### Abstract

- Top of page
- Abstract
- 1. Introduction
- 2. Experimental System
- 3. Experimental Results
- 4. Theoretical Models
- 5. Two-Current Model for Spreading With Convective Dissolution
- 6. Application to Carbon Sequestration
- 7. Discussion and Conclusions
- Acknowledgments
- References
- Supporting Information

[1] Injection of carbon dioxide (CO_{2}) into saline aquifers is a promising tool for reducing anthropogenic CO_{2} emissions. At reservoir conditions, the injected CO_{2} is buoyant relative to the ambient groundwater. The buoyant plume of CO_{2} rises toward the top of the aquifer and spreads laterally as a gravity current, presenting the risk of leakage into shallower formations via a fracture or fault. In contrast, the mixture that forms as the CO_{2} dissolves into the ambient water is denser than the water and sinks, driving a convective process that enhances CO_{2}dissolution and promotes stable long-term storage. Motivated by this problem, we study convective dissolution from a buoyant gravity current as it spreads along the top of a vertically confined, horizontal aquifer. We conduct laboratory experiments with analog fluids (water and a mixture of methanol and ethylene glycol) and compare the experimental results with simple theoretical models. Since the aquifer has a finite thickness, dissolved buoyant fluid accumulates along the bottom of the aquifer, and this mixture spreads laterally as a dense gravity current. When dissolved buoyant fluid accumulates slowly, our experiments show that the spreading of the buoyant current is characterized by a parabola-like advance and retreat of its leading edge. When dissolved buoyant fluid accumulates quickly, the retreat of the leading edge slows as further dissolution is controlled by the slumping of the dense gravity current. We show that simple theoretical models predict this behavior in both limits, where the accumulation of dissolved buoyant fluid is either negligible or dominant. Finally, we apply one of these models to a plume of CO_{2} in a saline aquifer. We show that the accumulation of dissolved CO_{2} in the water can increase the maximum extent of the CO_{2} plume by several fold and the lifetime of the CO_{2} plume by several orders of magnitude.

### 1. Introduction

- Top of page
- Abstract
- 1. Introduction
- 2. Experimental System
- 3. Experimental Results
- 4. Theoretical Models
- 5. Two-Current Model for Spreading With Convective Dissolution
- 6. Application to Carbon Sequestration
- 7. Discussion and Conclusions
- Acknowledgments
- References
- Supporting Information

[2] Injection of carbon dioxide (CO_{2}) into saline aquifers is a promising tool for reducing atmospheric CO_{2} emissions [*Lackner*, 2003; *Intergovernmental Panel on Climate Change*, 2005; *Bickle*, 2009; *Orr*, 2009; *Szulczewski et al.*, 2012]. Permanently trapping the injected CO_{2} is essential to minimize the risk of leakage into shallower formations. Leakage is a primary concern because the plume of injected CO_{2} is buoyant relative to the ambient groundwater at representative aquifer conditions, and will rise toward the top of the aquifer after injection and spread laterally as a buoyant gravity current.

[3] One mechanism that acts to trap the buoyant CO_{2}is the dissolution of free-phase CO_{2} into the groundwater. Dissolved CO_{2} is securely stored within the subsurface because it is no longer buoyant: the density of water increases with dissolved CO_{2} concentration, so groundwater containing dissolved CO_{2} will sink toward the bottom of the aquifer. As this mixture sinks in dense, CO_{2}-rich fingers, the resulting convective flow sweeps fresh groundwater upward. This convective dissolution process greatly enhances the rate at which the CO_{2} dissolves into the groundwater [*Weir et al.*, 1996; *Lindeberg and Wessel-Berg*, 1997; *Ennis-King et al.*, 2005; *Riaz et al.*, 2006; *Hidalgo and Carrera*, 2009; *Pau et al.*, 2010; *Kneafsey and Pruess*, 2010; *Neufeld et al.*, 2010].

[4] Estimates of the impact of convective dissolution on the lifetime and distribution of a plume of CO_{2} in the subsurface are essential for risk assessment. Recent numerical and experimental work has led to a greatly improved understanding of both the onset [*Ennis-King et al.*, 2005; *Riaz et al.*, 2006; *Hidalgo and Carrera*, 2009; *Slim and Ramakrishnan*, 2010; *Backhaus et al.*, 2011] and the subsequent rate of the convective dissolution of a stationary layer of CO_{2} overlying a reservoir of water [*Kneafsey and Pruess*, 2010; *Pau et al.*, 2010; *Neufeld et al.*, 2010; *Backhaus et al.*, 2011]. These results have been used to incorporate upscaled models for convective dissolution into models for the spreading and migration of buoyant plumes of CO_{2} after injection [*Gasda et al.*, 2011; *MacMinn et al.*, 2011]. However, convective dissolution has not been studied experimentally in the context of a gravity current that spreads as it dissolves, and the interaction between these two processes is not understood. In addition, in an aquifer of finite thickness the accumulation of dissolved CO_{2} in the water beneath the spreading plume may strongly influence the rate of convective dissolution.

[5] Here, we consider the simple model problem of convective dissolution from a buoyant gravity current as it spreads along the top boundary of a vertically confined, horizontal aquifer (Figure 1). We first study this system experimentally using analog fluids. Motivated by our experimental observations, we then study theoretical models for this system based on the well-known theory of gravity currents [*Bear*, 1972; *Huppert and Woods*, 1995], which has recently been used to develop physical insight into CO_{2} injection [*Lyle et al.*, 2005; *Nordbotten and Celia*, 2006] and postinjection spreading and migration [*Hesse et al.*, 2007, 2008; *Juanes et al.*, 2010; *MacMinn et al.*, 2011; *de Loubens and Ramakrishnan*, 2011; *Golding et al.*, 2011]. We show that the interaction between buoyant spreading, convective dissolution, and the finite thickness of the aquifer has a strong influence on the maximum extent and the lifetime of the buoyant current.

### 4. Theoretical Models

- Top of page
- Abstract
- 1. Introduction
- 2. Experimental System
- 3. Experimental Results
- 4. Theoretical Models
- 5. Two-Current Model for Spreading With Convective Dissolution
- 6. Application to Carbon Sequestration
- 7. Discussion and Conclusions
- Acknowledgments
- References
- Supporting Information

[19] We assume vertical flow equilibrium (i.e., the Dupuit approximation), neglecting the vertical component of the fluid velocity relative to the horizontal one and taking the pressure field to be hydrostatic [*Coats et al.*, 1971; *Yortsos*, 1995]. We further neglect the capillary pressure relative to typical gravitational and viscous pressure changes, and also assume that the interface between the two fluids remains sharp. Although both capillary pressure and saturation gradients can be included in such models [*Nordbotten and Dahle*, 2011; *Golding et al.*, 2011], the interaction of these effects with convective dissolution is not clear, and they are not present in our experimental analog system because the fluids are perfectly miscible. Lastly, we require for mass conservation that there be no net flux of fluid through any cross section of the aquifer, because it is vertically confined.

#### 4.1. Buoyant Spreading Without Convective Dissolution

#### 4.2. Buoyant Spreading With Convective Dissolution

[23] Previous studies of convective dissolution have shown that a stationary layer of CO_{2}will dissolve into a semi-infinite layer of water at a rate that is roughly constant in time [*Hidalgo and Carrera*, 2009; *Kneafsey and Pruess*, 2010; *Pau et al.*, 2010]. When the water layer has a finite thickness, recent results suggest that the dissolution rate is a weak function of the layer thickness [*Neufeld et al.*, 2010; *Backhaus et al.*, 2011], but that it can be approximated as constant provided that the thickness of the CO_{2} layer is small relative to the thickness of the water layer.

[27] Equation (10) is not strictly an asymptotic solution of equation (8) because convective dissolution causes some memory of the initial shape to be retained throughout the evolution, as with residual trapping [*Kochina et al.*, 1983; *Barenblatt*, 1996]. In addition, the concept of asymptotics has limited relevance here because the current dissolves completely in finite time.

[29] We begin by estimating the dissolution rate from this expression for 59.1 wt % MEG dissolving into water. We then treat the dissolution rate as a fitting parameter, calibrating its value around this estimate by comparing the predictions of the model with experimental measurements. We present the estimated and calibrated dissolution rates, and *q*_{d}, respectively, in Table 3. The calibrated values are within about a factor of two of the estimated values. That they do not agree exactly is not surprising, given that the correlation of *Neufeld et al.* [2010]was developed in the context of a stationary layer of MEG dissolving into water. Diffusion and flow-induced dispersion in the present context, where the interface has both advancing and receding portions, may enhance or inhibit convective dissolution relative to the case of a stationary layer.

[30] We compare these experiments with the predictions of equation (8) in Figure 5. We compare the evolution of the nose position for all three bead sizes, as well as the evolution of the shape of the current for the 2 mm beads. We include an envelope around the nose position corresponding to around the calibrated dissolution rate *q*_{d} to illustrate the sensitivity of the model to this parameter.

[31] These results suggest that the assumption of a constant rate of convective dissolution can capture the qualitative and quantitative features of the impact of convective dissolution on a buoyant current in this system, provided that dissolved buoyant fluid accumulates slowly beneath the buoyant current.

### 5. Two-Current Model for Spreading With Convective Dissolution

- Top of page
- Abstract
- 1. Introduction
- 2. Experimental System
- 3. Experimental Results
- 4. Theoretical Models
- 5. Two-Current Model for Spreading With Convective Dissolution
- 6. Application to Carbon Sequestration
- 7. Discussion and Conclusions
- Acknowledgments
- References
- Supporting Information

[32] Experimental and numerical studies of convective dissolution have thus far focused on dissolution from a stationary layer of CO_{2}overlying a deep or semi-infinite layer of water. In a confined aquifer, we expect that the accumulation of dissolved CO_{2} in the water beneath the buoyant current will limit the rate at which the CO_{2} can dissolve. Here, we extend the model discussed above (equation (8)) to include this accumulation effect in a simple way.

[34] Applying Darcy's law and conservation of mass for this system, and assuming sharp interfaces and vertical flow equilibrium as discussed at the beginning of section 4 above, we have in dimensionless form

where , , and are as defined in equation (3). The nonlinear function *f* now includes the presence of the dense current,

and we have a second such function

Finally, we redefine the dimensionless convective dissolution rate *ϵ* to be conditional,

so that it takes a constant, nonzero value where the buoyant current and the dense one are separate and vanishes where they are touching.

[35] This two-current model contains three new parameters relative to the simpler model: , which is the ratio of the viscosity of the ambient fluid, , to that of the dense mixture, ; , which is the ratio of the characteristic buoyancy velocity of the dense current, , to that of the buoyant one, *U*; and , which is the volume fraction of buoyant fluid dissolved in the dense current at mass fraction . All three of these parameters are uniquely defined by the properties of the buoyant and ambient fluids, the value of , and appropriate constitutive relations and for the mixture.

[36] The buoyant current loses volume due to convective dissolution at a rate *ϵ* per unit length, and this volume is transferred to the dense current at a rate per unit length. This model reduces to the simpler model (equation (8)) for , when one unit volume of the dense current can hold an arbitrary amount of dissolved buoyant fluid so that the dense current does not accumulate no matter how much buoyant fluid dissolves.

[37] We solve equations (13) and (14)numerically. To do so, we discretize the two equations in space using a second-order finite-volume method to guarantee conservation of volume. We then integrate the two equations in time using a first-order explicit method, which greatly simplifies the handling of the coupling between these two nonlinear conservation laws. Explicit time integration requires small, local corrections to the mass transfer between the two currents at the end of each time step in order to avoid local overshoot where the dense current rises to meet the buoyant one.

[38] We find that the accumulation of the dense current strongly inhibits convective dissolution from the buoyant current, leading to a marked departure from the behavior predicted by the single-current model when the two currents touch (Figure 10).

[40] We again estimate *q*_{d} from equation (12), and then calibrate *q*_{d} around this estimated value in order to match the early time spreading behavior, during which time the dense current plays little role. We develop an initial estimate of the mass fraction of MEG in the dense current based on the final volume of the dense current once the buoyant current has completely dissolved, and we then calibrate around this value. We report these values in Table 4.

### 6. Application to Carbon Sequestration

- Top of page
- Abstract
- 1. Introduction
- 2. Experimental System
- 3. Experimental Results
- 4. Theoretical Models
- 5. Two-Current Model for Spreading With Convective Dissolution
- 6. Application to Carbon Sequestration
- 7. Discussion and Conclusions
- Acknowledgments
- References
- Supporting Information

[43] We now consider these results in the context of CO_{2}sequestration in a saline aquifer. A key difference between the MEG-water system and the CO_{2}-water system is that MEG and water are fully miscible, whereas CO_{2} and water are immiscible. Although the impact of capillarity on convective dissolution is unknown, it has been shown that the impact of capillarity on the spreading of a gravity current is negligible when the capillary pressure is small relative to typical gravitational and viscous pressure changes [*Nordbotten and Dahle*, 2011; *Golding et al.*, 2011]. We assume that this is also the case for convective dissolution. We next compare the dimensionless parameters for the CO_{2}-water system with those for the MEG-water system.

[47] Based on these values of *ϵ*, *δ*, and , we expect dissolved CO_{2} to accumulate very quickly and slump downward very slowly relative to the rate at which the buoyant current spreads. As a result, we expect the rate at which CO_{2} is trapped to be controlled not by the rate of convective dissolution, but by the amount of dissolved CO_{2} the water can hold (i.e., ) and by the rate at which this water slumps downward. In Figure 11, we show that this is indeed the case: both the maximum extent and the lifetime of a plume of CO_{2} decrease as the dissolution rate increases, but both quantities approach limiting values that are independent of the dissolution rate if this rate is sufficiently large. The dissolution rate of estimated above is about 2 orders of magnitude above this threshold value. As a result, the spreading and convective dissolution of the plume is completely controlled by the accumulation of dissolved CO_{2} in this setting, and the plume spreads several times further and persists for several orders of magnitude longer than it would without this accumulation.

### 7. Discussion and Conclusions

- Top of page
- Abstract
- 1. Introduction
- 2. Experimental System
- 3. Experimental Results
- 4. Theoretical Models
- 5. Two-Current Model for Spreading With Convective Dissolution
- 6. Application to Carbon Sequestration
- 7. Discussion and Conclusions
- Acknowledgments
- References
- Supporting Information

[48] We have shown via experiments with analog fluids that simple models are able to capture the impact of convective dissolution on the spreading of a buoyant gravity current in a vertically confined, horizontal layer.

[50] When dissolved buoyant fluid accumulates quickly beneath the buoyant current, our experiments have shown that this accumulation can have an important limiting effect on the dissolution process. To capture the accumulation of dissolved buoyant fluid, we have developed a two-current model where a dense gravity current of ambient fluid with dissolved buoyant fluid grows and spreads along the bottom of the aquifer. We have used this model to show that the accumulation of dissolved buoyant fluid beneath the buoyant current can slow convective dissolution, and we have confirmed this prediction experimentally (Figure 6).

[51] Using this two-current model, we have shown that we expect CO_{2} spreading and dissolution in a horizontal aquifer to be controlled primarily by the mass fraction at which CO_{2} accumulates in the water, and to be nearly independent of the dissolution rate (Figure 11). This can be the case even in the presence of aquifer slope or background groundwater flow, both of which drive net CO_{2}migration and expose the plume to fresh water, when slope- or flow-driven migration is sufficiently slow [*MacMinn et al.*, 2011].

[52] The planar models used here rely on the fact that the transverse width of the buoyant current is much larger than its length in the *x* direction, , which is typically the case when large amounts of CO_{2} are injected via a line drive configuration [*Nicot*, 2008; *Szulczewski et al.*, 2012]. The models presented here can be readily adapted to a radial geometry for injection from a single well where appropriate. Where neither geometric approximation is appropriate, use of a more complicated, two-dimensional model will be necessary.

[53] We have also assumed here an idealized rectangular initial shape for the plume of CO_{2}. In practice, the specific details of the injection scenario will have some quantitative impact on the maximum extent and lifetime of the CO_{2}, but should have little qualitative impact on the interaction between plume spreading, convective dissolution, and the accumulation of dissolved CO_{2}.