WO2022182781A1 - Alkalinity concentration swing for direct air capture of carbon dioxide - Google Patents

Abstract

The invention features methods and systems for direct air capture of carbon dioxide using an Alkalinity Concentration Swing (ACS), where direct air capture of carbon dioxide is driven by concentrating an alkaline solution that has been exposed caron dioxide and loaded with dissolved inorganic carbon, which can then be extracted by concentrating the alkaline solution.

Description

ALKALINITY CONCENTRATION SWING FOR DIRECT AIR CAPTURE OF CARBON DIOXIDE

BACKGROUND OF THE INVENTION

Removal of carbon dioxide from the atmosphere has been proposed as an essential method for responding to anthropogenic climate change. Policymakers and scientists agree that in order to minimize future harm to society — which will be most felt by the world’s most vulnerable populations — priority should be devoted to efforts and technologies that reduce emissions from burning fossil fuels and other sources of greenhouse gases. But even after deep decarbonization efforts, some hard-to-avoid emissions will remain, either because they are unacceptable to avoid from a social-justice perspective (e.g., food security constraints) or extremely physically difficult to eliminate within the given timeframe, making some degree of carbon dioxide removal (CDR) necessary. A gigatonne-per-year scale of global CDR will likely be required by the end of the century, though aiming for larger scales, up to 20 billion tonnes of CO2 per year (GtCC>2/year) as some reports suggest has significant associated moral hazards and ethical considerations.

Carbon dioxide removal spans a wide range of approaches, each with different associated materials, energy, land, resource, and societal consideration. Biological CDR methods — including reforestation and soil carbon management — are projected to be able to achieve gigatonne-scale per year removal, though they tend to store carbon in impermanent reservoirs, meaning they are more susceptible to reversals. While these approaches confer co-benefits, such as increasing biodiversity and improving local water and soil quality, they also require significant land area to reach gigatonne scale and may compete with other land-use demands, such as agriculture or conservation objectives.

Other approaches that store carbon in a more durable form include bioenergy with carbon capture and storage, carbon mineralization processes that remove CO2 directly out of the air, or the addition of alkalinity to oceans, which increases dissolved carbon and ultimately drives the production of carbonate sediments. Mineralization processes could result in the long-term storage of concentrated CO2 streams in subsurface formations, products such as concrete, as well as mine tailings and alkaline industrial wastes.

An alternate strategy for carbon dioxide removal involves direct air capture (DAC), industrial technologies for separating atmospheric CO2 directly from the air through chemical or physical processes, coupled with sequestration (e.g., storage in a geological reservoir or through mineralization).

One class of approaches is based on solid sorbent technologies that typically use amine-based materials to reversibly bind CO2. This process can be cycled many times to capture CO2 out of ambient air and release a concentrated stream through a thermal or moisture swing. Alternatively, a faradaic electro swing adsorption system, which uses voltage to regenerate CO2. Another class of approaches relies on a basic aqueous solution to absorb CO2 from ambient air. One commercialized process is based on an aqueous potassium hydroxide contactor that absorbs CO2 directly from air and converts the CO2 to calcium carbonate; releasing the CO2 requires heating of calcium carbonate to approximately 900°C. A different approach makes use of an electrochemical swing, which changes the pH of the solution and allows for the release of CO2 without going through the steps of precipitation and heating. Accordingly, there is a need for new direct air capture methods and systems.

SUMMARY OF THE INVENTION

The invention features methods and systems for direct air capture of carbon dioxide using an alkalinity concentration swing.

In an aspect, the invention provides a method of capturing carbon dioxide. The method includes the steps of: providing an alkaline solution comprising dissolved carbon dioxide; e.g., by contacting a gas containing carbon dioxide with an alkaline solution for a time sufficient for carbon dioxide to dissolve therein; concentrating the solution; and extracting dissolved carbon dioxide from the concentrated solution.

In some embodiments, the method includes diluting the concentrated solution, capturing carbon dioxide in the diluted solution, and repeating the cycle. In some embodiments, the method includes collecting carbon dioxide extracted from the concentrated solution.

In some embodiments, the alkaline solution includes a weak base and/or weak acid. In some embodiments, the weak base and/or weak acid is polyprotic. In some embodiments, the alkaline solution includes boric acid.

In some embodiments, the alkaline solution is concentrated using reverse osmosis or capacitive deionization. In some embodiments, the concentrating selectively retains bicarbonate ions over carbonate ions in the concentrated solution. In some embodiments, the concentrating includes performing reverse osmosis with an ion selective membrane or performing monovalent-selective capacitive deionization. In some embodiments, the concentrating comprises performing monovalent- selective capacitive deionization with an anion exchange membrane. In some embodiments, the first step includes contacting a gas containing carbon dioxide with the alkaline solution for a time sufficient for carbon dioxide to dissolve therein.

In another aspect, the invention provides a system for capturing carbon dioxide. The system includes a reservoir for an alkaline solution having a gas inlet and means for concentrating the solution. In some embodiments, the system includes a means for dilution of the concentrated solution. In some embodiments, an ion-selective capacitive deionization module or an ion-selective reverse osmosis device.

By “about” is meant ±10% of a recited value.

By “alkalinity is meant the molar charge difference between the sum of the conservative cations and the sum of the conservative anions, i.e. , ions whose concentrations do not vary with pH, temperature, or pressure.

BRIEF DESCRIPTION OF THE DRAWINGS

Fig. 1A-1C. An Alkalinity Concentration Swing Cycle. The dots labeled Ί ’ to ‘4’ represent states of the cycle, and arrows therebetween (e.g., 1 2) represent steps of the cycle. (A) The line plots the dissolved inorganic carbon (DIC) concentration in equilibrium with atmospheric CO2 (p, = 0.4 mbar) as a function of alkalinity. An arrow (1 2) indicates the concentration step of the ACS and plots the trajectory when a solution, initially equilibrated at 0.01 M alkalinity (dot at Ί ’), is concentrated by a factor of 100 to an alkalinity of 1 M. In the concentrated state (dot at ‘2'), the solution has excess DIC over that in equilibrium with air. An arrow (2 3) indicates the amount of CO2 that outgasses as the system reaches a new equilibrium at high alkalinity and p_t = 0.4 mbar. The remaining 3 4 and 4 1 arrows indicate the dilution and CO2 absorption steps, which return the system to the initial state (Ί ’). Vertical extent of the shaded regions below the line indicate concentrations of bicarbonate (HCO3 ) and carbonate (CO3² ), respectively. Inset: The line plots the same DIC versus alkalinity relationship as the main plot, but from 0 to 0.02 M alkalinity, showing the transition between a roughly 1 :1 alkalinity to DIC relationship at low alkalinity to a 2:1 scaling at higher alkalinity. (B) A plot of DIC as a function of pco³ at a fixed alkalinity of 1 M. The dots ‘2’ and ‘3’, as well as the (2 3)arrow, correspond to (A). (C) The alkalinity, CDIC, pH, and pco³ values are listed corresponding to each state in (A).

Fig. 2A-2B. DIC outgassed based on the ACS. (A) Concentration of DIC in the feed solution outgassed as CO2 as a function of concentration factor. Dashed lines represent purity thresholds with respect to non-CC>2 gases. (B) The fraction of DIC in the feed solution outgassed as CO2 as a function of concentration factor. Each curve represents a different initial alkalinity concentration (legend in panel B applies also to panel A). The boundary of the gray region represents the precipitation threshold for potassium carbonate at 20°C of approximately 8M.

Fig. 3A-3C. ACS system schematic. (A) The four steps of the ACS represented in a full cycle. (B) A schematic of a reverse osmosis module driven by a high-pressure pump. (C) A schematic of a capacitive deionization module driven by applied current and voltage. Ion exchange membranes are not represented in the diagram. Fig. 4A-4B. RO energy models. (A) Energy per mole CO2 as a function of concentration factor for three RO models: ideal, multi-stage (ms), and single-stage (ss) at a representative initial alkalinity of 10 mM.

(B) Energy of the multi-stage RO model evaluated at four different initial alkalinity values. (A-B): energy is normalized to the scaling parameter a_ss ; curves terminate on the right at 8M precipitation threshold for potassium carbonate; for all curves p_/ = 0.4 mbar; msRO model assumes ssRO subcomponent of x_ss = 2. Associated vacuum work (~30 kJ/mol) is not included; see Table 1 for estimate of full implementation energies.

Fig. 5A-5B. Results of ion binding model, calculated for various fixed initial alkalinity values. (A) Dependence on initial alkalinity of required work, normalized by e_m to allow for rescaling to physical systems. Associated vacuum work is not included. In the ideal limit, the bicarbonate concentration fully disproportionates and half outgasses as CO2. (B) Dependence on initial alkalinity of the concentration of DIC outgassed as CO2. Curves cross 0 outgassed CO2 at the point where the initial alkalinity equals the final alkalinity. In all cases the final outgassing pressure is set to 0.4 mbar. The ideal limit here is the same as for A.

Fig. 6A-6B. Summary of the alkalinity concentration swing cycle (Fig. 6A) and the cycle with ion selectivity (Fig. 6B). The basic ACS cycle consists of four steps, moving between four states, is depicted in Fig. 6A without ion selectivity and in Fig. 6B with ion selectivity. The steps and states correspond to those described in Figs. 1A and 1 B. In Step 1 2, an alkaline solution, of initial alkalinity, A, that has been equilibrated with atmospheric CO2 at an initial pressure, pi (pi), of is concentrated, removing only water.

In Step 2 3, CO2 is extracted from the concentrated solution, now at a final alkalinity, At, by exposing it to a final pressure, p_å {pi), to drive equilibration via disproportionation of bicarbonate to carbonate and carbon dioxide (2HC03- CO2 (aq)+C03^-2 +H2O). In Step 3 4, water is added, and the solution is diluted back to and, in Step 4 1 , the now CC>2-depleted dilute solution again equilibrates by absorbing atmospheric CO2 at p,. In Fig. 6A, a molecular schematic of the ACS is depicted demonstrating the speciation between bicarbonate, carbonate, and carbon dioxide molecules. Step 2 3, during which disproportionation occurs, corresponds to panel Fig. 1 B. Fig. 6B shows a molecular schematic depicting the enhancement of the ACS due to bicarbonate selectivity.

Fig. 7. Schematic of an ion selective ACS-CDI module that uses an anion exchange membrane to select for bicarbonate ions over carbonate ions as voltage is applied across the two electrodes.

Fig. 8. Schematic of a capacitive deionization module including an anion exchange membrane and a cation exchange membrane and photographs of a working prototype thereof.

Fig. 9. Additional photographs of the capacitive deionization module of Fig. 8. Fig. 10. Current vs time profiles of the capacitive deionization module of Figs. 8-9 during desorption and adsorption.

Fig. 11. A schematic of a system for ACS CO2 capture using a capacitive deionization.

Fig. 12A-12B. Energy and CO2 extracted for ion selective ACS. (A) Required work per mode as a function of the initial alkalinity for varying selectivity factors. (B) The value of CO2 extracted as a function of the initial alkalinity for varying selectivity factors. For both panes, the left dot corresponds to A, = 30 mM and Q = 1 and the right dot corresponds to Ai = 200 mM and 0 = 10, with both at sharing the same energy of 250 kJ/mol.

Fig. 13. Value of CO2 extracted and the membrane selectivity as a function of the initial alkalinity for varying selectivity factors.

Fig. 14. pH as a function of alkalinity for fixed bicarbonate concentrations. pH is plotted as a function of alkalinity along lines of constant bicarbonate concentration, allowing pCC>2 to vary along each line.

Fig. 15. Illustration of experiments to determine the relationship of concentration factor and various features of the process and graph showing how the pH shifts after concentrating alkalinity.

Fig. 16. Graph showing effect of feed concentration on outgassing.

Fig. 17. Illustration of the experimental set-up for measuring outgassing as a function of concentration factor.

Fig. 18. Graph showing the effect of concentration factor on outgassing for 50 mM ad 20 mM alkalinity solutions

Fig. 19. Graph of DICout as a function concentration factor and feed concentration.

Fig. 20. Graph showing the effect of driving pressure on outgassed carbon dioxide amount.

Fig. 21. Graph of DICout (mM) as a function of concentration factor in the presence and absence of 20 mM boric acid.

DETAILED DESCRIPTION OF THE INVENTION

The invention provides methods and systems for direct air capture of carbon dioxide using a new principle

— the Alkalinity Concentration Swing (ACS) — in which direct air capture of carbon dioxide is driven by concentrating an alkaline solution that has been exposed to a source of carbon dioxide (e.g., atmosphere, industrial waste gases, etc.) and loaded with dissolved inorganic carbon. Upon concentration, the partial pressure of carbon dioxide increases, allowing for extraction and compression. The Alkalinity Concentration Swing for direct air capture

Our new approach for direct air capture is based on the recognition that an alkaline aqueous solution containing an air equilibrated concentration of dissolved inorganic carbon (DIC) — the sum of carbonate ion (CO3-²), bicarbonate ion (HCQr), and dissolved aqueous carbon dioxide (C02(aq)) concentrations in solution — will release CO2 to the air when that solution is concentrated. After the same alkaline aqueous solution is diluted, CO2 dissolves from the air and the DIC concentration increases. We use this phenomenon as a core component of the “Alkalinity Concentration Swing” (ACS) cycle for capturing atmospheric CO2. Herein, we describe the basis for this approach and present a set of idealized steps for realizing the ACS.

The equilibrium aqueous carbonate system for varied alkalinity

The concentration of DIC in equilibrium with atmospheric CO2 {pCCk 0.4 mbar; equivalent to roughly 400 ppm) depends on the alkalinity — the molar charge difference between the sum of the conservative cations and that of the conservative anions, i.e., ions whose concentrations do not vary with pH. For simplicity, this work may in places assume alkalinity to be the moles per liter of K⁺ ions, but it will be understood that in such cases, other conservative cations may be used with appropriate adjustments for, e.g., formal charge, atomic/molecular weight, etc. As the alkalinity of the solution increases and equilibrium with air is maintained, the pH increases and the amount of DIC increases, but at a decreasing rate. This is due to the transition of the dominant species of DIC from bicarbonate to carbonate as pH increases above ~9.5. Indeed, in very dilute solutions (alkalinity < 1 c 10² M), the slope of the DIC- alkalinity line is close to unity (Fig. 1 A, inset), where each unit of alkalinity, or conservative cations, is balanced by monovalent bicarbonate ions. At alkalinity > 0.1 M, the slope is closer to 0.5 (Fig. 1 A, main plot) and the charge balance required by this increase in alkalinity is accommodated primarily by the carbonate ion, which is divalent. The DIC to alkalinity relationship follows from carbonate and aqueous chemistry equilibrium relations, as well as the charge-neutrality condition requiring that the excess charge of conservative cations over conservative anions equal the excess charge of non-conservative anions over non-conservative cations. The relative ratios of carbon species in equilibrium is set by the following chemical reactions:

The following system of equations determines the relationship between CO2 partial pressure, alkalinity, and DIC:

Here, A is the alkalinity concentration in units of moles per liter.

DIC concentration is defined as CDIC = [CCh]aq +[HCCh-] + [CO2-³]. At a fixed temperature, K and K2 vary slightly with the ionic strength and hydrostatic pressure of the solution. Across the studied conditions, these effects modestly enhance the efficiency of the ACS, but are neglected in this study for simplicity; equilibrium constants are fixed for pure water conditions at 20°C and 101 .325 kPa: Ki = 9.6 c 10-⁷ M, K2 = 3.4 x 10^-10 M, K_w = 1 x 10-¹⁴ M², and H R = 0.034 M/bar.

The decrease of the ratio of DIC to alkalinity with increasing alkalinity is the principle underlying the ACS. Consider a dilute solution of any strong base initially in equilibrium with air. If that solution is isolated from air and concentrated, for example through the removal of water (e.g., by reverse osmosis), both the DIC and the alkalinity increase linearly in proportion to their relative concentrations in the solution. The DIC of a solution with the same corresponding alkalinity, but maintained in equilibrium with air, increases more slowly than that of the concentrated solution. Thus, the concentrated solution is supersaturated and spontaneously outgasses, which allows for the extraction of CO2. This process is depicted in numerically/graphically Fig. 1A and 1 B, and schematically in Fig. 6A, in which a solution with an initial alkalinity of 10 mM is concentrated by a factor of 100. When the solution reaches 1 M, pCO 2 becomes 40 mbar, which is a hundredfold increase over that in air. When the CO2 outgasses, restoring equilibrium with air, 0.3 moles of DIC per liter of concentrated solution have been captured (Fig.

1 B). Relative to the initial feed solution, 3 mM of CO2 or 35% of the DIC has been outgassed. The Alkalinity Concentration Swing cycle

The following is an idealized description of the ACS based entirely on equilibrium aqueous carbonate assumptions described above. Specific methods for implementing the ACS and associated energetics are also discussed herein. Step 1 2: Concentrating alkalinity

A solution with initial alkalinity Ai is at equilibrium with the atmosphere at a given partial pressure of CO2, pi = 0.4 mbar (State 1). The fraction of carbon species in solution and DIC concentration is set by Ai and pi based on the aqueous carbon chemistry relations described above: CDIC, 1 = C_Dic(Ai,pi). The system is then closed off from exchange with the atmosphere and the solution is concentrated such that the new effective alkalinity and DIC concentrations are increased by a concentration factor, c (Fig. 1 ; Concentrating step). Such a concentrating step does not change the absolute number of alkaline carrier ions or DIC molecules in solution but increases the concentration of both by confining the solutes in a smaller volume. This is equivalent to removing solvent water molecules from solution. The alkalinity and DIC concentrations in the concentrated state are given by: A= Ac and CDIC, 2 CDIC, 1 x, respectively (State 2).

Step 2 3: C0 outgassing

Once the system is in the concentrated state at the higher concentration of alkalinity, A_t, the aqueous CO2 activity increases such that its equilibrium partial pressure rises to p³ (State 2). In engineered systems, CO2 will generally be collected from the concentrated solution by exposing it to a fixed outgassing pressure, p_t that is lower than p³ (which we also refer to as ptmax)·

Exposing the system to pt in the concentrated state drives the following disproportionation reaction:

Outgassing occurs as shown in Fig. 1 A-B. The concentration of DIC outgassed as CO2 with respect to the feed solution as a result of the ACS is given by the following relationship:

The fraction of DIC species outgassed is given by:

The upper limit of f_out is 0.5; it occurs only if the initial DIC is entirely made up of bicarbonate ions, and so the alkalinity to DIC ratio is exactly 1 :1. If such a system is concentrated to a point where the DIC equilibrium shifts essentially entirely to carbonate at high alkalinity, in the 2:1 alkalinity to DIC regime, then half of the bicarbonate ions are converted to carbonate ions, and the other half become carbon dioxide molecules, which may be collected. In practice, the alkalinity to DIC ratio will fall between 1 and 2.

The maximum pressure at which outgassed CO2 can be removed from the system is also of interest. Over the range of initial alkalinity between 10⁴ and 10 M, the outgassing pressure limit is independent of initial alkalinity and is a direct relationship between the concentrating factor, c, and the initial pressure, pi, given by:

Step 2®3 is concluded once the system has reached its new equilibrium point at A_t and p_t, setting a DIC concentration of CDIC, 3 (State 3).

Step 3 4: Diluting alkalinity

The next step of the ACS involves returning the concentrated alkalinity, A_t, to its initial value. This can be done by recombining the concentrated solution with the removed water from Step 1 ®2. Alkalinity is diluted by a factor of 1 /c to A , and DIC is diluted by the same factor giving CDIC, 4 = CDIC, 3 /c (State 4).

Step 4 1 : Absorption of atmospheric C0

The final step, which returns the system to State 1 , exposes the solution to the atmosphere. Absorption occurs because the dilution step has created a condition with less DIC relative to the concentration in equilibrium with the atmosphere. CO2 is consumed via the comproportionation reaction: CCk{aq) + CO₃- ² + H2O ® 2HCO₃- (or, the reverse of disproportionation). Step 4®1 is concluded once the system returns to its equilibrium point at A , and p ,. Steps 3®4 and 4®1 can occur simultaneously, in principle, as can Steps 1 ®2 and 2®3.

C0₂ Outgassed from the ACS

For a given temperature, the exact choices of parameters for the initial and final alkalinity values, as well as initial and final CO2 partial pressures, uniquely determine the outputs of the ACS. Whereas the initial pressure is set by the concentration of atmospheric CO2, the outgassing pressure is a design parameter that should be set based on considerations relating to energy, rate, and water requirements. For the purposes of discussion herein, we fix the outgassing pressure at p f = 0.4 mbar. The energetic considerations of the outgassing pressure are discussed briefly herein and will be the subject of future studies.

Fig. 2 plots the result of the ACS for a fixed atmospheric and outgassing partial pressures of CO2 over a range of initial alkalinity values. The concentration factor specifies the concentration (C_oui; Equation 9) and fraction ( f_out Equation 10) of DIC outgassed as CO2. Outgassing purity thresholds are calculated based on partial pressures of other atmospheric gases (N2, O2, A_r); higher concentration factors yield higher CO2 purity. In general, higher initial alkalinity values for the same concentration factor yield larger total outgassing values. The fraction of DIC outgassed exhibits a more complicated relationship with concentration factor. The lower the initial alkalinity, the higher the outgassed fraction can be (with an absolute limit at 0.5); the limiting regime is set when all DIC is in bicarbonate form and entirely disproportionates. As given by Equation 11 , the maximum outgassing pressure is set only by the concentration factor, invariant of the initial alkalinity. Increasing the concentration factor therefore increases the difference between the outgassing pressure (pi) and the partial pressure of the solution in the concentrated state (/¾), which corresponds to higher absorption rates. Table 1 lists output values for different representative ACS input parameters.

Implementing the ACS

The primary energy-consuming driving mechanism behind the ACS can be separated into two components: 1) a process to concentrate solutes in water, and 2) applying pressure for outgassing of CO2 from solution (Fig. 3A). The remaining components, diluting alkalinity and absorbing CO2, do not consume energy but are critical for evaluating water and contacting area requirements.

In principle, any desalination method, which produces purified water, can also be used to concentrate a stream of solute-filled solution. Desalination methods, for this reason, are candidate drivers for the ACS; they can be based on the following mechanisms: reverse osmosis (RO) (see, e.g., C. Fritzmann, J. Lowenberg, T. Wintgens and T. Melin, Desalination, 2007, 216, 1 - 76 and M. Elimelech and W. A. Phillip, Science, 2011 , 333, 712 - 717), capacitive deionization (CDI) (see, e.g., M. E. Suss, S. Porada, X. Sun,

P. M. Biesheuvel, J. Yoon and V. Presser, Energy & Environmental Science, 2015, 8, 2296 - 2319.), electrodialysis (see, e.g., S. Al-Amshawee, M. Y. B. M. Yunus, A. A. M. Azoddein, D. G. Hassell, I. H. Dakhil and H. A. Hasan, Chemical Engineering Journal, 2020, 380, 122231 .), evaporation and distillation (see, e.g., A. Alkhudhiri, N. Darwish and N. Hilal, Desalination, 2012, 287, 2 - 18, or, e.g., M. M. A. Raj, K. K. Murugavel, T. Rajaseenivasan and K. Srithar, Desalination and Water Treatment, 2016, 57, 13462 - 13471), precipitation (see, e.g., Y. Shi, C. Zhang, R. Li, S. Zhuo, Y. Jin, L. Shi, S. Hong, J. Chang, C. Ong and P. Wang, Environmental Science & Technology, 2018, 52, 11822 - 11830), and solvent solubility (see, e.g., C. Boo, R. K. Winton, K. M. Conway and N. Y. Yip, Environmental Science & Technology Letters, 2019, 6, 359 - 364). In this study, RO and CDI are considered for implementing the ACS, serving as a comparison between pressure driven and electric field driven approaches (see, e.g., S. Lin, Environmental Science & Technology, 2019). Energetics of the ACS process using these two processes as examples are also discussed herein.

RO is a membrane-based separation process in which pressure is applied against a solvent-filled solution, overcoming the osmotic pressure of the solution, to create a concentrated and a dilute stream (Fig. 3B). RO methods can be applied to brackish (low salinity) waters and wastewater processing with more dilute solutions but are most commonly applied to seawater desalination. This application of RO is in broad commercial use, producing roughly 100 million cubic meters of purified water per day in 2018. Seawater desalination plants are typically designed to produce a stream of freshwater from an input feed of about 0.6 M of NaCI equivalent salt, yielding a concentrate output of roughly double the original salinity. In general, the RO process can be adapted to a broader range of initial salinities and higher overall concentration factors that may be desirable to achieve more optimal ACS output.

Existing technological developments and future prospects make RO an appealing candidate for implementing the ACS. For example, the development of energy recovery devices (ERDs) was crucial in reducing the power consumption of desalination to its current level. ERDs use the remaining energy stored in the pressure of the concentrate, which otherwise would be wasted, to apply part of the necessary pressure to the feed. One significant difference between an ACS process and desalination is that in the ACS, after CO2 has been extracted, the concentrated and diluted solution are recombined. It is therefore possible to recover some of the energy held in the salinity gradient between the concentrated and dilute streams through forward osmosis.

Another approach to the concentration step for ACS is CDI, which is a method of concentrating and removing anions and cations from solution by applying a voltage across two electrodes and creating an electric double layer made up of electrolyte ions (Fig. 3C). When voltage is applied (<1 .2 V to avoid splitting water), anions “electrosorb” to the positive electrode and cations to the negative electrode. When the voltage is switched off or reversed, the concentration of ions in the electrode pores and in the fluid between the electrodes sets the output concentration of a higher-alkalinity solution, driving the concentration step of the ACS. The material properties of the electrode (surface area, porosity, surface chemical groups, etc.) and the geometry constrain the overall capacity, rates, and energies of deionization. To increase efficiency, ion exchange membranes can be placed between the feed solution channel and the electrode material, in which case the process is called membrane CDI (MCDI).

Whatever approach is used to concentrate the alkaline solution, CO2 can be extracted from the concentrate stream by exposing it to a vacuum or a carrier gas. This can be done through a variety of standard methods in chemical engineering including vacuum pumps, or by making use of water vapor or another condensable gas (e.g., helium, argon, nitrogen, etc.). This outgassing process may be enhanced through the use of liquid-gas exchange membranes (see, e.g., H. D. Willauer, D. R. Hardy, M. K. Lewis,

E. C. Ndubizu and F. W. Williams, Energy & Fuels, 2009, 23, 1770 - 1774, or, e.g., D. Bhaumik, S. Majumdar, Q. Fan and K. K. Sirkar, Journal of Membrane Science, 2004, 235, 31 - 41 ), which create a gas-permeable barrier between gas and liquid phases and allow for CO2 extraction.

Once CO2 is extracted from solution, the concentrated and dilute streams may be combined, thereby diluting alkalinity to its initial concentration. At this point, the solution has less DIC relative to alkalinity than it would have at atmospheric conditions. Exposing this solution to the atmosphere will initiate an equilibration process of CO2 absorption. While not precluded, air-liquid contactors, which increase the surface area of solution and use fans to increase exposure to air, are likely to be ineffective as a result of slow absorption kinetics due to the relatively low hydroxide ion concentrations typically associated with ACS conditions. Preferably, the invention may use large contacting reservoirs, potentially with mechanisms to enhance convective mixing. The kinetics of gaseous CO2 absorbing into water and reacting with hydroxide ions to form bicarbonate ions is the rate limiting step in the absorption process. Overall, absorption rate increases with the square root for higher hydroxide concentrations (e.g., solutions with higher pH) and linearly for higher air-liquid surface area. Herein, we use an approximated absorption rate to estimate the water on hand requirement for an ACS system given a certain facility water processing rate. The absorption time scale sets the duration that processed water needs to reside in the reservoir to reload DIC back into solution, and thus sets the total amount of water needed in the reservoir to operate the system in a continuous manner.

In Example 1 , we discuss the energy requirements of the ACS including the work associated with CO2 extraction. We introduce two simple energy models to explore ACS energy trade-offs, referencing a range of energy values based on reported values from RO and CDI systems.

In methods of the invention, an alkaline solution including dissolved carbon dioxide is provided. The alkaline solution may be sourced from a natural source (e.g., a natural pool or lake having pH greater than 7) or an industrial source (e.g., an industrial waste stream or pool). The alkaline solution may already have dissolved carbon dioxide; or may be contacted with a mixture of gases containing carbon dioxide, e.g., atmosphere or an industrial waste gas output, to dissolve carbon dioxide.

The alkaline solution containing carbon dioxide is then concentrated, e.g., by reverse osmosis (RO), capacitive deionization (CDI) (e.g., membrane capacity deionization, MCDI), electrodialysis, evaporation and distillation, precipitation, solvent solubility, etc.

The concentrated solution, now having a higher partial pressure of carbon dioxide than the original solution, is then ready for extracting dissolved carbon dioxide. Extracting the carbon dioxide may involve exposing the concentrated solution to a low-pressure environment (e.g., applying vacuum), or a flow of carrier gas (e.g., water vapor (e.g., steam), helium, argon, nitrogen, etc.).

The alkaline solution may be concentrated by a concentration factor (c) of, e.g., from about 2 to about 1000, e.g., about 2-10, about 5-50, about 10-100, about 10-20, about 30-60, about 50-100, about 60-80, about 75-100, about 100-200, about 100-1000, about 100-500, about 150-450, about 300-600, about 500-750, about 600-1000, about 700-900, or about 800-1000, e.g., about 2, 3, 4, 5, 10, 15, 20, 25, 30, 40, 50, 100, 150, 200, 300, 500, or 1000.

The alkalinity of the alkaline solution after concentrating may be from, e.g., about 0.1 M to about 10 M, e.g., about 0.1 -1 M, about 0.5-1 M, about 0.2-0.6 M, about 0.25-0.5 M, about 0.5-0.75 M, about 0.8-1 .2 M, about 0.6-0.9 M, about 1 -2 M, about 1 .5-2.5 M, about 1 -5 M, about 2-4 M, about 3-6 M, about 4-8 M, about 5-10 M, about 6-9 M, about 2.5-7.5 M, about 7-9 M, about 6-8 M, about 7.5-10 M, or about 9-10 M, e.g., about 0.1 M, 0.15 M, 0.25 M, about 0.5 M, about 0.75 M, about 1 M, about 2, 3, 4, 5, 6, 7, 8, 9, or 10 M.

The alkaline solution may have an initial alkalinity of, e.g., from about 1 mM to about 5000 mM, e.g., about 1 to 2 mM, about 2 to 3 mM, about 3 to 4 mM, about 4 to 5 mM, about 5 to 6 mM, about 6 to 7 mM, about 7 to 8 mM, about 8 to 9 mM, about 9 to 10 mM, about 2 to 5 mM, about 5 to 10 mM, about 10 to 15 mM, about 10 to 20 mM, about 10 to 50 mM, about 25 to 50 mM, about 30 to 40 mM, about 40 to 50 mM, about 50 to 60 mM, about 50 to 100 mM, about 60 to 70 mM, about 60 to 90 mM, about 70 to 80 mM, about 75 to 100 mM, about 80 to 90 mM, about 90 to 100 mM, about 80 to 110 mM, about 90 to 120 mM, about 100 to 200 mM, about 200 to 300 mM, about 300 to 400 mM, about 400 to 500 mM, about 500 to 600 mM, about 600 to 700 mM, about 700 to 800 mM, about 800 to 900 mM, about 900 to 1000 mM, about 100 to 125 mM, about 125 to 250 mM, about 200 to 400 mM, about 250 to 500 mM, about 300 to 600 mM, about 400 to 800 mM, about 500 to 1000 mM, about 500 to 750 mM, about 600 to 900 mM, about 750 to 1000 mM, about 850 to 950 mM, about 950 to 1000 mM, e.g., about 1000 to 5000 mM, e.g., about 1100 to 1200 mM, about 1200 to 1300 mM, about 1300 to 1400 mM, about 1400 to 1500 mM, about 1500 to 1600 mM, about 1600 to 1700 mM, about 1700 to 1800 mM, about 1800 to 1900 mM, about 1900 to 2000 mM, about 1100 to 1125 mM, about 1250 to 2500 mM, about 2000 to 2400 mM, about 2250 to 2500 mM, about 2300 to 2600 mM, about 2400 to 2800 mM, about 2500 to 3000 mM, about 2500 to 2750 mM, about 2600 to 2900 mM, about 2750 to 3000 mM, about 2850 to 2950 mM, about 2950 to 3000 mM, about 3100 to 3200 mM, about 3200 to 3300 mM, about 3300 to 3400 mM, about 3400 to 3500 mM, about 3500 to 3600 mM, about 3600 to 3700 mM, about 3700 to 3800 mM, about 3800 to 3900 mM, about 3900 to 4000 mM, about 4100 to 4250 mM, about 4250 to 4500 mM, about 4200 to 4400 mM, about 4250 to 5000 mM, about 4300 to 4600 mM, about 4400 to 4800 mM, about 4500 to 5000 mM, about 4500 to 4750 mM, about 4600 to 4900 mM, about 4750 to 5000 mM, about 4850 to 4950 mM, or about 4950 to 5000 mM, e.g., about 1000 mM, about 2000 mM, about 2500 mM, about 3000 mM, about 3500 mM, about 4000 mM, about 4500 mM, or about 5000 mM.

The alkaline solution may have an initial pH of, e.g., 7-14, e.g., about 7-8, about 8-9, or about 9-10, about 9-11 , about 10-11 , about 10-12, about 11 -12, about 12-13, about 11 -13, about 12-14, or greater than 14, e.g., about 7.5, about 7.8, about 8, about 8.2, about 8.5, about 9, about 9.5, about 10, about 10.5, about 11 , about 11 .5, about 12, e.g., about 7.1 , about 7.2, about 7.5, about 7.8, about 8, about 8.2, about 8.5, about 9, about 9.5, about 10, about 10.5, about 11 , about 11 .5, or about 12.

The alkaline solution may have a pH after concentration and outgassing of, e.g., 7-14, e.g., about 7-8, about 8-9, about 9-10, about 8-10, about 9-11 , about 10-11 , about 10-12, about 11 -12, about 12-13, about 11 -13, about 12-14, or greater than 14, e.g., about 7.5, about 7.8, about 8, about 8.2, about 8.5, about 9, about 9.5, about 10, about 10.5, about 11 , about 11 .5, about 12, about 12.5, about 13, about 13.5, or about 14. In some embodiments, methods of the invention may further include diluting (e.g., to the original alkalinity) the concentrated solution and repeating steps the concentration, capture, and extraction steps with the diluted solution.

The carbon dioxide extracted from the concentrated solution may be collected, e.g., directly (e.g., when low pressure extraction is used), or, e.g., using gas separation techniques, e.g., condensation, membrane separation, adsorption (e.g., on solid supports), etc. Collected carbon dioxide may be stored, e.g., under pressure, or by geological sequestration.

The systems and methods of the invention may be enhanced by the inclusion of a weak base and/or weak acid in the alkaline solution. A weak acid or weak base may be monoprotic (or monobasic) or polyprotic (or polybasic). Suitable weak acids may include, boric acid, organic acids (e.g., methanoic acid, ethanoic acid, propanoic acid, phenols, etc.), ammonium salts (e.g., ammonium chloride), phosphoric acid, and hydrogen and dihydrogen phosphate, etc. Suitable weak bases include hydrogen borate, dihydrogen borate, phosphates, amines (e.g., ammonia, methylamine, ethylamine, triethylamine, etc.), and guanidines (e.g., guanidine). In particular embodiments, the weak acid is boric acid. Amino acids (e.g., 2-piperazinecarboxylic acid, asparagine, aspartic acid, glycine, leucine, lysine, proline, sarcosine, serine and valine) may also be suitable weak acids or weak bases, depending on their isoelectric point and the presence of other acids and bases in the solution. Amphoteric compounds may also be suitable, e.g., amphoteric metal oxides or hydroxides (e.g., aluminum oxide/hydroxide). The systems and methods may include polyols (e.g., diols, triols (e.g., glycerol), tetrols, etc., e.g., sugar alcohols, e.g., mannitol, maltitol, sorbitol, etc.) in the alkaline solution.

Exemplary concentration methods include reverse osmosis and capacitive deionization. When capacitive deionization is used, it may be membrane capacitive deionization (MCDI), which allows for ion-selective capacitive deionization (see, e.g., Figs. 7-11). Fig. 7 demonstrates capacitive deionization where the positive and negative electrodes are separated from the feed (e.g., the original/diluted alkaline solution) by, respectively, an anion exchange membrane and a cation exchange membrane. In Fig. 7 bicarbonate ions and alkalinity carrier cationic counterions (e.g., K⁺ ions) are captured by electro-adsorption when the electrodes are polarized, while the carbonate dianions and their respective counterions are allowed to pass. On depolarization of the electrodes, the bicarbonate ions and their counterions are released. By retaining bicarbonate ions over carbonate ions, methods and systems of the invention may enhance the overall efficiency of the direct air capture process (Example 2).

Capacitive deionization or reverse osmosis may be performed using ion exchange membranes (e.g., anion exchange membranes and cation exchange membranes) may include, e.g., ionomers, e.g., polymers containing anionic groups (e.g., polysulfonated fluoropolymers, e.g., NAFION®, e.g., as cation exchange membranes) or polymers containing cationic groups (e.g., polymers containing a plurality of tertiary ammonium groups, e.g., as anion exchange membranes). Bipolar membranes (e.g., FUMASEP® FBM) may include both polyanionic and polycationic ionomers. Membranes may include polymers with hydrocarbon or fluorocarbon repeat units, or both. Membranes may be inorganic, e.g., including graphene, oxides (e.g., metal or semimetal oxides), silicates (e.g., metal or semimetal silicates), nitrides (e.g., metal or semimetal oxides), etc. Membranes such as described herein may also be used to concentrate the alkaline solution by other means, e.g., by reverse osmosis or electrodialysis.

Electrodes suitable for use in methods of the invention (e.g., separation by capacitive deionization or electrodialysis) may include any conductive material that is chemically inert to the alkaline solutions under operating conditions of the methods. Examples include carbon electrodes, e.g., glassy carbon electrodes, carbon paper electrodes, carbon felt electrodes, or carbon nanotube electrodes. Other suitable electrodes may include metals, e.g., any metal that is chemically stable to components of the redox solutions (e.g., acids, bases, salts, and redox active species), examples include noble metals (e.g., gold, silver, iridium, platinum, etc.). Depending on the alkaline solutions, non-noble metals may also be suitable. Titanium electrodes may also be employed. Electrodes can also be made of a high specific surface area conducting material, such as a nanoporous metal sponge. Electrodes may be porous structures into which the alkaline solution (or ions of alkaline solution that have passed through ion exchange membranes) can enter or flow.

Systems of the invention may include a reservoir (e.g., a pool, e.g., a natural pool, pond, lake, etc., or industrial pool, tank, vat, etc.) for an alkaline solution. The pool has a gas inlet and means for concentrating the solution (e.g., a system of pumps, high surface area flow surfaces, mixing devices, membranes (e.g., for reverse osmosis, electrodialysis, capacitive deionization, etc.), electrodes (e.g., for capacitive deionization, electrodialysis, etc.), pressure gauges, valves, pH sensors, etc.). Systems may also include means for dilution of the concentrated solution, e.g., pumps, additional pools, a source of water, etc.

We have found that higher concentration factors result in proportionally higher outgassing pressure, and higher initial alkalinity concentrations at the same concentration factor outgas a higher concentration of CO2 relative to the feed solution. We examined two desalination technologies, reverse osmosis and capacitive deionization, as possible implementation for the ACS, and evaluated two simplified corresponding energy models. We compared the ACS to incumbent technologies and make estimates on water, land, and energy requirements for capturing one million tonnes of C0₂ per year. We found that estimates for the lower end of the energy range for both reverse osmosis and capacitive deionization approaches are lower than or roughly equal to incumbent direct air capture approaches. For most conditions, we found an inverse relationship between the required energy and water processing volume per million tonnes of C0₂.

Realizing the ACS requires a simple alkaline aqueous solvent (e.g., potassium alkalinity carrier) and does not require heat as a driving mechanism. More generally, the ACS can be implemented through industrial-scale desalination approaches, meaning current technology could be leveraged for scale-up. Examples

We describe a new DAC approach that is based on taking a dilute alkaline aqueous solution that has equilibrated with air, and concentrating it. Concentrating the alkalinity and the dissolved carbon increases the partial pressure of CO2 in the solution and allows for CO2 outgassing and extraction. We describe the chemical cycle underlying this approach, evaluate the thermodynamics of the process, and examine two commercially available technologies that are traditionally used for desalination, reverse osmosis and capacitive deionization, to drive the cycle. We then compare the potential advantages of this approach relative to other existing DAC methods and analyze its scale-up feasibility.

The invention will be further described by the following non-limiting examples.

Example 1 - Comparison of RO and CDI and Evaluation of ACS vs Other DAC Processes ACS thermodynamics and energy models

The process of concentrating ions in aqueous solution can be achieved, in general, by doing work to either confine ions to a smaller volume or to selectively remove water molecules from solution. Whereas the fundamental thermodynamic limit for the work required by a concentrating process is set by the entropic difference between the input and output streams, the particular mechanism for concentrating determines the additional associated dissipated energy.

This section describes the thermodynamic minimum work of the ACS, discusses the energy requirements associated with vacuum outgassing, and explores two high-level frameworks for evaluating the energetics of concentrating ions in solution to achieve Step 1 2 of the ACS. Two simplified energy models are proposed, one based on energy associated with reverse osmosis and another based on energy of binding ions in solution. Reverse osmosis and capacitive deionization are discussed as possible implementations of systems capable of concentrating ions to drive the ACS.

Irrespective of the particular concentrating mechanism, it is possible to set a thermodynamic limit on the ACS given an input and output partial pressure of CO2. If the ACS cycle takes an input partial pressure of CO2, i, and outgasses at a limiting output pressure of pt,max, the thermodynamic minimum work per mole CO2 is given by: wu_m = RTIn(p_f,max/pi), as long as it behaves as an ideal gas. Using carbonate chemistry assumptions (based on Equation 11), we rewrite the thermodynamic minimum work expression in terms of the concentration factor, c, as: wn_m = RTln(x) (12)

Work Needed for CO₂ Extraction from An Aqueous Solution The nature of the ACS is such that the CO2 partial pressure limit in the concentrated state over the parameter range of interest (alkalinity between 10 - 4 to 10 M) is essentially proportional to the concentration factor (Equation 11 ). In order to extract CO2 out of the concentrated solution, a CO2 partial pressure that is less than p _max must be chosen. If the concentration factor is lower than -2500, a vacuum could be applied to the solution to extract CO2, or the headspace could be filled with a separable carrier gas. For simplicity we analyze the application of vacuum. The thermodynamic minimum work needed to establish a vacuum at p_/to permit CO2 outgassing isothermally is w_{va ,min} = RTIn(po/p_f ), where po = 1 bar; if p _/ = 0.4 mbar, then the minimum work is 19.1 kJ/molCC>2 (abbreviated as kJ/mol whenever referring to moles of CO2). However, real physical systems incur additional losses from dissipation. Industrial vacuum pumps have process efficiencies in the range of 65-85% (J. Wilcox, Carbon Capture, Springer, 2012). There is a trade-off between the work needed to concentrate the feed solution and the work needed to establish a vacuum for extracting CO2 from solution. In this study, the work needed to establish the vacuum is held constant because we have chosen to fix the outgassing pressure, p_/, at 0.4 mbar, and subsequently bring the outgassed CO2 gas to 1 bar. Assuming an efficiency of h = 70% yields an additional work of w_vac = w_vac,min/n ~ 30 kJ/mol. The trade-off that emerges from varying the outgassing pressure is a subject for future study.

Finally, because we assume the thermodynamic limit of isothermal compression, there is no additional required work to compress water vapor. Assuming it begins at its equilibrium vapor pressure at 20°C of 40 mbar, it precipitates during isothermal compression with no additional work, and its partial pressure remains at 40 mbar as the CO2 is compressed to a partial pressure of 1 bar.

Reverse Osmosis-Driven ACS

Energy Model

We first pose a model for the work required to concentrate a solution through confining ions to a smaller volume. For an aqueous solution, when entropic effects are dominant, the relevant macroscopic state variables that determine free energy as the solution is concentrated and diluted are the osmotic pressure and concentration. The change in these state variables through the ACS sets the work necessary to concentrate the feed solution so that CO2 can be extracted.

In this “RO model,” we assume an idealized ion concentrating RO system in which water is driven through a perfectly selective semi-permeable membrane that blocks all non-water molecules. Given dilute conditions, the osmotic pressure (P) across the membrane is determined by the Van’t Hoff approximation to be proportional to the solute concentration in the reference solution: P = RTC. Here, C refers to the sum of the total solute concentrations, accounting for anions, cations, and non-charged molecules (e.g., [K⁺], [C0₂]aq, [HCO3-], [CO3-²]).

The following known effects are neglected in this model: interactions of ions in solution, entropic contribution based on the differentiation between solute species, partitioning of DIC species as the system is concentrated and diluted, and any membrane-specific effects, such as concentration polarization (C. Fritzmann, J. Lowenberg, T. Wintgens and T. Melin, Desalination, 2007, 216, 1 - 76; S. Sablani, M. Goosen, R. Al-Belushi and M. Wilf, Desalination, 2001 , 141 , 269 - 289; M; Qin, A. Deshmukh, R. Epsztein, S. K. Patel, O. M. Owoseni, W. S. Walker and M. Elimelech, Desalination, 2019, 455, 100 - 114). The ideal RO work per mole of concentrated CO2 for a reversible process with no dissipation is: HO M in — RT{Cj / C ont } I ft ( % ) (13)

Where C, = A , +CDIC (A,, pi), c is the concentration factor, and Cout is the concentration of outgassed CO2 calculated from carbonate equilibrium assumptions. The logarithmic scaling with c requires significantly less work at lower initial alkalinities (see Fig. 4A). Physical systems approach this bound if the driving pressure is varied so as to be minimized throughout the entire concentration process.

A “single-stage” RO (ssRO) mode is driven by a single, fixed applied pressure throughout the concentrating process. Because we assume a perfectly selective membrane, the choice of the applied pressure is set only by the maximum concentration in the concentrated state. A single-stage system is simpler to construct but has higher energy dissipation because the applied pressure is substantially greater than the counteracting osmotic pressure in the early phase of the concentrating process. The work per mole in the ssRO process is given by:

We include a_ss (³ 1) as a scalable parameter to account for additional dissipation in physical RO systems; in the limiting case for ssRO, a_ss = 1 . A “multi-stage” RO (msRO) process is made up of a series of ssRO modules. Instead of setting one driving pressure for the entire process, multiple driving pressures are chosen in order to reduce dissipation. If each ssRO subcomponent has an associated concentration factor of x_ss, the work per mole of CO2 is then:

Here, c is still the overall concentration factor of the entire msRO system. We use the log scaling as a simplification, even though physical systems would typically be constructed from discrete single-stage modules and thus would more closely be expressed mathematically through a summation series. Fig. 4A compares the energy cost of the ssRO, msRO, and ideal models at a single representative input alkalinity value (10 mM) over a range of concentration factors, normalized by the a_ss parameter. In the ssRO case, energy cost rapidly increases with concentration factor. In contrast, the msRO model, at the same initial alkalinity, is significantly more energetically favorable at high concentration factors than ssRO. The results of the msRO model are reported in Fig. 4B for various initial alkalinity values. The low initial alkalinity condition (1 mM) exhibits non-monotonic behavior, with a minimum around concentration factor of 100.

Technological implementation

RO technology can be implemented to drive the ACS by applying pressure to selectively pass water through a semi-permeable membrane, thereby concentrating the remaining solution. RO systems can operate across a wide range of concentrations, but have been most technologically tailored for seawater conditions, and tend to be tuned around producing a low-concentration, potable solution, rather than optimizing the concentrate parameters.

Typical seawater RO (SWRO) systems operate at around 80 bar and recover 50% by volume of the saline feed (roughly 0.6 M of NaCI equivalent or 35 g/L) as freshwater. For the purposes of the ACS, concentrating 0.6 M of input alkalinity by a factor of 2 outgasses 13 mM of CO2 relative to the feed. We relate the energy cost of actual RO facilities to the theoretical ssRO work of 0.78 kWh per cubic meter of feed solution (typically reported as 1 .56 kWh per cubic meter of freshwater), by evaluating the parameter ot_ss (the ideal RO work is 0.53 kWh per cubic meter of feed solution, or 1 .06 kWh per cubic meter of freshwater). Current energies of medium to large capacity industrial SWRO systems usually range from 1 .1 to 1 .25 kWh per cubic meter of feed (i.e., a_ss ranging between approximately 1 .4 and 1 .6), with newer facilities regularly achieving lower than 1 .0 kWh per cubic meter of feed ( a_ss < 1.3).

Brackish water RO tends to operate at lower salinities, typically 5-200 mM of NaCI equivalent. For the ACS at a concentration factor of 10, an initial alkalinity of 10 mM or 100 mM yields 1 .9 mM or 11 mM, respectively, of extracted CO2 (Fig. 2A). Currently deployed brackish water systems tend to be less efficient than seawater RO systems, although they have the capacity of having a much lower required energy — below 1 kWh per cubic meter of feed. For example, one industrial system that takes an input feed of 0.075 M NaCI equivalent with a concentration factor of 2 requires 0.445 kWh per cubic meter of feed ( ct_ss = 5.2); another industrial system, which takes 0.063 M of NaCI equivalent feed with a concentration factor of 4 requires 0.825 kWh per cubic meter of feed ( a_ss = 3.75). Initial concentrations below 10 mM (such as 1 mM in Fig. 4) are not considered in this analysis because a_ss values are not reliably reported at such dilute conditions.

Detailed modelling studies have looked at how much industrial brackish water systems can be further optimized through the use of energy recovery devices and by tuning operating conditions. One simulation study reports 0.48 kWh per cubic meter of feed, given 0.25 M NaCI equivalent feed and concentration factor of 2.5 ( a_ss = 1 .1 ). Another detailed modelling study reports 0.30 kWh per cubic meter of feed, given 0.25 M NaCI equivalent feed and a concentration factor of 5 ( a_ss = 1 .2).

The significantly smaller values of a_ss from detailed modeling results compared to those for deployed industrial systems indicate that industrial brackish water systems can approach seawater systems in terms of energetic efficiency through straightforward modifications. The improvement in a_ss values is seen for systems with concentration factors ranging from about 2 to 5, suggesting that efficiency improvements could be applied to a wide range of system designs.

Although we rely on demonstrated RO systems to estimate the work required for driving the ACS, there are significant differences between ACS and desalination applications that must be considered. For example, brackish and seawater desalination must account for a complex variety of naturally occurring salt ion species and foulants present in seawater, which would not in general be the case in engineered ACS systems. On the other hand, RO membranes are not designed to be used for gas extraction and separating gases during the desalination process, which suggests further engineering modifications must be explored. Moreover, increased hydrostatic pressure as a result of the RO process modestly affects the carbonate equilibrium constants that are at the core of the ACS approach.

Ion binding-driven ACS

Energy model

Second, the invention considers a model for the work required to selectively remove water molecules from solution. This idealized “ion binding model" assumes that the energy to concentrate is dominated by enthalpic interactions, where a characteristic energy is associated with binding ions in solution, rather than entropic effects as assumed in the RO model. For a reversible ion adsorption process, the energy of binding ions from a feed solution and then releasing them into a concentrated stream sets the work necessary to concentrate the feed solution.

Flere, a constant electrical energy cost associated with binding an ion of a given charge out of the feed solution is independent of the concentration of ions found in the feed solution. Assuming a value, e,·_0h, for the energy cost to bind a pair composed of a monovalent anion and a monovalent cation, and which is doubled for a pair of divalent ions (2e,_oh). This constant energy relationship may be observed when the selection mechanism applies charge or electric fields to do work on ions, rather than the uncharged water molecules of the solution, as in the RO energy model.

Such a model significantly simplifies physical effects as it neglects the following: ion-specific differences in binding energy, increasing binding energy as a function of number of bound ions, additional energy cost or energy recovered from unbinding the ion, including the concentration of the solution into which the ion is unbound, and entropic and electrostatic effects of confining ions to different concentrations. In general, entropic factors imply that the work to bind ions should depend at least weakly on solution concentration, and electrostatic factors imply that binding energy per ion will increase above some density of bound ions. Additionally, divalent ions may have different binding energies than pairs of monovalent ions, due to both entropic and enthalpic effects.

Nonetheless, the application of this formulation to the ACS allows us to evaluate the associated scaling relation of electrical work given initial and final alkalinities and partial pressures of CO2. The result of the model is that the required work, per unit volume, to concentrate the feed stream, assuming monovalent cations and bicarbonate and carbonate anions, is then directly proportional to the concentration of ion charges in solution. The binding energy per mole of ions is given by setting e_m = e_«,_pN_A, where NA is Avogadro’s number. The charge concentration is then set by the alkalinity, so the total binding energy per volume and per mole is given by e_mAi. The work per mole of outgassed CO2 is then:

In Fig. 5A shows the required work in the ion binding model per mole of CO2 vs. initial alkalinity for various final alkalinity values at an outgassing pressure of 0.4 mbar (a constant vacuum energy value must be added to compare the total necessary work). This type of plot is more useful to assess the ion binding model than plotting work vs. concentration factor, as in Fig. 4A and 4B, because the physical and geometric properties of an ion-binding device are likely to set a constraint on the final alkalinity rather than the concentration factor. The minimum work per mole of outgassed CO2 is reached at the limit in which the feed stream of DIC consists entirely of bicarbonate ions at low alkalinity. The “ideal limit” indicates the limit in which, at high alkalinity, all of the bicarbonate ions disproportionate to carbonate ions and CO2 (Equation 8) and a maximum of 50% conversion is reached. At this limit the work is 2/e_m because two alkalinity carrier ions are bound for each CO2 molecule outgassed.

For any initial alkalinity, Fig. 5B shows that the higher the final alkalinity, the higher is the CDIC outgassed as CO2 and the lower is the energy per mole of outgassed CO2. In the context of this model, it is optimal to concentrate as much as physically possible as it does not penalize higher concentration factors. Whereas energy efficiency is best for lower initial alkalinity values, the input stream CDIC is also accordingly low, which means more water handling is required per mole of outgassed CO2.

Fig. 5B shows that, for a given value of the final alkalinity, the total DIC outgassed as CO2 as a function of initial alkalinity exhibits a peak. This occurs because higher initial alkalinities hold higher DIC but, as the initial alkalinity approaches the final alkalinity value, a smaller fraction of that DIC is converted to CO2 and outgassed. This peak represents a further trade-off between outgassing concentration and outgassing energy built into the ACS as a result of the behavior of the carbonate system. Technology implementation

CDI technology can be implemented to drive the ACS by using electric fields to do work on ions at approximately a constant energy cost per ion. CDI systems tend to operate best in or just below brackish water salinities, with salt concentrations typically in the 5-200 mM range (M. E. Suss, S. Porada, X. Sun,

P. M. Biesheuvel, J. Yoon and V. Presser, Energy & Environmental Science, 2015, 8, 2296 - 2319).

Specifically, Zhao et al. (R. Zhao, P. M. Biesheuvel and A. v. d. Wal, Energy & Environmental Science, 2012, 5, 9520 - 9527) showed experimentally that MCDI technology, which makes use of ion exchange membranes placed between the feed solution channel and the electrode, can operate at a value of e,_oh that is nearly independent of concentration. This occurs under constant current conditions over the entirety of the brackish water range, from 10-200 mM of NaCI. In this study, as in the ion binding model, this energy is also independent of the ion concentration in the concentrate stream. These results justify applying the ion binding model to ACS-CDI systems as a first-order study of energy scaling.

The values from MCDI studies are optimized given a condition on dilute stream purity, which, in the case of the ACS, unlike desalination, is not a relevant optimization target. In a limiting case, an excess of feed solution could be passed by the electrodes such that the dilute stream alkalinity is essentially the same as the feed.

The potential to decrease e;_oh for differing solution optimization targets is an important subject for future studies.

Qin et at. describe existing CDI systems that are capable (for a 30 mM salt feed stream) of recovering 95% of the water while rejecting 90% of the incoming salt, producing a final alkalinity of 500 mM. Suss et at. state that CDI can achieve 50% water recovery for sea water (M. E. Suss, S. Porada, X. Sun, P. M. Biesheuvel, J. Yoon and V. Presser, Energy & Environmental Science, 2015, 8, 2296 - 2319), which would correspond to a final alkalinity of ~1 M, and has the potential to achieve even higher water recovery ratios. This range of final alkalinities sets the regime explored in Fig. 5A-5B, with the understanding that existing CDI systems, designed for desalination and not necessarily a high water recovery ratio, have not yet been optimized to produce a high-alkalinity concentrate stream.

An additional property of capacitive systems, which depends on operating parameters such as cycle rate, flow rate, and the current and voltage control, is that some amount of energy is able to be recovered as ions are released back into solution and current is reversed — analogous to energy recovery in the forward osmosis process. As described above, the ion binding model does not account for this energy recovered from unbinding an ion, but an overall energy recovery factor can be added in by hand. Energy recovery values for experimental systems operating at optimal conditions have commonly been reported around 50%, with some studies approaching 80%. Comparing estimated ACS implementation energies

Using the simplified models for reverse osmosis-driven and ion binding-driven ACS, we use parameters from the literature for implementations of RO and CDI, respectively, to estimate the energies per mole for different ACS processes if implemented with real physical systems. Here, we seek to estimate the energy that would be required to complete the full ACS and extract CO2 at 1 bar, so we include the additional work needed for vacuum outgassing.

The values presented in this section are estimates that stem from plugging physical values into the simplified models above and do not represent a comprehensive prediction of the energy that will be required for these processes, at either industrial- or lab-scale. The presentation of energies per mole, in Table 1 , is to provide a basis for understanding over which ACS parameter ranges either RO or CDI may be more practical and over which ranges each might be practical at all.

For ACS-RO, we recall that the energy values for current sea-water RO systems tend to be between 1 .0 to 1 .25 kWh per cubic meter of feed, corresponding to an a_ss range between approximately 1 .3 and 1 .6. We plug this range into the plots in Fig. 4A and 4B for an initial alkalinity of 0.6 M, corresponding to seawater, and a concentration factor of two, corresponding to typical SWRO, to obtain the energy estimates for RO in Table 1 , Row 3.

In Rows 1 and 2 in Table 1 , representing brackish water alkalinities, a_ss ranges from 1 .3 to 5.2, the latter coming from the higher end of the range of a_ss values for deployed brackish water systems. We justify extending the lower range of a_ss down to 1 .3 for lower initial alkalinities because of the simulation studies that suggest industrial-scale facilities could be built with even lower a_ss values. The feasibility of deploying ACS-RO for brackish water with an a_ss of 1 .3 is further substantiated in analysis by Qin et at. (2019), who show that the energy efficiency of existing brackish water RO deployments should not be taken as a limit because they have not yet reached the proper scale.

For ACS-CDI, we use the energies realized by MCDI systems because they can operate at a value of e,_oh that is nearly independent of concentration and are also uniformly more energetically efficient than CDI without ion exchange membranes operated under the same conditions. MCDI ion removal energy values range from approximately 17 to 42 kT per ion, or 85-210 kJ per mol NaCI equivalent salt. One experimental study reports a value independent of input concentration of 22 kT per ion, or 110 kJ per mol NaCI equivalent salt, for an MCDI system operating over the range 10-200 mM NaCI. We use Equation 16 to obtain the energy estimates for CDI in Table 1 . Table 1 ACS outgassing values and implementation energy estimates for various initial and concentrated alkalinities

ACS outgassing values Energy estimates”

A A_f Cout P f,max RO MCDI MCDI w/ 50%

X fout (M) (M) (mM) (mbar) (kJ/mol) (kJ/mol) Recovery (kJ/mol)

1e-2 1 100 3.0 0.34 40 160-190 310-730 170-380 0.1 1 10 11 0.16 4.0 190-220 790-1900 410-970 0.6 1.2 2 13 0.039 0.80 250-310 1 4 4 1 0.055 1.6 350-420 tt Here we assume a = 1.3 - 1.6 and _m = 85 - 210 kJ/mol, and we include the constant work to apply a vacuum at 0.4 mbar to be 30 kJ/mol. For the RO column, Row 3 corresponds to a ssRO model ofx = 2 for approximate seawater conditions; all other rows are based on msRO using x_ss = 2.

As an example, we estimate the ACS-CDI energy for a particular set of parameters by applying the 110 kJ per mol value. If 10 mM input alkalinity is concentrated by a factor of 100 to 1 M, 3.0 mM of CO2 would outgas at 330 kJ/mol. If we are able to achieve the commonly reported 50% energy recovery rate for the process, and then add the 30 kJ/mol for vacuum outgassing, we would estimate the total work for the process to be 195 kJ/mol. That value falls in the range corresponding to these parameters in the Row 1 of Table 1 , under “MCDI w/ 50% Recovery.”

Comparison to incumbent DAC technologies and feasibility of scale-up

In order for a particular DAC technology to contribute significantly to averting anthropogenic climate change, and contribute toward the gigatonne-per-year scale of global CDR that may be necessary by the end of the century, it needs to be able to be deployed at a large scale. To determine the feasibility of scale-up, we examine what challenges ACS implementations might face in reaching large-scale deployment levels and how these compare to incumbent technologies, using the benchmark set by the National Academies of Sciences (NAS) report of evaluating 1 MtCC>2/year DAC facilities. Whether through implementation using RO or CDI, the ACS possesses a number of potential advantages over incumbent DAC approaches but will also need to overcome some challenges.

Energy

The idealized energy requirement estimates provided for example ACS-RO and ACS-CDI implementations described herein can be compared to estimated requirements for incumbent DAC technologies. The lowest work estimated from the conditions in Table 1 comes from Row 1 , for which we estimate RO will require 160-190 kJ/mol and MCDI with recovery will require 170-380 kJ/mol. As discussed, these estimates incorporate the work required to bring the outgassed CO2 gas to 1 bar. This condition attains a purity of 99.8%. The NAS report estimates that the Carbon Engineering calcium loop- driven liquid solvent system has a work requirement of 360-480 kJ/mol (reported as 8.2-11 GJ/t) and that solid sorbent systems, for more realistic “mid-range scenarios,” have an energy requirement of 174-261 kJ/mol (reported as 3.95-5.92 GJ/t). These ranges are both for systems operating at a scale of 1 MtC02/year removed and for conditions comparable to our assumptions, capturing from a 400 ppm atmosphere at 25°C, with a 98% purity product. (Both NAS report energy ranges are also based on a CO2 capture efficiency of 75%. We do not directly consider capture efficiency for the ACS, however, because ACS processes rely on passive contacting pools. Instead, we consider the timescale associated with the passive equilibration of those pools).

While the ACS idealized energy requirement ranges fall below that of the liquid solvent system and within the approximate range of solid sorbent systems, these ACS values should be viewed as far more uncertain when compared to ranges based on systems that have been realized at demonstration scale. For example, the energy of liquid pumping has been neglected in this analysis. If the scale of the additional energy cost per mole of CO2 due to pumping is roughly approximated by the work needed to raise all processed water by 10 m then, for the conditions for which 3.0 mM and 31 mM of CO2 is outgassed (Table 1 ), this would correspond to roughly an additional 30 and 3 kJ/mol, respectively. We note that the work estimate for MCDI can be improved if higher energy recovery factors, approaching the 80% factor reported for some systems, can be attained, though MCDI quickly becomes unfavorable at higher initial alkalinities when compared to both ACS-RO work requirements and to incumbent technologies. For ACS-RO, the work requirement increases less quickly for higher initial alkalinities and each of the other conditions in Table 1 remains in the range of the liquid solvent system.

Even without a final accounting of the energy requirements for implementing the ACS, we can compare the sources of energy needed to incumbent DAC technologies. In the Carbon Engineering process, the core calcining step, for the final release of concentrated CO2 from calcium carbonate precipitate, requires heating to ~900°C. Even though heat recovery is used for other processes that require low-grade heat and electrical energy is chosen when it can be used efficiently, the Carbon Engineering process still uses 5.25 GJ of natural gas per tonne of captured CO2.

Though the cost and energy requirements of the Carbon Engineering process account for offsetting of direct emissions, scaling up such a process would entrench an ongoing need for production of natural gas, as well as any emissions associated with the natural gas supply chain. Incumbent technologies relying on solid sorbents typically require heating to ~100°C during the desorption step of a thermal swing. This low-grade heat doesn’t require fossil energy and can be sourced from solar thermal or nuclear energy sources, though these are often less energy efficient implementations. In contrast, the ACS can be implemented using entirely electrical energy and thus need only rely on renewable energy sources.

Outside of the module that operates the ACS cycle itself, fluid pumping, for vacuum extraction and solvent pumping, can all be powered by electrical energy. An ACS-CDI module would require only electrical energy for ion binding, as would an ACS-RO module operating in the majority of the optimal regime described herein.

Water

For any DAC approach that makes use of a liquid solvent for the initial capture of carbon dioxide from the air, it is important to determine the feasibility of the requirements for both overall water volume processing and water on hand. The ACS, as shown in Table 1 , can use an incoming solution ranging from 10 mM to 1 M alkalinity, resulting in respective output concentrations ranging from 3.0 mM to 31 mM.

For 10 mM initial alkalinity solution, removing 3.0 mM each cycle means 7.6 10⁹ m³ of water volume needs to be processed to remove 1 MtCC>2 total. This is roughly an order of magnitude more water than the annual processing rate for a large RO facility today, as described herein. For 1 M initial alkalinity solution, removing 31 mM each cycle means 7.4 10⁸ m³ of water needs to be processed, decreasing the processing requirement to roughly that of a large RO facility.

The liquid solvent system of Carbon Engineering is a DAC technology that has significant water use. Carbon Engineering inputs 35,000 tonnes of a 0.45 M CC>3 ² and 2.0 M K⁺ solution into its contactor per hour and uses it to capture 112 tonnes of CO2 per hour, for a captured CO2 concentration of 73 mM. Per unit of CO2 removed, an ACS system would then require between 2.4 and 24 times as much water to be moved through the system each cycle.

The Carbon Engineering system requires an incoming solution stream of high alkalinity and high DIC.

The ACS, however, takes a dilute incoming solution stream that is less constrained to a particular concentration. Air contact can thus be achieved with the additional surface area of the dilute solution, for example, with large pools for passive contacting. Large pools, with a high surface-area-to-volume ratio, do, of course, have significant water losses to evaporation as a function of humidity — these losses can be mitigated by either locating facilities in humid or rainy regions or by replenishing the pools. A dilute incoming solution stream also requires an increased energetic cost for fluid handling, although it reduces the energy requirement for operating contacting fans.

An ACS facility would require significant amounts of water to be stored on hand in reservoirs near the facility due to the slow equilibration of the CC>2-depleted solvent stream as it absorbs CO2 before again being cycled through. These pools are where the feed stream for the ACS process would be drawn and where the combined concentrated and dilute streams would be returned, as shown in Fig. 3A. For a 1 MtCC>2/year facility, assuming large passive contacting pools of 0.1 meter depth, Stolaroff etal. (J. K. Stolaroff, D. W. Keith and G. V. Lowry, Environmental Science & Technology, 2008, 42, 2728 - 2735; P. V. Danckwerts, Transactions of the Faraday Society, 1950, 46, 300 - 304) provide a method for estimating the passive CO2 uptake rate as a function of alkalinity. Using the ACS conditions, an instantaneous uptake rate of 5 c 10^{~ 7} mol/s/fn² of area for a 10 mM solution and 8 c 10^~9 mol/s for a 1 M solution. If we use this as an estimate for the rate throughout the equilibration process, for the 3.0 mM and 31 mM CO2 extraction quantities in Table 1 we obtain a characteristic equilibration timescale, T, of 7 days and 50 days, respectively. For the 10 mM condition, this would mean keeping roughly 10⁸ m³ of water on hand in the pools, equivalent to the volume of approximately 40,000 Olympic swimming pools, cycled approximately 50 times per year.

These rates are applicable for the concentration of hydroxide ions in the maximally C02-depleted solution, however, and therefore represent the largest absorption rate over the duration of the equilibration process, resulting in a lower bound for the equilibration timescale. Assuming that this uptake rate slows approximately exponentially, for an elapsed time t we expect only the first 1-e-^of the equilibration process to have been completed.

Over 7 days we would expect approximately 60% of the equilibration process to have completed. Cycling this solution through an ACS system would result in approximately 40% less CO2 to be extracted for a similar energy cost. An engineering tradeoff between rate and energy cost would thus need optimization; e.g., waiting twice as long permits the equilibration to proceed to roughly 90% completion but requires keeping roughly 3 c 10⁸ m³ of water on hand.

There is also a variety of ways to mitigate the extended timescales estimated above by introducing mixing into the contacting pools, instead of equilibrating in passive, unmixed pools. Depending on area constraints and the type of mixing used, this could be done either by continuously combining the outlet streams from the ACS system into one contacting pool, achieving a steady-state CDIC, or by using many smaller pools. Mixing can be done actively, as is done at some water treatment facilities, at an additional energetic cost. If we choose locations with high enough ground wind speeds, we can also expect the pools to remain well-mixed by the wind.

Land

As land continues to become a more limited resource, it is important to determine the land use requirement for any DAC technology. This land use requirement includes the footprint of the DAC facility itself (which, for the ACS, is predominated by the footprint of passive contacting pools) and the footprint of generation facilities required to power the DAC facility.

We estimate the land area requirement to power an ACS facility using only renewable energy sources, which requires substantially more land than using fossil energy, by using a result from Fthenakis and Kim (V. Fthenakis and H. C. Kim, Renewable and Sustainable Energy Reviews, 2009, 13, 1465 - 1474) that 1 Mha of land is required for 78.2 GW of solar capacity. Taking the upper end of the range for ACSRO for a 10 mM solution, 190 kJ/mol (or 4.3 GJ/tCC>2), we then determine that we would need 1 .7 c 10³ ha for the solar power to produce 1 MtCC /year. This land use requirement for power generation is much smaller than that for the contacting pools. From the water use estimate, determined herein: to remove 1 MtCC>2/year with pools of 0.1 meter depth would require 109 m² (105 ha). For context, this is a large area — the Great Salt Lake is about four times the size.

We compare the ACS to incumbent technologies’ land use requirement only for the facility itself, as the power generation footprint for each technology simply scales with the amount of power needed for a particular type of power source. Even when accounting for the indirect land impact, to ensure there are no detrimental environmental impacts when multiple facilities are built in the same area, the Carbon Engineering approach requires only approximately 700 ha to produce 1 MtCC>2/year, and much of this land could likely be used more flexibly; solid sorbent approaches require even less land.

To scale up the ACS to gigatonne-scale using passive contacting pools would require a likely unfeasibly large portion of land, on the order of 10% of the area of the US. Implementation of active mixing approaches, e.g., as described herein, could reduce this land requirement, though would carry an energetic cost. If mixing is used, the land use requirement can be reduced by an even larger factor than the water on hand requirement because, without the need for passive contacting, much deeper pools could be used.

Feasibility of scale-up and opportunities for optimization

An important advantage of the ACS approach to DAC is its ability to leverage existing technologies for water purification and desalination that are widely deployed at commercial scale around the world. Large RO facilities have capacities of more than 50 million m³ of purified water per year, with the largest plants having capacities of more than 350 million m³ of purified water per year. As already described, plants of this largest size implementing ACS (for example, using the condition from Table 1 , Row 4 outgassing 31 mM of CO2) would be able to capture up to 1 MtCC>2 /year. Global desalination capacity is currently roughly 35 billion m³ of water per year and growing rapidly. So, achieving a scale on the order of 100 MtC02 captured per year seems feasible based on current RO deployments, with larger scales achievable over time, though this would likely require substantial improvements in land use and water on hand requirements.

From the preceding sub-sections, we observe a clear trade-off between the required energy use, water on hand, and land use and the total water volume processing capacity to deploy a 1 MtC02/year ACS- DAC facility. In Table 1 , we see the general trend that higher initial alkalinities have increasing energy requirements. On the one hand, whereas the 1 M initial alkalinity condition in Row 4 remains in the range of the incumbent liquid solvent DAC system for RO, this condition is far too energetically costly for CDI. On the other hand, we have shown that the 10 mM initial alkalinity condition in Row 1 requires roughly an order of magnitude more water to be processed than the Row 4 condition, which itself already requires roughly the water processing of a large RO facility to achieve 1 MtC02/year. Without any improvements, then, the water processing scale for this low alkalinity Row 1 condition may be very difficult to achieve. Because its equilibration rate is more than twice as fast as the Row 2 condition, however, the low alkalinity Row 1 condition is favored with significantly lower water on hand and land use requirements. These trade-offs demonstrate both the challenges in scaling ACS-DAC for most conditions and the possibilities for tailoring the optimal ACS implementation.

Although contacting requirements pose challenging land and water demands, several mitigation options are possible to increase absorption kinetics and outgassing efficiency. For example, different choices of solvents and membranes may enhance the ACS. Whereas only a strong base solvent was considered here, preliminary analysis shows that the right choice of a weak base solvent could increase the ACS outgassing amount (Example 4). In CDI systems the use of an ion-exchange membrane tuned to select for bicarbonate ions over carbonate ions can increase ACS efficiency. More generally, engineering membrane or electrode properties around bicarbonate and carbonate ions is an important area of future study. Beyond the two specific technologies explored in this analysis, the broad suite of existing desalination approaches, as well as hybrid approaches that combine strengths of different methods, could be investigated as driving mechanisms for the ACS. Furthermore, principles from the ACS could be explored as a way of modifying and enhancing other solvent-based DAC methods. Finally, as described herein, there are several ways to mix the contacting pools to increase the liquid-air contact area and increase the CO2 absorption rate.

In addition to ensuring equitable allocation of scarce land and water resources, associated environmental hazards and material considerations must be considered before ACS systems are scaled up. Environmental impacts from traditional desalination facilities come predominantly from discharge of brine and from chemical treatment of water and membranes. Current membrane cleaning methods make use of toxic substances, which would need to be disposed of safely if large-scale systems are deployed. Because ACS systems can be operated in a closed cycle and, once operational, no significant discharge or uptake is necessary, these environmental harms can likely be mitigated. Although no significant loss of potassium or any other alkalinity carrier is expected, scaling up large alkaline reservoirs would need to be accompanied with local environmental assessments to evaluate risk and determine mitigation options for spills or leakage.

The Alkalinity Concentration Swing is a new approach to DAC in which the driving mechanism is based on concentrating an alkaline solution that has absorbed CO2, e.g., atmospheric CO2. Concentrating a solution with a given alkalinity and DIC results in disproportionation of bicarbonate ions into aqueous CO2 and carbonate ions, proportionally increasing the outgassing partial pressure (Equation 11). This allows for extraction and compression of CO2. For the same concentration factor, higher initial alkalinity solutions outgas a greater amount of CO2 relative to the initial feed (Fig. 2B). For a given final alkalinity, the amount of CO2 outgassed vs. initial alkalinity exhibits a peak as initial alkalinity approaches that final alkalinity because of a trade-off between higher DIC available and a smaller conversion fraction of that DIC (Fig. 5B). The ACS can be implemented based on desalination technologies. We propose and briefly evaluate two technological implementation approaches, RO and CDI, with two accompanying simplified energy models, the RO model and the ion binding model, respectively. For each, the CO2 capture energy (Table 1) is dependent on the initial alkalinity, the concentration factor, and the applied vacuum pressure, as well as the dissipation for the associated implementation mechanism. We use reported experimental values from existing RO and CDI desalination implementations to estimate associated capture energies for ACS- RO and ACS-CDI. The choice of initial alkalinity and concentration factor present complicated trade-offs between the quantity of outgassed DIC and energy requirements (Table 1 ). For example, a solution initialized at 10 mM alkalinity and concentrated by a factor of 100 outgasses approximately 3 mM of CO2 and requires a lower bound of 160 and 170 kJ/mol for the msRO and MCDI (with energy recovery) models, respectively. A solution that swings between 1 M and 4 M alkalinity, however, outgasses 31 mM of CO2, which corresponds to a factor of 10 less water processing, but requires a factor of about two more energy (lower bound of 350 kJ/mol, given the msRO model). In particular, studies of ACS kinetics are important in order to understand possible limitations in the absorption and outgassing steps. Our analysis further reveals a trade-off for the ACS between the total water processing requirement and both the capture energy demand and water on hand requirement. Although initial calculations point to challenging land and water requirements to scale up this technology, we propose several potential mitigation pathways. Both ACS-RO and ACS-CDI approaches can be run entirely on electricity and do not rely on high- or low-grade heat. The required materials are relatively simple (e.g., K⁺, membranes, electrodes, water). An initial assessment points to relatively environmentally safe deployment because no toxic chemicals, such as amines, are critical for this process. Lastly, the proposed approaches are based on existing technologies that have been deployed at large scale, and significant research and development can be leveraged from the desalination industry.

Example 2 - Alkalinity Concentration Swing with Ion Selectivity

The basic ACS cycle consists of four steps, moving between four states, depicted in Fig. 6. Throughout the cycle, we track two quantities: 1 ) the overall alkalinity concentration, A, defined as the molar charge difference between the sum of conservative cations and conservative anions, simplified here as the molar concentration of K⁺ ions, and 2) the total dissolved inorganic carbon, CDIC defined as the molar concentration of sum of aqueous carbon dioxide (CO2 (aq)), bicarbonate (HCQr) and carbonate (CQr²). A and CDIC have a fixed equilibrium relationship with one another for a given partial pressure of CO2, p.

Defining the concentration of bicarbonate ions, b, and the concentration of carbonate ions, c, then, from charge conservation, we obtain the expression

A = b+2c (17) where the concentration of OFF and H⁺ is negligible and can be ignored for alkalinities of at least 1 mM. Two key metrics of performance, the concentration of CO2 extracted with respect to the feed solution,

Cout, and the work per mole of extracted CO2, w, can be modeled as a function of how A, and as a result CDIC, evolves from states 1 to 3, for a given initial and final partial pressure of CO2, pi and pt, respectively.

Schematically, without considering ion selectivity, the core ACS functional relationship can be written:

FACS [Ai, pi,Af , pf] Cout ,w (18)

We will define Cout in this subsection and w in the next.

In Step 1 2, an alkaline solution, of initial alkalinity, A, that has been equilibrated with atmospheric CO2 at an initial pressure, p,, of 0.4 mbar is concentrated, removing only water. In Step 2 3, CO2 is extracted from the concentrated solution, now at a final alkalinity, At, by exposing it to a final pressure, p_t, to drive equilibration through the following disproportionation reaction:

2HCO3- CO2 (aq)+C0₃-² + H2O (19)

We note here that the ACS is, essentially, tied to the concentration of bicarbonate ions in solution that can bind and drive the outgassing of CO2. Carbonate ions already in solution can not result in any extracted CO2. That means, that any energy spent as a function of carbonate ions in solution is wasted.

The concentration of DIC outgassed as CO2 with respect to the feed solution during Step 2 3, or C_out, is given by Equation 9:

In Step 3 4, water is added, and the solution is diluted back to A, and, in Step 4 1 , the now CO2- depleted dilute solution again equilibrates by absorbing atmospheric CO2 at p,.

When contacting a solution with gaseous CO2, a solution with a higher pH has greater capacity to absorb the CO2; however, as pH increases the relative proportion of carbonate and bicarbonate shifts toward carbonate. Since only bicarbonate ions undergo disproportionation to CO2 in the CO2 extraction step, it is beneficial to only concentrate bicarbonate ions, both to minimize energy used in concentrating carbonate ions and to shift the equilibrium of the disproportionation of bicarbonate toward completion. Fig. 1 A and 1B summarizes alkalinity concentration swing cycle in numerical/graphical form, while Fig. 6A represents the same schematically and Fig. 6B shows the ACS cycle with ion selectivity. In Fig. 1 (A, B) The theoretical ACS cycle is depicted in panel (Fig. 1 A) for a particular solution condition starting at 10 mM alkalinity concentrated to 1 M. Step 1 2 (1 2 arrow) depicts the concentration step; Step 2 3 (2 3 arrow), also depicted in panel (Fig. 1 B) as a function of partial pressure p_å (pi), shows the outgassing of CO2; Step 3 4 (3 4 arrow) depicts dilution; Step 4 1 (4 1 arrow, inset) depicts CO2 absorption returning the solution to its initial condition in Fig. 6A the molecular schematic of the ACS is depicted demonstrating the speciation between bicarbonate, carbonate, and carbon dioxide molecules. Step 2 3, during which disproportionation (2HC03- CO2 (aq)+C03^-2 +H2O) occurs, corresponds to panel (B).

Fig. 6B shows the molecular schematic depicting the enhancement of the ACS due to bicarbonate selectivity. Separating carbonate ions away from the volume containing the selected bicarbonate ions allows for the concentration step to be applied to fewer ions.

Implementing the ACS using capacitive deionization

ACS can be implemented using capacitive deionization (CDI), which we refer to as ACS-CDI, and an accompanying ion binding-driven model, which assumes that the energy required to concentrate alkaline solution is dominated by the energy of binding ions in solution. CDI is a method of removing pairs of negatively charged anions and positively charged cations from solution by applying a voltage across two electrodes. Anions and cations adsorb onto the positive and negative electrodes, respectively, forming an electric double layer on each, as depicted in Fig. 7.

Fig. 7 shows a schematic of an ion selective ACS-CDI module that uses an anion exchange membrane to select for bicarbonate ions over carbonate ions as voltage is applied across the two electrodes. Ion selective alkalinity (A_sei) corresponds to the effective ion selective alkalinity at the electrode after the membrane has blocked a portion of ions.

When the voltage is switched off, the ions are released, and the minimum hold-up volume for the cell, the total volume of water contained in the electrode pores and in between the electrodes, set the maximum At that can be obtained for the cell. ACS-CDI can be implemented without use of ion-selective membranes, or by adding membranes between the solution channel and either or both electrodes, which is referred to as membrane CDI. Membrane CDI can increase the energy efficiency of implementing CDI and can be used to increase the proportion of bicarbonate ions, over carbonate ions, that bind to the positive electrode. In Fig. 7, the anion exchange membrane is preferentially selecting for bicarbonate ions.

Fig. 8 shows a schematic of a capacitive deionization module including an anion exchange membrane and a cation exchange membrane and photographs of a working prototype thereof. Fig. 9 shows additional photographs of the capacitive deionization module of Fig. 8.

Exemplary conditions for maximizing adsorption and desorption include:

Feed: 10 mM Na-DIC

Flow rate for adsorption: 60 mL/min

Voltage cycle: Positive V adsorption, 0 V desorption

Thick spacer, high compression

Membranes:

AEM: Selemion DSV-N or AMV-N

CEM: none Fig. 10 shows the current vs time profiles of the capacitive deionization module of Figs. 8-9 during desorption and adsorption.

Fig. 11 is a schematic of a system for ACS CO2 capture using a capacitive deionization

In a model consistent with experimental CDI data, there is a fixed energy cost to bind a pair of monovalent anions and cations out of solution, and we can define e, the binding energy per mole of anion-cation pairs. To concentrate a feed stream of solution, every ion must be bound, allowing water to pass through. The alkalinity sets the concentration of pairs, so the total energy per volume and per mole to bind all of the solute is given by eA. The work per mole of extracted CO2 is then given by Equation 16.

ACS-CDI could be operated at z_m values ranging from 85 to 210 kJ per mol, consistent with experimental membrane CDI data for initial solute concentrations ranging from 10-200 mM. Making use of the commonly reported ability to recover 50% of the energy used during CDI when discharging, we showed above that e range would correspond to an overall work requirement of 170-380 kJ per mole of CO2 for a swing from Ai = 10 mM to At = 1 M. While this work requirement is significantly lower than that of a calcining DAC approach, this swing has a much lower Cout of 3.0 mM, compared to Carbon Engineering’s 73 mM, so would require processing of on the order of 25 times more water to obtain the same amount of removed CO2. Maintaining the lower w value for ACS-CDI while improving Cout would further improve the process.

Because, from a work requirement perspective, ACS-CDI operates most effectively at low initial alkalinities, it also suffers from slow kinetics for absorbing CO2, which translates to effectively having a very large requirement for how much water is stored on hand for CO2 contacting and how much land is required to store that water. As described herein, the instantaneous uptake rate of CO2 is a function of the concentration of hydroxide ions that the CO2 can bind to in the maximally DIC-depleted solution, meaning the higher initial pH the better. As pH goes up with alkalinity, there is a benefit to being able to use a higher starting alkalinity.

To achieve significantly higher initial pH values would require an alkaline solution further from equilibrium, meaning much more CC>2-depleted. The DIC in these high pH solutions, however, is made up of almost entirely of carbonate ions, with a very small concentration of bicarbonate ions, meaning that virtually none of the absorbed CO2 is able to undergo disproportionation upon the solution being concentrated. So, to make high-pH ACS-CDI effective, there would need to be a mechanism for only expending energy binding the small concentration of bicarbonate ions available in solution without using energy to bind the carbonate ions.

By implementing a mechanism for selecting bicarbonate ions over carbonate ions: 1 ) it can be operated at a higher Cout for a fixed w, meaning the overall water processing requirement decreases and 2) it can be operated a higher overall initial pH, pH,, meaning the kinetics improve, and therefore the water on hand and land requirements decrease. While one implementation of bicarbonate: carbonate selectivity may be placing an anion exchange membrane between the electrode and the solution channel, e.g., as depicted in Figs. 7-9, there are other approaches that can facilitate bicarbonate ions being preferentially bound to the electrode over carbonate ions. So, for the purpose of presenting a generalizable model for the enhancement to Cout and the kinetics improvement that can be achieved through implementing ion selectivity, we will not refer to a particular mechanism in this section.

Ion- Binding Driven ACS with Bicarbonate Selectivity

We define the selectivity factor, Q, as the proportion of bicarbonate ions that are bound by our CDI electrodes for a single carbonate ion. While any laboratory method for implementing ion selectivity will reduce the rate of binding for all ions, we make a simplifying assumption here: our selectivity mechanism has no impact on the binding of bicarbonate ion. If every bicarbonate ion is active, that means 1/Q carbonate ions are active, or that a factor of (1 - 1/Q) of the carbonate ions in our initial solution will not be bound and will be flushed through our CDI cell along with the water being removed. Fig. 6B depicts a schematic of bicarbonate selective ACS, in which carbonate ions are separated away from the volume containing the selected, active bicarbonate ions. This allows for less energy to be spent on the concentration step, which is applied to fewer ions.

To maintain charge conservation, two alkalinity carrier ions must be flushed for each carbonate ion. Extending Equation 17, we can write an expression for the remaining alkalinity concentration, as a function of the feed solution volume, which we refer to as the effective ion selective alkalinity, A_sei:

Asei = b+2ci /0 (17)

Plugging this expression for the effective alkalinity that is now being operated on into Equation 9, we obtain an expression for the concentration of CO2 extracted from a system with a selectivity factor Q:

(21 )

We can also extend Equation 16, because we maintain the same functional relationship between A_sei, Counsel, and w_sei, the work per mole of extracted CO2 for a system with a selectivity factor Q.

Accessing Lower Energy, Higher Capacity Portions of the ACS Parameter Space Through Bicarbonate Selectivity Figs. 12A-12B show both the required work per mole, w_sei, and the concentration of CO2 extracted, Counsel, as a function of the initial alkalinity. (A) Required work per mode as a function of the initial alkalinity for varying selectivity factors. (B) The value of CO2 extracted as a function of the initial alkalinity for varying selectivity factors. For both panes, the blue dot corresponds to A, = 30 mM and Q = 1 and the red dot corresponds to = 200 mM and 0 = 10, with both at sharing the same energy of 250 kJ/mol. These replot the two plots in Fig. 14 with the new functional dependence.

Instead of learning how the work requirement and CO2 extracted improve as a function of increased ability to reach a larger final alkalinity, however, these plots explore the enhancements possible by varying 0 for a particular final alkalinity of 1 M. For any given initial alkalinity, increased selectivity has a significant impact on reducing the work requirement and, for starting alkalinities of greater than roughly 100 mM, it also has a significant impact on increasing the concentration of CO2 extracted.

For a particular work requirement in Fig. 12A, 250 kJ/mol for example, we can also see that this would be achievable at roughly 30 mM initial alkalinity for Q = 1 (blue dot) but would be achievable at roughly 2 M initial alkalinity for Q = 10 (red dot). If we then look at the same conditions in pane B, we see that the concentration of CO2 extracted increases from roughly 5 mM for = 30 mM (blue dot) and Q = 1 to roughly 70 mM for Ai = 2 M and 0 = 10 (red dot). This means that for a work requirement that is still significantly below that of the calcining method for DAC, the concentration of CO2 extracted is roughly equal, suggesting the water processing requirement would be similar if such a system could be realized.

We see a similar trend in Fig. 13. From Equation 16, we know that each iso-line corresponding to a fixed Asei also corresponds to a fixed w. In each case we see that the concentration of CO2 extracted increases significantly when moving along a particular iso-line, for example from a value of Q = 1 to Q = 10, and for Asei = 400 mM, C₀ut,sei increase by almost a factor of 10. It is worth noting that, for each iso-line, there is a shoulder where there is a significantly diminishing increase in C₀ut,sei after values of 0 between roughly 30 and 100, indicating that seeking to implement these larger values would only be valuable for larger values of Asei, which can only be accessed for higher initial pH values.

Fig. 13 shows the value of CO2 extracted and the membrane selectivity as a function of the initial alkalinity for varying selectivity factors. Red dots from left to right, for various A_sei values for 0 = 10: 1 ) A_sei = 100 mM ® [HCO3-] = 71 mM; 2) A_sei = 250 mM ® [HCOs ] = 141 mM; 3) A_sei = 400 mM ® [HCOs ] = 193 mM.

Enabling High-pH Contacting Through Bicarbonate Selectivity

With the inclusion of the selectivity factor, 0, we can expand on the ACS functional relationship in Equation 9. In a paradigm without selectivity, another way of saying we remain confined to the parameter space with 0 = 1 , our initial value of CDIC, as well as our initial pH, pH,, is simply fixed as a function of A and pi.

When we allow for 0 to vary, however, we need no longer confine our initial bicarbonate concentration, b, and carbonate concentration, c, to their equilibrium values for the particular p,. This is because it is possible to have a much larger value of ci, which is being selected against, such that having a relatively small value of b, does not necessarily make the cycle ineffective. With the inclusion of a Q dependence, we can thus shift from considering the pi for our cycle to considering the b, for our cycle, which more directly sets the maximum C_out of b/2, and rewrite our functional relationship for the ACS with ion selectivity:

F selACS [Aj,bj,Q,A_f , Pf] — > Cout ,w, pHi (22)

For a fixed alkalinity and bicarbonate concentration, there is only one equilibrium value of pCC>2, which then also sets the carbonate concentration and, in turn, CDIC for the state.

The right side of the relationship now includes the initial pH, pH_/, which is also fixed as a function of A, b, and c. This value pH, is the pH of the solution after Step 4®1 , when the dilute solution has finished uptaking atmospheric CO2 and is in State 1 , ready to be cycled back and concentrated again. By setting values of bi, pCC>2 can vary and determine the pH, as a function of Ai, which we see in Fig. 14.

Fig. 14 shows pH as a function of alkalinity for fixed bicarbonate concentration. pH is plotted as a function of alkalinity along lines of constant bicarbonate concentration, allowing pCC>2 to vary along each line. The line of 400 ppm pCC>2 is plotted in this pH vs Alkalinity space to indicate which conditions are at a partial pressure above 400 ppm (below the line) and would spontaneously outgas CO2 at ambient atmospheric conditions, and which conditions are below 400 ppm (above the line) and would spontaneously uptake CO2 at ambient atmospheric conditions. Operating at an initial condition above the line in this spontaneous uptake regime would thus enable operating at a disequilibrated steady-state, at an effective PCO2 lower than atmospheric conditions.

Because the CO2 uptake rate for an aqueous alkaline pool scales roughly with its hydroxide concentration, we estimate that for every pH, differential of 2, passive CO2 contacting proceeds approximately an order or magnitude more quickly, meaning the water on hand requirement, which scales inversely to the uptake rate, is approximately an order of magnitude lower. We again consider a comparison to the non-selective swing from Ai = 10 mM to At = 1 M, which has a Cout = 3.0 mM and a pH,

= 8.74.8 A similar Cout of 5 mM can be obtained on the blue line in Fig. 14 at an alkalinity of 200 mM, but with an uptake rate that is over an order of magnitude lower, thus having roughly an order of magnitude smaller water on hand requirement for contacting pools and land use.

Even at the extreme precipitation value of 5 M alkalinity and at the smallest value of b = 10 mM (top right point of the blue line in Fig. 14), however, the pH only just goes above 12.

Ion selectivity provides a practical implementation of the alkalinity concentration swing. A bicarbonate selective ACS allows a jump of over an order of magnitude in CO2 outgassing capacity in some regimes, for a fixed energy per mole of CO2. A bicarbonate selective ACS allows much higher initial pH values, enabling increases in the CO2 uptake rate of more than an order of magnitude for a fixed capacity in some regimes, thus lowering the water on hand and land requirement for operating the ACS by that same order of magnitude.

Example 3 - Measuring Effects of Concentration Factor The relationship of concentration factor and various features of the process was further investigated. Fig. 15 shows the experiment and how the pH shifts after concentrating alkalinity. Fig. 16 shows the effect of feed concentration on outgassing. Higher feed concentrations outgas more CO2 for the same concentration factor. Fig 17 shows the experimental set-up for measuring outgassing as a function of concentration factor. Fig. 18 shows the effect of concentration factor on outgassing for 50 mM ad 20 mM alkalinity solutions. Higher concentration factor outgasses more CO2. Fig. 19 shows DICout as a function concentration factor and feed concentration. Fig. 20 shows the effect of driving pressure on outgassed carbon dioxide amount.

Example 4 - Effect of Adding a Weak Acid or Base The amount of CO2 that can be outgassed from the concentrated alkaline solution can be enhanced by the inclusion of a weak acid or base in the alkaline solution. In this example, as shown in Fig. 21 , 20 mM of boric acid was added to an alkaline solution with sodium as the alkaline counterion. Fig. 21 shows that the addition of a weak acid (e.g., boric acid) can enhance the amount of carbon dioxide that may be outgassed from the concentrated solution. Other embodiments are in the claims.

Claims

What is claimed is: CLAIMS

1 . A method of capturing carbon dioxide comprising the steps of:

(a) providing an alkaline solution comprising dissolved carbon dioxide;

(b) concentrating the solution; and

(c) extracting dissolved carbon dioxide from the concentrated solution.

2. The method of claim 1 , further comprising diluting the concentrated solution, capturing carbon dioxide in the diluted solution, and repeating steps (b) and (c) with the diluted solution.

3. The method of claim 1 , further comprising (d) collecting carbon dioxide extracted from the concentrated solution.

4. The method of claim 1 , wherein the alkaline solution comprises a weak base and/or weak acid.

5. The method of claim 4, wherein the weak base and/or weak acid is polyprotic.

6. The method of claim 4 or 5, wherein the alkaline solution comprises boric acid.

7. The method of claim 1 , wherein the alkaline solution is concentrated using reverse osmosis or capacitive deionization.

8. The method of claim 1 , wherein the concentrating selectively retains bicarbonate ions over carbonate ions in the concentrated solution.

9. The method of claim 8, wherein the concentrating comprises performing reverse osmosis with an ion selective membrane or performing monovalent-selective capacitive deionization.

10. The method of any one of claims 7-9, wherein the concentrating comprises performing monovalent-selective capacitive deionization with an anion exchange membrane.

11 . The method of claim 1 , wherein step (a) comprises contacting a gas containing carbon dioxide with an alkaline solution for a time sufficient for carbon dioxide to dissolve therein.

12. A system for capturing carbon dioxide comprising a reservoir for an alkaline solution having a gas inlet and means for concentrating the solution.

13. The system of claim 12, further comprising means for dilution of the concentrated solution.

14. The system of claim 12 or 13, further comprising an ion-selective capacitive deionization module or an ion-selective reverse osmosis device.