WO2025137281A1

WO2025137281A1 - Capturing carbon dioxide

Info

Publication number: WO2025137281A1
Application number: PCT/US2024/061035
Authority: WO
Inventors: Kyle Wayne KEMP; Paulo Sergio Hernandez MONTES; Megan Lynn O'brien; Ian Ross HARVEY; Andrew Logan OSTERICHER
Original assignee: Carbon Engineering Ulc
Current assignee: Carbon Engineering Ulc
Priority date: 2023-12-19
Filing date: 2024-12-19
Publication date: 2025-06-26
Anticipated expiration: 2026-06-19
Also published as: WO2025137281A9

Abstract

A method for producing carbon dioxide (CO₂) includes contacting atmospheric air with a CO₂ capture solution including hydroxide to absorb CO₂ from the atmospheric air into the CO₂ capture solution and form a carbonate-rich solution; heating the carbonate-rich solution to form a heated carbonate-rich solution; slaking calcium oxide with the heated carbonate-rich solution to form a slaker output stream including calcium hydroxide and calcium carbonate; flowing the slaker output stream through a plurality of reaction vessels to form a vessel output stream including calcium carbonate solids; separating a calcium carbonate solids product stream from the vessel output stream; and calcining the calcium carbonate solids product stream to form a CO₂ product stream.

Description

CAPTURING CARBON DIOXIDE

TECHNICAL FIELD

[0001] The disclosure relates to systems, apparatus, and methods for capturing carbon dioxide.

BACKGROUND

[0002] Capturing carbon dioxide (CO₂) from the atmosphere is one approach to mitigating greenhouse gas emissions and slowing climate change. However, many technologies designed for CO2 capture from point sources of emissions, such as from flue gas of industrial facilities, are generally ineffective in capturing CO2 from the atmosphere due to the significantly lower CO2 concentrations and large volumes of atmospheric air required to process. In recent years, progress has been made in finding technologies better suited to capture CO2 directly from the atmosphere. Some of these direct air capture (DAC) systems use a solid sorbent where an active agent is attached to a substrate. These DAC systems typically employ a cyclic adsorption-desorption process where, after the solid sorbent is saturated with CO2, it releases the CO2 using a humidity or thermal swing and is regenerated.

[0003] Other DAC systems use a liquid sorbent (sometimes referred to as a solvent) to capture CO2 from the atmosphere. An example of such a DAC system would be one where a fan is used to draw air across a high surface area packing that is wetted with a solution comprising the liquid sorbent. CO2 in the air reacts with the liquid sorbent to generate a CO2 rich solution. The rich solution is processed to regenerate a lean solution and to release a concentrated carbon stream, for example, CO, CO2 or other carbon products.

SUMMARY

[0004] In an example implementation, a method for producing carbon dioxide (CO2) includes contacting atmospheric air with a CO2 capture solution including hydroxide to absorb CO2 from the atmospheric air into the CO2 capture solution and form a carbonate-rich solution; heating the carbonate-rich solution to form a heated carbonate-rich solution; slaking calcium oxide with the heated carbonate-rich solution to form a slaker output stream including calcium hydroxide and calcium carbonate; flowing the slaker output stream through a plurality of reaction vessels to form a vessel output stream including calcium carbonate solids; separating a calcium carbonate solids product stream from the vessel output stream; and calcining the calcium carbonate solids product stream to form a CO2 product stream.

[0005] An aspect combinable with the example implementation includes flowing the carbonate-rich capture solution through a nanofdtration (NF) unit to form: an NF retentate stream including a carbonate-rich mixture having a concentration of carbonate greater than a concentration of carbonate in the carbonate-rich capture solution, and an NF permeate stream including a hydroxide-rich mixture.

[0006] In another aspect combinable with one, some, or all of the previous aspects, contacting the atmospheric air with the CO2 capture solution includes contacting the atmospheric air with the NF permeate stream including the hydroxide-rich mixture; and heating the carbonate- rich solution includes heating the NF retentate stream to form the heated carbonate-rich solution. [0007] In another aspect combinable with one, some, or all of the previous aspects, flowing the carbonate-rich capture solution through the NF unit includes flowing the carbonate-rich capture solution having a first concentration of hydroxide, the NF permeate stream having a second concentration of hydroxide at least equal to the first concentration of hydroxide.

[0008] In another aspect combinable with one, some, or all of the previous aspects, calcining the calcium carbonate solids product stream includes calcining at least part of the calcium carbonate solids product stream to produce calcium oxide solids.

[0009] Another aspect combinable with one, some, or all of the previous aspects includes transporting at least some of the calcium oxide solids for slaking the calcium oxide with the heated carbonate-rich solution.

[00010] In another aspect combinable with one, some, or all of the previous aspects, separating the calcium carbonate solids product stream from the vessel output stream includes filtering the vessel output stream to form a retentate stream including the calcium carbonate solids product stream and a permeate stream including hydroxide; and contacting the atmospheric air with the CO2 capture solution includes contacting the atmospheric air with the permeate stream including hydroxide.

[00011] In another aspect combinable with one, some, or all of the previous aspects, filtering the vessel output stream to form a first retentate stream and a first permeate stream; and filtering the first retentate stream to form a second retentate stream forming the retentate stream including the calcium carbonate solids product stream, and to form a second permeate stream. [00012] In another aspect combinable with one, some, or all of the previous aspects, the first and second permeate streams form the permeate stream including hydroxide.

[00013] Another aspect combinable with one, some, or all of the previous aspects includes adding heated water to the vessel output stream to form a heated permeate stream.

[00014] In another aspect combinable with one, some, or all of the previous aspects, heating the carbonate-rich solution includes transferring heat from the heated permeate stream to the carbonate-rich solution and forming a cooled permeate stream.

[00015] In another aspect combinable with one, some, or all of the previous aspects, contacting the atmospheric air with the CO2 capture solution includes contacting the atmospheric air with the cooled permeate stream.

[00016] In another aspect combinable with one, some, or all of the previous aspects, flowing the slaker output stream through the plurality of reaction vessels includes flowing the slaker output stream through a plurality of stirred tanks.

[00017] Another aspect combinable with one, some, or all of the previous aspects includes separating the carbonate-rich solution into a first stream of the carbonate-rich solution and into a second stream of the carbonate-rich solution.

[00018] In another aspect combinable with one, some, or all of the previous aspects, heating the carbonate-rich solution includes heating at least one of the first stream of the carbonate-rich solution and the second stream of the carbonate-rich solution.

[00019] Another aspect combinable with one, some, or all of the previous aspects includes separating the carbonate-rich solution into a first stream of the carbonate-rich solution and into a second stream of the carbonate-rich solution.

[00020] In another aspect combinable with one, some, or all of the previous aspects, heating the carbonate-rich solution includes heating the first stream of the carbonate-rich solution to form a heated first stream of the carbonate-rich solution, and heating the second stream of the carbonate- rich solution to form a heated second stream of the carbonate-rich solution.

[00021] In another aspect combinable with one, some, or all of the previous aspects, slaking the calcium oxide with the heated carbonate-rich solution includes slaking the calcium oxide with the heated first stream of the carbonate-rich solution to form the slaker output stream.

[00022] In another aspect combinable with one, some, or all of the previous aspects, flowing the slaker output stream through the plurality of reaction vessels includes flowing the slaker output stream and the heated second stream of the carbonate-rich solution through the plurality of reaction vessels to form the vessel output stream.

[00023] In another aspect combinable with one, some, or all of the previous aspects, flowing the slaker output stream and the heated second stream of the carbonate-rich solution through the plurality of reaction vessels includes flowing to the plurality of reaction vessels the slaker output stream having a first temperature; and flowing the heated second stream of the carbonate-rich solution to the plurality of reaction vessels, the heated second stream of the carbonate-rich solution having a second temperature less than the first temperature.

[00024] In another aspect combinable with one, some, or all of the previous aspects, the first temperature is between 80°C - 95°C and the second temperature is between 5°C - 30°C.

[00025] In another aspect combinable with one, some, or all of the previous aspects, separating the calcium carbonate solids product stream from the vessel output stream includes filtering the vessel output stream to form a first retentate stream, and to form a first permeate stream including hydroxide; filtering the first retentate stream to form a second retentate stream including the calcium carbonate solids product stream, and to form a second permeate stream including hydroxide; and heating the first permeate stream to form a heated first permeate stream, and heating the second permeate stream to form a heated second permeate stream; heating the first stream of the carbonate-rich solution to form the heated first stream of the carbonate-rich solution includes transferring heat from at least one of the heated first and second permeate streams to the first stream of the carbonate-rich solution; heating the second stream of the carbonate-rich solution to form the heated second stream of the carbonate-rich solution includes transferring heat from the at least one of the heated first and second permeate streams to the second stream of the carbonate- rich solution.

[00026] Another aspect combinable with one, some, or all of the previous aspects includes forming a cooled permeate stream from the at least one of the heated first and second permeate streams after transferring heat therefrom.

[00027] In another aspect combinable with one, some, or all of the previous aspects, contacting the atmospheric air with the CO2 capture solution includes contacting the atmospheric air with at least some of the cooled permeate stream.

[00028] In another aspect combinable with one, some, or all of the previous aspects, separating the carbonate-rich solution into the first stream of the carbonate-rich solution and into the second stream of the carbonate-rich solution includes separating the NF retentate stream into the first stream of the carbonate-rich solution and into the second stream of the carbonate-rich solution.

[00029] Another aspect combinable with one, some, or all of the previous aspects includes selecting for at least one property of the calcium carbonate solids product stream by adjusting at least one of: a hydroxide concentration, a liming ratio for slaking the calcium oxide with the heated carbonate-rich solution, a temperature for slaking the calcium oxide with the heated carbonate-rich solution, or reactivity of the calcium oxide.

[00030] In another aspect combinable with one, some, or all of the previous aspects, for the at least one property of the calcium carbonate solids product stream includes increasing the hydroxide concentration to increase an average particle size of calcium carbonate solids in the calcium carbonate solids product stream.

[00031] In another aspect combinable with one, some, or all of the previous aspects, selecting for the at least one property of the calcium carbonate solids product stream includes increasing the liming ratio for slaking to decrease an average particle size of calcium carbonate solids in the calcium carbonate solids product stream.

[00032] In another example implementation, a method of capturing carbon dioxide (CO2) from atmospheric air includes contacting the atmospheric air with a CO2 capture solution including hydroxide to absorb CO2 from the atmospheric air into the CO2 capture solution and form a carbonate-rich solution; nanofiltering the carbonate-rich solution to form an NF retentate stream including a carbonate-rich mixture, and to form an NF permeate stream including a hydroxide-rich mixture; flowing the NF permeate stream for contacting the atmospheric air with the CO2 capture solution; reacting the NF retentate stream with calcium oxide in a reactor-clarifier to form a clarified effluent stream including hydroxide, and to form an output stream including calcium carbonate solids; and separating a calcium carbonate solids product stream from the output stream. [00033] An aspect combinable with the example implementation includes flowing the clarified effluent stream for contacting the atmospheric air with the CO2 capture solution.

[00034] Another aspect combinable with one, some, or all of the previous aspects includes calcining the calcium carbonate solids product stream to produce a CO2 product stream and to produce calcium oxide solids; and transporting at least some of the calcium oxide solids for reacting the NF retentate stream with the calcium oxide in the reactor-clarifier. [00035] In another aspect combinable with one, some, or all of the previous aspects, the NF retentate stream has a molarity of carbonate between 5 and 20 times greater than a molarity of carbonate in the carbonate-rich capture solution.

[00036] In another aspect combinable with one, some, or all of the previous aspects, separating the calcium carbonate solids product stream from the output stream includes filtering the output stream to form a retentate stream including the calcium carbonate solids product stream, and to form a permeate stream including hydroxide.

[00037] Another aspect combinable with one, some, or all of the previous aspects includes flowing the permeate stream for contacting the atmospheric air with the CO2 capture solution.

[00038] Another aspect combinable with one, some, or all of the previous aspects includes transferring heat from the clarified effluent stream to the NF retentate stream prior to reacting the NF retentate stream with calcium oxide in the reactor-clarifier.

[00039] Another aspect combinable with one, some, or all of the previous aspects includes transferring heat from the clarified effluent stream to the calcium carbonate solids product stream to remove moisture from the calcium carbonate solids product stream.

[00040] In another example implementation, a direct air capture (DAC) system for producing carbon dioxide (CO2) includes at least one gas-liquid contactor configured to contact atmospheric air with a CO2 capture solution to produce a carbonate-rich capture solution; at least one heating unit fluidly coupled to the at least one gas-liquid contactor and configured to heat the carbonate-rich capture solution to produce a heated carbonate-rich capture solution; and a plurality of reaction vessels arranged in series. The plurality of reaction vessels include a first reaction vessel fluidly coupled to the at least one heating unit and configured to slake the heated carbonate- rich capture solution with calcium oxide, to produce a first output stream including calcium hydroxide and calcium carbonate; and at least one downstream reaction vessel fluidly coupled to the first reaction vessel to receive the first output stream. The at least one downstream reaction vessel is configured to flow the first output stream therethrough to react the calcium hydroxide and the calcium carbonate and produce a vessel output stream including calcium carbonate solids. The system includes at least one solids-liquid separator unit fluidly coupled to the plurality of reaction vessels and configured to separate a calcium carbonate solids product stream from the vessel output stream; a piping network including pipelines fluidly coupling: the at least one gas-liquid contactor to the at least one heating unit, the at least one heating unit to the first reaction vessel, the first reaction vessel to the at least one downstream reaction vessel, and the plurality of reaction vessels to the at least one solids-liquid separator unit; and a calciner configured to receive the calcium carbonate solids product stream from the at least one solids-liquid separator unit, and configured to calcine the calcium carbonate solids product stream to produce a CO2 product stream and a solid oxide material.

[00041] An aspect combinable with the example implementation includes a nanofiltration (NF) unit fluidly coupled between the at least one gas-liquid contactor and the at least one heating unit, the NF unit operable to filter the carbonate-rich capture solution and produce a NF permeate stream and a NF retentate stream.

[00042] In another aspect combinable with one, some, or all of the previous aspects, the NF unit is operable to produce the NF permeate stream having a concentration of hydroxide greater than a concentration of hydroxide of the carbonate-rich capture solution.

[00043] In another aspect combinable with one, some, or all of the previous aspects, the pipelines include a NF permeate pipeline fluidly coupling the NF unit to the at least one gas-liquid contactor, the NF unit configured to flow at least a portion of the NF permeate stream to the at least one gas-liquid contactor.

[00044] In another aspect combinable with one, some, or all of the previous aspects, the at least one solids-liquid separator unit is configured to separate a permeate stream including hydroxide from the vessel output stream.

[00045] In another aspect combinable with one, some, or all of the previous aspects, the pipelines include a permeate pipeline fluidly coupling the at least one solids-liquid separator unit to the at least one gas-liquid contactor.

[00046] In another aspect combinable with one, some, or all of the previous aspects, the at least one solids-liquid separator unit is configured to flow at least a portion of the permeate stream to the at least one gas-liquid contactor.

[00047] In another aspect combinable with one, some, or all of the previous aspects, the at least one solids-liquid separator unit includes a first filtration unit and a second filtration unit fluidly coupled to the first filtration unit.

[00048] In another aspect combinable with one, some, or all of the previous aspects, the first filtration unit is configured to filter the vessel output stream and produce a first retentate stream and a first permeate stream, and the second filtration unit is configured to filter the first retentate stream and produce a second retentate stream and a second permeate stream.

[00049] In another aspect combinable with one, some, or all of the previous aspects, the second retentate stream includes the calcium carbonate solids product stream.

[00050] In another aspect combinable with one, some, or all of the previous aspects, the first and second permeate streams at least partially form the permeate stream including hydroxide.

[00051] Another aspect combinable with one, some, or all of the previous aspects includes a wash water system in fluid communication with the first and second filtration units and configured to generate a heated wash water stream.

[00052] In another aspect combinable with one, some, or all of the previous aspects, the first filtration unit is configured to wash the vessel output stream with the heated wash water stream to form a heated first retentate stream including hydroxide.

[00053] In another aspect combinable with one, some, or all of the previous aspects, the second filtration unit is configured to wash the heated first retentate stream with the heated wash water stream to form a heated second permeate stream including hydroxide.

[00054] In another aspect combinable with one, some, or all of the previous aspects, the at least one heating unit includes a heat exchanger configured to transfer heat from the second heated permeate stream to the carbonate-rich capture solution to produce the heated carbonate-rich capture solution, and to form a cooled permeate stream.

[00055] In another aspect combinable with one, some, or all of the previous aspects, the pipelines include a contactor return pipeline fluidly coupling the heat exchanger and the at least one gas-liquid contactor.

[00056] In another aspect combinable with one, some, or all of the previous aspects, the heat exchanger is configured to flow the cooled permeate stream to the at least one gas-liquid contactor.

[00057] In another aspect combinable with one, some, or all of the previous aspects, the pipelines include a first contactor outlet pipeline fluidly coupling the at least one gas-liquid contactor and the first reaction vessel, and a second contactor outlet pipeline fluidly coupling the at least one gas-liquid contactor and the at least one downstream reaction vessel.

[00058] In another aspect combinable with one, some, or all of the previous aspects, the at least one gas-liquid contactor is configured to flow a first stream of the carbonate-rich capture solution to the first reaction vessel via the first contactor outlet pipeline, and a second stream of the carbonate-rich capture solution to the at least one downstream reaction vessel via the second contactor outlet pipeline.

[00059] In another aspect combinable with one, some, or all of the previous aspects, the at least one heating unit includes a first heating unit fluidly coupled to the first contactor outlet pipeline and configured to heat the first stream of the carbonate-rich capture solution to form a heated first stream of the carbonate-rich capture solution; and a second heating unit fluidly coupled to the second contactor outlet pipeline and configured to heat the second stream of the carbonate- rich capture solution to produce a heated second stream of the carbonate-rich capture solution.

[00060] In another aspect combinable with one, some, or all of the previous aspects, the at least one solids-liquid separator unit includes a first filtration unit and a second filtration unit fluidly coupled to the first filtration unit.

[00061] In another aspect combinable with one, some, or all of the previous aspects, the first filtration unit is configured to filter the vessel output stream and produce a first retentate stream and a first permeate stream.

[00062] In another aspect combinable with one, some, or all of the previous aspects, the second filtration unit is configured to filter the first retentate stream and produce a second retentate stream and a second permeate stream that includes the calcium carbonate solids product stream.

[00063] Another aspect combinable with one, some, or all of the previous aspects includes a wash water system in fluid communication with the first and second filtration units and configured to generate a heated wash water stream.

[00064] In another aspect combinable with one, some, or all of the previous aspects, the first filtration unit is configured to wash the vessel output stream with the heated wash water stream to form a heated first retentate stream including hydroxide.

[00065] In another aspect combinable with one, some, or all of the previous aspects, the second filtration unit is configured to wash the heated first retentate stream with the heated wash water stream to form a heated second permeate stream including hydroxide.

[00066] In another aspect combinable with one, some, or all of the previous aspects, the first heating unit includes a first heat exchanger configured to transfer heat from the heated first permeate stream to the first stream of the carbonate-rich capture solution to form the heated first stream of the carbonate-rich capture solution. [00067] In another aspect combinable with one, some, or all of the previous aspects, the second heating unit includes a second heat exchanger configured to transfer heat from the heated second permeate stream to the second stream of the carbonate-rich capture solution to form the heated second stream of the carbonate-rich capture solution.

[00068] In another aspect combinable with one, some, or all of the previous aspects, the pipelines include a plurality of heat exchanger return pipelines fluidly coupling each of the first and second heat exchangers to the at least one gas-liquid contactor, the first and second heat exchangers configured to flow cooled first and second permeate streams to the at least one gasliquid contactor.

[00069] Another aspect combinable with one, some, or all of the previous aspects includes a nanofiltration (NF) unit between the at least one gas-liquid contactor and the first and second heating units.

[00070] In another aspect combinable with one, some, or all of the previous aspects, the NF unit is operable to filter the carbonate-rich capture solution and produce a NF permeate stream and a NF retentate stream upstream of the first contactor outlet pipeline and the second contactor outlet pipeline.

[00071] In another aspect combinable with one, some, or all of the previous aspects, the plurality of reaction vessels include a plurality of stirred tanks arranged in series.

[00072] In another aspect combinable with one, some, or all of the previous aspects, the CO2 capture solution includes at least one of KOH, NaOH, or a combination thereof.

[00073] In another aspect combinable with one, some, or all of the previous aspects, the calciner is configured to calcine the calcium carbonate solids and produce an exhaust gas stream including the CO2 product stream.

[00074] In another aspect combinable with one, some, or all of the previous aspects, the at least one gas-liquid contactor includes a plurality of gas-liquid contactors positioned side by side and forming at least one contactor wall extending along a wall axis.

[00075] In another aspect combinable with one, some, or all of the previous aspects, the at least one contactor wall includes a plurality of dividing walls, each dividing wall of the plurality of dividing walls being upright, the plurality of dividing walls separating plenums of the plurality of gas-liquid contactors of the at least one contactor wall. [00076] In another aspect combinable with one, some, or all of the previous aspects, the at least one contactor wall includes a plurality of contactor walls, each contactor wall of the plurality of contactor walls spaced apart from an adjacent contactor wall of the plurality of contactor walls. [00077] In another example implementation, a direct air capture (DAC) system for capturing carbon dioxide (CO2) includes at least one gas-liquid contactor configured to contact atmospheric air with a CO2 capture solution to produce a carbonate-rich capture solution; a nanofiltration (NF) unit fluidly coupled to the at least one gas-liquid contactor and operable to filter the carbonate-rich capture solution to produce an NF retentate stream including a carbonate- rich mixture, and to produce an NF permeate stream including a hydroxide-rich mixture; at least one reactor-clarifier fluidly coupled to the NF unit, the at least one reactor-clarifier configured to react the NF retentate stream with calcium oxide to form a clarified effluent stream including hydroxide, and to form an output stream including calcium carbonate solids; at least one solids- liquid separator unit fluidly coupled to the reactor-clarifier and configured to separate a calcium carbonate solids product stream from the output stream; and a piping network including pipelines fluidly coupling: the at least one gas-liquid contactor to the NF unit, the NF unit to the at least one reactor-clarifier, and the at least one reactor-clarifier to the at least one solids-liquid separator unit. [00078] In an aspect combinable with the example implementation, the pipelines include an effluent pipeline fluidly coupling the at least one reactor-clarifier to the at least one gas-liquid contactor.

[00079] In another aspect combinable with one, some, or all of the previous aspects, the at least one reactor-clarifier includes a reaction well delimited by a wall separator, the reaction well fluidly coupled to at least one weir configured to receive the clarified effluent stream.

[00080] In another example implementation, a direct air capture (DAC) system for capturing carbon dioxide (CO2) includes at least one gas-liquid contactor configured to contact atmospheric air with a CO2 capture solution to produce a carbonate-rich capture solution; a nanofiltration (NF) unit fluidly coupled to the at least one gas-liquid contactor and operable to filter the carbonate-rich capture solution to produce an NF retentate stream including a carbonate- rich mixture, and to produce an NF permeate stream including a hydroxide-rich mixture; at least one reactor fluidly coupled to the NF unit, the at least one reactor configured to react the NF retentate stream with calcium oxide to form an output stream including calcium carbonate solids; at least one solids-liquid separator unit fluidly coupled to the at least one reactor and configured to separate a calcium carbonate solids product stream from the output stream; and a calciner configured to receive the calcium carbonate solids product stream from the at least one solids- liquid separator unit, and configured to calcine the calcium carbonate solids product stream to produce a CO2 product stream and a solid oxide material.

[00081] In an aspect combinable with the example implementation, the at least one reactor includes a slaker, and a plurality of reaction vessels fluidly coupled to the slaker and arranged in series.

[00082] In another aspect combinable with one, some, or all of the previous aspects, the at least one reactor includes at least one reactor-clarifier fluidly coupled to the NF unit.

[00083] In another aspect combinable with one, some, or all of the previous aspects, the at least one reactor-clarifier is configured to react the NF retentate stream with calcium oxide to form a clarified effluent stream including hydroxide, and to form the output stream.

[00084] The details of one or more implementations of the subject matter described in this specification are set forth in the accompanying drawings and the description below. Other features, aspects, and advantages of the subject matter will become apparent from the description, the drawings, and the claims.

BRIEF DESCRIPTION OF DRAWINGS

[00085] FIG. 1 illustrates an example system for capturing CO2 from atmospheric air.

[00086] FIG. 2 illustrates another example system for capturing CO2 from atmospheric air.

[00087] FIG. 3 illustrates another example system for capturing CO2 from atmospheric air.

[00088] FIG. 4 illustrates another example system for capturing CO2 from atmospheric air.

[00089] FIG. 5 illustrates another example system for capturing CO2 from atmospheric air.

[00090] FIG. 6 illustrates another example system for capturing CO2 from atmospheric air.

[00091] FIG. 7 is a schematic flow diagram of a method for producing CO2.

[00092] FIG. 8 is a schematic flow diagram of a method of capturing CO2 from atmospheric air.

[00093] FIG. 9 is a schematic diagram of a control system (or controller) of the present disclosure.

[00094] FIG. 10A is a schematic illustration of another example gas-liquid contactor of the present disclosure.

[00095] FIG. 10B is a schematic illustration of another example gas-liquid contactor of the present disclosure.

[00096] FIG 10C is a schematic illustration of another example gas-liquid contactor of the present disclosure.

[00097] FIG 10D is a schematic illustration of another example gas-liquid contactor of the present disclosure.

[00098] FIG. 11A is a schematic illustration of another example calciner of the present disclosure.

[00099] FIG. 1 IB is a schematic illustration of another example calciner of the present disclosure.

[000100] FIG. 12A is a side elevational view of an example contactor wall of the present disclosure.

[000101] FIG. 12B is a top-down view of another example system for capturing CO2 from atmospheric air.

[000102] FIG. 13 illustrates another example system for capturing CO2 from atmospheric air.

DETAILED DESCRIPTION

[000103] Referring to FIG. 1, the present disclosure describes a system 10 and methods for capturing carbon dioxide (CO2) from the atmosphere (e.g., ambient or atmospheric air) or from another fluid source that contains dilute concentrations of CO2. The system 10 may be referred to herein as a direct air capture system 10, or a DAC system 10. Concentrations of CO2 in the atmosphere are dilute, in that they are presently in the range of 400-420 parts per million (“ppm”) or approximately 0.04-0.042% v/v, and less than 1% v/v. These atmospheric concentrations of CO2 are at least one order of magnitude lower than the concentration of CO2 in point-source emissions, such as flue gases, where point-source emissions can have concentrations of CO2 ranging from 5-15% v/v depending on the source of emissions.

[000104] The DAC system 10 has one or more gas-liquid contactors 100 operated to capture the dilute CO2 present in ambient air by ingesting the ambient air as a flow of CCh-laden air 101, and by treating the CCh-laden air 101 so as to transfer CO2 present therein to a CO2 capture solution 114 (e.g., a CO2 sorbent) via absorption. Some or all of the CO2 in the CCh-laden air 101 is removed, and the treated CCh-laden air 101 is then discharged by the gas-liquid contactor 100 as a flow of CCh-lean gas 105 (or, CO2-IOW air). In operating to treat atmospheric air in this manner, the gas-liquid contactor 100 may sometimes be referred to herein as an “air contactor” because it facilitates absorption of CO2 from the atmospheric air into the CO2 capture solution 114. In contrast to water cooling towers which function primarily to transfer heat between water and atmospheric air, the gas-liquid contactor 100 functions primarily to achieve mass transfer of CO2 from the atmospheric air to the CO2 capture solution 114. In operating in this manner, the gasliquid contactor 100 allows the DAC system 10 to operate as, or be part of, a direct air capture (DAC) system 10, whose other components are described in greater detail below.

[000105] In some implementations, and referring to FIG. 1, the CO2 capture solution 114 is a caustic solution. In some implementations, the CO2 capture solution 114 has a pH of 10 or higher. In some implementations, the CO2 capture solution 114 has a pH of approximately 14. Non-limiting examples of the CO2 capture solution 114 include aqueous alkaline solutions (e.g., KOH, NaOH, or a combination thereof), aqueous carbonate, ionic liquids, or a combination thereof. In some cases, the CO2 capture solution 114 can include promoters and/or additives that increase the rate of CO2 uptake. Non-limiting examples of promoters include carbonic anhydrase, amines (primary, secondary, tertiary), and boric acid. Non-limiting examples of additives include chlorides, sulfates, acetates, phosphates, surfactants, oxides and metal oxides. For example, a surfactant can be added to the CO2 capture solution 114 to lower the surface tension of the CO2 capture solution 114 to improve the ability of the CO2 capture solution 114 to wet the material of the packing. Non-limiting examples of rate-enhancing additives include carbonic anhydrase, piperazine, monoethanolamine (MEA), diethanolamine (DEA), zinc triazacycles, zinc tetraazacycles, copper glycinates, hydroxopentaaminecobalt perchlorate, formaldehyde hydrate, saccharose, fructose, glucose, phenols, phenolates, glycerin, arsenite, hypochlorite, hypobromite, or other oxyanionic species.

[000106] In some implementations, at a given reference temperature, the density of the CO2 capture solution 114 is greater than the density of water at the same reference temperature. At comparable reference temperatures, in some implementations, the density of the CO2 capture solution 114 is at least 10% greater than the density of water. In some implementations, at comparable reference temperatures, the density of the CO2 capture solution 114 is approximately 10% greater than the density of water. The density and the viscosity of the CO2 capture solution 114 can vary depending on the composition of the CO2 capture solution 114 and the temperature. For example, at temperatures of 0°C to 20°C, the CO2 capture solution 114 or a CCh-laden capture solution 111 can comprise 1 M KOH and 0.5 M K2CO3 and can have a density ranging from 1115 kg/m³ - 1119 kg/m³ and a viscosity ranging from 1.3 mPa-s - 2.3 mPa-s. In another example, at temperatures of 20°C to 0°C, the CO2 capture solution 114 or the CO2-laden capture solution 111 can comprise 2 M KOH and 1 M K2CO3, and can have a density ranging from 1260 kg/m³ - 1266 kg/m³ and a viscosity ranging from 1.8 mPa-s - 3.1 mPa-s. In comparison, water has a density of 998 kg/m³ and viscosity of 1 mPa-s at 20°C.

[000107] In some implementations, and referring to FIG. 1, CO2 from the CO2-laden air 101 is captured by contacting the CO2-laden air 101 with the CO2 capture solution 114 in the gasliquid contactor 100. Reacting the CO2 from the CCh-laden air 101 with an alkaline CO2 capture solution 114 (for example) can form a CCh-laden capture solution 111. In some embodiments, the CO2 capture solution 114 comprises an alkali hydroxide, and CO2 is absorbed by reacting with the alkali hydroxide to form a carbonate-rich capture solution (e.g., K2CO3, Na2CCh, or a combination thereof). The CCh-laden capture solution 111 can include the carbonate-rich capture solution and is thus sometimes referred to herein as the “carbonate-rich solution 111”. The CCh-laden capture solution 111 can be processed to recover the captured CO2 for downstream use and to regenerate the alkali hydroxide for use in the CO2 capture solution 114. In some implementations, recovered CO2 can be delivered downhole and sequestered in a geological formation, subsurface reservoir, carbon sink, or the like. In some implementations, the recovered CO2 can be used for enhanced oil recovery by injecting the recovered CO2 into one or more wellbores to enhance production of hydrocarbons from a reservoir. In some implementations, recovered CO2 can be fed to a downstream fuel synthesis system, which can include a syngas generation reactor. In some implementations, recovered CO2 can be fed to a downstream process used to produce polymers, such as plastics.

[000108] Referring to FIG. 1, in some implementations, the ratio of carbonate concentration ([CO3² ]) to hydroxide concentration ([OH ]) is higher in the CO2-laden capture solution 111 than it is in the CO2 capture solution 114, the different ratios reflecting the absorption of CO2 into the CO2-laden capture solution 111. The term “carbonate-rich,” in some aspects, can mean that a stream contains more CO2 than the associated CO2-lean stream (in this case, CO2 capture solution 114). Therefore, in implementations, the DAC system 10 provides a CO2 “lean” solution to the gas-liquid contactor 100, and also receives a CO2 “rich” solution from the gas-liquid contactor 100. [000109] The CCh-laden capture solution 111 can also include other components in smaller amounts, such as hydroxide ions, alkali metal hydroxide (e.g., KOH, NaOH), water, and impurities. For example, the carbonate-rich solution 111 can comprise between 0.4 M to 6 M K2CO3 and between 1 M to 10 M KOH. In another implementation, the carbonate-rich solution 111 can comprise an aqueous Na2CO3-NaOH mixture. In some implementations, the carbonate- rich solution 111 can comprise a mixture of K2CO3 and Na2COs.

[000110] The capture kinetics of capturing CO2 from the CO2-laden air 101 to form carbonate can be improved by the introduction of an additive such as a promoter species in the CO2 capture solution 114. The resulting carbonate-rich solution 111 produced by the gas-liquid contactor 100 includes carbonates and includes the promoter as well. An example composition of such a carbonate-rich solution 111 can include K2CO3/KHCO3 and a promoter. The carbonate-rich solution 111 resulting from such a CO2 capture solution 114 can have a pH in the range of 11-13 and can have little residual hydroxide from the CO2 capture solution 114. In some cases, additives that are not considered promoters can be used to improve the uptake of CO2 in the CO2 capture solution 114.

[000111] Referring to FIG. 1, the gas-liquid contactor 100 includes a housing 102. The housing 102 defines part of the corpus of the gas-liquid contactor 100 and provides structure thereto. The housing 102 includes exterior structure or walls that partially enclose any combination of interconnected structural members. The structural members provide structural support and stability to the gas-liquid contactor 100 and provide a body for supporting components of the gas-liquid contactor 100 within the housing 102. The structural members can include, but are not limited to, walls, panels, beams, frames, etc. The housing 102 can include other components as well, such as cladding, panels, etc. which help to close off parts of the housing 102 and define the enclosure of the housing 102. The housing 102 at least partially encloses and defines an interior 113 of the housing 102. The interior 113 of the housing 102 is an inner volume or inner space in which components of the gas-liquid contactor 100 are positioned. The housing 102 also includes openings 103 that allow for movement of gases into and out of the gas-liquid contactor 100. For example, and referring to FIG. 1, the housing 102 has one or more inlet(s) 1031. In the implementation of FIG. 1, the one or more inlet(s) 1031 are formed by the openings 103, such that the inlet(s) 1031 can be referred to herein as one or more inlet opening(s) 1031 through which the CCh-laden air 101 enters the interior 113 of the housing 102. The housing 102 has one or more outlet(s) 1030. In the implementation of FIG. 1 , the one or more outlet(s) 1030 are formed by the openings 103, such that the outlet(s) 1030 can be referred to herein as one or more outlet opening(s) 1030 through which the CO2-lean gas 105 exits the interior 113 of the housing 102. In the example implementation of the gas-liquid contactor 100 of FIG. 1, the housing 102 defines two inlets 1031 and one outlet 1030. The outlet 1030 can be defined by a component of the gasliquid contactor 100. For example, in the implementation of the gas-liquid contactor 100 of FIG. 1, the gas-liquid contactor 100 has a fan stack 107 with an upright orientation. The fan stack 107 extends upwardly from the housing 102 and helps to discharge the CCh-lean gas 105. The outlet 1030 is positioned along the fan stack 107. In such an implementation, the CO2-laden air 101 enters the interior 113 of the housing 102 along a substantially horizontal direction through one or both of the inlets 1031, and the CO2-lean gas 105 exits the interior 113 along a substantially vertical direction through the outlet 1030. The outlet 1030 is located at the upper extremity of the fan stack 107. In implementations of the gas-liquid contactor 100 without a fan stack 107, the outlet 1030 can be located elsewhere. Other configurations for the inlets 1031 and outlets 1030 of the housing 102 are possible.

[000112] The housing 102 at least partially encloses and protects components of the gasliquid contactor 100 positioned in the interior 113 of the housing 102. One example of such a component is a packing section 106, which is protected from the surrounding atmosphere by the housing 102. As can be seen in FIG. 1, one or more packing sections 106, which are sometimes referred to herein collectively as “fill 106” or “packing 106”, are located within the interior 113 in a position adjacent to the one ormore inlets 1031. In this position, the one or more packing sections 106 receive the CCh-laden air 101 which enters the interior 113 via the one or more inlets 1031. The one or more packing sections 106 function to increase transfer of CO2 present in the CO2- laden air 101 to a flow of the CO2 capture solution 114, in that the one or more packing sections 106 provide a large surface area for the CO2 capture solution 114 to disperse on, thereby increasing the reactive area between the CCh-laden air 101 and the CO2 capture solution 114. The CO2 capture solution 114 transforms the CCh-laden air 101 into the CCh-lean gas 105 which is discharged from the one or more outlet(s) 1030 of the gas-liquid contactor 100. The packing sections 106 receives the CO2 capture solution 114 and facilitates absorption of the CO2 present in the CO2-laden air 101 into the CO2 capture solution 114 on the packing sections 106, as described in greater detail below. [000113] Referring to FIG. 1, one possible arrangement of the packing sections 106 includes two or more packing sections 106A, 106B. Each packing section 106A, 106B is positioned adjacent to and downstream of one of the inlets 1031. The packing sections 106 A, 106B are spaced apart from each other within the housing 102. The direction along which the packing sections 106A, 106B are spaced apart is parallel to the direction along which the CCh-laden air 101 flows through the packing sections 106A, 106B. The space or volume defined between the packing sections 106A, 106B and/or one or more structural members of the housing 102 is a plenum 108. The plenum 108 is flanked by the packing sections 106A, 106B. The plenum 108 is a void or space within the housing 102 into which gases flow downstream of the packing sections 106A, 106B (e.g., the CCh-lean gas 105), and from which the CCh-lean gas 105 flows out of the housing 102 through the outlet 1030. The plenum 108 is part of the interior 113 of the housing 102. The volume of the plenum 108 is less than a volume of the interior 113. After the CO2-laden air 101 flows through the packing sections 106A, 106B, the CO2-lean gas 105 flows through the plenum 108 before being discharged to the ambient environment. In other implementations of the gasliquid contactor 100, the plenum is absent. The gas-liquid contactor 100 can include one or more portions of drift eliminators to remove or reduce CO2 capture solution 114 that can be entrained in the CCh-lean gas 105 flowing through the plenum 108.

[000114] In the example implementation of the gas-liquid contactor 100 of FIG. 1, the CO2- laden air 101 enters the interior 113 of the housing 102 along a substantially horizontal direction through both of the inlets 1031. The CCh-laden air 101 then flows through the packing sections 106A, 106B along a substantially horizontal direction, where the CO2 present in the CCh-laden air 101 contacts the CO2 capture solution 114 present on the packing sections 106A, 106B and/or flowing in a substantially downward direction over the packing sections 106A, 106B. The exposed surface of the liquid film on the packing sections 106 A, 106B is a gas-liquid interface between the CCh-laden air 101 and the CO2 capture solution 114. CO2 from the CCh-laden air 101 is absorbed into the liquid film to form the CCh-laden capture solution 111 and the CCh-lean gas 105. The CCh-laden capture solution 111 flows downwardly off the packing sections 106 A, 106B in a mixed solution with unreacted CO2 capture solution 114 and is collected. The CCh-laden air 101 treated by the packing sections 106A, 106B exits the packing sections 106A, 106B as the CCh-lean gas 105. The CCh-lean gas 105 from both packing sections 106A, 106B converges in the plenum 108, and then flows in a vertically upward direction out of the plenum 108 through the outlet 1030. The gas-liquid contactor 100 of FIG. 1 can be considered a dual-cell (because of the two packing sections 106A, 106B), cross-flow air contactor. Other configurations of a gas-liquid contactor are possible, as described in greater detail below.

[000115] Each packing section 106 defines a packing depth, which represents the distance traversed by the CO2-laden air 101 as it flows through the packing section 106. The packing depth can be in the range of 2-10 meters. Each packing section 106 also defines a packing liquid travel dimension (sometimes referred to herein as the “packing LTD”), which represents the distance traversed by the CO2 capture solution 114 as it flows through the packing section 106. In the gasliquid contactor 100 of FIG. 1, the packing depth is transverse to the packing LTD. In the gasliquid contactor 100 of FIG. 1, the packing depth is defined along a substantially horizontal direction, and the packing LTD is a vertical dimension. In some implementations, the packing LTD (e.g., the height of each packing section 106) is greater than 2 m. In some implementations, the packing LTD is greater than 5 m. In some implementations, the packing LTD is between 2 m and 20 m. In some implementations, the packing depth is greater than 3 m. In some implementations, the packing depth is greater than 5 m. In some implementations, the packing depth is between 3 m and 10 m. In other configurations of the gas-liquid contactor 100, the packing depth 106D and the packing LTD 106L can be defined differently.

[000116] In implementations, each packing section 106 includes multiple structured packings. In implementations, each packing section 106 is formed from multiple structured packings. Within one of the packing sections 106, each structured packing is arranged adjacent to another structured packing in the direction of one or more of the packing depth 106D, the packing LTD 106L, and a direction perpendicular to both of the packing depth 106D and the packing LTD 106L. One structured packing can be attached to another structured packing with minimal separation or gaps along one or more of the packing depth 106D, the packing LTD 106L, and a direction perpendicular to both of the packing depth 106D and the packing LTD 106L. Some of the structured packings of each packing section 106 can be mounted to one or both of 1) a structural member of the housing 102, and 2) at least one other structured packing. This support of the structured packings reinforces their arrangement within each packing section 106, helps to rigidify each packing section 106, and can also help each structured packing resist or support loads acting upon it during operation of the gas-liquid contactor 100. For example, in mounting the structured packings as described above, the structured packings become constrained which can result in an increase in the overall strength (e g., crush strength) of each packing section 106, compared to a packing structure that is unconstrained.

[0001171 Referring to FIG. 1, the gas-liquid contactor 100 has, includes components of, or is functionally linked to, a liquid distribution system 120. The liquid distribution system 120 operates to move, collect and distribute the CO2 capture solution 114 and/or the CCh-laden capture solution 111. At least some of the features of the liquid distribution system 120 are supported by the housing 102. In the example implementation of FIG. 1, the support provided by the housing 102 includes structural support, in that components of the liquid distribution system 120 are structurally supported by the housing 102, so that loads generated by these components are supported by the housing 102. Some or all of the features of the liquid distribution system 120 can be part of the gas-liquid contactor 100, or part of the DAC system 10.

[000118] Referring to FIG. 1, the liquid distribution system 120 includes one or more liquid collection devices 109. Each liquid collection device 109 is configured to receive one or both of the CO2 capture solution 114 and the CCh-laden capture solution 111 and to hold a volume thereof temporarily or for a longer duration, thereby serving as a source of the CO2 capture solution 114 and/or of the CCh-laden capture solution 111. Each liquid collection device 109 can have any configuration or be made of any material suitable to achieve the function ascribed to it in the present description. For example, one or more of the liquid collection devices 109 can be opentopped, or partially or fully covered. In FIG. 1, one or more of the liquid collection devices 109 include, or are in the form of, basins. Other configurations of the liquid collection device 109 are possible, such as a reservoir, a bed, a sheet, a trough, a pan, a tray, a pipe, a culvert, a container, a receptacle, a network of pressurized pipes with openings or spray nozzles, or any other device capable of retaining liquid. In one possible implementation, the liquid distribution system 120 includes piping and/or trough systems instead of basins.

[000119] The liquid collection devices 109 of the liquid distribution system 120 include one or more top basins 104 and one or more bottom basins 110. The top basins 104 are supported by the housing 102. In some implementations, the top basins 104 are formed from portions of the housing 102. The top basins 104 are configured to at least partially enclose or store the CO2 capture solution 114. Referring to FIG. 1, the top basins 104 are each positioned at least partially above the packing sections 106. Referring to FIG. 1, the top basins 104 are positioned above the inlets 1031. When stored (at least transiently) within the top basins 104, the CO2 capture solution 114 is positioned to be circulated (e.g., through pumping, gravity flow or both) downwards, through the packing sections 106 and ultimately into the bottom basin 110. As the CO2 capture solution 114 is circulated through the packing sections 106, the CCh-laden air 101 is circulated through the packing sections 106 to contact the CO2 capture solution 114, through the plenum 108, and to an ambient environment as the CChflean gas 105. Aprocess stream is formed by contacting the CO2-laden air 101 and the liquid CO2 capture solution 114, where the process stream is or includes the CCh-laden capture solution 111 having CO2 absorbed from the CCh-laden air 101 by the CO2 capture solution 114. The top basins 104 can each have any suitable form or feature for distributing the CO2 capture solution 114 over the packing sections 106. In the example implementation of the gas-liquid contactor 100 of FIG. 1, the liquid collection devices 109 include two top basins 104. Each top basin 104 is positioned above one of the packing sections 106A, 106B to distribute the CO2 capture solution 114 to the respective packing section 106A, 106B. The top basins 104 of FIG. 1 are fluidly isolated from one another (e.g., no fluid communication between the two top basins 104). Other configurations and numbers of the top basins 104 are possible. Other configurations for the distribution of the CO2 capture solution 114 over the packing sections 106 is possible. In one such possible configuration, the one or more of the liquid collection devices 109 include, or are in the form of, a network of pressurized pipes with openings or spray nozzles which distribute the CO2 capture solution 114 over the uppermost portions of the packing sections 106.

[000120] Referring to FIG. 1, the one or more bottom basins 110 are positioned at the bottom of the gas-liquid contactor 100 opposite the top basins 104. As can be seen in FIG. 1, the bottom basin 110 is positioned below the packing sections 106. The bottom basin 110 acts as a collection tank for the process stream (e.g., the CCh-laden capture solution 111). The CCh-laden capture solution 111 including absorbed CO2, as well as unreacted CO2 capture solution 114, collects in the bottom basin 110, and can then be pumped or otherwise moved out of the bottom basin 110 for further processing. For example, at least a portion of the liquids collected in the bottom basin 110 can be processed and then pumped for redistribution over the packing sections 106 for use in CO2 capture. In another possible implementation, some or all of the liquids collected in the bottom basin 110 is pumped to the top basins 104 without being processed, for redistribution over the packing sections 106 for CO2 capture. In another possible implementation, some or all of the liquids collected in the bottom basin 110 are pumped to components of the DAC system 10 for further processing, as described in greater detail below. The bottom basin 110 can be compatible with a containment structure and prevent loss of various CO2 capture solutions 114, many of which have corrosive, caustic or high pH properties. In some aspects, the bottom basin 110 can be lined or coated with one or more materials that are resistant to caustic induced corrosion or degradation. In some implementations of the gas-liquid contactor 100, components can be kept out of the bottom basin 110 holding the CO2 capture solution 114. Additionally, the gas-liquid contactor 100 can be designed to keep most or all the structural components out of the wettable area of the gas-liquid contactor 100, e g., any portion of the gas-liquid contactor 100 that is in contact with the CO2 capture solution 114. Examples of wettable areas of the gas-liquid contactor 100 includes components supporting the packing sections 106. FIG. 1 depicts a single bottom basin 110. However, other configurations and numbers of bottom basins 110 are possible.

[000121] In some implementations, the gas-liquid contactor 100 includes vertically sectioned packing sections 106 with redistribution of the CO2 capture solution 114 between the vertically- spaced apart packing. For example, the liquid collection devices 109 of the liquid distribution system 120 can include one or more redistribution basins.

[000122] In alternate implementations of redistribution of the CO2 capture solution 114 between the vertically-spaced apart packing, the packing sections 106 themselves include redistribution features. In alternate implementations of the gas-liquid contactor 100, the gas-liquid contactor 100 does not include vertically-sectioned packing or redistribution.

[000123] Referring to FIG. 1, the CO2 capture solution 114 flows over the packing sections 106 in a direction that is substantially perpendicular or transverse to the average direction along which the CCh-laden air 101 circulates through the packing sections 106, also known as a “cross flow” configuration. In another possible implementation, the CO2 capture solution 114 flows over the packing sections 106 in a direction that is opposite to the average direction along which the CCh-laden air 101 circulates through the packing sections 106, also known as a “counter flow” configuration. In another possible implementation, the CO2 capture solution 114 flows over the packing sections 106 in a direction that is parallel with the direction along which the CCh-laden air 101 circulates through the packing sections 106, also known as a “co-current flow” configuration. In another possible configuration, the CO2 capture solution 114 flows over the packing sections 106 according to a configuration that is a combination of one or more of cross flow, counter flow and co-current flow configurations. [000124] The gas-liquid contactor 100 can include supports positioned within the packing sections 106 between the top basins 104 and bottom basin 110. For example, the packing sections 106 can include additional support, such as one or more structural members, for a specific portion of the packing sections 106, such as for an upper portion of the packing sections 106, so that the loads (e.g., the weight of the portion of structured packings when dry plus the weight of the liquid hold up of the CO2 capture solution 114 on the portion of the structured packings) do not bear upon another portion of the packing sections 106 (e.g., a bottom portion of the packing sections 106). In some aspects, the packing sections 106 may not include the support. In some aspects, at least one structural support can be positioned between the structured packings of the packing sections 106.

[000125] The liquid distribution system 120 can include any suitable componentry, such as piping, weir(s), pump(s), valve(s), manifold(s), etc., fluidly coupled in any suitable arrangement, to achieve the functionality ascribed to the liquid distribution system 120 herein. One non-limiting example of such componentry is one or more pump(s) 122, an example of which is shown in FIG. 1. The pumps 122 function to move liquids under pressure, such as the CO2 capture solution 114 and/or the CO2-laden capture solution 111, from their source to where they are used. Some nonlimiting examples of possible functions of the pumps 122 include moving the CO2 capture solution 114 to the top basins 104, moving the process streams from the bottom basin 110 to the redistribution basins within the packing sections 106, moving the CO2 capture solution 114 and/or the CCh-laden capture solution 111 from the bottom basin 110 to the top basins 104 for redistribution over the packing sections 106, moving the CO2 capture solution 114 and/or the CCh- laden capture solution 111 from the bottom basin 110 to components of the DAC system 10 for further processing, and any combination of the preceding flows. The pumps 122 can thus be used to move liquid to, from and within the gas-liquid contactor 100.

[000126] A control system (e.g., control system 999 shown in FIG. 1) can be used to control the flow of fluid by the pumps 122 of the liquid distribution system 120. For example, a control system can be used to control the pumps 122 in order to pump the CO2 capture solution 114 from the bottom basin 110 to the top basins 104. The pumps 122 can also be controlled such that a constant velocity of flow is provided to the liquid distribution system 120 regardless of changes of liquid flow throughout the gas-liquid contactor 100. [000127] The pumps 122 can help to distribute the CO2 capture solution 114 over the packing sections 106 at relatively low liquid flow rates, which can help to reduce costs associated with pumping or moving the CO2 capture solution 114. Further, low liquid flow rates of the CO2 capture solution 114 over the packing sections 106 can result in a lower pressure drop of the CCh-laden air 101 as it flows through the packing sections 106, which reduces the energy requirements of the device used for moving the CCh-laden air 101 across the packing sections 106 (e.g., a fan 112 described below). The pumps 122 can be configured to generate intermittent or pulsed flow of the CO2 capture solution 114 over the packing sections 106, which can allow for intermittent wetting of the packing sections 106 using relatively low liquid flows. The CO2 capture solution 114 sprayed, flowed, or otherwise distributed over the packing sections 106 is collected in the bottom basin 110 and can then be moved by the pumps 122 back to the top basin 104, or sent downstream for processing.

[000128] In some implementations, and referring to FIG. 1, the one or more pump(s) 122 of the liquid distribution system are operable to flow the CO2 capture solution 114 over each packing section 106 at a liquid loading rate ranging from 0.5 L/m²s to 10 L/m²s. In some implementations, the liquid loading rate is between 2 L/m²s and 6 L/m²s. The units L/m²s of the liquid loading rate refer to a given volume of the CO2 capture solution 114 covering a given area of the packing section 106, each second. The given area of the packing section 106 can refer to a plane area of a top of the packing section 106, such as the area of the packing section 106 underneath the top basin 104 (i.e., looking down on the top part of the packing section 106 from the top basin 104). When determined using the plane area, a liquid loading rate of 2 L/m²s means that the pump(s) 122 is configured to flow the CO2 capture solution 114 over each packing section 106 such that every second each square meter of the plane area of the packing section 106 receives 2 L of the CO2 capture solution 114. The given area of the liquid loading rate may not refer to the area of a surface of the structured packing. The liquid loading rate can refer to, or be reflective of, an initial flow condition where the CO2 capture solution 114 is applied to the top of the packing section 106. The liquid loading rate may not reflect subsequent flow conditions present lower down the packing section 106.

[000129] The liquid process streams in the gas-liquid contactor 100, as well as process streams within any downstream processes with which the gas-liquid contactor 100 is fluidly coupled, can be flowed using one or more flow control systems (e.g., control system 999). A flow control system can include one or more flow pumps (including or in addition to the pumps 122), fans, blowers, or solids conveyors to move the process streams, one or more flow pipes through which the process streams are flowed and one or more valves to regulate the flow of streams through the pipes. Each of the configurations described herein can include at least one variable frequency drive (VFD) coupled to a respective pump that is capable of controlling at least one liquid flow rate. In some implementations, liquid flow rates are controlled by at least one flow control valve.

[000130] In some embodiments, a flow control system can be operated manually. For example, an operator can set a flow rate for each pump or transfer device and set valve open or closed positions to regulate the flow of the process streams through the pipes in the flow control system. Once the operator has set the flow rates and the valve open or closed positions for all flow control systems distributed across the system, the flow control system can flow the streams under constant flow conditions, for example, constant volumetric rate or other flow conditions. To change the flow conditions, the operator can manually operate the flow control system, for example, by changing the pump flow rate or the valve open or closed position.

[000131] In some embodiments, a flow control system can be operated automatically. For example, the flow control system can be connected to a computer or control system (e.g., control system 999) to operate the flow control system. The control system can include a computer- readable medium storing instructions (such as flow control instructions and other instructions) executable by one or more processors to perform operations (such as flow control operations). An operator can set the flow rates and the valve open or closed positions for all flow control systems distributed across the facility using the control system. In such embodiments, the operator can manually change the flow conditions by providing inputs through the control system. Also, in such embodiments, the control system can automatically (that is, without manual intervention) control one or more of the flow control systems, for example, using feedback systems connected to the control system. For example, a sensor (such as a pressure sensor, temperature sensor or other sensor) can be connected to a pipe through which a process stream flows. The sensor can monitor and provide a flow condition (such as a pressure, temperature, or other flow condition) of the process stream to the control system. In response to the flow condition exceeding a threshold (such as a threshold pressure value, a threshold temperature value, or other threshold value), the control system can automatically perform operations. For example, if the pressure or temperature in the pipe exceeds the threshold pressure value or the threshold temperature value, respectively, the control system can provide a signal to the pump to decrease a flow rate, a signal to open a valve to relieve the pressure, a signal to shut down process stream flow, or other signals. In other example embodiments, the flow control system can be a combination of manual and automatic operating commands.

[000132] The gas-liquid contactor 100 has a gas-circulating device which functions to move or circulate gas flows into and out of the gas-liquid contactor 100. In the implementation of the gas-liquid contactor of FIG. 1, the gas-circulating device of the gas-liquid contactor 100 is a fan 112. The fan 112 functions to circulate gases like ambient air, such that the CCh-laden air 101 is caused by the fan 112 to flow into the gas-liquid contactor 100, and such that the CCh-lean gas 105 is caused by the fan 112 to be discharged from the gas-liquid contactor 100. The fan 112 thus functions to circulate the CCh-laden air 101 and the CCh-lean gas 105 in the manner described herein. Referring to FIG. 1, the fan 112 is rotatable about a fan axis defined by a fan shaft. In the implementation of the fan 112 depicted in FIG. 1, the fan axis has an upright or vertical orientation. Other orientations for the shaft and for the fan axis are possible. Referring to FIG. 1, the fan 112 is positioned upstream of the end of the fan stack 107 that defines the outlet 1030 and functions to induce a flow of the CO2-lean gas 105 through the outlet 1030. In another possible configuration, the fan 112 is positioned elsewhere between the vertically-opposite ends of the fan stack 107 and upstream of the outlet 1030, such that the fan 112 flows the CO2-lean gas 105 through the outlet 1030. Referring to FIG. 1, the fan 112 is positioned downstream of, and above, the plenum 108. Rotation of the fan 112 about the fan axis causes gases to circulate into the inlets 1031 and through the gas-liquid contactor 100. For example, in the implementation of the gasliquid contactor of FIG. 1, rotation of the fan 112 causes the CCh-laden air 101 to be drawn into the gas-liquid contactor 100 and causes the CCh-lean gas 105 to be discharged from the gas-liquid contactor 100. The fan 112 can cause the CCh-laden air 101 to enter the packing sections 106 at airspeeds below 5 m/s. The fan 112 can cause the CO2-laden air 101 to enter the packing sections 106 at airspeeds between 0.1 m/s and 5 m/s. In some implementations of the gas-liquid contactor 100, a blower is used instead of, or in addition to, the fan 112 to flow the CCh-laden air 101. In some implementations the fan 112 or blower can be in an induced flow configuration, and in other implementations can be in a forced flow configuration. [000133] In some implementations, each structured packing of the packing sections 106 includes, or is composed of, multiple packing sheets attached together to form a three-dimensional structured packing. The packing sheets of each structured packing can be made of any suitable material, or have any suitable configuration, to achieve the function ascribed to the packing sections 106 herein. Some or all of the packing sheets can be made from PVC, which is relatively light, moldable, affordable, and resists degradation caused by many chemicals. The packing sheets are arranged, constructed, treated or otherwise configured to promote spreading of the liquid CO2 capture solution 114 into a thin film on the surfaces of the packing sheets, which can enable maximum exposure of the liquid CO2 capture solution 114 to the CO2 present in the CCh-laden air 101. For example, the liquid-gas interface surface of one or more of the packing sheets can be treated with a coating, have shapes or formations, and/or be made of a material that vary the surface energy (e g., increase the surface energy) of portions of the packing sheet and/or lower the contact angle of the liquid CO2 capture solution 114. For example, the hydrophilicity of the liquid-gas interface surface of one or more of the packing sheets can be increased by applying a coating to increase the surface free energy. Coatings can be applied to some or all of the structured packing to make the packing sections 106 even more suitable for low liquid loading rates ranging from 0.5 L/m²s to 2.5 L/m²s. In this regard, reference is made to such surface treatments and modifications described in U.S. Patent Application Publication No. 2022/0176312, the entire contents of which are incorporated herein by reference. Such “film-type” packing sheets are suitable for DAC systems (such as DAC system 10) since they have the capacity for more effective mass transfer per unit volume of fill space. For example, film-type fill offers a relatively high ratio of specific surface area to volume, the ratio defined in units of m²/m³. A high specific surface area helps to expose more CO2 to the surface of the CO2 capture solution 114, and also has cost and structural implications.

[000134] One or more of the packing section(s) 106 can include any material that fills a space and facilitates the contact between the CO2-laden air 101 and the CO2 capture solution 114. The packing section(s) 106 can be designed and positioned within the gas-liquid contactor 100 to enable liquid distribution and gas flow. The gas-liquid contactor 100 can include other configurations of the one or more packing section(s) 106 in addition to, or separate from, the packing sections 106 described above. Non-limiting examples of other types of packing, fill and packing/fill material include splash fill, film fill, random packing, mesh, panels, etc. The packing section(s) 106 can include corrugated sheets arranged in a crisscrossing relationship to create flow channels for the vapour phase. The packing section(s) 106 can include loose random or structured materials. The packing section(s) 106 can include: a cross flow geometry designed to limit or minimize the pressure drop in the CCh-laden air 101; can be efficiently wetted by intermittent liquid flows; and, has a liquid hold up enabling intermittent operation with long time durations between wetting.

[000135] Other configurations of the gas-liquid contactor 100 are possible, some of which are now described in greater detail. The gas-liquid contactor 100 can include cooling-tower style gas-liquid contactors, spray towers, liquid-gas scrubbers, venturi scrubbers, packed towers, and other systems designed to remove at least a portion of a gas component from a larger gas stream using a liquid sorbent. The gas-liquid contactor 100 can include single or multi cell air contactors, dual cell air contactors, dual flow air contactors, or a combination thereof. The gas-liquid contactor 100 can operate in crossflow, countercurrent flow, co-current flow, or a combination thereof [000136] In one such possible configuration, and referring to FIG. 10A, the gas-liquid contactor 100A can have an upright body and an air inlet 2103 along a bottom portion through which the CCh-laden air 101 is admitted into the gas-liquid contactor 100A. The fan 2112 rotates to draw the CCh-laden air 101 through the inlet 2103 in an upward direction to contact the packing section 2106. In the configuration of FIG. 10A, the gas-liquid contactor 100A is not a dual cell configuration, and instead has one packing section 2106, which may or may not consist of multiple sections and/or types of packing, and as such may be referred to as a "single cell" gas-liquid contactor 100A. This configuration may not include a plenum that stretches from the bottom basin 2110 to the fan cowling but can include a plenum chamber above the packing 2106 and between drift eliminators and the fan 2112 and/or fan cowling. The CO2 capture solution 114 circulates downwards by, for example, gravity flow, uniform or laminar flow, etc., within the packing 2106 and eventually flows into one or more bottom basins 2110. As the CO2 capture solution 114 circulates through and over the packing 2106, the CCh-laden air 101 is flowing (e.g., by action of the fan 2112) upwardly through the packing 2106 to contact the CO2 capture solution 114. Thus, the flow of the CO2 capture solution 114 through the packing 2106 in FIG. 10A is counter-current (or counterflow) to the flow of the CCh-laden air 101 through the packing 2106. The packing liquid travel dimension along which the CO2 capture solution 114 flows through the packing 2106 is defined along the vertical direction and is the same as the packing depth along which the CO2- laden air 101 flows upwardly through the packing 2106. A portion of the CO2 within the CO2- laden air 101 is transferred to (e.g., absorbed by) the CO2 capture solution 114, and the fan 2112 moves the CO2 lean gas 105 out of the gas-liquid contactor 100A to an ambient environment. The CO2 rich solution flows into the at least one bottom basin 2110.

[000137] Referring to FIG. 10B, another possible configuration of a gas-liquid contactor 100B has an upright body and an inlet 3103 along an upright side portion through which the CO2- laden air 101 is admitted into the gas-liquid contactor 100B. The fan 3112 rotates about a horizontal fan axis to draw the CCh-laden air 101 through the inlet 3103 in a substantially horizontal direction to contact the packing section 3106. In another possible implementation of the gas-liquid contactor 100B, the fan 3112 is upstream of the packing section 3106 relative to the flow direction of the CCh-laden air 101. In such an implementation, the gas-liquid contactor 100B employs forced draft in which the fan 3112 rotates about a horizontal fan axis to “push” the CCh- laden air 101 through the inlet 3103 in a substantially horizontal direction to contact the packing section 3106. In the configuration of FIG. 10B, the gas-liquid contactor 100B is not a dual cell configuration, and instead has one packing section 3106, which may or may not consist of multiple sections and/or types of packing, and as such may be referred to as a "single cell" gas-liquid contactor 100B. This configuration may not include a plenum that stretches from the bottom basin 3110 to the fan cowling but can include a plenum chamber above the packing 3106 and between drift eliminators and the fan 3112 and/or fan cowling. The CO2 capture solution 114 circulates downwards by, for example, gravity flow, uniform or laminar flow, etc., within the packing 3106 and eventually flows into one or more bottom basins 3110. As the CO2 capture solution 114 circulates through the packing 3106, the CCh-laden air 101 is flowing (e.g., by action of the fan 3112) substantially horizontally through the packing 3106 to thereby contact the CO2 capture solution 114. Thus, the flow of CO2 capture solution 114 through the packing 3106 in FIG. 10B is substantially perpendicular to the flow of the CCh-laden air 101 through the packing 3106. Such a configuration of the flows may be referred to as a “cross flow” configuration. The packing liquid travel dimension along which the CO2 capture solution 114 flows through the packing 3106 is defined along the vertical direction and is perpendicular to the packing depth along which the CCh- laden air 101 flows horizontally through the packing 3106. A portion of the CO2 within the CO2- laden air 101 is transferred to the CO2 capture solution 114, and the fan 3112 moves the CCh-lean gas 105 out of the gas-liquid contactor 100B to an ambient environment, The CCh rich solution flows into the at least one bottom basin 3110.

[0001381 Other possible configurations of the gas-liquid contactor 100 include a gas-liquid contactor 100 which receives the CO2-laden air 101, flows the CO2 capture solution 114 to contact the CO2 in the CO2-laden air 101, releases the CO2-lean gas 105, and allows for the CO2-laden capture solution 111 to be flowed to release CO2 gas and regenerate the CO2 capture solution 114. Such a gas-liquid contactor 100C, 100D is represented in FIG. 10C. The gas-liquid contactor 100C, 100D can have any suitable configuration of internal and external components.

[000139] Referring to FIG. 10D, another possible configuration of a gas-liquid contactor 100D has an upright body and an air inlet 403 along a top portion through which the CCh-laden air 101 is admitted into the gas-liquid contactor 100D. The fan 421 rotates to push the CCh-laden air 101 into the gas-liquid contactor 100D and contact the packing section 406. In the configuration of FIG. 2C, the gas-liquid contactor 100D has only one packing section 406 and can therefore be referred to as a “single cell” gas-liquid contactor 100D. The CO2 capture solution 114 circulates downwards by, for example, gravity flow, uniform or laminar flow, etc., within the packing 406 and eventually flows into one or more bottom basins 411 As the CO2 capture solution 114 circulates downward through and over the packing 406, the CCh-laden air 101 (e.g., by action of the fan 421) also flows downward through the packing 406 to contact the CO2 capture solution 114. Thus, the flow of the CO2 capture solution 114 through the packing 406 in FIG. 10D is cocurrent to the flow of the CCF-laden air 101 through the packing 406. The packing liquid travel dimension along which the CO2 capture solution 114 flows through the packing 406 is defined along the vertical direction and is the same as the packing depth along which the CCh-laden air 101 flows downwardly through the packing 406. At least a portion of the CO2 within the CO2- laden air 101 is transferred to (e.g., absorbed by) the CO2 capture solution 114, and the fan 421 pushes the CC ean gas 105 out of the gas-liquid contactor 100D to an ambient environment. The CO2-laden capture solution 111 and the CO2 capture solution 114 flow into the at least one bottom basin 411.

[000140] Some non-limiting examples of possible configurations for the gas-liquid contactor 100C, 100D include being a modular unit, being rounded or circular, being a cell of an array or train of gas-liquid contactors 100, 100A, 100B, 100C, 100D being a cell of a rounded or circular gas-liquid contactor 100, 100A, 100B, 100C, 100D, and being a component of a heating, ventilation, and air conditioning (HVAC) system. The gas-liquid contactor 100 can include, or be fluidly coupled to, devices for managing liquid level in the gas-liquid contactor 100. These devices can include, but are not limited to, evaporators to reduce liquid levels and/or maintain concentrations of the CO2 capture solution 114. These devices can include, but are not limited to, water make-up tanks or sources to manage liquid levels and/or maintain concentrations of the CO2 capture solution 114. The DAC system 10 can include multiple gas-liquid contactors 100, 100A, 100B, 100C, 100D. In some implementations, the DAC system 10 includes multiple gas-liquid contactors 100, 100A, 100B, 100C, 100D arranged adjacent each other to form an array or a train of gas-liquid contactors 100, 100A, 100B, 100C, 100D (see, for example, FIG. 12B). The DAC system 10 can include multiple arrays or trains of gas-liquid contactors 100, 100A, 100B, 100C, 100D. The description, units, componentry, features, streams, reference numbers and advantages of the gas-liquid contactor 100 provided in relation to FIG. 1 apply mutatis mutandis to the gasliquid contactor 100A, 100B, 100C, lOOD ofFIGS. lOA to 10D.

[000141] The gas-liquid contactor 100, 100A, 100B, 100C, 100D operates to absorb CO2 from the CCh-laden air 101, and can thus be referred to as, or including, a capture subsystem 180 of the DAC system 10. Referring to FIG. 1, the DAC system 10 also includes other subsystems, such as a regeneration subsystem 190. The regeneration subsystem 190 functions to regenerate the CO2-laden capture solution 111 received from the capture subsystem 180 to form regenerated CO2 capture solution 114 that is flowed back to the capture subsystem 180. The regeneration subsystem 190 also functions to release CO2 from the CCh-laden capture solution 111, to produce a CO2 product stream 116. The CO2 product stream 116 can be used for different purposes. In some implementations, the CO2 product stream 116 is delivered downhole and sequestered in a geological formation, subsurface reservoir, carbon sink, or the like. In some implementations, the CO2 product stream 116 is used for enhanced oil recovery by injecting the recovered CO2 into one or more wellbores to enhance production of hydrocarbons from a reservoir. In some implementations, the CO2 product stream 116 is fed to a downstream fuel synthesis system, which can include a syngas generation reactor. In some implementations, the CO2 product stream 116 is fed to a downstream process used to produce polymers, such as plastics. In some implementations, the CO2 product stream 116 is provided as a substantially pure CChgas stream to be used for any suitable purpose or product. The CO2 product stream 116 can be used for other purposes as well, or in any combination of the above-listed purposes. In addition to capturing CO2 from the CO2- laden air 101, the DAC system 10 can thus also produce CO2, and provide the produced CO2 as the CO2 product stream 116. A control system (e.g., the control system 999 shown in FIG. 1) can be used to control one or more components of the capture subsystem 180 and/or of the regeneration subsystem 190.

[000142] In other implementations, the gas-liquid contactor 100, 100A, 100B, 100C, 100D can be formed from removably attached packing supports that hold the packing sections 106. In such implementations, each packing support can be positioned above or below another packing support, such that a vertical stack of packing supports forms a vertically-extending cell of the gasliquid contactor 100, 100A, 100B, 100C, 100D. To position and secure the packing sections 106 within the gas-liquid contactor 100, 100A, 100B, 100C, 100D, each packing support can comprise a structure defining a bottom surface and a packing perimeter. The overall size and shape of the structure can vary. In example implementations, the structure can be, but is not limited to, a rectangular shape. The bottom surface can be defined by features of the structure and can be used for supporting the packing sections used in the gas-liquid contactor 100, 100A, 100B, 100C, 100D. [000143] Non-limiting examples of the regeneration subsystem 190 of the DAC system 10 are now described in greater detail. Referring to FIG. 1, the regeneration subsystem 190 includes componentry to grow and process calcium carbonate solids by regenerating the CCh-laden capture solution 111 to form regenerated CO2 capture solution 114 comprising hydroxide. The regeneration subsystem 190 includes the following non-exhaustive list of components: one or more heating units 130, one ormore slakers 140, multiple reaction vessels 150, one or more solids-liquid separator units 160, a piping network 170 having multiple pipelines 172, and a calciner 185, which are described in greater detail below. The regeneration subsystem 190 and its components perform a series of reactions which allow for regenerating the CCh-laden capture solution 111 to form regenerated CO2 capture solution 114, and for releasing CCh to form the CO2 product stream 116 for any suitable purpose.

[000144] Chemical reactions occur in the features of the regeneration subsystem 190 that allow for regenerating the CCh-laden capture solution 111 and forming the CO2 product stream 116. Two such reactions, Reaction 1 and Reaction 2 described below, take place in the slaker 140. Calcium oxide (CaO) or quicklime reacts with water in the CCh-laden capture solution 111 to form calcium hydroxide (Ca(OH)2, commonly known as slaked lime, hydrated lime, builder’s lime, pickling lime, or Chuna) via Reaction 1. [000145] CaO(s) + H2O(_aq) Ca(OH)_{2 (}s) (1)

[000146] Calcium hydroxide Ca(OH)₂ once formed begins reacting with the carbonate species in the CCh-laden capture solution 111 (e.g., K2CO3) to form solid calcium carbonate (CaCO₃), via Reaction 2.

[000147] Ca(OH)₂(s) + K₂CO₃(aq) CaCO_3(s) + 2KOH₍a_q) (2)

[000148] Reaction 1 is generally known as the slaking reaction and is exothermic, and Reaction 2 is generally known as the causticization reaction. The causticization Reaction 2 immobilizes some of the CO2 absorbed by the CO2 capture solution 114 in solid form in the calcium carbonate and regenerates the CCh-laden capture solution 111 to form the regenerated CO2 capture solution 114 comprising hydroxide, where the regenerated CO2 capture solution 114 can be reused in the gas-liquid contactor 100, 100A, 100B, 100C, 100D to absorb additional CO2. Both reactions can occur simultaneously anytime liquid containing carbonate is mixed with quicklime. The reaction vessels 150 and the slaker 140 form a causticization train, or series of reactors, in which the causticization Reaction 2 occurs.

[000149] The bulk of the causticization reaction takes place in the slaker 140. In some implementations, at least 70% of the causticization reaction takes place in the slaker 140. In some implementations, approximately 75% of the causticization reaction takes place in the slaker 140. In some implementations, between 70% and 95% of the causticization reaction takes place in the slaker 140. The exothermic slaking of Reaction 1 occurs in the first reactor of the causticization train (e.g., in the slaker 140). Thus, having the bulk of the causticization reaction take place in the same first reactor (e.g., the slaker 140) allows the bulk of the causticization reaction to occur in the highest temperature reactor in the causticization train. In implementations where the reaction kinetics are temperature dependent, the causticization reaction is thus allowed to occur quickly in the first reactor. Having the bulk of the causticization reaction take place in the first reactor (e.g., the slaker 140) allows for taking advantage of the high temperatures and favorable starting concentrations to drive the causticization reaction as far as possible in the first reactor (e.g., the slaker 140), which can help drive the causticization reaction to completion as quickly as possible, and can potentially allow for minimising the number of reactors in the causticization train.

[000150] The contents from the slaker 140 are fed into the reaction vessels 150 which are arranged in series. The reaction vessels 150, either alone or collectively with the slaker 140, are sometimes referred to as “causticizers” because they allow the causticization reaction to continue. The reaction vessels 150 and the slaker 140 form the causticization train. Thus, the slaker 140 can be considered the “first causticizer” in the causticization train. The contents from the reaction vessels 150 are flowed to the solids-liquid separator unit 160 to separate liquids from solids. The separated solids include calcium carbonate solids which are conveyed to the calciner 185 (via one or more intermediate units), while the separated liquids which include hydroxide are flowed to the capture subsystem 180.

[000151] The calcium carbonate solids are fed to the calciner 185 and undergo a thermal treatment called calcination, whereby the calcium carbonate solids are raised to a high temperature under a restricted supply of oxygen, for the purpose of converting the calcium carbonate solids into a solid oxide material (calcium oxide, or CaO) and a carbon dioxide (CO₂) gas stream. The resulting CO₂ gas stream can be processed and/or treated to form part of the CO₂ product stream 116, while some or all of the produced CaO is sent back to the slaker 140 for reaction with the CO2-laden capture solution 111. The calcination reaction in the calciner 185 involves the decomposition of CaCO₃ at a calcination temperature of between 700-1050°C into solid calcium oxide (CaO) and CO₂ gas, according to the following chemical reaction:

[000152] CaCO₃(s) CaO(s) + CO₂(g)

[000153] The operation of the features of the regeneration subsystem 190 and the relationship between these features is described in greater detail below.

[000154] Referring to FIG. 1, the heating unit 130 of the regeneration subsystem 190 is fluidly coupled to the gas-liquid contactor 100, 100A, 100B, 100C, 100D via a contactor outlet pipeline 172A of the piping network 170. The C Ch-laden capture solution 111 flows from the gasliquid contactor 100, 100A, 100B, 100C, 100D to the heating unit 130 via the contactor outlet pipeline 172A, for example under pressure from the one or more pump(s) 122. The heating unit 130 is also fluidly coupled to the gas-liquid contactor 100, 100A, 100B, 100C, 100D via a contactor return pipeline 172B through which the regenerated CO2 capture solution 114 flows from the heating unit 130 to the gas-liquid contactor 100, 100A, 100B, 100C, 100D. The heating unit 130 functions to increase the temperature of the CCh-laden capture solution 111 before it flows to other components of the regeneration subsystem 190, such as the slaker 140, and forms a stream of heated carbonate-rich solution 117. This heating functionality can be achieved in different ways. In some implementations, and referring to FIG. 1, the heating unit 130 is a heat exchanger which transfers heat from a warmer fluid stream to heat the CCh-laden capture solution 111, as described in greater detail below. Non-limiting examples of possible heat exchangers include plate and frame heat exchangers, spiral heat exchangers, hairpin exchanger, U-tube heat exchanger, and singlepass heat exchangers. In some implementations, the heat exchanger heating unit 130 transfers heat from other areas of the DAC system 10 to the CCh-laden capture solution 111 (as described in greater detail below). In some implementations, the heat exchanger heating unit 130 transfers heat to the CCh-laden capture solution 111 that is generated from facilities or areas outside of the DAC system 10, such a nuclear facility, a geothermal facility, etc. In other implementations, the heating unit 130 generates thermal energy using a dedicated energy source and transfers the thermal energy to the CCh-laden capture solution 111 to increase its temperature.

[000155] In some implementations, the heating unit 130 supplies the heated carbonate-rich solution 117 at a temperature close to the desired temperature at which the slaking reaction (Reaction 1 above) occurs in the slaker 140. In some implementations, the slaking reaction occurs above 80°C. In some implementations, the slaking reaction occurs above 90°C. In some implementations, the slaking reaction occurs between 80°C and less than 100°C. In some implementations, the slaking reaction occurs between 85°C and 95°C. In some implementations, the slaking reaction occurs between 85°C and 90°C. In some implementations, the slaking reaction occurs at a steady-state reaction temperature of approximately 90°C. Setting or maintaining the slaking temperature close to, but less than, 100°C can allow for the highest reaction rate for slaking to be achieved without boiling the water present in the slaker 140, when the slaker 140 operates at a pressure such that the equilibrium state of water is liquid. In some implementations, the heating unit 130 supplies the heated carbonate-rich solution 117 at a temperature between 60°C and 95°C. In some implementations, the heating unit 130 supplies the heated carbonate-rich solution 117 at a temperature between 80°C and 95 °C. In some implementations, the heating unit 130 supplies the heated carbonate-rich solution 117 at a temperature between 85°C and 90°C. In such implementations, the heating unit 130 provides the slaker 140 with a reaction stream (e.g., the heated carbonate-rich solution 117) whose temperature is at, or close to, the desired slaking temperature. In so doing, the heating unit 130 helps to address the difficulties which can arise if the CCh-laden capture solution 111 from the gas-liquid contactor 100, 100A, 100B, 100C, 100D was provided directly to the slaker 140. In this regard, challenges can arise when using colder CCh-laden capture solution 111 (e.g., CCh-laden capture solution 111 at standard ambient reference temperatures such as 25°C) in the slaker 140, as using such colder CCh-laden capture solution 111 can increase the difficulty in reaching the required slaking temperature. This can result in less reactivity in the slaker 140, and/or the production of more waste product (known as grit or residue). In the DAC system 10 implementation of FIG. 1, the heating unit 130 is a feature of the regeneration subsystem 190. In other implementations of the DAC system 10, the heating unit 130 is a feature of the capture subsystem 180. In other implementations of the DAC system 10, the heating unit 130 is a feature independent of both the capture subsystem 180 and the regeneration subsystem 190.

[000156] Referring to FIG. 1, the heated carbonate-rich solution 117 is flowed from the heating unit 130 to the slaker 140 via a slaker input pipeline 172C. Calcium oxide (CaO) is slaked with water in the heated carbonate-rich solution 117 as per Reaction 1 above, and the slaker 140 also allows for causticization to occur as per Reaction 2. The slaking and causticization reactions in the slaker 140 generate a slaker output stream 142 which is flowed from the slaker 140 to the reaction vessels 150 via a slaker output pipeline 172D. In an alternate implementation, the slaker output pipeline 172D branches into parallel lines fluidly coupling the slaker 140 to each of the reaction vessels 150, such that the slaker output stream 142 is fed to the reaction vessels 150 in parallel. The slaker output stream 142 includes unreacted calcium hydroxide produced by the slaking reaction, as well as calcium carbonate and hydroxide (e.g., KOH) produced by the causticization reaction. The slaker output stream 142 is a slurry due to the presence of low solubility solids like calcium carbonate and calcium hydroxide. In some implementations, such as in FIG. 1, the heated carbonate-rich solution 117 includes water in sufficient quantities for the slaking reaction and for generating a transportable slurry, such that no make-up water is added to the slaker 140. In such implementations, the heated carbonate-rich solution 117 serves two purposes: first a portion of the water in the heated carbonate-rich solution 117 is consumed during the slaking reaction to form the calcium hydroxide via Reaction 1, and second an excess of water in the heated carbonate-rich solution 117 helps to produce a transportable slurry of calcium hydroxide and calcium carbonate solids as part of the slaker output stream 142. In such implementations, the slaker 140 of FIG. 1 operates free of an external source of slaking water. The DAC system 10 of FIG. 1 has one slaker 140. The DAC system 10 can have multiple slakers 140 arranged in series, such that each slaker 140 receives the slaker output stream 142 from an upstream slaker 140. In some implementations, the DAC system 10 has multiple slakers 140 operating in parallel, such that the DAC system 10 has multiple causticization trains where each causticization train includes a slaker 140 feeding multiple reaction vessels 150. In the implementation of the DAC system 10 of FIG. 1, all (e.g., 100%) of the heated carbonate-rich solution 117 is configured to flow to the slaker 140. In other implementations, some of which are described below, less than 100% of the heated carbonate-rich solution 117 is configured to flow to the slaker 140.

[000157] The slaker 140 serves as a reactor for converting a portion of the carbonate in the heated carbonate-rich solution 117 to hydroxide and calcium carbonate in the slaker output stream 142. The slaker 140 receives an alkaline heated carbonate-rich solution 117 that can contain between 0.1 M and 4.1 M of carbonate [CCh^2-]. During causticization of Reaction 2, the produced calcium hydroxide will react with the dissolved carbonate to produce a precipitate of calcium carbonate. The slaker 140 can be operated at a desired slaker liming ratio, where the slaker liming ratio is defined as the moles of CaO provided to the slaker 140 over the moles of the carbonate compound (e.g., K2CO3) provided to the slaker 140. It is possible to decrease the slaker liming ratio by decreasing the amount of CaO added to the slaker 140, or by increasing the amount of carbonate added to the slaker 140. Similarly, it is possible to increase the slaker liming ratio by increasing the amount of CaO added to the slaker 140, or by decreasing the amount of carbonate added to the slaker 140. Adjusting the slaker liming ratio can impact the slaking reaction, the causticization reaction, the size of calcium carbonate solids, and/or the distribution of calcium carbonate solids, as described in more detail below. The DAC system 10 allows for relatively high lime loading, and thus relatively large slaker liming ratios, which can contribute to reducing flow rates through the remainder of the regeneration subsystem 190, as well as helping to reduce the flow of regenerated CO2 capture solution 114 returning to the gas-liquid contactor 100, 100A, 100B, 100C, 100D. With lower fluid flows, it can be possible to operate the causticization train at higher temperatures, which can increase reaction rates. In some implementations, the slaker liming ratio is between 3: 10 and 1:1. In some implementations, the slaker liming ratio is between 0.2 and 0.75. In some implementations, the slaker liming ratio is between 0.5 and 0.75. In some implementations, an example of which is described below, the slaker liming ratio can be greater than one, for example as high as 7.5.

[000158] The percent by weight of solids in the slaker output stream 142 can vary. In some implementations, the percent by weight of calcium carbonate solids in the slaker output stream 142 is between 2 wt % and 40 wt %. In some implementations, the percent by weight of calcium carbonate solids in the slaker output stream 142 is between 2 wt % and 10 wt %. In some implementations, the percent by weight of calcium carbonate solids in the slaker output stream 142 is between 2 wt % and 5 wt %. In some implementations, the percent by weight of calcium hydroxide and calcium carbonate solids in the slaker output stream 142 is between 10 wt % and 25 wt %. In some implementations, the percent by weight of calcium hydroxide and calcium carbonate solids in the slaker output stream 142 is between 20 wt % and 40 wt %. The slaker 140 can allow for the reactions therein to occur over a residence time between 1 minute and 120 minutes. The slaker 140 can allow for the reactions therein to occur over a residence time between 10 minutes and 50 minutes.

[000159] The slaker 140 can be any suitable reaction vessel or series of vessels to achieve the functionality ascribed to it herein. For example, and referring to FIG. 1, the slaker 140 is a hollow reactor vessel with one or more inlet port(s) and one or more outlet port(s). The inlet port(s) are in fluid communication with the piping network 170 to convey reactants to an interior of the slaker 140 in which Reactions 1 and 2 occur. The outlet port(s) are in fluid communication with the piping network 170 to convey product streams, such as the slaker output stream 142, to other components of the regeneration or capture subsystems 180,190. The slaker 140 of FIG. 1 is a mixed tank or a stirred-tank reactor and includes any suitable device (e.g., mixer, impeller, etc.) to agitate, mix or stir the contents in the interior. The slaker 140 can include components for removing un-reactable contaminants and disposing of them as a waste stream. The slaker 140 can be an industrial lime slaker. Another possible configuration for the slaker 140 includes a lime hydrator coupled to a mixing tank wherein additional water is mixed with the slurry produced from the lime hydrator to form the slaker output stream 142. The slaker 140 can also be, or include, a paste slaker, a detention slaker, a ball mill slaker, a batch slaker, and a hydrator system. The slaker 140 of FIG. 1 allows for both slaking and causticization reactions to occur, and thus provides reduced complexity compared to a system in which the slaking and causticization steps occur in separate reactors such that solids must be filtered and/or transported between the separate reactors. [000160] Referring to FIG. 1, the slaker output stream 142 is flowed from the slaker 140 to the reaction vessels 150 via the slaker output pipeline 172D. The reaction vessels 150 include a leading or first reaction vessel 150A, and a last reaction vessel 150B. The slaker output stream 142 is flowed to the first reaction vessel 150A, and then to all other reaction vessels 150 arranged in series. It follows that the output stream of each reaction vessel 150 is provided to a subsequent, downstream reaction vessel 150 until the last reaction vessel 150B, where “downstream” and “upstream” used in relation to the reaction vessels 150 is defined relative to the flow of reactants from the first reaction vessel 150A to the last reaction vessel 150B. The output stream of the last reaction vessel 150B is a vessel output stream 152. The vessel output stream 152 includes calcium carbonate solids and hydroxide (e.g., KOH), and is provided to the solids-liquid separator unit 160. Causticization as per Reaction 2, which begun in the slaker 140, continues in each of the reaction vessels 150, such that the collective vessel output stream 152 represents additional calcium carbonate solids and hydroxide converted from the carbonate in the slaker output stream 142. The series of reaction vessels 150 provide more residence time for the causticization reaction, in addition to that already provided by the slaker 140. In some implementations, the collective residence time provided by the slaker 140 and the reaction vessels 150 is between 10 minutes and 180 minutes. In some implementations, the collective residence time provided by the slaker 140 and the reaction vessels 150 is less than five hours. A vessel output pipeline 172E of the piping network 170 fluidly couples the last reaction vessel 150B to the solids-liquid separator unit 160. Some of the pipelines 172 can also extend between, and fluidly couple, each of the reaction vessels 150. The output stream of each reaction vessel 150 can be flowed to the next downstream reaction vessel 150 using gravity, a fluid-displacement device (e.g., a slurry pump), and/or a combination thereof. Each of the reaction vessels 150 are, in some implementations, gravity-fed stirred tanks which operate without fluidizing a bed of solids therein.

[000161] Each reaction vessel 150 can be any suitable body to achieve the functionality ascribed to it herein. For example, and referring to FIG. 1, each reaction vessel 150 is a hollow reactor vessel with one or more inlet port(s) and one or more outlet port(s). In some implementations, and referring to FIG. 1, each reaction vessel 150 has a single inlet port in fluid communication with either the slaker 140 or an upstream reaction vessel 150, to receive therefrom the output stream from the upstream reaction vessel 150 or slaker 140 and convey it to an interior of the reaction vessel 150 in which Reaction 2 continues to occur. The outlet port(s) are in fluid communication with the piping network 170 to convey product streams, such as each output stream or the vessel output stream 152, to other reaction vessels 150 or to other components of the regeneration subsystem 190. Each reaction vessel 150 of FIG. 1 is a stirred tank and includes any suitable device (e.g., mixer, impeller, etc.) to agitate, mix or stir the contents in the interior. Each reaction vessel 150 can include components for removing un-reactable contaminants or non- process elements (NPEs) via a dedicated outlet port and disposing of them as a waste stream. In some implementations, each reaction vessel 150 receives a single input, the single input being the output stream of the reactor immediately upstream. In some implementations, each reaction vessel 150 operates without its own source of calcium hydroxide, such that the sole source of calcium hydroxide for the reaction vessels 150 is provided in the slaker output stream 142. FIG. 1 shows four reaction vessels 150. The regeneration subsystem 190 can include more reaction vessels 150, or fewer reaction vessels 150.

[000162] In some implementations, and referring to FIG. 1, the slaker 140 and the reaction vessels 150 are identical to each other, except for the presence in the slaker 140 of inlet port(s) for receiving calcium oxide solids which are not features of the reaction vessels. In some implementations, and referring to FIG. 1, the slaker 140 and the reaction vessels 150 have the same dimensions, same materials of construction, and same internal componentry (e.g., mixers), with the primary difference being that the slaker 140 has inlet port(s) for receiving calcium oxide solids while the reaction vessels 150 do not. In such implementations, the slaker 140 can be considered the first reaction vessel 150A of the reaction vessels 150, and the one that produces a “first” output stream (e.g., the slaker output stream 142). In such implementations, the slaker 140 can be considered the first reaction vessel 150A of the causticization train of the regeneration subsystem 190. In such implementations, all reaction vessels 150, other than the first reaction vessel 150A in which the slaking of Reaction 1 occurs, can be referred to as “downstream” reaction vessels 150 because they receive the output stream from the first reaction vessel 150A. In such implementations, the term “slaker” used to describe the reactor 140 does not require or limit the reactor 140 to being substantially different from the other reaction vessels 150. The identicality of, or similarity between, the slaker 140 and the reaction vessels 150 of FIG. 1 help to reduce the complexity and maintenance of the regeneration subsystem 190.

[000163] In some implementations, the reaction vessels 150 are different from one another. For example, in such implementations, one reaction vessel 150 can be different from at least one other reaction vessel 150 in terms of the following non-exhaustive list of characteristics: size, diameter, height, capacity, materials of construction, inlet port(s), outlet port(s), number and location of connectivity, solids removal capabilities, internal componentry (e.g., mixers), thermal insulation and mixing speed or depth. It can be desirable to vary one or more of the reaction vessels 150 in order to vary a property of the causticization train, such as the overall residence time and the mixing of reactants.

[0001641 The reaction vessels 150 can allow for the reactions therein to occur over a combined residence time between 20 minutes and 120 minutes. The reaction vessels 150 can allow for the reactions therein to occur over a combined residence time between 40 minutes and 80 minutes. In some implementations, the steady-state or equilibrium temperature across the reaction vessels 150 is between 85°C and less than 100°C. In some implementations, the steady-state or equilibrium temperature across the reaction vessels 150 is between 85°C and 95°C. In some implementations, the steady-state or equilibrium temperature across the reaction vessels 150 is between 85°C and 90°C. In some implementations, the steady-state or equilibrium temperature across the reaction vessels 150 is approximately 90°C. Setting or maintaining the causticization temperature close to, but less than, 100°C can allow for the highest reaction rate to be achieved without boiling the water present in the reaction vessels 150, when the reaction vessels 150 operate at a pressure such that the equilibrium state of water is liquid.

[000165J In some implementations, the percent by weight of calcium carbonate solids in the output stream from a given one of the reaction vessels 150 is greater than the percent by weight of calcium carbonate solids in the output stream of the reaction vessel 150 immediately upstream. In some implementations, the percent by weight of calcium carbonate solids in the output stream from a given one of the reaction vessels 150 is approximately equal to the percent by weight of calcium carbonate solids in the output stream of the reaction vessel 150 immediately upstream, because the causticization reaction has reached equilibrium between the two reaction vessels 150 and/or the rate of reaction has significantly decreased, such that the causticization reaction from one reaction vessel 150 to the next one downstream may not result in increased calcium carbonate solids production. In some implementations, the concentration of hydroxide in the output stream from a given one of the reaction vessels 150 is greater than the concentration of hydroxide in the output stream of the reaction vessel 150 immediately upstream. In some implementations, the concentration of hydroxide in the output stream from a given one of the reaction vessels 150 is approximately equal to the concentration of hydroxide in the output stream of the reaction vessel 150 immediately upstream, because the causticization reaction has reached equilibrium between the two reaction vessels 150 and/or the rate of reaction has significantly decreased. [000166] Irrespective of the reaction kinetics between each reaction vessel 150, the result of causticizing through all the reaction vessels 150 from the first reaction vessel 150A to the last reaction vessel 150B is that the concentration of hydroxide in the vessel output stream 152 is greater than the concentration of hydroxide in the slaker output stream 142. The causticization train can thus allow for high conversion rates (>95%) of hydroxide due to relatively long residence times, and due to relative high reaction temperatures (e.g., approximately 90°C) achieved from heating the CCh-laden capture solution 111 in the heating unit 130 and from the exothermic slaking reaction. In some implementations, the concentration of hydroxide [OH'] in the vessel output stream 152 is between 1.5 M and 3.5 M. In some implementations, the percent by weight of the calcium carbonate solids in the vessel output stream 152 can be greater than the percent by weight of the calcium carbonate solids in the slaker output stream 142. In some implementations, the percent by weight of calcium carbonate solids in the vessel output stream 152 is between 2 wt % and 10 wt %.

[000167] The calcium carbonate solids present in the vessel output stream 152 can include precipitates and/or aggregates formed during causticization. The calcium carbonate solids present in the vessel output stream 152 can have a particle size diameter between 1 and 500 microns. The calcium carbonate solids present in the vessel output stream 152 can have a D50, or median, particle size diameter between 20 and 100 microns. The particle size and/or their size distribution (particle size distribution, or PSD) can be selected for or controlled by varying aspects of the slaking or causticization reactions, as explained in greater detail below.

[000168] In implementations of the DAC system 10 where all (e.g., 100%) of the heated carbonate-rich solution 117 is configured to flow to the slaker 140, such as in FIG. 1, the slaker 140 can be similar to the reaction vessels 150, as described above. The slaker 140 can differ from the reaction vessels 150 only in that the slaker 140 is the reactor of the causticization train which receives calcium oxide solids and includes componentry for handling the initial addition of calcium oxide solids, and which can have solids/grit removal componentry. Alternate implementations of the causticization train are possible. In one such alternate implementation, the regeneration subsystem 190 is free of a slaker 140 and includes only reaction vessels 150 arranged in series to facilitate both the slaking of Reaction 1 and the causticization of Reaction 2. In another such alternate implementation, and as described in greater detail below, the regeneration subsystem 190 is free of a slaker 140 and is free of reaction vessels 150 arranged in series, and instead uses a different reactor to complete both the slaking of Reaction 1 and the causticization of Reaction 2. [0001691 Referring to FIG. 1, the vessel output stream 152 is flowed from the last reaction vessel 150B via the vessel output pipeline 172E to the solids-liquid separator unit 160. The solids- liquid separator unit 160 functions to separate liquids from the solids in the vessel output pipeline 172E, such that the separated solids including calcium carbonate solids are conveyed using any suitable technique to their ultimate destination in the calciner 185, while the separated liquids which include hydroxide are returned to the capture subsystem 180. The solids separated from the vessel output stream 152 are provided as a calcium carbonate solids stream 162, to be conveyed via one or more pipelines 172 and/or solids conveyances (e.g., bucket conveyors, screw conveyors, belt conveyors, etc.) to the calciner 185. The percent by weight of calcium carbonate solids in the calcium carbonate solids stream 162 is greater than the percent by weight of calcium carbonate solids in the vessel output stream 152. In some implementations, the percent by weight of calcium carbonate solids in the calcium carbonate solids stream 162 is greater than 50 wt %. In some implementations, the percent by weight of calcium carbonate solids in the calcium carbonate solids stream 162 is between 60 wt % and 90 wt %. In some implementations, and referring to FIG. 1, the solids-liquid separator unit 160 treats a single solids stream, for example, the vessel output stream 152. The vessel output stream 152 can contain relatively small amounts of unreacted calcium hydroxide. In some implementations, the concentration of unreacted calcium hydroxide in the vessel output stream 152 is less than 0.5 wt %. In some implementations, the concentration of unreacted calcium hydroxide in the vessel output stream 152 is less than 0.2 wt %.

[0001701 The liquid separated from the vessel output stream 152, referred to herein as fdtrate or a permeate stream 164, includes hydroxides. The piping network 170 includes one or more permeate pipelines 172F that fluidly couple the solids-liquid separator unit 160 to the gas-liquid contactor 100, 100A, 100B, 100C, 100D, such that the solids-liquid separator unit 160 can flow at least some of the permeate stream 164 to the gas-liquid contactor 100, 100A, 100B, 100C, 100D as regenerated CO2 capture solution 114 (also referred to herein as “CCh-lean” capture solution 114). The regenerated CO2 capture solution 114 can be used again to absorb CO2 from the CO2- laden air 101. In some implementations, the concentration of hydroxide [OFF] in the permeate stream 164 is between 1 M and 3 M. In some implementations, the concentration of hydroxide [0H‘] in the permeate stream 164 is approximately equal to the concentration of hydroxide [OH ] in the CO2 capture solution 114.

[0001711 The solids-liquid separator unit 160 can include, or be comprised of, any suitable componentry to achieve the functionality of solids-liquids separation ascribed to the solids-liquid separator unit 160 herein. For example, in some implementations, the solids-liquid separator unit 160 can include any of the following, in any combination: a classifier, a screen, a clarifier, a pressure filter, a vacuum filter, a filter press, a candle filter, a settling tank, a centrifuge, or a hydrocyclone. In some implementations, the solids-liquid separation process of the solids-liquid separator unit 160 can include at least one of filtration, clarification, or centrifugation.

[000172] One possible implementation of the solids-liquid separator unit 160 is now described in greater detail with reference to FIG. 1. The solids-liquid separator unit 160 includes multiple filtration units. In the implementation of FIG. 1, the solids-liquid separator unit 160 includes a first filtration unit 166A and a second filtration unit 166B. The first and second filtration units 166A, 166B are fluidly coupled in series via a retentate pipeline 172G of the piping network 170, such that the second filtration unit 166B receives the solid retentate of the first filtration unit 166A and any residual liquid which can be conveyed with the solids. The first and second filtration units 166A, 166B operate together to separate calcium carbonate solids from the liquid slurry of the vessel output stream 152, in order to produce the calcium carbonate solids stream 162 and the permeate stream 164.

[000173] The first filtration unit 166 A operates to filter the vessel output stream 152 from the last reaction vessel 150B, to produce a first retentate stream 162A and a first permeate stream 164A. The first permeate stream 164A is flowed from the first filtration unit 166A, via one or more of the permeate pipelines 172F, to form part of the permeate stream 164 flowed back to the gas-liquid contactor 100, 100A, 100B, 100C, 100D as the regenerated CO2 capture solution 114. The percent by weight of calcium carbonate solids in the first permeate stream 164A is less than the percent by weight of calcium carbonate solids in the vessel output stream 152. In some implementations, the percent by weight of calcium carbonate solids in the first permeate stream 164A is less than 0.05 wt %. In some implementations, the concentration of hydroxide [OFF] in the first permeate stream 164A is between 1.5 M and 3.5 M. The first retentate stream 162A is flowed from the first filtration unit 166A, via the retentate pipeline 172G, to the second filtration unit 166B. The percent by weight of calcium carbonate solids in the first retentate stream 162A is greater than the percent by weight of calcium carbonate solids in the vessel output stream 152. In some implementations, the percent by weight of calcium carbonate solids in the first retentate stream 162A is greater than 20 wt %. In some implementations, the percent by weight of calcium carbonate solids in the first retentate stream 162A is between 30 wt % and 60 wt %. The concentration of hydroxide [OH ] in the first retentate stream 162A is less than the concentration of hydroxide [OH’] in the vessel output stream 152. In some implementations, the concentration of hydroxide [OH’] in the first retentate stream 162A is between 1.4 M and 3.4 M. The first filtration unit 166A can include any componentry or have any configuration to achieve the functionality ascribed to the first filtration unit 166A herein. For example, and referring to FIG. 1, the first filtration unit 166A is a pressurized filtration unit and can include filtration equipment such as pressurized tubular filters or pressurized disc filters. In some implementations, the first filtration unit 166A is a candle filter having at least one filter sock.

[000174] Referring to FIG. 1, the second filtration unit 166B operates to filter the first retentate stream 162A from the first filtration unit 166 A, to produce the calcium carbonate solids stream 162 as a second retentate stream, and to produce a second permeate stream 164B. The second permeate stream 164B is flowed from the second filtration unit 166B, via one or more of the permeate pipelines 172F, to form, with the first permeate stream 164 A, the permeate stream 164 flowed back to the gas-liquid contactor 100, 100A, 100B, 100C, 100D as the regenerated CO2 capture solution 114. The percent by weight of calcium carbonate solids in the second permeate stream 164B is less than the percent by weight of calcium carbonate solids in the first retentate stream 162A. In some implementations, the percent by weight of calcium carbonate solids in the second permeate stream 164B is less than 0.05 wt %. The calcium carbonate solids stream 162 is flowed from the second filtration unit 166B, via a solids pipeline 172H of the piping network 170 and/or solids conveyances (e.g., bucket conveyors, belt conveyors, screw conveyors, etc.), to downstream components of the regeneration subsystem 190 as described in greater detail below. The percent by weight of calcium carbonate solids in the calcium carbonate solids stream 162 is greater than the percent by weight of calcium carbonate solids in the first retentate stream 162A. The amount of hydroxide [OH’] in the calcium carbonate solids stream 162 is less than the amount of hydroxide [OH’] in the first retentate stream 162A In some implementations, the calcium carbonate solids stream 162 is a predominantly solids stream, and hydroxide (OH’) has a concentration of 1-3 wt %. The second filtration unit 166B can include any componentry or have any configuration to achieve the functionality ascribed to the second filtration unit 166B herein. For example, and referring to FIG. 1, the second filtration unit 166B is a rotary drum filter, such as a vacuum drum filter. The first and second filtration units 166 A, 166B can be any type of solids- liquid separator, include any componentry and/or have any configuration to achieve the functionality ascribed to them herein, and are not limited to the configurations suggested by their symbols in FIG. 1.

[000175] Filtration in the first and second filtration units 166A, 166B can be facilitated using wash water. The size, morphology, and/or physical properties of the calcium carbonate solids allow for them to be separated from the vessel output stream 152 by being washed with water, for example clean water, to remove a majority of any residual hydroxide solution on the surface of the calcium carbonate solids. Some or all of the solution removed by, and mixed with, the wash water can be recycled back to the gas-liquid contactor 100, 100A, 100B, 100C, 100D as part of the permeate stream 164, removed from the DAC system 10 altogether, or delivered to the slaker 140 as water input as it can have carbonate content. The separated calcium carbonate solids are sent as the calcium carbonate solids stream 162 to other units, including the calciner 185, which is designed to generate the CO? gas stream forming part of the CO? product stream 116, and calcium oxide which can be reused in the slaker 140.

[000176] The use of wash water can take different configurations. For example, and referring to FIG. 1, the regeneration subsystem 190 includes a wash water system 168 for distributing a heated wash water stream 168A to the first and second filtration units 166A, 166B. The wash water system 168 can include various componentry to achieve this function. For example, and referring to FIG. 1, the wash water system 168 includes a wash water tank 168B fluidly coupled to the first filtration unit 166A via the retentate pipeline 172G to receive the first retentate stream 162A from the first filtration unit 166A. Some of the heated wash water stream 168A is added to the wash water tank 168B with the first retentate stream 162A, so as to wash the calcium carbonate solids and dilute the first retentate stream 162A to form a heated and diluted first retentate stream 162AD. The diluted first retentate stream 162AD is flowed as a warm slurry, via the retentate pipeline 172G, to the second filtration unit 166B. The percent by weight of calcium carbonate solids in the diluted first retentate stream 162AD is less than the percent by weight of calcium carbonate solids in the first retentate stream 162A, due to the addition of wash water to dilute the first retentate stream 162A. The concentration of hydroxide [OH’] in the diluted first retentate stream 162AD is less than the concentration of hydroxide [OH’] in the first retentate stream 162A. [000177] The second filtration unit 166B receives the diluted first retentate stream 162AD. In some implementations, and referring to FIG. 1, the wash water system 168 includes one or more wash nozzles 168C fluidly coupled to, or part of, the second filtration unit 166B. Some of the heated wash water stream 168 A is distributed by the wash nozzles 168C to further wash the calcium carbonate solids of the diluted first retentate stream 162AD. In implementations where the second filtration unit 166B is a vacuum drum filter, the second filtration unit 166B dewaters the washed calcium carbonate solids, thereby separating the diluted first retentate stream 162AD into a heated second permeate stream 164B and the calcium carbonate solids stream 162. The percent by weight of calcium carbonate solids in the calcium carbonate solids stream 162 is greater than the percent by weight of calcium carbonate solids in the diluted first retentate stream 162AD, due to the removal of water from the diluted first retentate stream 162A. The concentration of hydroxide [OH‘] in the calcium carbonate solids stream 162 is less than the concentration of hydroxide [OH’] in the diluted first retentate stream 162AD. The use of the heated wash water stream 168A can allow for lowering the viscosity of solutions from which solids are being separated and can allow for better flow through the filter cake of the first and second filtration units 166A, 166B. In some implementations, the concentration of hydroxide [OH’] in the second permeate stream 164B is between 0.5 M and 1.2 M.

[000178] The thermal energy for the heated wash water stream 168 A of the wash water system 168 can be derived from any suitable source including, but not limited to, a dedicated liquid heating unit, thermal energy transferred from other heat sources in the DAC system 10, and a combination of the preceding. In some implementations, the temperature of the heated wash water stream 168A is greater than 50°C. In some implementations, the temperature of the heated wash water stream 168 A is between 80°C and 95°C. The wash water tank 168B is shown in FIG. 1 as being separate from, and downstream of, the first filtration unit 166A. In other implementations, the wash water tank 168B and the first filtration unit 166A are integral with each other. In light of the present disclosure, the wash water system 168 can be used to add heated water to facilitate washing and liquid-solid separation in the regeneration subsystem 190, and can be mixed, sprayed, rinsed, flushed, and/or a combination of the preceding, with the slurry streams. In an alternate implementation, the wash water system 168 provides a colder or ambient wash water stream 168 A to the first and second filtration units 166A, 166B. Tn an alternate implementation, the first filtration unit 166A includes one or more wash nozzles instead of, or in addition to, the wash water tank 168B.

[000179] In an alternate implementation, the solids-liquid separator unit 160 has a single filtration unit. An example implementation where the solids-liquid separator unit 160 has a single filtration unit can occur when the CO2 capture solution 114 of the capture subsystem 180 has a relatively high ionic strength, for example, greater than 2 M KOH and greater than 1.0 M K2CO3. In such an implementation, causticization reaction in the causticization train can result in a vessel output stream 152 with a relatively high concentration of solids (e.g., between 5 wt % and 10 wt %). The single filtration unit of the solids-liquid separator unit 160 in such an implementation can be sufficient to increase the concentration of solids to suitable levels for downstream purposes. In an alternate implementation, the solids-liquid separator unit 160 has more than two filtration units. [000180] Referring to FIG. 1, in implementations where the wash water system 168 adds heated water to the first and second permeate streams 164A,164B, at least some of the thermal energy of the heated permeate stream 164 can be recovered therefrom. This heat recovery allows for efficiencies in the DAC system 10 and can contribute to lowering the carbon intensity of the processes performed, and products generated, by the DAC system 10. The heating unit 130 of FIG. 1 includes a heat exchanger 130A which transfers heat from the heated permeate stream 164 to the CCh-laden capture solution 111. In some implementations, the heated permeate stream 164 has a temperature between 80°C and 95°C. The heat exchanger 130A can be considered a “crossflow” heat exchanger 130A. The heat transfer in the heat exchanger 130A generates the heated carbonate-rich solution 117, and a resulting cooled permeate stream 164C. The cooled permeate stream 164C is flowed, via the contactor return pipeline 172B, to the gas-liquid contactor 100, 100A, 100B, 100C, 100D as regenerated CO2 capture solution 114. If desired, for example to provide additional buffering or storage capacity in the DAC system 10, the cooled permeate stream 164C can be flowed to a lean capture solution storage tank 119, fluidly coupled to both the gasliquid contactor 100, 100A, 100B, 100C, 100D and to the heat exchanger 130A, where the cooled permeate stream 164C is stored (at least temporarily) before being flowed to the top basin(s) 104 of the gas-liquid contactor 100, 100A, 100B, 100C, 100D as regenerated CO2 capture solution 114. In such implementations, the regenerated CO2 capture solution 114 flows indirectly to the gasliquid contactor 100, 100A, 100B, 100C, 100D. If desired, for example to provide additional buffering or storage capacity in the DAC system 10, the heated permeate stream 164 can be flowed to a warm regenerated capture solution storage tank 119B, fluidly coupled to the heat exchanger 130A, where the heated permeate stream 164 is stored (at least temporarily) before being flowed to the heat exchanger 130A. The storage tank 119B can have appropriate insulation and/or heating to maintain process temperatures. In addition to, or separate from, recovering heat from the heated permeate stream 164, the heat exchanger 130A can recover waste heat from any other unit in the DAC system 10, such as one or more of the calciner 185, the dryer 183, and the slaker 140.

[000181] The calcium carbonate solids stream 162 is conveyed, via the solids pipeline 172H, one or more calcination pipelines 1721 and/or solids conveyances (e.g., bucket conveyors, belt conveyors, screw conveyors, etc.), to ultimately reach the calciner 185. In some implementations, and referring to FIG. 1, the calcium carbonate solids stream 162 is conveyed indirectly to the calciner 185, such that the calcium carbonate solids stream 162 are dried in a dryer 183 before being conveyed to the calciner 185. The dryer 183 heats the calcium carbonate solids at a temperature beneath the calcination temperature but sufficiently high to vaporize residual moisture from the calcium carbonate solids, and discharge steam. The dryer 183 produces a drier calcium carbonate solids stream 162E which has a lower moisture content than the calcium carbonate solids stream 162, and consequently the percent by weight of calcium carbonate solids in the drier calcium carbonate solids stream 162E is greater than the percent by weight of calcium carbonate solids in the calcium carbonate solids stream 162. In some implementations, the percent by weight of calcium carbonate solids in the drier calcium carbonate solids stream 162E is at least 90 wt %.

[000182] The dryer 183 can be of any type, have any suitable componentry, and/or have any suitable configuration, to achieve the functionality ascribed to the dryer 183 herein. For example, the dryer 183 can include fluidized bed dryers to make use of heat supplied using advanced drying processes like super-heated steam dryers, vapour recompression dryers, and in bed heat exchange tubes. Specifically, fluidized bed dryers can operate on low grade heat which could be below or only slightly above 100° C, hot gases from other points in the DAC system 10, or in the case of vapour recompression systems, electrical energy drives a heat pump which could deliver up to 60 kJ of heat by consuming 1 kJ of electricity. Alternatively, the dryer 183 can be a contact dryer such as, for example, vacuum tray, vertical agitated, double cone, horizontal pan, plate, vacuum band, horizontal, paddle or indirect rotary dryers. The dryer 183 can also be a dispersion convective dryer other than a fluidized bed dryer, such as spouted bed, direct rotary and pneumatic conveying dryers, or layer convective dryers such as convective tray, through-circulation, turbotray, tunnel, moving bed, paddle, or a rotary -louver dryer. The dryer 183 can be a heat exchanger transferring thermal energy from the exhaust gases of the calciner 185 to the calcium carbonate solids stream 162, and thus function as a pre-heater. The dryer 183 can include, or operate in conjunction with, other solids handling componentry like silos, conveyors, etc. In an alternate implementation, the regeneration subsystem 190 functions without a dryer 183, such that the calcium carbonate solids stream 162 is conveyed directly to the calciner 185.

[000183] Referring to FIG. 1, the drier content calcium carbonate solids stream 162E is conveyed, via the calcination pipelines 1721, to the calciner 185. In some embodiments, the necessary heat for calcining the calcium carbonate solids is supplied when fuel is combusted with the oxygen, such as from air or oxygen from an air separation unit (ASU). The products from combustion of fuel and the CO2 mix together and are discharged from the calciner 185 as offgases. The calcium oxide solids produced from calcining the calcium carbonate solids are conveyed, via a calciner output pipeline 172J, to the slaker 140 to be slaked with the heated carbonate-rich solution 117. The calciner 185 of FIG. 1 thus forms a closed calcium loop with the slaker 140. In some implementations, some or all of the calcium oxide solids from the calciner 185 are disposed of. In some implementations, some or all of the calcium oxide solids from the calciner 185 are provided as a product for other purposes. The off-gases from the calciner 185 can be treated (e.g., one or more of filtering, scrubbing, cooling, condensing, and compressing) to generate the CO2 product stream 116. The calciner 185 can include, or operate in conjunction with, other solids handling componentry like silos, conveyors, screw feeders, gas-solid filters, grinders, sieves, compressors, etc. to reduce the size of calcium oxide particles sent to the slaker 140. In some implementations, some of the drier calcium carbonate solids stream 162E are diverted from the calciner 185 and disposed of, or provided as, a product for other purposes. The calciner 185 of FIG. 1 is a rotary kiln or rotary calciner 185. The rotary kiln calciner 185 rotates about an axis closer to the horizontal. The rotary kiln calciner 185 can have a fuel inlet allowing a hydrocarbon fuel to enter the interior of the rotary kiln calciner 185. A solids feed chute conveys the drier calcium carbonate solids stream 162E into the interior, and a solids outlet allows the solid oxide material to exit the interior. An exhaust gas outlet allows the exhaust gas stream (including the CO2 product stream 116) to flow from the interior. In some implementations, the calciner 185 is an electrically-powered rotary kiln. Such an electric calciner can have a lower carbon intensity, or be an improvement from, a Life-Cycle Analysis (LCA) perspective, compared to a calciner which generates thermal energy by combusting fossil fuels.

[0001841 Iⁿ other possible implementations of the calciner 185, such as a gravity-type calciners 185, the solid oxide material is discharged from the interior using different techniques. For example, and referring to FIG. 11 A, the calciner 385 is a circulating fluidized bed (CFB) calciner 385. In another possible implementation of the calciner 485 and referring to FIG. 1 IB, the calciner 485 is a gravity -fed calciner 485. The drier calcium carbonate solids stream 162E falls due to gravity from a solids inlet near the top of the gravity-fed calciner 485 through an inner calciner chamber 312B. A hydrocarbon is combusted within the inner calciner chamber 312B to generate hot gases flowing in an upward direction within the inner calciner chamber 312B. The falling carbonate material 301 flows counter current to the hot gases and is calcined to generate the solid oxide material 303. The exhaust gas stream 308 (including the CO2 product stream 116) exits the inner calciner chamber 312B via an exhaust gas outlet 316EB, and the solid oxide material 303 exits via a solids outlet 316SB. In another possible implementation, the calciner 185 is a flash calciner, or a shaft kiln. The description, features, reference numbers and advantages of the calciner 185 provided in relation to FIG. 1 apply mutatis mutandis to the CFB calciner 385 of FIG. 11 A and to the gravity-fed calciner 485 of FIG. 1 IB.

[000185] A control system (e.g., the control system 999 shown in FIG. 1) can be used to control one or more components of the capture subsystem 180 and/or of the regeneration subsystem 190. For example, the control system 999 can be used to control the conveyance of solids or the flow of slurries to and between components of the regeneration subsystem 190. The control system 999 can also be used to one or more of the pump(s) 122) to flow streams to and between the units of the causticization train, and/or to and between the solids-liquid separator unit 160. The control system 999 can be used to control temperatures in one or more units of the causticization train. The control system 999 can be used to control liquid levels of the causticization train.

[000186] FIG. 2 shows another implementation of the DAC system 210. The description, units, componentry, features, reference numbers and advantages of the DAC system 10 provided in relation to FIG. 1 apply mutatis mutandis to the DAC system 210 of FIG. 2. The DAC system 210 includes a nanofdtration (NF) unit 235. The NF unit 235 is positioned between the gas-liquid contactor 100, 100A, 100B, 100C, 100D and the heating unit 130. In the DAC system 210 of FIG. 2, the NF unit 235 is fluidly coupled to both the gas-liquid contactor 100, 100 A, 100B, 100C, 100D and the heating unit 130 by the contactor outlet pipeline 172A. The NF unit 235 is upstream of the slaker 140, where “upstream” is defined here relative to the flow of the CCh-laden capture solution 111 from the gas-liquid contactor 100, 100A, 100B, 100C, 100D to the slaker 140. The NF unit 235 can thus be employed downstream of the gas-liquid contactor 100, 100 A, 100B, 100C, 100D (either as part of, or separate from, the capture subsystem 180) to produce a carbonate-rich mixture that is fed to the regeneration subsystem 190.

[000187] The NF unit 235 functions to increase the concentration of carbonate [CO.i^2-] in the CCh-laden capture solution 111 provided to the slaker 140. The NF unit 235 can selectively produce a particular concentration of carbonate without requiring water removal. The higher- concentration carbonate flow to the slaker 140 increases the quantity of carbonate provided to the slaker 140 per unit volume of solution, which can allow for correspondingly increased loading of calcium oxide solids provided to the slaker 140. This can result in greater production of calcium carbonate solids in the causticization train, such that the slurry of the vessel output stream 152 has a higher solids concentration (e.g., higher percent by weight of calcium carbonate solids) which might facilitate solids separation in the solids-liquid separator unit 160, and/or reduce the number of solids-liquid separator units 160. For a given slaker liming ratio, the higher-concentration carbonate flow to the slaker 140 can also allow for reducing the volume of the slaker output stream 142 flowed to the reaction vessels 150. The reduced-volume slaker output stream 142 can also enable smaller pipelines and lower pumping requirements due to lower volumetric flow rates.

[000188] Referring to FIG. 2, the CCh-laden capture solution 111 is flowed by the pump(s) 122 to enter the NF unit 235 under pressure. The NF unit 235 fdters the CCh-laden capture solution 111 to form an NF retentate stream 235 A and an NF permeate stream 235B. The NF retentate stream 235A is the higher-concentration carbonate stream flowed to the slaker 140 as described above. The concentration of carbonate [CCh²‘] in the NF retentate stream 235A is greater than the concentration of carbonate [CCh^2-] in the CCh-laden capture solution 111. In implementations where a potassium hydroxide (KOH) solution is used as the CO2 capture solution 114, the NF retentate stream 235A can include between 0.5 M to 6 M of K2CO3. The NF retentate stream 235A is heated in the heating unit 130 to form the heated carbonate-rich solution 117 provided to the slaker 140. [000189] In some implementations, the NF unit 235 also functions to provide the NF permeate stream 235B with a higher concentration of hydroxide [OFT] than the concentration of hydroxide [OH’] in the CO2-laden capture solution 111. In some implementations, the concentration of hydroxide [OH’] in the NF permeate stream 235B is greater than 1.5 M. In some implementations, the concentration of hydroxide [OH’] in the NF permeate stream 235B is between 1.5 M and 2.5 M. Such a hydroxide-rich NF permeate stream 235B can flowed, via an NF permeate pipeline 172K of the piping network 170, to the gas-liquid contactor 100, 100A,

IOOB, 100C, 100D to be used as CO2 capture solution 114. The NF permeate stream 235B can be flowed directly to the gas-liquid contactor 100, 100A, 100B, 100C, 100D, or indirectly via the lean capture solution storage tank 119 if buffering or storage is desired. Thus, the position of the NF unit 235 upstream of the slaker 140 allows for sending a high-concentration hydroxide solution to the gas-liquid contactor 100, 100A, 100B, 100C, 100D. The DAC system 210 thus allows for sending a high-concentration hydroxide solution to the gas-liquid contactor 100, 100A, 100B,

IOOC, 100D, such that the CO2 capture solution 114 can be selected and biased in favour of CO2 capture, in contrast to a capture solution that must also have properties making it suitable for the regeneration subsystem 190. Sending a high-concentration hydroxide solution to the gas-liquid contactor 100, 100A, 100B, 100C, 100D can also allow for reducing the number and/or size of gas-liquid contactors 100, 100A, 100B, 100C, 100D which are part of the DAC system 210. In alternate implementations, the concentration of hydroxide [OH’] in NF permeate stream 235B is approximately equal to the concentration of hydroxide [OH’] in the CO2-laden capture solution 111.

[000190] Different implementations of the NF unit 235 are possible to achieve the functionality ascribed to it herein. The NF unit 235 can include one or more fdtration membranes that are impermeable to or select for large divalent ions such as carbonate ions. The NF membranes can have an inherent surface charge, making them particularly suitable for separating ion mixtures. Rejection of species can depend on size, ionic charge, and membrane dielectric constant. The NF unit 235 can include membranes that have a wide pH tolerance and are durable enough to operate at a pH ranging from 0 to 14. In some implementations, the NF unit 235 can include membranes that are operable with hydroxide concentration of up to 10 M. In some implementations, the NF unit 235 can reject 85% to 100% of divalent ions (e.g., carbonate ions) to yield the NF retentate stream 235 A that is carbonate-rich, and the NF permeate stream 2 5B that is hydroxide rich or carbonate-lean. In some cases, the NF unit 235 can reject between 50% to 100% of divalent ions. In some cases, the NF unit 235 can include a forward osmosis-style fdtration unit that employs a high ionic strength draw solution and a pressure gradient to yield the carbonate-rich NF retentate stream 235 A. A high ionic strength draw solution is an electrolyte solution that can lower the osmotic pressure difference across the membrane and can allow water to flow more easily from the feed solution to the draw solution. The NF unit 235 can include a plate and frame module that holds a number of nanofiltration membranes (e.g., flat membrane sheets) clamped together with spacers and supports. The NF unit 235 can include poly ethersulfone as a membrane material and can have a molecular cut-off of 100-1000 daltons.

[000191] The NF unit 235 can receive K2CO3-rich solution as a feed from the gas-liquid contactor 100, 100A, 100B, 100C, 100D. The NF unit 235 can then produce concentrated K2CO3- rich solution as the NF retentate stream 235 A, and a KOH-rich solution as the NF permeate stream 235B. In some implementations, the NF unit 235 can receive a Na2CO3-rich capture solution as feed and produce concentrated Na2CO3-rich solution as the NF retentate stream 235 A and NaOH-rich solution as the NF permeate 235B. In some implementations, the NF unit 235 can receive a mixed K2CO3/ Na2CO3-rich capture solution as feed and produce concentrated mixed K2CO3/Na2CO3-rich solution as the NF retentate stream 235 A and mixed KOH/NaOH-rich solution as the NF permeate 235B. In some implementations, the NF unit 235 can include, or be fluidly coupled to, a feed tank configured to receive the CCh-laden capture solution 111 and a collection tank configured to receive the NF retentate stream 235 A. The NF unit 235 can be preceded by a primary filtration system (e.g., ultrafiltration system) configured to remove solids such as silicates, water hardness, surfactant additives, or salts that cause salinity concerns. This configuration can protect the NF unit 235 from potentially harmful contaminants and can prevent carry-over of species to downstream processes and units. In some cases, the NF retentate 235 A, including concentrated carbonate solution, can be polished in an ion exchange system to remove at least a portion of undesired ion species (including but not limited to Ca⁺², Mg⁺², Ba⁺², Sr⁺², silicates, borates) and then flow to the slaker 140.

[000192] By aggressively concentrating carbonate in the NF retentate stream 235A in some implementations (e.g., by 5-20 times), the NF unit 235 helps to further intensify the regeneration process of the regeneration subsystem 190, which can allow for less NF retentate stream 235 A being needed to be sent to the regeneration subsystem 190 for a given amount of calcium carbonate solids produced. In implementations where the carbonate concentration in the CCh-laden capture solution 111 is increased by the NF unit 235 by an order of magnitude or more, the relative flow of the NF retentate stream 235 A can be decreased proportionally, allowing for a reduction in the amount of solution that needs to be transported (and pumped) through the regeneration subsystem 190 and/or in the size/number/capacity of solids-liquid separator units 160.

[000193] FIG. 3 shows another implementation of the DAC system 310. The description, units, componentry, features, reference numbers and advantages of the DAC system 10 provided in relation to FIG. 1 apply mutatis mutandis to the DAC system 310 of FIG. 3. The DAC system 310 includes a NF unit 335. The description, units, componentry, features, reference numbers and advantages of the NF unit 235 provided in relation to FIG. 2 apply mutatis mutandis to the NF unit 335 of FIG. 3. In the DAC system 310 of FIG. 3, the NF retentate stream 335A flows directly to the slaker 140. The NF retentate stream 335A is not heated before being flowed to the slaker 140. Depending on ambient conditions, the capacity of the slaker 140, and flow rates to the slaker 140, it may not be necessary to heat the NF retentate stream 335A before reacting its contents in the slaker 140, particularly where the NF unit 335 functions to significantly increase the concentration of carbonate [CCh²'] in the CCh-laden capture solution 111 provided to the slaker 140.

[000194] FIG. 4 shows another implementation of a DAC system 410. The description, units, componentry, features, reference numbers and advantages of the DAC system 10 provided in relation to FIG. 1 apply mutatis mutandis to the DAC system 410 of FIG. 4. The DAC system 410 of FIG. 4 allows for dividing the CCh-laden capture solution 111 upstream of the regeneration subsystem 490, where some of the CCh-laden capture solution 111 can be sent to the slaker 140 and a remainder can be sent to the reaction vessels 150. As explained in greater detail below, splitting the flow of the CCh-laden capture solution 111 to send different volumes to different components of the regeneration subsystem 490 can allow for better controlling or determining properties of the calcium carbonate solids in the calcium carbonate solids stream 162, these properties including, but not limited to, their size, shape, and distribution. This can allow for optimising the production of calcium carbonate solids to better align with the operating and performance parameters of one or more units such as the slaker 140, the solids-liquid separator unit 160, and the calciner 185. Splitting the flow of the CCh-laden capture solution 111 to send different volumes to different components of the regeneration subsystem 490 can allow for minimizing the volume of CCh-laden capture solution 111 that needs to be heated in the slaker 140 to achieve the slaker reaction temperature at steady-state operation, thereby helping to reduce the duty on any heating units 130 used to warm the CCh-laden capture solution 111. For example, where the temperature of the CCh-laden capture solution I ll is relatively low due to lower ambient temperatures in which the gas-liquid contactor 100, 100A, 100B, 100C, 100D operates, splitting the flow of the CCh-laden capture solution 111 to send a smaller volume to the slaker 140 can help to minimize the possibility that the CCh-laden capture solution 111 might lower the slaker reaction temperature, and allows for the exothermic slaker reaction to warm the lower-volume flow of CO2- laden capture solution 111. In contrast, without splitting the flow of the CCh-laden capture solution 111, all of the relatively cool CCh-laden capture solution 111 would need to be heated before slaking.

[000195] Referring to FIG. 4, the pipelines 172 of the piping network 170 include a first contactor outlet pipeline 172AB and a second contactor outlet pipeline 173 that are fluidly coupled to the gas-liquid contactor 100, 100A, 100B, 100C, 100D. In the implementation of FIG. 4, the first and second contactor outlet pipelines 172AB, 173 branch out from the contactor outlet pipeline 172A. The first contactor outlet pipeline 172AB fluidly couples the gas-liquid contactor 100, 100A, 100B, 100C, 100D and the slaker 140, and allows for flowing a first stream of the carbonate-rich capture solution 111 A to the slaker 140. The second contactor outlet pipeline 173 fluidly couples the gas-liquid contactor 100, 100A, 100B, 100C, 100D and the first reaction vessel 150A and allows a second stream of the carbonate-rich capture solution 11 IB to flow to the first reaction vessel 150A. The piping junction 172L between the contactor outlet pipeline 172A, the first contactor outlet pipeline 172AB, and the second contactor outlet pipeline 173 can have any suitable liquid flow-control devices such as valves, flaps, flanges, flow meters, conduits, etc. to divide the CCh-laden capture solution 111 to flow into one or both of the first and second contactor outlet pipelines 172AB,173.

[000196] Different implementations are possible for flowing less than 100% of the CCh-laden capture solution 111 to the slaker 140. In one possible implementation, the first and second streams of the carbonate-rich capture solution 111A,111B have approximately equal volumes, and thus each represents approximately 50% of the CCh-laden capture solution 111. In one possible implementation, the first stream of the carbonate-rich capture solution 111A is less than 40% of the flow of the CCh-laden capture solution 111, and the second stream of the carbonate-rich capture solution 11 IB is greater than 60% of the flow of the CCh-laden capture solution 111. In one possible implementation, between 8%-l 00% of the CCh-laden capture solution I l l is sent to the slaker 140 as the first stream of the carbonate-rich capture solution 111 A.

[0001971 In some implementations, and referring to FIG. 4, one or both of the first and second streams of the carbonate-rich capture solution 111A,11 IB are heated before being flowed to their respective components of the regeneration subsystem 490. In such implementations, the heating unit 430 of FIG. 4 includes multiple heating units. Referring to FIG. 4, the heating unit 430 includes a first heating unit 432A and a second heating unit 432B. The first heating unit 432A is fluidly coupled to the first contactor outlet pipeline 172AB and configured to heat the first stream of the carbonate-rich capture solution 111 A to form a heated first stream of the carbonate-rich capture solution 417A flowed to the slaker 140 via the slaker input pipeline 172C. The second heating unit 432B is fluidly coupled to the second contactor outlet pipeline 173 and configured to heat the second stream of the carbonate-rich capture solution 11 IB to produce a heated second stream of the carbonate-rich capture solution 417B flowed to the first reaction vessel 150A via a first reaction vessel input pipeline 172M. The heated second stream of the carbonate-rich capture solution 417B is reacted with the slaker output stream 142 in the reaction vessels 150 to form the vessel output stream 152. In some implementations, the slaker output stream 142 has a temperature that is greater than the temperature of the heated second stream of the carbonate-rich capture solution 417B. In some implementations, the temperature of the slaker output stream 142 is between 80°C-95°C, and the temperature of the heated second stream of the carbonate-rich capture solution 417B can be between 10°C (in implementations where the second heating unit 432B is not heating the second stream of the carbonate-rich capture solution 417B, as described below) and 80°C (in implementations where the second heating unit 432B is fully heating the second stream of the carbonate-rich capture solution 417B).

[000198] The first and second heating units 432 A, 432B of FIG. 4 are heat exchangers operable to recover heat from the heated wash water stream 168A. The heated permeate stream 164 returned from the solids-liquid separator unit 160 is split into a heated first permeate stream 464 A and a heated second permeate stream 464B. The first heating unit 432A is operable to transfer heat from the heated first permeate stream 464A to the first stream of the carbonate-rich capture solution 111A to form the heated first stream of the carbonate-rich capture solution 417A flowed to the slaker 140 to slake with the calcium oxide. The second heating unit 432B is operable to transfer heat from the heated second permeate stream 464B to the second stream of the carbonate-rich capture solution 11 IB to form the heated second stream of the carbonate-rich capture solution 417B. The pipelines 172 include heat exchanger return pipelines 172N which fluidly couple both the first and second heating units 432A, 432B to the gas-liquid contactor 100, 100A, 100B, 100C, 100D. Each of the first and second heating units 432A, 432B are configured to flow their respective first and second cooled permeate streams 464C, 464D to the gas-liquid contactor 100, 100A, 100B, 100C, 100D via the heat exchanger return pipelines 172N, to be used as part of the CO2 capture solution 114. The first and second cooled permeate streams 464C, 464D can form a combined cool permeate stream that can be flowed directly to the gas-liquid contactor 100, 100A, 100B, 100C, 100D (such as to a top liquid distributor or to one or more basin(s)), or indirectly via storage in the lean capture solution storage tank 119 or a recirculation line of the gas-liquid contactor 100, 100A, 100B, 100C, 100D.

[000199] Configurations other than those provided above are possible for generating the heated first and second streams of the carbonate-rich capture solution 417A, 417B. In an alternate implementation, the heating unit 430 is positioned upstream of the piping junction 172L, and functions to heat all of the CCh-laden capture solution 111 before it is split into two streams. In such an implementation, the heating unit 430 can be a single heat exchanger transferring heat from all of the heated permeate stream 164 to the CCh-laden capture solution 111. In an alternate implementation, both the first and second streams of the carbonate-rich capture solution 111A,111B are heated in a single heating unit 430, before being flowed as separate heated first and second streams of the carbonate-rich capture solution 417A, 417B to their respective reactors. In some implementations, the first and second heating units 432A, 432B are operating at the same time to heat their respective streams. In some implementations, only one of the first and second heating units 432A, 432B are operating to heat their respective streams. In an example of such implementations, the ambient temperature can be relatively high and the volume of the first stream of the carbonate-rich capture solution 111 A can be relatively low such that there may be no need, or less need, to heat the first stream of the carbonate-rich capture solution 111A to raise its temperature closer to the slaker reaction temperature, because the exothermic slaking reaction can provide sufficient heating. In some implementations, neither one of the first and second heating units 432A, 432B are operating to heat their respective streams, such that the first and second streams of the carbonate-rich capture solution 417A, 417B are flowed unheated to their respective reactors. In an example of such implementations, this can occur if heating is not required due to seasonal temperatures, and/or the ability of the downstream slaker 140 and/or reaction vessels 150 to provide the necessary heat. In an example of such implementations, the temperature of the slaker output stream 142 is between 80°C-95°C, and the temperature of the second stream of the carbonate-rich capture solution 417B is less than 30°C. In some implementations, one or both of the first and second heating units 432A, 432B generate thermal energy using a dedicated energy source, in addition to or in lieu of exchanging heat between process streams, and transfer the thermal energy to their respective cold streams to increase their temperature.

[000200] In some implementations, the DAC system 410 has no heating unit 430, such that neither of the first and second streams of the carbonate-rich capture solution 111 A, 11 IB are heated before being flowed to their respective components of the regeneration subsystem 490. In such implementations, a relatively small amount of the CCh-laden capture solution 111 can be flowed to the slaker 140, while the remainder is flowed to the first reaction vessel 150A. For example, in such an implementation, the first stream of the carbonate-rich capture solution 111 A flowed to the slaker 140 can represent between 5-10% of the flow of the CCh-laden capture solution 111, while a remainder (approximately 90-95%) of the flow of the CCh-laden capture solution 111 is flowed to the first reaction vessel 150A as the second stream of the carbonate-rich capture solution 11 IB. In such an implementation, the exothermic slaking reaction can provide sufficient thermal energy to operate the slaker 140 and the reaction vessels 150 at the desired reaction temperatures.

[000201] In implementations where it is possible to flow less than 100% of the CCh-laden capture solution 111 to the slaker 140, such as in FIG. 4, the slaker liming ratio can be different from an overall liming ratio of the DAC system 410. As described above, in the implementation of FIG. 4, the slaker liming ratio is defined as the moles of CaO provided to the slaker 140 (such as from the calciner 185) over the moles of the carbonate compound (e.g., K2CO3) provided to the slaker 140 via the first stream of the carbonate-rich capture solution 111A (or the heated first stream of the carbonate-rich capture solution 417A). It is possible to decrease the slaker liming ratio by decreasing the amount of CaO added to the slaker 140, or by increasing the volume of the first stream of the carbonate-rich capture solution 111 A flowed to the slaker 140, which also entails decreasing the volume of the second stream of the carbonate-rich capture solution 11 IB flowed to the first reaction vessel 150A. Similarly, it is possible to increase the slaker liming ratio by increasing the amount of CaO added to the slaker 140, or by decreasing the volume of the first stream of the carbonate-rich capture solution 111 A flowed to the slaker 140, which also entails increasing the volume of the second stream of the carbonate-rich capture solution 11 IB flowed to the first reaction vessel 150A. In the implementation of FIG. 4, the overall liming ratio of the DAC system 410 is defined as the moles of CaO provided to the slaker 140 (such as from the calciner 185) over the moles of the carbonate compound (e.g., K2CO3) provided to the regeneration subsystem 490 as a whole via the CCh-laden capture solution 111. It is possible to decrease the overall liming ratio by decreasing the amount of CaO added to the slaker 140, or by increasing the amount of carbonate provided to the regeneration subsystem 490 (for example, by increasing the flow of the CO2-laden capture solution 111 sent to the regeneration subsystem 490). Similarly, it is possible to increase the overall liming ratio by increasing the amount of CaO added to the slaker 140, or by decreasing the amount of carbonate provided to the regeneration subsystem 490 (for example, by decreasing the flow of the CO2-laden capture solution 111 sent to the regeneration subsystem 490).

[000202] In implementations where the CO2-laden capture solution 111 is split into two streams, for example in FIG. 4, the slaker liming ratio can be greater than one. This can be achieved by providing more moles of CaO to the slaker 140 than the moles of K2CO3 provided to the slaker 140, by for example increasing the second stream of the carbonate-rich capture solution 417B flowed to the first reaction vessel 150A. In such implementations, the slaker liming ratio can be between 0.6 and 7.5. In such implementations, the slaker liming ratio can be between 3: 10 and 8: 1. The lower ratio values (i.e., less than 1) correspond to more of the CCh-laden capture solution 111 flowing to the slaker 140, and the higher ratio values (e.g., greater than 1) correspond to less of the CCh-laden capture solution 111 flowing to the slaker 140.

[000203] Adjusting one or both of the slaker and overall liming ratios can impact the slaking reaction, the causticization reaction, the size of calcium carbonate solids, and/or the distribution of calcium carbonate solids, as described in more detail below. In configurations where the DAC system 410 is operating to flow less than 100% of the CCh-laden capture solution 111 to the slaker 140 as the first stream of the carbonate-rich capture solution 111 A, the slaker liming ratio will be different from the overall liming ratio. In configurations where the DAC system 410 is operating to flow 100% of the CCh-laden capture solution 111 to the slaker 140 as the first stream of the carbonate-rich capture solution 111A (and in the DAC system 10, 210, 310 of FIGS. 1 to 3), the slaker liming ratio will be equal to the overall liming ratio. [000204] FIG. 5 shows another implementation of the DAC system 510. The description, units, componentry, features, reference numbers and advantages of the DAC system 10,210,410 provided in relation to FIGS. 1, 2 and 4 apply mutatis mutandis to the DAC system 510 of FIG. 5. The DAC system 510 of FIG. 5 allows for dividing the CCh-laden capture solution 111 upstream of the regeneration subsystem 590, where some of the CCh-laden capture solution 111 can be sent to the slaker 140 and a remainder can be sent to the reaction vessels 150. The DAC system 510 includes an NF unit 535 positioned between the gas-liquid contactor 100, 100A, 100B, 100C, 100D and the heating unit 530. The description, units, componentry, features, streams, reference numbers and advantages of the NF unit 235, 335 provided in relation to FIGS. 2 and 3 apply mutatis mutandis to the NF unit 535 of FIG. 5. The heating unit 530 of FIG. 5 includes a first heating unit 532A to form the heated first stream of the carbonate-rich capture solution 517A flowed to the slaker 140, and a second heating unit 532B to produce the heated second stream of the carbonate-rich capture solution 517B flowed to the first reaction vessel 150A. The description, units, componentry, features, streams, reference numbers and advantages of the first and second heating units 432A, 432B provided in relation to FIG. 4 apply mutatis mutandis to the first and second heating units 532A, 532B of FIG. 5.

[000205] The NF unit 535 of FIG. 5 can operate to filter the CCh-laden capture solution 111 and produce the NF permeate stream 535B and the NF retentate stream 535 A. The carbonate-rich NF retentate stream 535A of FIG. 5 is split at the piping junction 172L and heated in the first and second heating units 532A, 532B to form the heated first and second streams of the carbonate-rich capture solution 517A,517B. In other implementations, the NF unit 535 can also be integrated into the DAC system 510 in a different functional position to generate the NF retentate stream 535A. The DAC system 510 of FIG. 5 can operate to send heated, high-concentration carbonate streams to the slaker 140 and to the first reaction vessel 150A.

[000206] FIG. 6 shows another implementation of the DAC system 610. The description, units, componentry, features, reference numbers and advantages of the DAC system 10 provided in relation to FIG. 1 apply mutatis mutandis to the DAC system 610 of FIG. 6. The regeneration subsystem 690 of the DAC system 610 uses nanofiltration and clarification to form the calcium carbonate solids stream 662 and to regenerate the CO2 capture solution 114.

[000207] Referring to FIG. 6, the CCh-laden capture solution Ill is pumped at relatively high pressure to an NF unit 635. The NF unit 635 filters the CCh-laden capture solution 111 to form the NF retentate stream 635A and the NF permeate stream 635B. The NF retentate stream 635A is a higher-concentration carbonate stream. The concentration of carbonate [CCh²’] in the NF retentate stream 635 A is greater than the concentration of carbonate [COs²’] in the CCh-laden capture solution 111. In some implementations, the NF retentate stream 635 A has a concentration of carbonate [COs²’], measured in molarity, between 5 and 20 times greater than the molarity of carbonate in the carbonate-rich capture solution 111. In implementations where a potassium hydroxide (KOH) solution is used as the CO2 capture solution 114, the NF retentate stream 635A can include between 2.0 M to 6.0 M of K2CO3. In some implementations, the NF permeate stream 635B has a higher concentration of hydroxide [OH’] than the concentration of hydroxide [OH‘] in the CO2-laden capture solution 111. In some implementations, the concentration of hydroxide [OH ] in the NF permeate stream 635B is greater than 1.5 M. In some implementations, the concentration of hydroxide [OH’] in the NF permeate stream 635B is between 1.5 M and 3.0 M. Such a hydroxide-rich NF permeate stream 635B can flowed, via the NF permeate pipeline 172K of the piping network 170, to the gas-liquid contactor 100, 100A, 100B, 100C, 100D to be used as part of the CO2 capture solution 114. The description, units, componentry, features, streams, reference numbers and advantages of the NF unit 235, 335, 535 provided in relation to FIGS. 2, 3 and 5 apply mutatis mutandis to the NF unit 635 of FIG. 6.

[000208] The carbonate-rich NF retentate stream 635 A is flowed to a reactor-clarifier 640 of the regeneration subsystem 690. The NF retentate stream 635A reacts with calcium oxide in the reactor-clarifier 640. The calcium oxide solids are conveyed to the reactor-clarifier 640 via the calciner output pipeline 172J from the calciner 185. The reactor-clarifier 640 facilitates slaking as per Reaction 1 and causticization as per Reaction 2 and serves as a reactor which receives a solid material and reacts it with a liquid solution. The reactor-clarifier 640 is sized, shaped and/or has componentry to facilitate these reactions, so as to produce a liquid clarified effluent stream 641 and an output stream 642 that includes calcium carbonate solids.

[000209] Different configurations of the reactor-clarifier 640 are possible to achieve the functionality ascribed to it herein. For example, and referring to FIG. 6, an NF retentate pipeline 672A fluidly couples the reactor-clarifier 640 to the NF unit 635. The NF retentate stream 635 A is flowed via the NF retentate pipeline 672A to a reaction well 644 of the reactor-clarifier 640, and the calcium oxide solids are also conveyed to the reaction well 644 via the calciner output pipeline 172J. The reaction well 644 is partially delimited by a conical wall separator 644A which increases in cross-sectional area in a downward direction. The conical wall separator 644A divides an interior of the reactor-clarifier 640 into the reaction well 644 and into a clarification zone 646 outside of the conical wall separator 644A. Slaking as per Reaction 1 and causticization as per Reaction 2 occur in the reaction well 644 at a relatively high temperature (e.g., between 85°C- 100°C). The reaction products (e.g., calcium carbonate solids and calcium hydroxide solids) and liquids flow downwardly through the reaction well 644. As they do so, the percent by weight of produced solids and the reaction completion rate both increases. The reaction well 644 can include devices, such as impellers or blades 644B, which rotate about a vertical axis within the reaction well 644 to improve reactivity and facilitate the downward movement of reaction products. The reaction products are conveyed through a bottom cylindrical opening in the conical wall separator 644A and begin to flow upwardly within the clarification zone 646. Produced solids, such as calcium carbonate, settle toward the bottom of the reactor-clarifier 640, while clarified effluent begins to collect in effluent launders and/or overflow weirs 648. The clarified effluent forms the clarified effluent stream 641. When the slurry reaches the bottom of the reaction well 644, a densified sludge is collected and removed from the reactor-clarifier 640. The settled solids can be swept or scraped from the bottom of the reactor-clarifier 640 by rotating scraper blades 649 and directed to a solids outlet 647 to form the output stream 642 that includes calcium carbonate solids. [000210] The DAC system 610 of FIG. 6 has an effluent pipeline 672B fluidly coupling the reactor-clarifier 640 to the gas-liquid contactor 100, 100A, 100B, 100C, 100D. The clarified effluent stream 641 can be flowed, directly or indirectly, to the gas-liquid contactor 100, 100A, 100B, 100C, 100D via the effluent pipeline 672B for use as regenerated CO2 capture solution 114, with any suitable buffering capacity and/or liquid level control. In some implementations, the clarified effluent stream 641 has a higher concentration of hydroxide [OH ] than the concentration of hydroxide [OH ] in the NF permeate stream 635B. The DAC system 610 of FIG. 6 has a solids outlet pipeline 672C fluidly coupling the solids outlet 647 of the reactor-clarifier 640 to the solids- liquid separator unit 160. The output stream 642 can be flowed via the solids outlet pipeline 672C as a slurry for further washing and separation (e.g., in the solids-liquid separator unit 160), drying (e.g., in the dryer 183), and calcining (e.g., in the calciner 185), as described above. In some implementations, the percent by weight of calcium carbonate solids in the output stream 642 is between 20 wt % and 50 wt %. In some implementations, the percent by weight of calcium carbonate solids in the output stream 642 is between 25 wt % and 40 wt %. [000211] The DAC system 610 of FIG. 6 can include different implementations of heat recovery from the reactor-clarifier 640. For example, the clarified effluent stream 641 in some implementations has a temperature between 80°C and 95°C. The thermal energy from such a heated clarified effluent stream 641 can be recovered and transferred to the NF retentate stream 635A upstream of the reactor-clarifier 640, (i.e., before the NF retentate stream 635A reacts with the calcium oxide solids.) This heat transfer can allow for pre-heating the NF retentate stream 635A being sent to the reaction well 644 in order to achieve the desired slaking/causticization temperature. This heat transfer can be achieved with a heat exchanger, such as the ones described herein. If it is not required or desired to pre-heat the NF retentate stream 635 A, heat from the hot clarified effluent stream 614 can be used for drying the calcium carbonate solids in the dryer 183. Another alternative or supplemental use for the heat from the hot clarified effluent stream 614 involves heating the wash water stream 168A used by the solids-liquid separator unit 160. Other opportunities for heat and water integration are possible in the DAC system 610, depending on the degree of carbonate concentration and therefore, how much liquid must be sent to the reaction well 644. For example, if evaporation is required to maintain the liquid balance in the DAC system 610 (e.g., due to addition of wash water and reduced evaporation in the gas-liquid contactor 100, 100A, 100B, 100C, 100D because of the solution composition change and/or seasonal/diurnal conditions), vacuum can be pulled on the hot clarified effluent stream 641, and the vapour could be condensed and used to supplement and add heat to the wash water stream 168 A. In yet another example, if heat is available from one or more of the pump(s) 122 used to feed the CCh-laden capture solution 111 to the NF unit 635, the calciner 185, or compressor(s) used to compress the CO2 product stream 116, this heat can also be used at least in part to control the liquid balance and/or add heat to other areas of the process, like solids drying in the dryer 183.

[000212] The reactor-clarifier 640 of FIG. 6 has only a single step of solids-liquid separation (i.e., dewatering), such as in the solids-liquid separator unit 160, before drying the calcium carbonate solids in the dryer 183. This can be possible due to the nanofiltration step concentrating the carbonate in solution enough that a relatively high-density slurry (i.e., high percent by weight of calcium carbonate solids in the output stream 642) can be produced directly by slaking/causticizing in the reactor-clarifier 640, which means that the reactor-clarifier 640 allows for consolidating slaking, causticization, and the initial solids-liquid separation step of FIG. 1 into a single unit operation. By aggressively concentrating carbonate in the NF retentate stream 635 A in some implementations (e.g., by 5-20 times), the NF unit 635 helps to further intensify the regeneration process of the regeneration subsystem 690, which can allow for less NF retentate stream 635 A being needed to be sent to the regeneration subsystem 690 for a given amount of calcium carbonate solids produced. In implementations where the carbonate concentration in the CCh-laden capture solution Il l is increased by the NF unit 635 by an order of magnitude or more, the relative flow of the NF retentate stream 635 A can be decreased proportionally, allowing for a reduction in the amount of solution that needs to be transported (and pumped) through the regeneration subsystem 690 and in the size of the reactor-clarifier 640. This can allow or facilitate slaking, causticizing, and thickening the calcium carbonate slurry of the output stream 642 in a single unit (e.g., the reactor-clarifier 640), using settling and clarifying as a method for solids separation, with smaller pipelines and/or lower pumping/transfer energy required.

[000213] In alternate implementations, the DAC system 610 is free of the NF unit 635, such that the CCh-laden capture solution Ill is flowed directly from the gas-liquid contactor 100, 100A, 100B, 100C, 100D to the reactor-clarifier 640. In such an implementation, the carbonate concentration of the CCh-laden capture solution 111 can be increased using different techniques upstream of the reactor-clarifier 640, in order to achieve the benefits of reacting higher carbonate concentration in the reactor-clarifier 640 that are described herein.

[000214] The NF unit 635 can include membranes that have a wide pH tolerance and are durable enough to operate at a pH ranging from 0 to 14. In some implementations, the NF unit 635 can include membranes that are operable with hydroxide concentration of up to 10 M. In some implementations, the NF unit 635 can reject 85% to 100% of divalent ions (e.g., carbonate ions) to yield the NF retentate stream 635 A that is carbonate-rich, and the NF permeate stream 635B that is hydroxide rich or carbonate-lean. By aggressively concentrating hydroxide in the NF permeate stream 635B, the NF unit 635 allows for the CO2 capture solution 114 to be selected and biased in favour of CO2 capture, in contrast to a capture solution that must also have properties making it suitable for the regeneration subsystem 690. Regenerating the C Ch-laden capture solution 111 to provide a high-concentration hydroxide solution for the gas-liquid contactor 100, 100A, 100B, 100C, 100D can also allow for reducing the number and/or size of gas-liquid contactors 100, 100A, 100B, 100C, 100D which are part of the DAC system 610, and/or reducing water loss through evaporation in the gas-liquid contactor 100, 100A, 100B, 100C, 100D. [000215] In some implementations, the reaction temperature in the reactor-clarifier 640 is determined by the carbonate concentration in the NF retentate stream 635 A (and therefore, how much liquid needs to be heated), and the liming ratio. These parameters can be adjusted to achieve reaction conditions that produce desirable characteristics for the calcium carbonate solid particles. In some implementations, the maximum allowable liquid velocity within the reaction well 644 can be a function of the following non-exhaustive list of factors: the transport velocity of the solid calcium carbonate particles that are formed as slurry, the particle size distribution, the maximum allowable total suspended solids (TSS) in the clarified effluent stream 641 returning to the gasliquid contactor 100, 100 A, 100B, 100C, 100D, and liquid viscosities. Depending on the design of the reactor-clarifier 640 and the PSD of the calcium carbonate solid particles produced, the clarified effluent stream 641 can need to be passed through a secondary clarification or filtration step to reduce the TSS to tolerable levels for the gas-liquid contactor 100, 100A, 100B, 100C, 100D.

[000216] FIG. 13 shows another implementation of the DAC system 1310. The description, units, componentry, features, reference numbers and advantages of the DAC system 10, 210, 410, 510, 610 provided in relation to FIGS. 1-6 apply mutatis mutandis to the DAC system 1310 of FIG. 13. The DAC system 1310 of FIG. 13 shows another possible implementation of heat integration and solids-liquid separation. The DAC system 1310 includes a first heating unit 1332A and a second heating unit 1332B. The first heating unit 1332A is fluidly coupled to the contactor outlet pipeline 172A and configured to heat the carbonate-rich capture solution 111 to form a heated intermediate stream 1315 of the carbonate-rich capture solution 417A flowed to the second heating unit 1332B. The second heating unit 1332B is fluidly coupled to the first heating unit 1332A and in series flow therewith, via a heating unit pipeline 1720, and configured to heat the heated intermediate stream 1315 to produce a heated stream of the carbonate-rich capture solution 1317 flowed to the slaker 140 via the slaker input pipeline 172C. The heated stream of the carbonate-rich capture solution 1317 is reacted with the calcium oxide solids in the slaker 140 to form the slaker output stream 142. The first and second heating units 1332A, 1332B of FIG. 13 are heat exchangers operable to recover heat from different fluid streams. For example, and referring to FIG. 13, the first heating unit 1332A is operable to transfer heat from a heat load using any suitable heat transfer medium, such as heated fluid stream 1319, to the carbonate-rich capture solution 111 to form the heated intermediate stream 1315. In example implementations, the heated fluid stream 1319 is cooling water that has been used to cool one or more units or components in the DAC system 1310, thereby recovering waste heat from a heat source 1320 in the DAC system 1310. In other implementations, the heated fluid stream 1319 is any other refrigerant (e.g., glycol), in any phase, which has been used to cool one or more units or components in the DAC system 1310, thereby recovering waste heat from the heat source 1320. Non-limiting examples of such heat source(s) 1320 include the calciner 185, the dryer 183, the slaker 140, gas compressors, air separation unit(s), and safety showers. The heated fluid stream 1319 transfers heat in the first heating unit 1332A and is flowed from the first heating unit 1332A as cooling fluid stream 1321 back to the heat source(s) 1320 for reuse in cooling for the DAC system 1310.

[000217] The second heating unit 1332B is operable to transfer heat from the heated permeate stream 1364 to the heated intermediate stream 1315 to form the heated stream of the carbonate-rich capture solution 1317. The pipelines 172 include heat exchanger return pipelines 172N which fluidly couple the second heating unit 1332B to the gas-liquid contactor 100, 100A, 100B, 100C, 100D. The second heating unit 1332B is configured to flow the cooled permeate stream 1364D to the gas-liquid contactor 100, 100A, 100B, 100C, 100D via the heat exchanger return pipelines 172N, to be used as part of the CO2 capture solution 114. The cooled permeate stream 1364D can be flowed directly to the gas-liquid contactor 100, 100A, 100B, 100C, 100D (such as to a top liquid distributor or to one or more basin(s)), or indirectly via storage in the lean capture solution storage tank 119 or a recirculation line of the gas-liquid contactor 100, 100A, 100B, 100C, 100D. In some implementations, the first and second heating units 1332A, 1332B are operating at the same time to heat their respective streams. In some implementations, only one of the first and second heating units 1332A, 1332B are operating to heat their respective streams.

[000218] The DAC system 1310 of FIG. 13 includes another possible implementation of a solids-liquid separation unit 1360 using heated wash water. In the example implementation of FIG. 13, the first filtration unit 1366A is, or includes, one or more candle filters. In the example implementation of FIG. 13, the second filtration unit 1366B is, or includes, one or more filter presses. The vessel output stream 152 is fed to the first filtration unit 1366A to pre-thicken the solids slurry to increase the solids content (e.g., to approximately 10 wt% to 40 wt%). The first retentate stream 1362A is flowed from the first filtration unit 1366A, via the retentate pipeline 172G, to the second filtration unit 1366B. The filtrate 1364A from the first filtration unit 1366A can be flowed to any suitable unit or vessel, such as the second heating unit 1332B. The wash water system 1368 of the DAC system 1310 distributes heated wash water to the second fdtration unit 1366B so as to wash the calcium carbonate solids and dilute the hydroxide content of the first retentate stream 1362A. The second permeate stream 1364C is flowed from the second filtration unit 1366B, via one or more of the permeate pipelines 172F, to form, with the first permeate stream 1364A, the permeate stream 1364 flowed back to the gas-liquid contactor 100, 100A, 100B, 100D as the regenerated CO2 capture solution 114. In example implementations, the second filtration unit 1366B produces a filter cake with calcium carbonate solids having a solid content of at least 75 wt %, and a potassium content of less than 0.5 wt %. In example implementations of the solids- liquid separation unit 1360, and referring to FIG. 13, the heated wash water 1368 is used to wash the solids in the second filtration unit 1366B but not in the first filtration unit 1366 A.

[000219] It can be possible to optimize the reaction products and processes of the regeneration subsystem 190, 490, 590, 690 by adjusting properties or operating parameters of units of the DAC system 10, 210, 310, 410, 510, 610, 1310. For example, it can be possible to optimize, control, select for and/or determine one or more properties of the calcium carbonate solids product stream 162, 662 by adjusting properties or operating parameters of units of the DAC system 10, 210, 310, 410, 510, 610, 1310. These properties of the calcium carbonate solids product stream 162, 662 can include, but are not limited to, their size, density, hardness, porosity, and PSD.

[000220] For example, it can be desirable to increase the average particle size of calcium carbonate solids in the calcium carbonate solids product stream 162, 662. Increasing the average particle size can facilitate separating the calcium carbonate solids from liquid and can also facilitate solids handling by and between the dryer 183 and calciner 185. Increasing the average particle size can make the calcium carbonate solids more suitable for certain types of calciners 185, such as the CFB calciner 385 described herein. One possible technique for increasing the average particle size of calcium carbonate solids in the calcium carbonate solids product stream 162, 662 is to increase the concentration of hydroxide ([KOH] or [NOH]) flowed to the slaker 140 and/or reaction vessels 150. The molar concentration of KOH, for example, can be increased using different techniques. One possible technique involves selecting a composition for the CO2 capture solution 114 that has a suitably high concentration of KOH, such that the CO2-laden capture solution 111 retains a relatively high KOH concentration. Another possible technique involves evaporating water from the CO2 capture solution 114 and/or from the CO2-laden capture solution 111, so as to increase the molarity of KOH. Another possible technique involves flowing a slipstream of the high KOH concentration NF permeate stream 235B, 535B to the slaker 140. Increasing the concentration of potassium hydroxide ([KOH]) flowed to the slaker 140 and/or reaction vessels 150 can cause a shift in the PSD from a bimodal distribution to a monomodal one. This can assist in separating the calcium carbonate solids from liquid because the filter pores can be sized to process a more uniform particle size. This can assist in operation of the calciner 185 because particles with more uniform sizes are being reacted. Increasing the concentration of KOH flowed to the slaker 140 and/or reaction vessels 150 can reduce the reaction rate in the slaker 140 and/or reaction vessels 150, but this can be compensated for by increased residence time in these reactors, which can be an acceptable trade-off.

[000221] Another technique for increasing the average particle size of calcium carbonate solids in the calcium carbonate solids product stream 162, 662 is now described. This technique involves decreasing the slaking temperature in the slaker 140. The slaking temperature can be decreased using different techniques. One possible technique involves reducing the heat imparted to the CO2-laden capture solution 111 in the heating unit 130, 430, 530. In the DAC system 410 of FIG. 4, another possible technique involves increasing the flow of the first stream of the carbonate-rich capture solution 111 A sent to the slaker 140 and decreasing the flow of the second stream of the carbonate-rich capture solution 11 IB flowed to the first reaction vessel 150A. Decreasing the slaking temperature can reduce the reaction rate in the slaker 140 and/or reaction vessels 150, but this can be compensated for by increased residence time in these reactors, which can be an acceptable trade-off.

[000222] Adjusting the operation of units of the DAC system 10, 210, 310, 410, 510, 610, 1310 can also impact one or more properties of the calcium carbonate solids. For example, in implementations of the DAC system 10, 210, 310, 410, 510, 610, 1310 where little or no heat is available to warm the CCh-laden capture solution 111 upstream of the causticization train and it is desired to slake at a relatively high slaking temperature, a lower flow of CCh-laden capture solution 111 can be sent to the slaker 140 to achieve the desired slaking temperature. This will cause the slaker liming ratio to increase. While a higher slaking liming ratio can result in the production of calcium carbonate solids in the calcium carbonate solids product stream 162, 662 that have smaller average particle size, these effects can be acceptable if it facilitates or permits operating the DAC system 10, 210, 310, 410, 510, 610, 1310 where little or no heat is available to warm the CO2- laden capture solution 111. Increasing the slaker liming ratio can also cause a shift in the PSD from a bimodal distribution with a peak at larger particles to a bimodal one favouring smaller particles. It can in some instances be desirable to produce calcium carbonate solids that have smaller average particle size because smaller calcium carbonate solids can be better suited for certain types of calciners 185, such as the rotary kiln calciner 185 of FIG. 1. Having the causticization reaction occur at a lower temperature can reduce the reaction rate and/or reduce the equilibrium cap on the conversion of calcium hydroxide in the slaker 140 and/or reaction vessels 150, but this can be compensated for by increased residence time in these reactors, which can be an acceptable trade-off.

[000223] Adjusting the operation of other units of the DAC system 10, 210, 310, 410, 510, 610, 1310 can also impact one or more properties of the calcium carbonate solids. For example, it can be desirable to reduce the harshness of reaction conditions in the calciner 185. This can be done by adjusting the type, features and/or operating conditions of the calciner 185, such as the reactor type, the calcination temperature, the composition of gases within the calciner 185, and the residence time. The possible effect of reducing the harshness of the calcination reaction is to increase the reactivity of the calcium oxide solids produced by the calciner 185, which can result in a smaller average particle size for the calcium carbonate solids in the calcium carbonate solids product stream 162, 662 produced by the causticization train. While smaller average particle sizes for the calcium carbonate solids may not be a desired effect in all implementations, it can be considered an acceptable trade-off if it allows for a more resilient calciner 185 or one requiring longer intervals between maintenance. In some implementations, the solids stream from the calciner 185 can include CaO and some impurities. The availability of CaO is the amount of CaO that is present in the solids stream from the calciner 185 for slaking purposes in the slaker 140. The reactivity of CaO is the rate of which CaO reacts with water. The availability and the reactivity of the CaO can depend on factors including, but not limited to, temperatures, impurities, number of cycles through the regeneration subsystem 190, physical characteristic of the calciner 185, and operation modes of the calciner 185.

[000224] In another example of selecting for one or more properties of the calcium carbonate solids, it can be desirable to increase the average particle size of calcium carbonate solids in the calcium carbonate solids product stream 162, 662. Increasing the average particle size can facilitate separating the calcium carbonate solids from liquid and can also facilitate solids handling by and between the dryer 183 and calciner 185. One possible technique for increasing the average particle size of calcium carbonate solids in the calcium carbonate solids product stream 162, 662 is to decrease the causticization temperature in the slaker 140 and/or the reaction vessels 150. The causticization temperature can be decreased using different techniques. One possible technique involves reducing the heat imparted to the CO2-laden capture solution 111 in the heating unit 130,430,430. In the DAC system 410 of FIG. 4, another possible technique involves reducing the heat imparted to the heated second stream of the carbonate-rich capture solution 417B, and/or to the heated first stream of the carbonate-rich capture solution 417A. Such a technique can involve flowing the heated second stream of the carbonate-rich capture solution 417B at a temperature between 5-30°C to the reaction vessels 150, and flowing the heated first stream of the carbonate- rich capture solution 417A to the slaker 140 at a temperature between 30-100°C. Decreasing the causticization temperature can reduce the reaction rate and/or reduce the equilibrium cap on the conversion of calcium hydroxide in the slaker 140 and/or reaction vessels 150, but this can be compensated for by increased residence time in these reactors, which can be an acceptable tradeoff.

[000225] In some aspects, selecting for physical properties such as hardness and porosity, as well as the morphological properties such as size and distribution of the calcium carbonate solids created herein can enable several advantages. For example, the low porosity and larger size of the calcium carbonate solids can facilitate solution removal during the separation and washing operations, in comparison to material that is more porous and/or smaller in size. The hardness of the calcium carbonate solids can reduce some of the challenges associated with solids handling and/or calcination, because a harder particle can be more resistant to fracture and attrition, which are caused by solids transfer equipment such as conveyors and by fluidized bed systems. Fracture and attrition can lead to a reduction in the average particle size of the material and can lead to the creation of a portion of the material with a particle size less than the starting material. Large particle size of the solids can allow for higher gas velocities in the calciner and, therefore, higher capacities than material that is smaller in size and/or less spherical in shape.

[000226] Varying other operating parameters of the DAC system 10, 210, 310, 410, 510, 610, 1310 including, but not limited to, the degree of agitation during slaking, the viscosity of the slurry, slaking residence, and process solution temperature can also affect the particle size. It will be appreciated that any one of the ways described above for selecting for one or more properties of the calcium carbonate solids can be combined with any other one of the ways, in any combination. The description above of varying operating parameters of the DAC system 10, 210, 310, 410, 510, 610, 1310 demonstrates that it is possible to control or optimise for desired reaction kinetics or reaction products. For example, by varying easily controlled parameters such as the ratio between the first and second streams of the carbonate-rich capture solution 111A, 11 IB and/or liming ratios, it is possible to control characteristics of the calcium carbonate solid particles, such as their size and distribution.

[000227] The piping network 170 disclosed herein is a series of interconnected pipes, lines, and other similar conduits through which different materials are moved to, through and/or from the DAC system 10, 210, 310, 410, 510, 610, 1310. The piping network 170 includes multiple pipelines 172 through which materials are moved from one location to another. Each of the pipelines 172 of the piping network 170 can include, or be formed of, one or more pipes or one or more pipe segments, and include any other devices (e g., valves, flanges, ports, pumps, etc.) needed for the pipelines 172 to move the material associated with the pipeline 172 in the present disclosure.

[000228] Referring to FIG. 7, a method 700 for producing CO2 is disclosed. At 702, the method 1400 includes contacting atmospheric air with the CO2 capture solution 114 to absorb CO2 from the atmospheric air into the CO2 capture solution and form the carbonate-rich solution 111. At 704, the method 700 includes heating the carbonate-rich solution 111 to form the heated carbonate-rich solution 117, 417A, 417B, 517A, 517B. At 706, the method 700 includes slaking calcium oxide with the heated carbonate-rich solution 117, 417A, 417B, 517A, 517B to form the slaker output stream 142 comprising calcium hydroxide and calcium carbonate. At 708, the method 700 includes flowing the slaker output stream 142 through the reaction vessels 150 arranged in series, to form the vessel output stream 152 comprising calcium carbonate solids. At 710, the method 700 includes separating the calcium carbonate solids product stream 162 from the vessel output stream 152. At 712, the method 700 includes calcining the calcium carbonate solids product stream 162 to form the CO2 product stream 116.

[000229] Referring to FIG. 8, a method 800 of capturing CO2 from atmospheric air is disclosed. At 802, the method 800 includes contacting atmospheric air with the CO2 capture solution 114 to absorb CO2 from the atmospheric air into the CO2 capture solution and form the carbonate-rich solution 111. At 804, the method 800 includes nanofiltering the carbonate-rich solution 111 to form the NF retentate stream 235A, 335A, 535A, 635A comprising a carbonate- rich mixture, and to form the NF permeate stream 235B, 535B, 635B comprising a hydroxide-rich mixture. At 806, the method 800 includes flowing the NF permeate stream 235B, 535B, 635B for contacting the atmospheric air with the CO2 capture solution 114. At 808, the method 800 includes reacting the NF retentate stream 235 A, 335 A, 535 A, 635 A with calcium oxide in the reactorclarifier 640 to form the clarified effluent stream 641 comprising hydroxide, and to form the output stream 642 comprising calcium carbonate solids. At 810, the method 800 includes separating the calcium carbonate solids product stream 662 from the output stream 642.

[000230] FIG. 9 is a schematic diagram of a control system (or controller) 1600 for a DAC system, such as the DAC system 10, 210, 310, 410, 510, 610, 1310 disclosed herein. The system 1600 can be used for the operations described in association with any of the computer- implemented methods described previously, for example as or as part of the control system 999 or other controllers described herein.

[000231] The system 1600 is intended to include various forms of digital computers, such as laptops, desktops, workstations, personal digital assistants, servers, blade servers, mainframes, and other appropriate computers. The system 1600 can also include mobile devices, such as personal digital assistants, cellular telephones, smartphones, and other similar computing devices. Additionally the system can include portable storage media, such as, Universal Serial Bus (USB) flash drives. For example, the USB flash drives may store operating systems and other applications. The USB flash drives can include input/output components, such as a wireless transmitter or USB connector that may be inserted into a USB port of another computing device.

[000232] The system 1600 includes a processor 910, a memory 920, a storage device 930, and an input/output device 940. Each of the components 910, 920, 930, and 940 are interconnected using a system bus 950. The processor 910 is capable of processing instructions for execution within the system 1600. The processor 910 may be designed using any of a number of architectures. For example, the processor 910 may be a CISC (Complex Instruction Set Computers) processor, a RISC (Reduced Instruction Set Computer) processor, or a MISC (Minimal Instruction Set Computer) processor.

[000233] In one implementation, the processor 910 is a single-threaded processor. In some implementations, the processor 910 is a multi -threaded processor. The processor 910 is capable of processing instructions stored in the memory 920 or on the storage device 930 to display graphical information for a user interface on the input/output device 940.

1 [000234] The memory 920 stores information within the system 1600. In one implementation, the memory 920 is a computer-readable medium. In one implementation, the memory 920 is a volatile memory unit. In some implementations, the memory 920 is a non-volatile memory unit.

[000235] The storage device 930 is capable of providing mass storage for the system 1600. In one implementation, the storage device 930 is a computer-readable medium. In various different implementations, the storage device 930 may be a floppy disk device, a hard disk device, an optical disk device, or a tape device.

[000236] The input/output device 940 provides input/output operations for the system 1600. In one implementation, the input/output device 940 includes a keyboard and/or pointing device. In some implementations, the input/output device 940 includes a display unit for displaying graphical user interfaces.

[000237] In some implementations, the processor 910 is configured to implement one or more forms of artificial intelligence, such as a machine learning model that employs multiple layers of models to generate an output for a received input. A deep neural network is a deep machine learning model that includes an output layer and one or more hidden layers that each apply a non-linear transformation to a received input to generate an output. In some cases, the neural network may be a recurrent neural network. A recurrent neural network is a neural network that receives an input sequence and generates an output sequence from the input sequence. In particular, a recurrent neural network uses some or all of the internal state of the network after processing a previous input in the input sequence to generate an output from the current input in the input sequence. The machine learning model executed by the processor 910 can be, for example, a deep-learning neural network or a "very" deep learning neural network. For example, the machine learning model executed by the processor 910 can be a convolutional neural network or a recurrent network. The machine learning model 204 can have residual connections or dense connections.

[000238] In some implementations, the machine learning model executed by the processor 910 is an ensemble of models that may include all or a subset of the architectures described above. [000239] In some implementations, the machine learning model executed by the processor 910 is a graph neural network (GNN). GNNs are a designed to process data that can be represented in a graph form and feature pairwise message passing to enable iterative updating of node representation of the graph data.

[0002401 In some implementations, the machine learning model executed by the processor 910 can be a feedforward auto-encoder neural network. For example, the machine learning model executed by the processor 910 can be a three-layer auto-encoder neural network. The machine learning model executed by the processor 910 may include an input layer, a hidden layer, and an output layer. In some implementations, the neural network has no recurrent connections between layers. Each layer of the neural network may be fully connected to the next, e.g., there may be no pruning between the layers. The neural network may include an optimizer for training the network and computing updated layer weights. In some implementations, the neural network may apply a mathematical transformation, e.g., a convolutional transformation or factor analysis to input data prior to feeding the input data to the network.

[000241] In some implementations, the machine learning model executed by the processor 910 can be a supervised model. For example, for each input provided to the model during training, the machine learning model can be instructed as to what the correct output should be. The machine learning model executed by the processor 910 can use batch training, e g., training on a subset of examples before each adjustment, instead of the entire available set of examples. This may improve the efficiency of training the model and may improve the generalizability of the model. In some implementations, the machine learning model executed by the processor 910 may be an unsupervised model. For example, the model may adjust itself based on mathematical distances between examples rather than based on feedback on its performance. In some implementations, the machine learning model executed by the processor 910 can provide suggested additional data that could further improve the output of the machine learning model.

[000242] Certain features described can be implemented in digital electronic circuitry, or in computer hardware, firmware, software, or in combinations of them. The apparatus can be implemented in a computer program product tangibly embodied in an information carrier, e.g., in a machine-readable storage device for execution by a programmable processor; and method steps can be performed by a programmable processor executing a program of instructions to perform functions of the described implementations by operating on input data and generating output. The described features can be implemented advantageously in one or more computer programs that are executable on a programmable system including at least one programmable processor coupled to receive data and instructions from, and to transmit data and instructions to, a data storage system, at least one input device, and at least one output device. A computer program is a set of instructions that can be used, directly or indirectly, in a computer to perform a certain activity or bring about a certain result. A computer program can be written in any form of programming language, including compiled or interpreted languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment.

[000243] Suitable processors for the execution of a program of instructions include, by way of example, both general and special purpose microprocessors, and the sole processor or one of multiple processors of any kind of computer. Generally, a processor will receive instructions and data from a read-only memory or a random access memory or both. The essential elements of a computer are a processor for executing instructions and one or more memories for storing instructions and data. Generally, a computer will also include, or be operatively coupled to communicate with, one or more mass storage devices for storing data files; such devices include magnetic disks, such as internal hard disks and removable disks; magneto-optical disks; and optical disks. Storage devices suitable for tangibly embodying computer program instructions and data include all forms of non-volatile memory, including by way of example semiconductor memory devices, such as EPROM, EEPROM, and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical disks; and CD-ROM and DVD-ROM disks. The processor and the memory can be supplemented by, or incorporated in, ASICs (applicationspecific integrated circuits).

[000244] To provide for interaction with a user, the features can be implemented on a computer having a display device such as a CRT (cathode ray tube) or LCD (liquid crystal display) monitor for displaying information to the user and a keyboard and a pointing device such as a mouse or a trackball by which the user can provide input to the computer. Additionally, such activities can be implemented via touchscreen flat-panel displays and other appropriate mechanisms.

[000245] The features can be implemented in a control system that includes a back-end component, such as a data server, or that includes a middleware component, such as an application server or an Internet server, or that includes a front-end component, such as a client computer having a graphical user interface or an Internet browser, or any combination of them. The components of the system can be connected by any form or medium of digital data communication such as a communication network. Examples of communication networks include a local area network (“LAN”), a wide area network (“WAN”), peer-to-peer networks (having ad-hoc or static members), grid computing infrastructures, and the Internet.

[000246] Any DAC system 10, 210, 310, 410, 510, 610, 1310 disclosed herein can have one or more of the gas-liquid contactors 100, 100A, 100B, 100C, 100D, in any combination. The regeneration subsystem 190, 490, 590, 690 can be fluidly coupled to any suitable gas-liquid contactor, such as the gas-liquid contactor 100, 100A, 100B, 100C, 100D of the present disclosure. When implementing, or conceiving of, a DAC system 10, 210, 310, 410, 510, 610, 1310 each gasliquid contactor 100, 100A, 100B, 100C, 100D can be interchangeable with another gas-liquid contactor 100, 100A, 100B, 100C, 100D. Any DAC system 10, 210, 310, 410, 510, 610, 1310 disclosed herein can have one or more of the calciners 185, 385, 485 disclosed herein, in any combination. The regeneration subsystem 190, 490, 590, 690 can include any suitable calciner, such as the calciner 185, 385, 485 of the present disclosure. When implementing, or conceiving of, a DAC system 10, 210, 310, 410, 510, 610, 1310 each calciner 185,385,485 is interchangeable with another calciner 185, 385, 485.

[000247] Each gas-liquid contactor 100, 100A, 100B, 100C, 100D can be grouped together with one or more other gas-liquid contactors 100, 100 A, 100B, 100C, 100D to provide the DAC system 10, 210, 310, 410, 510, 610, 1310 with one or more wall(s), array(s) or train(s), where each wall, array or train has multiple gas-liquid contactors 100, 100A, 100B, 100C, 100D. For example, and referring to FIGS. 12A and 12B, multiple gas-liquid contactors 100, 100A, 100B, 100C, 100D are arranged next to one another to form a contactor wall 1502. The number of gas-liquid contactors 100, 100 A, 100B, 100C, 100D composing the contactor wall 1502 can vary (as represented by the ellipsis symbol “[...]” in FIG. 12A). The contactor wall 1502 can include a large number of gas-liquid contactors 100, 100A, 100B, 100C, 100D, for example between 10 and 100 gas-liquid contactors 100, 100A, 100B, 100C, 100D. In some implementations, the number of gas-liquid contactors 100, 100A, 100B, 100C, 100D in the contactor wall 1502 is greater than 1,000. The number of gas-liquid contactors 100, 100A, 100B, 100C, 100D in the contactor wall 1502 can be determined based on a variety of factors, such as a plume of CCh-lean gas 105 generated by the contactor wall 1502 during operation of the gas-liquid contactors 100, 100A, 100B, 100C, 100D. The contactor wall 1502 extends along its own wall axis 1509. The wall axis 1509 extends along a direction that is perpendicular to the packing depth 106D of the gas-liquid contactors 100, 100A, 100B, 100C, 100D, and perpendicular to the packing LTD 106L of the gasliquid contactors 100, 100A, 100B, 100C, 100D.

[000248] In implementations where the gas-liquid contactors 100, 100A, 100B, 100C, 100D are positioned (e.g., directly) adjacent each other, and referring to FIG. 12A, they can be abutted along a dividing wall 1525 which fluidly separates components of one gas-liquid contactor 100, 100A, 100B, 100C, 100D from an adjacent gas-liquid contactor 100, 100A, 100B, 100C, 100D. The dividing wall 1525 helps to ensure that the CCh-laden air 101 flowing through the air inlet 1031 of a gas-liquid contactor 100, 100A, 100B, 100C, 100D flows through the packing section(s) 106 of that gas-liquid contactor 100, 100A, 100B, 100C, 100D, rather than into an adjacent gasliquid contactor 100, 100 A, 100B, 100C, 100D. The dividing walls 1525 extend in an upright or vertical direction, and along a direction parallel to the packing depth 106D. In example implementations, the vertical extent of one or more of the dividing walls 1525 begins at, or below, the liquid level in the bottom basin 110. This configuration of the dividing walls 1525 can help to minimise or eliminate air bypassing the dividing walls 1525. The plenum 108 of each gas-liquid contactor 100, 100A, 100B, 100C, 100D is separated from the plenum 108 of an adjacent gasliquid contactor 100, 100A, 100B, 100C, 100D by one or more dividing walls 1525. At least some of the dividing walls 1525 are internal to the contactor wall 1502. Each dividing wall 1525 forms a barrier to airflow between the adjacent plenums 108 delimited by that dividing wall 1525, so as to prevent air from flowing between the plenums 108. The dividing walls 1525 can allow for multiple gas-liquid contactors 100, 100A, 100B, 100C, 100D of the contactor wall 502 to remain operational if one of the gas-liquid contactors 100, 100A, 100B, 100C, 100D or its fan 112, 2112, 3112, 421 is deactivated. The dividing walls 1525 of FIG. 12A are internal to the contactor wall 1502, and it will be appreciated that the contactor wall 1502 can have externally-applied dividing walls 1525 at opposite longitudinal ends of the contactor wall 1502. The plenums 108 are arranged adjacent each other along the length of the contactor wall 1502 defined along the wall axis 1509. In other implementations, the contactor wall 1502 includes a single plenum 108 that is continuous along its length defined parallel to the wall axis 1509, such that the contactor wall 1502 is free of internal dividing walls 1525. In other implementations, the contactor wall 1502 includes multiple plenums 108 delineated by the dividing walls 1525, where two or more gas-liquid contactors 100, 100A, 100B, 100C, 100D of the contactor wall 1502 share a common plenum 108. In some implementations, the dividing walls 1525 include doors or closeable openings, to provide access to the interior 113 of adjacent gas-liquid contactors 100, 100A, 100B, 100C, 100D. In example implementations, and referring to FIG. 12A, the contactor wall 1502 includes multiple plenums 108, where each gas-liquid contactor 100, 100 A, 100B, 100C, 100D forming the contactor wall 1502 has one plenum 108. Each plenum 108 is separated from an adjacent plenum 108 by one or more dividing walls 1525. In the example implementation of FIG. 12A, each dividing wall 1525 shown is located between two fan stacks 107 and forms a barrier to airflow between two plenums 108 delimited by that dividing wall 1525, where each plenum 108 is in fluid communication with a respective one of the fan stacks 107.

[000249] The contactor wall 1502 can be part of the DAC system 10, 210, 310, 410, 510, 610, 1310. Referring to FIG. 12B, each DAC system 10, 210, 310, 410, 510, 610, 1310 can include multiple contactor walls 1502 arranged on a plot of land 1505. Each contactor wall 1502 is spaced apart from another contactor wall 1502. In this disclosure, the terms “train”, “array” and “wall” can be used interchangeably. The DAC system 10, 210, 310, 410, 510, 610, 1310 of FIG. 12B is shown with multiple contactor walls 1502 for the purposes of illustration. The DAC system 10, 210, 310, 410, 510, 610, 1310 can alternatively have only one contactor wall 1502. Referring to FIG. 12B, the DAC system 10, 210, 310, 410, 510, 610, 1310 includes the regeneration subsystem 190, 490, 590, 690 such as one or more of those described above, in fluid communication with the contactor walls 1502. The regeneration subsystem 190, 490, 590, 690 functions to regenerate the CCh-rich sorbent (e g., the CCh-laden capture solution 111) received from the contactor walls 1502, or from other componentry that treats the CCh-laden capture solution 111 from the contactor walls 1502. The regeneration subsystem 190, 490, 590, 690 forms a regenerated sorbent (e.g., the regenerated CO2 capture solution 114) that is conveyed back to the contactor walls 1502. The regeneration subsystem 190, 490, 590, 690 can also function to release CO2 from the CO2-rich sorbent, to produce the CO2 product stream. In example implementations, and referring to FIG. 12B, each contactor wall 1502 has a single or common bottom basin 110. In such implementations, the bottom basin 110 of each contactor wall 1502 is in fluid communication with the regeneration subsystem 190, 490, 590, 690. In example implementations, the process streams from the bottom basin 110 of a contactor wall 1502 flows, or is flowed, to the bottom basin 110 of another contactor wall 1502. [000250] A number of implementations of the disclosure have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the disclosure. Accordingly, other implementations are within the scope of the following claims. Further modifications and alternative implementations of various aspects will be apparent to those skilled in the art in view of this description. Accordingly, this description is to be construed as illustrative only. It is to be understood that the forms shown and described herein are to be taken as examples of implementations. Elements and materials may be substituted for those illustrated and described herein, parts and processes may be reversed, and certain features may be utilized independently, all as would be apparent to one skilled in the art after having the benefit of this description. Changes may be made in the elements described herein without departing from the spirit and scope as described in the following claims. For example, advantageous results may be achieved if the steps of the disclosed techniques were performed in a different sequence, if components in the disclosed systems were combined in a different manner, or if the components were replaced or supplemented by other components. Further, in some implementations, one or more methods or processes disclosed here, such as, for example, methods 700 and 800, may be performed with additional steps, fewer steps, or may be performed in different orders than those disclosed herein, within the scope of the present disclosure. As another example, although a control system (e.g., control system 1600) is not illustrated in all figures, each of the aforementioned processes and systems may include a control system (e.g., control system 1600) communicably coupled to the illustrated components and configured to perform operations and/or execute instructions to implement such processes (and other processes). Accordingly, other implementations are within the scope of the following claims.

Claims

WHAT IS CLAIMED IS:

1. A method for producing carbon dioxide (CO2), the method comprising: contacting atmospheric air with a CO2 capture solution comprising hydroxide to absorb

CO2 from the atmospheric air into the CO2 capture solution and form a carbonate-rich solution; heating the carbonate-rich solution to form a heated carbonate-rich solution; slaking calcium oxide with the heated carbonate-rich solution to form a slaker output stream comprising calcium hydroxide and calcium carbonate; flowing the slaker output stream through a plurality of reaction vessels to form a vessel output stream comprising calcium carbonate solids; separating a calcium carbonate solids product stream from the vessel output stream; and calcining the calcium carbonate solids product stream to form a CO2 product stream.

2. The method of claim 1, comprising flowing the carbonate-rich capture solution through a nanofiltration (NF) unit to form: an NF retentate stream comprising a carbonate-rich mixture having a concentration of carbonate greater than a concentration of carbonate in the carbonate-rich capture solution, and an NF permeate stream comprising a hydroxide-rich mixture, wherein: contacting the atmospheric air with the CO2 capture solution comprises contacting the atmospheric air with the NF permeate stream comprising the hydroxide-rich mixture; and heating the carbonate-rich solution comprises heating the NF retentate stream to form the heated carbonate-rich solution.

3. The method of claim 2, wherein flowing the carbonate-rich capture solution through the NF unit comprises flowing the carbonate-rich capture solution having a first concentration of hydroxide, the NF permeate stream having a second concentration of hydroxide at least equal to the first concentration of hydroxide.

4. The method of any one of claims 1 to 3, wherein calcining the calcium carbonate solids product stream comprises calcining at least part of the calcium carbonate solids product stream to produce calcium oxide solids, the method comprising: transporting at least some of the calcium oxide solids for slaking the calcium oxide with the heated carbonate-rich solution.

5. The method of any one of claims 1 to 4, wherein: separating the calcium carbonate solids product stream from the vessel output stream comprises filtering the vessel output stream to form a retentate stream comprising the calcium carbonate solids product stream and a permeate stream comprising hydroxide; and contacting the atmospheric air with the CO2 capture solution comprises contacting the atmospheric air with the permeate stream comprising hydroxide.

6. The method of claim 5, wherein filtering the vessel output stream comprises: filtering the vessel output stream to form a first retentate stream and a first permeate stream; and filtering the first retentate stream to form a second retentate stream forming the retentate stream comprising the calcium carbonate solids product stream, and to form a second permeate stream; wherein the first and second permeate streams form the permeate stream comprising hydroxide.

7. The method of claim 5 or 6, comprising adding heated water to the vessel output stream to form a heated permeate stream.

8. The method of claim 7, wherein heating the carbonate-rich solution comprises transferring heat from the heated permeate stream to the carbonate-rich solution and forming a cooled permeate stream.

9. The method of claim 8, wherein contacting the atmospheric air with the CO2 capture solution comprises contacting the atmospheric air with the cooled permeate stream.

10. The method of any one of claims 1 to 9, wherein flowing the slaker output stream through the plurality of reaction vessels comprises flowing the slaker output stream through a plurality of stirred tanks.

11 . The method of any one of claims 1 to 10, comprising separating the carbonate- rich solution into a first stream of the carbonate-rich solution and into a second stream of the carbonate-rich solution, wherein: heating the carbonate-rich solution comprises heating at least one of the first stream of the carbonate-rich solution and the second stream of the carbonate-rich solution.

12. The method of any one of claims 1 to 10, comprising separating the carbonate- rich solution into a first stream of the carbonate-rich solution and into a second stream of the carbonate-rich solution, wherein: heating the carbonate-rich solution comprises heating the first stream of the carbonate- rich solution to form a heated first stream of the carbonate-rich solution, and heating the second stream of the carbonate-rich solution to form a heated second stream of the carbonate-rich solution; slaking the calcium oxide with the heated carbonate-rich solution comprises slaking the calcium oxide with the heated first stream of the carbonate-rich solution to form the slaker output stream; and flowing the slaker output stream through the plurality of reaction vessels comprises flowing the slaker output stream and the heated second stream of the carbonate-rich solution through the plurality of reaction vessels to form the vessel output stream.

13. The method of claim 12, wherein flowing the slaker output stream and the heated second stream of the carbonate-rich solution through the plurality of reaction vessels comprises: flowing to the plurality of reaction vessels the slaker output stream having a first temperature; and flowing the heated second stream of the carbonate-rich solution to the plurality of reaction vessels, the heated second stream of the carbonate-rich solution having a second temperature less than the first temperature.

14. The method of claim 13, wherein the first temperature is between 80°C - 95°C and the second temperature is between 5°C - 30°C.

15. The method of any one of claims 12 to 14, wherein: separating the calcium carbonate solids product stream from the vessel output stream comprises: filtering the vessel output stream to form a first retentate stream, and to form a first permeate stream comprising hydroxide; filtering the first retentate stream to form a second retentate stream comprising the calcium carbonate solids product stream, and to form a second permeate stream comprising hydroxide; and heating the first permeate stream to form a heated first permeate stream, and heating the second permeate stream to form a heated second permeate stream; heating the first stream of the carbonate-rich solution to form the heated first stream of the carbonate-rich solution comprises transferring heat from at least one of the heated first and second permeate streams to the first stream of the carbonate-rich solution; heating the second stream of the carbonate-rich solution to form the heated second stream of the carbonate-rich solution comprises transferring heat from the at least one of the heated first and second permeate streams to the second stream of the carbonate-rich solution; and the method further comprises forming a cooled permeate stream from the at least one of the heated first and second permeate streams after transferring heat therefrom.

16. The method of claim 15, wherein contacting the atmospheric air with the CO2 capture solution comprises contacting the atmospheric air with at least some of the cooled permeate stream.

17. The method of any one of claims 12 to 16, wherein separating the carbonate-rich solution into the first stream of the carbonate-rich solution and into the second stream of the carbonate-rich solution comprises separating the NF retentate stream into the first stream of the carbonate-rich solution and into the second stream of the carbonate-rich solution.

18. The method of any one of claims 1 to 17, comprising selecting for at least one property of the calcium carbonate solids product stream by adjusting at least one of: a hydroxide concentration, a liming ratio for slaking the calcium oxide with the heated carbonate-rich solution, a temperature for slaking the calcium oxide with the heated carbonate-rich solution, or reactivity of the calcium oxide.

19. The method of claim 18, wherein selecting for the at least one property of the calcium carbonate solids product stream comprises increasing the hydroxide concentration to increase an average particle size of calcium carbonate solids in the calcium carbonate solids product stream.

20. The method of claim 18, wherein selecting for the at least one property of the calcium carbonate solids product stream comprises increasing the liming ratio for slaking to decrease an average particle size of calcium carbonate solids in the calcium carbonate solids product stream.

21. A method of capturing carbon dioxide (CO2) from atmospheric air, the method comprising: contacting the atmospheric air with a CO2 capture solution comprising hydroxide to absorb CO2 from the atmospheric air into the CO2 capture solution and form a carbonate-rich solution; nanofiltering the carbonate-rich solution to form an NF retentate stream comprising a carbonate-rich mixture, and to form an NF permeate stream comprising a hydroxide-rich mixture; flowing the NF permeate stream for contacting the atmospheric air with the CO2 capture solution; reacting the NF retentate stream with calcium oxide in a reactor-clarifier to form a clarified effluent stream comprising hydroxide, and to form an output stream comprising calcium carbonate solids; and separating a calcium carbonate solids product stream from the output stream.

22. The method of claim 21, comprising flowing the clarified effluent stream for contacting the atmospheric air with the CO2 capture solution.

23. The method of claim 21 or 22, comprising: calcining the calcium carbonate solids product stream to produce a CO2 product stream and to produce calcium oxide solids; and transporting at least some of the calcium oxide solids for reacting the NF retentate stream with the calcium oxide in the reactor-clarifier.

24. The method of any one of claims 21 to 23, wherein the NF retentate stream has a molarity of carbonate between 5 and 20 times greater than a molarity of carbonate in the carbonate-rich capture solution.

25. The method of any one of claims 21 to 24, wherein separating the calcium carbonate solids product stream from the output stream comprises filtering the output stream to form a retentate stream comprising the calcium carbonate solids product stream, and to form a permeate stream comprising hydroxide, the method comprising; flowing the permeate stream for contacting the atmospheric air with the CO2 capture solution.

26. The method of any one of claims 21 to 25, comprising transferring heat from the clarified effluent stream to the NF retentate stream prior to reacting the NF retentate stream with calcium oxide in the reactor-clarifier.

27. The method of any one of claims 21 to 25, comprising transferring heat from the clarified effluent stream to the calcium carbonate solids product stream to remove moisture from the calcium carbonate solids product stream.

28. A direct air capture (DAC) system for producing carbon dioxide (CO2), the DAC system comprising: at least one gas-liquid contactor configured to contact atmospheric air with a CO2 capture solution to produce a carbonate-rich capture solution; at least one heating unit fluidly coupled to the at least one gas-liquid contactor and configured to heat the carbonate-rich capture solution to produce a heated carbonate-rich capture solution; a plurality of reaction vessels arranged in series, the plurality of reaction vessels comprising: a first reaction vessel fluidly coupled to the at least one heating unit and configured to slake the heated carbonate-rich capture solution with calcium oxide, to produce a first output stream comprising calcium hydroxide and calcium carbonate; and at least one downstream reaction vessel fluidly coupled to the first reaction vessel to receive the first output stream, the at least one downstream reaction vessel configured to flow the first output stream therethrough to react the calcium hydroxide and the calcium carbonate and produce a vessel output stream comprising calcium carbonate solids; at least one solids-liquid separator unit fluidly coupled to the plurality of reaction vessels and configured to separate a calcium carbonate solids product stream from the vessel output stream; a piping network comprising pipelines fluidly coupling: the at least one gas-liquid contactor to the at least one heating unit, the at least one heating unit to the first reaction vessel, the first reaction vessel to the at least one downstream reaction vessel, and the plurality of reaction vessels to the at least one solids-liquid separator unit; and a calciner configured to receive the calcium carbonate solids product stream from the at least one solids-liquid separator unit, and configured to calcine the calcium carbonate solids product stream to produce a CO2 product stream and a solid oxide material.

29. The DAC system of claim 28, comprising a nanofiltration (NF) unit fluidly coupled between the at least one gas-liquid contactor and the at least one heating unit, the NF unit operable to filter the carbonate-rich capture solution and produce a NF permeate stream and a NF retentate stream.

30. The DAC system of claim 29, wherein the NF unit is operable to produce the NF permeate stream having a concentration of hydroxide greater than a concentration of hydroxide of the carbonate-rich capture solution.

31. The DAC system of claim 29 or 30, wherein the pipelines comprise a NF permeate pipeline fluidly coupling the NF unit to the at least one gas-liquid contactor, the NF unit configured to flow at least a portion of the NF permeate stream to the at least one gas-liquid contactor.

32. The DAC system of any one of claims 28 to 31, wherein: the at least one solids-liquid separator unit is configured to separate a permeate stream comprising hydroxide from the vessel output stream; and the pipelines comprise a permeate pipeline fluidly coupling the at least one solids-liquid separator unit to the at least one gas-liquid contactor, the at least one solids-liquid separator unit configured to flow at least a portion of the permeate stream to the at least one gas-liquid contactor.

33. The DAC system of any claim 32, wherein the at least one solids-liquid separator unit comprises a first filtration unit and a second filtration unit fluidly coupled to the first filtration unit, the first filtration unit configured to filter the vessel output stream and produce a first retentate stream and a first permeate stream, the second filtration unit configured to filter the first retentate stream and produce a second retentate stream and a second permeate stream, the second retentate stream comprising the calcium carbonate solids product stream, the first and second permeate streams at least partially forming the permeate stream comprising hydroxide.

34. The DAC system of claim 32 or 33, comprising a wash water system in fluid communication with the first and second filtration units and configured to generate a heated wash water stream, the first filtration unit configured to wash the vessel output stream with the heated wash water stream to form a heated first retentate stream comprising hydroxide, the second filtration unit configured to wash the heated first retentate stream with the heated wash water stream to form a heated second permeate stream comprising hydroxide.

35. The DAC system of claim 34, wherein the at least one heating unit comprises a heat exchanger configured to transfer heat from the second heated permeate stream to the carbonate-rich capture solution to produce the heated carbonate-rich capture solution, and to form a cooled permeate stream.

36. The DAC system of claim 35, wherein the pipelines comprise a contactor return pipeline fluidly coupling the heat exchanger and the at least one gas-liquid contactor, the heat exchanger configured to flow the cooled permeate stream to the at least one gas-liquid contactor.

37. The DAC system of claim 28, wherein: the pipelines comprise a first contactor outlet pipeline fluidly coupling the at least one gas-liquid contactor and the first reaction vessel, and a second contactor outlet pipeline fluidly coupling the at least one gas-liquid contactor and the at least one downstream reaction vessel, the at least one gas-liquid contactor configured to flow a first stream of the carbonate-rich capture solution to the first reaction vessel via the first contactor outlet pipeline, and a second stream of the carbonate-rich capture solution to the at least one downstream reaction vessel via the second contactor outlet pipeline; and the at least one heating unit comprises: a first heating unit fluidly coupled to the first contactor outlet pipeline and configured to heat the first stream of the carbonate-rich capture solution to form a heated first stream of the carbonate-rich capture solution; and a second heating unit fluidly coupled to the second contactor outlet pipeline and configured to heat the second stream of the carbonate-rich capture solution to produce a heated second stream of the carbonate-rich capture solution.

38. The DAC system of claim 37, wherein the at least one solids-liquid separator unit comprises a first filtration unit and a second filtration unit fluidly coupled to the first filtration unit, the first filtration unit configured to filter the vessel output stream and produce a first retentate stream and a first permeate stream, the second filtration unit configured to filter the first retentate stream and produce a second retentate stream and a second permeate stream, the second retentate stream comprising the calcium carbonate solids product stream.

39. The DAC system of claim 38, comprising a wash water system in fluid communication with the first and second filtration units and configured to generate a heated wash water stream, the first filtration unit configured to wash the vessel output stream with the heated wash water stream to form a heated first retentate stream comprising hydroxide, the second filtration unit configured to wash the heated first retentate stream with the heated wash water stream to form a heated second permeate stream comprising hydroxide.

40. The DAC system of claim 39, wherein: the first heating unit comprises a first heat exchanger configured to transfer heat from the heated first permeate stream to the first stream of the carbonate-rich capture solution to form the heated first stream of the carbonate-rich capture solution; and the second heating unit comprises a second heat exchanger configured to transfer heat from the heated second permeate stream to the second stream of the carbonate-rich capture solution to form the heated second stream of the carbonate-rich capture solution.

41. The DAC system of claim 40, wherein the pipelines comprise a plurality of heat exchanger return pipelines fluidly coupling each of the first and second heat exchangers to the at least one gas-liquid contactor, the first and second heat exchangers configured to flow cooled first and second permeate streams to the at least one gas-liquid contactor.

42. The DAC system of any one of claims 37 to 41, comprising a nanofiltration (NF) unit between the at least one gas-liquid contactor and the first and second heating units, the NF unit operable to filter the carbonate-rich capture solution and produce a NF permeate stream and a NF retentate stream upstream of the first contactor outlet pipeline and the second contactor outlet pipeline.

43. The DAC system of any one of claims 28 to 42, wherein the plurality of reaction vessels comprise a plurality of stirred tanks arranged in series.

44. The DAC system of any of claims 28 to 43, wherein the CO2 capture solution comprises at least one of: KOH, NaOH, or a combination thereof.

45. The DAC system of any of claims 28 to 44, wherein the calciner is configured to calcine the calcium carbonate solids and produce an exhaust gas stream comprising the CO2 product stream.

46. The DAC system of any one of claims 28 to 45, wherein the at least one gasliquid contactor includes a plurality of gas-liquid contactors positioned side by side and forming at least one contactor wall extending along a wall axis.

47. The DAC system of claim 46, wherein the at least one contactor wall comprises a plurality of dividing walls, each dividing wall of the plurality of dividing walls being upright, the plurality of dividing walls separating plenums of the plurality of gas-liquid contactors of the at least one contactor wall.

48. The DAC system of claim 46 or 47, wherein the at least one contactor wall includes a plurality of contactor walls, each contactor wall of the plurality of contactor walls spaced apart from an adjacent contactor wall of the plurality of contactor walls.