Marc A. Hesse

Onset of convection in a gravitationally unstable diffusive boundary layer in porous media

We present a linear stability analysis of density-driven miscible flow in porous media in the context of carbon dioxide sequestration in saline aquifers. Carbon dioxide dissolution into the underlying brine leads to a local density increase that results in a gravitational instability. The physical phenomenon is analogous to the thermal convective instability in a semi-infinite domain, owing to a step change in temperature at the boundary. The critical time for the onset of convection in such problems has not been determined accurately by previous studies. We present a solution, based on the dominant mode of the self-similar diffusion operator, which can accurately predict the critical time and the associated unstable wavenumber. This approach is used to explain the instability mechanisms of the critical time and the long-wave cutoff in a semi-infinite domain. The dominant mode solution, however, is valid only for a small parameter range. We extend the analysis by employing the quasi-steady-state approximation (QSSA) which provides accurate solutions in the self-similar coordinate system. For large times, both the maximum growth rate and the most dangerous mode decay as t 1/4 . The long-wave and the short-wave cutoff modes scale as t 1/5 and t 4/5 , respectively. The instability problem is also analysed in the nonlinear regime by high-accuracy direct numerical simulations. The nonlinear simulations at short times show good agreement with the linear stability predictions. At later times, macroscopic fingers display intense nonlinear interactions that significantly influence both the front propagation speed and the overall mixing rate. A dimensional analysis for typical aquifers shows that for a permeability variation of 1 - 3000 mD, the critical time can vary from 2000 yrs to about 10 days while the critical wavelength can be between 200m and 0.3 m.

Gravity currents with residual trapping

Motivated by geological carbon dioxide (CO 2 ) storage, we present a vertical-equilibrium sharp-interface model for the migration of immiscible gravity currents with constant residual trapping in a two-dimensional confined aquifer. The residual acts as a loss term that reduces the current volume continuously. In the limit of a horizontal aquifer, the interface shape is self-similar at early and at late times. The spreading of the current and the decay of its volume are governed by power-laws. At early times the exponent of the scaling law is independent of the residual, but at late times it decreases with increasing loss. Owing to the self-similar nature of the current the volume does not become zero, and the current continues to spread. In the hyperbolic limit, the leading edge of the current is given by a rarefaction and the trailing edge by a shock. In the presence of residual trapping, the current volume is reduced to zero in finite time. Expressions for the up-dip migration distance and the final migration time are obtained. Comparison with numerical results shows that the hyperbolic limit is a good approximation for currents with large mobility ratios even far from the hyperbolic limit. In gently sloping aquifers, the current evolution is divided into an initial near-parabolic stage, with power-law decrease of volume, and a later near-hyperbolic stage, characterized by a rapid decay of the plume volume. Our results suggest that the efficient residual trapping in dipping aquifers may allow CO 2 storage in aquifers lacking structural closure, if CO 2 is injected far enough from the outcrop of the aquifer.

Convective dissolution of carbon dioxide in saline aquifers.

[1] Geological carbon dioxide (CO2) storage is a means of reducing anthropogenic emissions. Dissolution of CO2 into the brine, resulting in stable stratification, increases storage security. The dissolution rate is determined by convection in the brine driven by the increase of brine density with CO2 saturation. We present a new analogue fluid system that reproduces the convective behaviour of CO2‐enriched brine. Laboratory experiments and high‐resolution numerical simulations show that the convective flux scales with the Rayleigh number to the 4/5 power, in contrast with a classical linear relationship. A scaling argument for the convective flux incorporating lateral diffusion from downwelling plumes explains this nonlinear relationship for the convective flux, provides a physical picture of high Rayleigh number convection in a porous medium, and predicts the CO2 dissolution rates in CO2 accumulations. These estimates of the dissolution rate show that convective dissolution can play an important role in enhancing storage security. Citation: Neufeld,J.A.,M.A .Hesse,A.Riaz,M. A.H allworth, H. A. Tchelepi, and H. E. Huppert (2010), Convective dissolution of carbon dioxide in saline aquifers, Geophys. Res. Lett., 37, L22404, doi:10.1029/2010GL044728.

Iterative multiscale finite-volume method

The multiscale finite-volume (MSFV) method for the solution of elliptic problems is extended to an efficient iterative algorithm that converges to the fine-scale numerical solution. The localization errors in the MSFV method are systematically reduced by updating the local boundary conditions with global information. This iterative multiscale finite-volume (i-MSFV) method allows the conservative reconstruction of the velocity field after any iteration, and the MSFV method is recovered, if the velocity field is reconstructed after the first iteration. Both the i-MSFV and the MSFV methods lead to substantial computational savings, where an approximate but locally conservative solution of an elliptic problem is required. In contrast to the MSFV method, the i-MSFV method allows a systematic reduction of the error in the multiscale approximation. Line relaxation in each direction is used as an efficient smoother at each iteration. This smoother is essential to obtain convergence in complex, highly anisotropic, heterogeneous domains. Numerical convergence of the method is verified for different test cases ranging from a standard Poisson equation to highly heterogeneous, anisotropic elliptic problems. Finally, to demonstrate the efficiency of the method for multiphase transport in porous media, it is shown that it is sufficient to apply the iterative smoothing procedure for the improvement of the localization assumptions only infrequently, i.e. not every time step. This result is crucial, since it shows that the overall efficiency of the i-MSFV algorithm is comparable with the original MSFV method. At the same time, the solutions are significantly improved, especially for very challenging cases.

Gravity currents in horizontal porous layers : transition from early to late self-similarity

We investigate the evolution of a finite release of fluid into an infinite, two-dimensional, horizontal, porous slab saturated with a fluid of different density and viscosity. The vertical boundaries of the slab are impermeable and the released fluid spreads as a gravity current along a horizontal boundary. At early times the released fluid fills the entire height of the layer, and the governing equation admits a self-similar solution that is a function of the viscosity ratio between the two fluids. This early similarity solution describes a tilting interface with tips propagating as x ∝ t 1/2 . At late times the released fluid has spread along the boundary and the height of the current is much smaller than the thickness of the layer. The governing equation simplifies and admits a different similarity solution that is independent of the viscosity ratio. This late similarity solution describes a point release of fluid in a semi-infinite porous half-space, where the tip of the interface propagates as x ∝ t 1/3 . The same simplification of the governing equation occurs if the viscosity of the released fluid is much higher than the viscosity of the ambient fluid. We have obtained an expression for the time when the solution transitions from the early to the late self-similar regime. The transition time increases monotonically with increasing viscosity ratio. The transition period during which the solution is not self-similar also increases monotonically with increasing viscosity ratio, for mobility ratios larger than unity. Numerical computations describing the full evolution of the governing equation show good agreement with the theoretical results. Estimates of the spreading of injected fluids over long times are important for geological storage of CO 2 , and for the migration of pollutants in aquifers. In all cases it is important to be able to anticipate when the spreading regime transitions from x ∝ t 1/2 to x ∝ t 1/3 .

Experimental evidence for self-limiting reactive flow through a fractured cement core: implications for time-dependent wellbore leakage.

We present a set of reactive transport experiments in cement fractures. The experiments simulate coupling between flow and reaction when acidic, CO(2)-rich fluids flow along a leaky wellbore. An analog dilute acid with a pH between 2.0 and 3.15 was injected at constant rate between 0.3 and 9.4 cm/s into a fractured cement core. Pressure differential across the core and effluent pH were measured to track flow path evolution, which was analyzed with electron microscopy after injection. In many experiments reaction was restricted within relatively narrow, tortuous channels along the fracture surface. The observations are consistent with coupling between flow and dissolution/precipitation. Injected acid reacts along the fracture surface to leach calcium from cement phases. Ahead of the reaction front, high pH pore fluid mixes with calcium-rich water and induces mineral precipitation. Increases in the pressure differential for most experiments indicate that precipitation can be sufficient to restrict flow. Experimental data from this study combined with published field evidence for mineral precipitation along cemented annuli suggests that leakage of CO(2)-rich fluids along a wellbore may seal the leakage pathway if the initial aperture is small and residence time allows mobilization and precipitation of minerals along the fracture.

Buoyant dispersal of CO2 during geological storage

Carbon capture and storage is currently the only technology that may allow significant reductions in CO2 emissions from large point sources. Seismic images of geological CO2 storage show the rise of CO2 is influenced by horizontal shales. The buoyant CO2 spreads beneath impermeable barriers until a gap allows its upward migration. The large number and small scale of these barriers makes the prediction of the CO2 migration path and hence the magnitude of CO2 trapping very challenging. We show that steady buoyancy dominated flows in complex geometries can be modeled as a cascade of flux partitioning events. This approach allows the analysis of two-dimensional plume dispersal from a horizontal injection well. We show that the plume spreads laterally with height y above the source according to (y/h)1/2 L, where L is the width of the shales and h is their vertical separation. The fluid volume below successive shale layers, and therefore the magnitude of trapped CO2, increase as (y/h)5/4 above the source, so that every additional layer of barriers traps more CO2 than the one below. Upscaling small scale flow barriers by reducing the vertical permeability, common in numerical simulations of CO2 storage, does not capture the dispersion and trapping of the CO2 plume by the flow barriers.

Spreading and convective dissolution of carbon dioxide in vertically confined, horizontal aquifers

Injection of carbon dioxide (CO2) into saline aquifers is a promising tool for reducing anthropogenic CO2 emissions. At reservoir conditions, the injected CO2 is buoyant relative to the ambient groundwater. The buoyant plume of CO2 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 CO2 dissolves into the ambient water is denser than the water and sinks, driving a convective process that enhances CO2dissolution 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 CO2 in a saline aquifer. We show that the accumulation of dissolved CO2 in the water can increase the maximum extent of the CO2 plume by several fold and the lifetime of the CO2 plume by several orders of magnitude.

High-porosity channels for melt migration in the mantle: Top is the dunite and bottom is the harzburgite and lherzolite

High-porosity dunite channels are important pathways for melt migration in the mantle. To better understand the first order characteristics of the high-porosity melt channel and its associated peridotite lithologies in an upwelling mantle, we conducted high-resolution numerical simulations of reactive dissolution in a deformable porous medium. Results from this study show that high-porosity dunite channels are transient and shallow parts of pathways for melt migration in the mantle. The lower parts of a high-porosity channel are harzburgite and lherzolite. The size and dimension of dunite channels depend on the amplitude of lateral porosity variations at the base of the melting column, whereas the depth of dunite channel initiation depends on the melt flux entering the channel from below. Compaction and interaction between compaction and dissolution play a central role in distributing melt in the dunite channel. A wide orthopyroxene-free dunite channel may contain two or more high-porosity melt channels. A primary high-porosity melt channel developed in the deep mantle may excite secondary melt channels in the shallow part of the melting column. The spatial relations among the high-porosity melt channel and its associated lithologies documented in this study may shed new light on a number of field, petrological, and geochemical observations related to melt migration in the mantle. Citation: Liang, Y., A. Schiemenz, M. A. Hesse, E. M. Parmentier, and J. S. Hesthaven (2010), High-porosity channels for melt migration in the mantle: Top is the dunite and bottom is the harzburgite and lherzolite, Geophys. Res. Lett., 37, L15306, doi:10.1029/2010GL044162.

Constraints on the magnitude and rate of CO2 dissolution at Bravo Dome natural gas field

Significance Carbon capture and geological storage allow immediate and significant reductions in CO2 emissions from fossil fuels. CO2 dissolution into saline water enhances long-term storage security, but dissolution rates are too slow to be quantified during injection pilots. Therefore, we estimate dissolution rates over millennial timescales at the Bravo Dome gas field, a natural analog for geological CO2 storage. We show that 1.6 Gt CO2 have been stored at Bravo Dome since the beginning of CO2 emplacement 1.2–1.5 Ma. Approximately 10% of the CO2 dissolved during its emplacement, while another 10% dissolved into the underlying aquifer. This exceeds the amount expected from diffusion and provides field evidence for convective CO2 dissolution. The convective dissolution rate, however, is slow in typical US aquifers. The injection of carbon dioxide (CO2) captured at large point sources into deep saline aquifers can significantly reduce anthropogenic CO2 emissions from fossil fuels. Dissolution of the injected CO2 into the formation brine is a trapping mechanism that helps to ensure the long-term security of geological CO2 storage. We use thermochronology to estimate the timing of CO2 emplacement at Bravo Dome, a large natural CO2 field at a depth of 700 m in New Mexico. Together with estimates of the total mass loss from the field we present, to our knowledge, the first constraints on the magnitude, mechanisms, and rates of CO2 dissolution on millennial timescales. Apatite (U-Th)/He thermochronology records heating of the Bravo Dome reservoir due to the emplacement of hot volcanic gases 1.2–1.5 Ma. The CO2 accumulation is therefore significantly older than previous estimates of 10 ka, which demonstrates that safe long-term geological CO2 storage is possible. Integrating geophysical and geochemical data, we estimate that 1.3 Gt CO2 are currently stored at Bravo Dome, but that only 22% of the emplaced CO2 has dissolved into the brine over 1.2 My. Roughly 40% of the dissolution occurred during the emplacement. The CO2 dissolved after emplacement exceeds the amount expected from diffusion and provides field evidence for convective dissolution with a rate of 0.1 g/(m2y). The similarity between Bravo Dome and major US saline aquifers suggests that significant amounts of CO2 are likely to dissolve during injection at US storage sites, but that convective dissolution is unlikely to trap all injected CO2 on the 10-ky timescale typically considered for storage projects.