Convective Dissolution Research Articles

Convective dissolution in a fractured porous matrix using multi-component surface reaction lattice Boltzmann method

In this paper, an improved lattice Boltzmann method-based surface reaction model for studying the convective dissolution of a multi-component system in porous matrix is propose. This model treats the generation and the consumption of components as a source term in control equation. The accuracy of the model is validated by comparing it with an analytical solution of a two-dimensional square cavity diffusion problem and achieves a good agreement. Subsequently, this model is applied to simulate the dissolution of porous medium with a triangular fissure on the surface. By investigating the aspect ratio of the fissure, the results reveal that a low base-height ratio can promote the dissolution rate. By investigating the main dimensionless number of Sc and Da, the results show that Schmidt number has a dominant influence on the dissolution process, and Da is positively correlated with the total dissolution time.

Towards the understanding of convective dissolution in confined porous media: thin bead pack experiments, two-dimensional direct numerical simulations and physical models

We consider the process of convective dissolution in a homogeneous and isotropic porous medium. The flow is unstable due to the presence of a solute that induces a density difference responsible for driving the flow. The mixing dynamics is thus driven by a Rayleigh–Taylor instability at the pore scale. We investigate the flow at the scale of the pores using Hele-Shaw type experiment with bead packs, two-dimensional direct numerical simulations and physical models. Experiments and simulations have been specifically designed to mimic the same flow conditions, namely matching porosities, high Schmidt numbers and linear dependency of fluid density with solute concentration. In addition, the solid obstacles of the medium are impermeable to fluid and solute. We characterise the evolution of the flow via the mixing length, which quantifies the extension of the mixing region and grows linearly in time. The flow structure, analysed via the centreline mean wavelength, is observed to grow in agreement with theoretical predictions. Finally, we analyse the dissolution dynamics of the system, quantified through the mean scalar dissipation, and three mixing regimes are observed. Initially, the evolution is controlled by diffusion, which produces solute mixing across the initial horizontal interface. Then, when the interfacial diffusive layer is sufficiently thick, it becomes unstable, forming finger-like structures and driving the system into a convection-dominated phase. Finally, when the fingers have grown sufficiently to touch the horizontal boundaries of the domain, the mixing reduces dramatically due to the absence of fresh unmixed fluid. With the aid of simple physical models, we explain the physics of the results obtained numerically and experimentally. The solute evolution presents a self-similar behaviour, and it is controlled by different length scales in each stage of the mixing process, namely the length scale of diffusion, the pore size and the domain height.

Diffusive and convective dissolution of carbon dioxide in a vertical cylindrical cell

Diffusive and convective dissolution of carbon dioxide in a vertical cylindrical cell

Effects of the geothermal gradient on the convective dissolution in CO2sequestration

Convective dissolution is an important mechanism for long-term CO$_2$sequestration in deep saline aquifers. The presence of an unstable geothermal gradient can affect the process of dissolution. In this paper, we present direct numerical simulations in a three-dimensional porous medium at three different concentration Rayleigh numbers$Ra_S$with a set of thermal Rayleigh numbers$Ra_T$. Simulations reveal that the flow structures alter when${\textit {Ra}}_T$increases for a fixed${\textit {Ra}}_S$. Strong thermal gradient can yield large-scale convection rolls which change the horizontal distribution and motions of concentration fingers. The time evolution of fluxes also has different responses to different${\textit {Ra}}_T$. A theoretical model is developed and successfully describes the evolution of concentration flux and volume averaged concentration during the final shutdown stage. We further calculate the dissolved CO$_2$into the interior over time, which shows non-monotonic variations as${\textit {Ra}}_T$increases. At the end of our simulations, the maximum increment of dissolved CO$_2$occurs when density ratio is around unity for all three concentration Rayleigh numbers we have explored. We apply our results to a typical geological reservoir and discuss their implications.

Numerical Investigation of the Influence of Hydrodynamic Dispersion on Solutal Natural Convection

AbstractWe investigate numerically the effect of hydrodynamic dispersion on convective dissolution of carbon dioxide in saline aquifers. Solutions of the transport equations were used to describe the dissolution process in the aquifer and provide a systematic parametric analysis of the influence of dispersion on two important measures of convective dissolution, the wavenumber, and dissolution flux. The results suggest that dispersion decreases the dissolution rate and reduces the finger wavenumber. Based on the simulated results, new empirical scaling laws that predict the dissolution rate and wavenumber were developed. The application of the new laws to two storage sites shows that the currently available predictions overestimate the dissolution rates by ∼30%. We have identified some discrepancies between published scaling laws that were obtained for the dissolution rate. While most numerical studies identify a linear scaling, experimental investigations often suggest a sublinear behavior. Our findings resolve the controversy by suggesting that dispersion, which was not considered in these past numerical studies, is the reason for the apparent sublinear scaling.

Convective dissolution of carbon dioxide into brine in a three-dimensional free medium

Carbon dioxide (CO${}_{2}$) can be stored in huge quantities in deep saline reservoirs, thus providing a key contribution to the fight against global warming. A complete understanding of the convective dissolution process can help optimize CO${}_{2}$ storage. Observing in a different direction, i.e. parallel to gravity, highlights the 3-dimensional structure of convection dominated, at an early stage, by falling sheets. That allows an accurate measurement of the onset time of convection, verifying the predicted power-law master curve independent of the liquid phase composition. This demonstrates that adding salt simply shifts the thermodynamic state by to a different Rayleigh number.

Gravity Drainage of Bitumen Induced by Solvent Leaching.

Steam-based thermal recovery processes are energy-intensive and pose environmental concerns due to their high greenhouse gas emissions. The application of solvents has shown promise in reducing the environmental impact of these processes. In this work, the solvent chamber theory is used to study the gravity drainage of bitumen. The results reveal that the drainage rate can be scaled using the thermophysical properties of solvents. The drainage rate is shown to be directly related to the density difference between bitumen and solvent and inversely proportional to the mixture viscosity. A universal scaling relation between the Sherwood number, as a measure of the mass transfer, and Rayleigh number, as a measure of the natural convection, in the form of Sh = βRa is presented using the experimental data of various solvents. This linear relationship is consistent with the theoretical studies of buoyancy-driven convection. Moreover, the scaling prefactor β is found to decrease with increasing natural log of the mobility ratio (α), which results in a lower rate of convective mass transfer. Furthermore, a new critical Rayleigh number equation based on the power-law mixing rule (PLMR) is derived, and the results are compared with the available theories in the literature based on the exponential mixing rule (EMR). The findings provide insights into understanding the convective dissolution with large viscosity contrast. Furthermore, the developed scaling relation provides a useful tool to predict the convective mixing of different bitumen/solvent systems. The results find application in the design of the solvent-based bitumen recovery processes.

Linear stability analysis and nonlinear simulations of convective dissolution in an inclined porous layer between impermeable surfaces.

Convective dissolution can occur in porous media when a given solute dissolves in a host layer from above and increases the density of the host solution. Buoyancy-driven fingering can then develop, which increases the transfer flux of the solute. We investigate here numerically the properties of this convective dissolution when the porous host layer is inclined by an angle θ relative to the horizontal direction. We consider an incompressible flow in porous media governed by Darcy's law, driven by density gradients associated with the concentration of the dissolving solute. The model problem focuses on the case of a very long (infinite) tilted porous layer limited by two parallel impermeable surfaces. A linear stability analysis and nonlinear simulations are performed using the Boussinesq approximation. A vorticity-stream function formulation is adopted to solve the two-dimensional hydrodynamic field through the finite element method. We find that the inclination of the interface decreases the growth rate of the instability and the range of unstable wavenumbers, delaying or even suppressing the onset of the fingering instability. Moreover, it introduces a drift velocity on the perturbations, which is characterized here in both the linear stability analysis and the nonlinear simulations.

Convective dissolution of carbon dioxide in two- and three-dimensional porous media: The impact of hydrodynamic dispersion

Convective dissolution is the process by which CO2 injected in geological formations dissolves into the aqueous phase and thus remains stored perennially by gravity. It can be modeled by buoyancy-coupled Darcy flow and solute transport. The transport equation should include a diffusive term accounting for hydrodynamic dispersion, wherein the effective diffusion coefficient is proportional to the local interstitial velocity. We investigate the impact of the hydrodynamic dispersion tensor on convective dissolution in two-dimensional (2D) and three-dimensional (3D) homogeneous porous media. Using a novel numerical model, we systematically analyze, among other observables, the time evolution of the fingers' structure, dissolution flux in the quasi-constant flux regime, and mean concentration of the dissolved CO2; we also determine the onset time of convection, ton. For a given Rayleigh number Ra, the efficiency of convective dissolution over long times is controlled by ton. For porous media with a dispersion anisotropy commonly found in the subsurface, ton increases as a function of the longitudinal dispersion's strength (S), in agreement with previous experimental findings and in contrast to previous numerical findings, a discrepancy that we explain. More generally, for a given strength of transverse dispersion, longitudinal dispersion always slows down convective dissolution, while for a given strength of longitudinal dispersion, transverse dispersion always accelerates it. Furthermore, a systematic comparison between 2D and 3D results shows that they are consistent on all accounts, except for a slight difference in ton and a significant impact of Ra on the dependence of the finger number density on S in 3D.

CO2 convective dissolution in a three-dimensional granular porous medium: An experimental study

In the context of CO${}_{2}$ geological storage in deep saline aquifers, convective dissolution in porous media has been the subject of theory and numerical studies at the Darcy scale. By using both refractive index matching and planar laser induced fluorescence, we measure the onset characteristics (growth rate, wavelength, and flux) of the convective dissolution instability in a three-dimensional granular porous medium located below a gas compartment. The obtained results show large discrepancies with theoretical predictions based on Darcy scale models but are demonstrated to be consistent with a forcing of convection by porosity fluctuations, recently described in a theoretical model.

Morphological Attractors in Natural Convective Dissolution.

Recent experiments demonstrate how a soluble body placed in a fluid spontaneously forms a dissolution pinnacle-a slender, upward pointing shape that resembles naturally occurring karst pinnacles found in stone forests. This unique shape results from the interplay between interface motion and the natural convective flows driven by the descent of relatively heavy solute. Previous investigations suggest these structures to be associated with shock formation in the underlying evolution equations, with the regularizing Gibbs-Thomson effect required for finite tip curvature. Here, we find a class of exact solutions that act as attractors for the shape dynamics in two and three dimensions. Intriguingly, the solutions exhibit large but finite tip curvature without any regularization, and they agree remarkably well with experimental measurements. The relationship between the dimensions of the initial shape and the final state of dissolution may offer a principle for estimating the age and environmental conditions of geological structures.

Two-dimensional micromodels for studying the convective dissolution of carbon dioxide in 2D water-saturated porous media.

Convective dissolution is a perennial trapping mechanism of carbon dioxide in geological formations saturated with an aqueous phase. This process, which couples dissolution of supercritical CO2, convection of the liquid containing the dissolved CO2, and mixing of the latter within the liquid, has so far not been studied in two-dimensional porous media. In order to do so, two-dimensional (2D) porous micromodels (patterned Hele-Shaw cells) have been fabricated from UV-curable NOA63 glue. NOA63 is used instead of PDMS, which is permeable to CO2 and does not allow for a controlled no flux boundary condition at the walls. The novel fabrication protocol proposed here, based on the bonding of a patterned photo-lithographed NOA63 layer on a flat NOA63 base, shows good reproducibility regardless of the patterns' typical size, and allows for easy filling of the cell despite the small value of the gap. A pressure chamber allows pressurizing the CO2 and outside of the flow cell up to 10 bars. Experiments were performed in 11 different porous media geometries. As expected, a gravitational fingering instability is observed upon injection of gaseous carbon dioxide in the cell, resulting in the downwards migration of dissolved CO2 plumes through the 2D porous structure. The initial wavelength of the fingers is larger in the presence of a hexagonal lattice of pillars. This effect can be correctly predicted from the theory for the gravitational instability in a Hele-Shaw cell devoid of pillars, provided that the permeability of the hexagonal porous medium is considered in the theory instead of that of the Hele-Shaw cell. Fluctuations around the theoretical prediction observed in the data are mostly attributed to a hitherto unknown weak locking of the wavelength on the distance between closest pillars.

Development and application of computationally efficient 3D model of CO2 convective dissolution in saline aquifers.

Development and application of computationally efficient 3D model of CO2 convective dissolution in saline aquifers.

A Novel Experimental Study on Density‐Driven Instability and Convective Dissolution in Porous Media

AbstractGeological carbon dioxide (CO2) sequestration (GCS) in deep saline aquifers is a promising solution to mitigate the impact of anthropogenic CO2 emissions on global climate change. CO2 dissolved in formation water increases the solution density and can lead to miscible density‐driven downward convection, which significantly accelerates the dissolution trapping of injected CO2. Experimental studies on miscible density‐driven convection have been limited. In the laboratory, we found an empirical linear correlation between reflected green light intensity and solute concentration, which enabled in situ measurements of solute concentrations in the spatial and temporal domains and consequently the mass flux across the top boundary of the porous medium. Using the novel experimental techniques, we determined the critical Rayleigh‐Darcy number and critical time scales for the onset of density‐driven instability and convective dissolution. This is the first study to determine these critical system parameters using laboratory experiments.

Bi-dimensional plume generated by the convective dissolution of an extended source of CO2

The reduction of greenhouse gas emissions, such as carbon dioxide, is of utmost concern. In this context, carbon capture and storage (CCS) has been gaining attention as a promising midterm solution to limit CO${}_{2}$ emission. However, assessing storage efficiency of CO${}_{2}$ requires a better understanding of the processes involved in the convective dissolution of CO${}_{2}$, especially the nonlinear regime where developed solutal plumes coexist. As a first step towards a better understanding of the nonlinear dynamics of such a plume assembly, we propose an experimental/numerical study of a single bi-dimensional plume generated by CO${}_{2}$ dissolution from a source of finite lateral extension.

Spreading and mixing during solutal convection in uniform porous media with application to geologic CO2 storage

Convective dissolution in saline aquifers is expected to positively impact subsurface storage of carbon dioxide (CO2) by accelerating its dissolution rate into reservoir brines. By largely focusing on the dissolution flux, previous studies lack a systematic evaluation of the mixing process following CO2 emplacement, including a quantitative analysis at conditions representative of subsurface traps (Rayleigh number, Ra≤1 000). Here, we investigate solutal convection numerically in a two-dimensional uniform porous medium in the regime Ra=100−10 000. The macroscopic evolution of the convective process is characterized by means of fundamental macroscopic measures of mixing that use the local spatial structure of the solute concentration field. It is shown that the intensity of segregation closely mimics the evolution of the in situ convective pattern arising from the stretching and merging of downwelling plumes. The spreading length and the dilution index both confirm that the mixing process accelerates over time (t) with a power law scaling (∝tα) that transitions from diffusive (α=0.5) to superdiffusive mixing (α≥1) irrespective of Ra. This transition time scales τon∝Ra−2 and is used as a measure of the onset time of convection. The dilution index indicates that the time needed to reach close-to-complete mixing reduces linearly with Ra. On the contrary, the non-dimensional mass flux, expressed in terms of the Sherwood number, Sh, reveals a natural logarithmic scaling for Ra≤2 500.

Control of chemically driven convective dissolution by differential diffusion effects

Differential diffusion effects can impact chemically driven convective dissolution that occurs when a chemical reaction destabilizes an otherwise stable density stratification after dissolution of a given solute in a host phase.

Convective carbon dioxide dissolution in a closed porous medium at high-pressure real-gas conditions

We combine modeling and measurements to investigate the dynamics of convective carbon dioxide (CO2) dissolution in a pressure-volume-temperature cell, extending a recent study by Wen et al. (J. Fluid Mech., vol. 854, 2018, pp. 56–87) at low-pressure under ideal-gas conditions to high-pressure and real-gas conditions. Pressure-dependent compressibility and solubility are included to model the evolution of CO2 concentration in the gas phase and at the interface, respectively. Simple ordinary-differential-equation models are developed to capture the mean behavior of the convecting system at large Rayleigh number and are then verified by using both numerical simulations and laboratory experiments. The prefactor for the linear scaling of convective CO2 dissolution is evaluated – for the first time – by using pressure-decay experiments in bead packs at reservoir conditions. The results show that our models could quantitatively predict the process of the convective CO2 dissolution in pressure-decay experiments. Moreover, the results also reveal that for increasing gas pressure in closed systems, the negative feedback of the pressure drop – resulting from the dissolution of CO2 in the liquid – is weakened due to the decrease of the solubility constant at real-gas conditions. Our analysis provides a new direction for determination and validation of the convective dissolution flux of CO2 in porous media systems.

New Spectrophotometric Method for Quantitative Characterization of Density-Driven Convective Instability.

CO2 convective dissolution has been regarded as one of the fundamental mechanisms to accelerate the mass transfer of CO2 into brine. We present a new spectrophotometric method to characterize the convective instability and measure the dissolved CO2 mass, which enables the real-time quantitative visualization of CO2/brine transport mechanisms. Successive images were captured to identify the finger development regimes, and the convection morphologies were analyzed by the fingers length and affected area. CO2 solubility was experimentally studied, and the results are in agreement with the theoretical calculations. CO2 mass transfer flux was investigated as the Sherwood number changed. The increase in salinity and temperature has a negative effect on CO2 dissolution; here, numerical simulation and experimental phenomena are qualitatively consistent. In general, these findings confirm the feasibility of the method and improve the understanding of the physical process of CO2 convective dissolution, which can help assess the CO2 solubility trapping mass.

CO2 Convective Dissolution in Oil-Saturated Unconsolidated Porous Media at Reservoir Conditions

During CO2 storage, CO2 plume mixes with the water and oil present at the reservoir, initiated by diffusion followed by a density gradient that leads to a convective flow. Studies are available where CO2 convective mixing have been studied in water phase but limited in oil phase. This study was conducted to reach this gap, and experiments were conducted in a vertically packed 3-dimensional column with oil-saturated unconsolidated porous media at 100 bar and 50 °C (representative of reservoir pressure and temperature conditions). N-Decane and crude oil were used as oils, and glass beads as porous media. A bromothymol blue water solution-filled sapphire cell connected at the bottom of the column was used to monitor the CO2 breakthrough. With the increase of the Rayleigh number, the CO2 transport rate in n-decane was found to increase as a function of a second order polynomial. Ra number vs. dimensionless time τ had a power relationship in the form of Ra = c×τ−n. The overall pressure decay was faster in n-decane compared to crude oil for similar permeability (4 D), and the crude oil had a breakthrough time three times slower than in n-decane. The results were compared with similar experiments that have been carried out using water.