Electrolytic Seawater Mineralization and the Mass Balances That Demonstrate Carbon Dioxide Removal

We present the mass balances associated with carbon dioxide (CO2) removal (CDR) using seawater as both the source of reactants and as the reaction medium via electrolysis following the “Equatic” (formerly known as “SeaChange”) process. This process, extensively detailed in La PlanteE.C.; ACS Sustain. Chem. Eng.2021, 9, ( (3), ), 1073–1089, involves the application of an electric overpotential that splits water to form H+ and OH– ions, producing acidity and alkalinity, i.e., in addition to gaseous coproducts, at the anode and cathode, respectively. The alkalinity that results, i.e., via the “continuous electrolytic pH pump” results in the instantaneous precipitation of calcium carbonate (CaCO3), hydrated magnesium carbonates (e.g., nesquehonite: MgCO3·3H2O, hydromagnesite: Mg5(CO3)4(OH)2·4H2O, etc.), and/or magnesium hydroxide (Mg(OH)2) depending on the CO32– ion-activity in solution. This results in the trapping and, hence, durable and permanent (at least ∼10 000–100 000 years) immobilization of CO2 that was originally dissolved in water, and that is additionally drawn down from the atmosphere within: (a) mineral carbonates, and/or (b) as solvated bicarbonate (HCO3–) and carbonate (CO32–) ions (i.e., due to the absorption of atmospheric CO2 into seawater having enhanced alkalinity). Taken together, these actions result in the net removal of ∼4.6 kg of CO2 per m3 of seawater catholyte processed. Geochemical simulations quantify the extents of net CO2 removal including the dependencies on the process configuration. It is furthermore indicated that the efficiency of realkalinization of the acidic anolyte using alkaline solids depends on their acid neutralization capacity and dissolution reactivity. We also assess changes in seawater chemistry resulting from Mg(OH)2 dissolution with emphasis on the change in seawater alkalinity and saturation state. Overall, this analysis provides direct quantifications of the ability of the Equatic process to serve as a means for technological CDR to mitigate the worst effects of accelerating climate change.


■ INTRODUCTION AND BACKGROUND
The trapping of carbon dioxide (CO 2 ) as an aqueous (bi)carbonate ion (e.g., HCO 3 − , CO 3 2− ) or as a mineral solid ("mineralization") is attractive because of favorable thermodynamics and the safety and permanence of storage. 2−4 Furthermore, mineralization is a cost-effective pathway for CO 2 sequestration/removal (CDR), 5,6 which, at steady state, is estimated to cost <$100 per tonne (t) of CO 2 . 2 During CO 2 mineralization, the release of Ca and Mg from the precursor solids is rate-limiting, unless mass transport is hindered, which is seldom the case. 7 Thus, providing presolubilized cations that can readily react with CO 2 enormously facilitates mineralization rates and extents. Seawater is a vast reservoir of divalent cations (Ca 2+ , Mg 2+ ) and dissolved CO 2 that can form sparingly soluble carbonates (and/or hydroxides). Long-term (millions of years) storage of CO 2 on Earth occurs by mineralization through the formation of calcite (CaCO 3 ) and aragonite (CaCO 3 ). But, over the short term, the abiotic precipitation of Ca and Mg carbonates from seawater is kinetically inhibited, as implied by the supersaturation of oceans with respect to these minerals.
The oceans absorb and immobilize atmospherically derived CO 2 in the form of dissolved carbonate species (i.e., predominantly HCO 3 − at a prevailing pH of ∼8.1). Such aqueous immobilization is highly durable, although less so than mineral carbonate formation (i.e., which has a stability of up to billions of years), 8,9 and presents a lower bound of stability in excess of 10 000 years. 10, 11 As a result, 25% of all anthropogenic CO 2 emissions (∼9 gigatonnes, Gt) are removed from the atmosphere by the oceans annually. 12 But, as a function of their prevailing chemistry 1 and ongoing ocean acidification, the capacity of the oceans to absorb additional CO 2 (i.e., annually and per unit of seawater) is capped, unless prevalent CO 2 were to be removed. Toward this end, i.e., to remove CO 2 from the oceans and to expand the capacity of seawater to absorb additional CO 2 , several electrochemical processes have been proposed, which focus on increasing ocean alkalinity via the: (a) production of OH − from seawater (and the utilization of the HCl coproduct to accelerate silicate weathering), 13 (b) using hard water and ion-exchange membranes, 14,15 or (c) utilizing pH swing processes to extract and capture CO 2 . 16,17 Recently, in La Plante et al., we proposed an approach to rapidly precipitate Ca and Mg carbonates and hydroxides from seawater to achieve CDR. 1 This Equatic process electrolytically forces mineral carbonate precipitation thereby consuming prevalent CO 2 that is dissolved in seawater by locking it within carbonate minerals and, simultaneously, producing alkaline mineral hydroxides that, when dissolved in seawater, enable the drawdown of atmospheric CO 2 into the seawater ensuring net CO 2 removal. 1 As such, previously, in La Plante et al., we have carefully examined and assessed the Equatic approach via detailed evaluations of energy demands, process cost, implementation schemes, and the achievable scale of carbon removal. 1 Therefore, in the current paper we particularly (only) focus on describing the geochemical basis and the CO 2 (mass) balances of the Equatic process. Two scenarios are presented: (1) the precipitation of calcium carbonate and magnesium hydroxide (Mg(OH) 2 : brucite), with Mg(OH) 2 dispersed as solids or dissolved in seawater and preequilibrated with CO 2 under dilute conditions, and (2) the precipitation of calcium and hydrated magnesium carbonates, i.e., when Mg(OH) 2 is carbonated under nondilute conditions. Special focus is paid to offer detailed quantifications of carbon mass balances based on equilibrium calculations. The analysis, therefore, offers a quantitative basis for assessing the CDR potential of the technology and for developing a robust measurement, reporting, and verification (MRV) strategy. This manuscript provides limited discussion around the full life cycle of the process, including electrolyzer materials and systems, balance-of-plant equipment, operational considerations, etc. These aspects represent ongoing work that will be addressed in future publications. Taken together, these efforts contribute to the mitigation of ongoing climate change, which poses enormously negative effects on ecosystems and people's quality of life. 18

■ ANALYSIS METHODS
We use PHREEQC 19 to carry out detailed geochemical simulations. The llnl.dat database was used, which is appropriate for ionic strengths up to seawater salinity (up to ∼1 molal (mol/kg); for comparison, seawater's ionic strength is 0.7 molal) and which explicitly considers metal complexation with carbon. This database uses the Debye−Huckel model with the B-dot equation and includes an explicit expression for the activity coefficient of aqueous carbon dioxide (CO 2(aq) ) as a function of temperature and ionic strength. 19 The seawater composition used is based on Millero et al. (2008) (Table  1), 20 adjusted to pCO 2 (in atm) = −3.38 (420 ppm) 21 by charge balancing for the presence of inorganic C (carbon) species. Similar results are obtained using the pitzer.dat database, which is suitable for solutions having higher ionic strengths (>1 molal) but does not contain thermodynamic data for hydromagnesite and cannot be extended above 25°C. For example, the pH obtained after equilibration at 420 ppm of CO 2 is 8.258 when using the pitzer.dat database and 8.170 when using the llnl.dat database ( Table 1). The Saturation Index (SI) is defined as log Ω, where the saturation ratio, Ω = Q/K sp , and Q is the ion activity product and K sp is the solubility product with respect to a given mineral. The saturation indices and ratios with respect to relevant Mg-and Ca-based minerals in seawater are shown in Table 2. In brief, seawater is supersaturated with respect to aragonite, calcite, dolomite, and magnesite and undersaturated with respect to the hydrated magnesium carbonates and brucite. All the calculations assume thermodynamic equilibrium for T = 25°C, p = 1 bar (1 atm).
The CO 2 content (i.e., storage capacity) of seawater is dependent on its alkalinity. The total alkalinity (A T , mg/L) of seawater is given by  ], and [H 2 CO 3 *], are determined via the equilibrium constants K H , K 1 , and K 2 (see eqs 1−3), which are functions of the temperature and the salinity of the water. 26 In PHREEQC, there is a single equilibrium constant that can be applied across all concentrations because the underlying (law of) mass action equations are written in terms of discrete ion activities. While small differences are indeed possible for the absolute numerical values of temperature/salinity-dependent equilibrium constants when solved using eqs 1−3, we chose the approach embedded in PHREEQC because it allows for customized modeling of numerous scenarios while accounting for the effects of solution nonideality (i.e., wherein activity and concentration are inequivalent) explicitly.
Here, eq 1 is Henry's law, where K H is the Henry's law constant (0.03428 mol/L/atm for freshwater (0 per mil, ‰) and 0.02858 for seawater (35 ‰)), and p is the partial pressure in atm (i.e., 420 ppm is equivalent to 0.00042 atm). The equilibrium constant K 1 is taken as 4.498 × 10 −7 mol/kg for freshwater and 14.52 × 10 −7 mol/kg for seawater, whereas K 2 is taken as 0.479 × 10 −10 mol/kg for freshwater and 11.12 × 10 −10 mol/kg for seawater. 26, 28 Refinements to such equilibrium constants have been the subject of past studies 25,29−31 but are beyond the scope of the current work. The concentration of aqueous H + is equivalent to 10 −pH (where the ionic product of water K w = 10 −14 ). The speciation of CO 2 and the relative abundances of HCO 3 − and CO 3 2− show a strong dependence on the pH (Figure 1a). On the other hand, H 2 CO 3 * is controlled by pCO 2 and is independent of pH. The equilibrium between H 2 CO 3 and CO 2(aq) is given by [H 2 CO 3 ] = K 0 [CO 2(aq) ], where pK 0 = 2.97, indicating that CO 2(aq) is ∼1000 times more abundant than H 2 CO 3 . 32 Thus, the total dissolved CO 2 (total dissolved inorganic carbon: DIC, ΣCO 2 ) is given by the sum of the different carbon species and is equal to ∑CO 2 = [H 2 CO 3 *] + [HCO 3 − ] + [CO 3 2− ]. At pH 8.1 and 420 ppm of CO 2 , the total dissolved CO 2 concentrations in freshwater and seawater based on this analysis are 0.847 and 2.557 mmol CO 2 /kg water, in reasonable agreement with Table 1 albeit with a discrepancy that is caused by differences in the equilibrium constants that are used. 33 Importantly, since we are assuming cation-limited reactions, the calculated value of total dissolved CO 2 is not used in the carbon mass balances in this paper. Furthermore, as relevant, the discussion below is based on PHREEQC calculations that resulted in dissolved CO 2 concentrations lower than the calculations based on eqs 1−3. Notably, the equilibrium ΣCO 2 in seawater is greater than that in freshwater because of the higher ionic strength of seawater that results in the speciation of CO 2 into HCO 3 − and CO 3 2− by complexation of the bicarbonate and carbonate ions with cations such as Na + , Mg 2+ , and Ca 2+ (see Figure 1b,c). , and H 2 CO 3 *. H 2 CO 3 * represents the sum of CO 2(aq) and true carbonic acid (H 2 CO 3 ). The speciation of CO 2 is calculated using equilibrium constants that vary with temperature and salinity. 26 (b) The detail of (a) for 8 ≤ pH ≤ 9, showing the far greater solubility of CO 2 in seawater than freshwater. (c) The different aqueous species of DIC, including complexes with dissolved cations in seawater, and their relative amounts. The concentrations for each species are given in mol/kg (molal basis).
Electrolytic Carbon Removal. The Equatic process consists of the following steps.
Step 2a) The solids are separated from the catholyte effluent (Table 3). Residual Ca 2+ in the catholyte precipitates as CaCO 3 in a carbonation reactor, while Mg(OH) 2 solids are (a) discharged into the ocean (Case 1) or (b) pre-equilibrated with seawater and carbonated inside the plant's battery limits under dilute (mass) conditions (<∼0.002 mol Mg(OH) 2 /kg seawater, see Figure 7d) (Case 2a).
Step 2b) The catholyte effluent containing both solids and ions is carbonated inside plant limits, resulting in the dissolution of Mg(OH) 2 and equilibration with a CO 2enriched vapor under nondilute (mass) conditions to produce hydrated Mg carbonates, while the residual Ca 2+ in solution precipitates as CaCO 3 (Case 2b).
Step 3) The realkalinization of the anolyte stream to neutralize its acidity and replenish divalent cations that are consumed (and do not redissolve) during mineral precipitation.
Step 4) The discharge of the processed anolyte and catholyte streams back into the ocean. 1 Ultimately, the process traps CO 2 as (a) dissolved (i.e., aqueous HCO 3 − and CO 3 2− ) species stabilized via the redissolution of Mg(OH) 2 ) and/or (b) solid (e.g., CaCO 3 , a mineral carbonate) forms. This manner of CDR is represented by two limiting cases: (Cases 1, 2a) CaCO 3 + Mg(OH) 2 (i.e., 89 mass % aqueous, 11 mass % solid CO 2 immobilization) and (Case 2b) CaCO 3 + Mg−CO 3 hydrates (i.e., 100 mass % solid CO 2 immobilization). The CaCO 3 solids produced via this process can be discharged back into the ocean, where they will remain stable because of their native prevalence and persistence (e.g., seashells in the ocean) and seawater's supersaturation with respect to the mineral carbonates (Table 2), or they will be beneficially utilized, e.g., as sand in concrete, or as a carbon-neutral feedstock to produce cement. Obviously, if hydrated carbonate phases including nesquehonite ( form, alternative disposal strategies (e.g., on land) will be needed due to the tendency of these solids to dissolve if they were to be discharged into the ocean ( Table 2).
From stoichiometry, the formation of 1 mol of CaCO 3 or Mg−CO 3 hydrates (e.g., nesquehonite: MgCO 3 ·3H 2 O) captures 1 mol of CO 2 , while requiring 2 mol of OH − . For comparison, only 1.2 mol of OH − are required per mole of CO 2 stored as dissolved (bicarbonate: HCO 3 − and carbonate: CO 3 2− ) ions (Figures 1 and 7). 1,10 This implies that, per unit of alkalinity, it is more chemically and energy efficient to immobilize CO 2 in the form of dissolved aqueous carbonates, i.e., rather than mineral carbonate species. The Equatic process is based on the electrolysis of seawater. Such electrochemical Table 3. Representative Steady-State Composition of the Anolyte and Catholyte Effluent Exiting the Electrolyzer (see Figure 2) at Ambient (p,T) and in Equilibrium with Air   Figure 2. A schematic of the Equatic process showing major inlet and outlet feeds of the primary steps for CO 2 removal associated with the formation of: carbonate solids and (aqueous) dissolved CO 2 (Cases 1, 2a) and carbonate solids only (Case 2b). The major energy inputs include electrolysis, water processing and pumping, and rock grinding. 1 ACS ES&T Engineering pubs.acs.org/estengg Article stimulation of seawater implies the formation of alkalinity (OH − ) at the cathode and acidity (H + ) at the anode. In addition, gas-phase coproducts evolve, including hydrogen (H 2(g) ) at the cathode and oxygen (O 2(g) ) and chlorine (Cl 2(g) ) at the anode. These gas evolutions are described by the hydrogen evolution reaction (HER), oxygen evolution reaction (OER), and chlorine evolution reaction (ClER), respectively. During seawater electrolysis, unless an oxygen-selective anode is used, ClER is the predominant reaction at the anode because its 2e − basis (i.e., as compared to the 4e − basis of OER) makes its formation more kinetically favorable as compared to oxygen evolution, which is thermodynamically favored. The Equatic process's mass balances can be examined for a system that removes 1 t of CO 2 per day (TPD). For Cases 1 and 2a, this system requires the processing of ∼220 m 3 per day of seawater in the catholyte to yield 235 kg of CaCO 3 and 702 kg of Mg(OH) 2 (i.e., if the solids were suspended in the solution this translates to ∼0.4 mass % solids, corresponding to a dilute system) while assuming a CO 2 removal efficiency of 1.7 mol of CO 2 per mol of Mg(OH) 2 (see below). In addition, ∼29 kg of H 2(g) , ∼46 kg of O 2(g) , and ∼818 kg of chlorine (Cl 2(g) , HClO, and ClO − ) are produced when using an anode that is not OER-selective (e.g., platinum). The amount of free chlorine generated can be reduced greatly by the use of oxygen-selective anodes, without affecting the overpotential, and achieving >98 mass % selectivity of the OER as compared to ClER�a fast maturing effort that addresses obvious issues related to toxicity, handling, and atmospheric release of chlorine and chlorine derivatives. For these considerations independent of whether chlorine is evolved (and scrubbed) or suppressed, Cases 1 and 2a yields net 4.6 kg of CO 2 removal per m 3 of seawater processed as catholyte. Herein, CO 2 removal via the alkalinity enhancement enabled by the dissolution of brucite (Mg(OH) 2 ) can be effected in the ocean, i.e., following the oceanic discharge of the brucite, or within a captive carbonation/aeration reactor wherein air is sparged into the solution and CO 2 absorption and bicarbonate/carbonate ion formation occur following Henry's Law (see further discussion below; and Figure 2).
Alternatively, Case 2b requires 348 m 3 per day of seawater in the catholyte and produces 371 kg of CaCO 3 and 2635 kg of depending on which hydrated magnesium carbonate phase forms (i.e., if the solids were suspended in the solution this translates to ∼0.9 to 2.7 mass % solids, corresponding to a dilute system). In addition, ∼46 kg of H 2(g) , ∼73 kg of O 2(g) , and ∼1295 kg of free chlorine (Cl 2(g) , HClO, and ClO − ) are produced when using a platinum-based anode that is not OERselective. Thus, Case 2b yields net 2.9 kg of CO 2 removal per m 3 of seawater processed as catholyte. The carbonation of the catholyte to produce Mg−CO 3 hydrates (Step 2b) implies the bubbling of a CO 2 -enriched vapor into the catholyte effluent, e.g., as sourced from air, a fractional direct air capture (DAC) system, or a CO 2 -enriched flue gas emissions stream. The mass and energy inputs relevant to Cases 1, 2a, and 2b are shown schematically in Figure 2 and are described elsewhere. 1 Precipitation of Calcium Carbonate and Magnesium Hydroxide. The ocean is supersaturated with respect to aragonite by a factor of at least 2−3 ( Table 1), implying that the kinetic inhibition of precipitation is operative. 34 With decreasing Ω, the time elapsed before the onset of mineral precipitation increases gradually at Ω > 3 and then sharply at Ω ≈ 3, implying seawater stability at Ω < 3. 35 This kinetic inhibition of precipitation is caused by dissolved organic matter, 36,37 phosphate ions, 38 magnesium ions, 39 and sulfate ions. 40 To overcome the kinetic hindrance to precipitation we alkalinize the electrolyte such that, e.g., at pH 10−12, in the vicinity of the cathode we ensure Ω > 1400 (at pH 10) for calcite, and Ω > 7 (at pH 10) for brucite for seawater in equilibrium with air: i.e., for saturation ratios which are more than sufficient to overcome the thermodynamic and kinetic barriers to mineral precipitation.
If uncompensated, i.e., by cation replenishment (for CaCO 3 ) or by redissolution (for Mg(OH) 2 ), the precipitation of Ca and Mg minerals from seawater (i.e., resulting in the removal of aqueous Ca 2+ and Mg 2+ species) in the catholyte would lead to a net lower seawater pH and hence a reduction in its dissolved CO 2 storage capacity, as a function of CO 2 's pHdependent solubility in water (Figure 3a). Similarly, the decrease of the pH of the anolyte in an electrolysis system to pH ≈ 1 results in CO 2 's degassing to a limit of 2.141 mmol CO 2 /kg seawater as described by Henry's law (Figure 1a). But on the other hand, the net increase in the pH of the catholyte, on account of the electrolytic pH pump, and the subsequent . This indicates that the Equatic process can enhance seawater's intrinsic CO 2 storage capacity, while also accomplishing atmospheric CO 2 removal. This is in contrast to traditional direct air capture (DAC) processes since a decrease in atmospheric CO 2 concentrations, if effected in isolation via DAC, would in fact, in time, result in the degassing of CO 2 from the oceans on account of the oceanatmosphere partitioning/exchange equilibrium of CO 2 (eq 1). 1,41 Expectedly, if the catholyte effluent is not in equilibrium with atmospheric CO 2 , re-equilibration, i.e., the progressive absorption of CO 2 from the air, will decrease its pH ( Figure  3b). Thus, our simulations show that an exit (effluent) pH ≈ 11.5 is required to maintain a pH ≥ 8.5 upon equilibration with atmospheric CO 2 , for a catholyte effluent that is depleted in aqueous Ca 2+ and Mg 2+ ions (i.e., where Ca and Mg are contained within mineral solids). It is furthermore important to highlight that, in the Equatic process, due to the provisioning of a continuous (electrolytic) pH pump, the precipitation of mineral carbonates does not result in the degassing of CO 2 (i.e., due to acidification that results from the deprotonation of bicarbonate ions: HCO 3 − , during carbonate mineralization), as is the case for nonelectrolytically stimulated conditions.
Realkalinization of the Catholyte and Anolyte Effluent. The uncontrolled discharge of the anolyte (i.e., an acidic solution) effluent into the ocean could result in changes in seawater chemistry and saturation states (e.g., a decrease in SI with respect to aragonite, a reduced CO 2 storage capacity, etc., Table 2, Table 3). To counter such effects requires the realkalinization of the effluent by the dissolution of alkaline minerals such as those found in mafic and ultramafic rocks into the anolyte, to elevate the concentrations of divalent cations. Candidate solutes for this include pyroxenes (e.g., augite: (Ca,Na)(Mg,Fe,Al,Ti)(Si,Al) 2 O 6 , diopside: MgCaSi 2 O 6 ]) and olivines (e.g., forsterite: Mg 2 SiO 4 ]) that naturally occur in mafic (basalts, gabbro) and ultramafic (peridotites) rocks. As Ca 2+ and Mg 2+ species are dissolved into the effluent, its pH and total dissolved CO 2 content elevate ( Figure 4). It is evident that an increase in the ΣCO 2 occurs only when the pH exceeds ∼5 (Figure 1a). Furthermore, the replenishment of the cations increases not only the pH but also the salinity, enhancing CO 2 absorption (Figures 1 & 4b,c)�i.e., a reason why seawater contains much more dissolved CO 2 than freshwater.

ACS ES&T Engineering pubs.acs.org/estengg Article
The lower alkalinity requirement for Cases 1 and 2a is a result of the greater CO 2 removal efficiency of Mg(OH) 2 compared with Mg−CO 3 hydrates (i.e., since only 1.2 mol of OH − are required per mole of CO 2 stored as dissolved bicarbonate (HCO 3 − ) ions). For either case, if the catholyte effluent, i.e., including the suspended solids, were to be discharged into the ocean, the CaCO 3 solids that are present would remain stable, i.e., they would not dissolve given the significant oversaturation of the oceans with respect to this mineral (see Table 2). That said, we recognize that effluent alkalinization (i.e., ensuring equivalence of the pH of the influent and the combined, anolyte + catholyte effluent) and divalent cation regeneration (i.e., abundances of Ca and Mg in the influent and combined effluent are equal) are prerequisite to discharge into the ocean. But, beyond chemical parameters, other aspects require further consideration. For example, it is known that the [Ca]/[Mg] ratio in the oceans is of relevance to calcifying organisms, particularly the stability of their calcified exoskeletons in an acidifying ocean. 42−45 While we cannot yet assess if the Equatic process, if globally deployed for 10s of gigatonnes of CDR annually, would affect such aspects (albeit, not at the scale of a single or a few plants), further work is needed to better understand these details in due course.
Olivine ((Mg,Fe 2+ ) 2 SiO 4 ) is the most abundant mineral (ultramafic, and otherwise) in the Earth's upper mantle. On the Earth's surface, olivine is primarily found in ophiolites, which are sections of the uppermost mantle and oceanic crust that are exposed on land by tectonic activity and that are found worldwide along convergent and divergent plate boundaries. Ophiolites are composed of a specific sequence of mafic (basalt, gabbro) and ultramafic (peridotites such as harzburgite, dunite) rocks and can have thicknesses on the order of 5 to 10 km and encompass areas exceeding ∼100 000 km 2 . 46,47 Peridotites are intrusive rocks that are classified based on the amounts of olivine, clinopyroxene ((Ca,Na,Li)-(Mg,Fe 2+ ,Al,Fe 3+ )Si 2 O 6 ), and orthopyroxene ((Mg,Fe)Si 2 O 6 ). In ophiolites, lherzolite, harzburgite, and dunite peridotites are most common, containing at least 40 mass % olivine. Assuming a thickness of 1 km, an area of 10 000 km 2 , and 50 mass % fosteritic olivine (Mg 2 SiO 4 ) leads to a volume of 5000 km 3 , substantially exceeding the volume of olivine needed to sequester all anthropogenic CO 2 emitted into the atmosphere, i.e., including ongoing (17 km 3 per year; ∼36 Gt per year) and all legacy emissions (1225 km 3 ; ∼2500 Gt since 1850). 48 In other words, if appropriately harvested, natural mafic and ultramafic rocks and minerals are an effectively limitless supply of alkalinity for CO 2 management. Beyond such rocks, industrial processes produce ∼7 Gt of alkaline solids per year, including (but not restricted to) products and byproducts such as lime (∼430 Mt), cement kiln dust (∼478 Mt), slags (∼516 Mt), and coal ash (∼701 Mt). 49, 50 The Goldich stability series indicates that the relative reactivity of silicate minerals is dependent on their crystallization temperatures, i.e., minerals formed at higher temperatures are more reactive than those formed at lower temperatures (Figure 6a). This is further reflected in the degree of polymerization of tetrahedral silicate units, i.e., in general, a higher Si to O ratio signifies greater polymerization and lower temperature of cooling. For example, comparing the reactivities of anorthite and forsterite, both abundant silicates that are reservoirs of Ca and Mg, reveals that forsterite is more reactive owing to its structure in which all SiO 4 4− units are connected to each other by Mg 2+ ions. 54, 55 On the other hand, anorthite features a framework silicate structure with extensive sharing of O atoms by Si. 56 In addition, kinetic considerations such as the rates of water exchange around the cations in an atomic structure also influence reactivity; for instance, Ca-based silicates dissolve faster than Mg-based silicates despite having an equivalent  57 Using data from Pokrovsky and Schott (2000), 54 the rate of forsterite dissolution as a function of pH for 1 < pH < 7 can be expressed as R = 2.376 × 10 −11 e −1.15(pH) , where R is the dissolution rate in mol/cm 2 /s (see Figure 6a). Using this relation, the dissolution rates at pH 1, 2, 3, 4 can be estimated as 7.53 × 10 −12 , 2.38 × 10 −12 , 7.54 × 10 −13 , and 2.39 × 10 −13 mol/cm 2 /s, respectively. For a nonporous sphere, i.e., where the external surface area represents the reactive surface area, the specific surface area (SSA) and particle diameter (d) are related by d = 6/(SSA × ρ), where ρ is the density (Figure 6b). The effect of specific surface area on mass-normalized dissolution rates can be used to assess the fineness of particles and the residence time in a column reactor that are required to achieve a sufficient rate and extent of mineral dissolution in the highly acidic anolyte to ensure divalent cation abundance renewal and realkalization (Figure 6c). The rate equations can also be used to calculate time-dependent pH evolution during mineral dissolution. For example, progressively dissolving 50 kg of forsterite (d 50 = 10 μm) in 1000 kg of water (initial pH = 1) results in the release of ∼60 mol Mg 2+ (60 mmol Mg 2+ /kg) within 24 h. For comparison, ∼80 mmol Mg 2+ /kg is required to raise the pH of the anolyte from ∼1 to ∼8.2 (i.e., native seawater pH) ( Figure  4a). Decreasing the particle size increases the dissolution rate, at an energy expense. For instance, using a Bond Work Index (BWI) approach, for silicate rocks, we estimate that a grinding energy of around 70 MJ per tonne of rock (0.02 MWh/tonne) is needed to produce particles with d 50 ≈ 100 μm for dissolution. Significantly, the intense acidity (pH ≈ 1) of the  (Table 4). While exact abundances are nontrivial to assess, these materials are available at levels ranging from 10s-to-100s of millions (e.g., slags) to 1000s of billions of tonnes (e.g., olivine).   A range of diverse processes including riverine input, atmospheric and evaporite cycling, ion exchange, hydrothermal activity, low-temperature basalt weathering, and carbonate deposition control the input− output balance of divalent seawater ions (Ca 2+ , Mg 2+ ) and the net change in seawater's alkalinity. 58 Natural processes result in a net flux for Ca that is zero (i.e., the amount added to the oceans is equal to the amount removed from the oceans by carbonate deposition) and a net decrease in Mg concentration by 1.5 × 10 12 mol per year. 58 Cases 1 and 2a implies the dissolution of brucite in seawater, in which seawater is undersaturated, raising seawater's pH while drawing down atmospheric CO 2 thereby ensuring net CDR. The dissolution of brucite increases seawater's pH expanding its CO 2 storage capacity ( Figure 7a) such that between 1.3-to-1.7 mol of CO 2 are absorbed per mol of Mg(OH) 2 , assuming that no Mg− CO 3 hydrates form (Figure 7b). The precipitation of Mg−CO 3 hydrates (e.g., hydromagnesite: Mg 5 (CO 3 ) 4 (OH) 2 ·4H 2 O or nesquehonite: MgCO 3 ·3H 2 O) under nondilute mass conditions within the plant reduces this value to 0.8-to-1.0 mol of CO 2 removed per mol of Mg(OH) 2 (Figure 7c,d). However, additional CO 2 is absorbed if the Mg−CO 3 hydrate solids are released into the ocean and progressively dissolve.
Under static/batch conditions (i.e., R e → 0, where R e is the Reynolds number, unitless) where there is very slow solutal transport, locally, it is possible that increases in the alkalinity of seawater, e.g., caused due to brucite dissolution, could alter mineral saturation states. This could induce secondary carbonate formation (see Figure 8a,b) since the increase in alkalinity shifts the HCO 3 − −CO 3 2− distributions (e.g., see the Bjerrum diagram for dissolved inorganic carbon's speciation) in seawater thereby resulting in aragonite precipitation via the combination of Ca 2+ and CO 3 2− species. 59 Thus, in circumstances wherein the brucite-containing effluent is discharged into the oceans it is necessary to examine how quickly: (a) brucite may dissolve? and (b) how quickly dissolved brucite's species (i.e., particularly alkalinity) may be transported? While the release of CO 2 that typically accompanies secondary carbonate precipitation is not an issue (i.e., where the release of CO 2 occurs via bicarbonate rather than carbonate combination with calcium species via the reaction: Ca 2+ + At seawater pH, the dissolution rate of brucite is on the order of 10 −8 mol/m 2 /s. 61 To achieve CO 2 removal at the level of 10 Gt/year would require the dissolution of 8.3 Gt of Mg(OH) 2 corresponding to the addition of 1.1 × 10 −7 mol Mg(OH) 2 /kg seawater. If brucite's dispersion is assumed to be averaged across the world's oceans, an unrealistic and impractical assumption, changes in seawater pH and mineral saturation indices are irrelevant. For context, the critical saturation ratio, Ω, for runaway aragonite precipitation is reported to be 5 (SI = 0.69). 62 Using a model that considers ocean circulation, i.e., ECCO (Estimating the Circulation and Climate of the Ocean) LLC270 physical fields, 63 and constraints of ΔpH = 0.1 and ΔΩ aragonite = 0.5, regions within 300 km of the coast can accommodate 100s of megatons of atmospheric CO 2 removal. 64 This shows that simple nearcoastal alkalinity discharge, such as that proposed herein, can scale to several Gt per year of CDR if spread over available coastlines. 64 But, an important question related to the Equatic process involves answering the question: "What is the best approach for Mg(OH) 2 dissolution and atmospheric CO 2 drawdown: i.e., in the open ocean (Case 1), or within an (industrial) plant (Cases 2a,2b)?" Each approach has distinct benefits and challenges. First, we can consider the case wherein brucite's dissolution occurs following the discharge of the calcite and brucite (particulate) containing effluent into the ocean ("in ocean" approach). This requires two steps leading to CO 2 removal: Step A) brucite dissolution, and Step B) CO 2 drawdown from the atmosphere. At high brucite undersaturations and moderate convective conditions (e.g., turbulence in oceans varies by at least 8 orders of magnitude with characteristic R e reported to range between 70 and 4 × 10 8 ), 65−67 the dissolution of brucite is rapid, requiring on the order of a few to 10s of hours. On the other hand, the equilibration of air and sea (i.e., gas−liquid CO 2 concentrations) occurs over weeks to months depending on the mixed layer depth and Figure 9. Changes in (a) pH, (b) solid phase assemblage, and total dissolved CO 2 in the catholyte during reaction with CO 2 to achieve equilibrium pCO 2 equivalent to atmospheric conditions at 25°C. These simulations show that the catholyte solids discharged include hydromagnesite and aragonite, in general agreement with our experiments. ACS ES&T Engineering pubs.acs.org/estengg Article wind speed. 68 Therefore, to achieve atmospheric CO 2 drawdown, Mg(OH) 2 must not only fully dissolve but also the alkalinized seawater must remain in the mixed layer during this period. This results in an uncertainty regarding the amount of time and the extent of CO 2 absorbed required for carbon dioxide drawdown from the atmosphere. Second, we can consider a process configuration wherein air is sparged into the brucite-containing catholyte within a high surface-to-volume (s/v, m −1 ), high mass transfer rate aeration reactor, i.e., inside-the-battery limit ("ISBL" approach) of an industrial plant. While such aeration requires bubbling ∼2500 t of atmospheric air to derive ∼1 t of CO 2 (assuming ∼420 ppm of CO 2 in air) the absorption of CO 2 into the catholyte that contains CaCO 3 and Mg(OH) 2 results in progressive Mg-(OH) 2 dissolution and the immobilization of atmospherically derived CO 2 in the form of HCO 3 − and CO 3 2− species, while the CaCO 3 that is present remains unaffected. Careful analysis shows that, herein, all residual Ca 2+ in solution in fact precipitates as CaCO 3 , while the dissolution of Mg(OH) 2 in the presence of CO 2 at high solid loadings results in the precipitation of hydromagnesite and nesquehonite, since magnesite formation is unachievable at ambient conditions (see Figure 9a,b). This allows for direct quantification of CO 2 absorption as solid carbonates. Once released into the ocean, the hydrated magnesium carbonates redissolve, increasing alkalinity. This analysis matches our experimental observations, and as a result of progressive CO 2 dissolution and stabilization, the pH of the catholyte decreases from ∼12.1 to ∼9.0, corresponding with the dissolution of brucite. The formation of Mg−CO 3 hydrates can be avoided by employing low Mg(OH) 2 solid loadings in the aeration reaction, resulting in greater CDR efficiency. While this ISBL approach requires aeration that implies an energy demand it is desirable in that it eliminates the uncertainty of CO 2 removal and allows "direct and unambiguous, in plant" quantifications of both the rate and extent of CO 2 removal. The obvious disadvantage is that it implies moving large quantities of air, which enhances the overall energy need of the process.
Equatic's Measurement, Reporting, and Verification (MRV) Approach for CO 2 Removal. The net extent of CDR accomplished by the Equatic process must be measurable, verifiable, reportable, additional, and durable (permanent). In addition, the potential for leakage, harm, and cobenefits must be considered. Using the analysis presented in the sections above and in alignment with a recent approach suggested by CarbonPlan, 69 we can calculate the net extent of CO 2 removal effected by the Equatic process as follows: where, Emissions CO2e includes the total embodied CO 2 emissions from material and energy use (e.g., the grid emissions factor of electricity, and the amount of energy embodied in the coproduced hydrogen assuming typical purification demands, and conversion efficiencies), and

= +
Using Case 1 as an example, the CO 2 sequestered as dissolved HCO 3 − and CO 3 2− ions and solid carbonates can be quantified unambiguously by weighing the masses of Mg(OH) 2 and CaCO 3 produced and multiplying these masses by a carbon removal factor, as follows (in units of g CO 2 per m 3 of water processed). The total mass of the solids can be measured by separating the solids from the catholyte effluent stream, and the mass percentages of Mg(OH) 2 and CaCO 3 quantified�online, and in real-time, using thermogravimetric analysis. The mass percentages of Mg(OH) 2 and CaCO 3 are taken from the mass loss between 300-to-500°C and 600-to-900°C, respectively. The carbon removal factor for Equatic Dissolved, CO2e is affected by the extent of Mg(OH) 2 dissolution and the extent of CO 2 absorption (into water) from air. The ISBL approach discussed above eliminates these uncertainties. The evasion of CO 2 from seawater may result from secondary CaCO 3 precipitation or the mixing of un-neutralized acid (anolyte), especially in the case of the "in ocean" approach, considerations of which are addressed above. While there are uncertainties regarding increasing the dissolved inorganic carbon (DIC) content of the oceans, notably, the Equatic approach counteracts ocean acidification that poses a significant risk to ocean ecosystems via a multitude of ways. 70,71 ■ SUMMARY AND CONCLUSIONS This paper presents a rigorous analysis of Equatic, an oceanmediated process for CDR. We examine two limiting pathways for CDR, one in which CO 2 is trapped solely within calcium and magnesium carbonates, and another in which CO 2 is stored both as solid carbonates and as aqueous HCO 3 − and CO 3 2− by means of ocean alkalinity enhancement promoted by Mg(OH) 2 dissolution. We carefully examine how the anolyte and catholyte effluents of the process present unique opportunities for rock dissolution and durable and permanent CO 2 immobilization. We furthermore show how the process offers flexibility to eliminate the uncertainties associated with quantifying the rate and extent of CDR and minimize any detrimental changes in seawater composition and chemistry from the influent to the effluent. Furthermore, detailed considerations for realkalinization of the effluent including acid neutralization capacity and reactivity of diverse mineral solutes are discussed. This analysis provides the fundamental basis that justifies the viability of the approach and lays the foundation of a quantitative approach for MRV of the Equatic process.