Self-similar dynamics of two-phase flows injected into a confined porous layer

Abstract

We study the dynamics of two-phase flows injected into a confined porous layer. A model is derived to describe the evolution of the fluid–fluid interface, where the effective saturation of the injected fluid is zero. The flow is driven by pressure gradients due to injection, the buoyancy due to density contrasts and the interfacial tension between the injected and ambient fluids. The saturation field is then computed after the interface evolution is obtained. The results demonstrate that the flow behaviour evolves from early-time unconfined to late-time confined behaviours. In particular, at early times, the influence of capillary forces drives fluid flow and produces a new self-similar spreading behaviour in the unconfined limit that is distinct from the gravity current solution. At late times, we obtain two new similarity solutions, a modified shock solution and a compound wave solution, in addition to the rarefaction and shock solutions in the sharp-interface limit. A schematic regime diagram is also provided, which summarises all possible similarity solutions and the time transitions between them for the partially saturating flows resulting from fluid injection into a confined porous layer. Three dimensionless control parameters are identified and their influence on the fluid flow is also discussed, including the viscosity ratio, the pore-size distribution and the relative contributions of capillary and buoyancy forces. To underline the relevance of our results, we also briefly describe the implications of the two-phase flow model to the geological storage of $\text{CO}_{2}$, using representative geological parameters from the Sleipner and In Salah sites.

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

“…Whilst there are numerous papers on the Buckley-Leverett problem and its variants (McWhorter & Sunada 1990;Schmid & Geiger 2012;Deng & King 2015;Zheng & Neufeld 2019), there are none which address the transition between the viscous and capillary limits in the case of a heterogeneous medium. In the present study, we use our simplified semi-analytical expressions to address the dynamics of this transition, showing that regions of the aquifer near the injection point (or at early times) lie within the viscous limit, whereas regions far away from the injection point (or at late times) lie within the capillary limit.…”

Upscaling unsaturated flows in vertically heterogeneous porous layers

“…Golding et al. 2011; Golding, Huppert & Neufeld 2017; Zheng & Neufeld 2019). The pressure distribution within the invading and displaced fluids and is then given by where and denote the density of the fluids and is gravitational acceleration.…”

“…Bear 1972; Golding et al. 2011; Zheng & Neufeld 2019) in porous rocks in many situations (see also Zheng & Stone (2022) for a recent review of detailed descriptions of the connection and difference of a series of studies), there is a lack of quantitative descriptions of the pressure signal within a reservoir, which is also an important feature of the flow and is likely more convenient to measure/monitor in the field. The model problem of quasi-steady flows, as sketched in figure 1, also mimics those in rock-core flooding experiments (e.g. Brooks & Corey 1964; Jackson et al.…”

Growth of a fluid-infused patch from droplet drainage into a thin porous layer

“…Buckley & Leverett 1942; Golding et al. 2011; Zheng & Neufeld 2019; Zheng & Stone 2022). Detailed analysis is beyond the scope of the current study and is left for a separate work.…”

“…when the wet patch becomes a combination of both air and the invading fluid (e.g. Buckley & Leverett 1942;Golding et al 2011;Zheng & Neufeld 2019;Zheng & Stone 2022). Detailed analysis is beyond the scope of the current study and is left for a separate work.…”