Methods of producing dissolved inorganic carbon

Abstract

Disclosed herein are methods of producing solutions comprising dissolved inorganic carbon (DIC).

Description

[0001] METHODS OF PRODUCING DISSOLVED INORGANIC CARBON CROSS REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the benefit of priority to U. S. Provisional Application No.

[0003] 63 / 715,966, filed November 4, 2024, the contents of which are herein incorporated by reference in their entirety.

[0004] BACKGROUND

[0005] Measurement, reporting, and verification (MRV) strategies for carbon budgeting for carbon dioxide removal technologies are centered around additionality. Additionality refers to the carbon dioxide (CO2) removal (CDR) benefits achieved through a given process that otherwise would not have occurred without the intervention. The dissolution of alkaline compounds, such as magnesium hydroxide, in the ocean (e.g., ocean alkalinity enhancement), results in the uptake of CO2 from the atmosphere through the formation of dissolved inorganic carbon (DIC). However, the direct measurement of this uptake is difficult, precluding robust MRV. Therefore, new MRV strategies are required to support broader efforts to mitigate climate change through scalable atmospheric CDR technologies.

[0006] SUMMARY OF THE INVENTION

[0007] Disclosed herein are methods for producing DIC within the battery limits of a plant that is performing CDR, allowing for direct quantification of the amount of carbon that is removed from the atmosphere or another CO2 source.

[0008] In certain aspects, the disclosure provides a method of producing a solution comprising dissolved inorganic carbon (DIC), comprising: contacting an electrolyzer with a first aqueous solution; dividing the first aqueous solution into an anolyte in contact with an anode of the electrolyzer and a catholyte in contact with a cathode of the electrolyzer; applying a voltage to the electrolyzer to induce precipitation of first solid hydroxide particles in the catholyte, thereby forming a second aqueous solution comprising the first solid hydroxide particles; and contacting the second aqueous solution with a gaseous source of CO2.

[0009] In certain aspects, the disclosure provides a method of producing a solution comprising dissolved inorganic carbon (DIC) comprising: contacting an electrolyzer with a first aqueous solution; dividing the first aqueous solution into an anolyte in contact with an anode of the electrolyzer and a catholyte in contact with a cathode of the electrolyzer; applying a voltage to the electrolyzer to induce precipitation of first solid hydroxide particles in the catholyte, thereby forming a second aqueous solution comprising the first solid hydroxide particles; filtering the second aqueous solution comprising the first solid hydroxide particles to remove the first solid hydroxide particles, thereby forming a filtered aqueous solution; and contacting the filtered aqueous solution with a gaseous source of CO2.

[0010] In certain aspects, the disclosure provides a method of producing a solution comprising dissolved inorganic carbon (DIC) comprising: contacting an electrolyzer with a first aqueous solution; dividing the first aqueous solution into an anolyte in contact with an anode of the electrolyzer and a catholyte in contact with a cathode of the electrolyzer; applying a voltage to the electrolyzer to induce precipitation of first solid hydroxide particles in the catholyte, thereby forming a first aqueous solution comprising first solid hydroxide particles; filtering the second aqueous solution comprising the first solid hydroxide particles to remove the first solid hydroxide particles, thereby forming a filtered aqueous solution; contacting the filtered aqueous solution with a gaseous source of CO2 until a first pressure is reached, thereby forming a saturated aqueous solution; contacting the statured aqueous solution with second solid hydroxide particles, thereby forming a second aqueous solution comprising second solid hydroxide particles; and contacting the second aqueous solution comprising the second solid hydroxide particles with the gaseous source of CO2.

[0011] BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a diagram illustrating an annotated Bjerrum plot for CO2 and magnesium hydroxide.

[0012] FIG. 2 is a diagram illustrating that the precipitation of aragonite as evidenced by calcium reduction supported the formation of carbonate minerals. At equilibrium, either: DIC=39.9 mM, pH=9.25, [Mg]=36.2 mM, [Ca]=0 mM, [Nesq]=26.9 mM (with nesquehonite precipitation), or DIC=71.2 mM, pH=9.38, [Mg]=63.0 mM, [Ca]=0 mM (no nesquehonite precipitation).

[0013] FIG. 3 shows the rates of brucite dissolution and subsequent mineral precipitation were quantified from magnesium concentration changes. Plot shows two datasets (opaque / transparent) at an equivalent flow rate to volume ratio, showing consistency. Variance in reaction times can be attributed to differences in solution volume. At equilibrium, either: DIC=35.6 mM, pH=9.20, [Mg]=43.1 mM, [Ca]=0 mM, [Nesq]=20.0 mM (with nesquehonite precipitation), or DIC=59.1 mM, pH=9.32, [Mg]=63.0 mM, [Ca]=0 mM (no nesquehonite precipitation). FIG. 4 is a diagram illustrating that at pH 13 NaOH solution was carbonated under controlled conditions to mimic the brucite process. At equilibrium, DIC=76.0 mM, pH=9.47, [Mg]=4.5 mM, [Ca]=0 mM.

[0014] FIGs. 5A-5B are diagrams illustrating the maximum efficient CO2 flow rate for carbonation processes to avoid rate limitations.

[0015] FIGs. 6A-6C are diagrams illustrating the rate of carbonation with 3% CO2.

[0016] FIG. 7 is a diagram illustrating the experimental setups used for direct and sequential carbonation.

[0017] FIGs. 8A-C are diagrams illustrating the effect of gas flow rate-to-solution volume ratio (Q / V) on carbonation rate in a NaOH solution simulating the catholyte.

[0018] FIGs. 9A-C are diagrams illustrating the sequential carbonation of simulated catholyte using NaOH instead of brucite, wherein solid curves denote experimental data and dotted curves denote kinetic model predictions.

[0019] FIG. 10 is a diagram illustrating dissolution of brucite in air-equilibrated, filtered simulated catholyte, with the evolution of pH, DIC, [Mg], and [Ca] over time shown by solid curves and data points; dashed curves represent the best-fit kinetic model

[0020] FIG. 11A-B are diagrams illustrating sequential carbonation using (a) precipitated solids and (b) reagent-grade brucite, showing the time evolution of pH, dissolved inorganic carbon (DIC), and Mg and Ca concentrations.

[0021] FIG. 12A-D are diagrams illustrating (a) Temporal variations in pH, and DIC, Mg, and Ca concentrations during “sequential carbonation” (solid symbols, solid curve) and “direct carbonation” (open symbols, dashed curve), (b, c, d) Comparison of experimental data with kinetic model predictions (dotted curves) for (b) “direct carbonation”, (c) “sequential carbonation”, (d) “sequential carbonation - reagent-grade brucite”.

[0022] FIG. 13 is a diagram illustrating X-ray diffraction patterns of the residual solids at the end of the experiments corresponding to the following conditions: (a) “direct carbonation” and (b) “sequential carbonation”, with water evaporation compensation.

[0023] FIG. 14A-C are diagrams illustrating (a) Temporal variations in pH, and DIC, Mg, and Ca concentrations during “sequential carbonation” (solid symbols, solid curve) and “direct carbonation” (open symbols, dashed curve) with water evaporation compensation, (b, c) Comparison of experimental data with kinetic model predictions (dotted curves) for (b) “direct carbonation”, (c) “sequential carbonation”.

[0024] FIG. 15 is a diagram illustrating the quantification of carbon dioxide removed in solid and dissolved forms for sequential and direct carbonation. Tl, T2, and T3 correspond to theoretical CDR values for the case of (Tl) suppressed magnesium carbonate precipitation, (T2) forced nesquehonite precipitation, and (T3) forced hydromagnesite precipitation, and El and E2 correspond to (El) sequential and (E2) direct carbonation

[0025] DETAILED DESCRIPTION OF THE INVENTION

[0026] The urgent need to address rising atmospheric carbon dioxide (CO2) levels has driven the exploration of various methods for carbon removal and sequestration. The oceans have a vast capacity for carbon storage, and marine carbon dioxide removal (mCDR) technologies have been advancing rapidly. Among these, abiotic approaches that convert CO2 into stable solid forms, such as carbonate minerals, or into aqueous bicarbonate and carbonate ions offer a significant potential, as mineralization ensures long-term storage security of at least 10,000 years. One such method is an electrolysis-based approach that precipitates calcium carbonate and magnesium hydroxide from seawater while co-producing hydrogen. The process generates two streams: (1) an acidic stream (“anolyte”), which is neutralized using naturally occurring and industrial alkaline solids, and (2) an alkaline stream (“catholyte”) containing calcium carbonate and magnesium hydroxide. The alkaline stream undergoes carbonation within the facility, enabling the removal of carbon from the atmosphere.

[0027] To ensure that mCDR approaches effectively contribute to climate mitigation, robust quantification of the extent of CDR is essential. A fundamental challenge in mCDR methods such as ocean alkalinity enhancement (OAE) is that CDR occurs in an “open system” (i.e., the open ocean environment), downstream from the intervention site and over delayed and uncertain timeframes. However, this issue is avoided when the re-equilibration with atmospheric CO2 is performed within the plant; i.e., via so-called ISBL carbonation. Therefore, the ability to perform carbonation within the facility at reasonable energy costs and time scales enables the explicit and direct quantification of CDR, consistent with a reliable framework for measurement, reporting, and verification (MRV).

[0028] Disclosed herein are methods of capturing CO2 with hydroxides (e.g., mineral forms of hydroxides, such as brucite). To capture CO2 with brucite, the brucite is dissolved into solution, liberating two hydroxide ions (base) which react with CO2 in air (acid) to form carbonate / bicarbonate ions. As CO2 dissolves into solution, acidifying it, brucite dissolves, releasing OH' into solution, thereby maintaining the pH within a relatively narrow range. The carbonation process continues until brucite is fully dissolved and the solution reaches equilibrium. The carbonated solution can then be discharged into the ocean (e.g., in a way that it mixes with the ocean quickly enough that the elevated pCO2 does not result in degassing). Depending on the pH of the solution (e.g., basified seawater), the DIC will exist as a combination of HCO3-(bicarbonate) and CO32-(carbonate). At ocean pH, most DIC is in bicarbonate form and a single hydroxide anion is needed to neutralize one molecule of carbon dioxide. However, at other pHs, carbonate may dominate, which requires two hydroxide anions to neutralize one molecule of carbon dioxide.

[0029] Without wishing to be bound by theory or by particular implementations of the methods disclosed herein, at ocean pH, there is approximately 0.85 mol of CO2 per mol hydroxide; this is due to the balance of bicarbonate - 1.0 ratio - and carbonate - 0.5 ratio. Therefore, up to 1.7 mol CO2 per mol brucite can be captured. However, by carbonating solely with air at atmospheric pressure (approximately 0.04 kPa), the solution becomes saturated with CO2 at approximately pH 9.4 because the partial pressure of CO2 in solution (pCCh) is equal to the partial pressure in air. At this point, the catholyte has taken up about 3.2 g CO2 per liter of catholyte, whereas the full potential for CO2 uptake at infinite dilution (discharge into the ocean) is about 4.6 g CO2 per liter of catholyte. However, at pH 9.4, Mg-carbonates, such as nesquehonite and hydromagnesite, are present. Unfortunately, such carbonates are both stable in solution and have unfavorable CO2 / OH- ratios (0.5 and 0.4, respectively). What is more, the DIC is still in the carbonate-dominant region (FIG. 1, where the "limited dilution equilibrium" marks the point of equilibrium of the undiluted catholyte with air). In order to capture the full ~4.6 g CO2 per liter of catholyte inside the battery limit of the plant, a concentrated CO2 stream can be introduced (e.g., in the range of 2.5% to 5%). Doing so elevates pCCh in solution to above atmospheric and oceanic levels (atmosphere and surface ocean are in equilibrium, -0.04 kPa), forcing more CO2 (acidic gas) into solution in accordance with Henry's Law. The result is that the equilibrium pH of the solution to ocean pH is reduced, redissolving the Mg-carbonates and swinging the DIC towards the bicarbonate region, thereby achieving the full capture potential of the catholyte.

[0030] In certain aspects, disclosed herein are methods of producing a solution comprising dissolved inorganic carbon (DIC), comprising contacting a first aqueous solution comprising solid hydroxide particles with a gaseous source of CO2.

[0031] In certain aspects, disclosed herein are methods of producing a solution comprising dissolved inorganic carbon (DIC) comprising:

[0032] contacting an electrolyzer with a first aqueous solution;

[0033] dividing the first aqueous solution into an anolyte in contact with an anode of the electrolyzer and a catholyte in contact with a cathode of the electrolyzer; applying a voltage to the electrolyzer to induce precipitation of first solid hydroxide particles in the catholyte, thereby forming a second aqueous solution comprising the first solid hydroxide particles; and

[0034] contacting the second aqueous solution with the gaseous source of CO2.

[0035] In certain aspects, disclosed herein are methods of producing a solution comprising dissolved inorganic carbon (DIC) comprising:

[0036] contacting an electrolyzer with a first aqueous solution;

[0037] dividing the first aqueous solution into an anolyte in contact with an anode of the electrolyzer and a catholyte in contact with a cathode of the electrolyzer;

[0038] applying a voltage to the electrolyzer to induce precipitation of first solid hydroxide particles in the catholyte, thereby forming a second aqueous solution comprising the first solid hydroxide particles;

[0039] filtering the second aqueous solution comprising the first solid hydroxide particles to remove the first solid hydroxide particles, thereby forming a filtered aqueous solution; and contacting the filtered aqueous solution with the gaseous source of CO2.

[0040] In certain aspects, disclosed herein are methods of producing a solution comprising dissolved inorganic carbon (DIC) comprising:

[0041] contacting an electrolyzer with a first aqueous solution;

[0042] dividing the first aqueous solution into an anolyte in contact with an anode of the electrolyzer and a catholyte in contact with a cathode of the electrolyzer;

[0043] applying a voltage to the electrolyzer to induce precipitation of first solid hydroxide particles in the catholyte, thereby forming a first aqueous solution comprising first solid hydroxide particles;

[0044] filtering the second aqueous solution comprising the first solid hydroxide particles to remove the first solid hydroxide particles, thereby forming a filtered aqueous solution; contacting the filtered aqueous solution with the gaseous source of CO2 until a first pressure is reached, thereby forming a saturated aqueous solution;

[0045] contacting the statured aqueous solution with second solid hydroxide particles, thereby forming a second aqueous solution comprising second solid hydroxide particles; and contacting the second aqueous solution comprising the second solid hydroxide particles with the gaseous source of CO2.

[0046] In certain embodiments, the first pressure is about atmospheric pressure. In certain embodiments, the first aqueous solution is seawater. In other embodiments, the first aqueous solution is produced water. In certain embodiments, the dissolved inorganic carbon comprises HCOs' or CO32’. The second aqueous solution comprising solid hydroxide particles may be a suspension. In certain embodiments, the first solid hydroxide is magnesium hydroxide. In other embodiments, the first solid hydroxide is sodium hydroxide. In still other embodiments, the first solid hydroxide is calcium hydroxide. In certain embodiments, the first solid hydroxide comprises sodium hydroxide and magnesium hydroxide.

[0047] In certain embodiments, the second solid hydroxide is magnesium hydroxide. In other embodiments, the second solid hydroxide is sodium hydroxide. In still other embodiments, the second solid hydroxide is calcium hydroxide. In certain embodiments, the second solid hydroxide comprises sodium hydroxide and magnesium hydroxide.

[0048] In certain embodiments, contacting the first aqueous solution comprising solid hydroxide particles with the gaseous source of CO2 comprises passing CO2 across the surface of the first aqueous solution. In other embodiments, contacting the first aqueous solution comprising solid hydroxide particles with the gaseous source of CO2 comprises passing CO2 through the first aqueous solution (e.g., bubbling CO2 through the first aqueous solution). In various embodiments, contacting the first aqueous solution comprising solid hydroxide particles with the gaseous source of CO2 comprises agitating the first aqueous solution comprising solid hydroxide particles with the gaseous source of CO2. Contacting the first aqueous solution comprising solid hydroxide particles with the gaseous source of CO2 may be performed at atmospheric pressure. In other embodiments, contacting the first aqueous solution comprising solid hydroxide particles with the gaseous source of CO2 is performed at above atmospheric pressure. For example, contacting the first aqueous solution comprising solid hydroxide particles with the gaseous source of CO2 may be performed at about 10 psi, about 15 psi, about 20 psi, about 25 psi, about 30 psi, about 35 psi, about 40 psi, about 45 psi, about 50 psi, about 55 psi, or about 60 psi.

[0049] In certain embodiments, contacting the second aqueous solution comprising solid hydroxide particles with the gaseous source of CO2 comprises passing CO2 across the surface of the first aqueous solution. In other embodiments, contacting the second aqueous solution comprising solid hydroxide particles with the gaseous source of CO2 comprises passing CO2 through the first aqueous solution (e.g., bubbling CO2 through the first aqueous solution). In various embodiments, contacting the second aqueous solution comprising solid hydroxide particles with the gaseous source of CO2 comprises agitating the first aqueous solution comprising solid hydroxide particles with the gaseous source of CO2. In certain embodiments, contacting the second aqueous solution comprising solid hydroxide particles with the gaseous source of CO2 is performed at atmospheric pressure. In other embodiments, contacting the second aqueous solution comprising solid hydroxide particles with the gaseous source of CO2 is performed at above atmospheric pressure. For example, contacting the second aqueous solution comprising solid hydroxide particles with the gaseous source of CO2 may be performed at about 10 psi, about 15 psi, about 20 psi, about 25 psi, about 30 psi, about 35 psi, about 40 psi, about 45 psi, about 50 psi, about 55 psi, or about 60 psi.

[0050] In certain embodiments, the gaseous source of CO2 comprises about 2.5% to about 10% CO2, preferably about 2.5% to about 5% CO2. In certain embodiments, the gaseous source of CO2 is natural gas effluent or partially combusted natural gas effluent. In some embodiments, the gaseous source of CO2 is industrial effluent (e.g., combustion exhaust), flu gas, or gas from cement production. In certain embodiments, the gaseous source of CChis air.

[0051] In certain embodiments, the method comprises first contacting the first aqueous solution comprising a hydroxide with air and then contacting the first aqueous solution comprising a hydroxide with a gaseous source of CO2 which comprises about 2.5% to about 10% CO2, preferably with a gaseous source of CO2 which comprises about 2.5% to about 5% CO2. In certain embodiments, the method comprises first contacting the second aqueous solution comprising a hydroxide with air and then contacting the second aqueous solution comprising a hydroxide with a gaseous source of CO2 which comprises about 2.5% to about 10% CO2, preferably with a gaseous source of CO2 which comprises about 2.5% to about 5% CO2.

[0052] In certain embodiments, the solution comprising DIC is saturated with DIC. In certain embodiments, the solution comprising DIC is saturated with CO2. In other embodiments, contacting with the gaseous source of CO2 is performed until the solution comprising DIC is saturated with CO2. In some embodiments, contacting with the gaseous source of CO2 is performed until the solution comprising DIC is saturated with DIC.

[0053] In certain embodiments, the contacting with a gaseous source of CO2 is performed until the pH of the second aqueous solution comprising the first solid hydroxide particles is about 9, about 9.1, about 9.2, about 9.3, about 9.4, about 9.5, about 9.6, about 9.7, about 9.8, about 9.9, or about 10. In certain embodiments, the contacting with the gaseous source of CO2 is performed until the second aqueous solution comprising the first solid hydroxide particles is saturated with CO2. In certain embodiments, the contacting with the gaseous source of CO2 is performed until the second aqueous solution comprising the first solid hydroxide particles is saturated with DIC.

[0054] In certain embodiments, contacting with a gaseous source of CO2 is performed until the second aqueous solution comprising the second solid hydroxide particles is about 9, about 9.1, about 9.2, about 9.3, about 9.4, about 9.5, about 9.6, about 9.7, about 9.8, about 9.9, or about 10. In certain embodiments, contacting with the gaseous source of CO2 is performed until the second aqueous solution comprising the second solid hydroxide particles is saturated with CO2. In certain embodiments, contacting with the gaseous source of CO2 is performed until the second aqueous solution comprising the second solid hydroxide particles is saturated with DIC. In certain embodiments, contacting with a gaseous source of CO2 is performed until the pH of the filtered aqueous solution is about 9, about 9.1, about 9.2, about 9.3, about 9.4, about 9.5, about 9.6, about 9.7, about 9.8, about 9.9, or about 10.

[0055] In certain embodiments, contacting with the gaseous source of CO2 is performed until the filtered aqueous solution is saturated with CO2. In certain embodiments, contacting with the gaseous source of CO2 is performed until the filtered aqueous solution is saturated with DIC. In certain embodiments, contacting with a gaseous source of CO2 is performed until the filtered aqueous solution is about 9, about 9.1, about 9.2, about 9.3, about 9.4, about 9.5, about 9.6, about 9.7, about 9.8, about 9.9, or about 10.

[0056] In certain embodiments, the method is performed until the second aqueous solution comprising the first solid hydroxide particles does not comprise particles of the solid hydroxide (e.g., the solid hydroxide). For example, the method maybe performed until the second aqueous solution comprising the first solid hydroxide particles does not comprise particles of magnesium hydroxide. Alternatively, the method may be performed until the second aqueous solution comprising the first solid hydroxide particles does not comprise particles of sodium hydroxide. In some embodiments, the method is performed until the second aqueous solution comprising the first solid hydroxide particles does not comprise magnesium hydroxide or sodium hydroxide. In certain embodiments, contacting with a gaseous source of CO2 is performed until second aqueous solution comprising the second solid hydroxide particles does not comprise particles of a hydroxide (e.g., the first solid hydroxide or second solid hydroxide).

[0057] In some embodiments, contacting with a gaseous source of CO2 is performed until the second aqueous solution comprising the second solid hydroxide particles does not comprise particles of magnesium hydroxide. In other embodiments, contacting with a gaseous source of CO2 is performed until the second aqueous solution comprising the second solid hydroxide particles does not comprise particles of sodium hydroxide. In yet other embodiments, the method is performed until the second aqueous solution comprising the second solid hydroxide particles does not comprise particles of magnesium hydroxide or sodium hydroxide. In certain embodiments, the contacting with a gaseous source of CO2 is performed until the filtered aqueous solution does not comprise particles of a hydroxide (e.g., the first solid hydroxide or second solid hydroxide). For example, contacting with a gaseous source of CO2 may be performed until the filtered aqueous solution does not comprise particles of magnesium hydroxide. Alternatively, the contacting with a gaseous source of CO2 may be performed until the filtered aqueous solution does not comprise particles of sodium hydroxide. In certain embodiments, the method is performed until the filtered aqueous solution does not comprise particles of magnesium hydroxide or sodium hydroxide.

[0058] In certain embodiments, the contacting with the gaseous source of CO2 is performed until the second aqueous solution comprising the first solid hydroxide particles does not comprise particles of a hydroxide (e.g., the first solid hydroxide or second solid hydroxide). For example, the contacting with the gaseous source of CO2 may be performed until the second aqueous solution comprising the first solid hydroxide particles does not comprise particles of magnesium hydroxide. Alternatively, contacting with the gaseous source of CO2 may be performed until the second aqueous solution comprising the first solid hydroxide particles does not comprise particles of sodium hydroxide. In certain embodiments, the method is performed until the second aqueous solution comprising the first solid hydroxide particles does not comprise particles of magnesium hydroxide or sodium hydroxide.

[0059] In certain embodiments, contacting with a gaseous source of CO2 is performed until the second aqueous solution comprising the second solid hydroxide particles does not comprise particles of a hydroxide (e.g., the first solid hydroxide or second solid hydroxide). For example, the contacting with a gaseous source of CO2 may be performed until the second aqueous solution comprising the second solid hydroxide particles does not comprise particles of magnesium hydroxide. Alternatively, the contacting with a gaseous source of CO2 is performed until the second aqueous solution comprising the second solid hydroxide particles does not comprise particles of sodium hydroxide. In certain embodiments, the method is performed until the second aqueous solution comprising the second solid hydroxide particles does not comprise particles of magnesium hydroxide or sodium hydroxide.

[0060] In certain embodiments, contacting with a gaseous source of CO2 is performed until the filtered aqueous solution does not comprise particles of a hydroxide (e.g., the first solid hydroxide or second solid hydroxide). For example, the contacting with a gaseous source of CO2 may be performed until the filtered aqueous solution does not comprise particles of magnesium hydroxide. Alternatively, the contacting with a gaseous source of CO2 may be performed until the filtered aqueous solution does not comprise particles of sodium hydroxide. In certain embodiments, the method is performed until the filtered aqueous solution does not comprise particles of magnesium hydroxide or sodium hydroxide. In certain embodiments, the solution comprising DIC further comprises calcium carbonate.

[0061] Definitions

[0062] Unless otherwise defined herein, scientific and technical terms used in this application shall have the meanings that are commonly understood by those of ordinary skill in the art.

[0063] Chemistry terms used herein, unless otherwise defined herein, are used according to conventional usage in the art, as exemplified by “The McGraw-Hill Dictionary of Chemical Terms”, Parker S., Ed., McGraw-Hill, San Francisco, C. A. (1985).

[0064] All of the above, and any other publications, patents and published patent applications referred to in this application are specifically incorporated by reference herein. In case of conflict, the present specification, including its specific definitions, will control.

[0065] As used herein, the terms “optional” or “optionally” mean that the subsequently described event or circumstance may occur or may not occur, and that the description includes instances where the event or circumstance occurs as well as instances in which it does not.

[0066] Certain ranges are presented herein with numerical values being preceded by the term “about.” As used herein, the terms “substantially” and “about” are used to describe and account for small variations. When used in conjunction with an event or circumstance, the terms can refer to instances in which the event or circumstance occurs precisely as well as instances in which the event or circumstance occurs to a close approximation. For example, when used in conjunction with a numerical value, the terms can encompass a range of variation of less than or equal to ±10% of that numerical value, such as less than or equal to ±5%, less than or equal to ±4%, less than or equal to ±3%, less than or equal to ±2%, less than or equal to ±1%, less than or equal to ±0.5%, less than or equal to ±0.1%, or less than or equal to ±0.05%.

[0067] As used herein, the term “particle size” refers to the mean particle size (dso) as determined through, e.g., dynamic light scattering.

[0068] The term “produced water” as used herein refers to an aqueous solution that is obtained from underground sources as a byproduct of oil and / or natural gas extraction.

[0069] INCORPORATION BY REFERENCE

[0070] All publications and patents mentioned herein are hereby incorporated by reference in their entirety as if each individual publication or patent was specifically and individually indicated to be incorporated by reference. In case of conflict, the present application, including any definitions herein, will control. EQUIVALENTS

[0071] While specific embodiments of the subject invention have been discussed, the above specification is illustrative and not restrictive. Many variations of the invention will become apparent to those skilled in the art upon review of this specification and the claims below. The full scope of the invention should be determined by reference to the claims, along with their full scope of equivalents, and the specification, along with such variations.

[0072] EXAMPLES

[0073] Example 1: Sequential Carbonation Process with Brucite

[0074] Kinetics of CO2 carbonation using sequential steps involving the use of brucite were evaluated. In this implementation, a catholyte with an initial pH of around 10.5, filtered to remove precipitated brucite, was prepared and bubbled with CO2 to reach atmospheric pCO₂ levels. Reagent-grade Mg(OH)2 was added to the pre-carbonated solution to induce further CO2 absorption and mineral formation.

[0075] The pH and dissolved inorganic carbon (DIC) were monitored, pH decreases, and DIC increases were observed due to effective carbonation. Precipitation of aragonite as evidenced by calcium reduction supported the formation of carbonate minerals (FIG. 1). Sequential carbonation effectively facilitated the use of Mg(OH)₂, demonstrating a method to incrementally increase DIC while managing pH changes. The resultant data aligned with kinetic geochemical models, validating the approach for enhanced carbon sequestration. Example 2: Direct Carbonation with Simulated Catholyte

[0076] Direct carbonation of simulated catholyte was achieved using ambient air to assess brucite's dissolution and carbonation efficiency. A reactor was set up with the simulated catholyte directly bubbled with air enriched in CO2. Continuous measurements of pH, DIC, magnesium, and calcium concentrations were taken. The rates of brucite dissolution and subsequent mineral precipitation were quantified from magnesium concentration changes (FIG. 3). Plot shows two datasets (opaque / transparent) at an equivalent flow rate to volume ratio, showing consistency. Variance in reaction times can be attributed to differences in solution volume. At equilibrium, either: DIC=35.6 mM, pH=9.20, [Mg]=43.1 mM, [Ca]=0 mM, [Nesq]=20.0 mM (with nesquehonite precipitation), or DIC=59.1 mM, pH=9.32, [Mg]=63.0 mM, [Ca]=0 mM (no nesquehonite precipitation). Direct Carbonation showed immediate impacts on pH and DIC, with magnesium levels initially rising due to brucite dissolution and then stabilizing as magnesium carbonate formed. Example 3: NaOH Carbonation as a Comparative Study

[0077] NaOH was used to simulate the carbonation process and understand the kinetics without brucite's contribution. A pH 13 NaOH solution was carbonated under controlled conditions to mimic the brucite process (FIG. 4). Changes in pH, DIC, and calcium concentrations were extensively recorded. The rapid increase in pH, followed by a decrease due to CO2 absorption, was noted, along with aragonite precipitation, which indicated successful carbonation. Results of kinetic model fitting are shown in dashed curves, demonstrating the applicability of the theoretical framework. The pH data is used for fitting, and the geochemical model calculates corresponding DIC, [Mg], and [Ca], further demonstrating confidence on these measurements. At equilibrium, DIC=76.0 mM, pH=9.47, [Mg]=4.5 mM, [Ca]=0 mM.

[0078] Example 4: Determining the Limiting CO2 Flow Rate

[0079] This example establishes the maximum efficient CO2 flow rate for carbonation processes to avoid rate limitations (FIGs. 5A & 5B). CO2 was bubbled through a filtered synthetic catholyte at varying flow rates. pH changes were monitored to determine the point at which CO2 transfer ceased to be the rate-limiting step. Similar tests using a pH 13 NaOH solution were performed to simulate NaOH carbonation, which starts at a higher pH (and [OH ]). The limiting flow rate was successfully quantified, demonstrating that at certain flow rates, above 0.15 Volume (s⁻¹) for synthetic catholyte and above 0.22 volume(s⁻¹) for NaOH, the CO2 transfer does not limit overall carbonation rates, which is crucial for scaling up the process effectively.

[0080] Example 5: Carbonation with 3% CO2

[0081] This example establishes the rate of carbonation with 3% CO2. 3% CO2 was bubbled through a filtered synthetic catholyte at varying flow rates. pH changes were monitored, as well as pCO2of the effluent. Carbonation with concentrated CO2 reduces the time to equilibrium and allows for higher concentrations of CO2 to be contained within the catholyte, reaching DIC levels of 84.2 mM.

[0082] Example 6: Direct Versus Sequential Carbonation Comparison

[0083] This example compares the kinetics of direct versus sequential carbonation of various solutions. In the following examples, simulated seawater was prepared by dissolving 41.9 g of ASTM DI 141-98 sea salt in 1 L ultra-pure deionized water (Milli-Q, >18.2 MQ cm), yielding a solution with [Mg] = 56.0 to 61.0 mM and [Ca] = 10.0 to 10.6 mM. To match the process catholyte, the Mg concentration was adjusted to 63 mM by adding magnesium chloride (MgCh, 95.211 g / mol, 99%). Immediately prior to carbonation, a 20 M sodium hydroxide (NaOH, 39.999 g / mol, 98%) solution was titrated into 333 to 400 mL of the simulated seawater to generate the simulated catholyte. A separate titration conducted under comparable conditions identified an inflection point that corresponds to complete brucite precipitation at pH 11.5. Consequently, NaOH was added until the solution maintained a stable pH of 11.5 for at least 15 minutes.

[0084] Carbonation experiments were conducted using “direct carbonation” and “sequential carbonation” to identify potential rate-limiting steps (as shown in FIG. 7). In “direct carbonation,” the simulated catholyte (including all suspended precipitates) was carbonated without any pre-treatment. In “sequential carbonation,” the simulated catholyte was either vacuum filtered using 0.20 pm pore size filter paper or centrifuged at 4000 rpm for 20 minutes to separate the precipitated solids. The resulting supernatant was decanted and carbonated separately, while the solids were either dried in a vacuum desiccator for subsequent phase characterization or stored temporarily in sealed centrifuge tubes for later carbonation. After the supernatant equilibrated with atmospheric CO2, the previously separated solids were reintroduced into the reactor. This staged process was intended to lower the solution pH during the initial carbonation step, thereby enhancing brucite dissolution and accelerating reaction completion. A variation of this method substituted the precipitated solids with reagent-grade brucite (58.32 g / mol, 95%) to evaluate influences of solid composition and reactivity. To further decouple the effects of brucite dissolution, an additional variant involved the direct addition of sodium hydroxide (NaOH) to supply equivalent alkalinity. Because NaOH dissolves rapidly, this approach eliminated the kinetic constraints associated with solid brucite dissolution. Lastly, to determine the flow rate-to-volume ratio (Q / V) threshold for efficient carbonation, simulated seawater was titrated to pH 13 using NaOH, the resulting solids were removed by filtration, and the supernatant was carbonated under varying flow conditions. Details of the various experimental setups are summarized in Table 1 (below).

[0085] The carbonation experiments were conducted in a round glass reactor (5.75 inches in diameter and 2.75 inches in height). Laboratory air was humidified prior to introduction into the reactor by passing it through a sealed container filled with deionized water. Gas flow was regulated using a first and second flowmeters: one to control the flow to the humidifier, while the other regulated the flow of humidified air into the reactor. The humidified gas was introduced into the solution or slurry using an 80 cm acrylic diffuser, and the mixture was stirred off-center at 500 rpm using an overhead stirrer to promote uniform mixing. Higher stirring rates were avoided, as they tended to prolong the stabilization time of pH measurements. In experiments involving higher flow rates (>75 mL / s), excess gas was vented through an outlet port on the reactor lid.

[0086] The gas flow rate ranged from 30 to 150 mL / s depending on the experiment type, with most tests conducted at a flow rate of 150 mL / s and a solution volume of 333 mL. Although both parameters sometimes varied across experiments (30-150 mL / s and 333-500 mL), the flow rate-to-volume ratio (Q / V) was kept constant (see Table 1). All experiments were carried out at an ambient temperature of 21 ± 2 °C. Select experiments were conducted using ultra-high purity nitrogen gas instead of air, which allowed for evaluation of the dissolution behavior of brucite under alkaline conditions.

[0087] Throughout the experiments, pH was continuously monitored using a pH meter equipped with a Triode probe, calibrated from pH 4 to 12. Liquid samples were periodically collected for analysis of dissolved inorganic carbon (DIC) and for inductively coupled for plasma optical emission spectroscopy (ICP-OES) to measure magnesium (Mg) and calcium (Ca) concentrations. All samples were filtered through 0.22 pm nylon syringe filters. For DIC analysis, aliquots were diluted with deionized water and analyzed using a Total Organic Carbon Analyzer, calibrated for inorganic carbon concentrations ranging from 0–20 mg / L. For ICP-OES analysis, samples were diluted with 5% nitric acid and measured using a ICP-OES unit, with elemental calibration standards ranging from 0 to 10 ppm. The calibration standards were prepared by diluting 1000 ppm multi-element stock solutions with 5% nitric acid. Table 1: Experimental conditions, including gas flow rates, solution volumes, and the _ resulting flow rate-to-volume (Q / V) ratios. _

[0088] Gas Flow Solution Experiment Type* Rate, Q Volume, V Q / V (s-1)

[0089] (mL / s) (mL) Carbonation of supernatant only 100.0 500 0.20 (NaOH added to simulated seawater to pH 13; „, _ _ „ _v 1’ 150.0 333 0.45 solids removed; supernatant carbonated)

[0090] 200.0 250 0.80 Sequential carbonation

[0091] 146.7 326 0.45 (Solids reintroduced after air equilibration)

[0092] Sequential carbonation with reagent-grade

[0093] brucite 150.0 333 0.45 (63 mM brucite added after air equilibration)

[0094] Sequential carbonation with NaOH 30.0 333 0.09 (126 mM NaOH added after air equilibration)n nv 4’ 75.0 347 0.22

[0095] 150.0 333 0.45 Sequential carbonation with reagent-grade

[0096] brucite + UHP N2 (63 mM brucite; bubbled with 150.0 333 0.45 N2)

[0097] Direct carbonation

[0098] 150.0 333 0.45 (No separation; entire catholyte carbonated)

[0099] *A11 experiments were conducted by bubbling air in the final step, except for “Sequential carbonation - brucite + UHP N2”, which used ultra-high purity nitrogen (UHP N2) gas.

[0100] A separate set of sequential carbonation and direct carbonation experiments was performed to quantify CDR at the experimental endpoint, using the setup and procedure outlined above (FIG. 7, Table 1) Instead of using humidified laboratory air, solution evaporation was compensated for by continuously injecting an equivalent amount of deionized water using a syringe pump. At the end of the experiment, the mixture was centrifuged at 2000 rpm for 20 minutes. The residual liquid was decanted, and the solid was dried in a vacuum desiccator for 5 to 7 days at ambient temperature in preparation for subsequent solid characterization.

[0101] XRD characterization of the collected solids was conducted by using a X-ray Diffractometer with the following parameters: step size of 0.01°, speed of 4° / min, scan range of 5-80°, voltage of 40 kV, and current of 44 mA. Phase identification and quantification were carried out, incorporating reference patterns from an open-source Minerals and Metals Alloys Oxides database. The specific surface area of reagent-grade brucite was determined using a Surface Area Analyzer.

[0102] Geochemical modeling and kinetic fitting were performed using standard high-performance language and interactive environment for technical computing software and relevant databases as needed. These simulations utilized experimentally measured pH data to model reaction kinetics. In the models, the aqueous solution was assumed to be at equilibrium with nesquehonite (MgCO₃·3H₂O), such that precipitation of this phase was triggered once supersaturation was reached. The equilibrium constant was derived from a database and was used in simulations involving hydromagnesite precipitation (See Table 2 below). In the geochemical models, when water evaporation was not manually compensated for, a linear adjustment was applied to the solution volume based on the measured initial and final volumes to account for evaporation. As a result, the concentrations presented in the plots below are not corrected for evaporative volume loss, unless stated otherwise.

[0103] The carbonation of the simulated catholyte proceeds through a series of sequential steps. Step 1 involves the dissolution of CO2 gas into the liquid phase (Eq. 1). Step 2 involves CO2 hydration and speciation, i.e., dissolved CO2 (CO2 (aq)) hydrates to form carbonic acid, which then dissociates into bicarbonate and carbonate ions, consuming alkalinity in the process (Eqs. 2-4). The resulting drop in pH promotes Step 3, the dissolution of brucite, releasing Mg2+and OH into solution (Eq. 5). In Step 4, hydrated magnesium carbonates precipitate once the solution becomes supersaturated with respect to these phases (Eqs. 6-7). Because Mg2+ions are strongly hydrated, hydrate magnesium carbonates are kinetically favorable to precipitate instead of anhydrous magnesium carbonates. At higher pH, dissolved CO2 tends to react with OH to form bicarbonate ions (HCO3 ) (Eq. 8). Step 1: Gaseous CO2 dissolution

[0104] CO₂ (g) ⇌ CO₂ (aq) (Eq. 1) Step 2: CO2 speciation

[0105] CO2 (aq) + H2O <-> H2CO3 (aq) (Eq. 2) H₂CO₃ (aq) ⇌ HCO₃⁻ (aq) + H⁺(aq) (Eq. 3) HCO3 (aq) <-> CO₃²⁻ (aq) + H⁺(aq) (Eq. 4) Step 3: Brucite dissolution

[0106] Mg(OH)₂(s) + 2H⁺(aq) → Mg²⁺(aq) + 2H₂O (Eq. 5) Step 4: Magnesium carbonate precipitation

[0107] Mg²⁺(aq) + CO₃²⁻ (aq) + 3H₂O → MgCO₃·3H₂O(s) (Eq. 6) 5Mg²⁺(aq) + 4CO₃²⁻ (aq) + 2OH⁻ (aq) + 3H₂O → Mg₅(CO₃)₄(OH)₂·4H₂O(s) (Eq. 7) Alternative CO2 speciation pathway

[0108] CO₂ (aq) + OH⁻ → HCO₃⁻ (aq) (Eq. 8)

[0109] Because these reactions occur sequentially, the overall rate of carbonation is determined by the slowest step. In well-mixed systems, the reaction of CO2 (aq) with H2O (Step 2) or OH (Step 4) is considered the rate-limiting step. However, the slow diffusion of the gas phase across the gas-liquid interface and into the bulk liquid may result in mass transfer being the ratelimiting step. Therefore, CO2 transport has been enhanced by increasing agitation, increasing the gas-liquid interfacial area (e.g., through smaller gas bubbles), or increasing the partial pressure gradient across the interface. Additionally, reactor geometry significantly affects mass transfer rates. Therefore, the ratio of gas flow rate (Q) to liquid volume (V), or Q / V, is a key parameter influencing flow dynamics and mixing efficiency, with higher flow rates generally resulting in improved agitation and mass transfer.

[0110] To minimize the impact of CO2 mass transfer, an extrinsic factor influenced by variables outside the scope of this study, all experiments were conducted under conditions designed to minimize gas transfer limitations. Therefore, the optimal Q / V ratio was determined through a series of carbonation experiments that tracked the pH of a NaOH-spiked seawater (“carbonation of supernatant only” in Table 1) with starting pH of 13 (See FIG. 8A-C).

[0111] The results showed that pH declined more rapidly with increasing Q / V ranging from 0.20 to 0.45 s⁻¹, following a reverse sigmoidal trend (FIG. 8A). The time derivative of pH further illustrates this behavior: at higher Q / V values, the inflection point, which marks the period of most rapid pH decline, occurred earlier in the reaction, indicating faster CO2 uptake (FIG.8B).

[0112] This effect began to plateau between 0.22 (included from the “sequential carbonation - NaOH” series) and 0.45 s ', while raising Q / V further to 0.80 s⁻¹ yielded only a marginal improvement in the rate of OH neutralization and introduced a significant increase in water evaporation (FIG. 8C). Additionally, at Q / V = 0.80 s⁻¹, the carbonation curve deviated from the typical sigmoidal shape, exhibiting a slower reaction rate near pH ~10. This suggests a decline in CO2 transfer efficiency, possibly because of the formation of a continuous gas phase within the reactor that reduced the effective gas-liquid interfacial area. Consequently, a Q / V value of 0.45 s⁻¹ was selected for all subsequent experiments. These conditions represent those where gasside mass transfer limitations are minimized.

[0113] The precipitation of hydrated magnesium carbonates (Step 4) occurs rapidly and is generally not considered the rate-limiting step during carbonation. To better understand the relative contributions of CO2 hydration / speciation and brucite dissolution to the overall carbonation rate, a series of sequential carbonation experiments was conducted (Table 1). First, across the previously tested range of flow rates, the time-dependent rate of CO2 speciation, Rateco2(t) in mol / L / s, was estimated using a kinetic model that considers the influences of pH and saturation:

[0114]

[0115] In these equations, AT is the apparent mass transfer coefficient (dimensionless), fixed at 1 for the experiment with the highest Q / V ratio of 0.45 s ', and fitted for experiments with lower Q / V, k(t) represents the pH-dependent rate constant (in h⁻¹), as defined in Eq. 10, a and b are fitting parameters representing, respectively, a rate coefficient (in L / mol / h) and a unitless exponent describing the pH sensitivity of the rate, and {OH }(is the activity of hydroxide ions (in mol / L) at time t. {CO2 (aq)}eqand {CO2 (aq)}t represent the equilibrium and time-dependent activities of CO2 (aq), respectively (in mol / L), pCO₂ is the logarithm of the target CO2 partial pressure (-3.3767 in log atm), and Kco2 is the equilibrium constant for gaseous to aqueous CO2 conversion (Eq. 1, -1.468 in log L atm / mol), corresponding to {CO2(aq)}eqof 1.531x105M. This model assumes equilibrium among CO2 (aq), H2CO3, HCO3, and CO32. The incremental dissolution of CO2 lowers the solution pH, allowing the time-dependent pH data to be used to fit a and b. Although prior studies indicate that the CO2 speciation mechanism may shift at pH of around 10,5the best-fit values for parameters a = 1 and b = 0.25 remain consistent across the tested pH range. Therefore, the CO2 speciation rate is expressed as:

[0116]

[0117] The effect of Q / V on the rate of pH decrease during carbonation is evident when NaOH, providing equivalent alkalinity (126 mM), is used in place of brucite in sequential carbonation experiments (FIG. 9A-C). (Note: The precipitate removed after titration to pH 11.5 consists of approximately 63 mM brucite and 2 mM aragonite (CaCCh).) As shown in FIG. 9A, the pH of this solution (initial [Na] = 126 mM, pH - 13) decreased more rapidly with increasing Q / V, from 0.09 to 0.45 s ', consistent with the results discussed above. Using data from the experiment performed at Q / V = 0.45 s ', best-fit values for parameters a and b in Equation 10 were obtained and subsequently used to calculate the apparent mass transfer coefficients (M) for experiments at lower Q / V. These fits yielded AT values of 0.25 and 0.57 for Q / V = 0.09 and 0.21 s⁻¹, closely aligning with the ratios of the Q / V values (0.20 and 0.48). This correspondence indicates a near-linear relationship between Q / V and AT (FIG. 9B).

[0118] FIG. 9C presents a complete time series for one experiment (“sequential carbonation with NaOH” in Table 1). Following initial filtration of the simulated catholyte (pH - 11.5), the solution reached pH 8.5 within 2 hours of air bubbling, consistent with equilibrium at atmospheric pCO₂ (-0.0004 atm) that is predicted by geochemical modeling. Upon NaOH addition, the pH spiked to -12.8 and then gradually decreased as additional CO2 dissolved. A sharp decrease in [Ca] soon after indicated rapid precipitation of CaCOs, which in turn is constrained by the available DIC. The gradual reduction in pH was accompanied by a steady increase in DIC. An equilibrium pH of -9.6 was reached within 10 hours and remained stable thereafter, except for the slight decrease caused by evaporation. Both experimental DIC measurements and model predictions (pCO₂ = -3.3767, a = 1, b = 0.25) showed a postequilibrium increase in DIC that can also be attributed to evaporation. As expected, because brucite containing Mg was removed before carbonation, [Mg] remained near zero throughout the experiment. Lower Q / V experiments showed similar behavior, with slower pH decline and lower final DIC levels at given times. Collectively, these results validate the kinetic model described by Equations 8-10 in systems where alkalinity is readily available for carbonation.

[0119] The next experiment examined the dissolution rate of brucite using a variation of the sequential carbonation experiment (“sequential carbonation - reagent-grade brucite + UHP N2” in Table 1). In this setup, the filtered simulated catholyte was first carbonated to atmospheric equilibrium, following the same procedure as in FIG. 9B. In the second step, reagent-grade brucite (63 mM) was added and ultra-high purity (UHP) N2 was bubbled instead of air during the final step to evaluate the dissolution behavior of brucite in an initially airequilibrated solution without further CO2 input. This prevented additional CO2 from dissolving into the solution, which would otherwise alter pH and influence the dissolution of brucite. Bubbling N2 at the same flow rate also provided a comparable mixing environment to that of air bubbling experiments. The dissolution rate of brucite, based on transition state theory, is given by:

[0120] Ratebrucite(t) = kc[S]2(1 - Ω2) (Eq. 13)

[0121] where kcis the dissolution rate constant (h-1), [S] is the pH-dependent surface species concentration (mol / m2), and is the saturation ratio with respect to brucite, defined as the ion activity product divided by the solubility product (Ksp) in solution. Upon adding brucite to the CO2-equilibrated solution, pH increased rapidly, although less sharply than observed in FIG.

[0122] 9B. This behavior reflects the much slower dissolution rate of brucite (10-12to 10-13mol / cm2 / s) compared to the highly soluble NaOH at pH 8.5. In the experiment, the initial brucite dissolution rate, determined from [Mg], was 1.1 x 10-9mol / cm2 / s.

[0123] As [Mg] increased, [Ca] decreased, indicating rapid CaCO3precipitation that consumes dissolved inorganic carbon (DIC), which exhibited a brief increase. Notably, both [Ca] and DIC dropped by approximately 2 mM after 4 hours (FIG. 10), consistent with CaCO3precipitation being limited by DIC availability. Similar to the procedure described above, the time-dependent pH data was fitted to determine kc, yielding a value of 368.2 h-1(FIG. 10). The corresponding equilibrium concentrations were [Mg] = 2.96 mM, [Ca] = 4.51 mM, and DIC = 0.61 mM.

[0124] While the model captured the general trends, it predicted a faster initial rate of CaCO3precipitation and a more rapid decline in DIC, as well as lower equilibrium values than observed experimentally. This discrepancy likely stems from the model’s assumption of instantaneous equilibrium with aragonite. Additionally, the rapid increase in the concentration of Mg2+ions in solution within the first 20 minutes may have inhibited CaCO3precipitation, an effect not accounted for in the model. No further significant disolution of brucite was observed after this initial increase, indicating the rapid approach to saturation of the solution with respect to brucite in the absence of CO2 bubbling.

[0125] In the sequential carbonation experiment, reintroducing the centrifuged solid from the titration step into an air-equilibrated solution led to a rapid increase in pH to 10.5, followed by a gradual decline as CO2 continued to dissolve into the solution during the subsequent air bubbling (FIG. HA). As with NaOH carbonation (FIG. 9A-C), CO2 dissolution increased the DIC. A decrease in [Ca] indicates CaCO3precipitation, while the concurrent drop in pH promoted brucite dissolution, raising [Mg] (FIG. 11A). When reagent-grade brucite was used instead of the centrifuged precipitate in simulated catholyte, the pH increase was slower and less pronounced (FIG. 11B). This is consistent with the lower specific surface area of the reagent brucite (6.53 m2 / g) compared with the precipitate from simulated catholyte (278.94 m2 / g). Since dissolution is a surface-mediated process, the greater surface area of the precipitates likely contributed to the faster increase in [Mg], assuming equivalent surface area-normalized dissolution rate. This may also suggest that other components in the original precipitate, derived from ASTM seawater salts and CaCO3, enhanced brucite dissolution. For instance, Ca2+ions can accelerate brucite dissolution by enhancing the rate of water molecule exchange. Notably, although the experimental endpoints are markedly similar with respect to final [Mg], DIC, and pH, XRD analysis shows the persistence of hydrated magnesium carbonates when carbonating precipitated solids but not when carbonating reagent-grade brucite (see below), indicating a greater CDR in the former. This suggests a much smaller extent of dissolution, and carbonation, of less-reactive reagent-grade brucite.

[0126] When sequential carbonation is compared to direct carbonation (where the as-prepared simulated catholyte undergoes carbonation), similar trends were observed (FIG. 12A-D).

[0127] These included a pH decline occurring at similar reaction times, an initial rise followed by a decline in both DIC and [Mg], and a consistent decrease in [Ca], These similarities suggest that initiating brucite carbonation with a lower equilibrium pH of 8.5 in the sequential process (FIG.

[0128] 12A) had only a marginal impact on the extent of brucite dissolution. This is because although a lower pH typically enhances brucite dissolution, the pH in the sequential system rapidly rose to 10.5 within the first 2 minutes.

[0129] Significantly, both direct and sequential carbonation showed a sharp decline in pH approximately 15 hours into brucite carbonation (FIG. 12A), indicating that magnesium carbonate precipitation had become the dominant process over brucite dissolution. In both cases, [Mg] and DIC increased initially, peaked approximately 12 hours after the start of carbonation, and then declined to similar final concentrations (approximately 44.5-45.9 mM for Mg and 42.6-45.3 mM for DIC, corresponding to 23.1-21.5 mM for Mg and 25.2-21.5 mM for DIC after accounting for solution evaporation), consistent with the formation of hydrated magnesium carbonates.

[0130] When applying the kinetic model and best-fit parameters (i.e., kc= 368.2 h-1, a = 1 L / mol / h, b = 0.25) (Eq. 9-13) to brucite carbonation (FIGs. 12B-D), the model generally followed the experimental trend. However, notable discrepancies were observed in DIC, pH, and [Mg], A characteristic drop in pH occurred around 16 hours in both carbonation approaches, but the experimental equilibrium pH values were slightly lower than those predicted by the model. Unlike the experimental data, the model did not capture the peaking behavior of DIC and [Mg]; instead, it showed a plateau during the first 7 hours, followed by a gradual increase. This suggests that, in the model, the rates of brucite dissolution, hydrated magnesium carbonate precipitation, and DIC consumption were temporarily balanced, consistent with nesquehonite formation, which follows a 1: 1 Mg to C stoichiometric ratio. After the pH drop, the experimentally observed plateau in [Mg] suggests continued brucite dissolution and hydrated magnesium carbonate precipitation under lower pH conditions. These deviations may stem from simplifying assumptions in the kinetic model, particularly the assumption of instantaneous magnesium carbonate precipitation. Specifically, the deviations suggest that the solution remains metastable even though it is supersaturated with respect to hydrated magnesium carbonate until a critical saturation index of 0.47 is reached with respect to nesquehonite, as calculated from the maximum measured [Mg] and DIC. As expected, Ca concentrations remained at zero, indicating complete precipitation of Ca as CaCO3within the first two hours of carbonation. Notably, both sequential carbonation with precipitation from catholyte and reagent brucite showed agreement of the final DIC, final pH, and the time when equilibrium was reached with the kinetic models.

[0131] XRD analysis of the residual solids at the end of separate carbonation experiments with water evaporation compensation revealed that the primary hydrated magnesium carbonate formed was nesquehonite in both direct carbonation (higher starting pH) and sequential carbonation (lower starting pH) (FIG. 13). Temperature and supersaturation (Q) are known to influence phase selection in hydrated magnesium carbonates. At low temperatures, brucite carbonation typically yields nesquehonite as the predominant phase, consistent with the results herein. The corresponding measured and theoretical pH and results of sparse sampling of solution concentrations are shown in FIG. 14A-C.

[0132] The effectiveness of carbonation was evaluated using the CDR factor, expressed in grams of CO2 per liter of simulated catholyte, and compared with theoretical values (Table 2, FIG. 15) For theoretical CDR, three scenarios were considered: (1) suppressed magnesium carbonate precipitation, (2) forced nesquehonite precipitation, and (3) forced hydromagnesite precipitation. The theoretical CDR of 3.64 g / L is lower than 4.6 g / L previously calculated based on the CDR potentials of Mg(OH)₂ and CaCCh. This is because in previous calculations, fixed CDR efficiencies of 1.7 mol CCh / mol Mg(OH)2 and 1 mol CCh / mol CaCCh were applied, as applicable in dilute seawater conditions. While the CDR efficiency for CaCCh is unchanged, the actual CDR efficiency of Mg(OH)2 is related to the buffering capacity of water, and can range from -1.1 to ~1.7 depending on pH, salinity, temperature, with the highest CDR efficiencies obtained under near-neutral pH values between 6 to 8.

[0133] Because the two experiments (sequential and direct) used the same initial solution, their theoretical CDR values are identical. During carbonation, CO2 was stabilized as DIC and as solid carbonate minerals, particularly CaCCh and hydrated magnesium carbonates (i.e., nesquehonite and / or hydromagnesite). The total sequestered CO2 is calculated on the basis of the elemental concentrations in the liquid phase, and the phase assemblage obtained from quantitative analysis of the XRD data (Table 3). Therefore, the amount of carbon sequestered in the form of CaCCh (i.e., aragonite and calcite) was calculated based on the difference between initial and final [Ca] in solution, since the precipitation of 1 mol CaCCh requires the removal of 1 mol Ca from solution. Similarly, the difference between the initial and final [Mg] in solution, weighted by the mass percentages of Mg-containing phases in the solid (i.e., nesquehonite, hydromagnesite, brucite) and converted to moles using stoichiometry, gives the amount of carbon sequestered in the form of nesquehonite and hydromagnesite. In comparison, the Mg and Ca recoveries based on direct measurement of the solid’s total mass and the phase assemblage obtained from quantitative XRD are -85% and -75%. This observed discrepancy in mass balance has implications for choosing reliable methods of CDR quantification within an MRV framework. Table 2: CDR values for direct and sequential carbonation, along with the distribution of carbon between dissolved and solid phases.

[0134] DJC Hydromagnesi CDR Nesquehonite.

[0135]

[0136] ID Type (mMte

[0137] (mX1)(mM) mM g / L ) (mM)

[0138] Suppressed

[0139] magnesium

[0140] T1 72.19 0 0 10.48 82.67 3.64 carbonate

[0141] precipitation

[0142] Forced

[0143] Theoretical T2 nesquehonite 39.81 28.19 0 10.48 78.48 3.45 precipitation

[0144] Forced

[0145] hydromagne

[0146] T3 9.41 0 10.37 10.48 61.37 2.70 site

[0147] precipitation

[0148] Sequential

[0149] El 45.56 24.82 0.01 10.33 80.76 3.56 Experiment carbonation

[0150] a.

[0151] Direct

[0152] E2 42.64 26.54 0 10.37 79.55 3.50 carbonation

[0153] *1 mol of nesquehonite represents 1 mol C; 1 mol hydromagnesite represents 0.8 mol C. CaCO3represents the sum of calcite and aragonite. Table 3. Phase quantification results from Rietveld refinement of XRD data.

[0154] Mass percent (%)

[0155] Phase Chemical formulaDirectSequential carbonation carbonation Halite NaCl 21.66 20.46 Nesquehonite MgCO₃·3H₂O 57.92 58.18 Hydromagnesite Mg5(CO3)4(OH)2·4H2O 0.00 0.40 Aragonite CaCO318.22 10.85 Calcite CaCO32.20 10.11 Total 100.00 100.00

Claims

We claim:

1. A method of producing a solution comprising dissolved inorganic carbon (DIC) comprising:contacting an electrolyzer with a first aqueous solution;dividing the first aqueous solution into an anolyte in contact with an anode of the electrolyzer and a catholyte in contact with a cathode of the electrolyzer;applying a voltage to the electrolyzer to induce precipitation of first solid hydroxide particles in the catholyte, thereby forming a second aqueous solution comprising the first solid hydroxide particles; andcontacting the second aqueous solution with a gaseous source of CO2.

2. A method of producing a solution comprising dissolved inorganic carbon (DIC) comprising:contacting an electrolyzer with a first aqueous solution;dividing the first aqueous solution into an anolyte in contact with an anode of the electrolyzer and a catholyte in contact with a cathode of the electrolyzer;applying a voltage to the electrolyzer to induce precipitation of first solid hydroxide particles in the catholyte, thereby forming a second aqueous solution comprising the first solid hydroxide particles;filtering the second aqueous solution comprising the first solid hydroxide particles to remove the first solid hydroxide particles, thereby forming a filtered aqueous solution; and contacting the filtered aqueous solution with a gaseous source of CO2.

3. A method of producing a solution comprising dissolved inorganic carbon (DIC) comprising:contacting an electrolyzer with a first aqueous solution;dividing the first aqueous solution into an anolyte in contact with an anode of the electrolyzer and a catholyte in contact with a cathode of the electrolyzer;applying a voltage to the electrolyzer to induce precipitation of first solid hydroxide particles in the catholyte, thereby forming a first aqueous solution comprising first solid hydroxide particles;filtering the second aqueous solution comprising the first solid hydroxide particles to remove the first solid hydroxide particles, thereby forming a filtered aqueous solution;contacting the filtered aqueous solution with a gaseous source of CO2 until a first pressure is reached, thereby forming a saturated aqueous solution;contacting the statured aqueous solution with second solid hydroxide particles, thereby forming a second aqueous solution comprising second solid hydroxide particles; and contacting the second aqueous solution comprising the second solid hydroxide particles with the gaseous source of CO2.

4. The method of claim 3, wherein the first pressure is about atmospheric pressure.

5. The method of any one of claims 1-4, wherein the first aqueous solution is seawater.

6. The method of any one of claims 1-4, wherein the first aqueous solution is produced water.

7. The method of any one of claims 1-6, wherein the dissolved inorganic carbon comprises HCO3-or CO32-.

8. The method of any one of claims 1-7, wherein the second aqueous solution comprising solid hydroxide particles is a suspension.

9. The method of any one of claims 1-8, wherein the first solid hydroxide is magnesium hydroxide.

10. The method of any one of claims 1-9, wherein the first solid hydroxide is sodium hydroxide.

11. The method of any one of claims 1-10, wherein the first solid hydroxide is calcium hydroxide.

12. The method of any one of claims 1-11, wherein the first solid hydroxide comprises sodium hydroxide and magnesium hydroxide.

13. The method of any one of claims 1-12, wherein the second solid hydroxide is magnesium hydroxide.

14. The method of any one of claims 3-13, wherein the second solid hydroxide is sodium hydroxide.

15. The method of any one of claims 3-13, wherein the second solid hydroxide is calcium hydroxide.

16. The method of any one of claims 3-13, wherein the second solid hydroxide comprises sodium hydroxide and magnesium hydroxide.

17. The method of any one of claims 1-16, wherein contacting the first aqueous solution comprising solid hydroxide particles with the gaseous source of CO2 comprises passing CO2 across the surface of the first aqueous solution.

18. The method of any one of claims 1-16, wherein contacting the first aqueous solution comprising solid hydroxide particles with the gaseous source of CO2 comprises passing CO2 through the first aqueous solution (e.g., bubbling CO2 through the first aqueous solution).

19. The method of any one of claims 1-16, wherein contacting the first aqueous solution comprising solid hydroxide particles with the gaseous source of CO2 comprises agitating the first aqueous solution comprising solid hydroxide particles with the gaseous source of CO2.

20. The method of any one of claims 1-19, wherein contacting the first aqueous solution comprising solid hydroxide particles with the gaseous source of CO2 is performed at atmospheric pressure.

21. The method of any one of claims 1-19, wherein contacting the first aqueous solution comprising solid hydroxide particles with the gaseous source of CO2 is performed at above atmospheric pressure.

22. The method of any one of claims 1-19, wherein contacting the first aqueous solution comprising solid hydroxide particles with the gaseous source of CO2 is performed at about 10 psi, about 15 psi, about 20 psi, about 25 psi, about 30 psi, about 35 psi, about 40 psi, about 45 psi, about 50 psi, about 55 psi, or about 60 psi.

23. The method of any one of claims 1-22, wherein contacting the second aqueous solution comprising solid hydroxide particles with the gaseous source of CO2 comprises passing CO2 across the surface of the first aqueous solution.

24. The method of any one of claims 1-22, wherein contacting the second aqueous solution comprising solid hydroxide particles with the gaseous source of CO2 comprises passing CO2 through the first aqueous solution (e.g., bubbling CO2 through the first aqueous solution).

25. The method of any one of claims 1-22, wherein contacting the second aqueous solution comprising solid hydroxide particles with the gaseous source of CO2 comprises agitating the first aqueous solution comprising solid hydroxide particles with the gaseous source of CO2.

26. The method of any one of claims 1-22, wherein contacting the second aqueous solution comprising solid hydroxide particles with the gaseous source of CO2 is performed at atmospheric pressure.

27. The method of any one of claims 1-22, wherein contacting the second aqueous solution comprising solid hydroxide particles with the gaseous source of CO2 is performed at above atmospheric pressure.

28. The method of any one of claims 1-22, wherein contacting the second aqueous solution comprising solid hydroxide particles with the gaseous source of CO2 is performed at about 10 psi, about 15 psi, about 20 psi, about 25 psi, about 30 psi, about 35 psi, about 40 psi, about 45 psi, about 50 psi, about 55 psi, or about 60 psi.

29. The method of any one of claims 1-28, wherein the gaseous source of CO2 comprises about 2.5% to about 10% CO2.

30. The method of any one of claims 1-29, wherein the gaseous source of CO2 comprises about 2.5% to about 5% CO2.

31. The method of any one of claims 1-30, wherein the gaseous source of CO2 is natural gas effluent.

32. The method of any one of claims 1-30, wherein the gaseous source of CO2 is partially combusted natural gas effluent.

33. The method of any one of claims 1-30, wherein the gaseous source of CO2 is industrial effluent (e.g., combustion exhaust), flu gas, or gas from cement production.

34. The method of any one of claims 1-30, wherein the gaseous source of CO2 is air.

35. The method of any one of claims 1-34, wherein the method comprises first contacting the first aqueous solution comprising a hydroxide with air and then contacting the first aqueous solution comprising a hydroxide with the gaseous source of CO2 which comprises about 2.5% to about 10% CO2.

36. The method of any one of claims 1-34, wherein the method comprises first contacting the first aqueous solution comprising a hydroxide with air and then contacting the first aqueous solution comprising a hydroxide with the gaseous source of CO2 which comprises about 2.5% to about 5% CO2.

37. The method of any one of claims 1-36, wherein the method comprises first contacting the second aqueous solution comprising a hydroxide with air and then contacting the second aqueous solution comprising a hydroxide with the gaseous source of CO2 which comprises about 2.5% to about 10% CO2.

38. The method of any one of claims 1-36, wherein the method comprises first contacting the second aqueous solution comprising a hydroxide with air and then contacting the second aqueous solution comprising a hydroxide with the gaseous source of CO2 which comprises about 2.5% to about 5% CO2.

39. The method of any one of claims 1-38, wherein the solution comprising DIC is saturated with DIC.

40. The method of any one of claims 1-39, wherein the solution comprising DIC is saturated with CO2.

41. The method of any one of claims 1-40, wherein the contacting with the gaseous source of CO2 is performed until the solution comprising DIC is saturated with CO2.

42. The method of any one of claims 1-41, wherein the contacting with the gaseous source of CO2 is performed until the solution comprising DIC is saturated with DIC.

43. The method of any one of claims 1 and 3-42, wherein the contacting with a gaseous source of CO2 is performed until the pH of the second aqueous solution comprising the first solid hydroxide particles is about 9, about 9.1, about 9.2, about 9.3, about 9.4, about 9.5, about 9.6, about 9.7, about 9.8, about 9.9, or about 10.

44. The method of any one of claims 1 and 3-42, wherein the contacting with the gaseous source of CO2 is performed until the second aqueous solution comprising the first solid hydroxide particles is saturated with CO2.

45. The method of any one of claims 1 and 3-44, wherein the contacting with the gaseous source of CO2 is performed until the second aqueous solution comprising the first solid hydroxide particles is saturated with DIC.

46. The method of any one of claims 3-45, wherein the contacting with a gaseous source of CO2 is performed until the second aqueous solution comprising the second solid hydroxide particles is about 9, about 9.1, about 9.2, about 9.3, about 9.4, about 9.5, about 9.6, about 9.7, about 9.8, about 9.9, or about 10.

47. The method of any one of claims 3-46, wherein the contacting with the gaseous source of CO2 is performed until the second aqueous solution comprising the second solid hydroxide particles is saturated with CO2.

48. The method of any one of claims 3-47, wherein the contacting with the gaseous source of CO2 is performed until the second aqueous solution comprising the second solid hydroxide particles is saturated with DIC.

49. The method of any one of claims 2 and 4-42, wherein the contacting with a gaseous source of CO2 is performed until the pH of the filtered aqueous solution is about 9, about 9.1,about 9.2, about 9.3, about 9.4, about 9.5, about 9.6, about 9.7, about 9.8, about 9.9, or about 10.

50. The method of any one of claims 2, 4-42, and 49, wherein the contacting with the gaseous source of CO2 is performed until the filtered aqueous solution is saturated with CO2.

51. The method of any one of claims 2, 4-42, 49, and 50, wherein the contacting with the gaseous source of CO2 is performed until the filtered aqueous solution is saturated with DIC.

52. The method of any one of claims 2, 4-42, and 49-51, wherein the contacting with a gaseous source of CO2 is performed until the filtered aqueous solution is about 9, about 9.1, about 9.2, about 9.3, about 9.4, about 9.5, about 9.6, about 9.7, about 9.8, about 9.9, or about 10.

53. The method of any one of claims 1-52, wherein the method is performed until the second aqueous solution comprising the first solid hydroxide particles does not comprise particles of the solid hydroxide (e.g., the solid hydroxide).

54. The method of any one of claims 1-53, wherein the method is performed until the second aqueous solution comprising the first solid hydroxide particles does not comprise particles of magnesium hydroxide.

55. The method of any one of claims 1-54, wherein the method is performed until the second aqueous solution comprising the first solid hydroxide particles does not comprise particles of sodium hydroxide.

56. The method of any one of claims 1-55, wherein the method is performed until the second aqueous solution comprising the first solid hydroxide particles does not comprise magnesium hydroxide or sodium hydroxide.

57. The method of any one of claims 1-56, wherein the contacting with a gaseous source of CO2 is performed until second aqueous solution comprising the second solid hydroxide particles does not comprise particles of a hydroxide (e.g., the first solid hydroxide or second solid hydroxide).

58. The method of any one of claims 1-57, wherein the contacting with a gaseous source of CO2 is performed until the second aqueous solution comprising the second solid hydroxide particles does not comprise particles of magnesium hydroxide.

59. The method of any one of claims 1-58, wherein the contacting with a gaseous source of CO2 is performed until the second aqueous solution comprising the second solid hydroxide particles does not comprise particles of sodium hydroxide.

60. The method of any one of claims 1-59, wherein the method is performed until the second aqueous solution comprising the second solid hydroxide particles does not comprise particles of magnesium hydroxide or sodium hydroxide.

61. The method of any one of claims 1-60, wherein the contacting with a gaseous source of CO2 is performed until the filtered aqueous solution does not comprise particles of a hydroxide (e.g., the first solid hydroxide or second solid hydroxide).

62. The method of any one of claims 1-61, wherein the contacting with a gaseous source of CO2 is performed until the filtered aqueous solution does not comprise particles of magnesium hydroxide.

63. The method of any one of claims 1-62, wherein the contacting with a gaseous source of CO2 is performed until the filtered aqueous solution does not comprise particles of sodium hydroxide.

64. The method of any one of claims 1-63, wherein the method is performed until the he filtered aqueous solution does not comprise particles of magnesium hydroxide or sodium hydroxide.

65. The method of any one of claims 1-64, wherein the contacting with the gaseous source of CO2 is performed until the second aqueous solution comprising the first solid hydroxide particles does not comprise particles of a hydroxide (e.g., the first solid hydroxide or second solid hydroxide).

66. The method of any one of claims 1-65, wherein the contacting with the gaseous source of CO2 is performed until the second aqueous solution comprising the first solid hydroxide particles does not comprise particles of magnesium hydroxide.

67. The method of any one of claims 1-66, wherein the contacting with the gaseous source of CO2 is performed until the second aqueous solution comprising the first solid hydroxide particles does not comprise particles of sodium hydroxide.

68. The method of any one of claims 1-67, wherein the method is performed until the second aqueous solution comprising the first solid hydroxide particles does not comprise particles of magnesium hydroxide or sodium hydroxide.

69. The method of any one of claims 1-68, wherein the contacting with a gaseous source of CO2 is performed until the second aqueous solution comprising the second solid hydroxide particles does not comprise particles of a hydroxide (e.g., the first solid hydroxide or second solid hydroxide).

70. The method of any one of claims 1-69, wherein the contacting with a gaseous source of CO2 is performed until the second aqueous solution comprising the second solid hydroxide particles does not comprise particles of magnesium hydroxide.

71. The method of any one of claims 1-70, wherein the contacting with a gaseous source of CO2 is performed until the second aqueous solution comprising the second solid hydroxide particles does not comprise particles of sodium hydroxide.

72. The method of any one of claims 1-71, wherein the method is performed until the second aqueous solution comprising the second solid hydroxide particles does not comprise particles of magnesium hydroxide or sodium hydroxide.

73. The method of any one of claims 1-72, wherein the contacting with a gaseous source of CO2 is performed until the filtered aqueous solution does not comprise particles of a hydroxide (e.g., the first solid hydroxide or second solid hydroxide).

74. The method of any one of claims 1-73, wherein the contacting with a gaseous source of CO2 is performed until the filtered aqueous solution does not comprise particles of magnesium hydroxide.

75. The method of any one of claims 1-74, wherein the contacting with a gaseous source of CO2 is performed until the filtered aqueous solution does not comprise particles of sodium hydroxide.

76. The method of any one of claims 1-75, wherein the method is performed until the filtered aqueous solution does not comprise particles of magnesium hydroxide or sodium hydroxide.

77. The method of any one of claims 1-76, wherein the solution comprising DIC further comprises calcium carbonate.

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