Viscous fingering and deformation of a miscible circular blob in a rectilinear displacement in porous media

Abstract

The deformation of an initially circular miscible blob in a rectilinear displacement is investigated numerically for porous media when the blob is more viscous than the displacing fluid. We find in the parameter space spanned by the Péclet number and log-mobility ratio the existence of a new lump-shaped instability zone between two distinct regimes of comet and viscous fingering (VF) deformations. The more viscous circular blob is destabilized by VF only over a finite window of log-mobility ratio, contrary to the displacement of a more viscous finite slice with planar interfaces. This difference is attributed to the initial curvature of the miscible blob.

Dynamics of a Highly Viscous Circular Blob in Homogeneous Porous Media

“…For a valid comparison with the Fourier pseudo-spectral simulations [13], we use a mapped mesh but customize the elemental size by fixing the minimum and maximum size of the elements as ∆e (see Table 1). This results in a uniform-sized mapped mesh and helps to validate the role of curvature in triggering the instability, as no disturbance is given at the interface.…”

“…Its wide applicabilities, e.g., enhanced oil recovery [1], CO 2 sequestration [2], chromatographic separation [3,4], contaminant transport in aquifers [5], mixing in low-Reynolds number flow [6], intrinsic characteristics of nonlinear dynamics and pattern formation have fascinated active theoretical, numerical [6][7][8][9][10][11][12][13], and experimental [14] researchers for more than half a decade. Both rectilinear and radial displacements have been investigated rigorously and have their own significance that can be investigated independently as well as comparatively.…”

“…In many situations, e.g., aquifers, the contaminant can be of an arbitrary shape and miscible to the ambient fluid [15]. When the underlying fluids are miscible to each other, the finger-like patterns that develop at the fluid-fluid interface depend, to a great extent, on the shape of the interface [13], viscosity contrast [1], and diffusion rate [16]. As a consequence, mixing, spreading, and breakthrough time alter greatly [6,13,15].…”

“…When the underlying fluids are miscible to each other, the finger-like patterns that develop at the fluid-fluid interface depend, to a great extent, on the shape of the interface [13], viscosity contrast [1], and diffusion rate [16]. As a consequence, mixing, spreading, and breakthrough time alter greatly [6,13,15]. Pramanik et al used the Fourier pseudospectral method to capture the dynamics of a more viscous blob in a homogeneous porous medium [13], and the results are summarized in the R-Pe parameter plane.…”

“…As a consequence, mixing, spreading, and breakthrough time alter greatly [6,13,15]. Pramanik et al used the Fourier pseudospectral method to capture the dynamics of a more viscous blob in a homogeneous porous medium [13], and the results are summarized in the R-Pe parameter plane. Here, R is the log-mobility ratio and Pe is the Péclet…”