Impact of viscous fingering and permeability heterogeneity on fluid mixing in porous media

Abstract

Fluid mixing plays a fundamental role in many natural and engineered processes, including groundwater flows in porous media, enhanced oil recovery, and microfluidic lab-on-a-chip systems. Recent developments have explored the effect of viscosity contrast on mixing, suggesting that the unstable displacement of fluids with different viscosities, or viscous fingering, provides a powerful mechanism to increase fluid-fluid interfacial area and enhance mixing. However, existing studies have not incorporated the effect of medium heterogeneity on the mixing rate. Here, we characterize the evolution of mixing between two fluids of different viscosity in heterogeneous porous media. We focus on a practical scenario of divergent-convergent flow in a quarter five spot geometry prototypical of well-driven groundwater flows. We study by means of numerical simulations the impact of permeability heterogeneity and viscosity contrast on the breakthrough curves and mixing efficiency, and we rationalize the nontrivial mixing behavior that emerges from the competition between the creation of fluid-fluid interfacial area and channeling.

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

“…Understanding displacement and mixing of fluids in porous media (Jha, CuetoFelgueroso & Juanes 2011a;Nicolaides et al 2015) is an active area of research devoted to characterizing industrial and environmental processes, such as oil recovery (Homsy 1987), pollution remediation (Welty, Kane & Kauffman 2003), CO 2 sequestration (Ott, Berg & Oedai 2012;Huppert & Neufeld 2014) and chromatographic separation (De Wit, Bertho & Martin 2005), to name a few. The mixing and dispersion of one fluid within another one can usually be significantly increased by hydrodynamic instabilities such as viscous fingering (VF).…”

“…† Email address for correspondence: satyajit.math16@gmail.com c Cambridge University Press 2015 Several articles have been devoted to analysing miscible VF of either a single interface between two semi-infinite regions (Homsy 1987;Tan & Homsy 1988;Pramanik & Mishra 2013 or a finite-size rectangular plug in a rectilinear displacement De Wit et al 2005;Mishra, Martin & De Wit 2008). However, in numerous cases, a fluid sample of arbitrary initial geometry can be entrained by a carrier fluid of different viscosity and may deform because of dispersion or VF upon displacement (Nicolaides et al 2015). This is the case for instance in localized pollution events in soils where underground flows may entrain either more or less viscous spills of finite spatial extent.…”

“…De Wit & Homsy (1999) showed that an elliptic deformation and no fingering is observed for less viscous circular samples if the blob is too small and also investigated the influence of reactions on the dynamics. Nicolaides et al (2015) investigated the impact of VF and heterogeneity of permeability on fluid mixing of finite-size samples, showing that breakthrough times and mixing efficiency depend on the relative viscosity of the sample. Maes et al (2010) analysed experimentally in a horizontal Hele-Shaw cell the dispersion and miscible VF of an initially circular, more viscous sample within a rectilinear displacement.…”

Dynamics of a Highly Viscous Circular Blob in Homogeneous Porous Media

“…The majority of the studies are focused on the case when the defending fluid is separated from the invading fluid by a flat interface. 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].…”

“…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.…”