Scaling CO2 convection in confined aquifers: Effects of dispersion, permeability anisotropy and geochemistry
Introduction
Net-zero target refers to achieving a balance between the amount of greenhouse gas emissions produced and the amount removed from the atmosphere. This target aims to deliver the objectives of The Paris Agreement, adopted by 196 Parties at COP 21 in Paris, on 12 December 2015 (Rogelj et al., 2016). Extensive carbon capturing and geological storage (CCS) is one of the pathways to partially achieve the net-zero target. Deep saline aquifers have the greatest importance, as their available storage capacity is almost two orders of magnitude higher than depleted oil and gas reservoirs, additionally, they are more widely spread around the globe (Firoozabadi and Myint, 2010, Celia, 2017, Godec et al., 2011, Orr, 2009, Zahasky and Krevor, 2020, Nooraiepour et al., 2018, Erfani Gahrooei and Joonaki, 2018, Erfani et al., 2020b).
For CCS, CO is separated from emission sources and injected into geological formations. Careful selection of the storage sites is crucial for sustainable long term carbon sequestration. Ideally, the aquifer pressure will be sufficient to keep CO at supercritical conditions (sc). In such conditions, the scCO density and viscosity are around 260–760 kg/m and 0.02–0.06 cP, respectively. Main CO trapping mechanisms during this process are structural trapping, residual/capillary trapping, solubility trapping and mineralization (Emami-Meybodi et al., 2015, De Silva et al., 2015, Soltanian et al., 2019, Joekar-Niasar et al., 2013, Erfani et al., 2020a, Fazeli et al., 2019, An et al., 2020).
When scCO is injected into an aquifer, it will eventually override the aquifer brine, due to its lower density and viscosity, until it reaches the impermeable caprock. Then, CO will dissolve into the underneath brine, resulting in an unstable configuration of a denser phase (roughly 1%) being on top of a less dense, and miscible fluid (i.e., known as Rayleigh–Bénard instability Getling, 1998). Such an instability promotes convective mixing, which is beneficial for further solubility trapping of CO2 (Emami-Meybodi et al., 2015). Beyond carbon storage, convective mixing is relevant to a wide range of natural and industrial applications (e.g., fluid mixing in the Earth’s mantle Gurnis, 1986, saltwater intrusion into coastal aquifers Diersch, 1988, Anderson et al., 1979, enhanced oil recovery James et al., 2007, Kahrobaei et al., 2012, enhanced heat transfer Li et al., 2003, Guo et al., 1998, Lister, 1990, and chemical production Wylock et al., 2014, Wylock et al., 2017).
The natural convection for CCS starts with the diffusion of CO2 into the domain from the top boundary, which creates a diffusive layer. The convection becomes important once the diffusive layer is sufficiently thick so that, the Rayleigh () number (representing the ratio of buoyancy forces to the diffusive force) exceeds a critical value (Tilton et al., 2013). The time that this instability initiates, , is called the onset of instability. After some time, the instabilities become macroscopic with the formation of CO plumes, which enhance the dissolution (onset of convection). Therefore, the rate of solute dissolution increases until it reaches a maximum. Then, the process stabilizes in a constant flux dissolution regime, after which the domain starts to become saturated and the dissolution flux declines in a convection shutdown regime (Slim, 2014, Erfani et al., 2021). In fact, the constant flux regime is only significant if the -number is sufficiently high () (Hassanzadeh et al., 2007, Emami-Meybodi and Hassanzadeh, 2013, Neufeld et al., 2010, Pau et al., 2010). Dissolution flux ([mol m−2 s−1]) is the most practically significant measure of the convection process, which can be defined as: where stands for the total sequestered carbon (in case of reactive transport simulations, the summation of solubility and mineralogically trapped carbon), is the aquifer area perpendicular to the flow direction (i.e., -direction) and is time. Fig. 1 shows the time evolution of the dissolution flux for different -numbers, on which different events are marked for each simulation case. Moreover, Fig. A.1 shows the effect of boundary concentration perturbation on CO2 dissolution flux and the average domain concentration for three different -numbers.
As mentioned, a constant-flux regime exists for high -numbers and can be characterized by the Sherwood (Sh) number, which is a dimensionless ratio of convective mass transfer rate to the diffusive mass transfer rate. For the constant flux regime, where , Sh is defined as: where [m] is the domain height, [m s−1] is the diffusion coefficient, is the domain porosity and [mol kg] is the CO2 concentration difference between the upper boundary (CO2 saturated water) and the aquifer brine at the start of the simulation. denotes the density of water [kg m−3].
Most studies provided the scaling relations of convective mixing for ideal conditions and ignored the interplay of factors such as hydrodynamic dispersion, permeability anisotropy, and geochemistry, and a systematic study on the impact of such complexities on a wide range of domain properties (i.e., Rayleigh numbers) is still missing, which is addressed in this study. In this paper, we aim to answer the following research questions to fill the existing gaps concerning scaling the convective mixing process:
- 1.
How does the hydrodynamic dispersion change the onset of convection and CO dissolution flux over a wide range of Rayleigh numbers?
- 2.
How does the impact of permeability anisotropy change with the Rayleigh number? What is the exponent of permeability anisotropy ratio () in the scaling relations over a wide range of domain permeability?
- 3.
What is the impact of typical carbonate geochemical interactions on the and scaling?
The manuscript is organized as follows: in Section 2 the simulation domain and the governing equations of reactive convective mixing will be presented. Then, in Section 3 the scaling relations and literature survey, will be presented. Section 4 provides the simulation results and related discussions. In the end, a summary and concluding remarks will be provided.
Section snippets
Domain, boundaries and assumptions
Full details of the governing equations, assumptions and numerical scheme have been presented previously in Erfani et al., 2021, Erfani et al., 2020a. Here, we briefly review the mathematical foundation of the model. A 2D rectangular domain with the length of L [m] and height of H [m] was assumed to represent a confined, isothermal aquifer, saturated with brine. Aquifer brine was assumed to be in equilibrium condition with primary minerals at the aquifer temperature (i.e., 80 ℃) (Sainz-Garcia
Scaling relations and literature survey
The main function of scaling relations in the context of convection is relating behavioural characteristics of the process (i.e., instability onset, convection onset, maximum flux and Sherwood number) to physical properties of the domain (i.e., domain permeability, concentration difference, diffusion coefficient, etc.). As an example, the linear stability analysis suggests the following relation to scale the dimensional onset of instability () (Ennis-King and Paterson, 2005):
Results and discussion
In this section, we provide the numerical simulation results for different simulation scenarios along with relevant discussions about relevant literature results. First, we discuss the base case, which was considered as the non-reactive isotropic case without longitudinal dispersion. Afterwards, we present the effect of hydrodynamic dispersion. Then, we study the effect of permeability anisotropy on simulation results and scaling relations. The effect of carbonate geochemical interactions on
Summary and conclusions
This study presented high-resolution 2D numerical simulations of multicomponent reactive density-driven CO mixing in deep saline aquifers to obtain scaling relations for the onset of convection and the Sherwood number. The hydrodynamic dispersion, permeability anisotropy and a complex set of carbonate geochemical reactions over a wide range of Rayleigh numbers () were considered in the scaling relations, which to our best knowledge, have not been studied all together in former studies.
CRediT authorship contribution statement
Hamidreza Erfani: Investigation, Methodology, Software, Data curation, Writing – original draft. Masoud Babaei: Investigation, Methodology, Writing – review & editing. Carl Fredrik Berg: Writing – review & editing. Vahid Niasar: Supervision, Conceptualization, Methodology, Writing – review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The authors would like to acknowledge the University of Manchester for providing the PhD funding for Hamidreza Erfani through the President’s Doctoral Scholarship (PDS) award. This study was partially funded by the Research Council of Norway (Centers of Excellence funding scheme, project number 262644, PoreLab).
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