Three-dimensional buoyancy-driven flow along a fractured boundary

Abstract

We describe the steady motion of a buoyant fluid migrating through a porous layer along a plane, inclined boundary from a localized well. We first describe the transition from an approximately radially spreading current near the source, to a flow which runs upslope, as it spreads in the cross-slope direction. Using the model, we predict the maximum injection rate for which, near the source, the flow does not fully flood the porous layer. We then account for the presence of a fracture on the boundary through which some of the flow can drain upwards, and calculate how the current is partitioned between the fraction that drains and the remainder which continues running upslope. The fraction that drains increases with the permeability of the fracture and also with the distance from the source, as the flow slows and has more time to drain. We introduce new scalings and some asymptotic solutions to describe both the flow near the fracture and the three-dimensional surface of the injected fluid as it spreads upslope. We extend the model to the case of multiple fractures, so that the current eventually drains away as it flows over successive fractures. We calculate the shape of the region that is invaded by the buoyant fluid and we show that this flow, draining through a series of discrete fractures, may be approximated by a flow that continuously drains through its upper boundary. The effective small uniform permeability of this upper boundary is given by k b ≈ k f dx/D F , where k f dx is the integral of permeability across the width of the fracture and D F is the inter-fracture spacing. Finally, we discuss the relevance of the work for CO 2 sequestration and we compare some simple predictions of the plume shape, volume and volume flux derived from our model with data from the Sleipner project, Norway for the plume of CO 2 which developed in Horizon 1.

Buoyant convection in heterogeneous porous media with an inclined permeability jump: an experimental investigation of filling box-type flows

“…In contrast to porous media plumes, more attention has been devoted to porous media gravity currents, whether these flow along boundaries are categorized as impermeable (Huppert & Woods 1995; Vella & Huppert 2006), semi-impermeable (Vella et al. 2011; Farcas & Woods 2013) or permeable (Pritchard, Woods & Hogg 2001; Farcas & Woods 2009; Goda & Sato 2011). As regards the latter two scenarios, and assuming a gravity current of dense fluid, studies have sought to characterize the dynamical impact of basal draining be this owing to a point sink or fissure (Neufeld, Vella & Huppert 2009; Neufeld et al.…”

“…2011; Vella et al. 2011; Farcas & Woods 2013), edge drainage (Hesse & Woods 2010; Rayward-Smith & Woods 2011; Zheng et al. 2013; Hagemann, Panfilov & Ganzer 2016) or distributed leakage (Pritchard et al.…”

Buoyancy-driven plumes in a layered porous medium

“…A number of authors have considered the role of layers of differing permeability in the context of laterally spreading immiscible gravity currents (Pritchard, Woods & Hogg 2001;Pritchard & Hogg 2002;Zheng et al 2013), while the impact of leakage through discrete fractures or faults on such currents has also been widely studied (Pritchard 2007;Neufeld et al 2011;Farcas & Woods 2013;Pegler, Huppert & Neufeld 2014). Neufeld & Huppert (2009) focussed explicitly on the role of a thin, low-permeability horizontal layer on the dynamics of a spreading immiscible gravity current, and derived a simple model for the spread and rise of a buoyant fluid across a series of such layers.…”

Dispersion and dissolution of a buoyancy driven gas plume in a layered permeable rock

“…However, if a repository were to be located in a different geological formation, for example, composed of very low permeability hard rock, the processes controlling the transport of gas may be different. Indeed, hard rock formations may include a network of fractures of low permeability and very low porosity which can provide relatively high permeability, although low porosity pathways for flow [ Bear , ; Farcas and Woods , ]. With such formations, any gas that migrates from the GDF repository will enter the host rock and surrounding geology, and may rise under buoyancy.…”