Modelling and MATLAB-Based Optimisation of Carbon Dioxide Adsorption Using Zn-MOF-5 ^†

Abstract

The growing concern over greenhouse gas emissions has prompted the need for efficient carbon dioxide (CO₂) capture technologies. This study focuses on simulating CO₂ adsorption using a zinc-based metal–organic framework (Zn-MOF-5). The primary aim is to develop and refine a robust MATLAB-based approach for equilibrium and kinetic modelling using the Linear Driving Force (LDF) model and Langmuir isotherm, capable of accurately predicting CO₂ adsorption performance under varying operational conditions. By employing advanced computational methods, this research seeks to streamline the process design and enhance the feasibility of sustainable CO₂ capture solutions. Excel was used for statistical analysis and validation, while MATLAB R2025a was utilised for equilibrium and kinetic modelling using the LDF model and the Langmuir isotherm. The independent effects of temperature, pressure, and flow rate were evaluated using the variable effect method. The study found a significant negative association between temperature and CO₂ uptake, consistent with the exothermic nature of the adsorption process. Pressure had a significant impact on adsorption, whereas flow rate had little effect within the investigated range. The simulated CO₂ uptake (21.196 mmol/g) closely matched the experimental data (21.07 mmol/g) with a 0.59% variance, validating the model’s trustworthiness. The research shows that Zn-MOF-5 has a strong adsorption potential and that simulation tools can significantly minimise experimental costs and time. Furthermore, it underscores the potential of simulation tools to significantly reduce experimental costs and time, paving the way for more efficient and effective carbon capture solutions. This initiative not only contributes to optimising process design but also promotes sustainable practices in addressing global CO₂ emissions. By contributing to process optimisation, this study aligns with the United Nations Sustainable Development Goal (SDG) 13: Climate Action, which emphasises the urgent need for innovative solutions to combat climate change and its impacts. Furthermore, it promotes sustainable practices to address global CO₂ emissions, thereby supporting broader efforts for environmental sustainability.

1. Introduction

Environmental damage caused by pollution of land, water, and air have been colossal since the Industrial Revolution. Its most observable impact is air pollution, which has glaciers [1]. Atmospheric carbon dioxide (CO₂) concentrations have increased steadily over the past decades due to anthropogenic emissions [2]. Recent global measurements indicate that atmospheric CO₂ levels exceeded 422 ppm in 2024, with seasonal peaks approaching 430 ppm, representing the highest concentrations recorded in the modern observational record. Projections suggest that, without significant emission reductions, atmospheric CO₂ concentrations could exceed 550–600 ppm by 2100 [1], highlighting the urgent need for effective carbon mitigation strategies.

Traditional CO₂ capture from power plants relies on amine absorption, particularly monoethanolamine (MEA). Although effective, this process is energy-intensive and costly [2,3]. As a result, adsorption-based methods such as pressure swing adsorption (PSA), vacuum swing adsorption (VSA), and temperature swing adsorption (TSA) are being explored due to their lower energy requirements. However, their efficiency largely depends on the performance of the adsorbent material [4]. Captured CO₂ can be utilised as a carbon feedstock to produce fine chemicals, transportation fuels, polymers, pharmaceuticals, beverages, and various inorganic compounds [1,5,6].

Metal–organic frameworks (MOFs) have attracted significant attention for CO₂ capture and catalytic conversion due to their high surface areas and tunable structures [4]. These materials exhibit promising adsorption properties for CO₂ at moderate temperatures, with structural features such as pore size and shape controlled by the choice of metal ions and organic ligands [1]. Among them, Zn-MOF-5 is particularly notable for CO₂ adsorption, with performance strongly dependent on synthesis conditions, activation, and handling, which affect surface area, pore volume, and adsorption behaviour [7]. Accurate modelling of Zn-MOF-5 adsorption is therefore essential for assessing its potential in scalable CO₂ capture systems [1,8].

Experimental investigation of CO₂ adsorption under varying operating conditions is often time-consuming, costly, and limited in its ability to systematically evaluate multiple interacting variables. Computational and modelling approaches are increasingly employed to understand adsorption mechanisms and predict adsorption performance under different operating conditions. For instance, Abdi et al. [9] used machine-learning algorithms such as XGBoost, CatBoost, LightGBM, and Random Forest to model CO₂ uptake based on parameters including temperature, pressure, surface area, and pore volume. Similarly, Choudhury et al. [7] investigated CO₂ adsorption in MOF-5, ZIF-8, and UiO-66 using Grand Canonical Monte Carlo (GCMC) simulations and showed that MOF-5 exhibits superior adsorption performance at higher pressures. Although these models showed strong predictive capability, they mainly focus on equilibrium capacity prediction and provide limited insight into adsorption kinetics and mass-transfer behaviour. Rupa et al. [10] found that the LDF model accurately represents adsorption kinetics in porous adsorbents by simplifying intraparticle diffusion effects.

Although significant progress has been made in modelling CO₂ adsorption in MOFs, many studies focus primarily on machine learning predictions or equilibrium simulations. Dynamic adsorption modelling approaches, such as the LDF model coupled with adsorption isotherms, remain less explored for MOF systems, particularly Zn-based MOFs such as MOF-5. Therefore, integrating the Langmuir isotherm with the LDF kinetic model in a MATLAB framework can provide improved prediction of adsorption behaviour and support the design of efficient CO₂ capture processes.

This study addresses this gap by developing and validating a MATLAB–Excel simulation framework to model CO₂ adsorption on Zn-MOF-5 and to quantitatively evaluate the influence of key operating parameters on adsorption performance.

2. Methodology

2.1. System Definition and Objectives

This study focuses on the modelling and simulation of CO₂ adsorption using Zn-MOF-5 as the adsorbent material. The objective is to evaluate the influence of key operating parameters, namely temperature, pressure, and flow rate, on the adsorption performance of Zn-MOF-5. Equilibrium and kinetic adsorption behaviour were analysed using the Langmuir isotherm and the LDF model, respectively. MATLAB–Excel simulation tools were employed to quantify adsorption capacity and assess system performance under varying operating conditions. MATLAB version 2025a was used in the simulation process.

It is to be noted that this study is entirely simulation-based; no physical synthesis or laboratory characterisation of Zn-MOF-5 was carried out. The material properties used as model inputs were based on established experimental literature (Table S1). Qasem et al. [11] validated the structural and thermodynamic parameters for DEF-synthesized MOF-5, including a BET surface area of 2449 m²/g, pore volume of 1.39 cm³/g, maximum adsorption capacity qm = 23 mmol/g, enthalpic factor α = 20 J/mol, entropic factor β = 37.8 J/mol·K, and isotherm constant n = 7. The Langmuir saturation capacity (qsat = 21.2 mmol/g) and adsorption constant (b = 150 bar⁻¹) were taken from [12].

2.2. Simulation Framework and Modelling Approach

This study investigated CO₂ adsorption on MOF-5 using Langmuir (equilibrium) and LDF (kinetic) modelling approaches. The effects of temperature, pressure, and flow rate were analysed using a one-factor-at-a-time (OFAT) approach. The experimental ranges evaluated for the simulation included 280 to 320 K for temperature, 1 to 10 bar for pressure, and 10 to 100 kmol/h for flow rate. To assess the impact of these operating parameters on CO₂ adsorption, a variable-evaluation approach was employed. This method is both straightforward and effective in isolating the individual effects of temperature, pressure, and flow rate. The system inputs were primarily derived from literature data reported by Qasem et al. [11]. The MOF-5 parameters used in the simulation included a maximum adsorption capacity of qm = 23 mmol/g, an enthalpic factor α = 20 J/mol, an entropic factor β = 37.8 J/mol·K, an isotherm constant n = 7 and the reference pressure (P₀) was 72.14 × 10⁶ Pa. The universal gas constant (R) was used as 8.314 J/mol·K. These parameters were adopted from Qasem et al. [11].

For the Langmuir isotherm model, a saturation capacity (qsat) of 21.2 mmol/g and an adsorption constant $b$ = 150 bar⁻¹ were adopted from Costa et al. [12]. The LDF mass transfer coefficient (kL) was fixed at 0.025 s⁻¹, as reported by Qasem et al. [11]. The temperature dependence of adsorption was represented using an adsorption enthalpy change of ΔH = −3000 J/mol. The LDF mass transfer coefficient was fixed at kLDF = 0.01 s⁻¹ as reported by Qasem et al. [11], and a time range of 0–1000 s was applied for kinetic analysis. The flue gas composition was assumed constant throughout the simulations and consisted of 82% N₂, 12% CO₂, 5.5% O₂, 0.38% SO₂, and 0.12% NO₂.

The simulation framework employed MATLAB for equilibrium and kinetic calculations, while Excel was used for regression analysis and statistical validation. MATLAB was used to solve the Langmuir isotherm and LDF kinetic equations using iterative numerical loops.

The Langmuir isotherm equation used to describe equilibrium adsorption capacity is given by:

$$q_e={\displaystyle \frac{q_{sat}bP}{1+bP}}$$

(1)

where $qe$ is the equilibrium adsorption capacity of CO₂ (mmol g⁻¹), $q_{sat}$ is the saturation adsorption capacity (mmol g⁻¹), $b$ is the Langmuir adsorption constant (bar⁻¹), and $P$ is the gas pressure (bar). The LDF kinetic model was used to describe the rate of CO₂ diffusion within the adsorbent, implemented via iterative loops to generate the adsorption data. The Langmuir isotherm was solved simultaneously across the temperature-pressure grid, and the resulting values were stored as CO₂ adsorption data. The LDF solution was approximated using Equations (2) and (3):

$${\displaystyle \frac{d_{qt}}{dt}}=k_{LDF}(qe-qt)$$

(2)

With the integrated form:

$$qt=qe(1-e^{-k_{LDF}t})$$

(3)

where K_LDF is the LDF mass transfer coefficient (s⁻¹), and $qt$ is the adsorption capacity at time t (mmol g⁻¹). These equations were coded into MATLAB, enabling estimation of the transient approach to equilibrium.

2.3. Statistical Validation

Data from MATLAB outputs were exported to Excel, enabling systematic evaluation of parameter significance using analysis of variance (ANOVA) and the calculation of metrics such as R², F-value, and p-value statistics. Adsorption capacity for each simulation was calculated in MATLAB using the Langmuir isotherm for equilibrium and the LDF model for kinetic analysis. Model validation was performed by comparing simulated results with experimental data from the literature, whereas verification involved comparing the equilibrium adsorption values obtained in Excel with the input parameters for the LDF model in MATLAB.

3. Results and Discussion

3.1. Equilibrium Behaviour (Langmuir Isotherm)

Figure 1 displays the Langmuir isotherms obtained from simulated data, demonstrating how CO₂ uptake varies with pressure and temperature.

Uptake decreases as temperature rises due to a drop in the Langmuir equilibrium constant of $b$ = 150 bar⁻¹. Increased heat energy eliminates van der Waals connections, leading to fewer adsorbed CO₂ molecules. This tendency is consistent with literature data on CO₂-MOF-5 systems [13].

The Langmuir isotherm shows CO₂ uptake increases with pressure, reaching about 21.19 mmol/g at 10 bar. Uptake rises sharply from 1 to 3 bar due to high-energy sites, then plateaus beyond 8 bar, indicating saturation and monolayer coverage. This behaviour is consistent at constant temperature: an increase in temperature decreases adsorption, confirming its exothermic nature [9]. The trends shown in Figure 1 validate the Langmuir model’s suitability for CO₂ adsorption on MOF-5 and align with the literature [1].

3.2. Effect of Process Variables

Flow rate, pressure, and temperature were evaluated in the fixed-bed system, with their respective statistics presented in Tables S2, S3 and S4.

Figure 2 depicts the effect of temperature on CO₂ uptake. The uptake increased as the temperature rose from 280 K to 320 K, contrary to thermodynamic expectations. CO₂ adsorption on MOFs is an exothermic process; higher temperatures reduce adsorption capacity [9,14] by increasing desorption and decreasing adsorbate-adsorbent interaction [4,15]. The observed increase in CO₂ uptake with temperature is attributed to kinetic effects rather than thermodynamic behaviour. While adsorption is exothermic, higher temperatures enhance diffusion and reduce mass transfer resistance, leading to faster adsorption rates under dynamic conditions. This results in higher apparent uptake within a finite time, particularly in kinetically controlled systems [10,16]. In kinetically controlled systems or short-cycle adsorption processes, higher temperatures can enhance gas diffusion and mass transfer, even as equilibrium adsorption capacity decreases. Therefore, an observed increase in uptake might result from faster mass transfer in the reactor rather than improved adsorption affinity. This emphasises the need to distinguish between equilibrium-controlled and rate-controlled adsorption when analysing simulation results [16].

Figure 3 shows overlapping adsorption curves across the pressure range of 1–10 bar, indicating that CO₂ uptake remained practically constant under the simulated conditions (Table S5). This suggests that the adsorption process was not highly pressure-sensitive within this pressure range. The minimal change in adsorption observed in this study suggests that the process was limited by kinetic factors rather than equilibrium conditions. The overlapping curves suggest that CO₂ uptake remained consistent across the pressure range, indicating that adsorption was probably governed by internal diffusion within the MOF-5 structure rather than pressure-driven effects. In contrast to this study, Villarroel-Rocha et al. [17] reported a slight increase in CO₂ uptake of 2.5–7.8 mmol/g as pressure increases. The tests were conducted under static conditions, which restricted gas diffusion into the pores of MOF-5. A rate-based model for dynamic simulation was applied in this study, which enhanced mass transfer and enabled faster, more complete CO₂ adsorption, resulting in higher uptake values (18–21 mmol/g). Generally, an increase in partial pressure increases the driving force for CO₂ molecules to penetrate the porous structure and occupy available adsorption sites, thereby increasing adsorption. Metal–organic frameworks, such as MOF-5, typically exhibit a monotonic increase in CO₂ adsorption capacity with increasing pressure until the pores become saturated [7,11]. When high-energy adsorption sites were fully saturated, the process reached near-equilibrium, where increasing pressure had little influence on CO₂ uptake [9].

In Figure 4, a proportional increase in CO₂ adsorption is observed with increasing gas flow rate within the range of 10 to 100 kmol/h. At moderate flow rates, enhanced mass transfer leads to increased CO₂ absorption. However, excessively high flow rates can diminish contact time, ultimately reducing overall adsorption efficiency. Higher flow rates introduce more CO₂ into the system, thereby increasing mass transfer and adsorption rates [18]. Overall, the results indicate that within the measured range, flow rate had a small effect on the final CO₂ absorption capacity. The adsorption process was mainly controlled by surface diffusion and the number of active sites on the MOF, rather than by external mass-transfer limitations [19].

3.3. Kinetic Uptake (LDF Model)

After analysing the evaluation of process variables, the adsorption kinetics were examined using the LDF model. LDF kinetics are presented in Figure 5.

Studying the kinetic uptake profile of CO₂ on MOF-5 using the LDF equation revealed three distinct adsorption stages. In the first 200 s, there was a significant increase in adsorbed concentration (qi), indicating a rapid adsorption phase with many active sites accessible for CO₂ molecules. Between 400 and 600 s, the adsorption rate gradually slowed, signalling a shift towards equilibrium as the high-energy sites became increasingly occupied [10,16]. Beyond 600 s, the uptake curve plateaued at around 21.19 mmol/g, indicating MOF-5′s equilibrium and optimal adsorption capacity under the examined conditions (10 bar, 300 K). This equilibrium indicates that the surface was fully saturated and that mass transfer resistance dominated the adsorption process. Such behaviour is consistent with the LDF model’s theory that the adsorption rate is proportionate to the driving force differential between equilibrium and real loadings [20].

3.4. Statistical Results

Data analysis was performed in Excel to examine how flow rate, pressure, and temperature affect CO₂ adsorption with MOF-5. The regression results showed a poor association between flow rate and adsorption capacity (R² = 0.6683, p-value = 0.90), as evidenced by an F-value of 0.0157, suggesting that flow rate did not significantly influence adsorption performance within the investigated range. This observation is consistent with findings from CO₂ fixed-bed adsorption studies, where operating parameters such as temperature and concentration often dominate adsorption behaviour, while flow rate primarily influences breakthrough characteristics rather than equilibrium capacity [14]. Pressure had a moderate correlation with adsorption capacity (R² = 0.6683). The regression coefficient for pressure was positive, indicating that greater pressures boosted CO₂ uptake. As shown in

Table 1. Regression analysis of parameters.

Temperature		Flowrate	Pressure
R2	0.9997	0.6683	0.6683
Adjusted R2	0.9997	0.5578	0.5578
Standard Error	4.87 × 10−6	0.0104	0.0104
Observations	5	5	5

, temperature had the greatest effect, with the highest F-value of 12,173.08598, a significant p-value < 0.001 and a strong correlation (R² = 0.9997). The very low regression coefficient indicates that CO₂ adsorption decreases with increasing temperature, consistent with the exothermic character of physical adsorption processes [7,10]. This finding identifies temperature as the most important factor affecting adsorption, followed by pressure (F-value of 6.0451 and p-value of 0.091), while flow rate had no significant effect. The high R² values and low standard errors observed in the regression analysis indicate strong model consistency and minimal deviation within the investigated parameter range. These statistical results serve as an indirect error analysis, confirming the reliability of the simulation outcomes.

The ANOVA analysis evaluated the impact of flow rate, pressure, and temperature on CO₂ adsorption performance, which is presented in

Table 2. Analysis of Variance (ANOVA) results.

Flow Rate
	df	SS	MS	F	p-Value
Regression	1	1.438247254	1.438247254	0.015737254	0.9002
Residual	351	32,078.3281	91.39124815
Total	352	32,079.76635
Pressure
Regression	1	0.000658531	0.000658531	6.045085853	0.091
Residual	3	0.00032681	0.000108937
Total	4	0.00098534
Temperature
Regression	1	2.89515 × 10−7	2.89515 × 10−7	12,173.08598	1.6415 × 10−6
Residual	3	7.13497 × 10−11	2.37832 × 10−11
Total	4	2.89587 × 10−7

. The F-value (0.016) and the corresponding p-value (0.9002) indicated that flow rate had no statistically significant effect on adsorption capacity within the tested range. This suggests that variations in flow rate between 10 and 100 kmol/h did not notably influence the equilibrium uptake, as the adsorption system had already reached mass-transfer stability. Previous studies have also reported that gas flow rate primarily affects residence time, breakthrough time, and mass transfer behaviour rather than significantly altering the equilibrium adsorption capacity in packed-bed adsorption systems [10]. In comparison, pressure yielded an F-value of 6.05 with a p-value of 0.091, indicating a moderate effect on adsorption performance. This aligns with the physical behaviour of CO₂ adsorption, where increasing pressure enhances adsorption capacity due to higher CO₂ concentration and a stronger driving force for gas–solid interactions within porous adsorbents [21].

Table 3. CO₂ adsorption modelling and comparison.

Method	Adsorbent	CO2 Uptake (mmol/g)	Accuracy	Key Limitation
CFD + GCMC-informed parameters [11]	MOF-5, MOF-177	21.07 mmol/g at 30 bar (MOF-5 experimental benchmark)	Experimentally validated 2D/3D CFD	Requires ANSYS Fluent; high complexity; focused on storage (5–50 bar) [11]
LDF (time-adapted) [10]	General porous adsorbents	Not reported for CO2–MOF-5 specifically	Validated against general porous solid data	Not coupled with Langmuir isotherm for MOF-5; no equilibrium capacity for CO2 reported
LDF–Langmuir (MATLAB + Excel) (this study)	Zn-MOF-5	18.3–21.196 mmol/g (1–10 bar); plateau at ~21.19 mmol/g beyond 8 bar	0.59% deviation from Qasem et al. [11]	Simulation only; no experimental synthesis; single-cycle; no multi-component validation

compares the MATLAB–Excel LDF–Langmuir framework against CFD coupled with GCMC simulations [7,11] and an LDF kinetic model [10] using data drawn from literature and this study’s simulation outputs. Furthermore, the results in this study were compared with experimental data as shown in Table S6.

4. Conclusions

The developed simulation model successfully reproduced the CO₂ adsorption behaviour on Zn-MOF-5, demonstrating the capability of computational modelling to accurately represent experimental adsorption performance. The model’s reliability was confirmed by the predicted CO₂ uptake of 21.196 mmol g⁻¹, which deviated by only 0.59% from the experimental value of 21.07 mmol g⁻¹. By integrating the Langmuir isotherm with the LDF kinetic model, the simulation effectively captured both equilibrium and mass-transfer behaviour during adsorption. The analysis further showed that temperature had the greatest influence on CO₂ adsorption, followed by pressure, while flow rate had minimal impact, which is consistent with the thermodynamics and kinetics of exothermic adsorption processes. Overall, the results demonstrate that Zn-MOF-5 is a promising adsorbent for CO₂ capture, and that MATLAB-based modelling, combined with Excel validation, provides an efficient and cost-effective approach for simulating adsorption systems.