Sealing Porous Media through Calcium Silicate Reactions with CO 2 to Enhance the Security of Geologic Carbon Sequestration

Abstract

The injection of CO₂ deep underground, i.e., geologic carbon sequestration, has attracted considerable attention for climate change mitigation. A reliable caprock for secure containment is essential, alongside strategies for sealing flow paths to prevent leaks. In this study, we explore ways in which reactions of CO₂ with CaSiO₃ can be used for targeted mineral precipitation and permeability control in situ. Previous work has suggested that certain CaSiO₃ polymorphs can produce pore-filling precipitates that successfully inhibit flow, whereas others produce precipitates with little impact. In this work, a one-dimensional reactive transport model was developed for a centimeter-scale system to explore connections between the pore and continuum scale. The model considers four reactions involving CaSiO₃, CaCO₃, SiO_2(am), and the crystalline calcium silicate hydrate (CCSH) tobermorite. A key feature is incorporation of microporosity, with an attempt to represent favorable volume expanding changes from CCSH precipitation in porous media. At 150°C and 1.1 MPa CO₂, representing typical laboratory conditions, the model predicts significant permeability drop when reacting the pseudowollastonite CaSiO₃ polymorph at elevated pH to produce CaCO₃, SiO_2(am), and tobermorite. The effect of increasing pH via by NaOH addition, which increases CO₂ solubility, increases CaSiO₃ dissolution, and supports tobermorite supersaturation. In contrast, reaction of the wollastonite polymorph results in CaCO₃ and SiO_2(am) formation, with limited permeability impact. Wollastonite's lower solubility and slower dissolution rate inhibits tobermorite formation. Simulation at the high pressures representative of deep subsurface field conditions (40°C and 7.5 MPa CO₂) suggests that reaction of CaSiO₃ with CO₂ could reduce permeability and seal unwanted leakage pathways.

Introduction

Agrowing interest in deep subsurface environments for their importance in geologic CO₂ storage has resulted in concerns regarding the migration of fluids into the environment (White et al., 2020). Sites of undesired fluid migration underground may include natural faults, fractures, or degraded areas associated with wellbores (Deng and Peters, 2019, 2020; Spokas et al., 2019). In geologic sequestration of CO₂ deep underground, buoyant forces could allow CO₂ to leak from its storage location and escape into the atmosphere, undermining the goal of permanently sequestering CO₂ (Bohnhoff and Zoback, 2010; Bielicki et al., 2015, 2016; Deng et al., 2017). These risks highlight the need for approaches to seal leaks and control permeability and flow in the subsurface.

One possible solution for altering fluid flow in geologic CO₂ reservoirs is through controlled mineral precipitation by the targeted delivery of calcium silicates. The topic of carbon mineralization by silicate dissolution with subsequent precipitation of carbonate minerals has been well studied and that research has provided valuable insights about the controlling mechanisms of these geochemical reactions (Jun et al., 2013; Zhao et al., 2013; Stack et al., 2014). However, these reactions have only recently been proposed in the context of subsurface technologies in support of induced precipitation for permeability control (Deng and Peters, 2019, 2020; Spokas et al., 2019). Our recent work has examined the feasibility of such targeted mineral precipitation by delivering calcium silicate particles headed for leakage sites to produce secondary minerals that occupy pore space and decrease permeability (Fig. 1) (Tao et al., 2016; Plattenberger et al., 2019, 2020). Physical properties of the particles, including size, microporosity, and the use of polymer coatings (Lee et al., 2007; Plattenberger et al., 2020), can be engineered to control buoyancy, the extent of vertical migration during injection, and the temperature at which the reactions begin.

FIG. 1.

A CO₂ plume from a target formation can potentially be sealed using targeted delivery of calcium silicate particles. The CaSiO₃ particles would react with the diffusing CO₂, producing mineral precipitates to decrease permeability, sealing the leakage.

When considering CaSiO₃ reactions with CO₂, the mineral wollastonite has been widely studied for its ability to mineralize CO₂ into CaCO₃, while also forming SiO_2(am) and minor amounts of crystalline calcium silicate hydrate (CCSH) (Berner et al., 1983; Daval et al., 2009b).

In contrast, the CaSiO₃ polymorph pseudowollastonite produces relatively larger quantities of CCSH when reacting with CO₂ (Ashraf and Olek, 2016; Plattenberger et al., 2018, 2019; Monasterio-Guillot et al., 2019). These differences may be due to pseudowollastonite's stoichiometric dissolution and wollastonite's nonstoichiometric dissolution (Casey et al., 1993; Schott et al., 2012). The difference in release rates of Ca²⁺ and SiO_2(aq) is thought to affect whether CaCO₃ or CCSH forms (Plattenberger et al., 2018; Monasterio-Guillot et al., 2019).

The resulting CCSH phases exhibit properties that will likely benefit the development of targeted mineral precipitation technology for permeability control. CCSH phases show substantial resilience to redissolution in acid compared to CaCO₃ (Plattenberger et al., 2018, 2019), a desirable characteristic to ensure the long-term containment of CO₂, which exists in aqueous solution as carbonic acid. Furthermore, the molar volumes of CaCO₃ (3.12 × 10⁻⁵ m³) and CaSiO₃ (3.98 × 10⁻⁵ m³) are quite similar and may not be advantageous for sealing subsurface leakages. We suspect that the large molar volumes of CCSH in comparison to CaCO₃ minerals, the ability of some CCSHs to expand and hold structural water, and the extensive microporosity observed in their formation will contribute to the pore-filling effectiveness of CCSH in porous media.

In this study, we used reactive transport modeling to explore calcium silicates in porous media reacting with diffusing CO₂ and the extent of permeability reduction due to mineral precipitation. The modeling was aimed at addressing the following questions: Why does dissolution of different calcium silicates, wollastonite and pseudowollastonite, affect mineral formation? How do the properties of CCSH, their ability to create microporosity, and their co-occurrence with CaCO₃ and SiO_2(am) affect their ability to fill pore space? What pH conditions promote CCSH formation? Finally, how might changes in temperature and CO₂ pressure affect the reactions involved, particularly under field conditions for geologic CO₂ storage?

A one-dimensional (1D) reactive transport model was built to examine the conditions that allow for CCSH formation and quantify permeability alteration. Permeability was used as a metric to gauge the effectiveness of sealing the porous medium. For calibration of mineral precipitation kinetics and for model validation, simulations were compared with previously published experimental results in Plattenberger et al. (2019). In addition to the modeling, a single new experiment with a glass bead column was conducted, in which the column was filled with pseudowollastonite and reacted with CO₂. The column was examined using x-ray computed tomography (xCT) imaging to observe pore space filling and changes in pore connectivity.

One-Dimensional Reactive Transport Model

Model system

The model system was selected to represent a porous medium with nonadvective diffusive flux at one end, similar to that originally configured by Giammar et al. (2014). A diffusion-limited environment is expected at the edge of the CO₂ plume in a target formation (Fig. 1). A schematic of the model system is shown in Fig. 2. The constant boundary condition is represented as H₂O equilibrated with an overhead pressure of CO₂. Throughout this article, this boundary is referred to as the “CO₂ source.” The remainder of the cells represents the porous medium, initially containing CaSiO₃ and equilibrated with pH 7 solution. The last cell is a no-flux boundary. The cross-sectional dimensions of the 1D system were selected to allow comparison to experiments reported in Plattenberger et al. (2019) and cell volume calculations with changing porosity.

FIG. 2.

Schematic summarizing the components of the one-dimensional model and the simulation conditions. The parameter x_j represents the space step, ranging from 0 to 45 mm.

Reactions and rate laws

CaSiO₃ dissolution

CaSiO₃ dissolution and precipitation were modeled kinetically for both wollastonite and pseudowollastonite according to the following reaction: $C a S i O_{3} + 2 H^{+} C a^{2 +} + S i O_{2 (a q)} + H_{2} O$ (1)

The rate of dissolution for wollastonite is described by the rate law derived from transition state theory: $r_{D, C a S i O 3} = A k_{D, C a S i O 3} e x p (- \frac{E_{a}}{R T}) a_{H}^{n} (1 - Ω_{C a S i O 3})$ (2)

where the rate is in units of mol/s, A is the reactive surface area, $k_{D, C a S i O 3}$ is the rate constant, E_a is the activation energy, R is the gas constant, T is temperature, a_H is the activity of H⁺, and n is an exponent that quantifies the pH dependence of dissolution kinetics. The ratio of the ion activity product to the solubility constant for mineral i is $Ω_{i}$ . For CaSiO₃, $Ω_{C a S i O 3} = \frac{\{C a^{2 +}\} \{S i O_{2 (a q)}\}}{{\{H^{+}\}}^{2} K_{s p, C a S i O 3}}$ (3)

For wollastonite, kinetic rate parameter values were estimated from Casey et al. (1993), Schott et al. (2012), and Ptáček et al. (2011), giving $k_{D, C a S i O 3}$ = 10^−1.30 mol/[cm²·s], E_a = 47 kJ/mol, and n = 0.31. For pseudowollastonite, the dissolution rate constant of wollastonite was multiplied by 10^2.16 to represent the higher dissolution rate of pseudowollastonite in comparison to the average of the wollastonite dissolution rates (Casey et al., 1993). Dissolution was modeled as occurring when the saturation index ( $S I_{i}$ ) of mineral i was less than 0. $S I_{i}$ is expressed generally for all solids as follows: $S I_{i} = l o g Ω_{i}$ (4)

All reaction parameters are included in Table 1.

Table 1.

Modeled Reactions and Kinetic and Thermodynamic Parameters

Dissolution and precipitation reactions
Reaction	ΔH (kJ/mol)	logK_sp (25°C)	logK_sp (40°C)	logK_sp (150°C)	Kinetics modeled	Source	V_m (m³/mol)^*	V_m source	Specific Surface Area(m²/g)	Dissolution rate constant $k_{D, i}$ (mol/[cm²·s])	Calibrated $k_{P, i}$
CaSiO_3(s) + 2H⁺ ↔ Ca²⁺ + SiO₂ + H₂O	Woll: −76.5756	13.428	12.78	9.012	Dissolution and precipitation	SOLTHERM	3.98 × 10⁻⁵	SOLTHERM	1.38	10^−1.30	3.98 × 10⁻¹³
	Pseudo: −79.4625	14.169	13.47	9.456	Dissolution and precipitation	SOLTHERM	3.98 × 10⁻⁵	SOLTHERM	1.38	10^0.86
SiO_2(aq) ↔ SiO_2(am)	20.0539	−2.464	−2.37	−1.925	Dissolution and precipitation	SOLTHERM	2.90 × 10⁻⁵	SOLTHERM	0.21	10^−9.9	1.00 × 10⁻²
Ca²⁺ + CO₃²⁻ ↔ CaCO_3(s)	Calc: −9.61	−8.48	−8.56	−8.98	Dissolution and precipitation	PHREEQC LLNL	3.12 × 10⁻⁵	SOLTHERM	0.21	N/A	1.32 × 10⁻⁶
Ca²⁺ + CO₃²⁻ ↔ CaCO_3(s)	Arag: −10.83	−8.336	−8.427	−8.897	Dissolution and precipitation	SOLTHERM	3.42 × 10 − 5	SOLTHERM	0.21		1.32 × 10⁻⁶
Ca₅Si₆H₁₁O_22.5(s) + 10H⁺ ↔ 5Ca²⁺ + 6SiO_2(aq)	−286.9	65.6121	63.2	50.75	Equilibrium only	PHREEQC LLNL	2.83 × 10⁻⁴	MINCRYST	N/A	N/A

Aqueous speciation reactions
Reaction	ΔH (kJ/mol)	logK_sp (25°C)	logK_sp (40°C)	logK_sp (150°C)	Source
H₂CO₃ ↔ H⁺ + HCO₃⁻	9.7	−6.347	−6.26	−5.84	Phreeqc LLNL database
HCO₃⁻ ↔ H⁺ + CO₃^2–	−14.9	−10.33	−10.45	−11.1	Phreeqc LLNL database
H₂O ↔ H⁺ + OH⁻	55.91	−14	−13.53	−11.104	Phreeqc LLNL database

The molar volume for each reaction is the molar volume of the solid phase in that reaction.

CaCO₃ dissolution

The dissolution of CaCO₃ was modeled with the three parallel reactions: $C a C O_{3 (s)} + H^{+} C a^{2 +} + H C O_{3}^{-}$ (5) $C a C O_{3 (s)} + H_{2} C O_{3}^{*} C a^{2 +} + 2 H C O_{3}^{-}$ (6)

C a C O_{3 (s)} C a^{2 +} + C O_{3}^{2 -}

(7)

The dissolution of CaCO₃ follows the rate law (Plummer et al., 1978; Chou et al., 1989): $r_{D, C a C O 3} = A (k_{D, C 1} + k_{D, C 2} + k_{D, C 3}) (1 - Ω_{C a C O 3})$ (8)

where $k_{D, C 1}$ , $k_{D, C 2}$ , and $k_{D, C 3}$ (mol/[m²·s]) are empirical temperature dependent rate parameters, T is the temperature (Kelvin), and A is the reactive surface area (m²): $l o g k_{D, C 1} = 0.198 - \frac{444}{T}$ (9) $l o g k_{D, C 2} = 2.94 - \frac{2177}{T}$ (10)

l o g k_{D, C 3} = - 1.10 - \frac{1737}{T}

(11)

CaCO₃ dissolves when the solution is undersaturated ( $S I_{C a C O 3}$ < 0). Because Plattenberger et al. (2018) showed that wollastonite and pseudowollastonite reacted with CO₂ to produce calcite and aragonite, respectively, for wollastonite simulations, the solubility constant of calcite was used, while for pseudowollastonite simulations, the solubility constant of aragonite was used (Table 1).

SiO_2(am) dissolution

The dissolution of amorphous silica was modeled based on the experimental results of others that observed SiO_2(am) formation in the reaction of calcium silicates with CO₂ (Daval et al., 2009a; Plattenberger et al., 2018; Monasterio-Guillot et al., 2019). Dissolution was modeled according to the following reaction: $S i O_{2 (a q)} S i O_{2 (a m)}$ (12)

When the solution was undersaturated with respect to SiO_2(am), then dissolution was allowed to occur. The rate of dissolution, according to Dove and Crerar (1990), is as follows: $r_{D, S i O 2 (a m)} = k_{D, S i O 2} a_{S i O 2 (a q)} a_{H}^{2} (1 - Ω_{S i O 2 (a m)})$ (13)

The rate constant $k_{D, S i O 2}$ was calculated using the Arrhenius expression from Icenhower and Dove (2000). For SiO_2(am), $Ω_{S i O 2 (a m)} = \frac{\{S i O_{2 (a q)}\}}{K_{s p, S i O 2 (a m)}}$ (14)

Modeling of CaSiO₃, CaCO₃, and SiO_2(am) precipitation

Precipitation reactions for CaSiO₃, CaCO₃, and SiO_2(am), as described in Table 1, were modeled kinetically with rate equations. For all solids, precipitation was allowed to occur when the $S I_{i}$ > 0, and according to the rate law (Kim et al., 2011): $r_{P, i} = A k_{P, i} (1 - Ω_{i})$ (15)

where the rate is in units of mol/[cm²·s] and A is the reactive surface area. The precipitation rate constant, $k_{P, i}$ , accounts for both the rate of precipitation and the energy barrier needed to overcome nucleation for solid phase i. It is difficult to define a $k_{P, i}$ value from the literature, because metastable aqueous solutions do not nucleate immediately upon oversaturation and can exist as an oversaturated solution over a wide range of saturation values differing by several orders of magnitude of $Ω_{i}$ (Prieto et al., 1994). In this study, values of $k_{P, i}$ (Table 1) were chosen by calibration to the sand column experiment reacting pseudowollastonite at 150°C with 1.1 MPa CO₂ described in Plattenberger et al. (2019). The details are discussed in the Model Calibration section. In addition, because the rate of precipitation is proportional to reactive surface area, when no initial precipitate was present, an artificial “seed” of 1 × 10⁻¹¹ g was added to initiate precipitation. Chosen specific surface areas used to calculate reactive surface area based on the amount of this mineral phase are included in Table 1, although specific surface areas are known to vary widely.

CCSH dissolution and precipitation

CCSH dissolution and precipitation were modeled thermodynamically with no kinetic equations with tobermorite as the model CCSH. Tobermorite was chosen from many known CCSH phases because it is one of the most well-studied calcium silicate hydrates. In addition, Daval et al. (2009b) studied the reaction of wollastonite with CO₂ and identified small amounts of calcium silicate hydrate that was likely 14 Å-tobermorite. Monasterio-Guillot et al. (2019) also identified what was likely metastable tobermorite in pseudowollastonite carbonation reactions.

The dissolution reaction of 11 Å-tobermorite is described as follows: $C a_{5} S i_{6} H_{11} O_{22.5} + 10 H^{+} 5 C a^{2 +} + 6 S i O_{2 (a q)}$ (16)

The saturation index for tobermorite is, $S I_{C C S H} = l o g \frac{{\{C a^{2 +}\}}^{5} {\{S i O_{2 (a q)}\}}^{6}}{{\{H^{+}\}}^{10} K_{s p, C C S H}}$ (17)

In the model, dissolution occurs when $S I_{C C S H}$ < 0 to achieve equilibrium or until no tobermorite is present. Precipitation occurs when $S I_{C C S H}$ > 0 to achieve equilibrium, and was solved numerically using the bisection method (Burden et al., 2016).

Aqueous speciation

Table 1 includes all modeled aqueous speciation reactions along with their equilibrium constants and database sources. These species include H⁺, OH⁻, H₂CO_3(aq), HCO₃⁻, CO₃²⁻, SiO_2(aq), Na⁺, and Ca²⁺. Activity coefficients of all species were calculated using the Davies equation. CO₂ was modeled as an aqueous solute, not as a separate phase. The concentration of dissolved CO₂ was calculated using equations of state from Sterner and Pitzer (1994) and the solubility equations of Duan and Sun (2003). Speciation is calculated to satisfy the thermodynamic equilibrium of each species, listed in Table 1, and to satisfy the conservation of charge using the bisection method: $2 [C a^{2 +}] + [N a^{+}] + [H^{+}] = [H C O_{3}^{-}] + 2 [C O_{3}^{2 -}] + [O H^{-}]$ (18)

Transport

Diffusion

The governing equation for mass transport coupled with chemical reaction is as follows: $\frac{\partial (C_{i} φ_{d, x})}{\partial t} = D \frac{\partial}{\partial x} (\frac{\partial C_{i}}{\partial x} φ_{d, x}) + R$ (19)

where C_i is the concentration of species i, t is time, D is the diffusion coefficient, $φ_{d, x}$ is porosity available for diffusion, x is the spatial dimension, and R is the reaction term. The equation was discretized with a forward time-centered space scheme. Diffusion coefficients were calculated depending on temperature (Supplementary Table S1). The diffusion solver and the geochemical solver were verified numerically and separately from each other.

Porosity and microporosity

Porosity available for diffusion ( $φ_{d, x}$ ) in each cell was calculated based on the volumes occupied by each mineral phase and the available microporosity according to the following equation: $\begin{matrix} φ_{d, x} & = 1 - V_{s a n d, x} - V_{C a S i O 3, x} - V_{C a C O 3, x} \\ - V_{S i O 2 (a m), x} - V_{C C S H, x} + φ_{μ, x} \end{matrix}$ (20)

where $V_{i, x}$ is the volume fraction filled by i solid based on its molar volume (Table 1). The value for $V_{s a n d, x}$ (Fig. 2) was estimated by comparison with Plattenberger et al. (2019) from their column dimensions and the mass of water that could fill the pore space before injection of CaSiO₃. The microporosity ( $φ_{μ, x}$ ) represents the volume fraction of micron sized pore space that exists within precipitated solids. In the model, we assign the microporosity to be readily available for diffusion, but not for further precipitation. Extensive microporosity exists in layered calcium silicates (Richardson, 2008; Bonnaud et al., 2012; Plattenberger et al., 2019). To quantify this in the model, for the volume fraction of tobermorite present in a cell, the same volume fraction of microporosity would form according to the following equation: $φ_{μ, x} = V_{C C S H}$ (21)

In order for microporosity to limit further precipitation in a cell, the porosity available for precipitation ( $φ_{μ, P}$ ) was calculated as follows: $φ_{P, x} = φ_{d, x} - φ_{μ, x}$ (22)

Once $φ_{P, x}$ reaches 0, the pore space is no longer available for precipitation in that cell until one of the solid phases dissolves. We also refer to $φ_{P, x}$ as macroporosity.

This method of incorporating microporosity in the model provides a way to simulate continued reactive transport downstream from regions where reaction has stopped because there is no volume remaining for mineral precipitation.

Permeability

The permeability change that resulted from the mineral precipitation filling the pore space was calculated using the power law relation with porosity change: $\frac{k_{x}}{k_{0}} = {(\frac{φ_{d, x}}{φ_{d, x, 0}})}^{α}$ (23)

where k_x is the permeability of cell $x (m D)$ and $φ_{d, x}$ is the porosity of cell x. The value k₀ is the initial permeability (mD) for each cell. The value used for the constant $α$ was 5, within the range of values found appropriate for geologic subsurface CO₂ reservoirs (Nogues et al., 2013).

The initial permeability was calculated using the Kozeny-Carman relationship: $k_{0} = \frac{φ_{0}^{3}}{36 c {(1 - φ_{0})}^{2}} g^{2}$ (24)

where $φ_{0}$ is the initial porosity available for diffusion, c is a scaling constant for the rock type, which is ∼5.7 for sandstones (Rose and Bruce, 1949), and g is grain size (μm). To compare with experimental work by Plattenberger et al. (2019), the grain size was estimated by taking the weighted average of a 500 μm sand particle and the average CaSiO₃ particle size of 10.2 μm from those experiments, weighted based on their mass fractions. This grain size remained constant across simulations.

To find the permeability (K_P) of the entire length of the porous medium, the harmonic average of the individual k_x values for each cell was calculated (Khan, 2012) as follows: $K_{P} = \frac{N}{\sum^{1} ∕ k_{x}}$ (25)

where K_P is in mD and N is the number of cells.

Simulation Conditions and Model Parameters

Simulation conditions

The first model simulation was for calibration toward published experimental data to determine precipitation rate constants. Second, the pH was increased by adding 0.1 M NaOH to examine the effect of pH on the reaction front. The simulation was also used as validation by comparing with published experimental results from Plattenberger et al. (2019). A third set of simulations examined the effects of CaSiO₃ solubility constants and dissolution rates to understand differences between wollastonite and pseudowollastonite and their effects on mineral precipitation and permeability reduction. A fourth simulation was done for field conditions at 40°C and CO₂ pressures of 7.5 MPa (Crandell et al., 2010). All simulations were allowed to run to 96 h.

Model calibration

The calibration simulation (Simulation 1) results were compared to an experimental result from Plattenberger et al. (2019) in which a sand column containing pseudowollastonite was reacted at 150°C with boundary condition water equilibrated with 1.1 MPa CO₂. The precipitation rate constants $k_{P, i}$ were varied to yield a precipitation front most similar to the observed precipitation front of CaCO₃ (Fig. 3), forming near the inlet up to ∼2–3 mm. The fitted $k_{P, i}$ values are in Table 1. The CaCO₃ front in the calibrated model produced a front reaching 3 mm, although the largest amounts of CaCO₃ precipitation occurred nearer to the CO₂ source. Precipitation rates can vary with supersaturation, surface roughness, and particle surface area (Shiraki and Brantley, 1995; Noiriel et al., 2012). The same $k_{P, i}$ values were used for the remaining simulations, despite possible variability with ionic strength, temperature, and CO₂ pressure.

FIG. 3.

(a) Experimental results for Simulation 1, in which pseudowollastonite in a sand column is reacted with CO₂ after 96 h. Sr had been used as an indicator for CaCO₃ due to its ability to coprecipitate. The XRF map shows Sr in light blue where CaCO₃ forms, and areas without Sr in dark blue. The carbonation front extended ∼2–3 mm from the CO₂ source. (b) Model results for the calibration simulation show an observable amount of CaCO₃ in the model forming up to ∼2–3 mm from the CO₂ source after 96 h. Sr, Strontium.

Sensitivity analyses of these rate constants in pseudowollastonite reactions indicated that the CaSiO₃ precipitation rate constant largely controlled where the observable CaCO₃ precipitation front occurred (Supplementary Fig. S1a). As the rate constant $k_{P, C a S i O 3}$ decreases, the amount of CaCO₃ near the CO₂ source at 0 mm decreases, but the amount of CaCO₃ farther from the CO₂ source increases. This likely occurs because rapid precipitation of CaSiO₃ removes Ca²⁺ from solution making it unavailable for CaCO₃ precipitation. Some of this Ca²⁺ is used for CaCO₃ formation further from the CO₂ source when $k_{P, C a S i O 3}$ is lower.

The precipitation rate constant for CaCO₃ affects the mass of CaCO₃ precipitation occurring in the regions of CaCO₃ precipitation. As the $k_{P, C a C O 3}$ increases, the rate of CaCO₃ precipitation increases, resulting in higher accumulation of CaCO₃ near the inlet at 0 mm, and lower accumulation of CaCO₃ at 1 mm from the inlet (Supplementary Fig. S1b).

Model validation

The model was validated in Simulation 2 as a result of adjusting the boundary pH to 6.1 by adding 0.1 M NaOH and comparing simulations with experimental results from Plattenberger et al. (2019). Those sand column experiments showed that, with higher pH, a small amount of CaCO₃ precipitation occurred at the inlet, and CCSH precipitation was predominant from the inlet to ∼2–3 mm into the porous medium (Fig. 4a). The remainder of the porous medium stayed in its initial pseudowollastonite phase by 96 h of reaction, although permeability continued to decrease for 495 h. Similarly, the model showed that increased pH resulted in precipitation of CaCO₃ and SiO_2(am) largely within 1 mm from the CO₂ source. A region of tobermorite precipitation formed farther in, occurring from 1 to 25 mm from the inlet by 96 h (Fig. 4b), producing more extensive CCSH precipitation than Plattenberger et al. (2019). This difference can be attributed to simplifications made in the model regarding CCSH formation.

FIG. 4.

(a) Scanning electron microscopy images of three column regimes from sand column experiments with pseudowollastonite reacted for 96 h with boundary pH 6.1. Near the CO₂ source, large distinct crystals of CaCO₃ were found along with low amounts of CCSH and SiO_2(am). Around 2 mm beyond the inlet, significant amounts of plate-like crystals of CCSH were observed. The remainder of the column remained mostly unreacted pseudowollastonite. (b) Model simulations under the same conditions (Simulation 2) similarly produced three regimes, with CaCO₃ and SiO_2(am) nearest to the CO₂ source, followed by a second regime of tobermorite (CCSH), and a third, mostly unreacted regime of CaSiO₃. Microporosity formed in regions where CCSH was present, while the remaining unfilled volume consisted of macropores. CCSH, crystalline calcium silicate hydrate.

Simplifications in the model were made due to the complexity of CCSH forming in experiments. Many calcium silicate hydrates like tobermorite can exist as metastable solids intergrown with each other and with a range of molar volumes depending on the amount of water molecules held within its structure (Richardson, 2008; Houston et al., 2009). This model does not evaluate the effects of hydration on permeability, or the diversity of calcium silicate hydrates that can coexist in the same environment to similarly alter flow. Furthermore, the rate of tobermorite precipitation was not modeled due to the lack of known kinetic information regarding CCSH. Despite these differences, the simulated results still match at least the spatial regimes reasonably well, if not the actual length scales of those regimes.

Experimental Methods

Reactive diffusion column experiments

Glass beads (595–841 μm; Mo-Sci Corporation) were placed in a stainless steel tube (outder diameter: ¼,” Wall thickness: 0.049,” Length: 1”) and sintered together at 680°C following methods by Berge et al. (1995). A filter was placed at the outlet of the column and pseudowollastonite (Sigma-Aldrich) was flowed through the glass bead column by pressurized water to fill the pore space. The filter was then removed, and the column was allowed to dry at 105°C for 24 h. The glass bead column was then placed in a stainless steel pressure vessel (300 mL; Parr) and filled with 250 mL of deionized water. It was reacted at 120°C degrees with a CO₂ overhead pressure of 15 MPa, and allowed to react for 96 h. After reaction, the column was again dried at 105°C for 24 h. Permeability of the glass bead columns was measured before and after reaction with CO₂ using air permeability, which measures the flow rate and pressure potential of air in the column (Tanikawa and Shimamoto, 2009).

Analysis of the column and reacted solids

After removal of the steel casing, the entire reacted glass bead column was imaged with xCT using a Zeiss Xradia 520 Versa High-resolution three-dimensional (3D) X-ray tomography microscopy (Princeton Imaging and Analysis Center) with a spatial resolution of 7.5 μm. Radiographs were collected by energy 80 kV with exposure times of 8.0 s. Three-dimensional image reconstructions were carried out in Scout-and-Scan Control System Reconstructor on 2048 radiographs taken over 180 degrees. Image processing for phase segmentation was conducted using Avizo 9 (FEI Systems) software. Subvolumes (1074 × 1277 × 1756 pixels) removing curved edges of the glass bead cylinder were used for further analysis.

X-ray diffraction (PANalytical X-Pert Pro Multipurpose Diffractor, Cu-Kα) was used to analyze the CaSiO₃ before and after reaction with CO₂. Scanning electron microscopy (SEM) coupled with energy dispersive X-ray spectroscopy (EDS) (Quanta-650) was used to examine morphology and elemental abundance of the prereaction and postreaction materials. For SEM/EDS analysis, samples were coated with Au/Pd.

Results and Discussion

Effect of pH on calcium silicate hydrate precipitation

As expected, experiments indicate that increasing pH can cause more CCSH precipitation (Simulations 1, 2; Figs. 3 and 4), but our model reveals why this occurred by examining the concentrations of aqueous species and the coinciding precipitation over time. Mineral solubility, CO₂ solubility, and carbonate speciation all play a role.

Two boundary pH conditions of 3.5 (Fig. 3) and 6.1 (Fig. 4) were examined by maintaining an overhead pressure of 1.1 MPa CO₂ and adding 0.1 M NaOH to increase pH. The increase in pH increased the solubility of CO₂, increasing the total carbon concentration in solution at the boundary from 0.058 to 0.156 M (Fig. 5a, b), thereby increasing the amount of diffusing CO₃²⁻. Subsequently, because CaCO₃ formation [Eq. (7)] is generally limited by the CO₃²⁻ supply in the system, the simulations at increased pH had more rapid CaCO₃ precipitation within the first 48 h (Fig. 5c, d). CaCO₃ precipitation began to slow near the CO₂ source in simulations at increased pH after ∼48 h due to limited supply of CO₃²⁻, although minor CaCO₃ precipitation continued up to 85 h (Fig. 5c).

FIG. 5.

In Simulation 2 with pseudowollastonite reacted with boundary pH 6.1, (a) the total carbon of the CO₂ source, depicted in the boundary cell and throughout the porous medium, is higher than in (b) the simulations with boundary pH 3.5. Consequently, CaCO₃ formation occurs more rapidly over time within the first 85 h and in larger amounts when (c) the boundary pH is 6.1 than (d) when the boundary pH is 3.5.

As shown in Fig. 6a, after ∼94 h, Ca²⁺ began to significantly accumulate near the inlet. The accumulation of Ca²⁺ over time promoted tobermorite precipitation through its influence on the saturation index (Fig. 6b). Precipitation of tobermorite occurred by 95 h (Fig. 6c) when it became oversaturated based on the $S I_{C C S H}$ .

FIG. 6.

In Simulation 2 with pseudowollastonite reacting with boundary pH 6.1, (a) Ca²⁺ accumulates significantly after 94 h when CaCO₃ precipitation has slowed. This, in part, increases the (b) $S I_{C C S H}$ , resulting in (c) tobermorite precipitation to equilibrium. (d) At 96 h, the effect of Ca²⁺ on H⁺ and OH⁻ concentration to achieve charge neutrality throughout the porous medium leads to decreased H⁺, which also increases $S I_{C C S H}$ . (e) Increased Ca²⁺ also causes supersaturation of CaCO₃. The formation of CCSH leads to (f) significant decreases in the porosity available for precipitation in the last 2 h of the simulation.

Increased Ca²⁺ concentration from accumulation increased $S I_{C C S H}$ . In addition, increasing Ca²⁺ also increased pH. Based on the conservation of charge [Eq. (18)], if Ca²⁺ concentration increases, then H⁺ concentration needs to decrease to maintain net neutrality for the solution, and the OH⁻ concentration should increase to satisfy the equilibrium for the dissociation of water (Table 1). The decrease in H⁺ concentration results in further increase of $S I_{C C S H}$ according to Equation (17). The effect of Ca²⁺ accumulation on H⁺, OH⁻, and the $S I_{C C S H}$ is shown in Fig. 6d.

Spatial distribution of precipitating solids

The spatial distribution of solids throughout the porous medium in experiments with the boundary pH 6.1 can be explained by the order of reactions described above in Effect of pH on Calcium Silicate Hydrate Precipitation section. In the first regime reaching 1 mm from the inlet, CaCO₃ and SiO_2(am) dominate (Fig. 4). Because CaCO₃ begins precipitating within the first hour of reaction and is limited by the supply of CO₃²⁻, it forms near the CO₂ source. SiO_2(am) precipitation, which depends on the supply of SiO_2(aq) ions, forms where SiO_2(aq) is released from CaSiO₃ dissolution, coinciding with where CaCO₃ forms. We note that although dissolution of CaCO₃ and SiO_2(am) was included in the model, their dissolution did not play a role in our simulations due to the presence of supersaturated solutions. During the first 94 h of reaction, tobermorite remains undersaturated (Fig. 6b) and does not compete for ions near the inlet.

In the second regime from 1 to 25 mm from the inlet, tobermorite dominates by 96 h (Fig. 4). Because tobermorite precipitation depends on Ca²⁺, SiO_2(aq), and H⁺ concentrations as opposed to CO₃²⁻ concentrations, it forms where Ca²⁺ accumulates after CaCO₃ precipitation has slowed, occurring after 94 h. Note that this compares well with experiments by Plattenberger et al. (2019), which found that permeability differences between experiments with and without NaOH did not occur until after 96 h.

In the model, tobermorite's instantaneous precipitation to reach equilibrium removes Ca²⁺ and SiO_2(aq) ions from solution, which could be available for CaCO₃ and SiO_2(am) formation. In the second regime, once CaCO₃ and SiO_2(am) do become supersaturated, they are still modeled as rate-controlled precipitation reactions competing with the instantaneous, equilibrium-driven tobermorite precipitation. Although the high-volume fractions of tobermorite are partly an artifact of the different methods used to model CaCO₃, SiO_2(am), and CCSH precipitation, the correct spatial pattern reproduced in the model was similar to experimental results by Plattenberger et al. (2019), confirming the likelihood that CCSH formation in the second regime depletes ions for CaCO₃ and SiO_2(am) precipitation. On the other hand, the larger spatial extent of CCSH precipitation suggests that CCSH precipitation may be rate limited, like CaCO₃ and SiO_2(am) precipitation.

In the third regime from 25 mm to the end of the modeled porous medium (Fig. 4b), limited CaSiO₃ dissolution occurred with minor amounts of CaCO₃ formation. Although HCO₃⁻ and CO₃²⁻ are present in this regime, their concentrations are still less than concentrations near the inlet at 96 h, limiting CaCO₃ precipitation. The relatively stable pH also prevents rapid CaSiO₃ dissolution. Consequently, unreacted pseudowollastonite dominates the third regime.

Effects of CaCO₃, SiO_2(am), and CCSH on permeability change

The predicted changes in permeability in simulations 1 and 2 coincide with accumulating precipitates and their effects on porosity. When the boundary pH is 3.5 (Simulation 1), permeability does not start to significantly decrease until after ∼72 h (Fig. 7) when noticeable CaCO₃ and SiO_2(am) precipitation start (Fig. 5d and Supplementary Fig. S2a). By 96 h, the simulated permeability decreases by 1 order of magnitude. Model predictions of permeability were comparable to experimental results by Plattenberger et al. (2019). In those experiments conducted, sand columns under the same experimental conditions decreased by 0.46 orders of magnitude in 96 h and continued to decrease by 0.84 orders of magnitude after ∼168 h.

FIG. 7.

Permeability decreased for simulations with pseudowollastonite reacted with CO₂ for boundary pH 3.5 (Simulation 1) and 6.1 (Simulation 2), with a larger decrease occurring at higher pH.

For Simulation 2 with the boundary pH 6.1, permeability starts to decrease (Fig. 7) when CaCO₃ and SiO_2(am) precipitation occur from ∼30 to 94 h of reaction (Figs. 5c and 3b). By 94 h, the permeability for simulated porous media decreased by ∼8 orders of magnitude. After 94 h, the model shows that permeability remains relatively stable, coinciding with rapid tobermorite precipitation (Fig. 6c). Although one might expect large amounts of CCSH precipitation to decrease permeability, an explanation lies in the modeling of microporosity and its effect on permeability. In the model, microporosity is available for diffusion, but not for precipitation. However, microporosity is incorporated into the calculation of the porosity available for diffusion, $φ_{d, x}$ , and $φ_{d, x}$ is used to calculate permeability. If microporosity is not used in the calculation of $φ_{d, x}$ for permeability, the permeability of the porous medium at 96 h lowers by an additional ∼1.5 orders of magnitude from 2.96 × 10⁻⁶ to 7.04 × 10⁻⁸ mD, yielding a total permeability decrease of ∼9.5 orders of magnitude. When comparing model results to experiments by Plattenberger et al. (2019), the modeled permeability decrease of ∼8 to 9.5 orders of magnitude was less than experimentally measured permeability change. By 96 h, sand column experiments that had been reacted under the same conditions decreased by 0.75 orders of magnitude. By 495 h, the permeability continued to decrease by 2.83 orders of magnitude. The complicating effects of modeling microporosity will be discussed in the following section.

The role of microporosity

The modeling of microporosity opens new doors and generates new questions. First, the inclusion of microporosity with CCSH precipitation permits continued diffusion and reaction in the model over longer time scales. In particular, for Simulation 2 with pseudowollastonite reacting with CO₂ for the case of boundary pH 6.1 (Fig. 4), the pore space available for precipitation, $φ_{P}$ , decreased to 0 by 95 h of reaction at the inlet (0 mm), preventing further formation of solids at 0 mm until dissolution had occurred. Because the pore space available for diffusion, $φ_{d}$ , remained greater than 0, CO₂ was able to continue diffusing through the porous medium. As a result, continued precipitation of CCSH, CaCO₃, and SiO_2(am) occurred after 95 h, accumulating deep into the length of porous medium. We speculate that this may be appropriate due to other studies that have found decreasing pore space inhibits the nucleation process (Putnis, 2015; Prasianakis et al., 2017).

Microporosity plays an important role in filling pore space with mineral precipitation, although questions regarding its effect on permeability remain. Because microporosity represents pore space available for diffusion, it was included in the calculation of permeability. The designated amount of microporosity produced by CCSH formation, one in which the volume of micropores is equivalent to the volume of CCSH, resulted in no permeability decrease directly caused by CCSH precipitation. Despite this simulated result, we suspect that the formation of CCSH does, in fact, lead to permeability decrease, based on continued permeability decreases in sand column experiments by Plattenberger et al. (2019) when substantial CCSH formed. A decreased volume of microporosity resulting from CCSH formation would yield lower permeability. An improved estimation of the volume of microporosity produced from the different precipitation reactions would provide a better estimate of the actual effect of microporosity on permeability.

In addition, the model does not include microporosity from CaCO₃, SiO_2(am), or CaSiO₃. This may account for the larger decrease in permeability in our simulations than the values measured in experiments, although the relative changes in permeability for different experiments remain accurate. We note that, in general, the effect of microporosity on permeability is poorly understood and is further complicated by pore connectivity, pore geometry, and ratio relative to macropores (Weger et al., 2009; Mehmani and Prodanović, 2014; Apourvari and Arns, 2016). Nonetheless, the model provides interesting insight into how microporosity from CCSH precipitation might influence permeability.

Permeability, porosity, and pore connectivity

To better understand the role of precipitation on porosity and permeability, experiments were conducted using sintered glass bead columns containing CaSiO₃ to react with CO₂. The use of sintered glass beads allowed for xCT analysis and differentiation between the glass beads, pores, and minerals. Because the glass beads were sintered together, the steel casing, which would have made it difficult to differentiate between materials like CaSiO₃ and CaCO₃ that may have more similar densities, could be removed. On the other hand, the glass bead surfaces were found to undergo minor dissolution, likely releasing additional ions in solution. Due to the resulting uncertainties and complications, we did not directly model glass bead column experiments.

The xCT images of glass bead column experiments showed that material filling the pore space near the column inlet had a different density than material filling the pore space near the closed end of the column (Fig. 8a). X-ray diffraction informed by chemical compositions detected from SEM/EDS analyses indicated that calcite formed at the inlet, while the calcium silicate hydrate fedorite formed in the remaining column.

FIG. 8.

(a) xCT of reacted pseudowollastonite in glass bead columns showed different densities in the material filling the columns near the inlet and outlet. (b) An analysis of which pore spaces were connected, with each color representing a separate region disconnected from the main pore network, showed that pore connectivity decreased from the addition and reaction of CaSiO₃. xCT, x-ray computed tomography.

Analysis of the pore spaces showed that pore connectivity greatly decreased after CaSiO₃ was added and reacted with CO₂ (Fig. 8b), resulting in a permeability change of 2 orders of magnitude from 256 ± 29 to 7 ± 2 mD after 96 h of reaction. The pore connectivity arises from the 3D nature of a porous system and cannot be accounted for in a 1D model. However, the role of pore connectivity in permeability change should not be overlooked.

Comparison between wollastonite and pseudowollastonite in a diffusive system

To understand differences between wollastonite and pseudowollastonite dissolution on mineral precipitation, we modeled the effects of their distinct solubility constant, differences in dissolution rates for the two CaSiO₃ minerals, and differences in precipitating CaCO₃ mineral solubility constants.

In contrast to Simulation 2 for the 96-h simulations of pseudowollastonite reactions with CO₂ for the case of boundary pH 6.1, reactions using the wollastonite solubility constant and a slowed dissolution rate led to no tobermorite formation (Fig. 9a). The use of calcite or aragonite's solubility constant for the CaCO₃ phase did not affect tobermorite formation. The precipitation from CaCO₃ and SiO_2(am) led to decreases in permeability by 96 h (Fig. 9b), with the change larger than the simulations for pseudowollastonite reacting with CO₂ for the case of the pH 3.5 boundary, but less than the simulations with the pH 6.1 boundary (Fig. 7).

FIG. 9.

Simulation 3 with the pH 6.1 boundary using the K_sp of wollastonite, the dissolution rate of wollastonite, and the K_sp of calcite as opposed to aragonite for the precipitation CaCO₃ produced, (a) CaCO₃ and SiO_2(am) near the CO₂ source with no CCSH throughout the porous medium. (b) Permeability decreased as a result of the precipitating products.

Examination of all three parameters that varied between wollastonite and pseudowollastonite simulations, which include the $K_{s p, C a S i O 3}$ , the dissolution rate, and the $K_{s p, C a C O 3}$ , indicated that both the $K_{s p, C a S i O 3}$ of pseudowollastonite and the more rapid pseudowollastonite dissolution rate are necessary for tobermorite formation. The difference in solubility constants, with pseudowollastonite having a higher solubility than wollastonite, allowed for more Ca²⁺ and SiO_2(aq) to be released into solution upon CaSiO₃ dissolution. Similarly, the increased dissolution rate of pseudowollastonite released more Ca²⁺ and SiO_2(aq) into solution faster than the wollastonite simulations. With increased Ca²⁺ in solution, the H⁺ concentration should also decrease to satisfy the conservation of charge [Eq. (18)]. The combined effects of increased Ca²⁺, SiO_2(aq), and decreased H⁺ led to oversaturation of tobermorite according to [Eq. (17)] in certain regions of the porous medium for pseudowollastonite simulations.

The differences in precipitation products formed from wollastonite or pseudowollastonite highlight the importance of crystal structure in predicting reactions in the field if either CaSiO₃ was used to seal leakages from geologic CO₂ reservoirs. Pseudowollastonite has a structure consisting of isolated trisilicate rings (Yang and Prewitt, 1999), while wollastonite consists of silicate chains (Seryotkin et al., 2012). When reacting with CO₂, wollastonite dissolves nonstoichiometrically, while pseudowollastonite dissolves stoichiometrically (Casey et al., 1993; Schott et al., 2012). The type of dissolution has been attributed to the difference in precipitates formed between the two calcium silicates, although this work suggests that dissolution rate and solubility likely play important roles as well.

Extrapolation to field conditions for a geologic CO₂ reservoir

To examine the reactions relevant to a CaSiO₃-CO₂ system in a geologic CO₂ reservoir, the field conditions of 40°C and 7.5 MPa CO₂ were selected to run in the 1D model for Simulation 4. Although the boundary pH was 3.1, CCSH still formed throughout the porous medium, mostly from 1 to 44 mm at the closed end of the porous medium (Fig. 10a). In these regions, CCSH precipitates immediately at the start of the simulation. This results from the initial equilibration of pseudowollastonite throughout the porous medium at 0 h, which creates the conditions appropriate for CCSH to become supersaturated (Supplementary Fig. S3a).

FIG. 10.

Simulation 4 under field conditions at 40°C and 7.5 MPa CO₂ with no additional ions added formed (a) CaCO₃ and SiO_2(am) near the CO₂ source along with CCSH throughout the porous medium. (b) Permeability decreased initially from significant CCSH formation, followed by continued decrease due to CaCO₃ and SiO_2(am) precipitation until conditions became relatively stable.

The change in initial conditions at 40°C field conditions and 150°C experimental conditions results from changes in equilibrium constant values due to temperature. Although the $K_{s p, C C S H}$ of tobermorite is higher at 40°C than at 150°C (Table 1), which should make tobermorite precipitation more difficult at 40°C, the change in the $K_{H 2 O}$ with temperature (Table 1) and its influence on H⁺ and OH⁻ concentration have an even larger effect on tobermorite saturation. $K_{H 2 O}$ is lower at 40°C than at 150°C, yielding less dissociated H₂O at 40°C, and subsequently less H⁺ and OH⁻. A comparison of initial conditions at the two temperatures indicates that the initial pH throughout the porous medium at 0 h is 10.3 at 40°C, while the initial pH for the 150°C simulations is 8.1 (Supplementary Fig. S3). The significant effect of pH on $S I_{C C S H}$ [Eq. (17)], one that exceeds those of Ca²⁺ and SiO_2(aq), results in tobermorite precipitation at 40°C at the start of the simulation. We also note that limited CCSH formed at the inlet (0mm) due to competition with CaCO₃ and SiO_2(am). The initial formation of CCSH (Supplementary Fig. S4a) is largely responsible for the rapid decrease in permeability by 1 h of reaction (Fig. 10b).

The remaining significant decreases in permeability up to 11 h result from CaCO₃ and SiO_2(am) precipitation. Under field conditions, almost all CaCO₃ and SiO_2(am) formation occurred rapidly within 11 h of reaction (Supplementary Fig. S4b, c). Only minor increases in precipitation and decreases in permeability continued to occur due to <0.001 vol. fraction of CaCO₃ precipitation at the inlet from 11 to 96 h.

The fast approach to a relatively stable environment in porous media under field conditions was initially surprising, particularly because it occurred faster than in high temperature simulations. However, an understanding of CO₂ solubility explains the unexpected result. CO₂ solubility decreases with increasing temperature. As a result, CO₂ dissolves more readily at 40°C, yielding higher total carbon concentrations for the CO₂ source than at 150°C. In addition, the field conditions had a higher overhead CO₂ pressure at 7.5 MPa, higher than the experimental overhead CO₂ pressure at 1.1 MPa. Therefore, the simulation at 150°C had total carbon concentrations of 0.05776 M for the CO₂ source, while the simulations under field conditions had total carbon concentrations of 1.152 M carbon. These increased levels of CO₂ in solution led to faster precipitation reactions for all solid phases and a faster approach to equilibrium under field conditions in comparison to the simulated conditions at 150°C.

At the same time, we recognize the limitations of the model in correctly predicting expected results under field conditions. In particular, the precipitation rate constants for CaSiO₃, CaCO₃, and SiO_2(am) were calibrated to match with the CaCO₃ precipitation front produced in experiments at 150°C. These rate constants may change with temperature, but due to the complexity of precipitation rates, we chose to keep them constant across all simulations.

Implications

These modeling results using field conditions typical for a geologic CO₂ reservoir yield promising insights into deploying CaSiO₃ particles for targeted mineral precipitation. The predicted precipitation of CCSH under field conditions has positive implications for using pseudowollastonite for targeted mineral precipitation. CCSH formation will likely contribute to significant decreases in porosity and permeability, particularly considering the large molar volumes of different CCSH phases in comparison to aragonite and calcite.

The expected formation of CCSH under field conditions may also improve the long-term stability of precipitated minerals used to prevent further leakage of CO₂ or other subsurface contaminants. The observed acid resistivity of certain CCSH relative to CaCO₃ will likely prove useful. The spatial relationship between CaCO₃ and CCSH precipitation also results in the advantageous formation of a thicker precipitation barrier that would not be possible with only CaCO₃ formation. CaCO₃ formation relies largely on the supply of CO₃²⁻, which is heavily limited by CO₂ diffusion. In addition, the presence of CO₃²⁻ is also limited by pH, with CO₃²⁻ forming as the dominant carbonate species only at high pH. Most systems may not reach a high enough pH for CO₃²⁻ to be the dominating carbonate ion. CCSH formation, on the other hand, depends on the more abundant Ca²⁺ and SiO_2(aq) ions, along with an alkaline pH that can arise naturally from the presence of Ca²⁺. The formation of different regimes of precipitation resulting from diffusion-limited species emphasizes the complexity of transport in such systems, and hints at the possibility of engineering multilayered barriers for targeted mineralization.

In addition, this work elucidates the role that basic conditions may play in developing targeted mineralization technology. The presence of other ions can influence the solubility of CO₂, consequently affecting the rates of precipitation, the supply of diffusing ions, and the potential for taking advantage of multiple forms of precipitation in a mineralized barrier. The application of adding basic ions may be used for improving outcomes during the process of sealing leakages if CaSiO₃ nanoparticles were injected in a pH-adjusted solution. In addition to controlling injected mixtures, the presence of other ions can also affect the pH of diffusing solutions, determining the amount of dissolution and precipitation that may occur. Such considerations are relevant to leakages occurring in a wide variety of subsurface settings, including those that contain brines.

The development of this 1D model enabled us to explore the deployment of CaSiO₃ particles in the subsurface. We can now examine different solution conditions, a diversity of rock types, a variety of CaSiO₃ particle sizes, and the effects of uneven distribution of CaSiO₃ minerals within the porous medium depending on where they accumulate after deployment. This model will help tackle the complex systems in which targeted mineral precipitation technology will be implemented.

Footnotes

Acknowledgment

We thank Zhiyuan Tao for his contribution to glass bead column experiments.

Author Disclosure Statement

No competing financial interests exist.

Funding Information

This work was supported by the U.S. Department of Energy National Energy Technology Laboratory (Grant DE-FE0026583 to the University of Virginia and Grant DE-FE0026582 to Princeton University) and the National Science Foundation (Grant NSF CBET-1805075 to the University of Virginia). The authors acknowledge the use of Princeton's Imaging and Analysis Center, which is partially supported by the Princeton Center for Complex Materials through the National Science Foundation-MRSEC program (DMR-1420541).

Supplementary Material

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Supplementary Material

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Sealing Porous Media through Calcium Silicate Reactions with CO 2 to Enhance the Security of Geologic Carbon Sequestration

Abstract

Introduction

One-Dimensional Reactive Transport Model

Model system

Reactions and rate laws

CaSiO3 dissolution

CaCO3 dissolution

SiO2(am) dissolution

Modeling of CaSiO3, CaCO3, and SiO2(am) precipitation

CCSH dissolution and precipitation

Aqueous speciation

Transport

Diffusion

Porosity and microporosity

Permeability

Simulation Conditions and Model Parameters

Simulation conditions

Model calibration

Model validation

Experimental Methods

Reactive diffusion column experiments

Analysis of the column and reacted solids

Results and Discussion

Effect of pH on calcium silicate hydrate precipitation

Spatial distribution of precipitating solids

Effects of CaCO3, SiO2(am), and CCSH on permeability change

The role of microporosity

Permeability, porosity, and pore connectivity

Comparison between wollastonite and pseudowollastonite in a diffusive system

Extrapolation to field conditions for a geologic CO2 reservoir

Implications

Footnotes

Acknowledgment

Author Disclosure Statement

Funding Information

Supplementary Material

References

Supplementary Material

CaSiO₃ dissolution

CaCO₃ dissolution

SiO_2(am) dissolution

Modeling of CaSiO₃, CaCO₃, and SiO_2(am) precipitation

Effects of CaCO₃, SiO_2(am), and CCSH on permeability change

Extrapolation to field conditions for a geologic CO₂ reservoir