Effect of Convective Mixing Process on Storage of CO₂ in Saline Aquifers with Layered Permeability

Amir Taheri ^1,*, Ole Torsæter ¹, Erik Lindeberg ², Nanji J. Hadia ³, Dag Wessel-Berg ⁴

1. Department of Geoscience and Petroleum, NTNU, Trondheim, Norway

2. SINTEF Petroleum Research, Trondheim, Norway

3. Institute of Chemical and Engineering Science (ICES), Singapore

4. Department of Mathematical Sciences, NTNU, Trondheim, Norway

* Correspondence: Amir Taheri

Academic Editor: Sina R. Gomari

Special Issue: Applied Geological CO₂ Storage and Geochemistry

Received: October 19, 2020 | Accepted: February 07, 2021 | Published: February 25, 2021

Advances in Chemical Research 2021, Volume 3, Issue 1, doi:10.21926/acr.2101012

Recommended citation: Taheri A, Torsæter O, Lindeberg E, Hadia NJ, Wessel-Berg D. Effect of Convective Mixing Process on Storage of CO₂ in Saline Aquifers with Layered Permeability. Advances in Chemical Research 2021; 3(1): 012; doi:10.21926/acr.2101012.

© 2021 by the authors. This is an open access article distributed under the conditions of the Creative Commons by Attribution License, which permits unrestricted use, distribution, and reproduction in any medium or format, provided the original work is correctly cited.

1. Introduction

Carbon dioxide (CO₂) storage in saline aquifers of huge volume has been recognized as an effective option for decreasing CO₂ emission to the atmosphere. However, leakage of CO₂ from these storage sites is one of the main concerns. The associated risk to this leakage is reduced by understanding the trapping mechanisms of CO₂ into the brine and by taking suitable measures. One of these trapping mechanisms is the dissolution of supercritical CO₂ into underground formation water, which is considered as a medium to long-term trapping mechanism. Over a long period of time, the injected CO_2, which has formed a thin layer of free-phase CO₂ below the caprock, gradually diffuses and dissolves into brine. The CO₂ dissolution into brine, subsequently causes an increase in density of the brine-CO₂ solution, which overlies the less dense brine. This situation initiates gravitational instability and eventually leads to density-driven natural convection and increasing the dissolution rate of free phase CO₂ into the brine [1,2,3]. Density-driven natural convection occurs when the Rayleigh dimensionless number $R_a=(\Delta\rho gkh)⁄(\varphi\mu D$) is larger than 40, approximately [1]. The timing of the onset of this instability and the dissolution rate across the phase contact of CO₂ and brine solution are the two crucial operational issues when assessing the feasibility of a potential storage site.

Numerical studies for describing the convective mixing process and its effectiveness in storing CO₂ into the homogeneous saline aquifers are reported several years ago [2,3,4,5,6,7,8,9,10,11,12]. Furthermore, the gravitational instability of a diffusive boundary layer has been described using theoretical methodologies in recent years to predict the onset time of convection and the related unstable wavelength in the homogeneous models [13,14,15,16,17,18,19,20,21,22].

A limited number of experimental studies exist on the effectiveness of the convective mixing process in the homogeneous media regarding the storage of CO₂ in geological formations [2,6,23,24,25,26,27,28,29,30,31,32,33,34,35,36]. The occurrence of natural convection and the effectiveness of the convection mechanism (on the dissolution of CO₂ into brine) are investigated by recording the change in pressure in a bulk media, using a cylindrical PVT cell [25,26,27,28,33], and in a homogeneous porous media, using cylindrical core [6,30,31], where a fixed volume of CO₂ is overlaying a column of distilled water. Convective currents and dynamics of convective mixing are visualized at ambient conditions using Schlieren and pH indicator techniques, for bulk modules of gas-liquid systems, like CO₂-water [23,24,33], and for homogeneous Hele-Shaw cells without porous media [2,30,31,32,34,35] and with porous media [29,30,31,32,35] by using analog or CO₂-water fluids. The initiation, formation, and growth of small convective fingers and progress of this process as a function of time are discussed extensively [36]. The essential parameters of the convective mixing process, i.e., onset time of convection, critical wavelength, shape and growth of fingers over time, and the amount of dissolved CO₂ into water, are measured qualitatively (by snapshots of convective mixing of CO₂ and water) and quantitatively (by amounts of dissolved CO₂ into water) in different homogeneous Hele-Shaw cell geometries with Rayleigh numbers varying in the range of 700-9500 [36].

While heterogeneity and layered structure are the main characteristics of real geological formations, a limited number of studies exist about the gravitational instability of a diffusive boundary layer in such systems. Similar to homogeneous models, the onset conditions of natural convection in heterogeneous media (with simple geometry and boundary conditions) are also studied using linear stability analysis [37,38]. Effect of various types of heterogeneity, e.g., regular and irregular barrier patterns in porous media or multilayered porous media, on convective mixing are analyzed using numerical methods. In heterogeneous models with the distribution of horizontal impermeable barriers, the onset of convection is found to occur much sooner than the equivalent anisotropic homogeneous model. However, the constant dissolution flux (in the constant flux regime and after the onset of the instability) is not sensitive to barrier properties and depends only on the effective average properties [3,8,10,35,39]. It is also reported that the rate of CO₂ dissolution in these types of heterogeneous media is higher than the equivalent homogeneous media, and the numerical simulations in equivalent homogenous porous media often underestimate the mass transfer rate of CO₂ into water [11]. In multilayered porous media, though a top-layer with high permeability is more favorable for fast mass transfer, the natural convection process occurs with a top-layer of low permeability [40]. In such models with horizontal parallel layers and vertical variation of permeability, if the top layer has higher permeability, then the top layer properties govern the convective mixing in both strong and weak heterogeneity models. However, it is also seen that the top-layer with lower permeability can also be the governing one in the models with weak heterogeneity. Interestingly it is observed that in a model with a strong heterogeneity, the top layer with lower permeability has more effect on the amount of CO₂ dissolved in brine than the bottom layer, and the impact of the bottom layer with lower permeability is increased with an increase in the thickness (bottom layer) [3]. Considering the behavior of convective mixing process, multilayered models are converged to homogeneous anisotropic models by increasing the number of layers [41]. The existence of low permeability rectangular structures inside a high permeability body results in different free convective processes at different spatial and temporal scales [42].

Experimental studies on convective mixing of CO₂ and brine in two-layered porous media by quantifying pressure decline in a column of gas on top of a porous medium show that existence of a high permeable top layer is more desirable. This configuration causes an immediate start of convective mixing, but its strength decreases when the fingers penetrate into the low permeability layer [40]. It is also examined that strengthening the micro-heterogeneity in porous media accelerates the CO₂ dissolution [42] and the existence of low permeability layers (embedded between relatively higher permeability zones) causes significant diffusive mixing in the low permeability layers than the convective mixing [44].

Despite numerous analytical and numerical studies on the convective mixing of CO₂ and brine, insufficient experimental studies exist on the investigation of the accelerated mass transfer rate of CO₂ into saline aquifers, especially in heterogeneous porous media with layered permeability. This work aims to develop a basic understanding of the mechanism of convective flow in layered permeability models, using experimental tools for identifying the behavior of convection fingers that meet the interface of the layers. For this purpose, the previous experimental set-up of convective mixing studies [36,43] is upgraded using two-layered Hele-Shaw cells, and different tests are performed using CO₂ and water at atmospheric conditions. Recording qualitative (snapshots of convective mixing) and quantitative measurements (pressure, temperature, and pump volumes) simultaneously give a better understanding. The time-lapse movies are made from the snapshots that are collected during the experiments, which are suitable for improving public awareness. Lastly, the experimental results are compared qualitatively with numerical simulation models performed by Eclipse-100.

2. Experimental Set-up and Procedure

2.1 Experimental Set-up

The experimental set-up and procedure have been described elsewhere in detail [36,43]. In this study, the previously used experimental set-up is upgraded using two-layered Hele-Shaw cells, with different permeability and height of the top and bottom layer. Figure 1 shows the schematic of the used set-up consisting of two-layered permeability Hele-Shaw cells, a DIGIQUARTZ pressure transducer, a multi-step programmable CHEMYX OEM syringe pump, temperature recording apparatus (three Pt100 sensors on the syringe pump, CO₂ tank, and on top of the cell, and three EUROTHERM 2408i), CO₂ source, imaging system, and a PC with a system controller. The cell dimensions are 50 cm × 50 cm.

Figure 1 Schematic of the experimental set-up.

Two sheets of glass with dimensions of 50 cm x 40 cm and 50 cm x 10 cm are attached along their length (by glue) to produce the two-layered permeability cells. These two sheets should be placed at two different levels (representing two different gaps) for gluing. Afterward, another sheet of glass is fixed against this one, and shims of different thicknesses are placed on the sides in different layers. Small shims with the same thickness as those at the sides are placed between two glass sheets at different locations to ensure a uniform gap in different locations. The cell is tightened from four sides and center with small diagonal forces of the same magnitude.

A tank is attached to the bottom of the cell to uniformly fill the cell by water, and a stainless-steel tank is connected to the top to provide CO₂ (source) overlaying the water in the cell. After each test, the cell is cleaned using a mixture of distilled water and methanol. The permeability of each layer can be calculated using Equation (1),

where k and d are permeability (m²) and gap (m) of each layer, respectively.

The set-up is automated by maintaining a constant pressure (around atmospheric pressure) of the free-phase CO₂, on top of the water, to prevent movement of the top boundary with more accuracy. This is achieved by checking the CO₂ pressure at the top of the water by the pressure transducer and controlling the syringe pump based on this pressure. At each time step, when CO₂ starts to dissolve into the water, its pressure decreases gradually. At this time, the syringe pump injects CO₂ until reaching the initial pressure and maintains a steady pressure.

Images of the process are captured at every 10 sec, 20 sec, 1 min, and 2 min using a Canon EOS-1Ds Mark II camera, connected to a PC, and a video of the convection finger movement in the cell is made. A table light is positioned behind the cell to create high-quality images.

2.2 Fluid Composition and Properties

The fluids used in these experiments are a solution of 0.025 wt.% bromocresol green (Sigma-Aldrich, Inc.) and distilled and deionized water and CO₂ gas at the ambient condition. The small amount of bromocresol green does not affect the properties of water. At low pH, the indicator color is yellow, and at high pH, the color is blue. Table 1 presents the thermodynamic properties of the fluids used in the experiments [36,43].

Table 1 Properties of the used fluids.

2.3 Specifications of the Two-layered Cells

Four two-layered permeability Hele-Shaw cells, with the specifications given in Table 2, are used for understanding the effects of vertical variation of permeability and layer thickness (in saline aquifers) on the behavior of convective mixing of CO₂ and water. d, k, h, and R_a are the gap, permeability, height, and Rayleigh number of the layers, and subscripts 1 and 2 represent the top and bottom layers, respectively. The cells are oriented vertically, and their considered width and height for analysis are 0.50 m and 0.25 m, respectively (upper half of the cells). The calculations and analyses are performed for various durations before convection fingers touch the bottom boundary, and the experimental cells correspond to infinite depth aquifers with the gas-water contact situated at z = 0.

Table 2 Layered permeability Hele-Shaw cell models.

The behavior of convective mixing and dissolution of CO₂ into the water in the layered permeability cells are compared with the results of the vertical homogeneous cells (with the gaps of 0.25 mm (cell H2) and 0.50 mm (cell H5) with permeabilities of 5266 Darcy and 21065 Darcy, respectively) [36].

2.4 Experimental Procedure

After filling the cell with water (with a pH of around 5.4) from the bottom, an equilibrium temperature is obtained between the environment, cell, and table light behind the cell. The inlet valve (through which CO₂ enters the cell) and the outlet valve (through which CO₂/air exits from the cell) are opened simultaneously to purge the cell with CO₂ and remove the air above the water. After few seconds (to be sure that the air inside the lines, CO₂ tanks, and cell has been removed), the inlet and outlet valves are closed simultaneously, and the CO₂ pump and pressure transducer valves are opened. CO₂ is injected into the cell to maintain a constant pressure.

3. Results and Analysis

3.1 Analytical Approach

The experimental data consist of the quantitative (the amount of CO₂ dissolved into the water) and the qualitative data (the captured images from the Hele-Shaw cells during the tests). The selected snapshots from the Hele-Shaw cell are processed, and their colors are replaced to clearly visualize the changes in the dissolved CO₂. In these snapshots, the blue color is pure water in equilibrium with air (pH of 5.4). The red color on top of the water shows the gaseous phase CO₂, and the red color in the water represents water with maximum dissolved CO₂ (pH of about 3.9). The other colors in between represent water with dissolved CO₂ and acidity ranging between 3.9 to 5.4.

The amount of dissolved CO₂ in water is calculated by calculating the number of moles of in-situ gas-phase CO₂ present in the pump (first term), the tank (second term), and the cell above the water surface (third term) at each time duration, and subtracting them from the values obtained at the previous time duration to obtain the number of moles of the dissolved CO₂ in water at each time interval:

In these calculations, it is assumed that:

Subscripts p, t, c, and s indicate pump, tank, cell (above the water surface in the cell), and system, respectively. In this set-up and for this equation, tank (t) represents all lines, connections, valves, and stainless-steel tank attached on top of the cell, and its volume (V_t) is calculated as 4.25E-05 m³ [36,43]. V_c is the cell volume above the water surface (that is full of CO₂) and is calculated by measuring the water level in the cell before each test. Various data (measured at each time interval of 10 s) are as follows: CO₂ pressure in the system (P_{{CO}_2}), that is read by the pressure transducer and is fixed at a constant value, the pump volume (V_p), that represents the volume of CO₂ injected by the pump, the pump temperature (T_p) and cell temperature (T_c), that are read at each time interval, by Pt100 sensors attached to them. After calculating the number of moles of the dissolved CO₂ into the water at each time interval using Equation 2, and determining the cumulative mole of dissolved CO₂ into the water, the calculated values are transformed from mole to kg/m² unit by considering the molecular weight of CO₂ and the cross-sectional area of the contact surface. The calculated cumulative dissolved CO₂ in kg/m² (experimental value) is comparable with the diffusion equation (theoretical value) as stated in Equation 3,

Where M(t) represents the total amount of dissolved CO₂ per cross-sectional area at time span t. The observed time of deviation of the experimental values from the theoretical values is attributed to the quantitative onset time of convection. The suitable region for the diffusion equation can be selected by examining the graph of cumulative dissolved CO₂ vs. the square root of time, and the theoretical value (obtained from the diffusion equation) can be fitted on the experimental values (obtained from the experimental values of dissolved CO₂) by minimizing the root mean square differences. The quantitative onset time for convection or the time of deviation of experimental data from the theoretical data can be compared with the qualitative onset time for convection from the captured images after observing the first instabilities. The qualitative average value of the critical wavelength of convection fingers, observed after the onset of convection, is computed by selecting a centered horizontal segment (to remove the edge effect) of the CO₂-water interface and dividing this distance by the number of convection fingers in this segment. The onset time of convection and the critical wavelength of convection fingers (calculated from the experiments conducted in the homogeneous cell) are transferred to dimensionless forms using a length scale and a time scale as given in Equations 4 and 5, and the values can be compared with the numerically predicted values [14,15,18,19,21,22,44,45,46,47]

Another critical parameter is the dissolution flux (after the onset of convection in the constant-flux regime), which is also calculated for each test using experimental measurements.

3.2 Experimental Results and Analyses

Four tests are carried out using heterogeneous cells (two-layered cells with different heights and permeabilities), as shown in Table 2. The tests of the heterogeneous system with a 0.25 mm gap in the first layer (tests L1 and L2) are compared with a vertically homogeneous system with a uniform gap of 0.25 mm (test H2) and the tests of the heterogeneous system with 0.50 mm gap in the first layer (tests L3 and L4), are compared with a vertically homogeneous system with a uniform gap of 0.50 mm (test H5). Comprehensive results of convective mixing in the homogeneous cells are presented elsewhere [36]. The quantitative measurements of dissolved CO₂ in water are accurately made only in the layered permeability cell L3, and in the others, only images are analyzed, and qualitative data are acquired. The videos created from the images are speeded up with the scales of 1/1600 and 1/3200 and have been uploaded to the following URL address for public awareness of the process:

https://www.youtube.com/playlist?list=PLfLgKEdPkuBPIlO1JDrmUJ0XnSCJOIBJD

3.2.1 Low Permeable Top Layer

Snapshots of convective mixing of CO₂ and water, and the changes in the dissolved concentration of CO₂ in water, over a certain time duration in the layered permeability cell L1 (when a low permeability layer with a gap of 0.25 mm is on top of a high permeability layer with a gap of 0.50 mm) are shown in Figure 2. This figure also compares the convective mixing process of the layered permeability cell L1 with the homogeneous cell H2 (with a gap of 0.25 mm). The first snapshots (Figure 2a) show the cells at the initial state (i.e., before the introduction of CO₂). After the introduction of CO₂ on top of the cell (i.e., above the water), CO₂ starts to dissolve into the water by diffusion, and the color of the top layers of water changes from blue (with a pH of 5.4) to yellow (with a pH of less than 5.4), because of changes in the acidity level of water by the dissolved CO₂. When the thickness of this diffusive layer increased sufficiently, gravitational instability occurs, and convective mixing commences at this time (onset time for convection). The calculated onset time of convection (t_c^*) in these two systems are found to be 897 sec and 970 sec using quantitative and qualitative measurements, respectively. The average size of the convection fingers (the qualitative critical wavelength of convection fingers, λ_c^*) is found to be 0.01178 m approximately. Considering the length scale (L = 9.14E-05 m) and time scale (T = 4.43 sec) in the homogeneous cell H2, the dimensionless values of time corresponding to the onset of convection (t_c) calculated from quantitative and qualitative data are found to be 202.45 and 218.93, respectively, and the critical wavelength of convection fingers (λ_c) is 128.83 [36]. By comparing the snapshots of the tests carried out in the layered -permeability cell and homogeneous cell at the same time, it is observed that tests of both cells display almost similar behavior before the convection finger touches the second layer (in the layered cell) at around 21591 sec (Figure 2b and 2c). This means that the top layer of the layered permeability cell is the dominant layer, which affects the behavior of convection fingers, like the onset time of convection, critical wavelength, size, and growth of convection fingers after convection starts and in the constant flux regime (before the bottom layer comes in contact with the convection fingers). Even though the convection fingers in the H2 cell proceed downward with time, the convection fingers in the L1 cell do not penetrate the high permeable bottom layer. After the convection fingers touch the interface (between two layers) at around 21591 sec in the L1 cell, they merge together to form fingers of higher wavelengths (Figure 2d, 2e, and 2f). No further downward penetration of fingers is observed.

Figure 2 Snapshots of convective mixing of CO₂ and water in layered permeability cell L1 and homogeneous cell H2; (a) t = 0 sec, (b) t = 3391 sec, (c) t = 21591 sec, (d) t = 39853 sec, (e) t = 58034 sec, (f) t = 76274 sec.

The changes in the dissolved concentration of CO₂ in water over a time duration in layered permeability cell L2 and homogenous cell H2 are shown in Figure 3, where a low permeability layer (with a gap of 0.25 mm) is on top of a high permeability layer (with a gap of 0.50 mm). The water height in this cell is less than the L1 cell. A comparison of the snapshots of the cell L2 with the cell H2 (at the same time) from Figure 3 shows similar results. While the behavior of L2 and H2 cells are identical initially (after starting the test), the convection fingers in the cell L2 do not enter into the bottom layer (with higher permeability and pore volume) until 76269 sec (that is the final recorded time). They grow and their wavelength increases when they touch the interface (between two layers). However, the convection fingers of the H2 cell grow and move downward.

Figure 3 Snapshots of convective mixing of CO₂ and water in layered permeability cell L2 and homogeneous cell H2; (a) t = 0 sec, (b) t = 3405 sec, (c) t = 21669 sec, (d) t = 39788 sec, (e) t = 58029 sec, (f) t = 76269 sec.

By comparing the layered permeability cells L1 and L2, it can be stated that the behavior of convection fingers formed in the top layer (of lower permeability) when they touch the interface is not dependent on the size of the fingers (width and length). The convection finger wavelength increases without any advancement into the bottom layer because there is no sufficient mass of CO₂ present on top of the bottom layer to continue the convective flow and the fingering process in that layer. In this condition, the diffusion mechanism dominates the convection flow. These results are consistent with previous numerical simulation results [3], which have concluded that in a layered permeability cell, the properties of the top layer (of lower permeability) only dominate the whole process till the end.

3.2.2 High Permeable Top Layer

The changes in the dissolved concentration of CO₂ in water, over a certain time period, in a layered permeability cell L3, are displayed in Figure 4, when a high permeability layer (with a gap of 0.50 mm) is on top of a low permeability layer (with a gap of 0.25 mm). Moreover, the behavior of convection fingers in this cell and the homogeneous cell H5 (with the gap of 0.50 mm) is also compared (at the same time) in Figure 4, which shows that the behavior of both cells is almost similar before the convection fingers touch the second layer in the L3 cell, e.g., at about 771 sec and 6341 sec (Figures 4b and 4c). Similar onset time of convection, the critical wavelength, shape, position, and growth of convection fingers with time, are observed in both L3 and H5 cells. The onset time values of convection (t_c^*) in these two cells calculated using quantitative and qualitative measurements are found to be 489 sec and 230 sec, respectively, which are much lower than the calculated time values for the previous tests (where the low permeable layer was on the top). The qualitative critical wavelength of the convection fingers (the) (λ_c^*) is 0.00514 m, which is lower than the value found in the previous tests (0.01178 m). Considering the length scale (L = 2.29E-05 m) and time scale (T = 0.2769 sec) in the homogeneous cell H5, the dimensionless onset time values for convection (t_c) calculated from the quantitative and qualitative data (t_c) are 1765.88 and 830.58, respectively, and the critical wavelength of convection fingers (λ_c) is 224.86 [36]. When the convection fingers of the L3 cell touch the bottom layer (of less permeability and pore volume), the downward movement speed of convection fingers decreases than cell H5 (Figure 4c). Then these convection fingers (formed in the top layer of higher permeability) start to merge and then penetrate the bottom layer with higher wavelengths. Although the convection fingers in the H5 cell reach the bottom boundary of the cell after 22965 sec (Figure 4f), the fingers in this layered cell can reach only till the middle of the cell at this time (Figure 4f).

Figure 4 Snapshots of convective mixing of CO₂ and water in layered permeability cell L3 and homogeneous cell H5; (a) t = 0 sec, (b) t = 771 sec, (c) t = 6341 sec, (d) t = 11881 sec, (e) t = 17500 sec, (f) t = 22965 sec.

Figure 5 compares cumulative dissolved CO₂ in the layered permeability cell L3 with homogeneous cells H2 and H5 with gaps of 0.25 mm and 0.50 mm, respectively. It can be seen that the rate of dissolution of CO₂ in the L3 cell is the same as the rate of dissolution in the H5 cell with the gap of 0.50 mm until 12693 sec (≈5.986E-10 kg/s), and it seems that the top layer with higher permeability is dominant until this time, while the convection fingers have touched the bottom layer at around 6341 sec. After 12693 sec, the rate of dissolution of CO₂ into the water in the L3 cell (with k₁/k₂ of 4) is reduced by 50% (to 3.152E-10 kg/s) due to the effect of the bottom layer (of lower permeability). However, it is still more than twice the dissolution rate of CO₂ in the H2 cell (1.265E-10 kg/s) with the same properties of the bottom layer. It causes a considerable difference between the amount of dissolved CO₂ into the water in L3 and H2 cells (cumulative dissolved CO₂ of 1.9E-5, 1.5E-5, and 5.4E-6 kg till 30000 sec in the cells H5, L3, and H2, respectively). It can be seen as that the final cumulative dissolved CO₂ in the L3 cell is more than the H5 cell, as at the final recorded time, the convection fingers reach the bottom boundary of the H5 cell, but the convection fingers reach only till the interface (almost middle of the cell) of the L3 cell at that time. This comparison reveals the impact of the high-permeable top layer of a layered cell on increasing the rate of CO₂ dissolution into the water and approaching the rate of CO₂ dissolution of the layered permeability cell to the homogeneous cell H5.

Figure 5 Comparing the cumulative amount of dissolved CO₂ in layered permeability cell L3 with homogeneous cells H2 and H5.

Figure 6 presents the changes in the dissolved concentration of CO₂ in water over time in layered permeability cell L4, when a high permeability layer (with a gap of 0.50 mm) is on top of a low permeability layer (with a gap of 0.25 mm). The height of water in this test is lower than the layered permeability cell L3. By comparing these images with the homogeneous cell H5 (with the gap of 0.50 mm) in this figure at the same time periods, it is observed that cell L4 shows similar results to the cell L3 (mentioned in the previous section). The behaviors of layered and homogeneous cells are identical until the convection fingers touch the bottom layer at around 780 sec (Figure 6b). After the convection fingers touch the bottom layer of lower permeability and pore volume in the L4 cell, the downward movement speed of convection fingers decreases, compared to the H5 cell. The convection fingers formed in the top layer (with higher permeability) grow, and they penetrate the bottom layer with higher wavelengths. This result confirms that the behavior of convection fingers when they touch the layer interface is independent of the height of the top layer (with high permeability) and dimension (width and length) of the fingers.

Figure 6 Snapshots of convective mixing of CO₂ and water in layered permeability cell L4 and homogeneous cell H5; (a) t = 0 sec, (b) t = 780 sec, (c) t = 6340 sec, (d) t = 11879 sec, (e) t = 17519 sec, (f) t = 22979 sec.

A previous numerical simulation study has confirmed this behavior of the convection fingers for layered permeability models with strong heterogeneity (e.g., with a permeability-ratio of 6.0). In contrast, in layered permeability models with weak heterogeneity (e.g., with a permeability ratio of 2), the top layer properties dominate the whole process [3]. While in this work, it is shown that convection fingers form fingers of higher wavelength and penetrate the bottom layer of low permeability, another simulation study has demonstrated that the convection fingers disappear in the bottom layer of low permeability, and reduce the convection effect [40].

3.3 Numerical Simulation Models

Eclipse-100 flow simulator (black oil) is used to visualize the behavior of convection fingers in the layered permeability models when they reach the bottom layer [48]. A more detailed quantitative study of this problem is presented before [3]. Similar to the experimental tests, the simulation models are of two-phase flow, two-dimensional, and are initialized with a gas cap containing free-phase CO₂ with constant pressure on top and an aquifer with water below. This CO₂ phase causes maximum CO₂ concentration on top of the aquifer after the first time-step due to the dissolution of CO₂ into the water by diffusion. Darcy and Fick's laws are considered as the governing equations in the simulation models, and the boundary conditions in simulation models are identical to those in the experiments. The thermodynamic properties of the used fluids in the experiments are given in Table 1. The size and other features of the simulation models and experimental models are the same. In the simulation models, the porosity is considered as one, and the permeabilities are changed a bit to have an equal length scale (L) and time scale (T) in the simulation and experimental models. The grid sizes are very fine, and the critical wavelength of the perturbations, which most easily gives rise to instability, can be considered as an indication of an appropriate grid size of the models in a numerical simulation. The horizontal grid block size with 1/20 of critical wavelength, obtained from linear stability analysis (by considering the higher permeability value), is a suitable size for simulation of this behavior [3,10]. The vertical grid block size equals the horizontal grid block size, and the same grid block resolution is considered in both layers. The time steps are fine enough to capture the onset time of convection with high accuracy. The simulation results in this section are based on perturbation introduced by numerical round-off errors in the finite-difference flow simulations, and the convective mixing starts when one introduces a perturbation from the pure diffusion profile of CO₂ into the water (below the phase contact).

Figure 7 compares the convection finger behavior in the experimental and simulated layered permeability models L1 and L3, when they encounter the bottom layer. The results of the simulated model L1 are consistent with the experimental results of cell L1, which show similar behavior of the convection fingers, where the convection fingers (formed in the top layer of low permeability) merge and form fingers of higher wavelengths after reaching the bottom layer of high permeability. In the simulated model, the fingers penetrate the bottom layer at some points with smaller wavelengths, but the penetrated fingers do not continue to grow downward and vanish. While in the experimental tests, penetration in the bottom layer by fingers is not observed. In the simulated model L3, where the top layer is of higher permeability, the finger wavelengths are seen to increase after convection fingers touch the bottom layer of lower permeability. The convection fingers are found to penetrate the bottom layer when their wavelength increases enough. Similar results are observed in the experimental layered permeability cell L3 also, which concludes that simulated and experimental results are consistent with each other.

Figure 7 Comparison of conve ction fingers in experimental and simulation layered permeability models L1 and L3.

4. Conclusions

For investigating the effect of layer properties (thickness and permeability) on the convective mixing process and dissolution of CO₂ into the water, four tests with two-layered permeability Hele-Shaw cells (heterogeneous system) were carried out, and the behavior of convection fingers was analyzed and compared with the test results of homogeneous cells. The observed experimental results were consistent with the numerically simulated results. The achieved results are concluded below:

• 1. In the dissolution of CO₂ into the water in two-layered permeability geometries, the top layer controls the onset time of convection, critical wavelength of convection fingers, and early dissolution flux of CO₂ into water. 
• 2. In early times, the behavior of convection fingers and the rate of CO₂ dissolution in the layered permeability cells is similar to the homogeneous cells with the same properties of the top layer in the layered permeability cells. However, the properties of the bottom layer can affect the whole mixing process. 
• 3. In the case of a low permeability top layer, the convection fingers merge, and their wavelengths increase after touching the bottom layer. However, the fingers do not penetrate the bottom layer and continue the convective flow further due to insufficient mass of CO₂ on top of the bottom layer, and the diffusion mechanism dominates the convective flow. 
• 4. In the case of a high permeability top layer, the convection fingers formed in the top layer form fingers of higher wavelengths after touching the bottom layer and then penetrate the bottom layer. 
• 5. In the layered cell, the existence of a low permeable bottom layer below a high permeable top layer reduces the dissolution rate of CO₂ by 50% (k₁/k₂ of 4) after fingers reach the bottom layer. However, this rate is still much higher (more than twice) than the dissolution rate in the homogeneous cell with the same permeability of the bottom layer. This means that the existence of a high permeable layer on top where the instability occurs is favorable for fast and early dissolution of CO₂ into the water. 
• 6. The behaviors of convection fingers (when they touch the interface) are independent of the height of the layers and the size of the fingers.

Nomenclature

Acknowledgments

This work was supported by the BIGCCS Centre under the Norwegian research program Centres for Environment-friendly Energy Research (FME). The authors acknowledge the following partners for their contributions: Gassco, Shell, Statoil, TOTAL, GDF SUEZ and the Research Council of Norway (193816/S60).

Author Contributions

Conceptualization: Amir Taheri, Erik Lindeberg, Dag Wessel-Berg; Methodology: Amir Taheri, Erik Lindeberg, Nanji J. Hadia; Validation: Amir Taheri, Erik Lindeberg, Dag Wessel- Berg; Analysis: Amir Taheri, Erik Lindeberg, Dag Wessel- Berg; Investigation: Amir Taheri; Supervision: Ole Torsæter, Dag Wessel-Berg; Project adminisration: Ole Torsæter, Dag Wessel-Berg; Funding acquisition: Ole Torsæter, Dag Wessel-Berg.

Competing Interests

The authors have declared that no competing interests exist.