Session AF: Porous Media I: CO2 Sequestration

Onset and cessation of porous convection in the context of geological carbon sequestration

In geological carbon sequestration, CO$_2$ injected into a saline aquifer is less dense than the resident brine and floats above it. It is slightly soluble in brine and progressively dissolves, making the brine slightly denser than ``pure" brine. Motivated by this, we consider conditions for free convection in a porous medium from a one-dimensional, time-dependent, pure-diffusion base state. This problem has been addressed in several previous studies using a variety of approximations. We present a simple but rigorous calculation, showing where in time and wavenumber space a perturbation exists (of infinitesimal or finite amplitude) whose mean square amplitude grows. The critical Rayleigh-Darcy number, $Ra$, below which instability cannot occur is $Ra=32.50$. Above $Ra\approx 100$, the earliest possible onset time becomes independent of porous-layer thickness. We discuss implications for realistic reservoir conditions.   

Dissolution-driven convection in porous media: Experiments

The carbon geo-sequestration proposal has received extensive theoretical and numerical scrutiny in recent times, but few supporting experimental observations exist. Here we experimentally investigate this proposal, and study the onset of convection away from a time-dependent pure diffusion base state. The experimental setup comprises a Hele-Shaw cell containing Potassium Permanganate (representing carbon dioxide) and water (representing brine). Upon coming in instantaneous contact, Potassium permanganate dissolves in water and produces an initially clean diffusion layer. The Potassium Permanganate solution being slightly denser than pure water, becomes gravitationally unstable and sinks by forming fingers, and heralds the onset of convection. Inclining the Hele-Shaw cell at steep angles extends the diffusive range and allows us to capture the cross-over from diffusive to convective regimes. System dynamics are captured by digitally imaging the light transmitted across the Hele-Shaw cell by a back-lit diffuse illumination source. Pre-calibration of the transmitted light at various Potassium Permanganate concentrations allows us to convert the digital images into concentration fields and calculate the local and global flux in the system. We present preliminary results from this experimental study.   

The Effect of Geochemical Reaction on Convective Mixing in a Gravitationally Unstable Diffusive Boundary Layer in Porous Media: Geological Storage of CO$_{2}$ in Saline Aquifers

The storage of carbon dioxide and acid gases in deep geological formations is considered a promising option for mitigation of greenhouse gas emissions. Understanding of the primary mechanisms, such as convective mixing and geochemistry that affect the long-term geostorage process in deep saline aquifers is of prime importance. First, a linear stability analysis of an unstable diffusive boundary layer in porous media is presented, where the instability occurs due to a density difference between the carbon dioxide saturated brine and the resident brine. The linear stability results have revealed that geochemistry stabilizes the boundary layer. A detailed physical discussion is also presented with an examination of vorticity and concentration eigenfunctions and streamlines' contours to reveal how the geochemical reaction may affect these physical terms. Second, nonlinear direct numerical simulations are presented, in which the evolution of density-driven instabilities for different reaction rates are discussed. The results indicate that the boundary layer will be more stable for systems with a higher rate of reaction. However, the quantitative analyses show that more carbon dioxide may be removed from the supercritical free phase as the flux at the boundary is higher for flow systems coupled with stronger geochemical reactions.   

Drainage in Two-dimensional Porous Media: From Capillary Fingering to Viscous flow

We report some experimental results on two-phase flows in model 2D porous media. Standard microfluidic techniques are used to fabricate networks of straight microchannels having a controlled throat size distribution. We focus on the drainage of a wetting fluid by a non-wetting one of various viscosities and take advantage of image analysis to characterize the velocities of the menisci that are simultaneously moving. In the range of applied capillary numbers (Ca) from $10^7$ to $10^2$, the system exhibit a clear transition from a fractal fingering to a stable front, which depends mainly on the size heterogeneity of the medium. The experimental results are accounted by a simple model that accounts for the scaling behaviour of the local velocities as a function of Ca. We also obtain a very good quantitative agreement when comparing the experimental results to numerical simulations based on a pore network model. This allows us to propose a general prediction of the capillary fingering extent as a function of the capillary number, the channel geometries and the pore size heterogeneity.   

Leakage from inclined porous reservoirs

We investigate the effect of localized leakage on the injection of buoyant fluids in porous, inclined reservoirs, with application to the geological storage of $\mathrm{CO}_2$. We consider a simplified two-dimensional geometry and find that the resulting gravity current reaches a steady-state shape apart from a nose, which propagates at constant velocity. Crucially, this means that the efficiency of storage (defined as the instantaneous proportion of the injected fluid that does not leak) tends to a finite value at late times. This is in contrast to previous studies of localized leakage in horizontal reservoirs, which found that the efficiency of storage tends to zero at late times. We analyze the steady-state efficiency and relevant time scales for leakage points located upslope and downslope of the injection point using analytical and numerical methods, and compare our findings with the results of model laboratory experiments. Finally, we consider the implications of our results for the geological storage of $\mathrm{CO}_2$ in the presence of sloping cap rocks compromised by the presence of fractures or fissures.   

Convective dissolution in porous media

Motivated by the geological storage of buoyant carbon dioxide (CO$_2$) we investigate dissolution of CO$_2$ into brine which increases security of storage over time. The rate of CO$_2$ dissolution is determined by convection in the brine driven by the increase of brine density with CO$_2$ saturation. We present a new analogue fluid system that reproduces the nonlinear density behaviour of CO$_2$ and brine. We show that the convective flux is proportional to the Rayleigh number to the $4/5$ power through a combination of laboratory experiments and high-resolution numerical simulations, in contrast with a classical linear relationship. This relationship allows us to extrapolate from the laboratory scale to geophysical scales. A scaling argument that incorporates the effect of the large-scale flow on mixing at the CO$_2$-brine interface confirms this nonlinear relationship for the convective flux and provides a physical picture of high Rayleigh number convection in a porous medium. The resultant model makes quantitative predictions of the CO$_2$ dissolution rates in natural and anthropogenic CO$_2$ accumulations. For example, at the Sleipner field we estimate a dissolution rate of roughly 10\% of the annual injected mass suggesting that storage security is significantly enhanced.   

Spreading and dissolution of CO$_2$ in horizontal aquifers: theory and experiments

Injection of carbon dioxide into saline aquifers is widely regarded as a promising tool for reducing atmospheric CO$_2$ emissions. While an accurate assessment of the post-injection spreading and migration of the CO$_2$ is essential for estimates of storage security, many of the physical processes controlling CO$_2$ migration are poorly understood. CO$_2$ is buoyant relative to groundwater at reservoir conditions. This is undesirable because the presence of a pre-existing well or fracture, or the activation of a fault, could lead to leakage. It is well known, however, that the dissolution of CO$_2$ increases the density of the groundwater, resulting in convective currents that dramatically enhance CO$_2$ dissolution. Once dissolved, the CO$_2$ is considered to be securely stored within the subsurface. Recent numerical and experimental work has led to a greatly improved understanding of the resulting rate of CO$_2$ dissolution into groundwater. Here, we use analog experiments and simple theoretical models to study dissolution from a plume of CO$_2$ as it spreads upward against the caprock in an aquifer of finite thickness. We show that the interaction between spreading, dissolution, and the finite thickness of the aquifer has a strong influence on the ultimate distribution of the CO$_2$.   

Unstable Diffusion Layers: Laboratory Experiments on Carbon Sequestration Phenomena

The sequestration of carbon dioxide in aqueous porous media involves a process where the initial formation of diffusion layers subsequently becomes unstable with respect to fingering. We will present experimental examples of this transient growth process from mass diffusion to fingering instability using a pair of fluids that mimic the behavior of carbon dioxide and salt water (brine), namely water and propylene glycol. In this experiment, performed in a Hele-Shaw cell, the permeability is adjusted by the plate thickness, the porosity is unity, and the Rayleigh number depends on the cell height. The diffusion layer and the fingers are visualized using optical shadowgraph techniques. We obtain the time evolution of the selected pattern wavelength, the distribution and scaling of the plume velocities, and the mass transfer rates for Ra in the range 5000 to 90,000 and for permeabilities in the range $5-20 \times 10^{-5}\rm{cm}^2$. Comparisons with linear stability calculations and implications for carbon sequestration are discussed.   

CO$_2$ migration in saline aquifers: a gravity current model with capillary and solubility trapping

Injection of carbon dioxide into geological formations is widely regarded as a promising tool for reducing global atmospheric CO$_2$ emissions. While an accurate understanding of the post-injection spreading and migration of the plume of mobile CO$_2$ is essential, many aspects of the fundamental physics of CO$_2$ migration are poorly understood. Here, we develop a sharp-interface mathematical model for the post-injection migration of a CO$_2$ plume driven by groundwater flow in a sloping aquifer, subject to both residual trapping and CO$_2$ dissolution. We show that the interplay between dissolution and migration leads to three regimes, depending on how quickly the water beneath the plume saturates with dissolved CO$_2$. We develop some semi-analytical solutions to the migration equation when the water beneath the plume saturates very slowly or very quickly relative to plume motion, and we solve the migration equation numerically in general. We use these solutions to study the relative importance of capillary and solubility trapping, and the impacts of these physical mechanisms on the storage capacity of an aquifer.