Techno-Economic Analysis of Hybrid Adsorption–Membrane Separation Processes for Direct Air Capture

Abstract

Direct air capture (DAC) has recently gained interest as a carbon dioxide removal (CDR) method to reduce atmospheric CO₂. DAC is mainly studied through standalone separation technologies, especially adsorption and absorption. Hybrid DAC, combining separation technologies, is rarely investigated and is the main topic of this work. This study investigates hybrid DAC using adsorption for pre-concentration up to a few percent or tens of percent depending on the case studied and membrane separation to concentrate the CO₂ stream to high purity (>90%). Adsorption regeneration by temperature swing adsorption (TSA) and vacuum thermal swing adsorption (VTSA) are compared, and VTSA regeneration achieved higher pre-concentration outlet CO₂ purity (15–30%) than TSA regeneration (1–10%). Membrane separation is studied depending on inlet CO₂ purity and outlet-required purity (90 or 95%), which influence the energy requirement and cost of capture. For all cases studied, the cost of capture remained high (>1700 €/tCO₂) with a high energy requirement (>2 MWh_e/tCO₂ and >27 GJ/tCO₂). The adsorption pre-concentration step accounted for the majority (>80%) of the energy requirement and cost of capture, and future work should be focused on preferentially improving adsorption step performance.

1. Introduction

The escalating issue of climate change is largely driven by the surge in greenhouse gases, particularly CO₂, in the atmosphere. Recently, carbon dioxide removal (CDR) processes have attracted considerable attention [1,2]. These solutions involve extracting CO₂ directly from the air and storing it in geological formations to lower atmospheric CO₂ levels. Unlike point-source capture, CDR allows for the decoupling of CO₂ capture locations from emission sources. This makes CDR especially beneficial for sectors with challenging emissions. Direct air capture (DAC) has become a promising solution among CDR solutions to reduce atmospheric CO₂ [3,4,5]. DAC processes involve extracting CO₂ directly from the atmosphere, then storing it safely or converting it into useful products. Although the DAC concept to reduce atmospheric CO₂ was introduced by Lackner et al. in the late 1990s, recent technological advances have considerably improved its feasibility [6,7].

The high cost of capturing CO₂ from the atmosphere, ranging from 94 $/tCO₂ in optimistic scenarios to over 1000 $/tCO₂, is one of the primary challenges for DAC [3,8,9,10,11,12]. Despite this, recent studies indicate a downward trend in DAC costs, which are expected to continue decreasing with technological advancements, economies of scale, and ability to generate valuable products (i.e., synthetic fuels, construction materials, etc.) with captured CO₂ [3,13]. The need for low-carbon, dispatchable energy further underscores the importance of advancing DAC technologies [14].

DAC processes are dominated today by standalone solutions, mostly through adsorption technologies [15,16]. Solid sorbent-based plants are currently the most implemented with the most operational and commercial feedbacks [3,17]. The main hurdles to address include improving energy efficiency, scaling up capacity, and lowering overall costs. A key area of research focuses on developing sorbent materials capable of capturing CO₂ at very low partial pressures (~40 Pa). Among the most studied are amine-functionalized materials, zeolites, metal–organic frameworks (MOFs), metal-based compounds, and silicas [18]. Due to chemisorption mechanisms, amine-based adsorbents typically offer high CO₂ uptake (generally > 1 molCO₂/kg) in air conditions (ca. 15 °C and with humidity) and are preferred in the literature to physisorbents, which present generally lower CO₂ uptake [19]. Moreover, DAC sorbents must demonstrate high selectivity and be robust under ambient and regeneration conditions, including variations in temperature and humidity. Amine sorbents such as Lewatit VP OC 1065 (Lanxess) present high CO₂ uptake in air conditions but their resistance is limited in the presence of air constituents (i.e., oxidative degradation), especially for high air temperatures (>70 °C) [20,21]. Absorption in chemical solvents is also, to a lesser extent, investigated, while membrane or electrochemical separation remains exploratory [8,22,23,24]. Absorption is mainly developed in Carbon Engineering using potassium carbonate as a chemical solvent, which has a high liquid-vapor equilibrium, but it requires a two-loop system with high-temperature regeneration (ca. 900 °C) [8,25]. Amine solvents such as monoethanolamine are studied for simulation purposes mainly [12,26]. Membrane separation has the advantage of being easy to operate, with energy in the form of electricity only, but the separation performance of polymer membranes is not currently sufficient as a standalone technology for DAC, even if new high-performance materials are under development at a low TRL (technology readiness level) [22,27,28]. Electrochemical separation technologies are gaining interest but remain at a low TRL [23,24].

Surprisingly, the possibilities of hybrid systems are largely unexplored. Given the very high dilution level of the starting CO₂ concentration for DAC (i.e., 400 ppm) and the target purity level (typically 90% or above), it is likely that the combination of two distinct separation processes could be of interest. Adsorption processes are known to offer high performance for diluted feeds, but reaching high purity systematically translates into increased cost and specific energy. Membrane processes are often considered as inappropriate for diluted feeds and can hardly compete with adsorption for DAC [22,27]. Membrane separation is, however, of major interest for moderate to concentrated CO₂ feeds (i.e., 15 to 50% or above) in terms of energy efficiency and cost. Based on this statement, the combination of an adsorption pre-concentration step and a membrane CO₂ final concentration unit is proposed in this study. The feasibility of such hybrid DAC was introduced by Huang et al. [29]. To our knowledge, no study has investigated up to now the separation performance, energy efficiency, and overall cost of such a hybrid process for DAC. The objective is to evaluate the potentialities and limitations of the concept through a preliminary set of parametric simulations. State-of-the-art solutions for carbon capture by sorbents and membranes are thus explored in order to analyze their association in a two-step process.

2. Process and Modeling

2.1. Process Modeling

2.1.1. Hybrid DAC Overview

A hybrid direct air capture adsorption–membrane process is modeled and simulated to evaluate the techno-economic performance of such a hybrid DAC system (Figure 1). CO₂ is first pre-concentrated by an adsorption step from air (0.04%) to a concentration of 1 to 30% CO₂ at 1 bar, using hot air rather than steam for sorbent regeneration. Then, the CO₂ is sent to a membrane separation step to concentrate the CO₂ from 1–30% to ≥90–95%. A compression and purification unit (CPU) is added at the end to ensure that the CO₂ is purified of water content (95–99% CO₂ purity) and in supercritical condition for transport and storage (150 bars, 35 °C).

2.1.2. Adsorption Step Modeling

The separation step by adsorption consists of two main discontinuous phases: adsorption and regeneration. During the adsorption phase, air is pushed by fans into the adsorbent fixed bed, where the CO₂ in the air is adsorbed to the solid sorbent. The air leaving the bed is depleted of CO₂ and returned to the atmosphere. When the adsorption phase ends, the bed is heated indirectly using a heat exchanger and direct thermal heating with hot air to desorb the CO₂. The desorption can be improved by applying a low pressure in the bed using a vacuum pump. The concentrated CO₂ is then released, and the cycle is then ready to start again. The process is referred to as temperature swing adsorption (TSA) or vacuum thermal swing adsorption (VTSA) when a vacuum pump is used during desorption.

To represent the average properties of amine sorbents, a commercially available sorbent was selected. Thus, the adsorption step is modeled using Lewatit VP OC 1065, chosen due to its high affinity for CO₂ and its physico-chemical and isotherm data being available in the literature, especially at low CO₂ pressure (~40 Pa) and under humid conditions [21,30,31,32,33,34,35,36,37,38,39]. Adsorption equilibrium of species onto a solid surface (i.e., adsorbent) is typically described by isotherm thermodynamics models. Lewatit is known to have a high affinity for CO₂, and also for H₂O. Moreover, previous experimental studies on Lewatit have shown that H₂O significantly enhances CO₂ adsorption [30,31,32,35,37]. The isotherms of CO₂ are based on the Toth isotherm model for pure CO₂ under dry conditions (Equation (1)) and modified using an empirical expression from Schellevis (Equation (2)) to consider the CO₂ enhancement caused by the water content in the air (i.e., relative humidity) [31]. Thanks to its simplicity, this correlation uses only two fitting parameters, $b$ and $c$ (Equation (2)), to describe the humidity effect. At 15 °C, the CO₂ uptake increases from 1.17 mol/kg under dry conditions to 1.98 mol/kg under humid conditions (relative humidity of 0.8), showing the CO₂ uptake enhancement under humid conditions. On amine-functionalized adsorbents, CO₂ has little effect on the equilibrium adsorption of H₂O, which remains largely unaffected by the presence of CO₂, and this study assumes that H₂O adsorption is unaffected by CO₂ pressure [35,40]. The H₂O isotherm is based on the Guggenheim–Anderson–de Boer (GAB) isotherm (Equation (3)) [32,33,34,40,41].

$$q_{CO2}^{dry}\left(T,p_{CO2}\right)=q_S.{\displaystyle \frac{b\left(T\right).p_{CO2}}{{\left(1+{\left(b\left(T\right).p_{CO2}\right)}^{t\left(T\right)}\right)}^{\frac{1}{t\left(T\right)}}}}$$

(1)

$$q_{CO2}^{wet}\left(q_{CO2}^{dry},RH\right)=\left(b.e^{c.q_{CO2}^{dry}\left(T,p_{CO2}\right)}.RH+1\right).q_{CO2}^{dry}\left(T,p_{CO2}\right)$$

(2)

$$q_{H2O}(T,RH)=q_G.{\displaystyle \frac{C_G\left(T\right).K_G\left(T\right).RH}{\left(1-K_G\left(T\right).RH\right).\left(1+\left(C_G\left(T\right)-1\right).K_G\left(T\right).RH\right)}}$$

(3)

where $RH$ is the relative humidity and $b\left(T\right)$, $t\left(T\right)$ $C_G\left(T\right)$, and $K_{GAB}\left(T\right)$ are temperature-dependent parameters:

$$\left(T\right)=b_0.e^{{\displaystyle \frac{{∆H}_0}{R.T_0}}.\left({\displaystyle \frac{T_0}{T}}-1\right)}$$

(4)

$$t\left(T\right)=t_0+\alpha .\left(1-{\displaystyle \frac{T_0}{T}}\right)$$

(5)

$$RH={\displaystyle \frac{p_{H2O}}{p_{vap}\left(T\right)}}$$

(6)

$$C_G\left(T\right)=e^{{\displaystyle \frac{(E_1-E_{10+})}{R.T}}}$$

(7)

$$K_G\left(T\right)=e^{{\displaystyle \frac{(E_{2-9}-E_{10+})}{R.T}}}$$

(8)

$$E_1=C-e^{D.T}$$

(9)

$$E_{2-9}=F+G.T$$

(10)

$$E_{10+}=-44.38.T+57220$$

(11)

Based on previous work by the authors, the isotherm models were fitted using experimental data, especially at low CO₂ pressure and under humid conditions [21,30,31,32,33,34,35,37,42]. The fitted parameters are given in

Table 1. Fitted parameters of isotherm models, based on previous work [42].

Isotherm Model	Parameter	Value
Toth isotherm (Pure CO2)	$q_s$(molCO2/kg)	3.7604
	$b_0$(1/Pa)	0.001382
	${∆H}_0$(kJ/molCO2)	103.05
	$T_0$(K)	353.15
	$t_0$(-)	0.30894
	$\alpha$(-)	0.34148
Co-adsorption isotherm CO2	$b$(-)	3.5803
	$c$(kg/molCO2)	−1.2153
GAB isotherm (H2O)	$q_G$(molH2O/kg)	2.15
	$C$(J/molH2O)	48,459
	$D$ (1/K)	0.02342
	$F$ (J/molH2O)	57,197
	$G$ (J/(molH2O.K))	−44.931

.

The physico-chemical properties of the sorbent are summarized in

Table 2. Main sorbent properties for modeling.

Parameter	Symbol	Value	Unit	Source
Intra-sorbent voidage	${\epsilon }_p$	0.34	-	[34]
Pore radius	$r_{pore}$	28.5	nm	[43]
CO2 heat of adsorption	${\mathsf{\Delta }H}_{CO2}$	73	kJ/mol	[42]
H2O heat of adsorption	${\mathsf{\Delta }H}_{H2O}$	44	kJ/mol	[42]

. The intra-sorbent voidage corresponds to the pore voidage inside the sorbent material.

Because of the potential for the monolithic geometry to reduce the pressure drop of air across the bed, the design is considered to be a hypothetical structured adsorbent bed (i.e., monolithic sorbent with squared channels, Figure 2). The sorbent is coated on a support considered to be stainless steel [44]. The characteristic dimensions of the monolith are given in

Table 3. Characteristic dimensions of the monolith geometry.

Parameter	Unit	Value
Coating thickness	mm	0.3
$\mathrm{Gas}\mathrm{channel}a$	mm	1
$\mathrm{Support}\mathrm{half}\mathrm{thickness}d$	mm	0.25
$\mathrm{Active}\mathrm{bed}\mathrm{volume}\mathrm{voidage}{\epsilon }_i$	m3/m3	0.39
$\mathrm{Bed}\mathrm{volume}\mathrm{voidage}\epsilon$	m3/m3	0.23
Sorbent volume fraction	m3sorbent/m3	0.35
Support volume fraction	m3support/m3	0.42
Bed density (i.e., sorbent)	kg/m3	281
Support density	kgsupport/m3	3301
Apparent sorbent interfacial area	m2/m3	907

. Considering this geometry, the specific surface area of the adsorbent is given by $a_p={\displaystyle \frac{4a}{{(c+2d)}^2}}$, fixed at 907 m²/m³; the active bed volume voidage is given by ${\epsilon }_i={\displaystyle \frac{a^2}{c^2}}$, equal to 0.39; the bed volume voidage is given by $\epsilon ={\displaystyle \frac{a^2}{{(c+2d)}^2}}$, equal to 0.23; the sorbent bulk density is ${\rho }_B=$ 281 kg/m³; and the inlet interstitial gas velocity is calculated as $v_r={\displaystyle \frac{v_g}{{\epsilon }_i}}$.

Aspen Adsorption V14 software was used in the simulation of the dynamic adsorption process [45]. The dynamic bed model is based on the fundamental equations of an adsorbent bed: isotherms, mass and energy balances of gas and solid, including mass and heat transfer, and pressure drop across the bed. The fundamental equations and the physico-chemical parameters required for a complete description of the model and the complete set of assumptions are presented in previous work by the co-authors; only the main parameters and assumptions are presented here [42].

The adsorption model is based on the main following assumptions:

• CO₂ and H₂O are the only adsorbed substances. N₂, O₂, and Ar adsorption loadings are neglected in the study [34].
• A 1-D spatial dimension model with axial dispersion is considered.
• The gas mass transfer of components to adsorbent is expressed using the linear driving force (LDF) model.

The VTSA cycle of co-current adsorption/regeneration is composed of the consecutive steps described below:

• Adsorption: Air is pushed by the fan into the bed, where the CO₂ and H₂O are adsorbed. This step ends when the adsorption criterion is satisfied. The adsorption criterion corresponds to the ratio of the outlet CO₂ concentration to the inlet CO₂ concentration and is equal to $C_{{\mathit{CO}}_2}^{\mathit{out}}/C_{{\mathit{CO}}_2}^{\mathit{in}}=\mathrm{50\%}$. So, the step ends when the outlet CO₂ concentration reaches 50%.
• Evacuation: Air inlet flow stops, and the vacuum pump is turned on until the bed pressure is close to the vacuum pump pressure.
• VTSA: Indirect heating and air sweeping at 70 °C or 100 °C (depending on the cases presented later), along with vacuum pressure at 0.1 bar, induce the desorption of CO₂ and H₂O. The desorption temperature is limited to 100 °C to avoid thermal degradation of the sorbent [21,43].
• Repressurization: Air enters the bed until the pressure reaches ambient pressure before starting another cycle.

The TSA cycle is composed of only two steps: the adsorption is similar to VTSA and regeneration is achieved only by indirect heating and air sweeping at high temperature, without any vacuum pumping. Care was taken to ensure that there are no cycle effects: cycle n is equivalent (on CO₂ and H₂O loading, and cycle duration) to cycle n − 1 and cycle n + 1.

The environmental and process parameters of the adsorbent step are presented in

Table 4. Environmental and process parameters of adsorption step.

Parameter	Unit	Value
Bed height	m	0.5
Bed diameter	m	2
Superficial air velocity	m/s	2
Air temperature	°C	15
Relative humidity (RH)	-	0.8
Regeneration vacuum pressure	bar	0.1
Regeneration temperature	°C	70 or 100

. The dimensions of the bed were calculated to reach a productivity on the order of magnitude of tens of tonnes of CO₂ captured per year (i.e., module dimension). The bed shape, with a bed height lower than the bed diameter, was chosen to limit the pressure drop. The typical air conditions were an air temperature of 15 °C and a relative humidity of 80%. The weather conditions were based on the typical temperature and relative humidity met around the south part of the North Sea, where industrial areas are favorable to run a large DAC plant (CO₂ transport and storage proximity and available low-carbon and dispatchable energy). The typical air molar composition was N₂ (77.02%), O₂ (20.67%), Ar (0.92%), CO₂ (0.04%), and H₂O (1.35%). Superficial air velocity was chosen on the order of magnitude of meters per second, which yielded high productivity with a limited pressure drop. The regeneration vacuum pressure was chosen based on a known value for similar application of carbon capture [42,46]. The regeneration temperature was studied for two temperatures: 70 and 100 °C. Indeed, a sorbent like Lewatit is known to undergo chemical degradation in the presence of oxygen above 70 °C [21]. Cases with regeneration at 70 °C represent conservative cases to avoid degradation. Cases with regeneration at 100 °C represent cases where the Lewatit is replaced by a comparable amine adsorbent or chemically modified to reduce oxidative degradation up to 100 °C [47].

2.1.3. Membrane Step Modeling

Membrane separation is a two-stage gas–gas membrane separation process with recycling of the permeate from the second stage into the feed from the first stage (called fast configuration, Figure 1). First, the gas is sent to the first membrane stage, where the CO₂ passes preferentially through the membrane compared to the other gas constituents. Parts of other constituents pass through the membrane, so a second stage is required to concentrate the CO₂ to a higher purity (>95%). To improve the CO₂ capture rate, the retentate of the second stage is sent back to the feed of the first stage [48,49,50,51]. The passage of CO₂ through the membrane is made possible by the application of a partial pressure difference (i.e., driving force) on either side of the membrane (i.e., lower CO₂ partial pressure on the permeate side). The pressure difference is applied by a vacuum pump. The performance of polymeric membranes is mainly based on a trade-off between the permeance (in GPU) and the selectivity of CO₂ over other constituents [52,53].

The membrane process is simulated using MEMSIC V1 software, which is dedicated to gas–gas membrane permeation using a solution diffusion model [54]. MEMSIC V1, a simulation software that is compliant with the CAPE-OPEN communication protocol, is used to model the separation of a multi-constituent gas mixture through a membrane module. The process simulation considers cross-plug flow conditions under steady-state and isothermal conditions. The differential mass balance of the different permeants can be solved using a mass transfer expression. The ideal gas behavior without flux coupling (i.e., each compound permeates according to its own driving force) and with constant gas permeability along the membrane is considered. The pressure drop effect and concentration polarization in upstream and downstream sides are neglected.

A commercially available dense polymer membrane dedicated to carbon capture is used in the two-stage process, with its selectivities and permeance at 30 °C displayed in

Table 5. Polyactive membrane selectivities and permeance at 30 °C [55,56,57,58].

Parameter	Unit	Value
CO2 permeance	GPU	1000
CO2/N2 selectivity	-	45.9
CO2/O2 selectivity	-	16.8
CO2/Ar selectivity	-	16.8
CO2/H2O selectivity	-	0.1

[55,56,57,58]. High selectivity for CO₂ over other air constituents and high CO₂ permeance are preferable for CO₂ separation performance. Selectivity mainly influences the recovered CO₂ purity. Permeance primarily affects the capture rate and operating parameters such as membrane area and vacuum pressure. A flat sheet module with alternating retentate and permeate (compacity of 1000 m²/m³) is considered for simplification of the geometry of the membrane modules (Figure 3).

The membrane module results are determined via optimization of the vacuum work of the membrane step and by constraining the outlet CO₂ purity and capture rate. The capture rate must therefore be higher than 80%, while the outlet CO₂ purity must be higher than 0.9 or 0.95, depending on the case (discussed in the Section 3). The vacuum work represents the main energy requirement, explaining why the optimization is performed on the vacuum work. The optimization results indicated lower vacuum work for a set of stage cut $\theta$ and pressure ratio $\psi$ between the downstream side (i.e., permeate) and upstream side (i.e., retentate). Stage cut $\theta$ is the ratio between the permeate flowrate $Q_{permeate}$ and the air flowrate entering $Q_{in}$ the membrane stage: $\theta ={\displaystyle \frac{Q_{permeate}}{Q_{in}}}$. The upstream side is at an ambient pressure of 1.013 bar, whereas the downstream side is at vacuum pressure.

Table 6. Membrane optimization ranges, constraints, and objective.

Parameter	Range
$\mathrm{Stage}\mathrm{cut}(\theta$)	0.05–0.95
$\mathrm{Pressure}\mathrm{ratio}(\psi$)	0.05–0.5
Capture rate constraint	>80%
Purity constraint	>0.9–0.95
Objective	$\min W_{vp}$

shows the ranges over which the stage cut and the pressure ratio are studied for optimization. The constraints and objective are also presented. The ranges are wide enough to ensure that the optimum is efficiently located.

The compression and purification unit (CPU in Figure 1), for purification of water content and compression to supercritical conditions (150 bars, 35 °C) for transport and storage, is simulated using Aspen Plus V14 and is detailed in Appendix A.

2.2. Techno-Economic Methodology

2.2.1. Cases and Key Performance Indicators

In order to evaluate an adsorption–membrane hybrid process, different cases using TSA or VTSA regeneration are evaluated. These cases are composed of four different adsorption cases followed by membrane separation. The four adsorption cases, summarized in

Table 7. Regeneration conditions of adsorption cases.

Case	Regeneration	Pressure, bar	Temperature, °C
VTSA-100 °C	VTSA	0.1	100
VTSA-70 °C	VTSA	0.1	70
TSA-100 °C	TSA	1.013	100
TSA-70 °C	TSA	1.013	70

, are based on the regeneration process (TSA or VTSA) and regeneration temperature (70 °C or 100 °C).

The adsorption step is a discontinuous process with CO₂ outlet composition variations, i.e., simulation in transient regime, whereas the membrane step is continuous, i.e., simulation in steady-state regime. As a first approximation, the CO₂ composition at the outlet of the adsorption process is considered constant and averaged, considering a large number of adsorption modules in parallel.

The key performance indicators (KPI) of the hybrid process discussed in the results and their definitions are presented in

Table 8. Key performances indicators.

Parameter	Unit	Description
Outlet CO2 purity	molCO2/mol	% CO2 purity in the outlet
Separation ratio	-	Ratio of inlet % CO2 purity over outlet % CO2 purity
Capture rate	%	CO2 capture rate
Ads. CO2 working capacity	molCO2/kgsorbent	CO2 captured by sorbent per mass of sorbent
$\mathrm{Memb}.\mathrm{surface}A$	m2	$\mathrm{Membrane}\mathrm{surface}\mathrm{of}\mathrm{first}{A}_1$$\mathrm{and}\sec \mathrm{ond}{A}_2$ membrane stages
CO2 productivity	kgCO2/(h.m3)	Ratio of the flux of CO2 captured per bed volume, adjusted with an annual load factor of 0.9
H2O production	kgH2O/kgCO2	Ratio of the mass of H2O captured per mass of CO2 captured
Indirect heat	GJ/tCO2	Indirect heating requirement for ads. regeneration
Direct heat	GJ/tCO2	Regeneration air heating requirement for ads. regeneration
Fan work	MWh/tCO2	Fan work
Vacuum work	MWh/tCO2	Vacuum pump work
Heat. energy	GJ/tCO2	Sum of direct and indirect
Elec. energy	MWh/tCO2	Sum of fan work and/or vacuum work and/or CPU compressors work
Primary energy	GJ/tCO2	Energy requirements using a primary energy factor of 2.3 for electricity (=thermal energy + electrical energy × 2.3) [59]
Cost of capture	€/tCO2	Cost of capture per tonne of CO2 captured

.

The energy requirement of the hybrid DAC process is broken down into heat and electrical requirements:

• The thermal heat requirement for adsorption regeneration is provided by indirect heating (heat exchanger) and by direct heating (hot air). The heat requirement includes the heat of desorption, the heat capacity of the amine sorbent and support for a monolithic design, the heat capacity of the bed enclosure and indirect heating system, and other heat requirements (adsorbed CO₂ and H₂O heat capacity, respectively, and gas capacity). Hot air is partially pre-heated by the bed outlet flowrate, considering a 10 °C pinch. These requirements are assessed using Aspen Adsorption V14.
• During the VTSA step and membrane step, vacuum ($P_{\mathit{vp}}$) is provided by a vacuum pump. The vacuum work per tonne of CO₂ (MWh/tCO₂) is given by:

$$W_{vp}={\displaystyle \frac{W_{vp,isen}}{{\eta }_{vp}}}$$

(12)

where $W_{vp,isen}$ is the isentropic compression work (MWh/tCO₂) assessed using Aspen Plus V14 and ${\eta }_{vp}$ is the performance efficiency, calculated using the following expression [60]:

$${\eta }_{vac}=0.8{\displaystyle \frac{19.29P_{vp}}{1+19.29P_{vp}}}$$

(13)

As can be seen in Figure 4, the vacuum pump performance efficiency can be low at low pressure and is typically 0.53 at $P_{vp}=$0.1 bar.

• Air/gas is pushed through the adsorption bed or membrane module by a fan to compensate for the pressure drop across the adsorption bed or the membrane module in the upstream side (i.e., retentate). The pressure drop in a monolith is calculated using the Hagen–Poiseuille equation for a squared channel [61]:

$${\displaystyle \frac{\mathsf{\partial }P}{\mathsf{\partial }z}}=-{\displaystyle \frac{28.4\mu }{{\epsilon }_i{a}^2}}{\nu }_g$$

(14)

where $\mu$ is the air viscosity (Pa.s), ${\nu }_g$ is the superficial air velocity (m/s), ${\epsilon }_i$ is the active bed volume voidage, and $a$ is the dimension (1 mm) of the gas squared channel.

The pressure drop in a membrane module is calculated by the following equation for laminar flow between two parallel plates [62]:

$${\displaystyle \frac{\mathsf{\partial }P}{\mathsf{\partial }z}}=-{\displaystyle \frac{12\mu }{h^2}}{\nu }_g$$

(15)

where ${\nu }_g$ is the superficial air velocity (m/s) and $h$ is the height of the channel (0.5 mm).

The fan work, assessed using Aspen Plus V14 per tonne of CO₂ (MWh/tCO₂), considers isentropic (0.75) and electromechanical efficiencies (0.95) [63].

2.2.2. Cost Analysis

To assess the performance of hybrid DAC, a techno-economic analysis is conducted for initial deployment at an industrial scale of 100 ktCO₂/yr. The cost estimation of component capital costs is performed in euros 2022 using Aspen Process Economic Analyzer (APEA) V14, part of the AspenTech suite of process engineering software used for conducting economic evaluations of process plants, except for membrane cost, which are not included [64]. APEA was selected due to its industry-recognized capabilities for early-stage economic evaluation and its integration with process simulations, providing a consistent framework for comparing alternatives. The condenser (heat exchanger and flash vessel) and CPU are estimated directly at plant capacity scale. Adsorber, membrane surface, membrane frame, vacuum pump, and fan are estimated at unit scale/module scale, and then the cost is extrapolated at plant capacity scale using a learning rate. Due to the high modularity and innovative adsorption module, a learning rate of 15% is applied for the adsorption module [65]. The learning rate of the membrane step is considered to be 10% due to the new application of gas membrane permeation for DAC and the high modularity of membrane modules [66,67]. The membrane cost considered is 50 €/m², and the membrane frame cost is evaluated as a function of membrane surface [50]. The cost is estimated considering a membrane module of 100 m² with a compacity of 1000 m²/m³, so a module volume of 0.1 m³.

The total capital requirement (CAPEX) is calculated using multiplying factors from component costs, as described in

Table A2. Economic methodology of Hybrid DAC.

Capital Cost
Component capital costs of adsorber, fans, and vacuum pumps at unit scale	APEA estimation
Component capital costs of membrane surface at unit scale	50 €/m2
Component capital costs of membrane frame at unit scale, with $A$ being the membrane surface in m2	$42A^{0.7}$ €
Component capital costs of membrane, membrane frame, fan, and vacuum pump at plant capacity scale (100 ktCO2/yr)	10–15% learning rate on above cost
Component capital of condensers and CPU at plant capacity scale (100 ktCO2/yr)	APEA estimation
Total field cost (TFC: total direct cost + total indirect cost)	Sum of above at scale
Other costs (power supply, water treatment and conditioning components, steam integration, temporary installations, transport, etc.)	20% of TFC
Engineering, procurement, and construction	9% of TFC
Risks and contingencies	30% of sum of above
Total Plant Cost (TPC)	Sum of above
Spare parts	0.5% of TPC
Start-up	2% of TPC
Operator costs (other studies, enquiry, land purchase, site access, permits, etc.)	7% of TPC
Insurance	0.5% of TPC
Local taxes	0.5% of TPC
Interim interest	17.5% of TPC
Total Capital Requirement (TCR)	Sum of above from TPC
O&M Cost
Operational labor cost	10 jobs/100 ktCO2/yr; 60 k€/(jobs.yr)
Annual maintenance cost	3% of TPC
Other Assumptions
Cost basis	€2022, Rotterdam, The Netherlands
Load factor	90%
Discount rate	8%
Economic lifetime	20 years
Electricity cost	70 €/MWh
Heat cost	10 €/GJ
Lewatit cost	15.6 €/kg
Monolith support cost	2 €/kg
Lewatit/monolith lifetime	2 years
Membrane replacement cost (MRC), per m2 of membrane	6.25 €/(m2.yr)
H2O cost	0.5 €/tH2O

in Appendix B.1. More details on APEA models, assumptions for material costs and replacement, load factor, discount rate, energy costs, material costs, and O&M costs for components are also provided in Appendix B. H₂O cost is considered a positive or negative value depending on whether the process produces or consumes water. The sorbent cost is evaluated as 15.6 €/kg using the Hart and Sommerfield method for extrapolation from laboratory-scale price to bulk price [42,68]. The monolith consists of a support (i.e., stainless steel sheet) at a cost of 2 €/kg, upon which the sorbent is coated. As a first approximation, the sorbent lifetime is considered to be 2 years and should be replaced every two years [69]. The membrane replacement cost is considered to be 6.25 €/(m².yr) [50].

3. Results

3.1. Adsorption Pre-Concentration Step

The purpose of this section is to present the performance and characteristics of the adsorption pre-concentration step for the four adsorption cases presented above. The desorption criterion and hot air regeneration flowrate are adapted to promote productivity performance and vacuum work for each case (

Table 9. Adsorption pre-concentration step key performances results.

Parameter	Unit	VTSA-100 °C	VTSA-70 °C	TSA-100 °C	TSA-70 °C
Desorption criterion	molCO2/kg	0.4	0.6	0.3	0.5
Hot air flowrate	mol/s	0.005	0.005	0.01	0.1
Ads. outlet CO2 purity	molCO2/mol	0.321	0.15	0.093	0.01
Ads. separation ratio	-	803	374	233	25.5
Ads. capture rate	%	63	59	61	62
CO2 working capacity	molCO2/kgsorbent	1.05	0.83	1.16	0.98
Ads. CO2 productivity	kgCO2/(h.m3)	2.2	1.6	1.7	1.6
H2O production	kgH2O/kgCO2	3.3	4.1	3.1	4.4
Indirect heat	GJ/tCO2	27.7	27.2	27.1	22.7
Direct heat	GJ/tCO2	0.06	0.09	0.2	1.5
Ads. fan work	MWh/tCO2	1.3	1.4	1.4	1.3
Ads. vacuum work	MWh/tCO2	1.4	1.9	0	0
Ads. heat. energy	GJ/tCO2	27.7	27.3	27.3	24.2
Ads. elec. energy	MWh/tCO2	2.7	3.3	1.4	1.3
Ads. primary energy	GJ/tCO2	50.1	54.9	38.5	35.5
Ads. cost of capture	€/tCO2	1630	1991	1651	1688

) [42]. Table 9 presents the key results of the adsorption step. The results are presented considering an 80% capture rate of the following membrane step.

The capture rate is not an imposed criterion, unlike flue gas capture, with capture rates of around 60%, which can improve productivity and thus better amortize the investment cost of the process [42]. The productivity is on the order of magnitude of kgCO₂/(h.m³) for the four cases with the highest value for the VTSA-100 °C case (2.2 kgCO₂/(h.m³)). A vacuum pump in combination with high temperature and/or a high regeneration air flowrate improve productivity by reducing the time to regenerate the bed. But the results must be put into perspective with the outlet CO₂ purity, which is first improved by vacuum pumping and then by high regeneration temperature. The highest outlet CO₂ purity is obtained for the VTSA-100 °C case (32.1% CO₂), whereas the lowest is obtained for the TSA-70 °C case (1% CO₂). This difference in purity will have an influence on the following membrane separation step. Because of the high affinity of the amine sorbent for water, the adsorption process is a net producer of fresh water, with about 3–4 times (in mass) more water captured than CO₂.

Heating energy is divided into two requirements: indirect heating, which is provided through a heat exchanger inside the bed, and direct heating, which is provided by direct injection of hot air in contact with the sorbent. The indirect heat is significant for the four cases, from 24.2 GJ/tCO₂ for the TSA-70 °C case to 27.7 GJ/tCO₂ for the VTSA-100 °C. By comparison, the direct heat (hot air inlet flowrate during the regeneration) is negligible for the VTSA cases (<0.1 GJ/tCO₂) but becomes more important for TSA cases, where the regeneration air flowrate is higher. So, the total heating energy is close to the indirect heat energy. Since the heating requirement is evaluated as specific (GJ/tCO₂), the CO₂ working capacity has an influence on the heating requirement for sensible heat. The total heat required includes the desorption of CO₂/H₂O, as well as the heating of the sorbent, the steel support, the bed enclosure, and the indirect heating system. Most of the heat is not from CO₂ desorption (1.7 GJ/tCO₂) but from H₂O desorption (6–9 GJ/tCO₂) due to the sorbent’s strong affinity for water. The other significant demands are for heating the monolith (the sorbent and steel support: 8.5–12.5 GJ/tCO₂), the bed enclosure, and the indirect heating system (2.5–3.5 GJ/tCO₂). In fact, the sensible heat of the monolith, the bed enclosure, and the indirect heating exchanger is independent of the amount of CO₂ captured (unlike the CO₂ heat of desorption) and will always require heating from ambient temperature to regeneration temperature. So, a low CO₂ working capacity leads to higher heat consumption. The CO₂ working capacity is low (0.82 to 1.16 kgCO₂/mol_sorbent) compared to the equilibrium loading at 15 °C (and relative humidity of 0.8) and for complete regeneration (1.98 kgCO₂/mol_sorbent).

The electrical requirement is the addition of fan work and vacuum pump work for the VTSA cases, whereas it is limited to fan work for the TSA cases because regeneration is carried out without vacuum. So, the TSA cases require a lower electrical requirement (about 1.3 MWh/tCO₂) compared to the VTSA cases (about 3 MWh/tCO₂). The fan work results from the pressure drop of 13 mbar in the bed during the adsorption phase at a superficial velocity of 2 m/s. This difference in electrical requirement has an influence on the total primary energy requirement, which is higher for the VTSA cases than for the TSA cases.

The cost of capture is high for the four cases, ranging from 1630 €/tCO₂ to 1991 €/tCO₂, and should be highlighted with CO₂ outlet purity. As can be seen on the left in Figure 5, the cost of capture follows a near 50/50 repartition between capital investment (CAPEX) and OPEX. The monolith (i.e., sorbent coated on support), through cost assumptions, represents a large part of the cost of capture (about 20%). Because of the vacuum pumping, the electricity share is larger for the VTSA cases. The right of Figure 5 shows that the adsorber, including the vessel pair, distributors, packing supports, valve skid, and heater (and excluding the monolith cost), represents the main part of CAPEX, meaning that a reduction in capital cost should be targeted first based on the adsorber cost.

3.2. Membrane Step

This section aims to present the characteristics and performances of the membrane finishing step that follows the pre-concentration adsorption step. The membrane step concentrates the CO₂ from adsorption outlet purity (i.e., 1–32% CO₂ depending on cases) to a CO₂ purity of 90–95% CO₂ (wet basis). The CO₂ adsorption outlet stream is saturated with water at 30 °C (condenser at 30 °C), so the feed of the membrane step is saturated at 30 °C. The detailed membrane feed composition (= adsorption outlet composition) is given in

Table 10. Membrane feed composition (%mol).

Case	CO2	N2	O2	H2O	Ar
VTSA-100 °C	32.1	49.8	13.3	4.2	0.6
VTSA-70 °C	15	62.9	17.2	4.2	0.7
TSA-100 °C	9.3	67.6	18.1	4.2	0.8
TSA-70 °C	1	74	19.9	4.2	0.9

.

As explained in the Section 2, the outlet purity is studied for CO₂ outlet purities higher than 90–95% CO₂, close to those required for supercritical CO₂ transport after the CPU (where water is condensed and CO₂ is dehydrated to an H₂O concentration below 50 ppm_mol to prevent corrosion of carbon steels) [70]. A minimal capture rate of the membrane is imposed to 80% because of the influence on the cost of capture of the adsorption pre-concentration step. Unfortunately, the TSA-70 °C (1% CO₂) case does not meet the requirements (90%CO₂ purity and 80% capture rate) with the chosen membrane fast configuration design (2 membrane stages with second retentate recycled in the feed) and the explored ranges of stage cut and pressure ratio. Figure 6 presents the trade-off, the so-called Pareto front of the TSA-70 °C case on the outlet CO₂ purity and the capture rate. The maximum outlet purity is about 70%CO₂ for an 80% capture rate. Even at a lower capture rate, higher purity than 80% CO₂ is not feasible in this case with the fast configuration. This suggests the need to explore alternative membrane designs with more than two stages or much lower vacuum levels. Nevertheless, this would allow the purity to be improved but at the expense of an increased cost of capture. Consequently, the choice was made to discard the TSA-70 °C case due to the impossibility of meeting the purity requirement.

Table 11. Membrane step key performance results.

Parameter	Unit	VTSA-100 °C-0.95	VTSA-70 °C-0.945	VTSA-70 °C-0.9	TSA-100 °C-0.9
Memb. inlet CO2 purity	molCO2/mol	0.321	0.15	0.15	0.093
Memb. outlet CO2 purity	molCO2/mol	0.95	0.945	0.9	0.9
Memb. separation ratio	-	3	6.3	6	9.6
Memb. capture rate	%	80	80	80	80
$\mathrm{Memb}.\mathrm{surface}{A}_1$	m2	30,371	131,896	3915	7808
$\mathrm{Memb}.\mathrm{surface}{A}_2$	m2	3536	3892	7808	7060
Memb. CO2 productivity	kgCO2/(h.m3)	336	84	95	58
Memb. fan work	MWh/tCO2	0.001	0.004	0.002	0.003
Memb. vacuum work	MWh/tCO2	0.48	1.22	0.35	0.68
Memb. elec. energy	MWh/tCO2	0.48	1.22	0.35	0.68
Memb. cost of capture	€/tCO2	101	226	82	140

shows the membrane step results for the three remaining cases, with the 80% capture rate constraint. The cases are studied for purities after the membrane step of 90% and 95%, depending on the case. The VTSA-100 °C case is studied for an achievable purity of 95% (VTSA-100 °C-0.95). The VTSA-70 °C case is studied for two achievable purities of 90% (VTSA-70 °C-0.9) and 94.5% (VTSA-70 °C-0.945) in order to compare the influence on separation performance. The results for the TSA-100 °C case are presented only for an outlet purity of 90%. The TSA-100 °C case with 94.5% purity already shows a high vacuum pump energy requirement (>3 MWh/tCO₂) and was therefore discarded. Note that because of the saturated feed stream and high water permeance (Table 5), the water permeates largely through the membranes and is processed by the vacuum pump, having an influence on the vacuum work and vacuum pump size. The excess water (i.e., above saturation at 1 bar and 30 °C) is condensed after each membrane stage (Figure 1).

Productivity is highest in the VTSA-100 °C-0.95 case due to the higher inlet CO₂ purity and therefore a lower separation ratio than in the other cases. However, it is not the VTSA-100 °C-0.95 case that has the lowest consumption and costs. It is the VTSA-70 °C-0.9 case, in particular because of the lower purity requirement of 90%. When comparing the VTSA-70 °C-0.9 and VTSA-70 °C-0.945 cases, the energy requirements and capture costs to go from 90% purity to 94.5% are more than three times higher. Capture costs range from 82 €/tCO₂ for the cheapest case (VTSA-70 °C-0.9) to 226 €/tCO₂ for the most expensive case (VTSA-70 °C-0.945). Furthermore, the fan work is negligible compared to the vacuum work, justifying optimization solely based on the vacuum pump work.

As can be seen in the left of Figure 7, there is a roughly 50/50 distribution of costs between capital investment (CAPEX) and OPEX, with electricity accounting for around one-third of capture costs. Among CAPEX costs, vacuum pumps are by far the biggest cost item, accounting for over 90% of CAPEX (Figure 7, right).

3.3. Complete Hybrid DAC Process

To compress and transport the CO₂ as a supercritical fluid, a compression and purification unit (CPU) is added at the membrane step outlet. The CPU enables compression up to 150 bars and 35 °C using an eight-stage compressor and purification of water content through condensation and dehydration below 50 ppm_mol using a molecular sieve [71]. The CPU accounts for an electrical requirement (i.e., compression work) of about 0.1 MWh/tCO₂. More details on the CPU are available in the SI.

Table 12. Complete DAC performance results.

Parameter	Unit	VTSA-100 °C-0.95	VTSA-70 °C-0.945	VTSA-70 °C-0.9	TSA-100 °C-0.9
Ads. outlet CO2 purity	molCO2/mol	0.321	0.15	0.15	0.093
Ads. separation ratio	-	803	374	374	233
Ads. heat. energy	GJ/tCO2	27.7	27.3	27.3	27.3
Ads. elec. energy	MWh/tCO2	2.7	3.3	3.3	1.4
Ads. cost of capture	€/tCO2	1630	1991	1991	1651
Memb. outlet CO2 purity	molCO2/mol	0.95	0.945	0.9	0.9
Memb. separation ratio	-	3	6.3	6	9.6
Memb. elec. energy	MWh/tCO2	0.48	1.22	0.35	0.68
Memb. cost of capture	€/tCO2	101	226	82	140
CPU outlet CO2 purity	molCO2/mol	0.995	0.99	0.94	0.94
CPU elec. energy	MWh/tCO2	0.1	0.1	0.1	0.1
CPU cost of capture	€/tCO2	62	62	63	63
DAC heat. energy	GJ/tCO2	27.7	27.3	27.3	27.3
DAC elec. energy	MWh/tCO2	3.3	4.6	3.8	2.2
DAC primary energy	GJ/tCO2	54.9	65.6	58.4	45.4
DAC cost of capture	€/tCO2	1793	2279	2136	1854

summarizes the performance of each step and the complete DAC process. The cost of capture is high for all cases, with a minimal value of 1793 €/tCO₂ for the VTSA-100 °C-0.95 case. The adsorption step is the only step that uses heating energy, whereas the membrane and CPU are only electro-intensive. TSA enables a reduction in the total electrical requirement thanks to the absence of a vacuum pump. In addition, Figure 8 presents the distributions of the primary energy and cost of capture between each step of the complete DAC process. The energy requirement is mainly derived from the adsorption step, which represents more of 80% of the primary energy need. The trend is similar regarding the cost of capture (Figure 8, right) with more than 85% of the cost due to the adsorption step. However, this can be partly explained by the fact that, by comparison, the separation ratio of the adsorption stage is about two orders of magnitude higher than that of membrane separation. Furthermore, the CPU accounts for a few percent of the energy requirement and cost.

4. Discussion

Analysis of the different cases studied reveals several key observations regarding the performance and economic viability of the hybrid direct air capture (DAC) process.

One key finding is the significant impact of the adsorption step on the total capture cost. With pre-concentration costing over €1600/tCO₂, this stage accounts for the largest part of the cost. Even optimizing the membrane step’s capture rate (currently 80%) to 100% would only reduce the cost to around €1300/tCO₂. This value remains in the high range of the cost estimation for CO₂ capture by a conventional amine sorbent [10,11,72]. This high cost is mainly due to the cost of the adsorber, the cost of the monolith, and the significant energy demand. In our analysis, we used process data derived from our simulations as inputs for APEA. APEA operates with built-in cost correlations and default parameters, which typically yield estimates with an accuracy range of −30% to +50%, which are suitable for feasibility studies. While current productivity is in line with figures reported in the literature [72,73,74] and improved performance would lower the overall cost, further research focusing specifically on cost, productivity, or energy requirements would be necessary to refine operational parameters. Such optimization is beyond the scope of this study, which aims to provide an order of magnitude for the results.

From an operational perspective, the TSA process does not require vacuum and can be easier to handle in operation compared to the VTSA process. However, the TSA process is less efficient in regeneration, resulting in lower outlet CO₂ purity and a higher capture cost. Indeed, VTSA is more commonly employed for DAC systems [10,11,16,72,75]. Using an amine sorbent in the adsorption step results in significant water co-production due to its high moisture affinity. At 15 °C and 80% relative humidity, net water production can reach several tonnes per tonne of captured CO₂. This can be advantageous in regions with limited freshwater supplies, in contrast to aqueous solvents, which cause substantial water losses [8,12]. However, desorbing this H₂O is energy intensive.

The membrane step as a fast configuration following adsorption is limited by the inlet CO₂ purity. Indeed, the TSA-70 °C case with 1%CO₂ after pre-concentration was not sufficient for the membrane step to obtain an outlet CO₂ purity higher than about 80%. To treat such low CO₂ purity, alternative technologies such as electro-swing adsorption, which uses electrochemistry for capture and regeneration, could be considered [23,24]. As expected, higher inlet CO₂ purity led to a lower energy requirement and cost of capture because of a smaller required separation ratio. The outlet CO₂ purity constraint (0.9–0.95) had a large influence on the energy requirement and cost of capture. A smaller purity constraint (0.9) reduced the energy and cost by ca. 3 compared to higher purity (0.945) for the VTSA-70 °C case, but 0.9 CO₂ purity might be insufficient for transporting and storing CO₂. Depending on the case, the energy requirement of the membrane step ranged from 0.35 to 1.22 MWh/tCO₂, which was comparable to that of post-combustion capture [48,49].

A CPU is included after the membrane step in order to compress and dry the final outlet CO₂. Membrane cases where the membrane step outlet CO₂ purity was constrained to 0.945–0.95 yielded a final outlet CO₂ purity of 99% after the CPU, which was in accordance with CO₂ supercritical transport and storage. Membrane cases where the membrane step outlet CO₂ purity was constrained to 0.9 provided a final outlet CO₂ purity of 0.94, just below the recommended purity of 0.95 for supercritical CO₂ [71]. A significant challenge is the O₂ content. For supercritical transport and storage, the molar O₂ content is recommended to be below 0.001% to prevent oxidative degradation. Because of O₂ membrane permeation, the O₂ concentration was higher in the cases studied, and especially for cases with a 0.9 purity constraint (

Table 13. O₂ concentration in the final outlet CO₂ flow.

Parameter	Unit	VTSA-100 °C-0.95	VTSA-70 °C-0.945	VTSA-70 °C-0.9	TSA-100 °C-0.9
O2 concentration after CPU	molO2/mol	0.0014	0.0027	0.035	0.035

). An additional O₂ purification unit would be necessary, but this was not evaluated in this work. Another solution would be to regenerate the adsorption step by a sweep of hot N₂ instead of hot air to reduce the O₂ content after the adsorption module. The N₂ would be then recovered at the retentate of the first membrane stage to be recycled again to the adsorption module. The use of N₂ for regeneration in addition to a well-managed adsorption cycle with a purge (to eliminate O₂ gas in the bed) would also reduce the potential oxidative degradation of the amine sorbent during regeneration at high temperature [21]. However, this modification would add complexity to the hybrid DAC and require an on-site N₂ storage system.

Overall, complete hybrid DAC presented a high cost of capture (>1700 €/tCO₂) and energy requirement (>45 GJ/tCO₂ of primary energy) in the cases studied. Compared to a previous study with similar assumptions (for process operation and cost evaluation), the cost of hybrid DAC was slightly higher than that of an adsorption VTSA process with steam regeneration at 100 °C, which presents a cost of capture of ca. 1700 €/tCO₂ [42]. Hybrid DAC is easier to operate due to dry regeneration with air in the adsorption step, which does not need steam for regeneration. Hybrid DAC consists of the adsorption pre-concentration step, which accounts for the major part of the energy requirement (>80%) and cost (>85%), and the membrane step and CPU, which account for the other part. This in accordance with the fact that the separation ratio of the adsorption step is much higher (about two order of magnitude) than that of the membrane step. Consequently, from a cost reduction perspective, it therefore seems preferable to focus on reducing the energy requirement and cost of the adsorption stage, whether by reducing energy consumption or the cost of the membrane module. Cost reduction measures should focus on the cost of the adsorber by innovating with low-cost materials, as well as on the cost of the monolith material by improving material transfer to increase productivity and the material’s capacity to capture CO₂ during one cycle. In addition, energy consumption could be reduced by using a monolith that requires less sensible heat by changing the support material or reducing its volume. Furthermore, an adsorbent that is hydrophobic while having good uptake performance with CO₂ would be preferable to avoid the cost of H₂O desorption. Increasing the capture rate of the membrane stage would also reduce the energy consumption and cost of the adsorption stage but would increase the energy consumption and cost of the membrane stage.