Sequestration of carbon dioxide in deep saline aquifers has been proposed and investigated as a viable solution to help mitigate carbon emissions from fossil fuels. Much research has been directed at understanding the transitions of supercritical CO2 from being a mobile fluid phase to being trapped by capillarity or dissolved in groundwater; such transitions lead to a reduction in mobility of CO2 and hence in the risk of leakage to the surface. Following injection, buoyant plumes of CO2 migrate updip towards structural traps in the geological strata; however, some of this CO2 may be capillary trapped in pore spaces or dissolved in groundwater en route. Since CO2 saturated groundwater only has a small CO2 concentration, the dissolution of any large, structurally trapped plumes of CO2 may be controlled by the availability of unsaturated groundwater. In an aquifer of finite vertical extent, this may be rate limited by a combination of (i) the background hydrological flow coupled with (ii) the slow lateral exchange of relatively dense, CO2saturated groundwater with unsaturated groundwater. In an inclined aquifer, this may be controlled by the slow along-aquifer component of gravity. Structurally trapped plumes of CO2 may therefore persist for many thousands of years, and, since they are potentially highly mobile, may represent an important contribution to the long term risks associated with CO2 sequestration at particular sites.
 Many studies have explored the flow physics and geochemistry of these different processes, for the purpose of assessing storage efficiency and for informing studies of the risk that CO2 can return to the surface within a timescale of 103–104 years. Particular attention has been given to leakage through faults or seal rock and to capillary trapping [Hesse et al., 2008; MacMinn et al., 2011; Woods and Farcas, 2009] and to dissolution of the CO2 plumes into the groundwater [Riaz et al., 2006; Pau et al., 2009]. In any risk assessment of the long term storage efficiency of CO2, the timing of the transition from a mobile plume of CO2 into a cloud of CO2 dissolved in the groundwater is key, owing to the dramatic reduction in mobility relative to a free CO2 phase. Furthermore, the dissolution process transforms the CO2 from a relatively buoyant fluid to a relatively dense aqueous solution, this impedes the continued upward transport of CO2-saturated water and can trigger highly non-linear convection [Riaz et al., 2006; Pau et al., 2009; Neufeld et al., 2010]. As CO2 diffuses into the undersaturated water, a boundary layer of dense CO2-saturated water develops and breaks up into series of dense convective plumes which mix into the underlying water. A key feature of such convection is the requirement that water unsaturated in CO2is continually re-supplied to the CO2 front, in order that the dissolution can continue. Depending on the water temperature, pressure and dissolved solutes, the water can become saturated with CO2 mass fractions of order a few wt%. It follows that in a structural trap, the vertical extent of the aquifer, H, compared to that of the trapped CO2 plume, h, is key: with a thin trapped CO2 plume and an aquifer of considerable vertical extent, h/H ≪ 0.01, there may be sufficient water directly below the CO2 to enable dissolution, but with a thinner aquifer or deeper trapped plume, h/H > O( 0.01 ), the lateral supply of unsaturated aquifer water may be the rate limiting process for such dissolution, since the fluid directly beneath the plume may become saturated through dissolution of only a small fraction of the CO2 plume.
 The purpose of this paper is to provide some bounds on the dissolution time for such a trapped plume of CO2 in the limit that the lateral supply of aquifer water controls the dissolution. We first provide some estimates for the trapped volume of CO2 in a model anticline, accounting for the role of the background aquifer flow; this provides some constraints on the possible values h/H. We then develop a simple, bounding model for the lateral supply of unsaturated aquifer water to the CO2 plume in order to inform estimates of the minimum dissolution time of a trapped CO2 plume for which h/H > 0.01.
2. Model of Structural Trap
 There are a variety of geometries for structural traps, and the details of calculations of trapped plumes of CO2 will vary with geometry. However, the requirement for lateral supply of groundwater to dissolve the CO2is common to many aquifers of relatively small vertical extent, as described above. In a number of cases, structural traps have the form of approximately two-dimensional fold-type structures. For example, the Hewitt unit located in the Upper Bunter Sandstone in the North Sea offshore UK is about 20 km long, 2 km across and about 40m thick, with an elevation of about 100m above the main Bunter sandstone formation [Cooke-Yarborough and Smith, 2003]. In this work, we develop an approximately two-dimensional model for the flow through such an idealized structural closure, as shown in the schematicFigure 1. We assume there is regional saline aquifer, of thickness H and angle of tilt θ, which includes a laterally extensive structural trap with elevation b(x) relative to the aquifer, in the along slope direction x, given by the idealised form
Here xo is the centre of the trap where the elevation is bo and σ is the scale for the width of the trap. We assume there is a line of wells which produces a laterally extensive plume of CO2 which fills the trap. The maximum volume of injected CO2 per unit length along the trap can be found by calculating the volume at which the CO2plume just begins overflow on the up-dip face of the trap (Figure 1). Note that depending on the regional hydrogeology, the background flow may be migrating up or down dip at the anticline.
 If the anticline is laterally extensive in comparison to the depth, as is typically the case, then the flow is parallel to the boundaries, with the cross-flow pressure gradient being hydrostatic [Yortsos, 1995; Lake, 1996]. In the limit of small interfacial tension between the water and CO2, the capillary transition zone between the CO2 and the water will be thin; for example, Bennion  measured CO2 capillary entry pressures of about 3.5 kPa in some sandstones, implying capillary transition zones of about 0.5–1.0 m thickness. In formations with larger capillary entry pressures, the transition zones may be deeper, >10–100 m, leading to saturation gradients across the main water flow region, and a larger surface area to promote dissolution; however, we focus on the limiting case of a localised transition zone to provide a bound on the trapping volume. In order that the CO2 plume remains static, the dynamic pressure gradient in the water below the transition zone matches the difference between the gradient of the hydrostatic head in the CO2 and the water parallel to the transition zone [Bear, 1972]. Darcy's law then gives the relation for the water transport velocity
where the density of the CO2 is assumed constant, ρc, the pressure is p, the along-slope position is x, the aquifer slope isθ ≪ 1, the permeability is k, g is the acceleration of gravity, and the current has depth h. Given that the water flux (H-h)u = Qa is constant, the depth of the CO2 plume, in the limit of a thin capillary transition zone, is given by the relation
The maximum trapped volume of CO2 may then be estimated by noting that, in the limiting case, at the downstream part of the anticline, the depth of the CO2 plume just falls to zero. The volume of the trapped plume of CO2 may then be found by integrating equation (3) across the anticline from this point back to the upstream end of the plume, at which h = 0 again. Figure 2 illustrates the variation of both the plume shape and the trapped volume with flow rate as a function of the inclination of the aquifer for σ = 2000 m and bo = 100 m (equation (1)); values comparable to the dimensions of typical structural traps in the Bunter Sandstone. In estimating the volume of the trapped CO2, we assume that as the CO2 displaces the original ground water, there is a residual saturation of about 0.25 [Iglauer et al., 2011].
3. Dissolution of the CO2 Plume
 The trapped pockets of CO2 dissolve as water from the aquifer flows past the anticline. The local rate of dissolution of the CO2 plume depends on the rate of convective exchange between the dense CO2laden water and the relatively buoyant unsaturated aquifer water; this convective exchange acts to mix the water across the depth H-h(x). Provided there are no impermeable baffles embedded within the formation [Bickle et al., 2007; Hesse and Woods, 2010], the timescale required for a convective plume to descend across the aquifer scales as (for θ ≪ 1)
where ρ denotes density, and subscripts s and w denote the CO2saturated and original far-field water. Typically, with H ∼ 10–100 m, k ∼ 10–100 mD, andρs − ρω ∼ 10 kg/m3 we estimate τc ∼ 3–300 yrs. In contrast, the time required for the background aquifer flow to migrate a distance L ∼ 3 km along the aquifer is 103–105 yrs for aquifer speeds of order 10−7–10−9 m/s [Ingebritsen et al., 2006]. In high permeability, thinner formations, typical of the Hewitt unit, the convective mixing would therefore be rapid compared to the aquifer flow, and buoyancy driven convection would tend to mix the dissolved CO2 throughout the water directly below the CO2 plume. As the water beneath the CO2 plume becomes saturated in CO2, the maximum CO2 flux removed from the trapped plume, Fc, would become rate limited by the background aquifer flow, Fc = Qa(Cs − Cw) where C is the concentration of the CO2 in the saturated, s, and original, w, aquifer water.
 However, with a sufficiently slow background flow in the aquifer, a buoyant counterflow Qd may develop, as a result of the dense, CO2 saturated water running downslope into the aquifer. If this downflow has depth h1 (Figure 3) it will advance with flux
where the density contrast between the CO2saturated and far-field aquifer water isροβ(Cs − Cw) with β the solutal expansion coefficient of the dissolved CO2 in the water. This produces an additional flow of aquifer fluid to the CO2 plume in addition to the background flow. In the case that the background aquifer flow is upslope (Figure 3a), the total groundwater flux supplied to the plume is
Combining these relations, the dimensionless flux of CO2 saturated water running downslope can be expressed in terms of the depth of the flow and the parameter
which represents the ratio of the buoyancy driven speed of the CO2 saturated water compared to the background flow speed, leading to the expression
Since we require Qd > 0, we deduce that the convective exchange flow can only develop for low aquifer flow rates, Ψ > 1, and in this case, the maximum value of Qd is given by
 The maximum rate of dissolution is then given by the sum of the convective and the background flux of ground water, supplied to the CO2 plume, times the difference between the saturated and the original concentration of CO2, and this has value
The dimensionless CO2 flux, Fmax/Qa (Cs − Cw ), is shown in Figure 4 as a function of 1/Ψ. Following a similar analysis, it can also be shown that in the case that the background aquifer flux is downdip (Figure 3b), the maximum rate of dissolution is again given by expression (11) in the case of a weak background flow for which the convective recirculation can develop in addition to the background flow.
 In Figure 4, the reference case, ψ = 1, corresponds to the case in which the convective circulation matches the background flow; typically, the scaling for the convective circulation of water, per unit distance normal to the page, as given by Qa Ψ (equation (8)), has value of order 0.3–30 m2/yr for k = 10–100 mD , H = 10–100 m with angle of inclination of order sinθ∼ 0.1. This corresponds to aquifer speeds of order 3.0–0.03 m/yr, suggesting that in the case of a slow background flow, the convective circulation may enhance the dissolution process through transport of additional far-field groundwater to the CO2 plume (Figure 3). For a 1000 m wide plume of CO2 in the anticline, with these values for transport from the anticline, we expect the maximum effective CO2 dissolution flux per unit area (equation (11)) to have value of order 0.02–2.0 kg/m2/yr when Ψ ∼ 1. With larger background flux the dissolution rate may be higher. These estimates can be compared with numerical and experimental estimates of the local vertical convective dissolution of CO2 into underlying unsaturated groundwater, which suggest dissolution rates of order 10 kg/yr/m2 may develop [Pau et al., 2009; Neufeld et al., 2010]. We infer that with relatively shallow aquifers relative to the depth of the trapped CO2 plume, h/H ≫ 0.01, the lateral transport of unsaturated water through the aquifer may be the rate limiting process regulating the dissolution of the CO2 plume, rather than the local convective mixing.
 For example, with a mass of 10–100 Mtonnes CO2 in a structural trap, the lateral transport limited dissolution suggests that such the plume of CO2 may persist for times of order 104 – 106yrs before it becomes fully dissolved. Although the seal rock may provide an effective trap if it retains its integrity, tectonic movement and any associated faulting over this time-scale could enable remobilisation of an extensive plume of CO2in highly mobile form; this may inform calculations of the long-term risk associated with injection of CO2 into the subsurface.
 The editor thanks the two anonymous reviewers.