Convective carbon dioxide dissolution in a closed porous medium at low pressure

Abstract

Motivated by geological carbon dioxide (CO 2 ) storage, many recent studies have investigated the fluid dynamics of solutal convection in porous media. Here we study the convective dissolution of CO 2 in a closed system, where the pressure in the gas declines as convection proceeds. This introduces a negative feedback that reduces the convective dissolution rate even before the brine becomes saturated. We analyse the case of an ideal gas with a solubility given by Henry's law, in the limits of very low and very high Rayleigh numbers. The equilibrium state in this system is determined by the dimensionless dissolution capacity, Π, which gives the fraction of the gas that can be dissolved into the underlying brine. Analytic approximations of the pure diffusion problem with Π > 0, show that the diffusive base state is no longer self-similar and that diffusive mass transfer declines rapidly with time. Direct numerical simulations at high Rayleigh numbers show that no constant flux regime exists for Π > 0; nevertheless, the quantity F/C 2 s remains constant, where F is the dissolution flux and C s is the dissolved concentration at the top of the domain. Simple mathematical models are developed to predict the evolution of C s and F for high-Rayleigh-number convection in a closed system. The negative feedback that limits convection in closed systems may explain the persistence of natural CO 2 accumulations over millennial timescales.

Convective Dissolution of Carbon Dioxide in Deep Saline Aquifers: Insights from Engineering a High-Pressure Porous Visual Cell

“…This is because of the predominant decrease of pressure following the onset of convection, which in turn decreases the solubility of CO 2 in brine at the interface and accordingly the dissolution-induced density change, i.e., the driving force for buoyancy-driven convection. The final outcome of this nonlinear dynamics is the decreasing trend, rather than a constant average value, of flux in the intermediate regime before the onset of final shut-down, as predicted theoretically by Wen et al [42].…”

“…Despite the decreasing trend of flux in this regime, a quasi-steady regime, however, is attainable in closed systems with the introduced compensation of dissolution flux as Fc Figure 3. This is a modification to the scaling suggested by Wen et al [42] as F c /C 2 s . The results of experiments are analyzed based on the new correction to obtain transition times between dissolution regimes and the associated scaling relations.…”

“…However, as time goes on fingers start to merge to their neighboring fingers and create stronger fingers. At this time, the dissolution flux (or mixing rate) increases with time in a flux-growth (or dissipation-growth) regime [41,42]. After the convective regime has well developed, the quasisteady state regime starts [42], during which the convective flow brings the fresh brine to the gas-brine interface and the process continues in a quasi-steady regime until the brine brought to the gas-brine interface begins to contain dissolved CO 2 .…”

Reduced modeling of porous media convection in a minimal flow unit at large Rayleigh number

“…Rayleigh-Bénard convection in a fluid-saturated porous layer is a prime example of a spatiotemporal pattern-forming system that exhibits rich nonlinear dynamics despite its comparably simple mathematical formulation [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Recently, there has been renewed interest in this system owing to the potential impact of buoyancy-driven convective flows on geological carbon dioxide (CO 2 ) storage, which is one promising means of reducing CO 2 emissions into the atmosphere [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. In a wide horizontal porous layer uniformly heated from below and cooled from above, the basic conduction state becomes unstable via a stationary bifurcation when the Rayleigh number Ra > 4π 2 [1,2], and convection sets in as steady O(1) aspect-ratio rolls.…”

A short review on porous media convection

“…Buoyancy-driven convection in a fluid-saturated porous layer has been extensively studied due to its numerous applications in oil recovery [1], groundwater flow and geothermal energy extraction [2][3][4][5][6][7], transport in biological tissues [8], and carbon dioxide sequestration [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Moreover, porous media convection is also used as a classical example to study instabilities, bifurcations, pattern formation, and spatiotemporally chaotic dynamics [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41].…”