations, we arrive at hui52K ðð hrpi (15) K ðð 5 a 2 4ld…”

Anomalous dynamics of capillary rise in porous media

“…The Darcy equation (3) is written in the form already accounting for gravity with ρ being the density of the liquid, g the gravitational acceleration, z the coordinate directed against gravity, κ the permeability of the porous matrix and µ the liquid's viscosity; the coordinates are represented in terms of the position vector r; hereafter the pressure is measured with respect to the (presumed constant) pressure in the displaced gas. An appropriate starting point for the modelling is the recently developed approach [26] that gives boundary conditions for Laplace's equation for p,…”