Memoria Investigaciones en Ingeniería, núm. 28 (2025). pp. 269-286
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ISSN 2301-1092 ISSN (en línea) 2301-1106 Universidad de Montevideo, Uruguay
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Direct Air Carbon Capture Using Metal-Organic Frameworks (MOFs):
Techno-Economic Performance of Temperature Vacuum Swing Adsorption
(TVSA) Systems
Captura directa de carbono en el aire mediante estructuras metalorgánicas
(MOF): Rendimiento técnico-económico de los sistemas de adsorción por
oscilación de temperatura y vacío (TVSA)
Captura direta de carbono no ar usando estruturas metal-orgânicas (MOFs):
desempenho técnico-econômico de sistemas de adsorção por oscilação de
temperatura e vácuo (TVSA)
Haider Ali
1
(*), Duraid Uddin
2
, Asad A. Naqvi
3
, Umair Naeem
4
, Nomaan Akhtar
5
, Saqib Shams
6
, Ali Karim
7
Recibido: 20/11/2024 Aceptado: 02/03/2025
Summary. - Direct Air Carbon Capture (DACC) technology is used to remove CO₂ directly from the atmosphere,
helping tackle climate change and excessive greenhouse gas emissions efficiently. In this study, a techno-economic
analysis of DACC has been carried out, including its working mechanisms, energy needs, and costs, as well as a
summary of the current research status. This research compares two leading metal-organic frameworks (MOFs)
MIL-101(Cr)-PEI-800 and mmen-Mg₂(dobpdc) focusing on their energy consumption, CO₂ adsorption, and cost.
This study investigates the performance of these MOFs in a temperature vacuum swing adsorption (TVSA) process,
which cyclically varies temperature and pressure to capture CO₂ and regenerate adsorbents. Among all materials,
mmen-Mg₂(dobpdc) achieves the best performance with a much higher capacity and a favourable nonlinear isotherm
shape, indicating significantly improved efficiency and lower energy input. DACC systems based on advanced MOFs
hold great promise for minimizing non-point source emissions and should thus be considered essential components of
a climate change mitigation strategy. This study contributes to direct future research and development toward more
efficient and cost-effective MOFs in DACC applications.
Keywords: Direct Air Carbon Capture, Temperature Vacuum Swing Adsorption, Metal-Organic Framework.
(*) Corresponding author.
1
Researcher, Department of Mechanical Engineering, NEDUET (Pakistan), haider.ali@neduet.edu.pk
ORCID iD: https://orcid.org/0000-0001-8242-3696
2
Researcher, Department of Mechanical Engineering, NEDUET (Pakistan), duraid_uddin2000@yahoo.com,
ORCID iD: https://orcid.org/0009-0009-4351-1162
3
Researcher, Department of Mechanical Engineering, NEDUET (Pakistan), asadakhter@neduet.edu.pk,
ORCID iD: https://orcid.org/0000-0001-6290-3115
4
Student, Department of Mechanical Engineering, NEDUET (Pakistan), umairnaeem139@gmail.com,
ORCID iD: https://orcid.org/0009-0003-0763-4081
5
Student, Department of Mechanical Engineering, NEDUET (Pakistan), nomaan.akhtar2@gmail.com,
ORCID iD: https://orcid.org/0009-0007-2969-675X
6
Student, Department of Mechanical Engineering, NEDUET (Pakistan), saqibshams200204@gmail.com,
ORCID iD: https://orcid.org/0009-0009-3932-6095
7
Student, Department of Mechanical Engineering, NEDUET (Pakistan), alikarimptcl@gmail.com,
ORCID iD: https://orcid.org/0009-0008-0495-0237
H. Ali, D. Uddin, A. A. Naqvi, U. Naeem, N. Akhtar, S. Shams, A. Karim
Memoria Investigaciones en Ingeniería, núm. 28 (2025). pp. 269-286
https://doi.org/10.36561/ING.28.16
ISSN 2301-1092 ISSN (en línea) 2301-1106 Universidad de Montevideo, Uruguay 270
Resumen. - La tecnología de Captura Directa de Carbono en el Aire (DACC) se utiliza para eliminar CO₂
directamente de la atmósfera, lo que contribuye a combatir eficientemente el cambio climático y las emisiones
excesivas de gases de efecto invernadero. En este estudio, se realizó un análisis tecnoeconómico de la DACC,
incluyendo sus mecanismos de funcionamiento, necesidades energéticas y costes, así como un resumen del estado
actual de la investigación. Esta investigación compara dos estructuras metalorgánicas (MOF) líderes MIL-101(Cr)-
PEI-800 y mmen-Mg₂(dobpdc)—, centrándose en su consumo energético, adsorción de CO₂ y coste. Este estudio
investiga el rendimiento de estas MOF en un proceso de adsorción por oscilación de temperatura y vacío (TVSA), que
varía cíclicamente la temperatura y la presión para capturar CO₂ y regenerar los adsorbentes. Entre todos los
materiales, mmen-Mg₂(dobpdc) alcanza el mejor rendimiento, con una capacidad mucho mayor y una forma de
isoterma no lineal favorable, lo que indica una eficiencia significativamente mejorada y un menor consumo de energía.
Los sistemas DACC basados en MOF avanzados son muy prometedores para minimizar las emisiones de fuentes no
puntuales y, por lo tanto, deberían considerarse componentes esenciales de una estrategia de mitigación del cambio
climático. Este estudio contribuye a orientar la investigación y el desarrollo futuros hacia MOF más eficientes y
rentables en aplicaciones DACC.
Palabras clave: Captura directa de carbono en aire, adsorción por oscilación de temperatura y vacío, estructura
metalorgánica.
Resumo. - A tecnologia de Captura Direta de Carbono no Ar (DACC) é usada para remover CO₂ diretamente da
atmosfera, ajudando a combater as mudanças climáticas e as emissões excessivas de gases de efeito estufa de forma
eficiente. Neste estudo, foi realizada uma análise técnico-econômica do DACC, incluindo seus mecanismos de
funcionamento, necessidades energéticas e custos, bem como um resumo do status atual da pesquisa. Esta pesquisa
compara duas estruturas metal-orgânicas (MOFs) líderes MIL-101(Cr)-PEI-800 e mmen-Mg₂(dobpdc) com foco
em seu consumo de energia, adsorção de CO₂ e custo. Este estudo investiga o desempenho dessas MOFs em um
processo de adsorção por oscilação de temperatura e cuo (TVSA), que varia ciclicamente a temperatura e a pressão
para capturar CO₂ e regenerar adsorventes. Entre todos os materiais, o mmen-Mg₂(dobpdc) atinge o melhor
desempenho com uma capacidade muito maior e uma forma isotérmica o linear favorável, indicando eficiência
significativamente melhorada e menor consumo de energia. Os sistemas DACC baseados em MOFs avançados são
bastante promissores para minimizar as emissões de fontes difusas e, portanto, devem ser considerados componentes
essenciais de uma estratégia de mitigação das mudanças climáticas. Este estudo contribui para direcionar futuras
pesquisas e desenvolvimentos em direção a MOFs mais eficientes e econômicos em aplicações DACC.
Palavras-chave: Captura direta de carbono no ar, adsorção por oscilação de temperatura e vácuo, estrutura metal-
orgânica.
H. Ali, D. Uddin, A. A. Naqvi, U. Naeem, N. Akhtar, S. Shams, A. Karim
Memoria Investigaciones en Ingeniería, núm. 28 (2025). pp. 269-286
https://doi.org/10.36561/ING.28.16
ISSN 2301-1092 ISSN (en línea) 2301-1106 Universidad de Montevideo, Uruguay 271
1. Introduction. - In recent years, there has been a continuous debate about humanity's contribution to the rise of
atmospheric greenhouse gases and the resulting global warming. While the exact causal relationship is still under
discussion, it is now widely accepted that human activities have significantly increased these gases in the atmosphere
[1]. Human activities generate greenhouse gases (GHGs) in the atmosphere, primarily carbon dioxide (CO2), methane
(CH4), chlorofluorocarbons (CFCs), and nitrous oxide (N2O). These gases significantly contribute to global warming,
which is one of the most pressing environmental threats facing humanity today. Among these GHGs, CO2 has the
largest impact, accounting for about 55% of the observed greenhouse effect and global warming. The emissions from
thermal power plants (TPPs) are a major source of CO2, as approximately 30% of the world's fossil fuel consumption
is dedicated to power generation, leading to substantial CO2 emissions [2]. The ongoing rise in atmospheric GHGs
concentrations is the most significant factor driving global warming. Since the onset of industrialization, the substantial
release of CO2 from human activities has played a major role in enhancing the greenhouse effect, becoming a pressing
environmental issue that requires urgent attention. Additionally, other gases, such as methane (CH4), nitrous oxide
(N2O), and ozone-depleting substances (ODSs), including fluorinated gases, also contribute to climate change [3], [4].
The current level of CO2 in the atmosphere is over 400 ppm and rising by about 2 ppm per year, mainly due to burning
fossil fuels [5]. The International Energy Agency reports that more than two-thirds of greenhouse gas emissions and
over 80% of carbon dioxide emissions stem from energy-related activities. The global CO2 emissions grew by an
average of 2.6% annually. Many studies have documented the statistics and detrimental effects of global warming,
revealing that around 60% of the planet is now facing unprecedented high temperatures each year [6].
Currently, the most prevalent techniques for capturing CO2 from gas mixtures include absorption, membrane
separation, and low-temperature CO2 capture. Absorption typically involves using solvents that selectively absorb CO2
from flue gases, making it effective for large-scale industrial applications. Membrane separation utilizes selective
permeability to separate CO2 from other gases, offering a more energy-efficient and compact alternative. Low-
temperature CO2 capture, on the other hand, leverages cryogenic processes to condense and separate CO2 from gas
streams, which can be particularly advantageous in high-purity applications. Each of these methods presents unique
advantages and challenges, making them suitable for different operational contexts and carbon capture goals [7].
Fossil fuels will continue to be a major energy source, so we need technologies to capture and store CO2 directly from
the air, which is known as Direct Air Capture (DAC). Traditional carbon capture methods target specific sources like
power plants, but DAC can capture CO2 from any location, making it more versatile. There has been research into
various DAC methods, including using solutions like sodium hydroxide [8]. However, these can be expensive and
energy intensive.
More recent studies have focused on using solid materials called Metal-Organic Frameworks (MOFs), which are more
efficient in capturing CO2. Metal-organic frameworks (MOFs) offer numerous significant benefits that make them
highly attractive for a range of applications, particularly in gas separation, storage, and catalysis. One of their standout
features is their exceptionally high surface area, which enhances their capacity for gas adsorption and storage, making
them efficient materials for capturing gases like CO2 and hydrogen. Additionally, the tunability of MOFs allows for
easy modification of their structural and chemical properties by altering the metal ions or organic linkers used in
synthesis, enabling the design of materials tailored to specific applications, such as selective gas separation. Their
highly porous structure facilitates efficient gas diffusion and adsorption, which is crucial for processes like carbon
capture and air purification. Furthermore, their lightweight nature is advantageous in applications where weight is a
concern, such as gas storage for transportation [7], [9]. Two promising MOFs are MIL-101(Cr)-PEI-800 and mmen-
Mg2(dobpdc), which are known for their high capacity to adsorb CO2 and their stability [8].
Solid adsorbents like MOFs can capture CO2 through processes that use temperature and pressure changes. Studies
have shown that these materials can be effective and potentially less costly than liquid solutions [10]. The research
also explores different designs to improve efficiency, such as using monolith structures, which reduce pressure drops
and increase mass transfer rates. Steam can be used as a stripping agent to regenerate the adsorbents, and some
experiments have shown that certain adsorbents can withstand repeated cycles of adsorption and desorption using
steam [11].
This paper evaluates the economic and energy performance of DAC using MIL-101(Cr)-PEI-800 and mmen-
Mg2(dobpdc) in a temperature vacuum swing adsorption (TVSA) process. The study aims to optimize the conditions
for DAC and guide future materials development to improve performance. Numerical models are used to analyze the
effect of air and steam velocity on the system's CO2 capture efficiency.
H. Ali, D. Uddin, A. A. Naqvi, U. Naeem, N. Akhtar, S. Shams, A. Karim
Memoria Investigaciones en Ingeniería, núm. 28 (2025). pp. 269-286
https://doi.org/10.36561/ING.28.16
ISSN 2301-1092 ISSN (en línea) 2301-1106 Universidad de Montevideo, Uruguay 272
2. Methodology. - The study focuses on Direct Air Carbon Capture (DACC) technology using solid adsorbents and
emphasizes the importance of material selection in its performance and cost-effectiveness, as illustrated in Figure I.
Two metal-organic frameworks (MOFs), MIL-101(Cr)-PEI-800 and mmen-Mg2(dobpdc), are evaluated for their CO2
capture capabilities. These MOFs are crucial because they offer high surface areas and tunable pore structures that
enhance CO2 adsorption, making them suitable for DACC applications. The study explores how these materials are
used in monolithic contactors, structures designed to maximize the contact surface between the adsorbent and air.
These contactors play a vital role in improving CO2 capture efficiency by reducing pressure drops and increasing the
adsorption rate, which leads to better overall performance in capturing atmospheric CO2.
Figure I. Methodology of Study
The effectiveness of monolithic contactors is highlighted, as they allow for more efficient airflow and CO2 adsorption,
making them a viable option for large-scale DACC operations. In terms of cost evaluation, the study examines the
energy demands and overall expenses of implementing these MOFs in a DACC system. mmen-Mg2(dobpdc) emerges
as the more effective and cost-efficient material due to its higher CO2 adsorption capacity and favorable non-linear
isotherm behavior, which allows it to perform better under varying conditions. This material also requires less energy
for regeneration compared to MIL-101(Cr)-PEI-800, making it a superior option for reducing CO2 emissions. Overall,
mmen-Mg2(dobpdc) demonstrates better performance and economic viability, positioning it as a promising material
for future DACC applications.
A TVSA-based DAC system is presented by Sinah [12] to compare the performance of two MOF sorbents, namely,
MIL-101-(Cr)-PEI800 and mmen-Mg2(dobpdc). The monolith channel/ as shown in Figure II, through which the
reactant, i.e., air flow, is assumed to be cylindrical for analysis. Each of these channels is coated with an absorbent
film. The characteristics of the monolith channel are presented in Table I.
Table 1: Parameters of Monolith Channel
Parameters of Monolith Channel [12]
Absorbent film Thickness
60 microns
Diameter of Monolith Channel
1270 microns
Cell Density
400 cpsi
Figure II. Monolith channel [12]
Identify Key
Material MOF Selection Analyzing
Monolitic
Contractor
Evaluate MOF
Performance
Techno
Economic
Analysis
Energy demand
and Cost
Identify Best
performing
MOF
H. Ali, D. Uddin, A. A. Naqvi, U. Naeem, N. Akhtar, S. Shams, A. Karim
Memoria Investigaciones en Ingeniería, núm. 28 (2025). pp. 269-286
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ISSN 2301-1092 ISSN (en línea) 2301-1106 Universidad de Montevideo, Uruguay 273
The process (as illustrated in Figure 3) consists of the following five steps.
1. Air at ambient conditions (298K, 1 atm., 25% Relative Humidity) enters the channel. The CO2 concentration in
the air is assumed to be 400 ppm. Adsorption of CO2 by the film begins in this step.
2. The second step involves the evacuation of air from the channel. This is done mainly to prevent the amine groups
in the MOFs from being oxidized at high temperatures. The channel at the front end is closed and is evacuated by
the use of a vacuum pump. The step continues until the oxygen concentration falls below 4%.
3. The third step involves pressurizing the channel to prevent any backflow of air (oxygen) from the rear end. This
is done by closing the rear end and passing saturated steam at 1 atm through the front end.
4. Desorption occurs in step four by temperature swing. The rear end of the channel is opened, and saturated steam
at 1 atm is fed to the channel from the front end. The steam condenses on the surface of the absorbent, increasing
its temperature.
5. The last step involves cooling the system down to 348K from the desorption temperature of 373K. This is done to
prevent the oxidative degeneration of the amine groups in the MOF. The vacuum pump is used for cooling using
evaporating the water vapours out of the channel. As in the evacuation step, the front of the channel is closed, and
pressure is dropped at the rear.
Figure III. Process Flow of TVSA.
3. Background. -
3.1 Air Capture System. - The research by J. K. Stolaroff et al. [13] explores the feasibility of capturing carbon
dioxide (CO₂) directly from ambient air using a sodium hydroxide (NaOH) spray-based system. This approach is
distinct from traditional methods that capture CO₂ from large, stationary sources such as power plants. The primary
advantage of capturing CO₂ from ambient air is the potential to address emissions from diffuse sources and even past
emissions. This can be particularly useful in achieving significant reductions in atmospheric CO₂ levels to mitigate
climate change effects [14].
3.1.1 Process Overview. -
System Description. - The system involves spraying a solution of NaOH into the air, where it reacts with CO₂ to form
sodium carbonate (Na₂CO₃). The CO₂-laden solution is then processed to regenerate NaOH and capture pure CO₂,
which can be sequestered or utilized in various applications.
Contractor Design. - The contactor is the component where air interacts with the NaOH solution to absorb CO₂.
Different designs for contactors include convection towers, open pools, and packed scrubbing towers [15]. This study
focuses on a spray-based contractor.
Spray-Based Contactor: The system utilizes fine spray nozzles to create a mist of NaOH solution that increases
the contact surface area between the air and the absorbing liquid. A critical aspect of the design is managing drop
coalescence, which can reduce the efficiency of CO₂ absorption [16].
The description of Direct Air Capture using the wet scrubbing method is given in Table II.
H. Ali, D. Uddin, A. A. Naqvi, U. Naeem, N. Akhtar, S. Shams, A. Karim
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ISSN 2301-1092 ISSN (en línea) 2301-1106 Universidad de Montevideo, Uruguay 274
Aspect
Details
CO2 Capture Method
Direct capture from ambient air using wet scrubbing
Absorbent Used
Sodium hydroxide (NaOH)
Recovery Process
Two-step precipitation and crystallization followed
by customization with sodium tri-titanate
Energy Requirement
Approximately 50% less high-grade heat than
conventional; lower maximum temperature required
Contactor Design
Packed scrubbing towers or open towers with NaOH
spray
Advantages
Reduces CO2 systematically from dispersed
emissions, substantial cost reduction, pure CO2
stream generated
Table II. DAC using wet scrubbing method [17]
3.1.2 Temperature Swing Adsorption. - Temperature Vacuum Swing Adsorption (TVSA) combines temperature and
vacuum swings, which significantly lowers the energy required for the desorption process compared to TSA, which
relies solely on heating. This makes TVSA more energy efficient. The comparison of different CO2 capture methods
is given in Table IV.
Method
Process
Description
Efficiency
Disadvantages
Key
References
TVSA
(Temperature
Vacuum Swing
Adsorption)
Involves the
adsorption of CO₂
at lower
temperatures and
desorption at
higher
temperatures under
vacuum
conditions.
High
Requires precise
temperature
control and
vacuum systems.
[18], [19]
TSA
(Temperature
Swing Adsorption)
Adsorption of CO₂
occurs at ambient
temperature and
desorption at
elevated
temperatures.
Moderate to
High
Higher energy
consumption due
to heating
requirements.
[20], [21]
Capture from
Ambient Air Using
Sodium Hydroxide
Spray
Involves spraying
a sodium
hydroxide solution
to capture CO₂
from ambient air,
forming sodium
carbonate.
Variable
Chemical
handling and
disposal issues,
lower efficiency
for high CO₂
concentrations.
[13]
Electrochemical
Conversion
Electrochemical
reduction of CO2
to valuable
products using
electrical energy
Moderate to
high
Complex catalyst
development,
high energy
consumption,
scalability
challenges
[22]
Table III. Different CO2 Capture Methods.
The addition of vacuum swing in TSA reduces the desorption time, leading to shorter cycle times and higher
throughput. This efficiency can result in lower operational costs and improved overall process economics. TVSA
systems typically produce high-purity CO₂ streams due to the effective desorption facilitated by vacuum. This high
purity can be advantageous for subsequent CO₂ utilization or sequestration. It has a lower environmental impact as it
requires less water compared to the NaOH spray method, which involves significant water use and potential chemical
H. Ali, D. Uddin, A. A. Naqvi, U. Naeem, N. Akhtar, S. Shams, A. Karim
Memoria Investigaciones en Ingeniería, núm. 28 (2025). pp. 269-286
https://doi.org/10.36561/ING.28.16
ISSN 2301-1092 ISSN (en línea) 2301-1106 Universidad de Montevideo, Uruguay 275
handling issues. This makes the process more sustainable and environmentally friendly. TVSA is more cost-effective,
especially for large-scale applications, due to its lower energy requirements and efficient operation. While initial capital
costs for vacuum equipment may be higher, the long-term savings in operational costs make it a better economic
choice.
Temperature Swing Adsorption (TSA) is a cyclic process used for the capture of CO2 and other gases; details are given
in Table 5. It leverages temperature changes to adsorb and desorb gases from solid adsorbents.
i. Adsorption. - During the adsorption phase, a gas mixture containing CO2 is passed through an adsorbent bed.
Materials like zeolites, activated carbons, and MOFs are used due to their high surface area and selective adsorption
properties. The CO2 molecules adhere to the surface of the adsorbent at lower temperatures, while other gases pass
through the bed. This selective adsorption is influenced by the adsorbent's affinity for CO2 and its operating temperature
[23], [24].
ii. Heating. - Once the absorbent bed is saturated with CO2, the heating phase begins. The bed is heated, typically
using steam or other heat sources, to increase the temperature. This heat causes the CO2 molecules to desorb from the
adsorbent surface. The efficiency of this step depends on the thermal properties of the adsorbent and the design of the
heating system. Effective heat integration can significantly lower the energy penalty associated with this step [23],
[24].
iii. Desorption. - As the temperature rises, the CO2 is released from the adsorbent. This desorption process generates
a concentrated CO2 stream, which can be captured and stored. The purity and recovery rate of CO2 depend on the
adsorbent material and the operational parameters of the TSA cycle. MOFs, for example, have shown promising results
due to their tunable properties and high selectivity for CO2 [23], [24].
iv. Cooling. - After desorption, the adsorbent bed is cooled down to its initial temperature, readying it for the next
cycle. Cooling can be achieved through heat exchange with ambient air or other cooling media. Efficient cooling
ensures that the adsorbent retains its adsorption capacity for subsequent cycles [23], [24].
Step
Description
1. Adsorption
CO2 laden gas is passed through the adsorbent bed, where CO2 is
selectively adsorbed at a lower temperature. The bed typically contains
materials like zeolites, activated carbons, or metal-organic frameworks
(MOFs)
2. Heating
The adsorbent bed is heated to desorb the captured CO2. This step
increases the temperature of the bed to release the CO2, making the
adsorbent ready for the next cycle
3. Desorption
CO2 is released from the adsorbent material due to the increased
temperature. This step produces a concentrated stream of CO2, which can
be captured for further use or storage
Table V. TSA Process Steps [25]
3.2 Evaluating Metal-Organic Frameworks (MOFs) for CO2 Capture. - Two MOFs, Zn4O(BTB)2 (MOF-177)
and Mg2(dobdc) (Mg-MOF-74), were evaluated. Mg-MOF-74 demonstrated a higher working capacity and selectivity
for CO2 over N2, which is critical for efficient CO2 capture [26].
The study analyzed CO2 adsorption isotherms at various temperatures, revealing that Mg2(dobdc) had superior
performance, including a high working capacity of 17.6 wt% at 200°C. The presence of strong CO2 adsorption sites
in Mg-MOF-74 was crucial for its effectiveness in TSA processes [26].
3.3 Electrochemical Conversion. - The electrochemical conversion of CO2 involves using electrical energy to drive
chemical reactions that transform CO2 into valuable products such as hydrocarbons, alcohols, and other chemicals.
This process typically takes place in an electrochemical cell consisting of a cathode, an anode, and an electrolyte [22],
[27].
i. Cathode Reactions. - At the cathode, CO2 molecules are reduced to form products such as carbon monoxide
(CO), formate, methanol, methane, ethylene, and other hydrocarbons. The specific product depends on the catalyst
used and the operating conditions, such as potential and electrolyte composition.
H. Ali, D. Uddin, A. A. Naqvi, U. Naeem, N. Akhtar, S. Shams, A. Karim
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ISSN 2301-1092 ISSN (en línea) 2301-1106 Universidad de Montevideo, Uruguay 276
The reduction of CO2 involves multiple electron and proton transfer steps, making it a complex process. Effective
catalysts are crucial to enhance selectivity and efficiency towards desired products [22], [27].
ii. Anode Reactions. - At the anode, water is typically oxidized to produce oxygen gas (O2) and protons (H+).
This oxidation reaction provides the necessary protons and electrons for the reduction reactions at the cathode.
The overall efficiency of the process depends on the ability of the anode to facilitate the oxygen evolution reaction
(OER) efficiently [22], [27].
iii. Electrolyte. - The electrolyte facilitates the movement of ions between the cathode and anode. It can be an
aqueous solution, solid oxide, or ionic liquid, depending on the specific electrochemical system.
The choice of electrolyte affects the conductivity, stability, and overall efficiency of the electrochemical cell [22],
[27].
iv. Metallic Catalysts. - Transition metals such as copper, silver, gold, and zinc are commonly used as catalysts
for CO2 reduction. Copper, in particular, is known for its ability to produce a wide range of hydrocarbons and alcohols.
Alloying and modifying these metals with other elements can enhance their catalytic properties and product
selectivity [22], [27].
v. Metal-Organic Frameworks (MOFs). - MOFs are a class of porous materials that have shown promise as
catalysts for CO2 electroreduction. Their high surface area and tunable chemical environment make them suitable for
optimizing catalytic activity and selectivity.
MOFs can be functionalized with various active sites to target specific reduction pathways [28].
vi. Electrocatalyst Optimization. - Research focuses on optimizing the structure, composition, and morphology
of electrocatalysts to improve their performance. This includes developing nanostructured catalysts, bimetallic
systems, and hybrid materials that combine the advantages of different components [28].
3.4 Mathematical Modelling of the TVSA system. - The following assumptions were made to develop the
mathematical model:
Air is considered to have oxygen and nitrogen components in addition to the CO2 (and 25% relative humidity),
and the saturated steam is pure.
Ideal gas law and ideal mixtures are assumed for the non-condensable components [29].
Temperature and concentration variations are neglected in the radial direction in the adsorbent film and monolith
wall leading to a lumped model in the radial coordinate for these model elements [30].
Adsorbent film thickness is uniform in the axial direction [31].
During the desorption step, condensed water does not penetrate inside the MOF pores due to the high flow rate of
desorbed CO2 from the MOF pores in the opposing direction. Thus, heat is conducted into the MOF and wall and
is not transferred by diffusion of steam within the MOF phase following steam condensation [32], [33].
Heat loss from the channel is negligible during all steps of the cycle
The pressure drop across the channel is given by the Hagen Poiseuille equation:
 
(1)
where, = length of the channel
= velocity of gas inside the channel
= gaseous viscosity
= Channel Inner Radius
The other source of pressure drop is due to drag on the system, which is assumed to be negligible as compared to
pressure drop by Hagen- Poiseuille Equation [eqn. (1)].
The CO2 absorption rate is approximated by the linear driving force model as given by:

 󰇛
 󰇜
(2)
H. Ali, D. Uddin, A. A. Naqvi, U. Naeem, N. Akhtar, S. Shams, A. Karim
Memoria Investigaciones en Ingeniería, núm. 28 (2025). pp. 269-286
https://doi.org/10.36561/ING.28.16
ISSN 2301-1092 ISSN (en línea) 2301-1106 Universidad de Montevideo, Uruguay 277
Where,  = absorbed CO2 concentration

 = equilibrium concentration of CO2
= overall mass transfer coefficient
The mass transfer coefficient is calculated by the method proposed by A Sinha [12], which gives the final equation
as:


(3)
where, = convective heat transfer coefficient of moist air
= Molar mass of water vapor
 = Specific heat of moist air
= Molar mass of air
 = Log Mean Mole Fraction
 = Lewis number of H2O
 = Log mean mole fraction
  
󰇛
󰇜
(4)
Where,  = mole fraction of the non-condensable gases at the gas film interface
 = mole fraction in the bulk flow
The concentration at the interface is assumed to be in equilibrium with pure liquid water and thus estimated using the
Antoine equation [eqn. (6)]:


(5)


(6)
where,
= saturation concentration of water vapor in the MOF channel interface
 = Antoinne constants
The heat of absorption of CO2 is determined using the Clausius−Clapeyron equation.


(7)
The heat of absorption of CO2 is calculated at 25°C, 50°C and 75°C
The system design specifications and mass and heat transfer properties are tabulated in Table VI and Table VII,
respectively.
Name
Symbol
Value
Unit
Air thermal conductivity
kg
0.0257

Air heat capacity
Cp,g
1003

Air density
ρg
1.1839

Adsorbent Thermal Conductivity
kads
0.32

Adsorbent Heat Capacity
Cp,ads
892.5

Adsorbent Density
ρads
500

Wall Thermal Conductivity
kwall
1.6

Wall Heat Capacity
Cp,wall
840

Wall density
ρwall
2050

Antoine Constants

5.2,1733.9, -39.5
-
Table VI. Properties of the TVSA CO2 Capture System [12].
H. Ali, D. Uddin, A. A. Naqvi, U. Naeem, N. Akhtar, S. Shams, A. Karim
Memoria Investigaciones en Ingeniería, núm. 28 (2025). pp. 269-286
https://doi.org/10.36561/ING.28.16
ISSN 2301-1092 ISSN (en línea) 2301-1106 Universidad de Montevideo, Uruguay 278
Parameter
Value
(m)
0.000016
h (W/m2-K)
75
Tambient
298
CCO2o (mol/m3)
0.016
Cinerto (mol/m3)
40.88
H (J/mol)
55000
H (J/mol)
70000
A1 (m)
0.00063
A2 (m)
0.00052
Table VII. Heat and Mass Transfer Properties [12]
3.5 Estimating Energy Requirements
1) Electrical energy is required for the running of the fan. Higher air flow rates cause a larger pressure drop
across the channel.
2) Energy required by the vacuum pump to decrease the pressure inside the channel.
3) Energy is required to provide sensible heat to the adsorbent.
4) Use of vacuum pumps to lower the partial pressure of water vapour.
The efficiency of the pump is considered to be 85 % [12]. The equations for the energy requirement for the various
components are given in Table VII.
Components
Energy requirement (Joules per mole of CO2)
Electrical energy for blowers
E1 = 
Adsorbent sensible heat
E2 
 󰇛
 󰇜



Monolithic wall sensible heat
E3 = 
 󰇛
 󰇜



CO2 desorption heat
E4 = H
Electrical energy for vacuum
Pump
󰇛 󰇜

Energy in uncondensed steam
󰆒
󰇛 󰇛󰇜󰇜

 


Table VIII. Energy Requirements [12]
3.6 Economic Modelling of the System
O&M cost of the device (includes energy, loading and unloading of a sorbent (NO&M))
Scrap value of the sorbent at the end of its lifetime (NS)
NS = Sorbent Price Vs + Installation cost Is
The amount spent on the hardware is taken into consideration; hence, the running expense is the capital cost of
the plant NBoP.
For NPV of a DAC system:
 󰇛  󰇜
(8)
The net present value of the system has to be zero or greater than zero at some point during the operation.
To find tlife, the first derivative of the NPV equation concerning time must be zero:
 
  󰇛 󰇜
(9)
H. Ali, D. Uddin, A. A. Naqvi, U. Naeem, N. Akhtar, S. Shams, A. Karim
Memoria Investigaciones en Ingeniería, núm. 28 (2025). pp. 269-286
https://doi.org/10.36561/ING.28.16
ISSN 2301-1092 ISSN (en línea) 2301-1106 Universidad de Montevideo, Uruguay 279
Revenue generated per unit of time can be calculated as,
󰇛󰇜
 

 (10)
where P is the market price of carbon dioxide per unit mass, C0 is the initial capacity of sorbent (the amount of CO2
captured per cycle), and tcycle is the duration of one loading/unloading cycle. D is the time constant of the sorbent
capacity degradation, and M is a time constant that accounts for the time value of money. The costs of MIL-101(Cr)-
PEI-800 and mmen-Mg2 (dobpdc) are taken as $15/kg and $50/kg, respectively taken from local market survey.
In summary, achieving economic viability for a Direct Air Capture (DAC) device necessitates meeting the conditions
outlined in Equations (8), (9) and (10). While equation (9) allows for the calculation of the device's lifetime, a
positive value for tlife does not automatically ensure a positive Net Present Value (NPV).
4. Results and Discussions. - The flow of CO2 through the material is shown in Figure 4, which shows how quickly
CO2 starts to pass through the material without being captured. For MIL-101(Cr)-PEI-800, CO2 breaks through earlier,
meaning this material gets saturated faster and starts letting CO2 through sooner, while for mmen-Mg2(dobpdc), CO2
breaks through later, indicating this material can capture more CO2 before it gets saturated. At a time, step of
approximately 4200s, the concentration stays constant since most of the CO2 is adsorbed on the surface by the
adsorbent.
Figure IV. CO2 breakthrough curve.
The holding time of CO2 for each material is shown in Figure 5. From where one can conclude that since mmen-
Mg2(dobpdc) has a higher capacity of approximately 2.9 mmol/g, so it can hold more CO2 while MIL-101(Cr)-PEI-
800 has a lower capacity of approximately 1.2 mmol/g, so it holds less CO2. In simple terms, mmen-Mg2(dobpdc) is
better at capturing and holding more CO2 for a longer time compared to MIL-101(Cr)-PEI-800.
Figure V. Adsorbed average CO2 concentration.
H. Ali, D. Uddin, A. A. Naqvi, U. Naeem, N. Akhtar, S. Shams, A. Karim
Memoria Investigaciones en Ingeniería, núm. 28 (2025). pp. 269-286
https://doi.org/10.36561/ING.28.16
ISSN 2301-1092 ISSN (en línea) 2301-1106 Universidad de Montevideo, Uruguay 280
Energy requirements of the both MOFs mmen-Mg2 (dobpdc) and MIL-101 (Cr)-PEI-800 are given in Figure VI and
Figure VII, respectively. Since the thermal efficiency was taken to be 85% [12], the minimum primary combustion
energy requirements for the MIL-101(Cr)-PEI-800 and mmen-Mg2 (dobpdc) adsorbents are around 0.150 MJ/mole
and 0.125 MJ/mole.
Figure VI. Energy requirements for mmen-Mg2 adsorbent.
Figure VII. Energy requirements for MIL-101 (Cr)-PEI-800 adsorbent.
The cost comparison of both MOFs is shown in Figure 6. The curve shows the cost components for MIL-101(Cr)-PEI-
800 and mmen-Mg-2(dobpdc), indicating that mmen-Mg-2(dopdc) generally incurs lower costs in key areas such as
steam and blower operation. Specifically, MIL-101(Cr)-PEI-800 shows higher costs for blower Opex and steam,
suggesting it is less economical in operational expenditure. While both materials have similar costs for monoliths and
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Energy Requirement in MJ/mol
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
Blower
Energy (E1) Adsorbent
Sensible heat
(E2)
Monolithic
wall sensible
heat (E3)
Energy due
to CO2
desorption
(E4)
Vacuum
pump
consumption
(E5)
Minimum
Primary
Combustion
Energy
requirements
(E1+…+E5)
Energy due
to
uncondensed
steam (E-6)
Energy requirements in MJ/mol
H. Ali, D. Uddin, A. A. Naqvi, U. Naeem, N. Akhtar, S. Shams, A. Karim
Memoria Investigaciones en Ingeniería, núm. 28 (2025). pp. 269-286
https://doi.org/10.36561/ING.28.16
ISSN 2301-1092 ISSN (en línea) 2301-1106 Universidad de Montevideo, Uruguay 281
vacuum pump Capex, mmen-Mg-2(dobpdc) offers cost savings in most categories, highlighting it as the more cost-
effective option for these processes.
Figure VIII. Cost comparison between both adsorbents.
The Figure 7 looks at how the cost of the Direct Air Capture (DAC) process changes with different steam velocities
for two materials MIL-101(Cr)-PEI-800 and mmen-Mg2(dobpdc). The curve shows that cost is the strong function of
steam velocity. For MIL-101(Cr)-PEI-800, the cheapest operation is found at a steam velocity of 0.04 m/s while for
mmen-Mg2(dobpdc), the lowest cost is at a steam velocity of about 0.06 m/s.
The study performed an analysis to find the best adsorption and desorption times by varying certain parameters and
keeping the air velocity constant at 3 m/s. For this analysis, the steam velocity was kept at the optimal points identified
(0.04 m/s for MIL-101(Cr)-PEI-800 and 0.06 m/s for mmen-Mg2(dobpdc)). This helps to optimize the DAC process
for cost and efficiency.
Figure IX. Total DAC Cost v/s Steam velocity.
MOF-based adsorbents, such as mmen-Mg₂(dobpdc), can potentially reduce energy demands and operational costs in
DACC systems. However, transitioning these materials from lab-scale success to industrial deployment requires
addressing unresolved challenges. These include energy-intensive synthesis (e.g., solvent reliance, high-temperature
$-
$5.00
$10.00
$15.00
$20.00
$25.00
$30.00
Blowers Steam Vacuum
Pump Opex Monolith Adsorbent Blower Vacuum
Pump
Capex
MIL-101(Cr)-PEI-800
mmen-Mg-2(dopdc)
H. Ali, D. Uddin, A. A. Naqvi, U. Naeem, N. Akhtar, S. Shams, A. Karim
Memoria Investigaciones en Ingeniería, núm. 28 (2025). pp. 269-286
https://doi.org/10.36561/ING.28.16
ISSN 2301-1092 ISSN (en línea) 2301-1106 Universidad de Montevideo, Uruguay 282
activation), mechanical brittleness during pelletization (critical for industrial reactor integration), and stability under
cyclic TVSA conditions, where thermal degradation or moisture sensitivity could compromise long-term performance.
It also requires advancements in scalable synthesis methods like continuous flow reactors [34]. A thorough
understanding of how MOFs integrate into different CO2 capture technologies and regeneration processes [35], and
the effective use of computational tools for material design and performance prediction under realistic operating
conditions [36]. Addressing these multifaceted challenges is crucial for transitioning the promise of MOFs into
practical, large-scale solutions for carbon capture.
5. Conclusion. - This study investigates the performance of a TVSA (Temperature Vacuum Swing Adsorption) process
for Direct Air Capture (DAC) of CO2 using two advanced materials, MIL-101(Cr)-PEI-800 and mmen-Mg2(dobpdc).
The latter material demonstrated superior CO2 adsorption capacity (2.9 mmol/g compared to 1.2 mmol/g for MIL-
101(Cr)-PEI-800). Key optimizations included air and steam flow rates, with 3 m/s airflow and steam velocities of
0.04 m/s for MIL-101(Cr)-PEI-800 and 0.06 m/s for mmen-Mg2(dobpdc). Energy requirements were minimized to
below the CO2 combustion energy, and costs were estimated at $77-142 per tonne for MIL-101(Cr)-PEI-800 and $64-
194 per tonne for mmen-Mg2(dobpdc). Future improvements could include using solar energy and enhancing material
stability, aiming to further optimize energy efficiency and reduce costs in scalable DAC solutions. The thickness of
the adsorbent film is crucial in determining energy costs, as a thicker film captures more CO2, thereby reducing the
energy required for the desorption step. Maintaining a normal air flow rate is essential, since higher air flow rates
would lead to CO2 bypassing the adsorbent without being captured. It was observed that increasing air velocity beyond
3 m/s does not enhance adsorption. Additionally, utilizing a solar thermal cycle to produce steam can further decrease
the system's overall energy cost.
On the other hand, the economic modelling of the Direct Air Capture (DAC) system includes the operation and
maintenance (O&M) costs, which cover energy and the loading/unloading of the sorbent (NO&M), and the scrap value
of the sorbent at the end of its lifetime (NS). The scrap value (NS) is calculated as the sum of the sorbent price (Vs) and
the installation cost (Is). The hardware cost is also considered, making the capital cost of the plant (NBoP) part of the
running expenses. The net present value (NPV) of the DAC system is determined by eq (8). For the system to be
economically viable, the NPV must be zero or greater at some point during operation. To find the lifetime (tlife) of the
system, the first derivative of the NPV equation with respect to time is set to zero in eq (9). Key takeaways include
that the NPV starts negatively due to the initial sorbent cost, increases with revenue from captured CO2, and tlife is the
point where the NPV reaches its maximum. The revenue generated per unit of time is calculated using eq (10).
The economic analysis indicates that MOFs can significantly reduce storage costs compared to traditional methods.
The study evaluated the lifecycle costs of MOF-based storage systems and found that they offer competitive advantages
in terms of both capital and operational expenses. This makes MOFs a cost-effective option for carbon capture.
Acknowledgment. - The Authors acknowledge the support provided by Sindh Higher Education Commission through
the project SRSP/NPS SC. & Tech-09/314/2023-24.
H. Ali, D. Uddin, A. A. Naqvi, U. Naeem, N. Akhtar, S. Shams, A. Karim
Memoria Investigaciones en Ingeniería, núm. 28 (2025). pp. 269-286
https://doi.org/10.36561/ING.28.16
ISSN 2301-1092 ISSN (en línea) 2301-1106 Universidad de Montevideo, Uruguay 283
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Memoria Investigaciones en Ingeniería, núm. 28 (2025). pp. 269-286
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ISSN 2301-1092 ISSN (en línea) 2301-1106 Universidad de Montevideo, Uruguay 286
Author contribution:
1. Conception and design of the study
2. Data acquisition
3. Data analysis
4. Discussion of the results
5. Writing of the manuscript
6. Approval of the last version of the manuscript
MMUZS has contributed to: 1, 2, 3, 4, 5 and 6.
AT has contributed to: 1, 2, 3, 4, 5 and 6.
Acceptance Note: This article was approved by the journal editors Dr. Rafael Sotelo and Mag. Ing. Fernando A.
Hernández Gobertti.