In the saline aquifer system, the mass conservation equation governing two-phase flow in a porous medium can be expressed as follows: 1∂(ϕρwSw)∂t-∇⋅ρwkkrwμw∇pw-ρwg=Qw,2∂(ϕρnSn)∂t-∇⋅(ρnkkrnμn(∇pw+∇pc-ρng))=Qn, where subscript α (w or n) represents the wetting phase (w, brine) and nonwetting phase (n, CO₂). ϕ denotes the porosity, ρα and Sα represent the phase density and saturation. Assuming that only two fluid phases coexist in the pore space, the saturation of the non-wetting phase satisfies Sn=1-Sw. The intrinsic permeability tensor k is assumed to be that of a homogeneous and isotropic formation. krα and μα respectively denote the relative permeability and viscosity of phase α, while g represents the gravitational acceleration. The term Qα refers to the mass source terms arising from geochemical reaction and dissolution processes.

Dissolved carbon dioxide in brine is treated as a solute component. The transport equation for dissolved CO₂, based on Fick's law, is expressed as follows: 3∂(ϕρwSwXc)∂t+∇⋅ρwuwXc-ϕρwSwDc∇Xc=QwD+QwC, where Xc represents the mass fraction of CO₂, uw is brine velocity and Dc is diffusion coefficient. The source terms QwD and QwC represent the dissolution and chemical reaction terms, respectively. The dissolution source term QwD is formulated as a function of CO₂ saturation with the mass transfer coefficient κ serving as a key parameter (Martinez and Hesse, 2016). The dissolution of the CO₂ phase into the brine phase is assumed to occur only in the two-phase region. Treating the dissolution mass as a source term in this way simplifies the simulation of multi-component two-phase flow problems and improves computational efficiency. The mechanical dispersion and adsorption of solutes in brine are neglected. 4QwD=κϕSnρwXc,max-Xc, where Xc,max is the maximum dissolution mass fraction. Furthermore, the density of brine is assumed to be directly proportional to the local concentration, an approximation commonly referred to as the Boussinesq approximation (Diersch and Kolditz, 2002). 5ρw=ρ0+ΔρXcXc,max, where ρ0 is the density of pure brine and Δρ is the density difference between CO₂-saturated and pure brine.

Some studies have shown that the capillary transition zone has a significant impact on the buoyant flow of CO₂ dissolution in saline aquifer (Elenius et al., 2014; Emami-Meybodi and Hassanzadeh, 2015). The capillary pressure is defined as the pressure difference between the non-wetting phase and the wetting phase, pc=pn-pw. The capillary pressure–saturation relationship and relative permeability curves of the media are typically described by the Brooks–Corey model. The parameters used are listed in Table 1. The parameter values are selected from reservoir survey data and relevant literature. 6aSw*=Sw-Swr1-Swr-Snr,6bpc=pc0Sw*-(1/λ),6ckrw=Sw*(2+3λ)/λ,6dkrn=1-Sw*21-Sw*2+3λλ, where Sw* is normalized wetting phase saturation, Swr and Snr are the residual saturation of the two phases. pc0 denotes entry pressure and λ represents pore-size distribution index.

According to previous studies, calcite has a relatively fast reaction rate among all mineral components in sandstone (Xu et al., 2019b). The full-cycle model focuses on a relatively short timescale and concentrates on calcium minerals (calcite, dolomite), considering quartz, feldspar, and other minerals as insoluble substances because their dissolution/precipitation processes take thousands of years (De Silva et al., 2015). The formation of carbonate is considered to be the main way to sequester CO₂ and an important process for achieving permanent trapping in GCS (Bachu et al., 1994). To simplify the model, it is assumed that only calcite is included as a reactive mineral, with an initial content of 5 % (Sainz-Garcia et al., 2017). The main geochemical reactions of calcite dissolution in CO₂-rich plume are as follows: 7aCO2aq+H2O↔H++HCO3-,7bCaCO3s+H+↔Ca2++HCO3-, (aq) and (s) denote the aqueous and solid phases, respectively. The transport equation for reactive solute transport, accounting for convection, diffusion, and geochemical reactions, can be expressed as follows: 8a∂ϕρwSwXc∂t+∇⋅ρwuwXc-ϕρwSwDc∇Xc=QwC,8bQwC=rC=-kravcCO2cCaCO3n,8c∂cCaCO3∂t=-kravcCO2cCaCO3n, where rC is the reaction term of dissolved CO₂, kr and av respectively represent reaction rate constant and mineral surface area available for reaction per volume of the medium. n is the rate of the reaction which is 1 for the second-order reaction. The concentration of component i (CaCO₃ and CO₂) is represented as ci = ρi×xi. Mineral dissolution occurs rapidly near the injection wells, leading to a rapid increase in pore structure connectivity. Calcite can quickly dissolve in acid in the form of separating particles and biogenic debris fragments, causing changes in the pore network (Lamy-Chappuis et al., 2014). The resulting enhancement in pore connectivity–particularly when dissolution is localized at constricted pore throats–can significantly increase permeability (Dai et al., 2020). In our study, we assume that only dissolution reactions take place within the simulation domain and salt precipitation processes are neglected. The corresponding evolution of porosity and permeability is updated by the following relationship (Saaltink et al., 2013): 9ϕ=ϕ0+xCaCO3cCaCO3,rcCaCO3,0,10k=k0ϕϕ031-ϕ01-ϕ2, where xCaCO3 and cCaCO3 represent the mass fraction and concentration of calcite, subscript 0 and r represent the initial state and the quantity involved in the reaction.

Residual trapped bubbles undergo mass transfer toward the top of the reservoir via Ostwald ripening under the influence of gravity. The timescale for the system to reach thermodynamic equilibrium through ripening in a 50 m-thick formation can extend to several tens of thousands of years–approximately two to three orders of magnitude longer than that of density-driven convection.

The following assumptions are introduced in the analysis of the long-term Ostwald ripening process:

The gas distribution stabilizes and attains the initial ripening state under the assumption that the maximum concentration has been achieved throughout the domain. Our simulation results show that after 500 years, the average CO₂ saturation in the reservoir approaches the residual saturation, and according to Eq. (4), dissolution no longer occurs. Therefore, the simulation results at 500 years were selected as the initial condition for the gravity-induced Ostwald ripening process.

Due to the strong nonlinearity inherent in the density-dependent flow equations, a fully coupled approach is employed for the fluid flow and mass transport governing equations. The resulting system of discrete nonlinear equations is solved using the Newton-Raphson method. Simulations of solute transport and multiphase flow processes are conducted using the finite element software OpenGeoSys (OGS), version 5. Geochemical reactions are handled by a dedicated Python-based module, OGS-Chem. An interface module has been implemented within OGS to exchange data on CO₂ and calcite concentrations with OGS-Chem (Chen et al., 2020). Porosity is updated at each time step through the variation of the volume fraction of individual minerals, while permeability is modified by applying Eq. (10).

A script was developed to extract the final longitudinal saturation and permeability distributions from the flow and transport simulation, which then served as the initial conditions for the Ostwald ripening analysis in MATLAB. The ripening simulation models vertical (z-direction) mass transfer only, treating each horizontal column of the grid as a separate, independent 1D simulation. Since the timescale of gravity-induced Ostwald ripening is 2–3 orders of magnitude larger than that of convective mixing and reactions, the mass transfer term associated with ripening is very limited. To balance computational efficiency and convergence, we used the final results of the finite element computation as the initial condition for the ripening post-processing calculation.

During the injection period, the numerical model was validated through comparison with the semi-analytical solution derived from the theoretical model of Mathias et al. (2011). Simulation results demonstrated good agreement with this semi-analytical solution. To further assess the model's performance, a convective mixing scenario was also considered for verification. Due to its sensitivity to mesh discretization (Pau et al., 2010), the model reproduces finger-flow patterns and migration distances similar to those shown in Fig. 3 of Elenius et al. (2015). Details of the validation of the injection and dissolution modules can be found in our previous research (Chen et al., 2024).

Due to the contradiction between the simulation of the field scale and the fine-scale requirement of dissolved CO₂ flow, there is a conflict in grid discretization. The grid size also determines the difficulty of model convergence. Different grid sizes (δx, δz=0.8, 1, 2, 2.5) are analyzed in turn, and the average dimensionless concentration (c*=ccmax) in the domain of dissolved CO₂ is selected as the evaluation index to assess the grid convergence. When the finger flow reaches the bottom boundary (200 years), the difference in dimensionless average concentration c* within the domain does not exceed 0.01 between δx=0.8 and δx=1. Therefore, in order to balance computational efficiency and accuracy, a resolution of δx=1 was selected in subsequent simulations (Wang et al., 2022).

Based on the numerical results, saturation-time curves were extracted for monitoring points located along the top boundary of the reservoir at x=20, 40, 60, 80, 100, and 120 m, as illustrated in Fig. 3. During the injection period, the CO₂ plume migrates rapidly upward, causing a sharp increase in saturation at all monitored locations. Points in close proximity to the injection well continue to exhibit a brief saturation increase even after injection ceases, attributable to post-injection buoyancy-driven redistribution. Near the top surface of the reservoir, the CO₂ gradually accumulates beneath the caprock, with the maximum saturation at any location not exceeding 0.45.

After cessation of injection, the plume spreads laterally beneath the caprock and gradually dissolves into the brine. As density-driven convection intensifies, the dissolution rate increases, leading to a progressive retreat of the plume's leading edge. This retraction signifies that dissolution limits the lateral extent of the CO₂ plume, thereby enhancing the security of the storage complex. This behavior is supported by the saturation evolution observed at x=100 m and x=120 m over several hundred years after injection.

Figure 4 illustrates the evolution of the CO₂ plume following the cessation of injection. The plume exhibits a classical funnel-shaped morphology. Within 100 d, buoyancy drives the lower portion of the plume upward to the base of the caprock. The horizontal migration velocity of CO₂ decreases markedly due to the rapid dissipation of injection-induced pressure.

After 10 years (Fig. 4c), the leading edge of the plume has advanced approximately 165 m from the injection well. The overall plume thickness is significantly reduced, with the maximum thickness decreasing from 10 to about 5 m. As dissolution continues, physically trapped CO₂ is progressively converted into the dissolved phase. By 50 years, the plume front has retreated to within 150 m of the well, with a maximum thickness below 5 m and a peak saturation of less than 0.3 in the domain.

Figure 5 illustrates the temporal evolution of dissolved CO₂ following the injection period. After injection ceases, the plume accumulation zone exhibits a relatively uniform dissolution pattern. The region of highest concentration is observed at the top of the reservoir, resulting from the elevated CO₂ saturation in this zone. By 50 years, a high-density fingering flow begins to develop, marking a transition from uniform dissolution to distinct convective fingers. The most rapidly migrating finger forms nearest to the injection well, with its tip approaching the bottom of the reservoir.

Within 100 years, the dissolved CO₂ at the top has spread through the finger flow into the saline aquifer, reaching approximately half the reservoir height. After 200 years, interaction between individual fingers becomes evident: those close to the injection well have entered the shutdown period, causing high-concentration fluid to spread laterally along the bottom boundary, which in turn suppresses the development of subsequent fingers. Fingers located farther from the well begin to merge, significantly increasing their width, with the leading edges advancing toward the reservoir base.

Figure 6 illustrates the spatial-temporal evolution of reservoir permeability induced by geochemical reactions. The simulated results indicate that significant alterations are predominantly concentrated at the top of the reservoir. The impact of dissolution reactions becomes markedly evident approximately 100 years after injection. By 200 years, the preferential flow pathways formed by permeability enhancement exhibit a strong spatial correlation with the fingering structures depicted in Fig. 6. Under sustained acidic conditions, dissolution of calcite results in a local permeability increase of up to approximately 15 %.

Figure 7 illustrates the temporal evolution of the contribution of each trapping mechanism in the study case. Given the practical difficulty in distinguishing between structural and residual trapping, these are collectively categorized as free-phase CO₂. The results indicate that free-phase CO₂ remains the dominant mechanism throughout the simulated period, accounting for 79.66 % of total trapped CO₂ during the early injection period (within 1 year). As dissolution and geochemical reactions progress, the proportion of free-phase CO₂ gradually decreases to 56.45 % (500 years). After 500 years, dissolved CO₂ accounted for 42.80 % of the total sequestered fraction. Reactive CO₂ constitutes less than 1 % of the total. As dissolved CO₂ concentration declines in later stages, the reactive fraction stabilizes at 0.75 %.

Figure 8 shows the distribution of CO₂ saturation across the domain at 500 years post-injection. Most of the formation maintains a residual gas saturation close to the minimum value. A thin gas layer persists near the top of the injection well, with a saturation below 0.2 and a thickness of less than 5 m. Over an extended period of gravity-driven Ostwald ripening, the residual gas undergoes upward mass transfer, accumulating at the top of the reservoir. This process ultimately forms a gas cap approximately 2 m thick, leaving a bubble-free zone about 45 m thick at the bottom of the formation. However, the complete mass transfer process spans approximately 80 000 years–two to three orders of magnitude longer than the timescale of the geochemical reactions considered in this study. As a result, this long-term ripening behavior can only be evaluated through post-processing calculations based on extracted saturation and permeability data from the primary numerical model.

Based on comparative analyses of cases with varying calcite contents (0 %, 5 %, 10 %, and 20 %), simulations reveal significant alterations in reservoir porosity after 200 years of geochemical reactions. As illustrated in Figs. 9 and 10, the spatial distribution of porosity variation aligns closely with the finger flow pattern across all calcite content scenarios. In the case with an initial calcite content of 20 %, the porosity increase near the top of the reservoir reaches approximately 0.01, corresponding to a relative change of about 10 %. According to Eq. (10), the permeability has increased by approximately 36 % relative to the initial value.

Figure 10 illustrates the distribution of CO₂ finger flows under different calcite content conditions after 300 years. As the calcite content increases, a slight increase in the number of fingers is observed, particularly in the 10 % and 20 % cases. This behavior may be attributed to the formation of localized preferential pathways near the top of the reservoir, which facilitate the development of finger flows along these zones of enhanced permeability. Interestingly, the case with 5 % calcite content exhibits the smallest spatial extent of fingering, suggesting that at lower concentrations, the geochemical reactions may inhibit rather than promote the evolution of convective fingers. Overall, the density-driven convective behavior of dissolved CO₂ exhibits low sensitivity to calcite content.

The distribution of the plume in the anisotropic formation at the time of the cessation of injection is shown in Fig. 11. A permeability anisotropy index γ (kh/kv) was used to represent the ratio of horizontal permeability to vertical permeability. It is assumed that the horizontal permeability remains constant at k0, while the vertical permeability changes according to the permeability anisotropy index. When γ=0.5, the vertical migration of the plume is more efficient, and the injected CO₂ can rapidly accumulate at the top of the reservoir to form a funnel shape with a larger thickness. In contrast, when γ=10, the plume exhibits a thinner geometry at the top and migrates laterally over a greater distance. The actual reservoir with smaller vertical permeability is more conducive to the utilization of reservoir space.

Figure 12 displays the spatial distribution of CO₂ concentration and flow path characteristics after 200 years with different anisotropic properties of the formation. It can be observed that as the value of γ increases, it takes longer for the CO₂ in the physically trapped state to be transformed into the dissolved state, which is due to the lower convective strength, and therefore, the finger flow develops more slowly. As shown in Fig. 12a, for γ=0.5, the finger flow has reached the bottom boundary and formed back-flow to inhibit the vertical migration of the top finger flow. There is no strong convective interaction between the finger flows, and the overall vertical development of the finger flows is maintained in case of γ=2. When γ=10, a high-concentration zone develops at the reservoir top, and fingering flow is largely restricted to the vicinity of the injection well. The resulting fingers exhibit limited vertical development, reaching only about 20 m in height. Under such conditions, the phase transition of physically trapped CO₂ is significantly hindered, which compromises long-term storage security.

Figure 13 illustrates the temporal evolution of the average dissolved CO₂ concentration in formations with varying γ. Taking the case of γ=0.5 as an example, the rapid increase in the total dissolved storage occurs in two distinct stages. Stage I is governed by the dissolution and phase transition of CO₂, enhanced by the high saturation conditions established during injection. Stage II is characterized by large-scale convective mixing driven by gravitational instability, which significantly augments the dissolution flux. A threefold reduction in the total dissolution amount is observed as γ increases from 0.5 to 10 over the 500-year simulation.