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(a) Distributions of the CO2‐rich plume in nine different cases (Cases 1A–1I) at a specific time point (tD = 2.89). (b) Total flux at the fracture (TFf) as a function of the domain width (W) for Case 1B. (c) Total flux at the fracture (TFf) as a function of the domain width (W) for Case 1C.
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Dissolution trapping is one of the primary mechanisms of carbon dioxide (CO2) storage in a geological formation. In this study, a numerical model was used to examine the impacts of single and multiple fractures on the transport of dissolved CO2 plumes in various geological settings. The effects of the fracture angle, fracture‐matrix permeability ra...
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As part of the In-situ Stimulation and Circulation (ISC) experiment, hydraulic fracturing (HF) tests were conducted in a moderately fractured crystalline rock mass at the Grimsel Test Site (GTS), Switzerland. The aim of these injection tests was to improve our understanding of processes associated with high-pressure fluid injection. A total of six...
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... An alternative and widely adopted modeling approach treats fractures as an ðn À 1Þ dimensional element in an n-dimensional computational domain. [24][25][26] Specifically, in a two-dimensional (2D) flow domain, fractures are depicted as one-dimensional line segments, while in a three-dimensional (3D) domain, the fractures are represented by planes. An early study conducted by Graf and Therrien 27 investigated variable-density groundwater flow in a 3D porous medium with a single inclined fracture. ...
... Xu et al. 28 investigated the effects of roughness of the fracture using a 3D discrete fracture model, and found that the rough fracture surface can lead to a more tortuous path for CO 2 . Kim et al. 24 observed small eddy-like flow structures near the fractures, suggesting the active mass transfer between the fracture and matrix. Wang et al. 25 investigated the effects of fractures in a full cycle process. ...
... To model the density-driven flow shown in Fig. 1(a), we consider a simplified 2D porous medium at the vertical plane with height and width L [ Fig. 1(b)], similar to the 2D models employed in previous studies. 14,15,21,24 An instantaneous saturated CO 2 aqueous fluid with concentration C sat is put at the top impermeable boundary. This assumption is based on the fact that convection occurs more slowly than lateral movements, suggesting that CO 2 saturation reaches a stable state before convection starts. ...
In this study, CO2 transport in density-driven flows within an ideal model of a fractured porous medium, which contains a single or two intersecting fractures, is investigated numerically. The study employs a multi-scale modeling in which the flow in the matrix is modeled by Darcy's law, while the flow in the fracture is modeled by the Navier–Stokes equations. Our study shows that a horizontal fracture minimally impacts CO2 distribution, and depending on its length, slightly reduces dissolved CO2 during sequestration by 1.5%–2.5%. Vertical fractures play a crucial role in redirecting CO2 movement within the matrix, guiding it toward the fractures and altering its original pathway. Notably, the observed oscillations of CO2-rich water between the interfaces of the vertical fracture highlight the flow consistency with the pore scale. The domain-scale circulation induced by the vertical fracture leads to a rapid increase in flux and dissolved CO2 mass, but early convection shuts down. The results demonstrate that a longer vertical fracture leads to earlier shut down of convection and a potential decrease in storage of over 11%. The flow behaviors observed in inclined fractures are akin to those in vertical fractures, as they disrupt the fingerlike structure of CO2 around the fracture, form the circulation around the fracture, and are accompanied by vortices at the top. Additionally, intersecting fractures can lead to dynamic interactions between the fractures, with high-angle fractures dominating mixing flow. Different fracture angle combinations minimally affect dissolution mass.
... VVF processes have been largely investigated in unfractured domains (Zidane, 2023;Graf & Therrien, 2007;Shafabakhsh et al., 2021). Past studies have examined the behavior of VVF in fractured domains with respect to CO 2 storage (Kim et al., 2019;Raad & Hassanzadeh, 2018;Shafabakhsh et al., 2021;Wang et al., 2022), saltwater intrusion (Grillo et al., 2010;Hosseini et al., 2020;Koohbor et al., 2020;Sebben et al., 2015;Werner et al., 2013), nuclear waste disposal (Follin & Stigsson, 2014), thermal convection (Gruais & Poliševski, 2021;Mezon et al., 2018), and oil and gas production (Shen et al., 2016). ...
Explicit fracture models often use analytical solutions for predicting flow in fractured media, usually assuming uniform fluid viscosity for simplicity. This assumption, however, can be inaccurate as fluid viscosity varies due to factors like composition, temperature, and dissolved substances. Our study, recognizing these discrepancies, abandons this uniform viscosity assumption for a more realistic model of variable viscosity flow, focusing on viscous displacement scenarios. This includes instances like injecting viscous surfactants for hydrocarbon recovery in fractured reservoirs or soil decontamination. This presents a significant challenge, enhancing our understanding of transport within fractures, mainly governed by advection. Our study centers on a low‐permeability rock matrix intersected by two fractures with variable apertures. We employ two methods: an analytical approach with a new solution and numerical simulations with two distinct in‐house codes, discretizing both the rock matrix and fractures with two‐dimensional triangular elements. The first code uses a Discontinuous Galerkin finite element method, while the second utilizes a finite‐volume method, allowing a comprehensive comparison of solutions. Additionally, we investigate parameter identifiability, like fracture apertures and viscosity ratios, using breakthrough curves from our analytical solution, applying the Markov Chain Monte Carlo technique.
... The density-driven convection process in the fracturematrix system is significantly different from that in a homogeneous medium, and the convection between the fractures accelerates mass transfer (Simmons et al., 2008;Vujevic & Graf, 2015). Highpermeability fractures provide preferential channels for downward migration of CO 2 -rich finger flow and upward movement of freshwater, thus enhancing mass transfer between the fracture and matrix (Kim et al., 2019). In contrast to fractures in cap rock, which are leakage channels (Gholami et al., 2021), fractures in reservoirs contribute to the long-term safety of CO 2 geological storage and reduce the risk of leakage. ...
... Moreover, β denotes the volume expansion coefficient related to density, which was set as 0.01 in the simulation (Ennis-King & Paterson, 2005). The densities of pure (ρ 0 ) and CO 2 -saturated (ρ max ) Table 1 The parameter values of the matrix and fractures (Hidalgo & Carrera, 2009;Hu et al., 2022;Kim et al., 2019). brine were respectively 1000 and 1010 kg/m 3 . ...
... It is found that ignoring this roughness effect to assess dissolved trapping of CO 2 in the reservoir, it may result in an underestimation of the dissolved flux by 20 % or more. This understanding is generally consistent with previous studies of density-driven convection in heterogeneous system (Farajzadeh et al., 2011b;Green & Ennis-King, 2014;Kim et al., 2019). The simulation results of the 20 cases generated for uncertainty analysis support the above point of view. ...
Dissolution trapping is a permanent and safe mechanism for geological carbon sequestration. An increase in density caused by the dissolution of CO 2 into brine can trigger a density-driven convection process. In this study, the effect of fracture roughness on the density-driven convection process in heterogeneous saline aquifers is numerically analyzed by using a three-dimensional rough fracture-matrix model. The results show that the variation of the fracture aperture, a microscale heterogeneity phenomenon, can result in the change of the macroscopic flow characteristics. The rough fracture surface intensifies the convection inside the fracture and makes the migration path of the solute more tortuous. The spatial variability of the aperture generates the merging of convective fingers and suppresses the development of weak convective fingers, thus further enhancing the longitudinal extent of convective mixing. It is indicated that neglecting roughness during the flux growth stage can lead to an underestimation of dissolved fluxes by about 20%. The consideration of fracture roughness variation can contribute to the better understanding and prediction of the dynamics of dissolved CO 2 in real reservoirs.
... Soltanian et al. (2016) investigated the effect of the facies-based heterogeneity on convective mixing and upgraded it to three dimensions. Concerning fractures, the effects of fracture angle, fracture density, fracture permeability, fracture aperture, fracture surface roughness, fracture-matrix permeability ratio, and intersected fractures on the convective mixing were investigated (Kim et al., 2019;Rezk and Foroozesh, 2019;Shafabakhsh et al., 2021). Numerous experimental studies have also been conducted to explore the impact of heterogeneous porous media on CO 2 convective mixing. ...
... The simulation parameters used in this study are shown in Table 2. The model is validated by the published model constructed by Kim et al. (2019) on the base case without H 2 S and fractures, as shown in the Supplementary Appendix. ...
... As a result, the merged plumes flow through fracture B and reach the bottom boundary before the plume in the left area, leading to accelerated convective mixing within the fractures. These findings are in agreement with the convective mixing analysis results for pure CO 2 presented by Kim et al. (2019). Concerning the case of θ = 60°( 10% H 2 S), the merged central plume flows in the fracture and coalesces with the left plume before hitting the bottom boundary, which slows down the accelerated convective mixing in the central region. ...
Dissolution trapping stands as a critical mechanism for the geological carbon storage (GCS) and can be notably improved through density-driven convection. However, to the best of the author’s knowledge, the discussion on density-driven convection of CO 2 -H 2 S mixture has been limited to the exclusion of intersected fractures and lithology sequence effects. Therefore, this study aims to systematically investigate the impact of H 2 S concentration, fractures, and lithology sequence on convective mixing. Four distinct mechanisms that influence convective mixing of CO 2 -H 2 S mixtures in the presence of fractures were identified: 1) accelerated downward solute transportation in fractures, 2) coalescence between plumes around fractures and primary down-swelling plumes, 3) high fracture conductivity inhibiting plume migration across fractures, and 4) upward flow in fractures facilitating the transport of high-concentration solute out of the system. Additionally, the effects of lithology sequence on the shape of CO 2 plumes and the curve shape of the total flux at the top boundary were described. The results demonstrated that density-driven convection is enhanced with decreasing H 2 S concentration and increasing fracture interaction angle and fracture conductivity ratio. The magnitudes of density-driven convection, ranked from high to low, are fining downward, uniform, and fining upward lithology sequences. Furthermore, the H 2 S concentration affects the flow direction within fractures and alters the relative magnitude of the dimensionless concentration in the noise sequences. The findings of this study on a small scale were proven to be applicable on a large scale.
... The injected CO 2 can be trapped through various physical and chemical mechanisms. This covers stratigraphic, residual, solubility, and mineral trappings (Kim et al., 2019). Physical or stratigraphic trapping is a crucial mechanism to ensure long-term entrapment of CO 2 . ...
... Several studies addressed the non-reactive convective flow (Farajzadeh et al., 2011;Hamann et al., 2015;Hewitt et al., 2014;Hidalgo and Carrera, 2009;Riaz et al., 2006;Singh and Islam, 2018). Convective-reactive CO 2 dissolution is extensively investigated in the literature (e.g., (Andres and Cardoso, 2011;Emami-Meybodi et al., 2015;Ghesmat et al., 2011;Ghoshal et al., 2017;Hidalgo et al., 2015;Kim et al., 2019;Shafabakhsh et al., 2021). For instance, Babaei and Islam (2018) (Babaei and Islam, 2018) investigated convective-reactive CO 2 dissolution in aquifers with an immobile water zone, while Erfani et al. (2020) (Erfani et al., 2020) studied the effect of geochemical reactions on CO 2 dissolution in sandstone aquifers. ...
... For instance, Babaei and Islam (2018) (Babaei and Islam, 2018) solved the stream function form of the governing equations using finite difference methods. The standard FE method is used in Kim et al. (2019) (Kim et al., 2019). The finite volume method is used in Farajzadeh et al. (2011) (Farajzadeh et al., 2011). ...
Geological CO2 sequestration (GCS) remains the main promising solution to mitigate global warming. Understating the fate of CO2 behavior is crucial for securing its containment in the reservoir and predicting the impact of dissolved CO2 on the host formation. Most modeling-based studies in the literature investigated the convective-reactive transport of CO2 by assuming isothermal conditions. The effect of temperature on the convective-reactive transport of CO2 is still poorly understood, particularly at the field scale. The objective of this study is to provide an in-depth understanding of CO2-related reactive thermohaline convection (RTHC) processes at field scale. Thus, a new numerical model based on advanced finite element formulations is developed. The new model incorporates an accurate time integration scheme with error control. Numerical experiments confirm high accuracy and efficiency of the newly developed model. The effect of temperature on CO2 transport is investigated for a field case in the Viking reservoir in the North Sea. Results show that including the temperature effect intensifies the fingering processes and, consequently, CO2 dissolution. Neglecting the thermal convection processes and the impact of temperature on the dissolution rate can significantly impact the model predictions. A sensitivity analysis is developed to understand the effect of parameters governing the dissolution rate on the fingering phenomenon and the total CO2 flux.
... Deng et al. [31] investigated the effect of multi-scale heterogeneity on storage capacity, designs of injection wells, injection rate, CO 2 plume migration, and CO 2 potential leakage. Kim et al. [32] and Paiman et al. [33] investigated the fracture heterogeneity, and revealed that fractures can significantly affect the predicted amount of trapped CO 2 . Galkin et al. [34] adopted X-ray tomography and electron microscopy for description of rock pore space considering reservoir heterogeneity, considered to be an important method to introduce new methods for the development of complex reservoirs. ...
Carbon dioxide (CO2) dissolution is the secondary trapping mechanism enhancing the long-term security of CO2 in confined geological formations. CO2 injected into a randomly multilayered formation will preferentially migrate along high permeability layers, increasing CO2 dissolution efficiency. In this study, sequential Gaussian simulation is adopted to construct the stratified saline formations, and two-phase flow based on MRST is established to illustrate the spatial mobility and distribution of CO2 migration. The results show that gravity index G and permeability heterogeneity σY2 are the two predominant factors controlling the spatial mobility and distribution of CO2 transports. The CO2 migration shows a totally different spatial mobility under different gravity index and heterogeneity. When the permeability discrepancy is relatively larger, CO2 preferentially migrates along the horizontal layer without accompanying the vertical migration. For the formation controlled by gravity index, CO2 migration is governed by supercritical gaseous characteristics. For the medium gravity index, the upward and lateral flow characteristics of the CO2 plume is determined by gravity index and heterogeneity. When the gravity index is smaller, permeability heterogeneity is the key factor influencing CO2 plume characteristics. Permeability heterogeneity is the decisive factor in determining final CO2 dissolution efficiency. This investigation of CO2 mobility in randomly multilayered reservoirs provides an effective reference for CO2 storage.
... Instabilities are triggered by artificially imposing perturbations, which eventually evolve into macroscale natural convection. It has been shown that implementing periodic perturbations in the top solute inlet boundary can generate realistic fingers (Farajzadeh et al., 2007(Farajzadeh et al., , 2013Kim et al., 2019), ...
We 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.
... Rezk and Foroozesh [19] used numerical simulations to find that high permeability and big inclination angle of fractures favored the CO 2 solubility trapping process in the single fracture system. Similar findings were found by Kim et al. [140] that a small inclination single fracture structure in the aquifer enhanced the mass transfer between the fracture and matrix, while the large inclination fractures promoted brine movement toward the top boundary, facilitating circulation in the region and enhancing CO 2 dissolution. ...
... The permeability of matrix and fracture also has an impact on CO 2 solubility trapping. Kim et al. [140] investigated the effects of fracture-matrix permeability ratio on convection. When the permeability values of the matrix and the fracture are similar, the influence of fracture on density-driven convection was negligible. ...
Industrial development has significantly increased the concentration of CO2 in the atmosphere, resulting in the greenhouse effect that harms the global climate and human health. CO2 sequestration in saline aquifers is considered to be one of the efficient ways to eliminate atmospheric CO2 levels. As an important mechanism, the solubility trapping greatly determines the efficiency of CO2 sequestration in saline aquifers, and this depends, in turn, on the density-driven convection that occurs during the sequestration. Density-driven convection is influenced by multiple factors. However, existing discussions on some of these influential factors are still ambiguous or even reach contradictory conclusions. This review summarizes the common modeling approaches and the influence of factors on density-driven convection. We suggest that saline aquifers with high values of depth, permeability, pH, and SO2 impurity concentration are the ideal CO2 sequestration sites. A certain degree of porosity, fractures, stratification, slope, hydrodynamic dispersion, background flow, and formation pressure are also considered advantageous. Meanwhile, the geological formation of the Permian White Rim Sandstone or carbonate is important, but it should not contain brine with excessive viscosity and salinity. Finally, we discuss the contents in need of further research.
... Variable-density flow (VDF) processes have been largely investigated in unfractured domains, but studies in fractured domains remain relatively scarce. VDF in fractured domains is encountered in several applications such as fractured coastal aquifers contamination by saltwater intrusion [1][2][3][4][5][6], nuclear waste management [7], CO 2 storage [8][9][10][11] thermal convection [12,13] or oil and gas production [14]. ...
Modeling variable density flow (VDF) in fractured porous media is computationally challenging. The challenges are mainly related to: (i) the high permeability contrast between the matrix and the fractures and, (ii) the nonlinearity induced by density variations. Due to their local mass conservation property, cell-centered methods, such as finite volumes (FV), mixed finite elements (MFE) or Discontinuous Galerkin (DG) methods are well suited for modeling mass transfer in highly heterogeneous domains. When applied for fractured media, these methods require small grid cells next to fractures because of the cross-flow equilibrium assumption (i.e. the pressure and concentration in the fracture and in the adjacent matrix grid-cells are assumed the same). To avoid this constraint, an efficient model is developed in this work using advanced cell-centered numerical methods for VDF in fractured porous media with cross-flow equilibrium assumed only across the fractures. The new model uses the hybrid MFE method for the flow discretization in the matrix and in the fracture continua. Mass transport in the matrix is modeled using a monotonic upwind MFE scheme. Advection-dominated transport in fractures is discretized with the DG method, which is well adapted for hyperbolic equations. The new model ensures continuity of pressure, concentration, fluid mass flux, advective and dispersive contaminant fluxes at matrix-fracture interfaces as well as at the intersection of several fractures. The time discretization is performed using high-order adaptive time integration techniques via the method of lines (MOL). The developed model is first validated by comparison against a 2D-2D model for a test problem dealing with linear flow and transport in a 2D domain involving a “+”-shaped barrier/fracture network. Then, the MFE-DG model is used for the simulation of the Henry saltwater intrusion problem and the results are validated by comparison against the semi-analytical solution in the case of unfractured and fractured aquifers. Finally, the simulation of a transport problem with variable viscosity in a fractured heterogeneous domain points out the superiority of the new model in terms of accuracy and efficiency when compared to a standard finite element model.
... Moreover, the X-FEM was proposed by Al-Khoury (2015, 2017) to develop a fully coupled model for crack propagation in cap-rock during CO 2 sequestration. There are also some research works focused on the density-driven dissolution of CO 2 component into the brine phase in naturally fractured aquifers (Kim et al. 2019;Rezk and Foroozesh 2019). ...
In this paper, a numerical model is developed for the assessment of carbon dioxide transport through naturally fractured cap-rocks during CO2 sequestration in underground aquifers. The cap-rock contains two types of fracture with different length scales: micro-cracks (fissures) and macro-cracks (faults). The effect of micro-cracks is incorporated implicitly by modifying the intrinsic permeability tensor of porous matrix, while the macro-cracks are modeled explicitly using the extended finite element method (X-FEM). The fractured porous medium is decomposed into the porous matrix and fracture domain, which are occupied with two immiscible fluid phases, water and CO2. The flow inside the matrix domain is governed by the Darcy law, while the flow within the fracture is modeled using the Poiseuille flow. The mass conservation law is fulfilled for each fluid phase at both porous matrix and fracture domain; moreover, the mass exchange between the matrix and fracture is guaranteed through the integral formulation of mass conservation law. Applying the X-FEM technique, the explicit representation of macro-cracks is modeled by enriching the standard finite element approximation space with an enrichment function. Finally, several numerical examples of CO2 injection into a brine aquifer below a naturally fractured cap-rock are modeled in order to investigate the effects of cracks’ aperture and orientation as well as the temperature of aquifer and the depth of injection on the leakage pattern of the carbon dioxide through the cap-rock.
