Stable and unstable miscible displacements in layered porous media

Abstract

The effect of permeability heterogeneities and viscosity variations on miscible displacement processes in porous media is examined using high-resolution numerical simulations and reduced theoretical modelling. The planar injection of one fluid into a fluid-saturated, two-dimensional porous medium with a permeability that varies perpendicular to the flow direction is studied. Three cases are considered, in which the injected fluid is equally viscous, more viscous or less viscous than the ambient fluid. In general it is found that the flow in each case evolves through three regimes. At early times, the flow exhibits the concentration evolves diffusively, independent of both the permeability structure and the viscosity ratio. At intermediate times, the flow exhibits different dynamics including channelling and fingering, depending on whether the injected fluid is more or less viscous than the ambient fluid, and depending on the relative magnitude of the viscosity and permeability variations. Finally, at late times, the flow becomes independent of the viscosity ratio and dominated by shear-enhanced (Taylor) dispersion. For each of the regimes identified above, we develop reduced-order models for the evolution of the transversely averaged concentration and compare them to the full numerical simulations.

Upscaling multiphase viscous-to-capillary transitions in heterogeneous porous media

“…The flow of immiscible fluids in heterogeneous porous media has widespread applications in energy and the environment. Nearly all subsurface rocks have a significantly heterogeneous structure, often in the form of sedimentary layers, and it is well known that such heterogeneities play an important role in the resultant flow properties (Corey & Rathjens 1956;Jackson et al 2018;Nijjer, Hewitt & Neufeld 2019). One very topical application is the geological storage, or sequestration, of carbon dioxide (Bickle 2009;Huppert & Neufeld 2014).…”

“…Additionally, in pressure driven flows, heterogeneities result in the unstable displacement of phases (so long as capillary forces are large enough to overcome the driving pressure), and fingering (Dawe, Wheat & Bidner 1992;Dawe, Caruana & Grattoni 2011). Hence, an analogy can be drawn between the capillary-driven mixing of immiscible fluids, and the classic diffusion/dispersion-driven mixing of miscible fluids (Tchelepi et al 1993;Nijjer et al 2019). However, for this study we focus on the case of immiscible fluid flow in a layered porous medium.…”

A new flow-kinematics-based model for time-dependent effective dispersion in mixing-limited reactions

“…and Lx and Ly are the lengths of the domain in the x and ỹ coordinate directions. Equation 2 describes either the reactive transport problem in a free fluid, with D0 the diffusion coefficient, or reactive transport problem in porous media at the Darcy scale, in which case D0 is the dispersion coefficient, taken here as a constant for simplicity (Le Bandopadhyay et al, 2018;Wright et al, 2017;Nijjer et al, 2019). Note that in the latter case, perfect mixing is assumed at the support scale.…”

Scaling Analysis of Two‐Phase Flow in Fractal Permeability Fields

“…This finding is similar to the results of scaling analysis for miscible displacements reported by Sajjadi and Azaiez (2013). Despite recent advances in understanding the impact of heterogeneity on fluid mixing for miscible or partially miscible flows (Amooie et al, 2017; Connolly & Johns, 2016; Cusini et al, 2019; Nicolaides et al, 2015; Nijjer et al, 2019), few studies have explored self‐similarity of the evolution of mixing for both miscible and immiscible flows in fractal permeability fields.…”