WO2025064523A1

WO2025064523A1 - Electrochemical regeneration of high purity co2 and basic sorbent from carbonates and/or bicarbonates for efficient carbon capture

Info

Publication number: WO2025064523A1
Application number: PCT/US2024/047244
Authority: WO
Inventors: Haotian WANG; Xiao Zhang
Original assignee: William Marsh Rice University
Current assignee: William Marsh Rice University
Priority date: 2023-09-19
Filing date: 2024-09-18
Publication date: 2025-03-27
Anticipated expiration: 2026-03-19

Abstract

Systems for electrochemical carbon dioxide and basic sorbent regeneration comprising a modular porous solid electrolyte reactor and corresponding method and process for electrochemical carbon dioxide and basic sorbent regeneration. The modular porous solid electrolyte reactor comprises an anode chamber, a cathode chamber, and a membrane system. The membrane system comprises a proton exchange membrane, a cation exchange membrane, and a porous solid electrolyte layer located between the proton exchange membrane and the cation exchange membrane. The membrane system is configured to receive a feed stream comprising a basic sorbent and sorbed carbon dioxide in the form of carbonates and/or bicarbonates and produce a high purity stream comprising carbon dioxide. The anode chamber is configured to receive a hydrogen source and produce protons at the anode so as to provide protons to the membrane system. The cathode chamber is configured to receive a water source, receive cations from the membrane system, and produce a regenerated basic sorbent stream.

Description

ELECTROCHEMICAL REGENERATION OF HIGH PURITY CO2 AND BASIC SORBENT FROM CARBONATES AND/OR BICARBONATES FOR EFFICIENT CARBON CAPTURE BACKGROUND [0001] Before renewable energy can fully displace traditional fossil fuels used to power industry, transportation, and many other human activities, carbon capture from point sources, or directly from the atmosphere, followed by either carbon sequestration or utilization will remain the most effective and powerful tool to mitigate climate change. As carbon dioxide (CO2) is an acidic gas, one popular class of carbon capture technologies is based on the simultaneous neutralization reaction between low- concentration CO₂ and a basic solution (such as monoethanolamine or NaOH) to form carbon-containing products, followed by a regeneration process to produce high concentration CO2 while restoring the basic solution for the next round or capture process. This regeneration step, driven either thermally, chemically, or electrochemically, involves chemical bond dissociation to release CO₂ and thus is usually the most energy- and cost-intensive step. For example, in amine scrubbing carbon capture technologies, the CO₂ desorption process needs ~ 110 to 140 ℃ water vapor stripping which is estimated to account for ~ 70% of the overall operating cost. [0002] Compared to the amine-based sorbents, basic aqueous solutions (such as NaOH or KOH) show distinct advantages for large scale carbon capture applications including low corrosion, high stability, high capture rates, no sensitivity to oxygen, as well as environmental benignity. However, due to the strong CO2 absorption capability to form very stable carbonate compounds, the thermal regeneration process typically requires even more energy than amine-based sorbents. [0003] Electrochemical regeneration processes, which can use renewable electricity as the energy input, are considered green, efficient, and sustainable alternatives to the thermal regeneration counterpart to release CO₂ from carbon-containing solutions. The electrochemical reactions are operated under room temperature and ambient pressure, which avoids complicated infrastructures like the case of thermal regeneration and are also more energy efficient. The working mechanism is typically based on the pH sensitivity of the carbon-containing solutions, such as the acidification of carbonate/bicarbonate to regenerate high concentrations of CO2 via electrolysis- induced acid and alkaline solutions. [0004] Representative studies including electrochemical pH-swing or electrodialysis have been investigated using cation exchange membranes (CEM), anion exchange membranes (AEM), bipolar membranes (BPM), and their mixture modules. However, these investigations tend to be limited by complicated acid/alkaline separation and re- mixture steps, small CO2 regeneration rates (or small operation current densities), or generation of side products such as H2, O2 or Cl2. Additionally, similar electrochemical devices have been proposed to extract CO₂ from seawater for direct air capture (DAC) applications, which suffer from harsh seawater environments such as Ca²⁺/Mg²⁺ impurities that clog membranes/electrodes, cause bacteria fouling, and side reactions due to the high concentration of NaCl. Further, the carbon capture rates and efficiencies reported in the seawater studies were based on pH measurements and equilibrium assumptions instead of direct CO2 gas collections, which may not accurately reflect the carbon capture rates or energy consumptions when deployed in practice. Accordingly, there exists a need for an efficient, low energy consumption, carbon capture and recovery system. [0005] This invention was made with support from The Robert A. Welch Foundation under Grant No. C-2051-20200401. SUMMARY [0006] This summary is provided to introduce a selection of concepts that are further described below in the detailed description. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as an aid in limiting the scope of the claimed subject matter. [0007] In one aspect, embodiments disclosed herein relate to a system for electrochemical carbon dioxide and basic sorbent regeneration, comprising a modular porous solid electrolyte reactor. The modular porous solid electrolyte reactor comprises an anode chamber with an anode, a cathode chamber with a cathode, and a membrane system. The membrane system is located between the anode chamber and the cathode chamber and comprises a first side facing the anode chamber and a second side facing the cathode chamber. The membrane system is configured to receive a feed stream comprising a basic sorbent and sorbed carbon dioxide in the form of carbonates and/or bicarbonates, and to electrochemically split cations from the carbonates and bicarbonates, producing a high purity stream comprising carbon dioxide. The anode chamber is configured to receive a hydrogen source and produce protons at the anode, and to separate protons from the hydrogen source so as to provide protons to the membrane system. The cathode chamber is configured to receive a water source, receive cations from the membrane system, and produce anions at the cathode, reacting the cations with the anions so as to produce a regenerated basic sorbent stream. The membrane system further comprises a proton exchange membrane facing the first side, a cation exchange membrane facing the second side, and a porous solid electrolyte layer located between the proton exchange membrane and the cation exchange membrane. [0008] In another aspect, embodiments disclosed herein relate to a method for electrochemical carbon dioxide and basic sorbent regeneration. The method includes providing a modular porous solid electrolyte reactor that comprises an anode chamber with an anode, a cathode chamber with a cathode, and a membrane system. The membrane system is located between the anode chamber and the cathode chamber and comprises a first side facing the anode chamber and a second side facing the cathode chamber. The membrane system further comprises a proton exchange membrane facing the first side, a cation exchange membrane facing the second side, and a porous solid electrolyte layer located between the proton exchange membrane and the cation exchange membrane. The method further comprises providing a feed stream including a basic sorbent and sorbed carbon dioxide in the form of carbonates and/or bicarbonates to the membrane system to electrochemically split cations from the carbonates and bicarbonates, producing a high purity stream comprising carbon dioxide; providing a hydrogen source to the anode chamber and producing protons at the anode, and separating the protons from the hydrogen source so as to provide protons to the membrane system; and providing cations from the membrane system and a water source to the cathode chamber, producing anions at the cathode, and reacting the cations with the anions so as to produce a regenerated basic sorbent stream. [0009] In yet another aspect, embodiments disclosed herein relate to a system for electrochemical carbon dioxide and basic sorbent regeneration, comprising a modular porous solid electrolyte reactor. The modular porous solid electrolyte reactor comprises an anode chamber with an anode, a cathode chamber with a cathode, and a membrane system. The membrane system is located between the anode chamber and the cathode chamber and comprises a first side facing the anode chamber and a second side facing the cathode chamber. The membrane system is configured to receive a feed stream comprising a basic sorbent and sorbed carbon dioxide in the form of carbonates and/or bicarbonates, and to electrochemically split cations from the carbonates and bicarbonates, producing a high purity stream comprising carbon dioxide. The anode chamber is configured to receive a hydrogen source and produce protons at the anode, and to separate protons from the hydrogen source so as to provide protons to the membrane system. The cathode chamber is configured to receive a water source, receive cations from the membrane system, and produce anions at the cathode, reacting the cations with the anions so as to produce a regenerated basic sorbent stream. The membrane system further comprises a first membrane unit comprising the first side; a terminal membrane unit comprising a cation exchange membrane comprising the second side; and optionally one or more repeating membrane units between the first membrane unit and the terminal membrane unit, where each repeating membrane unit comprises a cation exchange membrane, a porous solid electrolyte layer, a bipolar membrane, and a porous solid electrolyte layer. [0010] In still yet another aspect, embodiments disclosed herein relate to a process for electrochemical carbon dioxide and basic sorbent regeneration. The process comprises feeding a carbon dioxide source into an absorption unit configured to absorb carbon dioxide and produce a feed stream comprising a basic sorbent and sorbed carbon dioxide in the form of carbonates and/or bicarbonates, feeding the feed stream into a modular porous solid electrolyte reactor in accordance with one or more embodiments, contacting the feed stream with the membrane system of the modular porous solid electrolyte reactor, to produce a carbon dioxide rich stream comprising regenerated carbon dioxide and regenerated basic sorbent, feeding the carbon dioxide rich stream into a separator to separate the regenerated carbon dioxide from the carbon dioxide rich stream to produce a carbon dioxide lean stream, and storing the regenerated carbon dioxide in a carbon dioxide storage unit. [0011] Other aspects and advantages of the claimed subject matter will be apparent from the following description and the appended claims. BRIEF DESCRIPTION OF DRAWINGS [0012] FIG. 1 is a schematic diagram of a device in accordance with one or more embodiments. [0013] FIGs.2A, 2B, and 2C are schematic diagrams of devices in accordance with one or more embodiments. [0014] FIG. 3 is a schematic diagram of a process in accordance with one or more embodiments. [0015] FIG. 4 is a schematic diagram of a process in accordance with one or more embodiments. [0016] FIG. 5 is a schematic diagram of a method in accordance with one or more embodiments. [0017] FIGs. 6A and 6B are schematic diagrams of comparative thermal (6A) and exemplary electrochemical (6B) carbon capture loops. [0018] FIGs. 7A and 7B are schematic diagrams of a comparative electrochemical process (7A) and a comparative pH swing process (7B) for the generation of CO2. _[0019] FIG. 8 is a schematic diagram of a system for CO₂ regeneration in accordance with one or more embodiments. [0020] FIG. 9 is a schematic diagram of a device in accordance with one or more embodiments. [0021] FIG. 10 is a schematic diagram of a device in accordance with one or more embodiments. [0022] FIGs. 11A and 11B are schematic diagrams of a device in accordance with one or more embodiments (11A) and a comparative MEA reactor (11B). [0023] FIGs. 12A and 12B are schematic diagrams of devices in accordance with one or more embodiments. [0024] FIGs.13A, 13B, and 13C illustrate the current density versus cell voltage curve for varying NaHCO3 concentrations (13A), the corresponding Na⁺ ion transport number of Na⁺ crossover (13B), and the CO₂ regeneration rate (13C) of devices according to one or more embodiments. [0025] FIGs.14A, 14B, and 14C illustrate the current density versus cell voltage curve for varying Na₂CO₃ concentrations (14A), the corresponding Na⁺ ion transport number of Na⁺ crossover (14B), and the CO2 regeneration rate (14C) of devices according to one or more embodiments. [0026] FIGs.15A, 15B, and 15C illustrate the cell voltage comparison between the PSE layer according to one or more embodiments and sand (15A), electrochemical energy consumption of CO2 release (15B), and the Na⁺ ion transport number and corresponding CO₂ regeneration rates under higher current densities (15C) of devices according to one or more embodiments. [0027] FIGs. 16A and 16B are schematic illustrations of a CO2 capture and regeneration process according to one or more embodiments (16B), and an analogous battery charging and discharging process (16A). [0028] FIGs. 17A and 17B illustrate the Na⁺ concentration in the membrane system and cathode chamber as a function of electrolysis time (17A) and the cell voltage, FE Na⁺, and energy consumption (17B) of the device according to one or more embodiments. [0029] FIG. 18 illustrates the results of practical cycle operations of the device according to one or more embodiments. [0030] FIGs.19A and 19B illustrate the resistance results for a device with conductive solid electrolyte (a PSE layer) in the middle chamber according to one or more embodiments (19A) and the resistance results for a reactor without solid electrolyte in the middle chamber (19B). [0031] FIG. 20 illustrates the I-V curve of the porous solid electrolyte device without conductive solid electrolyte measured while flowing different concentrations of NaHCO3. [0032] FIGs. 21A and 21B illustrate the I-V curve (21A) and corresponding FE Na⁺ (21B) with varying Na2CO3 concentrations using the OER and HER reactions described in one or more embodiments. [0033] FIG. 22 illustrates the transport number of Na⁺ using a PTFE-reinforced Nafion® membrane as the CEM, according to one or more embodiments. [0034] FIG. 23 illustrates the FE Na⁺ reported as a function of current density of a device according to one or more embodiments. [0035] FIG. 24 illustrates the cell voltage reported as a function of time of a device according to one or more embodiments. [0036] FIG. 25 illustrates an I-V curve of a modular porous solid electrolyte reactor according to one or more embodiments. [0037] FIGs.26A and 26B illustrate the thermal conductivity (TCD) response (26A) of the membrane system collected gas flow showing neglectable O2 gas under all current densities and the flame ionization response (26B), of a device according to one or more embodiments. [0038] FIG. 27 illustrates the collection efficiency of CO2 when plotted as a function of the cell current of a device according to one or more embodiments. [0039] FIG. 28 illustrates the collected CO₂ gas volume under 400 mA current (100 mA cm^-2 current density) when plotted as a function of electrocatalysis time of a device according to one or more embodiments. [0040] FIGs. 29A and 29B illustrate the cell voltage as a function of current density with variable CEM thickness, PSE layer thickness, and operating temperatures (29A) and the ion transport number of Na⁺ (29B) in a device according to one or more embodiments, as a function of current density using a CEM-50μm membrane. [0041] FIGs. 30A and 30B are SEM images of the porous solid electrolyte powder according to one or more embodiments, at the scale of 200 μm (30A), and 50 μm (30B). DETAILED DESCRIPTION [0042] In one aspect, embodiments disclosed herein relate to an efficient electrochemical regeneration of carbon dioxide (CO2) gas and alkaline, also termed basic, sorbent from carbonate or bicarbonate solutions in a modular porous solid electrolyte (PSE) reactor using a proton exchange membrane and a cation exchange membrane. By performing hydrogen evolution reaction and hydrogen oxidation reaction (HER/HOR) redox electrolysis (or water splitting if byproduct H₂ is desired), a carbonate or bicarbonate solution flowing through the porous solid electrolyte (PSE) layer can be continuously converted back into high purity (>99%) CO2 gas at practical rates (up to 18 mmol cm⁻² h⁻¹ or 190 kgCO₂ m^-2 day⁻¹), during which a high concentration of basic sorbent in solution is regenerated for the next round carbon capture process. [0043] One or more embodiments disclosed herein relate to a modular electrochemical reactor, also termed herein a modular porous solid electrolyte (PSE) reactor, a porous solid electrolyte PSE reactor, or a reactor, with a membrane system including a porous solid electrolyte (PSE) layer separated by a cation exchange membrane (CEM) and a proton exchange membrane (PEM) between the cathode and anode for efficient and scalable CO2 and basic sorbent regeneration from carbonates or bicarbonates. Herein, the terms include or including means includes but is not limited to. The carbonate and/or bicarbonate solutions (such as Na₂CO₃ or NaHCO₃) may be continuously pumped into the membrane system, specifically the middle porous solid electrolyte layer, for regeneration, where the regenerated CO₂ gas may be separated from the cathode or anode gas during electrolysis. By continuously performing redox electrolysis at the cathode and anode, protons (H⁺) generated at the anode/PEM interface may be electrically driven into the membrane system to replace the carbonate and/or bicarbonate cations, such as sodium ions (Na⁺), that move across the CEM into the cathode chamber. In one or more embodiments, Na2CO3/NaHCO3 in the membrane system may be split into H2CO3 in the PSE layer to produce high-purity regenerated CO₂ gas (from H₂CO₃ decomposition) and regenerated NaOH solutions in the cathode chamber which may be recycled for subsequent rounds of CO2 capture. [0044] According to one or more embodiments, the porous solid electrolyte layer is arranged as a thin layer of porous materials or a pack of non-porous or porous materials. The PSE layer may be made of one or more materials selected from polymers, organic compounds, inorganic compounds, and combinations thereof. The PSE layer thickness may range from 0.01 mm to 100 mm. The PSE particle size may range from 100 nm to 10 mm, and the PSE particles could be individual particles packed inside the PSE layer or could be bound together via binders. The PSE layer allows for efficient fluid (both gas and liquid) flow inside the layer and facilitates ion conduction. In one or more embodiments, the PSE layer is an integrated piece or a pack of smaller size materials, like particles, which form the pores. The PSE layer may contain dense but water- and gas-permeable polymers that are functionalized with cation-conducting sulfonate groups, which may play a central role in nucleating CO₂ bubbles and minimizing ohmic loss, especially under low Na⁺ ion conditions for low energy consumptions during the CO2 regeneration process. In one or more embodiments, the PSE layer includes sodium form styrene-divinylbenzene sulfonated copolymer Dowex 50WX8 hydrogen form (Na-PPS, Sigma-Aldrich) cation conductor. Depending on the area and size of the PSE layer chamber, the flow rate of the liquid stream into one PSE layer could range from 0.001 mL/min to 10,000 L/min. [0045] In one or more embodiments, the membrane system includes a cation exchange membrane (CEM) and a proton exchange membrane (PEM). Without being bound by any particular theory, the terms PEM and CEM are used to differentiate their purpose of use: PEM is used when H⁺ is the target ion and CEM is used when Na⁺ or other alkali metal cations are the target ion. The CEM may be any suitable membrane that allows cation conduction with a thickness of between 5 µm to 500 µm. In one or more embodiments, the CEM is selected from the group consisting of chlori-alkaline membranes, Nafion® membranes such as Nafion®-N2100X and Nafion® 117, PTFE fabric reinforced Nafion® alternatives, and bipolar membranes. The PEM may be any suitable membrane that allows proton conduction, such as Nafion® 117. [0046] Without being bound by any particular theory, the fundamental working mechanism of electrochemical CO2 and basic sorbent regeneration from carbonate and bicarbonate solutions (such as Na₂CO₃ or NaHCO₃) is accomplished by performing electrochemical reactions involving proton consumption (equivalent to OH- generation) and generation on the cathode and anode. Alkali metal cations (M⁺) and carbonate ions can be separated into the cathode and anode chamber via ion exchange membranes, respectively, to form MOH and H₂CO₃ with charges balanced. In one or more embodiments, the hydrogen evolution reaction and hydrogen oxidation reaction (HER/HOR) redox couple are chosen for the cathodic and anodic reactions, respectively, due to their facile reaction kinetics compared with other redox couples such as oxygen reduction reaction and oxygen evolution reaction (ORR/OER), as well as much lower energy consumptions compared with other reactors performing water splitting with H₂ generated as a by-product. Typically, HOR or ORR is not used in traditional two chamber pH swing reactors where both the cathode and anode chambers have liquid streams that block gas transport channels. [0047] According to one or more embodiments, the anode includes a catalyst configured to catalyze a proton-producing reaction. The proton-producing reaction may be achieved in multiple steps and/or phases. The proton-producing reaction may be a water oxidation reaction, a hydrogen oxidation reaction, or an oxygen evolution reaction. In one or more embodiments, the catalyst configured to catalyze the proton- producing reaction is any suitable hydrogen oxidation reaction catalyst or any suitable oxygen evolution reaction catalyst. In one or more embodiments, the catalyst configured to catalyze the proton-producing reaction is selected from the group consisting of Pt, Pt/C, Ir, IrO2, Ir black, Ru, RuO2, Ru black, RuIr alloys and oxides (IrxRuyOz), RuPt alloys and oxides, transition metals and oxides, transition metal single atom catalysts, and transition metal alloys and oxides. The anode catalyst loading may range from 0.001 mg/cm² to 1 g/cm². In one or more embodiments, the hydrogen source is pure hydrogen gas, hydrogen gas mixtures, recycled hydrogen, hydrocarbons, organic small molecules, alcohols, oxygenates, or water. [0048] According to one or more embodiments, the cathode includes a catalyst configured to catalyze a proton-consuming reaction. The proton-consuming reaction may be achieved in multiple steps and/or phases. The proton-consuming reaction may be a hydrogen evolution reaction, an oxygen reduction reaction, a carbon dioxide reduction reaction, a nitrate reduction reaction, or a nitrogen reduction reaction. In one or more embodiments, the catalyst configured to catalyze the proton-producing reaction is any suitable hydrogen evolution reaction catalyst. In one or more embodiments, the catalyst configured to catalyze the proton-consuming reaction is Pt/C. The cathode catalyst loading may range from 0.001 mg/cm² to 1 g/cm². [0049] The mixed regenerated stream generated at the cathode chamber during the proton-producing reaction includes regenerated basic sorbent in the form of hydroxide solutions such as LiOH, NaOH, KOH, or CsOH. Fluid flow at the cathode chamber can be either continuous flow (single path) or batch recirculation. Depending on the area and size of the PSE layer chamber, the flow rate of the liquid stream into one unit cathode chamber may range from 0.001 mL/min to 10,000 L/min. Water in the cathode chamber may come from external sources or from the carbon dioxide lean stream out of the PSE layer after the CO2 regeneration and gas-liquid separation. This carbon dioxide lean stream may need pre-treatment or purification before being fed into the cathode chamber to remove some possible impurities (originally from the absorption step), such as dissolved sulfur species, nitrogen species, phosphorus species, organic carbon, dust, particles, and hardness. The concentration of the regenerated basic sorbent in the mixed regenerated stream may range from 0.01 mol/L to 10 mol/L. The regenerated basic sorbent and generated H2 gas may be separated into a hydrogen lean regenerated basic sorbent stream and a generated H2 stream by a gas/liquid separator, and the hydrogen lean regenerated basic sorbent stream may be fed back to the absorption unit for the next round of carbon capture loop. [0050] The modular porous solid electrolyte reactor with a membrane system according to one or more embodiments further includes a carbon dioxide source and an absorption unit. The absorption unit includes a basic sorbent and is configured to absorb carbon dioxide from the carbon dioxide source to produce the feed stream including the basic sorbent and sorbed carbon dioxide in the form of carbonates and/or bicarbonates, also termed the carbon rich stream, that may be flowed through the membrane system. The absorption unit allows the recycled hydrogen lean regenerated basic sorbent stream from the reactor to react with CO₂ gas, to produce sorbed carbon dioxide in the form of carbonates and/or bicarbonates which is fed to the modular porous solid electrolyte reactor, specifically the PSE layer of the membrane system as a feed stream including the basic sorbent and sorbed carbon dioxide in the form of carbonates and/or bicarbonates. The carbon rich stream may contain unreacted basic sorbent (hydroxides). The concentration of carbonates/bicarbonates in the carbon rich stream may range from 0.001 mol/L to 11 mol/L in water. [0051] In one or more embodiments, the absorption unit is selected from the group consisting of one or more air contactors, one or more gas absorbers, one or more cooling towers, and one or more absorption columns. The absorption unit may be configured to receive the hydrogen lean regenerated basic sorbent stream from the cathode chamber, after separation from the mixed regenerated stream. [0052] The carbon dioxide source may be selected from the group consisting of air, flue gas, HVAC exhaust, bio-fermentation tail gas, point source streams, and combinations thereof, and may include carbon dioxide at varying concentrations. Depending on the carbon dioxide source, the feed stream including the basic sorbent and sorbed carbon dioxide in the form of carbonates and/or bicarbonates may contain contaminants such as nitrogen species, sulfur species, phosphorus species, carbon species other than carbonate/bicarbonate/CO₂/carbonic acid, bacteria, dusts, particles, hardness, and organics (see Table 1). A pre-filtration, or purification step such as water treatment, may be needed to exclude species that could degrade the reactor. Some contaminants may not affect the stability of the reactor and may not need specific treatment, such as nitrates, sulfates, particles with sizes smaller than 1 micrometer, until they reach certain levels of concentration. Purification can be done either before or after the carbon dioxide gets regenerated and can be separated into multiple steps regarding different contaminants. Some certain contaminants (such as sulfates) could accumulate over multiple carbon capture-regeneration cycles and be removed after it reaches undesirable concentration levels (when the contaminant starts to affect the electrochemical performance of the reactor, or the pH of the PSE layer electrolytes). The carbon dioxide source and the feed stream including the basic sorbent and sorbed carbon dioxide in the form of carbonates and/or bicarbonates could have fixed or varying compositions, and can be a mixture with Na⁺, K⁺, Li⁺, Cs⁺ and many other soluble salts and insoluble solids with particle sizes below 1 micrometer. The carbon dioxide source and the feed stream including the basic sorbent and sorbed carbon dioxide in the form of carbonates and/or bicarbonates could have additives to facilitate the electrolysis process (and/or the CO2 absorption process in the absorption unit), including but not limited to surfactants for easy bubble nucleation, additives to improve cation transport number, additives to reduce CO₂ solubility in the solution, and any other suitable additive. Table 1. Contaminant level in feeding solutions from different CO2 gas sources, direct-air capture (DAC) or flue gas (FG)

[0053] The modular porous solid electrolyte reactor with a membrane system according to one or more embodiments includes a liquid and/or gas separator fluidly connected to the membrane system and configured to separate the high purity stream including carbon dioxide. [0054] The reactor may include a temperature control system to independently control the temperature of each of the components of the modular porous solid electrolyte reactor, specifically the anode chamber, the cathode chamber, the membrane system, and the interface between each chamber. The temperature control system may control, monitor, and/or change the temperature of each of the components of the modular porous solid electrolyte reactor. The temperature control system may include temperature sensors, heat exchangers, heating or insulating jackets, and combinations thereof. Each chamber’s temperature can be independently controlled, therefore, there could be temperature differences across different parts of the reactor. Without being bound by any particular theory, the desired operation temperature is decided by balancing the following several factors: a) higher operation temperatures can improve the reaction kinetics and ionic conductivity, improving the cell voltages of the reactor for reduced energy consumption during cell operation; b) lower operation temperatures can reduce the gas bubble evolution inside the membrane system, specifically the PSE layer, reducing the in-chamber fluid flow pressure drop; c) operations under different temperatures could affect the stability of different components in the reactor, including catalysts, ion exchange membranes, PSE layers, gaskets, etc. The modular porous solid electrolyte reactor can be operated under different temperatures ranging from -20 °C to 150 °C. The lower bound is limited by the freezing point of the electrolyte, and the upper bound is limited by the boiling point of the electrolyte under operation conditions. The temperature of the feeding solutions (such as water, carbonate/bicarbonate solutions, acids, alkalines, ionic liquids, organic solutions, and other salt solutions) to each chamber can range from -20 °C to 150 °C. Controlling the temperature of these feeding solutions into the reactor can help to control the operation temperature of the reactor. Other separate streams of heat exchange fluids can also be designed to heat up or cool down the reactor (in addition to the intrinsic cooling from the liquid flow in the membrane system) to maintain the reactor’s desired operation temperature. [0055] The reactor may further include a pressure control system to independently control the pressure of each of the components of the modular porous solid electrolyte reactor, specifically the gas or liquid or their mixture pressure inside the cathode chamber, anode chamber, and the membrane system. The pressure control system may control, monitor, and/or change the pressure of each of the components of the modular porous solid electrolyte reactor. The pressure control system may include compressors, back-pressure controllers, and combinations thereof. Each component’s pressure can also be independently controlled or balanced. The pressure difference between two neighboring components will be within the pressure limit of the ion exchange membrane that separates the two components. There could be pressure differences across different parts of the reactor and there could be pressure drops along the fluid flow direction inside each component. Without being bound by any particular theory, the desired operation pressure is decided by balancing the following factors: a) higher operation pressures can improve the reaction kinetics (such as the hydrogen oxidation reaction), b) reduce the gas bubble evolution inside the membrane system, specifically the PSE layer, by increasing the gas solubility, and c) reduce the energy consumption needed to further pressurize regenerated CO2 gas or H2 for transportation or storage. Lower operation pressures may reduce the risk of gas/liquid leaking, membrane fracture, and unwanted inter chamber materials exchange. The modular porous solid electrolyte reactor can be operated under different pressures ranging from 0.01 bar to 100 bar. The pressure of feeding solutions (such as water, carbonate/bicarbonate solutions, acids, alkalines) to each component can range from ambient pressure to 100 bar. The pressure of the output fluids (gas, liquid, or their mixture) can range from ambient pressure to 100 bar. Controlling the pressure of these input and output fluid streams of the reactor can help to control the operation pressure of the reactor as well as the output gas pressures, including H₂ gas, O₂ gas, and regenerated CO₂ gas. [0056] According to one or more embodiments, the basic sorbent includes an alkali hydroxide compound selected from the group consisting of lithium hydroxide, potassium hydroxide, cesium hydroxide, and sodium hydroxide. The basic sorbent, or liquid sorbent, may be an absorbent. When the basic sorbent includes sodium hydroxide, the mixed regenerated stream includes sodium hydroxide, and the feed stream including the basic sorbent and sorbed carbon dioxide in the form of carbonates and/or bicarbonates includes sodium carbonate and sodium bicarbonate. [0057] According to one or more embodiments, the modular porous solid electrolyte reactor operates under specific current densities and cell voltages. The current density under steady state operation per geometrical area of the active electrode ranges from 0.1 mA/cm² to 10 A/cm². The operation voltage of one PSE layer chamber (or repeating unit of the PSE layer) ranges from 0.1 V to 20 V. The current and voltages may be individually controlled and monitored by external power sources. The modular porous solid electrolyte may be dynamically operated to match the intermittent power generation of renewable energy sources. The reactor’s operation current density may be ramped up in practical applications, with a ramping rate of less than 1A/cm² per second, or ramped down in practical applications, with a ramping rate of less than 1000A/cm² per second. When the reactor is off, the modular porous solid electrolyte reactor should be kept under wetting conditions. The reactor’s performance may be resumed after operation disruption from 1 second to 12 months, as each of the components involved in the system can be regenerated if needed. [0058] FIG. 1 is a schematic diagram of the device in one or more embodiments. The system 100 includes an anode chamber 110, a cathode chamber 116 and a membrane system 120 including a PEM 124, a PSE layer 122, and a CEM 126. The anode chamber 110 includes an anode electrode 112 and the cathode chamber 116 includes a cathode electrode 118. Cations from the membrane system 120 and a water source (not shown) are introduced to the cathode compartment 116. The cations and water are reacted in a proton-consuming reaction with species generated at the cathode electrode 116 or reduced directly at the cathode electrode 118 to form a mixed regenerated stream, which may be purified and separated to produce the regenerated basic sorbent stream, which may be recycled to an absorption unit (not shown). The proton-consuming reaction performed at the cathode electrode 118 may be any suitable reaction that can consume protons to generate hydroxide groups. A hydrogen source is introduced to the anode chamber 110 and protons are formed at the anode electrode 112 by a proton-producing reaction. The proton-producing reaction at the anode electrode 112 may be any suitable reaction that can release protons to the membrane system 120. The protons formed at the anode electrode 112 are driven to the PSE layer 122 through a PEM 124. The membrane system 120 includes PSE layer 122 in which a carbonate and/or bicarbonate solution and the protons are reacted to form an exit product including CO2. The cations in the membrane system 120 are driven through the CEM 126 to compensate charge and form a regenerated basic sorbent stream. The exit product in the PSE layer 122 is then removed from the membrane system 120. The exit product may be directed to a liquid and/or gas separator fluidly connected to the membrane system and configured to separate the exit product into a high purity stream including carbon dioxide (not shown). [0059] One or more embodiments disclosed herein relate to a modular porous solid electrolyte reactor with a membrane system including alternating layers of at least one CEM and at least one bipolar membrane (BPM) separated by a PSE layer. The modular porous solid electrolyte reactor may be any one of the reactors disclosed herein. In one or more embodiments, the reactor configuration consists of multiple PSE layers separated by a BPM and a CEM, to efficiently and effectively scale up the process of CO2 and basic sorbent regeneration from carbonates/bicarbonates. In these embodiments, the BPM facilitates the electrolysis of water, splitting it into OH- and H⁺ ions. Carbonate and/or bicarbonate solutions, such as Na₂CO₃ or NaHCO₃, are continuously pumped into the PSE layer for regeneration, where they combine with the H⁺ ions, are transported across the CEM side of the BPM, to release high-purity CO2 gas. Simultaneously, the alkali metal cations, such as sodium ions (Na+), migrate across the CEM to the next PSE layer, where they combine with the OH- ions transported across the anion exchange membrane side of the BPM, to form a NaOH solution which may be used for the subsequent rounds of CO₂ capture. This membrane system may be replicated for multiple duplicates with no need for internal current collectors. In one or more embodiments, the modular electrochemical reactor with a membrane system including alternating layers of at least one CEM and at least one BPM separated by a PSE layer, includes an anode chamber and a cathode chamber as described above. [0060] In one or more embodiments, the membrane system includes alternating layers of at least one cation exchange membrane and at least one bipolar membrane (BPM), where the alternating layers of the at least one cation exchange membrane and the at least one bipolar membrane are separated by a porous solid electrolyte layer. A first layer of the membrane system faces the first side of the membrane system and includes one of the at least one cation exchange membrane or one of the at least one bipolar membrane, and the terminal layer of the membrane system faces the second side of the membrane system and includes one of the at least one cation exchange membranes. The BPM may be a membrane that includes an anion exchange membrane, a cation exchange membrane, and a thin water splitting catalyst layer between the anion exchange membrane and the cation exchange membrane. The thin water splitting catalyst layer may range from 1 nm to 10 mm in thickness and may include any suitable water splitting catalyst such as metal oxides and carbon nanomaterials. Without being bound by any particular theory, water splitting occurs inside the BPM such that protons and hydroxide anions can be separately supplied into the CO₂ regeneration chamber and the alkaline solvent regeneration chamber, respectively. [0061] FIG.2A is a schematic diagram of the device in one or more embodiments. The device 200 includes an anode chamber 202, a cathode chamber 206, and a membrane system 210 located between the anode chamber 202 and the cathode chamber 206 and including a first side facing the anode chamber 202 and a second side facing the cathode chamber 206. The membrane system 210 includes a first membrane unit 220a including the first side of the membrane system 210, a terminal membrane unit 222 including the second side of the membrane system 210, and optionally one or more repeating units 230 (shown in FIG. 2C). The first membrane unit 220a includes a CEM 218 and two PSE layers 214 separated by a BPM 216. The terminal membrane unit 222 includes a CEM 218. [0062] FIG.2B is a schematic diagram of the device in one or more embodiments. The device 250 includes an anode chamber 202, a cathode chamber 206, and a membrane system 211 located between the anode chamber 202 and the cathode chamber 206 and including a first side facing the anode chamber 202 and a second side facing the cathode chamber 206. The membrane system 211 includes a first membrane unit 220b including the first side of the membrane system 211, a terminal membrane unit 222 including the second side of the membrane system 211, and optionally one or more repeating units 230 (shown in FIG.2C). The first membrane unit 220b includes a BPM 252 and a PSE layer 254. The terminal membrane unit 222 includes a CEM 218. [0063] FIG. 2C is a schematic diagram of the repeating membrane unit 230 used to extend or duplicate the membrane system of the device in one or more embodiments. The repeating membrane unit 230 includes a CEM 234, a PSE layer 232, a BPM 236, and an additional PSE layer 232. Looking at FIG.2A, to extend the membrane system 210, the repeating unit 230 would be inserted between the PSE layer 214 and the terminal membrane unit 222 including a CEM 218. Looking at FIG. 2B, to extend the membrane system 211, the repeating unit 230 would be inserted between the PSE layer 254 and the terminal membrane unit 222 including a CEM 218. [0064] One or more embodiments disclosed herein relate to a process for electrochemical carbon dioxide and basic sorbent regeneration utilizing a modular porous solid electrolyte reactor. The modular porous solid electrolyte reactor may be any one of the reactors disclosed herein. The process includes feeding a carbon dioxide source into an absorption unit configured to absorb carbon dioxide and produce a carbon rich stream, feeding the carbon rich stream into the modular porous solid electrolyte reactor, contacting the carbon rich stream with the membrane system of the modular porous solid electrolyte reactor to produce a carbon dioxide rich stream including regenerated carbon dioxide, feeding the carbon dioxide rich stream into a separator, such as a liquid/gas separator, to separate the regenerated carbon dioxide from the carbon dioxide rich stream to produce a carbon dioxide lean stream, and storing the regenerated carbon dioxide in a carbon dioxide storage unit. The carbon dioxide source and the absorption unit may be any suitable carbon dioxide source and absorption unit disclosed above. The regenerated carbon dioxide may be purified after separation and may be compressed prior to storage. Once separated from the regenerated carbon dioxide, the carbon dioxide lean stream may be purified and recycled into the cathode chamber of the modular porous solid electrolyte reactor, either alone or mixed with an external water source, for basic sorbent (hydroxide) regeneration which reduces water use throughout the process, producing a mixed regenerated stream including gases generated at the cathode, such as hydrogen gas, and a regenerated basic sorbent (hydroxide). The mixed regenerated stream is then fed into a separator, such as a liquid/gas separator, to produce a generated gas stream and a regenerated basic sorbent stream. The regenerated basic sorbent stream may be purified and recycled into the absorption unit, while the generated gas stream may be purified and/or compressed and fed into a storage unit. According to one or more embodiments, when hydrogen gas is generated at the cathode, the storage unit is a hydrogen storage unit configured to provide a stored hydrogen gas stream, either alone or mixed with an external hydrogen source, to the anode chamber of the modular porous solid electrolyte reactor to produce protons and an unreacted hydrogen gas stream, which may be purified and fed back into the hydrogen storage unit, as exemplified in FIG. 3. In yet another embodiment, an acidic aqueous stream is fed into the modular porous solid electrolyte reactor to contact the anode and produce an oxygen gas stream, as exemplified in FIG. 4. The acidic aqueous stream may comprise water, acid, and combinations thereof. The oxygen gas stream may be compressed and stored in an oxygen gas storage unit. [0065] FIG. 3 is a schematic diagram of a process for electrochemical carbon dioxide and basic sorbent regeneration 300 according to one or more embodiments. A source of carbon dioxide 302 is fed into an absorption unit 308 configured to absorb carbon dioxide and produce a carbon rich stream 310, a carbon dioxide lean stream 304, and excess water and sorbent 306. The carbon dioxide source 302 may include air, flue gas, bio-fermentation exhaust, or any suitable source of carbon dioxide. The carbon rich stream 310 may include carbonates, bicarbonates, carbonic acid, aqueous carbon dioxide, unreacted basic sorbent, or any suitable carbon capture product. The carbon rich stream 310 may undergo purification 312 to remove contaminants such dissolved sulfur species, nitrogen species, organic carbon, bacteria, dust, particles, hardness, and any suitable contaminant that may negatively affect the modular porous solid electrolyte reactor 314. From the absorption unit 308, the carbon rich stream 310 is fed to the modular porous solid electrolyte reactor 314 to contact the membrane system 318 and produce a carbon dioxide rich stream 322. The carbon dioxide rich stream 322 may undergo purification to remove contaminants. The carbon dioxide rich stream 322 is fed to a separator 324 to separate the regenerated carbon dioxide 326 and produce a carbon dioxide lean stream 330. The regenerated carbon dioxide 326 may undergo purification to remove contaminants and/or compression prior to being fed into a carbon dioxide storage unit 328. The carbon dioxide lean stream 330 may be fed into the cathode chamber 316 of the modular porous solid electrolyte reactor 314, either alone or mixed with a water source 332, to reduce water consumption and produce a mixed regenerated stream 334 including generated hydrogen gas and a regenerated basic sorbent. The mixed regenerated stream 334 is fed into a separator 336 to separate the generated hydrogen gas from the regenerated basic sorbent and produce a generated hydrogen gas stream 338 and a hydrogen lean regenerated basic sorbent stream 342. The hydrogen lean regenerated basic sorbent stream 342 may undergo purification to remove contaminants prior to being fed to the absorption unit 308. The generated hydrogen gas stream 338 may undergo purification to remove contaminants such as oxygen, water, and ammonia, and/or compression prior to being fed into a hydrogen storage unit 340. A stored hydrogen gas stream 344 may be removed from the hydrogen storage unit 340 and fed, either alone or mixed with an external hydrogen source (not shown), to the anode chamber 320 of the modular porous solid electrolyte reactor 314 to produce protons and an unreacted hydrogen gas stream 346. The unreacted hydrogen gas stream 346 may be fed to the hydrogen storage unit 340, fed to another hydrogen storage unit (not shown) or vented. [0066] FIG. 4 is a schematic diagram of a process for electrochemical carbon dioxide and basic sorbent regeneration and hydrogen generation 400 according to one or more embodiments. A source of carbon dioxide 402 is fed into an absorption unit 408 configured to absorb carbon dioxide and produce a carbon rich stream 410, a carbon dioxide lean stream 404, and excess water and sorbent 406. The carbon dioxide source 402 may include air, flue gas, bio-fermentation exhaust, or any suitable source of carbon dioxide. The carbon rich stream 410 may include carbonates, bicarbonates, carbonic acid, aqueous carbon dioxide, or any suitable carbon capture product. The carbon rich stream 410 may undergo purification 412 to remove contaminants such dissolved sulfur species, nitrogen species, organic carbon, bacteria, dust, particles, hardness, and any contaminant that may negatively affect the modular porous solid electrolyte reactor 414. From the absorption unit 408, the carbon rich stream 410 is fed to the modular porous solid electrolyte reactor 414 to contact the membrane system 418 and produce a carbon dioxide rich stream 422. The carbon dioxide rich stream 422 may undergo purification to remove contaminants. The carbon dioxide rich stream 422 is fed to a separator 424 to separate the regenerated carbon dioxide 426 and produce a carbon dioxide lean stream 430. The regenerated carbon dioxide 426 may undergo purification to remove contaminants and/or compression prior to being fed into a carbon dioxide storage unit 428. The carbon dioxide lean stream 430 may be fed into the cathode chamber 416 of the modular porous solid electrolyte reactor 414, either alone or mixed with a water source 432, to reduce water consumption and produce a mixed regenerated stream 434 including generated hydrogen gas and a regenerated basic sorbent. The mixed regenerated stream 434 is fed into a separator 436 to separate the generated hydrogen gas from the regenerated basic sorbent and produce a generated hydrogen gas stream 438 and a hydrogen lean regenerated basic sorbent stream 442. The hydrogen lean regenerated basic sorbent stream 442 may undergo purification to remove contaminants prior to being fed to the absorption unit 408. The generated hydrogen gas stream 438 may undergo purification to remove contaminants such as oxygen, water, and ammonia, and/or compression prior to being fed into a hydrogen storage unit 440. An acidic aqueous stream 444 is fed to the anode chamber 420 of the modular porous solid electrolyte reactor 414 to produce an oxygen gas stream 446. The oxygen gas stream 446 may be compressed and fed to an oxygen gas storage unit 448. [0067] One or more embodiments disclosed herein relate to a method for electrochemical carbon dioxide and basic sorbent regeneration utilizing a modular electrochemical reactor. The modular porous solid electrolyte reactor may be any one of the reactors disclosed herein. The method includes providing the modular porous solid electrolyte reactor, providing a feed stream including the basic sorbent and sorbed carbon dioxide in the form of carbonates and/or bicarbonates to the membrane system to electrochemically split cations from the carbonates and bicarbonates to produce a high purity stream including carbon dioxide, providing a hydrogen source to the anode chamber to produce protons at the anode and separate the protons from the hydrogen source so as to provide protons to the membrane system, and providing cations from the membrane system and a water source to the cathode chamber, produce anions at the cathode, and react the cations with the anions so as to produce a regenerated basic sorbent stream. The method further includes providing a carbon dioxide source to an absorption unit, absorbing, in the absorption unit, carbon dioxide from the carbon dioxide source and producing the feed stream including the basic sorbent and sorbed carbon dioxide in the form of carbonates and/or bicarbonates. The carbon dioxide source and the absorption unit may be any suitable carbon dioxide source and absorption unit disclosed above. The regenerated basic sorbent stream may be recycled into the absorption unit. [0068] The method may further include independently controlling the temperature and/or pressure of each of the components of the modular porous solid electrolyte reactor, specifically the anode chamber, the cathode chamber, and the membrane system. Without being bound by any particular theory, the desired operation temperature is decided by balancing the following several factors: a) higher operation temperatures can improve the reaction kinetics and ionic conductivity, improving the cell voltages of the reactor for reduced energy consumption during cell operation; b) lower operation temperatures can reduce the gas bubble evolution inside the membrane system, specifically the PSE layer, reducing the in-chamber fluid flow pressure drop; c) operations under different temperatures could affect the stability of different components in the reactor, including catalysts, ion exchange membranes, PSE layers, gaskets, etc. The modular porous solid electrolyte reactor can be operated under different temperatures ranging from -20 °C to 150 °C. Without being bound by any particular theory, the desired operation pressure is decided by balancing the following factors: a) higher operation pressures can improve the reaction kinetics (such as the hydrogen oxidation reaction), b) reduce the gas bubble evolution inside the membrane system, specifically the PSE layer, by increasing the gas solubility, and c) reduce the energy consumption needed to further pressurize regenerated CO2 gas or H2 for transportation or storage. Lower operation pressures may reduce the risk of gas/liquid leaking, membrane fracture, and unwanted inter chamber materials exchange. The modular porous solid electrolyte reactor can be operated under different pressures ranging from 0.01 bar to 100 bar. [0069] FIG. 5 is a schematic diagram of a method for electrochemical carbon dioxide and basic sorbent regeneration according to one or more embodiments. The method includes first providing a modular porous solid electrolyte reactor including an anode chamber including an anode, a cathode chamber including a cathode, and a membrane system 510. Then, providing a feed stream including the basic sorbent and sorbed carbon dioxide in the form of carbonates and/or bicarbonates to the membrane system to electrochemically split cations from the carbonates and bicarbonates to produce a high purity stream including carbon dioxide 512. Followed by providing a hydrogen source to the anode chamber to produce protons at the anode and separate the protons from the hydrogen source so as to provide protons to the membrane system 514 and providing cations from the membrane system and a water source to the cathode chamber, produce anions at the cathode, and react the cations with the anions so as to produce a regenerated basic sorbent stream 516. EXAMPLES Preliminary Comparisons [0070] FIG. 6A shows a comparative pilot-scale CO₂ capture process for thermal CO₂ capture via calcium carbonate looping 608. The system 600 in FIG. 6A recieves air and/or flue gas 602. The air and/or flue gas 602 enters an absorber unit 604 containing amine-based sorbents, including basic aqueous solutions such as sodium hydroxide (NaOH) or potassium hydroxide (KOH) to absorb carbonate species and produce potassium carbonate (K2CO3) and sodium carbonate (Na2CO3) in liquid form 618 which is sent to a reactor 614. Calcium hydroxide (Ca(OH)₂) in liquid form 616 is added to the reactor 614, and solid calcium carbonate (CaCO3) is produced. The CO2 regeneration step 611 involves high temperature (900 ℃) annealing of CaCO3 which consumes natural gas and a large portion of overall energy consumption to produce pure CO₂612 and solid CaO 610. The solid CaO 610 is combined with water 607 to regenerate the basic aqueous solutions 618 and produce clean air 606. [0071] FIG. 6B shows an exemplary illustration of the present electrochemical CO2 regeneration from carbonate or bicarbonate solutions using a solid electrolyte reactor for a complete carbon capture loop. The system 650 in FIG.6B receives air and/or flue gas 602. The air and/or flue gas enters an absorber unit 658 containing NaOH to absorb carbonate species and produce a stream 652 containing Na2CO3 and sodium bicarbonate (NaHCO₃). The stream 652 is sent to a modular PSE reactor 654 which produces pure CO2612 and clean air 606. [0072] FIG. 7A illustrates a comparative electrochemical CO2 release process using cation exchange membrane-based (CEM-based) membrane electrode assembly (MEA) device. The system 700 of FIG.7A is a two-chamber MEA, a first chamber containing an anode 704, a second chamber containing a cathode 720, and a CEM 712 located between the anode 704 and the cathode 720. A carbonate and bicarbonate solution 708, such as a solution of Na2CO3 and NaHCO3, contacts the anode 704 where an oxygen evolution reaction (OER) 702 occurs, electrochemically separating the sodium (Na⁺) ions from CO₂ and oxygen (O₂) in stream 710. At the same time, a portion of Na⁺ ions 706 permeates through the CEM 712 to the cathode 720. H2O 724 is added to the second chamber containing a cathode 720 where a hydrogenation evolution reaction (HER) 722 occurs, producing NaOH 716 and carbonic acid (H2CO3), which simultaneously decomposes into CO2 gas and H2O. The NaOH 716 can be used for the next round of carbon capture 714 to form additional carbonate and bicarbonate solutions 708. The regenerated CO2 gas in the anode chamber is inevitably mixed with O2 in stream 710 produced from an OER 702. [0073] FIG. 7B illustrates a comparative pH swing method for carbon capture and release. The system 750 of FIG.7B is a two-chamber MEA, a first chamber containing an anode 704, a second chamber containing a cathode 720, and a CEM 712 located between the anode 704 and the cathode 720. A sulfate solution 730, such as a solution of Na2SO4, contacts the anode 704, where an oxygen evolution reaction (OER) 702 occurs, electrochemically separating the sodium (Na⁺) ions from SO4 and producing sulfuric acid (H₂SO₄) 732. At the same time, a portion of Na⁺ ions 728 permeates through the CEM 712 to the cathode 720. H₂O 724 is added to the second chamber containing a cathode 720, where a hydrogenation evolution reaction (HER) 722 occurs, producing NaOH 748 and H2CO3, which simultaneously decomposes into CO2 gas and H₂O. The NaOH 748 can be used for the next round of carbon capture 752 to form additional carbonate solution 736 (such as Na2CO3 and NaHCO3) and CO2734. Due to an acid/carbonate solution mixing step, this method typically involves excessive water to be evaporated to restore its original salt concentration, which consumes extra energy. In addition, the choices of half-cell reactions are restricted to gas evolution reactions due to liquid streams in both cathode and anode, resulting in excessive energy consumption to produce hydrogen (H₂) gas by-product. [0074] When the different carbon capture technologies are compared using a radar plot, the modular porous solid electrolyte reactor, coupled with HER/HOR redox, has lower energy consumption and higher reaction rates when compared to other water-splitting electrolyzers. The process of CaCO3 calcination necessitates high temperatures, resulting in relatively lower energy efficiency. Furthermore, additional water is required due to substantial evaporation during the process. PEM systems without solid electrolytes demand more energy and incur higher regeneration costs as the solution concentration decreases to a critical point, resulting in increased ohmic resistance. On the other hand, the bipolar membrane method exhibits a relatively high cell voltage due to water splitting and produces H₂ as a by-product. [0075] FIG. 8 illustrates a system for CO2 regeneration using a modular PSE reactor according to one or more embodiments. FIG. 8 illustrates a full cycle of direct air capture process where a CO₂ source 802 is directly purged into an absorption unit 804 containing a basic sorbent 805. CO2 from the CO2 source 802 is absorbed by the basic sorbent 805, producing a mixed stream containing carbonates and bicarbonates 806. The mixed stream containing carbonates and bicarbonates 806 is fed into a modular PSE reactor 808. The modular PSE reactor 808 receives a water stream 810 and produces CO2 in a high purity CO2 stream 818, as well as regenerated basic sorbent stream 812. The regenerated basic sorbent stream 812 may be held in a chemical storage tank 814, where it may be recycled via recycle stream 816 to the absorption unit 804. [0076] FIG. 9 illustrates a modular PSE reactor designed for CO₂ regeneration from carbonate or bicarbonate solutions according to one or more embodiments. The reactor 900 of FIG. 9 includes three chambers, a first chamber containing an anode 961 for hydrogen oxidation reaction (HOR) 968, a second chamber containing a cathode 995 for HER 990, and a third chamber containing a membrane system 996 located between the anode 961 and the cathode 995. The cathode 995 and the anode 961 may both be loaded with a platinum/carbon (Pt/C) catalyst 970. The membrane system 996 contains a proton exchange membrane (PEM) 972 located at a first side of the membrane system 996 which is adjacent to the anode 961. The membrane system 996 also contains a CEM 984 located at a second side of the membrane system 996 which is adjacent to the cathode 995. In addition, the membrane system 996 contains a PSE layer 975 located between the PEM 972 and the CEM 984. [0077] Keeping with FIG.9, carbonate and bicarbonate solutions 980 (such as Na2CO3 or NaHCO₃) are continuously pumped into the PSE layer 975 for regeneration, where the regenerated CO2 gas 976 will be separated from the cathode or anode gas during electrolysis. By continuously performing redox electrolysis (HER 990 and HOR 968) at the cathode 995 and anode 961, respectively, protons (H⁺) 974 generated at the anode 961/PEM 972 interface will be electrically driven into the membrane system 996 to replace the sodium ions (Na⁺) 982 that move across the CEM 984 into the second chamber containing a cathode 995. As a result, carbonate and bicarbonate solutions 980 (such as Na2CO3 or NaHCO3) in the PSE layer 975 will be split into H2CO3 978 to produce high-purity regenerated CO2 gas 976 (from H2CO3978 decomposition), and NaOH solution which immediately decomposes to Na⁺ ions 982 for the next round of carbon capture. The Na⁺ ions 982 move across the CEM 984 into the second chamber containing a cathode 995 where the Na⁺ ions 982 are combined with H2O 988 to undergo the HER 990 reaction, producing H2 gas 962. The HOR 968 reaction, which requires a H₂ source 964, may receive a recycle stream of H₂ gas 962 produced from the HER 990 reaction. [0078] FIG. 10 illustrates a system for CO2 regeneration using a modular PSE reactor 1000 according to one or more embodiments. FIG. 10 illustrates a carbon generation process where a CO2 source, a NaHCO3 tank 1012, is directly fed into the PSE layer 1022 of the membrane system 1008. The anode chamber 1002 of the reactor 1000 receives hydrogen 1014 from a hydrogen source and produces protons 1016, which flow through a PEM 1006 into the PSE layer 1022 of the membrane system 1008. The protons 1016 react with the HCO3- anions 1020 from the CO2 source 1012 to produce CO2 1024 and sodium ions 1018 that flow through the CEM 1010. The cathode chamber 1004 of the reactor 1000 receives water 1028 from a water source and produces hydrogen 1030 which is vented and hydroxide ions 1026, which react with the sodium ions 1018 that flow through the CEM 1010 to produce NaOH 1032. [0079] FIGs. 11A and 11B illustrate and compare the present modular porous solid electrolyte with a comparative MEA reactor. FIG. 11A illustrates a modular porous solid electrolyte reactor 1100 according to one or more embodiments for CO₂ release by the direct flowing of a carbon rich stream 1132 into the PSE layer 1108 of the membrane system. Protons 1114 produced at the anode 1102 from hydrogen gas 1112 penetrates the PEM membrane 1106 and moves into the PSE layer 1108, which acidifies the HCO₃ ⁻ 1120 to release CO₂ gas 1118. Sodium ions 1122 flow through the CEM 1110 to combine with the hydroxide anions 1124 produced at the cathode 1104 from water 1126 to produce sodium hydroxide 1130 and hydrogen gas 1128. FIG.11B illustrates a comparative reactor design and ion flows. The reactor 1150 includes an anode 1152 that receives a water source 1156 to produce oxygen gas 1160 and protons 1162. The protons flow through a PEM 1156 to a PSE layer 1158 and react with water 1168 and CO₃ ^2- anions 1164 from the cathode 1154, to produce CO₂1166. The cathode 1154 receives oxygen gas 1172 to produce hydroxide anions 1174 and CO3^2- anions 1164 that flow through an anionic exchange membrane (AEM) 1170. [0080] FIG. 11A illustrates different ion flows and working mechanisms compared with FIG.11B, as the exemplary modular porous solid electrolyte reactor of the present design shown in FIG. 11A is specifically focused on the carbon regeneration process (decoupled from its absorption process) for DAC applications, while the comparative reactor design illustrated in FIG. 11B integrates both absorption and regeneration processes in the electrochemical device, which becomes challenging for practical DAC applications due to limited current density operation. Specifically, the exemplary modular porous solid electrolyte reactor using the HER/HOR reaction couple to regenerate CO2 from DAC applications utilizes Na⁺ as the cathode charge carrier. The exemplary modular porous solid electrolyte reactor with an electrolyzer area of about 15-60 m² and a current density of about 50-200 mA/cm² is able to achieve a DAC capacity of 1 ton/day. Table 2, below, highlights select properties of the exemplary modular porous solid electrolyte reactor.

Table 2. Comparison of different electrochemical carbon capture methods with an exemplary modular porous solid electrolyte reactor.

[0081] FIGs. 12A and 12B illustrate a modular porous solid electrolyte reactor according to one or more embodiments. FIG. 12A illustrates an electrochemical stack using BPM-CEM configuration driven by the HER/HOR redox couple for CO2 generation. FIG. 12A outlines a reactor configuration 1200 consisting of multiple porous solid electrolyte (PSE) layers 1216 separated by a bipolar membrane (BPM) 1214 and a cation exchange membrane (CEM) 1212, designed to efficiently and effectively scale up the process of CO₂ regeneration 1224 from carbonates/bicarbonates 1218. In this design, the bipolar membranes 1214 facilitates the electrolysis of water, splitting it into OH- 1222 and H+ ions 1210. Carbonate or bicarbonate solutions 1218, such as Na2CO3 or NaHCO3, are continuously pumped into the PSE layer 1216 for regeneration, where they combine with the H+ ions 1210, transported across the cation exchange membrane side of the BPM 1214, to release high-purity CO2 gas 1224. Simultaneously, the sodium ions (Na+) 1220 or other alkali cations migrate across the CEM 1212 to the next PSE layer 1216, where they combine with the OH- ions 1222, transported across the anion exchange membrane side of the BPM 1214, to form NaOH solution 1226 for the subsequent round of CO2 capture. This design can be replicated for multiple duplicates with no need of internal current collectors. The hydrogen evolution reaction and hydrogen oxidation reaction (HER/HOR) redox couple, or any other suitable electrochemical reactions, may be selected for the cathodic 1206 and anodic reactions 1204. Alternatively, the hydrogen evolution reaction and oxygen evolution reaction (HER/OER) couple can also be utilized for the cathodic and anodic reactions, as shown in FIG. 12B. Materials [0082] All chemicals used in the following Examples, including sodium hydroxide (NaOH), sodium carbonate (Na2CO3), sodium bicarbonate (NaHCO3), and Nafion®- 117 solution (527084-25mL), were purchased from Sigma Aldrich. Pt/C powder, Nafion®-117 membrane, and Nafion®-NX2100 membrane were purchased from Fuel Cell Store. IrO2 electrode was purchased from the Dioxide Materials. Millipore water (18.2 MΩ·cm) was used throughout all the following Examples. Preparation of Pt/C electrodes for HER reaction [0083] 40 mg active catalyst (Pt/C) and 80 μL of Nafion®-117 binder solution were mixed with 4 mL of 2-proponal from Sigma-Aldrich. After sonication in ice water for 30 min, the resulting homogeneous ink was air-brushed onto a 5×5-cm² hydrophilic carbon cloth (ELAT-Hydrophilic Plain Cloth, Fuel Cell Store) electrode at 60 ^oC. Then the as-prepared electrode was hot-pressed on the Nafion®-NX2100 membrane at 90 ^oC for 10 min. Preparation of Pt/C electrodes for HOR reaction [0084] The procedure for the fabrication Pt/C anodes for the HOR reaction followed the same procedure as described above, except the hydrophobic gas diffusion layer carbon paper (GDL, Sigracet 28 BC, Fuel Cell Store) was used. Briefly, after sonication of the mixture of 40 mg active catalyst (Pt/C), 80 μL of Nafion®-117 binder, and 4 mL of 2-proponal, the obtained homogeneous ink was air-brushed onto a 5 × 5-cm² gas diffusion layer (GDL, Sigracet 28 BC, Fuel Cell Store) electrode at 60 ^oC. Then the prepared electrode was further dried in a vacuum at room temperature before use. Solid State Electrolyte Cell with Double-CEM Configuration [0085] The CO2 recovery process was conducted in a solid electrolyte (SE) cell, the modular porous solid electrolyte reactor according to one or more embodiments. The cell configurations and the production setup are illustrated in FIG.9. The cation exchange membrane (CEM) close to the cathode (Pt/C on carbon cloth) is Nafion® N2100TX (or PTFE fabric reinforced Nafion® alternatives), and the proton exchange membrane (PEM) close to the anode (Pt/C on carbon paper) is the Nafion®-117 membrane. The cathode chamber was supplied with DI water for HER reaction. The water flow rate was controlled by a syringe pump. The flow rate at the outlet was calibrated using a measuring cylinder. In the membrane system, the sodium form styrene-divinylbenzene sulfonated copolymer Dowex 50WX8 hydrogen form (Na-PPS, Sigma-Aldrich) cation conductor was employed as the PSE layer. The Na₂CO₃ or NaHCO₃ flowed into the PSE layer controlled by a syringe pump. The anode chamber was provided with 30 sccm H2 gas for HOR reaction. All cell resistance was measured by the potentiostatic electrochemical impedance spectroscopy (PEIS), and all cell voltages were reported without any IR compensation. CO2 concentration by cycling carbon-containing solution and catholyte using PSE device _[0086] To maximumly release CO₂ from the NaHCO₃/Na₂CO₃ solution, the H⁺ produced at the anode should react with all HCO₃-/CO₃ ^2- groups. Therefore, a closed- loop cycling system according to one or more embodiments was developed. The cell configuration and experiment setup are schematically shown in Fig. 16B. A certain volume of 0.5 M NaHCO₃ solution (200 mL for the first cycle, and 400 mL for other cycles) was supplied into the PSE layer with a flow rate of 4.5 ml min^-1 controlled by a syringe pump. At the anode, the H2 gas was supplied with a flow rate of 30 sccm. At the cathode, the same volume of DI water (200 mL for the first cycle, and 400 mL for other cycles) was cycled with a flow rate of 4.5 ml min^-1. Along with the reaction proceeding, the carbon-containing solution in the PSE layer would be gradually acidified to release CO₂ gas. Once the concentration of Na⁺ in the middle chamber decreases to a low concentration, the cell voltage will be increased suddenly. To start a new batch, fresh 0.5 M NaHCO3, and DI water were first flowed into the membrane system and cathode chamber respectively for 10 min to remove residue Na⁺, and then fresh 0.5 M NaHCO₃ (400 mL) and DI water (400 mL) were used respectively to start a new batch. The residual Na⁺ from the PSE layer and the concentration of NaOH produced at the cathode were determined by using Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES, Perkin Elmer Optima 8300 ICP-OES) and Ion Chromatography (IC). Direct CO2 capture from air [0087] The direct air capture process was operated in a plastic flask. The air was purged into 1.0 N NaOH solution through a gas dispersal for one month. The gas bubbles were dispersed into small bubbles to increase the capture efficiency of CO2. The Na⁺ concentration of the final product was determined using ICP, and the residual CO₃ ^2- and HCO3- were determined by using the titration method. Membrane system gas and liquid analysis [0088] After recycling electrolysis, the dissolved CO₂ and remaining carbon content (in the form of HCO3-) in the liquid was measured using the acid titration method. Firstly, 4 mL of the PSE layer output stream containing dissolved CO2 was collected directly with adding 200 µl of 1 M NaOH and then the collected liquid was titrated using 0.1 M HCl. The titrant was dropped slowly into the sample, and the change of pH was monitored using a pH meter (Orion Star A111). The volume difference between two equivalence points on the titration curve determines how many moles of (bi)carbonate species exist inside the liquid samples. The dissolved CO₂ and remaining carbon concentration was then calculated as below in Equation 1.

[0089] For only detection of the remaining carbon content (in the form of HCO3-), 4 mL of the PSE layer output stream containing dissolved CO2 was collected without adding NaOH and continuous Ar flow was used to purge out the dissolved CO₂ after the sample collection. Then, the same titration procedure was followed as mentioned above and the remaining carbon concentration was then calculated as below in Equation 2. #$₍×& !_' = $ (Eq. 2) [0090] !1 is the total remaining carbon concentration, !2 is the total remaining carbon concentration (in the form of HCO3-), and (!1-!2) is the dissolved CO2 concentration. Δ)1, Δ)2 is the volume of HCl between two equivalence points on the titration curve, c is the concentration of the HCl solution used, and ) is the volume of the sample titrated (without including the volume of the added NaOH). [0091] Water displacement measurement was used to measure the gaseous CO2 flow rate and released CO₂ volume. CO₂-saturated 0.01 M H₂SO₄ was used as the solvent during the water displacement measurement to measure the CO₂ bubble flow rate. It was pre-saturated with CO2 to minimize the gas dissolution, and the acid was used to further suppress the CO₂ gas solubility during the bubble flowrate measuring process. Ion transport number, Faradic efficiency, and CO₂ gas collection efficiency calculations [0092] The Na⁺-ion transport number (t_*+ ^,)describes the ratio of the number of Na⁺ ions crossed through the CEM over the total number of electrons transferred during electrolysis. The concentration of Na⁺ was determined using ICP and IC. The transport number of Na⁺ at the cathode under continuous catholyte flowing is calculated using the following Equations, Equation 3 and Equation 4. ._/0 ^, = 1 ∗ 3 × 4 × ⁽676189:;6 >96>^)?" (Eq. 3) 100 % (Eq. 4)

[0093] 1 is the Na⁺ concentration determined by ICP, 3 is the catholyte flow rate (mL s^-1), and F is the Faradaic constant. For recirculation of the catholyte, the ion transport number for Na⁺ is calculated using the following equation, Equation 5, below.

100 (`>b^`c` 100%) (Eq.5) [0094] 4d_Je( is defined as the ratio of the total number of CO₂ molecules regenerated over the total number of electrons transferred. It describes the electron efficiency in releasing CO₂ molecules. [0095] The Faradaic efficiency for CO2 gas regeneration in the case of NaHCO3 was calculated as below in Equations 6 and 7. [ l_Je' = $_mDE × _4 (Eq. 6) 100 % (Eq. 7)

[0096] 3 is the gaseous CO2 volumetric flowrate (mL s^-1) determined by the water displacement method, )_LMN is the volume of an ideal gas at room temperature, n is the number of electrons involved (n=1 for bicarbonate case and n=2 for carbonate case), and F is the Faradaic constant. [0097] Capacity retention of Na⁺ (CR_Na+) is defined according to Equation 8, below. Capacity retention = (1 − ^{% {_|) × 100 % (Eq. 8) [0098] M_~ and M_" represent the Na⁺ mass in the PSE layer electrolyte before and after reaction, respectively, determined using ICP and IC. Techno-Economic Analysis (TEA) analysis: TEA criteria for comparing PSA separation and solid electrolyte reactor CO2 recovery [0099] A techno-economic analysis (TEA) was performed to assess the economic viability and adaptability of the modular porous solid electrolyte reactor. Several process assumptions were made based on current feedstock prices and electrolyzer performance, with sensitivity analysis considering potential fluctuations in these values in the future. The analysis of NaHCO₃ input case indicates a total system cost of approximately US $126 ton_CO2 ⁻¹. The primary cost is contributed by electrolyzer stack manufacturing ($34.2 tonCO2⁻¹), raw material ($17.7 tonCO2^-1), and electricity ($49.7 ton_CO2 ⁻¹ assuming $0.05 kWh electricity price). Other expenses, including daily maintenance and stack replacement, account for approximately 19.4% of the total cost. Further improvements can be achieved by reducing the cost of the electrolyzer and enhancing the reaction performance. By reducing the cell voltage and increasing the Na⁺-ion transport efficiency, the carbon capture cost may be further reduced by ~$7 and ~$13 tonCO2⁻¹, respectively. Sensitivity analysis also reveals that the regeneration cost is highly sensitive to variations in electricity price (ranging from $0.03 to 0.07 kWh⁻¹) and electrolyzer stack cost (ranging from $5000 to 10000 m⁻²). The carbon regeneration cost of carbonate input is nearly double that of bicarbonate, due to doubled size of electrolyzers as well as doubled energy consumption, while the sensitivity analysis shows a similar tendency. [00100] To have a rough estimation of the carbon regeneration cost from bicarbonate using the PSE reactor according to one or more embodiments, a cell operation of 200 mA cm^-2, which has a Na⁺-ion transport number of 87% and cell voltage of 1.42 V was assumed. Assuming a capture capacity of 1 ton-CO₂ day⁻¹, the total current needed is calculated according to Equation 9, below. 8:8>71c996_8 = 1000 ^{^^ ^0Y X ^LMN ? J "} ^0Y ∗ 'T X ∗ ^S~~a ∗ TT ^^ ∗ 16 ∗ 96485 LMN ∗ U^% = 29171.0 ^ (Eq. 9) [00101] The electrolyzer area needed is the total current divided by the current density, as shown in Equation 10. 14.58 `^' (Eq. 10)

[00102] The power needed is given from P=UI, the cell voltage is 1.42 V for 200 mA cm^-2 _, as shown in Equation 11. ^:^69 = ):78>^6 ∗ 29171.0 ^ ∗ ^{^} "~^{^}^^ = 1.42 ∗ 29171.0 = 41.4 ^^ (Eq. 11) [00103] The water flow rate for the HER reaction is calculated by Equation 12, below. " ^ ^ ^7:^ 9>86 = 2 ^{~.~"U ^^ UST~~ a ^^} ' 9171.0 ^ ∗ ^{P o} ∗ ∗ = 235.1 'Z ∗RSTUV LMN ^0Y ^0Y mDE (Eq. 12) [00104] If H2 is used as the anode reaction reactant, the required hydrogen amount is calculated from Equation 13, below. ^_' `>^^ ^7:^ 9>86 = 29171.0

(Eq. 13) [00105] However, the cathode chamber reaction will generate the same amount of H2 simultaneously, which could be recycled to the anode, and results in no net consumption of H₂. To consider practical operation conditions in the TEA, a 2.5% loss of hydrogen gases ($5/kg) and 2.5% loss of NaHCO3 ($250/ton) chemicals during daily operation is assumed. Example 1 [00106] Example 1 demonstrates CO2 regeneration performance under a continuous flow of NaHCO3 and Na2CO3 solutions through the PSE layer with different concentrations of NaHCO₃ and Na₂CO₃. FIGs. 13A-15C illustrate the CO₂ regeneration performance according to Example 1. FIG. 13A shows a current density (I) versus cell voltage (V) curve for varying NaHCO3 concentrations. FIG. 13B shows corresponding Na⁺ ion transport number of Na⁺ crossover and FIG. 13C shows CO₂ regeneration rate of the electrochemical device according to one or more embodiments by directly flowing different concentrations of NaHCO3 solution into the middle PSE layer, as corresponds to FIG. 13A. FIG. 14A shows an I−V curve for varying Na₂CO₃ concentrations. FIG. 14B shows corresponding Na⁺ ion transport number, and FIG. 14C shows CO2 regeneration rate of the electrochemical device according to one or more embodiments with different concentrations of Na2CO3 solution into the middle PSE layer, as corresponds to FIG. 14A. FIG. 15A shows cell voltage comparison between the middle PSE layer according to one or more embodiments and sand filling in the middle layer, where the PSE layer greatly decreases the cell resistance and voltage. FIG. 15B shows electrochemical energy consumption of CO₂ release (kJ mol⁻¹CO2) as a function of the CO2 regeneration rate under the flow of 0.5 M Na2CO3 or 0.5 M NaHCO3 through the PSE layer according to one or more embodiments. As shown in FIG. 15B, the onset energy consumption is as low as 50 kJ mol^-1 _CO2 in 0.5 M NaHCO3 solution, suggesting a high energy efficiency. FIG. 15C shows Na⁺ ion transport number and corresponding CO2 regeneration rates under higher current densities. As shown in FIG. 15C, the Na⁺ ion transport number can be maintained as high as over 60% when delivering industrially relevant current density of up to 1.5 A cm^-2 in the system of one or more embodiments. Example 2 [00107] Example 2 demonstrates carbon balance analysis in electrolyte recirculation mode. FIGs. 16A, 16B, 17A, and 17B illustrate the results of carbon balance analysis according to Example 2. FIG. 16A is a schematic illustration of CO₂ capture and regeneration process, which is analogous to a battery’s charging and discharging process. FIG. 16B is a schematic illustration of recirculation operation mode for CO2 and NaOH regeneration according to one or more embodiments. FIG. 17A shows the Na⁺ concentration in the middle and cathode chamber as a function of electrolysis time. The total Na⁺ mass remains almost unchanged during the electrocatalysis. FIG. 17B shows cell voltage, FE_Na+, and energy consumption of the PSE reactor of one or more embodiments under recirculation operation mode. In the analysis of Example 2, the cell current density was maintained at 100 mA cm^-2 and the electrode area was 1 cm². Example 3 [00108] Example 3 demonstrates practical cycle operations for CO2 regeneration in the PSE reactor of one or more embodiments. FIG. 18 illustrates results of practical cycle operations according to Example 3. FIG. 18 shows chronopotentiometry stability of the PSE reactor of one or more embodiments for cycles of CO₂ regeneration. In the experimental setup for the system of CO2 regeneration according to Example 3, a balloon is attached to the reactor to capture the CO2 output. In Example 3, the volume of NaHCO₃ stock solution and catholyte in the first cycle were both 200 mL, and then changed to 400 mL for the following cycles. The concentration of the NaHCO3 stock solution was 0.5 M, and the total cell current was 400 mA with an electrode area of 4 cm² (current density is 100 mA cm^-1). In these equations, n is the number of electrons involved, F is the Faradaic constant, jtotal is the total current density, M0 and M1 represent the Na⁺ mass concentration before and after the cycling process. The PSE reactor can stably run for more than 100 hours. Example 4 [00109] Example 4 demonstrates a comparison of different materials used in a PSE reactor according to one or more embodiments. FIGs. 19A and 19B illustrates results of Example 4, showing resistance of the double-CEM electrochemical device (i.e. the PSE reactor) with the layer between the two CEM membranes having an active area of 1 cm². FIG. 19A shows resistance results for a PSE reactor with conductive solid electrolyte in the middle chamber, according to one or more embodiments. FIG. 19B shows resistance results for a PSE reactor without solid electrolyte in the middle chamber. Instead, to balance the pressure at the two sides of CEM membrane, the silicon oxide without ionic conduction groups is used in the middle chamber instead of highly conductive proton conductor. The impedance testing results show that the cell without conductive solid electrolyte (FIG. 19B) exhibits a very high ohmic loss as compared to FIG. 19A. Example 5 [00110] Example 5 shows the effect of NaHCO₃ concentration on current density for a PSE reactor without solid electrolyte in the middle chamber. FIG. 20 illustrates the results of Example 5, where the I-V curve of the porous solid electrolyte device without conductive solid electrolyte measured while flowing different concentrations of NaHCO3 in the middle layer is shown. From FIG. 20, it is obvious that the cell voltage is much higher than that with conductive solid electrolytes in the middle chamber, as in the system according to one or more embodiments. Example 6 [00111] Example 6 shows an optimization study of operating conditions for the PSE reactor according to one or more embodiments. The optimized operating conditions of the porous solid electrolyte device for CO₂ release was determined with contour plots of the calculated rate of CO2 output. The calculated electrochemical energy consumption for CO₂ release (kJ/molCO₂) as a function of the applied current density and the input carbon-containing NaHCO₃ solution flow rate was also determined with contour plots of the calculated total energy consumption. Example 7 [00112] Example 7 demonstrates the effect of concentration of Na₂CO₃ on current density and FE for electrochemical CO2 releasing in the porous solid electrolyte reactor of one or more embodiments by employing OER reaction at the anode and HER at the cathode. In Example 7, different concentrations of Na₂CO₃ solutions flow into the middle layer directly without circulation. The active area of the electrode is 1 cm², and the cell voltage represents the true value without iR compensation. DI water is supplied at the anode for providing H⁺ through OER reaction. FIGs. 21A and 21B show results of Example 7. FIG. 21A shows I-V curve and FIG. 21B shows corresponding FE Na⁺ for with varying Na2CO3 using the OER and HER reactions described in one or more embodiments. Example 8 [00113] Example 8 demonstrates the effect of varying membrane types on the CO2 regeneration system of one or more embodiments. In Example 8, different types of CEM were used between the cathode and PSE layer. As an alternative to the Nafion® N2100X membrane, using a PTFE fabric reinforced Nafion® membrane shows a similar performance to the original Nafion® N2100X membrane, as shown in FIG.22. However, the use of Nafion® 117, a well-known proton conductor, on the cathode side improves H+ conduction and thus decreases the transport number of Na+, as shown in FIG. 23. When two of the same Nafion®-117 membranes were used instead of Nafion® N2100X membrane at the cathode in the PSE reactor of one or more embodiments, the transport number of Na+ dropped to ~ 50 to 60. A 0.5 M Na2CO3 is directly supplied with a flow rate of 4.5 mL min^-2 in the middle SE layer. The DI water was supplied at the cathode with a fast flow rate of 9 ml min^-2 to minimize the possible mass transportation limit. FIG.23 illustrates the results of Example 8, where FE Na⁺ is reported as a function of current density. Example 9 [00114] Example 9 demonstrates the effect of varying membrane types on the CO2 regeneration system of one or more embodiments. In Example 9, a Nafion®-117 membrane was used at the cathode instead of a Nafion® N2100X membrane. A 0.1 M solution of Na2CO3 flows through the middle layer at 100 mA total current. DI water was supplied in both cathode and anode with a flow rate of 4.5 mL min^-1 for HER and OER, respectively. The resistance of the cell is 2.6 Ω. FIG. 24 shows the results of Example 9, where cell volage is reported as a function of time. Example 10 [00115] Example 10 demonstrates the effect on current density when a 0.5 M NaHCO₃ solution flows through the PSE reactor or one or more embodiments. In Example 10, 0.5 M NaHCO3 solution flows through the PSE layer using 4 cm² active area electrodes. The HOR and HER are operated at anode and cathode, respectively. The cell voltage represents the true value without iR compensation. FIG. 25 shows the results of Example 10 in an I-V curve of the porous solid electrolyte reactor for CO2 concentration is shown. Example 11 [00116] Example 11 demonstrates purity of CO2, as measured by different gas chromatography techniques, captured from the middle layer of the PSE reactor of one or more embodiments. In Example 11, gaseous CO2 is captured from the middle layer containing 0.5 M NaHCO3 solution. FIGs.26A and 26B shows results of Example 11, where FIG. 26A shows thermal conductivity (TCD) response of middle layer collected gas flow showing neglectable O2 gas under all current densities and FIG. 26B shows flame ionization response (FID) response of middle layer collected gas flow showing increasing peak intensity for CO₂ gas as the current increases. Table 3 below shows CO2 gas peak from FID and O2 gas peak from TCD (of FIGs. 26B and 26A, respectively) were used together to calculate the CO2 purity (%) at different current densities. Note that the gas purity did not take into consideration water vapors. No cross over H₂ was detected in the gas flow, and trace amount of O₂ was detected, which may be contributed by the dissolved O2 in the DI water. _[00117] Table 3. CO₂ gas peak from FID and O₂ gas peak from TCD were used together to calculate the CO₂ purity (%) at different current densities. Please note that the gas purity did not take into consideration water vapors. No crossover H2 was detected in the gas flow, and trace amount of O₂ was detected, which may be contributed by the dissolved O₂ in the DI water.

Example 12 [00118] Example 12 demonstrates the effect of varying cell current on the collection efficiency (i.e., FE) of CO2. In Example 12, the active electrode area is 4 cm² and cell current is varied under a continuous flow of 0.5 M NaHCO₃ in the PSE layer of one or more embodiments. FIG. 27 shows the results of Example 12, where collection efficiency of CO2 is plotted as a function of cell current. FIG 27 shows that higher electrolysis current showed higher FECO2, indicating that there could be some gas leakage during the CO2 gas collection process, which would affect the quantification of FE of CO2 under smaller current as the CO2 output flow rate is lower than that of a higher current. Example 13 [00119] Example 13 demonstrates remaining CO2 in solution following the CO2 regeneration process of one or more embodiments. In Example 13, acid titration of the remaining solution is performed to find out the remaining CO₂ (in the form of HCO₃-). In Example 13, titration curves of dissolved CO2 in the solid electrolyte water flow for middle-layer downstream carbon content detection after 100 mA recycling electrolysis process without Ar purging and with Ar purging. After electrolysis, the remaining carbon content includes dissolved CO2 and unreacted NaHCO3. By using Ar bubbling, the dissolved CO₂ is purged out in the collected samples. 4 mL of the middle layer output stream containing dissolved CO₂ was collected directly in 200 µl of 1 M NaOH. [00120] The remaining carbon dioxide concentration as measured in Example 13 is calculated by the following Equations.

2.95 `^ ∗ 0.1 (^¡^)/3.8 `^ = 0.0776 (Eq. 14) _[00121] Considering the initial NaHCO₃ concentration is 0.5 M, which means the remaining uncaptured CO2 ratio is calculated by Equation 15, below. £:8>796`>^_^_^ 1>9¤:_ 9>8^: = 0.0776 /0.5 = 15.5% (Eq. 15) [00122] 4 mL of the middle layer output stream containing dissolved CO2 was collected without adding NaOH. And continuous Ar flow was used to purge out the dissolved CO₂ after the sample collection. Then the remaining unreacted NaHCO₃ concentration is calculated by Equation 16, below.

0.1 (^¡^)/4 `^ = 0.04875 (Eq. 16) [00123] Therefore, by Equations 17 and 18, ¥_96>186; ¦>^¡^_^ 9>8^: = 0.04875 /0.5 = 9.75% (Eq. 17) §^^^:736; ¡^_' 9>8^: = 15.5% − 9.75% = 5.75% (Eq. 18) Example 14 [00124] Example 14 demonstrates amount of CO2 gas collected as a function of electrocatalysis time. FIG. 28 shows the results of Example 14, where collected CO2 gas volume under 400 mA current (100 mA cm^-2 current density) is plotted as a function of electrocatalysis time by cycling 100 mL air-captured carbon-containing solution. The active electrochemical area of the electrolyzer is 4 cm². Example 15 [00125] Example 15 demonstrates some representative factors that can help to significantly improve the energy efficiency particularly under high operation current densities. FIG.29A shows the cell voltage (V) as a function of current density (mAcm- ²) with variable Nafion®-N2100X CEM thickness (50 µm or 200 µm), PSE layer thickness (2.0 mm versus 2.5 mm) and operating temperatures (90 °C, 60 °C, or room temperature). FIG.29A shows that the I-V curve improved due to improved membrane conductivity. The cell voltage at 50 mA cm⁻² and 200 mA cm⁻² was improved by 30 mV and 125 mV, respectively. When a thinner PSE layer is used, the I-V curve was further improved on top of the thinner CEM. Without being bound by any particular theory, the thickness of the PSE layer can be further reduced by optimizing the PSE layer’s porosity and the middle layer flow design, as well as utilizing advanced machining tools or 3D printing technologies, which will further improve the I-V curve of the reactor. As shown in FIG. 29A, higher temperature does have profound impacts on device performance, where the cell voltage under 50 and 200 mA cm⁻² was further decreased by 85 and 270 mV, respectively, when operated under 90℃. FIG.29B shows the ion transport number of Na+ in the PSE reactor as a function of current density using a CEM-50μm membrane, 2.0 mm thickness PSE under 90℃, suggesting no obvious changes compared with original performance. Example 16 [00126] Example 16 demonstrates the effect of varying carbonate types on CO2 regeneration. In Example 16, the simulated I-V curve of the electrolyzer for CO₂ concentration is presented by flowing 0.5 M Na2CO3 solution and 0.5 M NaHCO3 solution in the PSE layer. [00127] The current density for 0.5 M Na₂CO₃ solution simulation is shown in Equation 19, below. ¨DECB©ª (¨) ¨DECB©ª (¨) ¡c996_8 ;6_^^8^ (`^ 1`^?') = 13.15646 ^|.«¬|% + 13.15286 ^|.«¬|%¯ − 40.5352 (Eq. 19) [00128] The current density for 0.5 M Na₂HCO₃ solution simulation is shown in Equation 20, below. ¨DECB©ª (¨) ¨DECB©ª (¨) ¡c996_8 ;6_^^8^ ⁽`^ 1`^?') = 61.53956 ^%.««¬¬ + 61.50666 ^%.««¬¬ − 166.4233 (Eq. 20) Example 17 [00129] Example 17 demonstrates the particle size of the PSE layer. FIGs.30A and 30B show SEM images of the porous solid electrolyte powder. The surface of the solid electrolyte is smooth, devoid of any inherent porosity within the PSE. But the stack of solid electrolytes forms microchannels between each other. Scale bar: 200 μm, FIG. 30A; 50 μm, FIG. 30B. [00130] Although only a few example embodiments have been described in detail above, those skilled in the art will readily appreciate that many modifications are possible in the example embodiments without materially departing from this invention. Accordingly, all such modifications are intended to be included within the scope of this disclosure as defined in the following claims.

Claims

CLAIMS What is claimed is: 1. A system for electrochemical carbon dioxide and basic sorbent regeneration, comprising: a modular porous solid electrolyte reactor comprising, an anode chamber comprising an anode, a cathode chamber comprising a cathode, and a membrane system, wherein the membrane system is located between the anode chamber and the cathode chamber, wherein the membrane system comprises a first side facing the anode chamber and a second side facing the cathode chamber; wherein the membrane system is configured to receive a feed stream comprising a basic sorbent and sorbed carbon dioxide in the form of carbonates and/or bicarbonates, and to electrochemically split cations from the carbonates and bicarbonates, producing a high purity stream comprising carbon dioxide; wherein the anode chamber is configured to receive a hydrogen source and produce protons at the anode, and to separate protons from the hydrogen source so as to provide protons to the membrane system; wherein the cathode chamber is configured to receive a water source, receive cations from the membrane system, and produce anions at the cathode, reacting the cations with the anions so as to produce a regenerated basic sorbent stream; and wherein the membrane system comprises: a proton exchange membrane facing the first side, a cation exchange membrane facing the second side, and a porous solid electrolyte layer located between the proton exchange membrane and the cation exchange membrane.

2. The system of claim 1, further comprising a carbon dioxide source and an absorption unit, wherein the absorption unit comprises a basic sorbent and wherein the absorption unit is configured to absorb carbon dioxide from the carbon dioxide source and produce the feed stream comprising the basic sorbent and sorbed carbon dioxide in the form of carbonates and/or bicarbonates.

3. The system of claim 2, wherein the carbon dioxide source is selected from the group consisting of air, flue gas, HVAC exhaust, bio-fermentation tail gas, point source streams, and combinations thereof.

4. The system of claim 2, wherein the absorption unit is selected from the group consisting of one or more air contactors, one or more gas absorbers, one or more cooling towers, and one or more absorption columns.

5. The system of claim 2, wherein the basic sorbent comprises an alkali hydroxide compound selected from the group consisting of lithium hydroxide, potassium hydroxide, cesium hydroxide, and sodium hydroxide.

6. The system of claim 5, wherein the basic sorbent comprises sodium hydroxide, the regenerated basic sorbent stream comprises sodium hydroxide, and the feed stream comprising the basic sorbent and sorbed carbon dioxide in the form of carbonates and/or bicarbonates comprises sodium carbonate and sodium bicarbonate.

7. The system of claim 2, wherein the regenerated basic sorbent stream is recycled to the absorption unit.

8. The system of claim 1, wherein the anode comprises a catalyst configured to catalyze a proton-producing reaction.

9. The system of claim 8, wherein the catalyst configured to catalyze a proton-producing reaction is selected from the group consisting of Pt, Pt/C, Ir, IrO₂, Ir black, Ru, RuO₂, Ru black, RuIr alloys and oxides, RuPt alloys and oxides, transition metals and oxides, transition metal single atom catalysts, and transition metal alloys and oxides.

10. The system of claim 1, wherein the cathode comprises a catalyst configured to catalyze a proton-consuming reaction.

11. The system of claim 1, wherein the cation exchange membrane is selected from the group consisting of chlori-alkaline membranes, nafion® membranes, and bipolar membranes.

12. The system of claim 1, wherein the modular porous solid electrolyte reactor further comprises a temperature control system that independently controls the temperature of the anode chamber, the cathode chamber, and the membrane system.

13. The system of claim 1, wherein the modular porous solid electrolyte reactor further comprises a pressure control system that independently controls the pressure of the anode chamber, the cathode chamber, and the membrane system.

14. A method for electrochemical carbon dioxide and basic sorbent regeneration, comprising: providing a modular porous solid electrolyte reactor comprising, an anode chamber comprising an anode, a cathode chamber comprising a cathode, and a membrane system, wherein the membrane system is located between the anode chamber and the cathode chamber, wherein the membrane system comprises a first side facing the anode chamber and a second side facing the cathode chamber; wherein the membrane system comprises: a proton exchange membrane facing the first side, a cation exchange membrane facing the second side, and a porous solid electrolyte layer located between the proton exchange membrane and the cation exchange membrane; providing a feed stream comprising a basic sorbent and sorbed carbon dioxide in the form of carbonates and/or bicarbonates to the membrane system to electrochemically split cations from the carbonates and bicarbonates, producing a high purity stream comprising carbon dioxide; providing a hydrogen source to the anode chamber and producing protons at the anode, and separating the protons from the hydrogen source so as to provide protons to the membrane system; and providing cations from the membrane system and a water source to the cathode chamber, producing anions at the cathode, and reacting the cations with the anions so as to produce a regenerated basic sorbent stream.

15. The method of claim 14, further comprising: providing a carbon dioxide source to an absorption unit; absorbing, in the absorption unit, carbon dioxide from the carbon dioxide source; and producing the feed stream comprising a basic sorbent and sorbed carbon dioxide in the form of carbonates and/or bicarbonates.

16. The method of claim 15, wherein the carbon dioxide source is selected from the group consisting of air, flue gas, HVAC exhaust, bio-fermentation tail gas, point source streams, and combinations thereof.

17. The method of claim 15, wherein the absorption unit is selected from the group consisting of one or more air contactors, one or more gas absorbers, one or more cooling towers, and one or more absorption columns.

18. The method of claim 15, wherein the absorption unit comprises a basic sorbent.

19. The method of claim 18, wherein the basic sorbent comprises an alkali hydroxide compound selected from the group consisting of lithium hydroxide, potassium hydroxide, cesium hydroxide, and sodium hydroxide.

20. The method of claim 18, wherein the basic sorbent comprises sodium hydroxide, the regenerated basic sorbent stream comprises sodium hydroxide, and the feed stream comprising the basic sorbent and sorbed carbon dioxide in the form of carbonates and/or bicarbonates comprises sodium carbonate and sodium bicarbonate.

21. The method of claim 15, wherein the regenerated basic sorbent stream is recycled to the absorption unit.

22. The method of claim 14, wherein the anode comprises a catalyst configured to catalyze a proton-producing reaction.

23. The method of claim 22, wherein the catalyst configured to catalyze a proton-producing reaction is selected from the group consisting of Pt, Pt/C, Ir, IrO2, Ir black, Ru, RuO2, Ru black, RuIr alloys and oxides, RuPt alloys and oxides, transition metals and oxides, transition metal single atom catalysts, and transition metal alloys and oxides.

24. The method of claim 14, wherein the cathode comprises a catalyst configured to catalyze a proton-consuming reaction.

25. The method of claim 14, wherein the cation exchange membrane is selected from the group consisting of chlori-alkaline membranes, nafion® membranes, and bipolar membranes.

26. The method of claim 14, wherein the modular porous solid electrolyte reactor further comprises a temperature control system that independently controls the temperature of the anode chamber, the cathode chamber, and the membrane system.

27. The method of claim 14, wherein the modular porous solid electrolyte reactor further comprises a pressure control system that independently controls the pressure of the anode chamber, the cathode chamber, and the membrane system.

28. A system for electrochemical carbon dioxide and basic sorbent regeneration, comprising: a modular porous solid electrolyte reactor comprising, an anode chamber comprising an anode, a cathode chamber comprising a cathode, and a membrane system, wherein the membrane system is located between the anode chamber and the cathode chamber, wherein the membrane system comprises a first side facing the anode chamber and a second side facing the cathode chamber; wherein the membrane system is configured to receive a feed stream comprising a basic sorbent and sorbed carbon dioxide in the form of carbonates and/or bicarbonates, and to electrochemically split cations from the carbonates and bicarbonates, producing a high purity stream comprising carbon dioxide; wherein the anode chamber is configured to receive a hydrogen source and produce protons at the anode, and to separate protons from the hydrogen source so as to provide protons to the membrane system; wherein the cathode chamber is configured to receive a water source, receive cations from the membrane system, and produce anions at the cathode, reacting the cations with the anions so as to produce a regenerated basic sorbent stream; and wherein the membrane system comprises: a first membrane unit comprising the first side; a terminal membrane unit comprising a cation exchange membrane comprising the second side; and optionally one or more repeating membrane units between the first membrane unit and the terminal membrane unit, wherein each repeating membrane unit comprises a cation exchange membrane, a porous solid electrolyte layer, a bipolar membrane, and a porous solid electrolyte layer.

29. The system of claim 28, wherein the first membrane unit comprises a cation exchange membrane, a porous solid electrolyte layer, a bipolar membrane, and a porous solid electrolyte layer.

30. The system of claim 28, wherein the first membrane unit comprises a bipolar membrane and a porous solid electrolyte layer.

31. The system of claim 28, further comprising a carbon dioxide source and an absorption unit, wherein the absorption unit comprises a basic sorbent and wherein the absorption unit is configured to absorb carbon dioxide from the carbon dioxide source and produce the feed stream comprising the basic sorbent and sorbed carbon dioxide in the form of carbonates and/or bicarbonates.

32. The system of claim 31, wherein the carbon dioxide source is selected from the group consisting of air, flue gas, HVAC exhaust, bio-fermentation tail gas, point source streams, and combinations thereof.

33. The system of claim 31, wherein the absorption unit is selected from the group consisting of one or more air contactors, one or more gas absorbers, one or more cooling towers, and one or more absorption columns.

34. The system of claim 31, wherein the basic sorbent comprises an alkali hydroxide compound selected from the group consisting of lithium hydroxide, potassium hydroxide, cesium hydroxide, and sodium hydroxide.

35. The system of claim 34, wherein the basic sorbent comprises sodium hydroxide, the regenerated basic sorbent stream comprises sodium hydroxide, and the feed stream comprising the basic sorbent and sorbed carbon dioxide in the form of carbonates and/or bicarbonates comprises sodium carbonate and sodium bicarbonate.

36. The system of claim 31, wherein the regenerated basic sorbent stream is recycled to the absorption unit.

37. The system of claim 28, wherein the anode comprises a catalyst configured to catalyze a proton-producing reaction.

38. The system of claim 37, wherein the catalyst configured to catalyze a proton-producing reaction is selected from the group consisting of Pt, Pt/C, Ir, IrO₂, Ir black, Ru, RuO₂, Ru black, RuIr alloys and oxides, RuPt alloys and oxides, transition metals and oxides, transition metal single atom catalysts, and transition metal alloys and oxides.

39. The system of claim 28, wherein the cathode comprises a catalyst configured to catalyze a proton-consuming reaction.

40. The system of claim 28, wherein the cation exchange membrane is selected from the group consisting of chlori-alkaline membranes, nafion® membranes, and bipolar membranes.

41. The system of claim 28, wherein the modular porous solid electrolyte reactor further comprises a temperature control system that independently controls the temperature of the anode chamber, the cathode chamber, and the membrane system.

42. The system of claim 28, wherein the modular porous solid electrolyte reactor further comprises a pressure control system that independently controls the pressure of the anode chamber, the cathode chamber, and the membrane system.

43. A process for electrochemical carbon dioxide and basic sorbent regeneration, comprising: feeding a carbon dioxide source into an absorption unit configured to absorb carbon dioxide and produce a feed stream comprising a basic sorbent and sorbed carbon dioxide in the form of carbonates and/or bicarbonates, feeding the feed stream into a modular porous solid electrolyte reactor of any one of claims 1-13 or 28-42 contacting the feed stream with the membrane system of the modular porous solid electrolyte reactor, to produce a carbon dioxide rich stream comprising regenerated carbon dioxide and regenerated basic sorbent, feeding the carbon dioxide rich stream into a separator to separate the regenerated carbon dioxide from the carbon dioxide rich stream to produce a carbon dioxide lean stream, and storing the regenerated carbon dioxide in a carbon dioxide storage unit.

44. The process of claim 43, wherein the feed stream is purified prior to feeding the feed stream into the modular porous solid electrolyte reactor.

45. The process of claim 43, wherein the regenerated carbon dioxide is purified prior to storing in the carbon dioxide storage unit.

46. The process of claim 43, further comprising compressing the regenerated carbon dioxide prior to storing in the carbon dioxide storage unit.

47. The process of claim 43, further comprising feeding the carbon dioxide lean stream into the cathode chamber of the modular porous solid electrolyte reactor.

48. The process of claim 47, further comprising mixing the carbon dioxide lean stream with water prior to feeding the carbon dioxide lean stream into the cathode chamber of the modular porous solid electrolyte reactor.

49. The process of claim 47 or claim 48, further comprising contacting the carbon dioxide lean stream with the cathode chamber of the modular porous solid electrolyte reactor, to produce a mixed regenerated stream comprising generated hydrogen gas and a regenerated basic sorbent.

50. The process of claim 49, further comprising feeding the mixed regenerated stream into a separator to separate the generated hydrogen gas from the regenerated basic sorbent stream to produce a generated hydrogen gas stream and a hydrogen lean regenerated basic sorbent stream.

51. The process of claim 50, wherein the generated hydrogen gas stream is purified and stored in a hydrogen storage unit.

52. The process of claim 50, further comprising feeding the hydrogen lean regenerated basic sorbent stream to the absorption unit.

53. The process of claim 51, further comprising feeding a stored hydrogen gas stream through the modular porous solid electrolyte reactor, contacting the stored hydrogen gas stream with the anode chamber of the modular porous solid electrolyte reactor to produce protons and an unreacted hydrogen gas stream, and feeding unreacted hydrogen gas stream to the hydrogen storage unit.

54. The process of claim 43, further comprising feeding an acidic aqueous stream to the modular porous solid electrolyte reactor, contacting the acidic aqueous stream with the anode chamber of the modular porous solid electrolyte reactor to produce an oxygen gas stream, and feeding the oxygen gas stream to an oxygen gas storage unit.