EP4658398A1 - Sorbent structures for carbon dioxide capture - Google Patents

Abstract

A sorbent structure comprising: a first end and a second end; a plurality of flow channels; and a plurality of channel walls. The channel walls comprise a carbonate in an amount in a range from greater than 5 wt% and up to 50 wt%. The carbonate being of at least one of (i) an alkali metal (X₂CO₃) and (ii) an alkaline earth metal (YCO₃). The channel walls further comprise a metal-containing support in an amount in a range from 40 wt% and up to 95 wt%. The metal-containing support is selected from the group consisting of a metal alloy, metal oxide, metal-non-metal alloy, ceramic, and any combination thereof. The metal-containing support comprises a total accessible porosity (ε) in a range from 0.4–0.8.

Description

SP2907 SORBENT STRUCTURES FOR CARBON DIOXIDE CAPTURE Field of the Invention [0001] The present specification generally relates to the field of carbon dioxide capture, and more specifically, to sorbent structures for capturing carbon dioxide (CO2) from a gas stream and methods for making and using same. Background of the Invention [0002] This section is intended to introduce various aspects of the art, which may be associated with exemplary embodiments of the present invention. This discussion is believed to assist in providing a framework to facilitate a better understanding of particular aspects of the present invention. Accordingly, it should be understood that this section should be read in this light, and not necessarily as admissions of any prior art. [0003] The atmospheric carbon-dioxide (CO2) level is increasing at least in part due to emissions from various sources, including industrial sites like thermal power plants, oil refineries, and other processing plants such as cement, steel, aluminium, and the like. The increased level of atmospheric carbon-dioxide (CO₂) has been linked to global warming. Various technologies are being used and/or developed to reduce the amount of CO2 emitted into the atmosphere as one precautionary measure to address global warming. In addition, various governments have established or plan to establish programs that either provide economic incentives to reduce CO2 emissions and/or regulations limiting CO2 emissions, all of which encourage the development of CO₂ capture technologies. [0004] One such type of CO2-reduction technologies involves capturing or removing CO₂ from a gas stream using a sorbent. The sorbent typically comprises a significant portion of the overall capital and operating costs, particularly in sorbent replacement. The performance of the sorbent, in terms of capacity and stability, has a direct economic impact. For instance, a process would need less amount of a better performing (more efficient) sorbent to capture a similar amount of CO2 from the same volume of gas stream, which can result in lower capital and operating costs. Current known sorbents and processes for capturing CO2 from a gas stream, however, still suffer from low efficiency and/or are too costly. [0005] For instance, a number of sorbents employ organic amines to capture carbon dioxide, which are prone to oxidation, thereby increasing the chance of sorbent degradation and loss of CO2 sorption capacity over time. These sorbents include WO2010027929A1, WO2017009241A1, WO2010091831A1, and WO21189042A1. SP2907-PD [0006] WO21189042A1 further discloses a solid mass formed of sintered, compact, mesoporous particles, the particles being sintered together so as to be structurally coherent; wherein each of the particles is mesoporous and the solid sintered mass is macroporous. The solid mass further comprising a plurality of longitudinal channels extending between and opening through opposing faces of the solid mass. The exposed walls of the channels are formed of the sintered mesoporous particles and contain a sorbent for CO2 in its mesopores. WO21189042A1 discloses various coating methods to achieve the sintered coating of mesoporous particles, which can lead to lower volumetric CO2 capture capacity. [0007] Another set of sorbents use potassium carbonate as a sorbent for CO₂, which addresses the increased chance of oxidation of amine. They, however, disclose capturing carbon-dioxide from a gas stream using adsorbent particulates. For instance, the adsorbent particulates of WO2016185387A1 are transported from the adsorber to the desorber in a circulating fluidized bed. The adsorbent material comprising potassium carbonate impregnated support is crushed and sieved to form the particulates. Likewise, US20210016220 discloses a plurality of fixed sorbent beds that contain an alkalized sorbent. [0008] Similarly, US2021187480A1 discloses a particulate activated carbon material for capturing CO2 from air. The particulate activated carbon is impregnated with alkali carbonate salt such as K2CO3. Also, the paper “Sorption of carbon dioxide by the composite sorbent ‘potassium carbonate in porous matrix’” (Okunev, A. et al., Russian Chemical Bulletin 2003, 52. 359-363) discloses particulates of potassium carbonate on alumina for flue gas capture. [0009] The paper by Rodríguez-Mosqueda et al. (Parametrical Study on CO₂ Capture from Ambient Air Using Hydrated K2CO3 Supported on an Activated Carbon Honeycomb, Ind. Eng. Chem. Res.2018, 57, 3628−3638, 6) discloses an activated carbon honeycomb monolith that was coated with K2CO3 and treated with moist N2 to hydrate it. [0010] As such, there still exists a need for sorbents that provide efficient capturing of CO2 from a gas stream. Summary of the Invention [0011] According to certain aspects, there is provided a sorbent structure for capturing carbon dioxide from a gas mixture, the sorbent structure comprising: a first end and a second end; a plurality of flow channels; and a plurality of channel walls. The flow channels are formed by at least one channel wall, and the flow channels extend from the first end to the second end. The channel walls comprise: (i) a carbonate in an amount in a range from SP2907-PD greater than 5 wt% and up to 50 wt%, preferably greater than 5 wt%, including from 10 wt% and up to 30 wt%, based on the total weight of the channel walls, wherein the carbonate being at least one of (i) an alkali metal (X2CO3) and (ii) an alkaline earth metal (YCO3); and (ii) a metal-containing support in an amount in a range from 40 wt% and up to 95 wt%, based on the total weight of the channel walls. The metal-containing support comprises a metal and is selected from the group consisting of a metal alloy, metal oxide, metal-non-metal alloy, ceramic, and any combination thereof. The metal-containing support further comprises a total accessible porosity (εsupport) in a range from 0.4 – 0.8, preferably 0.5 – 0.7. [0012] The total accessible porosity of the metal-containing support (ε_support) can be determined at least by: ε_support = WPV_support/(WPV_support + 1/ρ_support) where WPVsupport is the gravimetric water pore volume (ml/g) of the metal-containing support and where ρsupport is the gravimetric skeletal density of the metal- containing support. [0013] Optionally, the gravimetric water pore volume (ml/g) of the metal-containing support (WPVsupport) can be determined at least by: WPVsupport = (M2−M1)/ρliquid/(M1) where M₁ is the mass (in grams) of a dry sample of the metal-containing support, where M₂ is the mass (in grams) of the wet sample of the metal-containing support, and ρ_liquid is the gravimetric density of liquid used to wet the sample. [0014] Optionally, the sorbent structure can comprise a residual total accessible porosity (ε_residual) in a range from 5% to 75%, preferably from 10% to 65%, more preferably from 20% to 65%. Optionally, the εresidual can be determined at least by: εresidual = ^support - (wcarbonate / (1- wcarbonate))*(1- ^ ^support)* ρsupport/ρcarbonate ^ where εsupport is total accessible porosity of the metal-containing support, and where Wcarbonate is the mass loading of carbonate on the sorbent (wt%) and where ρ_support is the gravimetric skeletal density (g/ml) of the metal-containing support, and SP2907-PD where ρcarbonate is the gravimetric density of the metal of the carbonate (g/ml). [0015] Optionally, a sum of the amount of the carbonate and the amount of the metal- containing support can be at least 95 wt%, preferably 97 wt%, more preferably 99 wt% of the sorbent structure. [0016] Optionally, the X can be an alkali metal cation selected from the group consisting of K⁺, Na⁺, Cs⁺, Li⁺, and any combination thereof and the Y is an alkaline earth metal cation selected from the group consisting of Mg²⁺, Ca²⁺, Sr²⁺, Ba²⁺, and any combination thereof. Optionally, the metal of the metal-containing support can be selected from the group consisting of aluminium, silicon, titanium, zirconium, magnesium, calcium, iron, and any combination thereof; optionally wherein the metal-containing support is selected from the group consisting of silica, alumina, titania, zirconia, cordierite, mullite, silicon carbide, aluminosilicates, preferably zeolites, and any combination thereof. Optionally, the carbonate can be selected from one or more alkali metal and the metal-containing support is selected from titania and/or zirconia. Optionally, the carbonate can be selected from one or more alkali metal and the metal-containing support is alumina, preferably thermally-treated alumina, more preferably selected from the group consisting of potassium aluminate, sodium aluminate (2NaAlO2═Na2O*Al2O3), hydrated alumina (Boehmite, Al2O3*H2O), bayerite, gibbsite, boehmite, pseudo-boehmite, bauxite, gamma-alumina, delta-alumina, chi-alumina, rho-alumina, kappa-alumina, eta-alumina, theta-alumina, magnesium aluminate, trine, bermire, and any combination thereof. [0017] Optionally, the metal-containing support can further comprise an enhancing material to improve or facilitate the mechanical strength and/or fabrication process in an amount of less than 20 wt% of the total weight of the metal-containing support. [0018] Optionally, from 40% and up to 100% of the total accessible porosity comprises a pore size of less than or equal to 50 nm and from 0% and up to 60% of the total accessible porosity comprises a pore size of greater than 50 nm. Optionally, from 0% and up to 20% of the total accessible porosity comprises a pore size of greater than 500 nm. Optionally, the sorbent structure can further comprise a cell density in a range from 50 and up to 400 cells per square inch (cpsi), preferably in a range from 50 and up to 300 cpsi and open frontal area in a range from 60% and up to 85%, preferably in the range 65% to 75%. Optionally, the channel walls can further comprise an average thickness in a range from 150 microns and up to 1000 microns. SP2907-PD [0019] According to another aspect, the present disclosure provides a method for capturing carbon dioxide from a gas mixture. The method comprises: (a) providing an embodiment of the sorbent structure disclosed herein, (b) passing a gas comprising carbon dioxide (CO2-containing gas) through at least a portion, including all, of the flow channels; and allowing at least a portion of the CO2 in the CO2-containing gas to react with the carbonate to produce at least a partially loaded (including fully loaded) sorbent structure. Optionally, the CO2-containing gas stream consists essentially of air. [0020] Optionally, the step of passing the CO2-containing gas through at least a portion of the flow channels is conducted at or near atmospheric pressure. Optionally, the method can further comprise (d) contacting the at least partially loaded sorbent structures with steam to regenerate the sorbent structures, wherein the steam is introduced at or near atmospheric pressure or has a slightly elevated pressure just above atmospheric pressure (e.g. >1 bar), suitably around 1.3 bar/130 KPa (around 18.9 psi), and at a temperature of around 100 to 130 ˚C. [0021] Generally, for capturing carbon dioxide from a gas stream, it is desirable for the sorbent material to impose minimal pressure drop on the gas flow to minimize the energy required for moving the gas stream through the removal process and at the same time achieve maximum contact between the sorbent and the gas stream to maximize the mass transfer rates of the CO2 to be removed from the gas stream. If the gas stream from which carbon dioxide is being captured is atmospheric air, the concentration of CO₂ available for capture is very low, in the atmospheric air, currently between 400 and 420 ppm, which is expected to rise in the future. In such scenario, very large air volumes have to flow through any capture system to extract a meaningful amount of CO2. The increase in energy demands from moving large amounts of air through the system while maintaining the desired CO2 capture efficiency is one of the primary factors in achieving economic feasibility. [0022] As described herein, the sorbent structure and its various embodiments provides removal of carbon dioxide where a comparably small volume of sorbent structure can absorb a large amount of carbon dioxide in a short period of time. This is at least due to the relatively high total accessible porosity that enables the relatively high loading of carbonate to CO2 capture. The small volume of sorbent structure required decreases costs associated with building an operating carbon dioxide removal systems. The described structure, particularly parallel channels, also reduces the pressure drop experienced by the process gas SP2907-PD passing through the sorbent structure. The reduced pressure drop reduces the operating cost due to the reduced fan power required to move the gas through the sorbent structure. Brief Description of the Drawings 5 [0023] FIG.1 depicts an illustrative perspective view of an exemplary embodiment of a sorbent structure according to certain aspects described herein. [0024] FIG.2 depicts an illustrative enlarged perspective view of an embodiment of a sorbent structure according to certain aspects described herein, such as the sorbent structure depicted in FIG.1. 10 [0025] FIG.3 depicts an illustrative perspective, partial cross-sectional view along the length of another exemplary embodiment of a sorbent structure according to certain aspects described herein. [0026] FIG. 4 is an SEM (scanning electron microscope) image of a portion of the channel wall of an embodiment of a metal-containing support of the sorbent structure 15 according to certain aspects disclosed herein. [0027] FIG.5 illustrates a schematic representation of an exemplary DAC system in which embodiments of the sorbent structure disclosed herein can be employed. Detailed Description of the Invention [0028] The present invention will now be described in detail with reference to 20 embodiments thereof as illustrated in the accompanying drawings. References to “one embodiment”, “an embodiment” “an example embodiment”, etc., indicate that the embodiment described may include a particular feature, structure, or characteristic, but every embodiment may not necessarily include the particular feature, structure, or characteristic. Moreover, such phrases are not necessarily referring to the same embodiment. Further, when 25 a particular feature, structure, or characteristic is described in connection with an embodiment, it is submitted that it is within the knowledge of one skilled in the art to affect such feature, structure, or characteristic in connection with other embodiments whether or not explicitly described. Other suitable modifications and adaptations of the variety of conditions and parameters normally encountered in the field, and which would be apparent 30 to those skilled in the art, are within the spirit and scope of the invention. [0029] Although the description herein provides numerous specific details that are set forth for a thorough understanding of illustrative embodiments, it will be apparent to one skilled in the art that embodiments may be practiced without some or all of these specific SP2907-PD details. In other instances, well known process steps and/or structures have not been described in detail in order to not unnecessarily obscure the present invention. The features and advantages of embodiments may be better understood with reference to the drawings and discussions that follow. 5 [0030] In addition, when like elements are used in one or more figures, identical reference characters will be used in each figure, and a detailed description of the element will be provided only at its first occurrence. Some features or components of the systems or processes described herein may be omitted in certain depicted configurations in the interest of clarity. 10 [0031] FIG.1 schematically depicts a perspective view of sorbent structure 100, which is an exemplary embodiment of the sorbents for capturing carbon dioxide from a gas mixture disclosed herein. FIG.2 schematically depicts an enlarged view of sorbent structure 100, and FIG.3 schematically depicts a sectional view of sorbent structure 100 along its length 112. Although sorbent structure 100 is depicted as having a generally rectangular block15 shape (or cuboid), it is understood that sorbent structure 100 can have any suitable cross- sectional shape, including geometrical shapes such as trapezoidal, triangular, rectangular, square, sinusoidal, hexagonal, oval, circular, and the like. In the embodiment shown in FIGS.1 - 3, sorbent structure 100 comprises first end 102 and second end 104. Referring to FIG.2, sorbent structure 100 further comprises a plurality of flow channels 106, and a 20 plurality of channel walls 108. [0032] Flow channels 106 are formed by at least one channel wall 108 and extend from first end 102 to the second end 104. Flow channels 106 have a shape formed by at least one (such as two or more) channel wall. The shape of flow channels 106 is preferably a polygon, more preferably selected from triangle, square, and hexagon, trapezoid, 25 rectangular, sinusoid, or round like oval or round. Flow channels 106 preferably provide parallel flow passages extending from an inlet face (e.g., 102) to an outlet face (e.g., 104) of the substrate such that passages are open for fluid to flow through sorbent structure 100. [0033] As described herein, essentially all flow channels 106 can have substantially the same shape, or additionally or alternatively, a portion of flow channels 106 may take on 30 different shapes as compared to the remaining portion of flow channels 106, depending on other specifications, such as the overall configuration of sorbent structure 100. For instance, at least a major portion (>50%, preferably >80%), including all, of flow channels 106 has a polygon or circular shape; if polygon, preferably selected from the group SP2907-PD consisting of a triangle, rectangle, square, hexagon, and any combination thereof. For example, in an embodiment where the sorbent has a cylindrical shape, it is understood that the inner flow channels around the center may have different shape (such as square) than the flow channels at the circular edge, which are defined by a circular outer channel wall. 5 [0034] Flow channels 106 preferably occupies a relatively large amount of the front cross-sectional area such that resistance of the flow of gas through the channels is relatively low, thus minimizing the pressure drop which is the energy needed to force the gas through sorbent structure 100. For instance, referring to FIG.2, sorbent structure 100 preferably comprises an open frontal area (OFA) or free cross-sectional area in a range from 60% and 10 up to 85%, and more preferably in the range 65% to 75%. As used herein, “open frontal area” or “free cross-sectional area” has its ordinary meaning. For instance, a sorbent structure that has an OFA of 60%, it means that 60% of the cross-sectional area of the frontal area (e.g., 102 or 104) is open for the flow of a gas through the sorbent structure. That is, the cross-sectional area of flow channels 106 occupies 60% of the cross-sectional area of the 15 sorbent structure. One way the number of flow channels 106 making up the OFA of sorbent structure 100 can be characterized is cell density, where certain dimensions of flow channels 106 (or “cell”) can be designed to meet various objectives, including OFA. [0035] For instance, referring to FIGS.1 and 2, an exemplary suitable sorbent structure, such as structure 100, with a cross-sectional square shape of 150 mm by 150 mm can have 20 1600 cells or flow channels 106 (40 cells by 40 cells), where each cell opening (d) is about 3.2 mm, and OFA of 72.8 %. Optionally, structure 100 can comprise a cell density in a range from 50 and up to 400 cells per square inch (cpsi), preferably in a range from 50 and up to 300 cpsi and open frontal area in a range from 60% and up to 85%, preferably in the range 65% to 75%. Additionally or alternatively, at least a portion of the channel walls 108 25 can further comprise an average thickness in a range from 150 microns and up to 1000 microns. It is understood that the thickness of channel walls 108 can vary from one portion of sorbent structure 100 to another portion, including whether a particular channel wall is an exterior wall. [0036] Optionally, sorbent structure 100 can comprise a nominal cross-sectional area 30 (for instance D² in FIGS 1 or π(0.5D)² in FIG.3 (with D being 110 as a side or diameter, respectively) if the sorbent structure had a square or cylindrical cross-sectional shape, respectively) of at least 10 x 10 mm², such as in a range from 50 x 50 mm² to 600 x 600 SP2907-PD mm², preferably in a range from 100 x 100 mm² to 500 x 500 mm², more preferably in a range from 150 x 150 mm² to 300 x 300 mm². [0037] Optionally, sorbent structure 100 comprises a length 112 (L) in a range of 50 mm to 2000 mm, preferably in a range from 100 mm to 1000 mm, and most preferably in a range from 200 mm to 500 mm. [0038] Preferably, sorbent structure 100 is a monolithic unit that is self-supporting and comprises parallel flow channels 106 that extend from first end 102 to second end 104 (e.g., flow through monolith), such as a honeycomb structure. For instance, the metal-containing support provides structural integrity (functioning as a substrate) as well as functions as part of the active material to facilitate the sorption of CO2 by the carbonate. Such a monolithic unit may be formed using methods known in the art such as extrusion, co-mulling, 3-D printing and/or impregnation. [0039] Channel walls 108 comprise a carbonate of at least one of (i) an alkali metal with a chemical formula of X2CO3 and (ii) an alkaline earth metal with a chemical formula YCO3 in an amount in a range from 5 wt% and up to 50 wt%, preferably greater than 5 wt% to 30 wt%, based on the total weight of the channel walls. Preferably, the X is an alkali metal cation selected from the group consisting of K⁺, Na⁺, Cs⁺, Li⁺, (thereby forming K2CO3, Na2CO3, Cs2CO3, Li2CO3), and any combination thereof. Preferably the Y is an alkaline earth metal cation selected from the group consisting of Mg²⁺, Ca²⁺, Sr²⁺, Ba²⁺, (thereby forming MgCO₃, CaCO₃, SrCO₃, BaCO₃) and any combination thereof. The recited weight amounts are preferably determined when the carbonate is in anhydrous form. [0040] The wt% amount of carbonate in anhydrous form is preferably calculated from the wt% amount carbonate as determined by chemical analysis, preferably X-ray Fluorescence Spectroscopy (XRF). Before analysis of the wt% of carbonate is performed, the sample for testing is dried, preferably at around 300 °C for at least one hour, to determine the dry sample mass. The wt% amount of carbonate can be calculated using the following equation (A): Wcarbonate = Wmetal / f (A) where Wcarbonate is the mass loading of carbonate on the sorbent (wt%), Wmetal is the mass loading of the metal of the carbonate on the sorbent structure as determined by XRF (wt%) and f is the mass fraction of the metal of the carbonate in anhydrous or salt form, which can be calculated using the following equation (B): f = M_metal * n_metal / M_carbonate (B) SP2907-PD where Mmetal is the molar mass of the metal (g / mol), Mcarbonate is the molar mass of the carbonate and n_metal is the number of moles of metal per mole of carbonate salt (for instance nmetal = 2 for potassium carbonate (K2CO3) and nmetal = 1 for magnesium carbonate (MgCO3). For instance, a sample of a sorbent structure according to aspects described herein was analysed with XRF, which showed a mass loading of the metal potassium (WK) on a dry basis of 4.33 wt%. The carbonate loading of potassium carbonate on the metal- containing support can be calculated using equations (A) and (B) as shown below. f = 39.10 (g/mol) * 2 / 138.205 g/mol = 0.566 (B) Wpotassium carbonate = 0.433 wt%/0.566 = 7.66 wt% of K2CO3 in anhydrous form in the sample of the sorbent structure analyzed (A). [0041] The recited carbonates are hygroscopic salts with a tendency to absorb moisture from the air and becomes hydrated. The hygroscopicity of each carbonate can vary depending on the particular metal cation. Both the anhydrous and hydrated forms of the carbonates are prone to react with carbon dioxide and water to form a bicarbonate, thereby capturing the carbon dioxide as the bicarbonate. As such, the recited carbonates function as sorbents for CO2. [0042] Channel walls 108 further comprise a metal-containing support in an amount in a range from 40 wt% and up to 95 wt%, based on the total weight of the channel wall. The metal-containing support is preferably an inorganic material and comprises metal. The metal-containing support is preferably selected from the group consisting of a metal alloy, metal oxide, metal-non-metal alloy, ceramic, and any combination thereof. The metal is selected from the group consisting of aluminium, calcium, silicon, titanium, zirconium, magnesium, iron, and any combination thereof. Preferably, the metal-containing support is selected from the group consisting of silica, alumina, titania, zirconia, cordierite, mullite, silicon carbide, aluminosilicates, preferably zeolites, aluminium phosphate, and any combination thereof. More preferably, the metal-containing support is selected from the group consisting of alumina, titania, and any combination thereof. [0043] The carbonate and metal-containing support are considered to be active material as known to one of ordinary skill. The present disclosure provides for sorbent structures that comprise a majority (greater than 50 wt%, more preferably greater than 80 wt% of the total weight of the sorbent structure) of active material. SP2907-PD [0044] One preferred embodiment of the sorbent structure comprises an alkali metal salt, more preferably potassium carbonate and/or sodium carbonate, as the carbonate. For embodiments employing an alkali metal salt, it is preferred that the metal-containing support is one that minimally reacts with the alkali metal salt during carbon capture conditions. 5 Examples of such metal-containing support includes titania or zirconia. For instance, a preferred embodiment is a sorbent structure where the carbonate is selected from one or more alkali metal carbonate and where the metal-containing support is selected from titania, zirconia, or a combination thereof. [0045] In another aspect, the reaction between the carbonate and metal-containing 10 support can be minimized at least by using a metal-containing support, particularly alumina, that has been thermally treated. Preferably, the metal-containing support can be selected from the group consisting of potassium aluminate, sodium aluminate (2NaAlO₂═Na₂O*Al₂O₃), hydrated alumina (Boehmite, Al₂O₃*H₂O), bayerite, gibbsite, boehmite, pseudo-boehmite, bauxite, gamma-alumina, delta-alumina, chi-alumina, rho- 15 alumina, kappa-alumina, eta-alumina, theta-alumina, magnesium aluminate, trine, bermire, and any combination thereof. [0046] The metal-containing support is porous, meaning it contains pores or spaces. In particular, the metal-containing support comprises a total accessible porosity (εsupport) in a range from 0.4 and up to 0.8, preferably from 0.5 and up to 0.7. As known in the art, these 20 ranges for the total accessible porosity (ε) of the metal-containing support can be expressed as percentages as well, from 40% and up to 80%, preferably from 50% and up to 70%. As used herein, the term “total accessible porosity” has its ordinary meaning, which includes the percentage or fraction of void space (i.e., pores) in a substance that is accessible to water (i.e., open pores). For this disclosure, the total accessible porosity of the metal-containing 25 support refers to the percentage or fraction of void space in the metal-containing support that is accessible to water. [0047] The higher the total accessible porosity the more accessible pores are present on the surface of a substance, which means the less rigid the substance, and vice versa. Although less rigid, having relatively more accessible pores enables a higher loading of a 30 material of interest. Without wishing to be bound by theory, the inventors have found that the preferred range of at least 0.5, including from 0.5 and up to 0.7 or 0.8, provides more accessible space or voids in the support or channel walls to contain the carbonate, thereby allowing for relatively greater amounts of loading of the carbonate while still allowing the SP2907-PD metal-containing support to provide structural integrity to enable such embodiments to be self-supporting. [0048] The total accessible porosity of the metal-containing support (εsupport) is preferably determined by the following equation (C): εsupport = WPVsupport/(WPVsupport + 1/ρsupport) (C) where WPVsupport is the gravimetric water pore volume (ml/g) of the metal-containing support and ρsupport is the gravimetric skeletal density (g/ml) of the metal-containing support. As used herein, the term “gravimetric skeletal density” means the density of the metal-containing support which excludes the volume occupied by the total accessible porosity (εsupport) but includes the volume of inaccessible porosity. The gravimetric skeletal density can be measured using the Helium pycnometry method according to ASTM D3766. [0049] The water pore volume (WPV) of the metal-containing support is preferably determined by the following equation (D): WPV_support = (M₂−M₁)/ρ_liquid/(M₁) (D) [0050] M1 is the mass (in grams) of a dry sample of the metal-containing support. M1 is preferably determined by providing a sample of the metal-containing support in a range from 5 grams and up to 100 grams, drying the sample for at least 60 minutes at an operating temperature of about 300 °C, and then weighing the dried sample with a two-digit scale. [0051] M₂ is the mass (in grams) of the wet sample of the metal-containing support. This is determined as follows. After the dried sample is weighed to define M1, it is placed in a container and water is slowly added to the sample until it is immersed. After it is immersed in water, a vacuum of at least 0.1 bar is applied to the container, which expands any air inside the immersed sample. Pressure is applied at least until no more air bubbles come out of the sample and the pressure is switched back to ambient pressure (which refers to the pressure of the surrounding environment, typically around 1 bar). It generally takes around 30 minutes of applying pressure until no more air bubbles come out of the sample. [0052] After the pressure is switched back to ambient pressure, the immersed sample is removed from the container and placed on paper to allow excess liquid from the flow channels of the sample to be removed, preferably for about two minutes on a filter paper grade 4. After removal of excess water in the flow channels, the wet sample is weighed to provide M2. SP2907-PD [0053] In equation (D), ρliquid is the density of the liquid used, which typically is water with a density of 1.0 g/ml. After M₁, M₂, and ρ_support are determined, then the water pore volume of the metal-containing support (WPVsupport) can be calculated using equation (D). With the values of WPVsupport and ρsupport known, the total accessible porosity of the metal- containing support (εsupport) can be calculated using equation (C). [0054] The pores of metal-containing support hold the carbonate, thereby providing support to the carbonate. That is, the carbonate is present in or occupies a least a portion of the total accessible porosity of the metal-containing support (εsupport), thereby reducing the ε_support and providing the sorbent structure with a residual total accessible porosity (ε_residual) that is less than the εsupport. During CO2 removal operation using the sorbent structure, CO2- containing gas (such as air) flows through the flow channels and comes in contact with the carbonate in the channel walls, where the CO2 in the gas reacts with the carbonate and gets extracted. The residual total accessible porosity (ε_residual) of the sorbent structure is preferably calculated using the following equation (E): εresidual = ^support - (wcarbonate / (1- wcarbonate))*(1- ^ ^support)* ρsupport/ρcarbonate (E) ^ where εsupport is total accessible porosity of the metal-containing support as defined by equation (C) where Wcarbonate is the mass loading of carbonate on the sorbent (wt%) where ρ_support is the gravimetric skeletal density (g/ml) of the metal-containing support as already defined elsewhere herein, and where ρ_carbonate is the gravimetric density of the metal of the carbonate (g/ml). This value is widely available and known to one of ordinary skill in the art. [0055] Optionally, the residual total accessible porosity (εresidual) of sorbent structure 100 is in a range from 5% to 75%, preferably from 10% to 65%, more preferably from 20% to 65%. [0056] Preferably, impregnation is used to load at least a portion of total accessible porosity of the metal-containing support with the carbonate, as described herein. As used herein, “impregnated” or “impregnation” refers to permeation of the carbonate into the total accessible porosity of the support. [0057] With the total accessible porosity as described (such as in a range from 0.4 and up to 0.8), the metal-containing support provides high loading of the carbonate, which enables good contact and CO2 efficiency as the CO2-containing gas can pass through flow SP2907-PD channels 106, while still resulting in a low pressure drop, which provides for low operating costs. [0058] Preferably, the sum of the amount of the carbonate and the amount of the metal- containing support is at least 95 wt%, preferably 97 wt%, more preferably 99 wt%, of the total weight of channel wall 108. That is, sorbent structure 100 is preferably self-supporting where channel walls 108 preferably comprise mostly (i.e., at least 95 wt%), including consisting essentially, of the carbonate and the metal-containing support. Preferably, sorbent structure 100 (with its first and second ends) comprises mostly (at least 95 wt%) of channel walls 108 forming flow channels 106. [0059] FIG.4 is an electronic microscope image of the various pores for an exemplary embodiment of the metal-containing support as described herein, which relate to the total accessible porosity ( ^support) and the space in at least a portion of which holds the carbonate. [0060] Optionally, from 40% and up to 100% (preferably at least 50% and up to 100%) of the total accessible porosity ( ^support) comprises a pore size of 0.5 nm and up to 50 nm. For instance, the black holes in FIG. 4 are pores of roughly 20 nm. Additionally or alternatively, from 0% and up to 60% of the total accessible porosity ( ^support) comprises a pore size of greater than 50 nm. Additionally or alternatively, from 0% and up to 20% of the total accessible porosity ( ^_support) comprises a pore size of greater than 500 nm. As used herein, pore size refers to the pore width or diameter. The optional distribution of pore sizes in the total accessible porosity ( ^_support) ensures adequate void space in the nano-scale to contain the carbonate, thereby improving the volumetric carbon dioxide capture capacity of embodiments of the disclosed sorbent structure as compared to those with (i) less total accessible porosity and/or (ii) a smaller percentage of the total accessible porosity having a pore size 0.5 nm and up to 50 nm. [0061] The fraction of the total accessible porosity of the metal-containing support ( ^_support) having a pore size of less than or equal to 50 nm (F<50nm) is preferably determined using the following equation (G): F<50nm = (WPVsupport-(PV>50nm))/WPVsupport (G) where WPV is determined using equation (B) and PV>50nm is the pore volume of pores with a diameter above 50 nm as preferably determined using mercury porosimetry. [0062] The PV>50nm value, meaning the fraction of the total accessible porosity having a pore size of greater than 50 nm (F>50nm), is preferably determined using the method described in ASTM D4284 (Determining pore volume distribution of catalysts and catalyst SP2907-PD carriers by mercury intrusion porosimetry). When applying a contact angle of 140° using this method of ASTM D4284, the diameter of 50 nm corresponds to 296 bar (4240 PSI). PV>50nm therefore will correspond to the mercury volume that intruded between 0 and 296 bar. [0063] The fraction of the total accessible porosity having a pore size of greater than 500 nm (F>500nm) is preferably determined using the method described in ASTM D4284. When applying a contact angle of 140° using the method of ASTM D4284, F>500nm corresponds to the mercury volume that intrudes between 0 and 29.6 bar. [0064] It is understood that the metal-containing support can comprise materials that are known in the art to improve or facilitate the mechanical strength and/or fabrication process. Examples of such materials include tungsten trioxide, aluminum oxide, silicon dioxide, fibers, such as glass fibers, ceramic fibers (aluminosilicates), silicon carbide. The amount of these material is typically less than 20 wt%, 15 wt%, preferably less than 10 wt%, of the total weight of the metal-containing support. [0065] For embodiments that are self-supported monolith structures, the external surface area per unit volume is directly associated to the mass transfer rate. The external surface area of self-supported monoliths is proportional to the cell density and wall thickness. The cell density has a typical unit of cells per square inch. [0066] The present disclosure provides for methods of using the sorbent structures described herein (such as sorbent structure 100) to capture carbon dioxide from any gas stream containing CO2. The method comprises providing sorbent structure 100 that comprises first end 102 and second end 104, and a plurality of flow channels 106, and a plurality of channel walls 108. The method further comprises passing a gas comprising carbon dioxide (CO₂-containing gas) through at least a portion, including all, of flow channels 106. As the CO2-containing gas passes through flow channels 106, it comes in contact with channel walls 108, including the carbonate and metal-containing support. The method further comprises allowing at least a portion of the CO2 in the CO2-containing gas to react with the carbonate in channel walls 108. Preferably, the CO2-containing gas stream comprises carbon dioxide in an amount of less than 500 ppm, more preferably from 300 and up to 500 ppm. More preferably, CO2-containing gas consists essentially of atmospheric air (generally a mixture of gases comprising the Earth’s atmosphere). [0067] Suitable equipment (such as reactors) and operating conditions are known to one of ordinary skills. Examples of such suitable equipment and conditions can be found in SP2907-PD EP2173322.3, EP21207908.1. For instance, FIG.5 shows a representation of a direct air capture (DAC) carbon dioxide adsorber unit 100 in top or plan view. The exemplary adsorber unit 100 comprises one or multiple rows of monolith beds or slabs 501 that are comprised of one or more embodiments of the sorbent structure disclosed herein. Preferably, the 5 embodiment of the sorbent structure employed is a monolith where feed gas 550 comprising carbon dioxide is drawn through flow channels 106 (not shown in FIG. 5) by suitable equipment, such as impellers 503, such as fans. Typically, the feed gas 550 is air but in embodiments of the invention it may comprise a conditioned gas enriched with carbon dioxide, such as a flue exhaust gas from an industrial or biological process. As the feed gas 10 550 passes across the surfaces comprised within the monolith, at least a portion of the carbon dioxide reacts with the carbonate and is captured, thereby providing carbon dioxide depleted gas 560 leaving the monolith and vented to the atmosphere. [0068] Eventually as the sorbent material approaches desired saturation with adsorbed carbon dioxide there is a need to regenerate the sorbent material and strip away the carbon 15 dioxide. The adsorber unit 500 can include a movable regenerator unit 502 that is able to move along a track and encompasses an adjacent pair of monolith blocks at any given time whilst allowing neighbouring monolith blocks to continue to adsorb carbon dioxide. In this way the cycle of adsorption and regeneration within the DAC unit can occur continuously without interruption and significant downtime. It will be appreciated that the configuration 20 of a movable regenerator unit 502 depicted in FIG.5 is merely exemplary and alternative assemblies of monoliths and regenerator units are possible, for example, as mentioned previously United States Patent No.10,512,880 describes an arrangement whereby monolith beds are arranged in a rotating drum around a static regeneration unit. [0069] The regenerator unit 502 comprises an inlet that is in fluid communication 25 with a source of a regenerant vapour, such as steam via a low-pressure (LP) steam line 570. Typically, the steam may be derived from an external heat exchange system that is able to heat a supply of water by way of a boiler and generate output of LP steam. The LP steam may also be obtained as output from a back pressure turbine or reclaimed from one or more parallel industrial processing apparatus and systems that generate excess or waste energy, 30 suitably in the form of thermal energy, such as comprised within steam or other heated fluids. [0070] The regenerator unit further comprises at least one outlet that is in fluid communication with a vent line 580 that comprises a vacuum pump 504. In this way steam may be introduced and drawn into the regenerator unit from the LP steam line via reduction SP2907-PD of pressure. Alternatively, steam of slightly elevated pressure just above atmospheric pressure (e.g. >1 bar), suitably around 1.3 bar/130 KPa (around 18.9 psi), and at a temperature of around 100 to 130 ˚C may be introduced directly into the regenerator unit. That is, in certain embodiments, the sorbent structure is regenerated at least via temperature- swing adsorption (TSA) rather than pressure-swing adsorption (PSA). [0071] Accordingly, the present disclosure provides a method for capturing carbon dioxide from a gas mixture. The method comprises: (a) providing an embodiment of the sorbent structure disclosed herein, including sorbent structure 100; (b) passing a gas comprising carbon dioxide (CO₂-containing gas) through at least a portion, including all, of the flow channels (e.g., 108) of the structure; and (c) allowing at least a portion of the CO2 in the CO₂-containing gas to react with the carbonate to produce at least partially loaded (including fully loaded) sorbent structures. Optionally, the CO2-containing gas stream consists essentially of air. [0072] Optionally, the step of passing the CO2-containing gas through at least a portion of the flow channels is conducted at or near atmospheric pressure, which is known to one of ordinary skill and typically is 1 atm +/- 5%. Additionally or alternatively, the method further comprises (d) contacting the at least partially loaded sorbent structures with steam to regenerate the sorbent structures, wherein the steam is introduced at or near atmospheric pressure or has a slightly elevated pressure just above atmospheric pressure (e.g. >1 bar), suitably around 1.3 bar/130 KPa (around 18.9 psi), and at a temperature of around 100 to 130 ˚C. [0073] According to another aspect, the present disclosure also provides methods of making a sorbent structure as described herein for capturing carbon dioxide from a CO2- containing gas. In embodiments wherein the metal-containing support is produced separately (such as through extrusion or 3D printing), the carbonate can be applied to the metal-containing substrate using impregnation. The method of wash-coating is not preferred because the material is applied on top of the surface of the sorbent structure as a layer, which tends to unnecessarily reduce the total accessible porosity of the metal-containing substrate. On the other hand, impregnation applies the carbonate in the total accessible porosity without unnecessary reduction of pore space and/or width of the flow channels 106 as compared to wash-coating, thereby allowing for better accessibility to the carbonate by the carbon dioxide and/or improved gas flow through the sorbent structure 100. SP2907-PD [0074] In various embodiments, the metal-containing support material and the carbonate material may be combined, for example in a paste, and extruded together to form the sorbent structure. In this embodiment, the carbonate may be dispersed throughout the metal- containing support when the combined paste is extruded into a monolithic form to achieve the desired physical and structural properties. One advantage of combining the metal- containing support material and the carbonate material in one single step is that fewer process steps are required. A further advantage is that it is easier to obtain a good mixing and distribution of the metal-containing support material and the carbonate material when they are combined and formed together (such as via extrusion or 3D printing). [0075] An advantage of the various embodiments described herein is that the sorbent structure of the present disclosure provides for efficient contact between the gas mixture flowing through the sorbent structure and the sorbent structure (both metal-containing support material and carbonate) on a micro-scale level, and the metal-containing support provides for efficient transport of the process gas through the sorbent structure itself on a macro-scale level, without the need for a separate substrate, which can lead to increased production costs as well as reduced flow. [0076] Various embodiments of the sorbent structures disclosed herein enables enhanced flow paths and provides higher volumetric efficiency in the configurations as compared to packed adsorbent beds employing catalyst in particulate form or to structures that employ substrates (that is, does not contain a majority of active material) or apply active material through washcoating. The packed adsorbent beds have higher pressure drops and slower mass transfer rates which are inefficient in operating the adsorption or catalytic processes for large volume gas separation processes, such as those employed in direct air capture processes. The sorbent structures of the present disclosure are particularly suitable for large volume gas separation processes that rely upon low pressure drop and high volumetric efficiency through rapid cycling. [0077] Examples [0078] Example 1: Preparation of 10% K2CO3 on TiO2 (Sorbent Structure A) [0079] 12.2 g of a porous straight-channel monolithic titania substrate was used as a metal-containing support, which has 100 cpsi, 0.35 mm walls, an open frontal area of 0.74, total accessible porosity (ε_support) of 0.50, and an average pore size of 22 nm.74.07 g of K2CO3 was dissolved in demineralized water to obtain a solution volume of 200 ml. The monolith (metal-containing support) was completely immersed in the solution for 30 minutes SP2907-PD for impregnation of the carbonate. Excess liquid from the flow channels and on the outer surface of the monolith was removed with a compressed air nozzle. The sample was subsequently dried at 120 °C for 2 hours and calcined at 300 °C for 2 hours to produce Sorbent Structure A. A sample of Sorbent Structure A was analyzed, which showed it contains 10.0% K2CO3 in anhydrous form on TiO2 as the metal-containing support. The residual total accessible porosity of Sorbent Structure A (εresidual) was calculated to be 0.41 using the process disclosed herein. [0080] Example 2: Preparation of 20% K2CO3 on TiO2 (Sorbent Structure B) [0081] 12.2 g of a porous straight-channel monolithic titania substrate was used as a metal-containing support, which has 100 cpsi, 0.35 mm walls, an open frontal area of 0.74, total accessible porosity (ε_support) of 0.50, and an average pore size of 22 nm. 166.7 g of K2CO3 was dissolved in demineralized water to obtain a solution volume of 200 ml. The monolith (metal-containing support) was completely immersed in the solution for 30 minutes for impregnation of the carbonate. Excess liquid from the flow channels and on the outer surface of the monolith was removed with a compressed air nozzle. The sample was subsequently dried in air flow at 65°C for 15 minutes, followed by drying at 120 °C for 2 hours and calcination at 300 °C for 2 hours A sample of Sorbent Structure B was analyzed, which showed it contains 20.0% K2CO3 in anhydrous form on TiO2 as the metal-containing support. The residual total accessible porosity of Sorbent Structure B (εresidual) was calculated to be 0.31 using the process disclosed herein. [0082] Example 3: Preparation of 10% K2CO3 on Al2O3 (Sorbent Structure C) [0083] 8.1 g of a porous straight-channel monolithic Al₂O₃ substrate was used as a metal-containing support, which has 100 cpsi, 0.45 mm walls, an open frontal area of 0.58, a total accessible porosity (ε_support) of 0.68 and an average pore size of 12 nm wherein 100% of the total accessible porosity comprises a pore size of less than or equal to 50 nm.27.8 g of K₂CO₃ was dissolved in demineralized water to obtain a solution volume of 200 ml. The monolith (metal-containing support) was completely immersed in the solution for 30 minutes for impregnation of the carbonate. Excess liquid from the channels and on the outer surface of the monolith was removed with a compressed air nozzle. The sample was subsequently dried in air flow at 65°C for 15 minutes, followed by drying at 120 °C for 2 hours and calcination at 300 °C for 2 hours. A sample of Sorbent Structure C was analyzed, which showed it contains 10.0% K2CO3 in anhydrous form on Al2O3 as the metal-containing SP2907-PD support. The residual total accessible porosity of Sorbent Structure C (εresidual) was calculated to be 0.63 using the process disclosed herein. [0084] Example 4: Preparation of 25% K2CO3 on Al2O3 (Sorbent Structure D) [0085] 20 g of a porous straight-channel monolithic Al2O3 substrate was used as a metal- containing support, which has 100 cpsi, 0.45 mm walls, an open frontal area of 0.68, a total accessible porosity (εsupport) of 0.70 and an average pore size of 12 nm wherein 100% of the total accessible porosity comprises a pore size of less than or equal to 50 nm.34.8 g of K2CO3 was dissolved in demineralized water to obtain a solution volume of 100 ml. The monolith (metal-containing support) was completely immersed in the solution for 30 minutes for impregnation of the carbonate. Excess liquid from the flow channels and on the outer surface of the monolith was removed with a compressed air nozzle. The sample was subsequently dried at 120 °C for 2 hours and calcined at 300 °C for 2 hours. A sample of Sorbent Structure D was analyzed, which showed it contains 25.0% K₂CO₃ in anhydrous form on Al2O3 as the metal-containing support. The residual total accessible porosity of Sorbent Structure D (ε_residual) was calculated to be 0.52 using the process disclosed herein. [0086] Example 5: Preparation of 10% Na²CO³ on Al²O³ (Sorbent Structure E) [0087] 20 g of a porous straight-channel monolithic Al2O3 substrate was used as a support having 100 cpsi, 0.45 mm walls, an open frontal area of 0.68, a porosity of 0.70 and an average pore size of 12 nm wherein 100% of the total accessible porosity comprises a pore size of less than or equal to 50 nm.13.9 g of Na₂CO₃ was dissolved in demineralized water to obtain a solution volume of 100 ml. The monolith was completely immersed in the solution for 30 minutes. Excess water from the channels and on the outer surface of the monolith was removed with a compressed air nozzle. The sample was subsequently dried at 120 °C for 2 hours and calcined at 300 °C for 2 hours. The sorbent contains 10.0% Na2CO3 on Al2O3. The residual porosity was 0.63. [0088] The carbonate loading on a particular metal-containing support is defined as K2CO3 in anhydrous form, which does not necessarily represent the final state of the alkali metal precursor on a particular sorbent structure. Various sorbent structures were prepared, ranging from 7.5% K2CO3 on γ-Al2O3 to 40% K2CO3 on γ-Al2O3. Sorbent preparations were also carried out with carbonates, bicarbonates, hydroxides, acetates, and citrates as precursor compounds. [0089] Example 6: CO2 capacity fixed bed testing SP2907-PD [0090] Sorption capacity was tested over 5 adsorption-desorption cycles in a fixed bed setup with a sorbent volume of 5 cm³. The setup was equipped with calibrated mass flow controllers to control gas flow (air, nitrogen) and a membrane vapor generator to humidify the gasses. Prior to the adsorption and desorption cycles the sample was dried in argon at 120 °C for 2 hours. Then the bed was cooled to 30 °C and the sorbent and humid nitrogen gas with 18% RH at 30 °C was passed over the sorbent bed for 75 minutes. Maintaining a bed temperature of 30 °C the flow was switched to air containing 380 – 420 ppm CO2 with a relative humidity of 18% at 30 °C. Humid air was passed through the sorbent bed for 2 hours at a gas hourly space velocity of 24,000 h-1 (under atmospheric pressure). Then the flow was switched to nitrogen and the bed was flushed for 15 minutes to remove any physisorbed water. The sorbent was then heated to 120 °C in nitrogen for 30 minutes followed by 45 minutes in a mixture of 5% steam with balance nitrogen to regenerate the sorbent and desorb CO₂. Afterwards, the sorbent was cooled to 30 °C to complete the first adsorption-desorption cycle. Subsequent cycles were carried out according to the same protocol. The off gasses were passed through an IR analyzer to measure the CO₂ and H₂O breakthrough profiles. Gas lines were heated to prevent condensation of water. CO2 capacity was determined by integration of the CO2 breakthrough profile and reported based on the dry mass of the sample. Table 1 summarizes the CO2 desorption capacities of various sorbents of the 5th cycle. Table 1: summary of sorbent CO₂ capacities Sorbent K2CO3 on activated Sorbent carbon (AC) Honeycomb Structure Sorbent Structure (Reference Sample)* A B CO₂ Capacity [wt%] 0.88 1.06 2.14 * as reported in Rodríguez-Mosqueda et al. (Parametrical Study on CO2 Capture from Ambient Air Using Hydrated K2CO3 Supported on an Activated Carbon Honeycomb, Ind. Eng. Chem. Res.2018, 57, 3628−3638) 6 [0091] Sorbents generally show a higher CO2 capacity in the first adsorption-desorption cycle. Therefore, we tested the sorbents over 5 adsorption-desorption cycles and report in Table 1 the CO₂ desorption capacity of the last cycle. Sorbent Structure A was impregnated with 10% K2CO3 (as described in Example 1) on a titania honeycomb substrate with a residual porosity of 41%. The CO₂ capacity of Sorbent Structure A was 1.06 g of CO2 per 100 g of sorbent (1.06 wt%), which is higher than the capacity of the Reference Sample, which is an activated carbon honeycomb impregnated with K₂CO₃ tested at 30 °C and 28% relative humidity as reported by Rodríguez-Mosqueda et al. SP2907-PD [0092] Sorbent Structure B was impregnated with 20% K2CO3 on a titania honeycomb substrate (as described in Example 2) with a residual porosity of 31%. The capacity for Sorbent Structure B was 2.14 g CO2 per 100 g sorbent (2.14 wt%). It was unexpected that Sorbent Structures A and B remain observably in better condition than the Reference Sample. It is believed that Sorbent Structures A and B should be able to adequately function, in terms of structural integrity and CO2 capacity, in further adsorption-desorption cycles beyond the five cycles tested in these Examples. In contrast, Rodríguez-Mosqueda et al. has observations of unstable adsorbents that got destroyed after a few cycles. Without wishing to be bound by theories, it is believed that in the Reference Sample, the carbonate salt undergoes phase changes from one set of adsorption-desorption cycle to the next (from carbonate to bicarbonate due to reaction with CO₂ during adsorption, and dissolution and re- crystallization due to humidity swing in desorption). These phase changes impose stress on the activated carbon material, which is believed to lead to its destruction after a few cycles. Similar detrimental reaction was unexpectedly not observed for embodiments of the structural sorbents described herein. [0093] While specific embodiments have been described herein, it is understood that such descriptions are not intended to limit the described embodiments. Instead, any combination of the features and elements provided above, whether related to different embodiments or not, is contemplated to implement and practice contemplated embodiments. Furthermore, although embodiments disclosed herein may achieve advantages over other possible solutions or over the prior art, whether or not a particular advantage is achieved by a given embodiment is not limiting of the scope of the present disclosure. Thus, the aspects, features, embodiments and advantages described herein are merely illustrative and are not considered elements or limitations of the appended claims except where explicitly recited in a claim(s).

Claims

SP2907-PD C L A I M S ` 1. A sorbent structure for capturing from a gas mixture, the sorbent structure comprising: ^ a first end and a second end; ^ a plurality of flow channels; and ^ a plurality of channel walls, wherein the flow channels are formed by at least one channel wall, wherein the flow channels extend from the first end to the second end, and wherein the channel walls comprise: o a carbonate in an amount in a range from greater than 5 wt% and up to 50 wt%, preferably greater than 5 wt%, including from 10 wt% and up to 30 wt%, based on the total weight of the channel walls, wherein the carbonate being at least one of (i) an alkali metal (X₂CO₃) and (ii) an alkaline earth metal (YCO3); o a metal-containing support in an amount in a range from 40 wt% and up to 95 wt%, based on the total weight of the channel walls; wherein the metal-containing support comprises a metal and is selected from the group consisting of a metal alloy, metal oxide, metal-non-metal alloy, ceramic, and any combination thereof, wherein the metal-containing support comprises a total accessible porosity (εsupport) in a range from 0.4 – 0.8, preferably 0.5 – 0.7; wherein the total accessible porosity of the metal-containing support (ε_support) is determined at least by: ε_support = WPV_support/(WPV_support + 1/ρ_support) where WPVsupport is the gravimetric water pore volume (ml/g) of the metal-containing support where ρ_support is the gravimetric skeletal density of the metal- containing support, and wherein from 40% and up to 100% of the total accessible porosity comprises a pore size of less than or equal to 50 nm and from 0% and up to 60% of the total accessible porosity comprises a pore size of greater than 50 nm. SP2907-PD 2. The sorbent structure of claim 1 wherein the gravimetric water pore volume (ml/g) of the metal-containing support (WPVsupport) is determined at least by: WPVsupport = (M2−M1)/ρliquid/(M1) where M1 is the mass (in grams) of a dry sample of the metal-containing support, where M2 is the mass (in grams) of the wet sample of the metal-containing support, and ρ_liquid is the gravimetric density of liquid used to wet the sample. 3. The sorbent structure of any one of the prior claims comprising a residual total accessible porosity (ε_residual) in a range from 5% to 75%, preferably from 10% to 65%, more preferably from 20% to 65%. 4. The sorbent structure of claim 3, wherein the ε_residual is determined at least by: εresidual = ^support - (wcarbonate / (1- wcarbonate))*(1- ^ ^support)* ρsupport/ρcarbonate ^ where ε_support is total accessible porosity of the metal-containing support, and where W_carbonate is the mass loading of carbonate on the sorbent (wt%) and where ρsupport is the gravimetric skeletal density (g/ml) of the metal-containing support, and where ρcarbonate is the gravimetric density of the metal of the carbonate (g/ml). 5. The sorbent structure of any one of the prior claims, wherein a sum of the amount of the carbonate and the amount of the metal-containing support is at least 95 wt%, preferably 97 wt%, more preferably 99 wt% of the sorbent structure. 6. The sorbent structure of any previous claims, wherein the X is an alkali metal cation selected from the group consisting of K⁺, Na⁺, Cs⁺, Li⁺, and any combination thereof and the Y is an alkaline earth metal cation selected from the group consisting of Mg²⁺, Ca²⁺, Sr²⁺, Ba²⁺, and any combination thereof. 7. The sorbent structure of any previous claims, wherein the metal of the metal- containing support is selected from the group consisting of aluminium, silicon, titanium, zirconium, magnesium, calcium, iron, and any combination thereof; optionally wherein the metal-containing support is selected from the group consisting of silica, alumina, titania, zirconia, cordierite, mullite, silicon carbide, aluminosilicates, preferably zeolites, and any combination thereof. SP2907-PD 8. The sorbent structure of claim 7 wherein the carbonate is selected from one or more alkali metal and the metal-containing support is selected from titania and/or zirconia. 9. The sorbent structure of claim 7 wherein the carbonate is selected from one or more alkali metal and the metal-containing support is alumina, preferably thermally- treated alumina, more preferably selected from the group consisting of potassium aluminate, sodium aluminate (2NaAlO2═Na2O*Al2O3), hydrated alumina (Boehmite, Al2O3*H2O), bayerite, gibbsite, boehmite, pseudo-boehmite, bauxite, gamma-alumina, delta-alumina, chi-alumina, rho-alumina, kappa-alumina, eta- alumina, theta-alumina, magnesium aluminate, trine, bermire, and any combination thereof.. 10. The sorbent structure of any previous claims, wherein the metal-containing support further comprises an enhancing material to improve or facilitate the mechanical strength and/or fabrication process in an amount of less than 20 wt% of the total weight of the metal-containing support. 11. The sorbent structure of any previous claims, wherein from 0% and up to 20% of the total accessible porosity comprises a pore size of greater than 500 nm. 12. The sorbent structure of any previous claims, further comprising a cell density in a range from 50 and up to 400 cells per square inch (cpsi), preferably in a range from 50 and up to 300 cpsi and open frontal area in a range from 60% and up to 85%, preferably in the range 65% to 75%. 13. The sorbent structure of any previous claims, wherein the channel walls further comprise an average thickness in a range from 150 microns and up to 1000 microns. 14. A method for capturing carbon dioxide from a gas mixture, the method comprising: - providing the sorbent structure of any one of claims 1 - 13; - passing a gas comprising carbon dioxide (CO2-containing gas) through at least a portion, including all, of the flow channels; and - allowing at least a portion of the CO2 in the CO2-containing gas to react with the carbonate to produce at least partially loaded sorbent structures. 15. The method of claim 14 wherein the CO₂-containing gas stream consists essentially of air. SP2907-PD 16. The method of any one of claims 14 – 15, wherein the step of passing the CO2- containing gas through at least a portion of the flow channels being conducted at or near atmospheric pressure, the method further comprises: - contacting the at least partially loaded sorbent structures with steam to 5 regenerate the sorbent structures, wherein the steam is introduced at or near atmospheric pressure or has a slightly elevated pressure just above atmospheric pressure (e.g. >1 bar), suitably around 1.3 bar/130 KPa (around 18.9 psi), and at a temperature of around 100 to 130 ˚C. 10