Multiscale, techno-economic evaluation of isoreticular series of CALF-20 for biogas upgrading using a pressure/vacuum swing adsorption (PVSA) process

Abstract

Cyclic swing adsorption processes, such as pressure/vacuum swing adsorption (PVSA), is a promising technology for upgrading biogas by separating carbon dioxide (CO₂) from methane (CH₄). The rational design of adsorbent materials with tailored properties is important for deployment of high-performance PVSA technology. Metal–organic frameworks (MOFs), particularly the CALF-20 isoreticular series, have attracted interest due to their high CO₂ selectivity, thermal and water stability. In this study, we report a multiscale assessment of CALF-20 and its isoreticular five derivatives by integrating molecular simulations with PVSA process optimization and techno-economic analysis. Structural and adsorption characteristics were calculated and employed to assess how each material performs in terms of energy efficiency and cost. The analysis reveals distinct differences in cost performance among the CALF-20 series, with CALF-20 showing the most favorable economics with >97% purity CH₄ production cost at $4.31 per kg of CH₄ and energy consumption of 9.35 kWh kg⁻¹ of CH₄. This study demonstrates that the integrated material-process optimization framework can effectively guide the search for adsorbent materials for biogas upgrading.

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Design, System, Application

The rational design of adsorbent materials is critical for energy and cost efficient gas separation, such as biogas upgrading. We systematically investigated an isoreticular series of six CALF-20 MOFs, where the original oxalate linker was computationally substituted to modulate pore size, pore volume, and adsorption enthalpy. This molecular-level engineering was designed to optimize the trade-offs between CO₂/CH₄ selectivity and working capacity. The molecular-level designed adsorbent materials were then evaluated through an integrated multiscale modeling and optimization system to bridge the gap between molecular properties and process-level performance. This system couples GCMC-derived adsorption isotherms (fitted to the DSL model) with dynamic PVSA process simulations and a detailed techno-economic cost model. The entire system was optimized using the Thompson sampling efficient multi-objective optimization (TSEMO) algorithm to identify operating conditions that minimize CH₄ production cost for all the adsorbent materials. The modeling framework and the analyses revealed that high CO₂ selectivity and moderate working capacity, as seen in the parent CALF-20 MOF, translated to the lowest energy consumption (9.35 kWh kg⁻¹ of CH₄) and the most favorable production cost ($4.31 per kg of CH₄). Conversely, derivatives with higher working capacity but lower selectivity suffered from high energy demands to pull the vacuum to remove co-adsorbed CH₄, rendering them less economical. This work provides a robust multiscale evaluation methodology for identifying economically viable adsorbents for biogas upgrading.

Introduction

With the growing importance of greenhouse gas reduction due to global warming, the capture and utilization of major greenhouse gases such as carbon dioxide (CO₂) and methane (CH₄) have emerged as critical research topics in the energy and environmental sectors. Methane, in particular, has a global warming potential (GWP₁₀₀) approximately 40 times higher than that of carbon dioxide, making the effective management of its emission sources essential.¹ The major sources of methane emission into the atmosphere are from organic wastes, such as sewage sludge, food waste, and livestock manure. As a sustainable solution to the issue, biogas technology, which converts waste gases into high-value energy, has gained increasing attention. Modern biogas plants utilize sealed anaerobic digesters to process waste and capture the resulting gas mixture efficiently, thereby minimizing the unintended atmospheric release of methane. The biogas is typically composed of 50–60% CH₄ and 35–45% CO₂, which can be purified to high-purity methane, offering one of the most practical alternatives to fossil-derived natural gas.² Accordingly, advances in biogas upgrading not only promote waste-to-energy valorization but also contribute directly to greenhouse gas reduction and the decarbonization of energy systems.³ The steady global increase in biogas production and utilization in recent years further underscores the strategic importance of this technology.⁴

Representative biogas separation technologies include absorption, membrane separation, cryogenic separation, and pressure/vacuum swing adsorption (PVSA), each differing in separation principles, energy consumption, and operational stability.^5–10 Among these technologies, PVSA has attracted attention as an economically viable option due to its relatively low energy consumption, high product purity, immunity to corrosion, and the absence of chemical solvents or water usage.^9,11 PVSA is also highly adaptable to variable biogas compositions,¹² enabling optimized separation performance through the selection of operating conditions and adsorbent materials.^13,14 Over the past years, advancements in cycle design,¹⁵ the implementation of high-performance adsorbents,^16–18 and the incorporation of various optimization strategies^19,20 have gradually enhanced the competitiveness of PVSA processes over other separation technologies. The performance of PVSA processes is largely determined by the structural characteristics of the adsorbent material and its dynamic characteristics during adsorption and desorption cycles.^21,22 In this context, multiscale modeling, which bridges molecular-level atomistic simulation with process-level modeling, has become a key strategy for evaluating adsorbent materials' performance under process conditions.^23–28

Given the central role of adsorbent materials in the PVSA cycle, recent research has focused extensively on MOFs as promising candidates for gas separation. In this context, significant efforts have been devoted to developing high-performance MOF adsorbents and applying them to PSA processes for selectively removing CO₂ and N₂ from methane-based gas mixtures, thereby enhancing CH₄ purity. To this end, various studies have employed isotherm measurements, breakthrough experiments, and simulation-based evaluations of separation performance. Additionally, some studies have adopted multiscale approaches that bridge molecular-level simulations with process-level modeling. For example, Singh et al. investigated the CO₂/N₂ and CH₄/N₂ selectivity of an Fe₄O₂-based MOF (IISERP-MOF30) using GCMC and MD simulations, and proposed a two-step PSA process for natural gas upgrading.²⁹ Karimi et al. experimentally quantified the CO₂/CH₄ and CO₂/N₂ adsorption performance of MIL-160(Al) using breakthrough experiments and response surface methodology (RSM),¹⁷ and further applied its pelletized form to a PSA setup, achieving 99% CH₄ purity and 63% recovery.³⁰ Abd et al. optimized the PSA performance of UiO-66 under various operating conditions through experimental and dynamic modeling, obtaining 99.99% CH₄ purity, 99.99% recovery, and a productivity of 8.57 mol kg⁻¹ h⁻¹.³¹ More recently, Rogacka et al. performed a systematic numerical screening of MOFs for biogas purification under humid conditions, demonstrating that the presence of water can significantly affect adsorption capacity, regenerability, and selectivity.³² These studies demonstrate the importance of quantitatively linking the structural characteristics of MOF adsorbents with process-level parameters, highlighting the critical role of material selection in designing high-performance PSA systems for methane purification. In addition, techno-economic assessments of biogas upgrading, including PVSA-based processes³³ and market-level evaluations,³⁴ have also been reported, underscoring that process performance needs to be coupled with cost and scalability considerations.

Recently, the isoreticular series of CALF-20 has been computationally proposed in the literature as promising CO₂ capture materials under post-combustion (CO₂/N₂) conditions, owing to its high CO₂ selectivity in the presence of water.^35,36 CALF-20 is a highly thermal and chemically stable zinc triazolate MOF made of 1,2,4-triazolate-bridged zinc(II) layers pillared by the oxalate ligand. This adsorbent material is the current benchmark MOF sorbent for CO₂ capture from cement flue gas conditions and has been scaled up and deployed in a pilot plant.³⁷ Inspired by this material, Gopalsamy et al. computationally constructed an isoreticular series of CALF-20 derivatives.³⁶ The oxalate ligand of the parent CALF-20 was substituted by alternative small linkers, including squarate (Squ), fumarate (Fum), benzenedicarboxylate (Bdc), thieno[3,2-b]thiophene-2,5-dicarboxlate (Ttdc), and cubanedicarboxylate (Cub). Based on GCMC simulations, they found that SquCALF-20 is the best candidate combining high CO₂ uptake at 0.15 bar (3.6 mmol g⁻¹) and very high CO₂/N₂ selectivity (500), exceeding the performance of pristine CALF-20. However, the potential for biogas upgrading for the isoreticular series of CALF-20 materials under process conditions has not yet been evaluated.

We evaluate the performance of isoreticular CALF-20 adsorbent materials by integrating atomistic molecular modeling with PVSA process simulation and multi-objective optimization using the TSEMO algorithm. The geometric structures of the CALF-20 derivatives were first optimized using the MACE machine learning potential, and GCMC simulations were carried out to generate single-component isotherms. These isotherms were subsequently fitted to the dual-site Langmuir (DSL) equation, and PVSA simulations were performed to evaluate the process-level performance.

Methods

1. Crystal structures

A pristine CALF-20 and a series of its ligand-substituted derivatives proposed by Gopalsamy et al.³⁶ were considered. The crystal structure of CALF-20 was obtained from the Cambridge Crystallographic Data Centre (CCDC) (REFCODEL: TASYAR).³⁷ A total of five ligand-substituted derivatives were constructed by replacing the oxalate linker in CALF-20 with squarate (Squ), fumarate (Fum), benzenedicarboxylate (Bdc), thieno[3,2-b]thiophene-2,5-dicarboxylate (Ttdc), and cubanedicarboxylate (Cub), using PoreMatMod.jl.³⁸ CALF-20 and its ligand-substituted derivatives were geometrically optimized using a two-step cell optimization protocol. Firstly, initial cell optimizations were performed using the Forcite module in Materials Studio³⁹ using the universal force field (UFF)⁴⁰ to obtain physically reasonable initial crystal structures. Ligand substitutions were then carried out on these pre-optimized structures using PoreMatMod.jl to ensure consistent geometry generation. After each substitution, the resulting structures were re-optimized to relax the framework geometry before subsequent simulations. These structures were further refined to higher accuracy level theory through final cell optimization using the atomic simulation environment (ASE)⁴¹ package with the MACE-MP-0 model.⁴² The BFGS algorithm was applied with a force convergence threshold of 0.001 eV Å⁻¹ during the final optimization. The geometric properties, including the pore volume, pore limiting diameter (PLD), and largest cavity diameter (LCD), were calculated using the Zeo++ software package.⁴³ All relevant input files for structure generation are available at https://github.com/Chung-Research-Group/reproducible-workflows/2025-Biogas.

2. Molecular simulation

The single-component adsorption isotherms of CO₂ and CH₄ in an isoreticular series of CALF-20 materials were obtained by carrying out GCMC simulations. Non-bonded interactions between adsorbate molecules and framework atoms were modeled with a Lennard-Jones (12–6) potential plus Coulomb terms, truncated at a 14.0 Å cutoff and with tail corrections. LJ parameters for the framework atoms of the adsorbent were taken from the DREIDING force field,⁴⁴ while those for the adsorbates were obtained from the TraPPE force field.^45,46 Interactions between different atom types were approximated using the Lorentz–Berthelot mixing rules. CO₂ was modeled as a rigid three-site molecule consisting of one carbon and two oxygen interaction sites, whereas CH₄ was represented as a single-site united atom model. To satisfy the minimum image convention and prevent self-interactions between atoms, periodic boundary conditions were imposed by replicating the unit cell along the x, y, and z directions such that the shortest box length exceeded twice the vdW cutoff distance (28.0 Å). Partial atomic charges for the framework were assigned using the PACMAN DDEC06 model.⁴⁷ Simulations were carried out over a pressure range of 1 to 500 000 Pa at three different temperatures: 273 K, 298 K, and 323 K. Each simulation ran for 20 000 cycles. The first 10 000 cycles were discarded to allow for the system to reach equilibrium, and the remaining 10 000 cycles were averaged to calculate statistically meaningful uptake values. Each cycle included a minimum of 20 Monte Carlo (MC) moves, or the number of adsorbate molecules inside the simulation box, whichever is greater. These MC moves consisted of translation, rotation, reinsertion, and swap moves, each performed with equal probability. Additionally, the isosteric heats of adsorption for CO₂ and CH₄ in six isoreticular series of CALF-20 materials were calculated using Widom particle insertion simulations.⁴⁸ For each gas species, 20 000 Monte Carlo cycles were performed to determine the heats of adsorption. All GCMC and Monte Carlo simulations were conducted using the RASPA 2.0 simulation package.⁴⁹ All simulations were carried out with a rigid framework assumption where the positions of framework atoms do not change during the course of the simulation.

3. Adsorption isotherm model

The adsorption isotherms of CO₂ and CH₄ were fitted to an analytical model equation based on the assumption that two types of adsorption sites exist on the adsorbent surface, each exhibiting different adsorption strengths. Single-component adsorption isotherms were fitted using the dual-site Langmuir (DSL) model, which distinguishes between strong and weak binding sites.^50,51 The DSL model parameters were obtained by fitting the single-component CO₂ and CH₄ isotherms, with site capacities constrained to ensure thermodynamic consistency. For mixture isotherm predictions, both the extended dual-site Langmuir (EDSL) model and the ideal adsorbed solution theory (IAST)⁵² were applied. The DSL and EDSL model equations are provided in section S1 of the SI, along with the IAST formulation. To validate the mixture predictions from these models, CO₂/CH₄ binary adsorption isotherms were also computed by GCMC simulations. Selectivity (α) is defined as the ratio of the molar loading of CO₂ to CH₄, normalized by their respective gas-phase mole fractions at a given pressure:The working capacity (WC) is defined as the difference in gas uptake between adsorption and desorption pressures, reflecting the usable adsorption capacity within a PVSA cycle:

WC_A = q_ads,A − q_des,A (2)

We set adsorption and desorption pressures to 1 bar and 0.1 bar, respectively, to calculate the working capacity used throughout this work.

4. Pressure/vacuum swing adsorption (PVSA) cycle

Based on the mixture prediction methods above, we performed a modified 5-step Skarstrom cycle as the PVSA simulation model, consisting of pressurization, adsorption, heavy reflux, counter-current depressurization, and light reflux (Scheme S1). This configuration was selected because it effectively balances CH₄ recovery and CO₂ removal under PSA-relevant conditions. The feed gas was assumed to be a binary mixture of CH₄ (55%) and CO₂ (45%), representing a typical composition from biogas sources such as wastewater sludge and livestock manure digestion. During the cycle, CO₂ is preferentially adsorbed, and the product stream produces high purity CH₄. A detailed schematic and stepwise description of the cycle are provided in the SI section S2.

5. PVSA modeling

The adsorption column in this PVSA model follows the same assumptions as the MATLAB model developed by Leperi et al., which are as follows:^50,53

1) The gas phase follows the ideal gas law.

2) There is axially dispersed plug flow in the column.

3) The gas and solid phases are in thermal equilibrium.

4) No radial gradients in concentration, temperature, or pressure are considered.

5) The solid-phase mass transfer rate is represented using the linear driving force (LDF) model.

6) The pressure drops along the column is calculated using Ergun's equation.

7) No heat transfer occurs across the column wall.

8) The void fraction and particle size remain constant along the column.

We used a one-dimensional, non-isothermal, and non-isobaric dynamic column to model the adsorption column. The transport phenomena within the column were described by a set of coupled fundamental equations, including component mass balance, total mass balance, energy balance, and momentum balance. Equilibrium mixture adsorption behavior was described by the dual-site Langmuir isotherm or IAST as described above. The energy balance accounts for convection, conduction, heat generated by adsorption, and heat losses to the surroundings. To improve computational efficiency, the resulting set of coupled partial differential equations (PDEs) was nondimensionalized using appropriate scaling factors. The spatial domain was discretized using the finite volume method (FVM) with a weighted essentially non-oscillatory (WENO) scheme.⁵⁴ This led to a system of time-dependent ordinary differential equations (ODEs), which were numerically integrated using the stiff ODE solver ode15s available in MATLAB. The dynamic model comprises a set of dimensionless governing equations describing overall mass conservation, component mass balances, adsorption kinetics, pressure drop, and energy balances for both the gas phase and the column wall. These equations account for axial dispersion, convection, adsorption–desorption dynamics, and heat transfer phenomena such as conduction, convection, heats of adsorption, and external heat transfer. The full set of nondimensional model equations and parameter definitions are provided in section S2 of the SI.

To simulate the full adsorption cycle, a commonly adopted uni-bed modeling approach was employed. In this method, a single adsorption column sequentially undergoes all steps of the cycle in a time-dependent manner. This approach enables efficient evaluation of the overall cycle performance while significantly reducing computational cost, as it avoids modeling multiple columns in parallel. The simulation proceeds through repeated cycles until the system reaches cyclic steady state (CSS). CSS was defined as the condition where the relative differences between the dimensionless variables (mole fraction, pressure, temperature, and molar loading) at the end of the final step and the beginning of the first step in a cycle were all within 1%. Additionally, the total mass balance error, defined as the difference between the total mass input and output over one cycle, was required to be less than 0.01. The maximum number of cycle iterations was limited to 150. Simulations that did not meet the CSS criteria within this limit were considered non-converged and excluded from further analysis.

6. Process technical performance indicators

To evaluate the performance of adsorption-based separation processes, it is essential to quantitatively define the product composition, the extent of recovery relative to the feed, and the energy consumption required for operation. In this study, CO₂ purity, CO₂ recovery, and energy consumption were employed as the fundamental technical performance indicators. These metrics not only represent the fundamental performance of the separation process but also impact the techno-economic feasibility of the process. The evaluation of these performance indicators requires both process-level operating conditions and adsorbent-specific physical properties. Table 1 summarizes the process parameters, including adsorption pressure, feed velocity, and reflux ratios, which were optimized during the PVSA simulation. Table 2 provides the intrinsic physical properties of the adsorbent materials, such as crystal density and specific heat capacity, calculated from the MACE-optimized structures, used as inputs to the process simulation. The heat capacities of the MOF adsorbents were predicted using XGBoost-based machine learning models,^55,56 and these values were applied as constant inputs across all PVSA simulations to capture the thermal and mass-transfer behavior of each adsorbent material. The detailed definitions for CH₄ purity, CH₄ recovery, and energy consumption are provided in the SI (section S3).

Table 1 Parameters and decision variables with lower and upper bounds used in simulations and optimizations of the PVSA cycle

Parameter	Unit	Value	Type
Column void fraction	—	0.37	Constant
Viscosity of gas	Pa s	1.28 × 10^−5	Constant
Specific heat of gas	J mol^−1 K^−1	36.7	Constant
Radius of the pellets	m	1 × 10^−3	Constant
Molecular diffusivity	m^2 s^−1	1.30 × 10^−5	Constant
Thermal conduction in gas phase	W m^−1 k^−1	0.09	Constant
Mass transfer coefficient for CH4	1 s^−1	0.33	Constant
Mass transfer coefficient for CO2	1 s^−1	0.16	Constant
Feed temperature	K	298.15	Constant
Feed composition (CO2 : CH4)	—	45:55	Constant
Column length	m	[2, 9]	Variable
Adsorption pressure	Bar	[1, 10]	Variable
Desorption pressure	Bar	[0.1, 0.5]	Variable
Pressurization time	S	[10, 100]	Variable
Depressurization time	s	[10, 100]	Variable
Feed time	s	[10, 1000]	Variable
Feed velocity	m s^−1	[0.1, 2]	Variable
Light reflux ratio	—	[0.01, 0.99]	Variable
Heavy reflux ratio	—	[0, 1]	Variable

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Table 2 Physical parameters of adsorbent materials used in simulations of the PVSA cycle

Materials	Crystal density (kg m^−3)	Heat capacity (J kg^−1 K^−1)
CALF-20	1515.86	727.6
SquCALF-20	1380.50	733.4
FumCALF-20	1176.39	744.7
BdcCALF-20	1113.45	775.1
CubCALF-20	1197.47	795.9
TtdcCALF-20	1107.91	776.6

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7. Process economic performance indicators

We conducted a techno-economic analysis of the adsorption process, which involves consideration of the scaling up of the adsorption column using parallel unit train operations.

7.1. Unit train design. The procedure of Khurana and Farooq (2017)⁵¹ was adopted to design the unit train for continuous PVSA operation. In a cyclic process, a single adsorption column alternates between adsorption and regeneration and therefore cannot continuously process the feed. To guarantee uninterrupted operation, multiple columns must be arranged in parallel and operated in different cycle steps. The sizing of auxiliary equipment was considered first. Since the feed stream is directed to one column at a time, only a single feed compressor is required. Similarly, as adsorption and heavy reflux occur simultaneously, one heavy-reflux compressor is sufficient per train. In contrast, the counter-current depressurization and light reflux steps can overlap across columns, requiring additional vacuum pumps. The detailed equations used to calculate the minimum numbers of vacuum pumps, columns per train, and idle step duration are provided in the SI (section S5.1.).

7.2. Parallel unit trains. When the required feed throughput exceeds the handling capacity of a single unit train, additional trains are deployed in parallel. This parallelization strategy enables large-scale PVSA operation without disrupting the cycle sequence across columns. The average molar flow of methane into a single train was calculated from the pressurization and adsorption intervals, and the number of parallel trains required to process the total CO₂/CH₄ feed was determined accordingly. The detailed mathematical expressions for these calculations are also provided in the SI (section S5.2.).

7.3. Cost model. The capital cost (CAPEX) and operating cost (OPEX) of the PVSA system were estimated following the methodology and correlations reported by Turton et al.⁵⁷ and implemented within the techno-economic framework proposed by Yoon et al.,⁵⁸ with all estimates expressed in US dollars. Major cost components included adsorption columns, vacuum pumps, and compressors, with bare module costs (BMCs) calculated using standard purchase cost correlations. CAPEX was obtained by aggregating equipment costs, contingency, fees, and site-related costs, and subsequently annualized using the equivalent annual cost (EAC) approach. OPEX was estimated as the sum of electricity consumption, adsorbent replacement, labor, maintenance, supervisory expenses, operating supplies, administrative overhead, and plant overhead. Among these, electricity costs associated with vacuum pumps and compressors were the most significant contributor. Finally, the methane production cost was calculated based on the total annualized cost (TAC), defined as the sum of EAC and OPEX, normalized by the recovered methane throughput. The detailed correlations and calculation equations used for CAPEX, OPEX, and CH₄ production cost are provided in the SI (section S5.3.). The economic parameters applied in the estimation of both EAC and OPEX are summarized in Table 3.

Table 3 Key parameters for techno-economic evaluation

Parameter	Unit	Value
Discount rate,^59d	—	0.08
Economic lifetime,^59t	Year	25
Electricity unit cost,^57Celec	$ per kWh	0.07
Adsorbent cost,^19Cads	$ per kg	10
Chemical engineering plant cost index, CEPCI
2024	—	798.8
2001	—	397

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8. Cost optimization

The optimal design and operating conditions that minimize the CH₄ production cost in the PVSA system were identified through CH₄ production cost optimization. Among the obtained solutions, only those with CH₄ purity ≥97% were considered, and the lowest-cost case within this feasible set was identified as the optimum. Eight operating variables, namely the adsorption pressure (P_H), feed velocity (v_F), desorption pressure (P_L), light reflux ratio (α_LR), heavy reflux ratio (β_HR), adsorption time (t_ads), counter-current depressurization time (t_depres), and pressurization time (t_pres), together with one design variable, the column length (L), were chosen as decision variables. The column length-to-diameter ratio (L/D) was fixed at 3,⁵⁹ and the bounds for the decision variables are summarized in Table 2.

We employed TSEMO¹⁹ to optimize the process. The implementation of TSEMO was adapted from the open-source MATLAB code.⁶⁰ The initial dataset size was set to 150, and the algorithm was configured to run for 200 consecutive iterations. TSEMO enables efficient exploration of high-dimensional objective spaces with a minimal number of simulations, allowing for performance evaluation and comparison of adsorbents based on the resulting Pareto fronts.⁶¹ To account for accurate mixture adsorption from CH₄/CO₂ mixtures, the optimization framework was based on the IAST model fitted to single component GCMC data.

Results and discussion

1. Structural optimization and pore characteristics

The optimized crystal structures of CALF-20 and its derivatives are presented in Fig. 1 and highlight the pore-level structural differences with the incorporation of different organic linkers. These structural differences influence overall material properties such as pore size, pore volume, and adsorption enthalpy, which leads to variations in adsorption isotherms and ultimately process performance.

Fig. 1 Side views (top) and channel views (bottom) of optimized: a. CALF-20, b. SquCALF-20, c. FumCALF-20, d. Bdc-CALF-20, e. CubCALF-20, and f. Ttdc-CALF-20. Atom colors: gray (C), red (O), blue (N), white (H), yellow (S), and light blue (Zn).

Table 4 summarizes the pore characteristics and CO₂/CH₄ adsorption enthalpies of each adsorbent material. The pore volume ranges from 0.35 to 0.56 cm³ g⁻¹, with CALF-20 exhibiting the lowest pore volume and TtdcCALF-20 the highest. Despite having a relatively large LCD of 4.7 Å, SquCALF-20 has a narrow PLD of 2.9 Å, which restricts the accessibility of adsorbate molecules. TtdcCALF-20, with the highest pore volume and LCD (0.56 cm³ g⁻¹ and 5.0 Å, respectively), provides a more open pore characteristic. However, TtdcCALF-20 shows a relatively moderate adsorption affinity, with a CO₂ adsorption enthalpy of −28.7 kJ mol⁻¹, almost 10 kJ mol⁻¹ lower than CALF-20 (−36.3 kJ mol⁻¹). FumCALF-20 and BdcCALF-20 materials both feature large pore volumes (0.52 cm³ g⁻¹ and 0.55 cm³ g⁻¹, respectively), with PLD and LCD values above 3.1 Å. These materials show moderate CO₂ adsorption enthalpies (−27.7 and −27.6 kJ mol⁻¹, respectively) and relatively low CH₄ affinities (−18.9 and −19.8 kJ mol⁻¹), which may contribute to improved CO₂/CH₄ selectivity. CubCALF-20 shows a relatively high CO₂ enthalpy of −31.7 kJ mol⁻¹, along with a well-balanced pore structure (PLD of 3.2 Å and LCD of 4.8 Å).

Table 4 Structural properties and adsorption enthalpies of adsorbent materials

Materials	Pore volume (cm^3 g^−1)	PLD (Å)	LCD (Å)	ΔH (kJ mol^−1)
				CO2	CH4
CALF-20	0.35	3.0	4.4	−36.3	−24.7
SquCALF-20	0.40	2.9	4.7	−29.4	−21.6
FumCALF-20	0.52	3.4	5.0	−27.7	−18.9
BdcCALF-20	0.55	3.1	4.7	−27.6	−19.8
CubCALF-20	0.48	3.3	4.8	−31.7	−23.1
TtdcCALF-20	0.56	3.2	5.0	−28.7	−20.2

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2. Single-component adsorption isotherms

The adsorption behavior of CO₂ and CH₄ in CALF-20 and its derivatives was investigated using GCMC simulations. To validate our computational approach, the simulated isotherm for CALF-20 was compared with available experimental data (Fig. 2).³⁶ Simulated results for the other materials are provided in the SI (Fig. S1 and S2). For CO₂, all the materials exhibited a steep uptake at low pressures followed by saturation at higher pressures. TtdcCALF-20, BdcCALF-20, and CubCALF-20, which possess structurally open pores and sufficiently large pore openings, showed relatively high CO₂ uptake capacities. FumCALF-20 also demonstrated good CO₂ adsorption characteristic. In contrast, SquCALF-20 showed the lowest CO₂ uptake across the pressure range, likely due to restricted molecular accessibility caused by its narrow pore limiting diameter. For CH₄, the overall uptake was lower than that of CO₂, yet distinct differences were observed among the MOFs. TtdcCALF-20, BdcCALF-20, FumCALF-20, and CubCALF-20 exhibited relatively high CH₄ uptakes under elevated pressures. Such an adsorption characteristic is unfavorable in a cyclic process since the adsorbed CH₄ results in lower CH₄ recovery. Finally, SquCALF-20 shows low CH₄ uptakes due to limited pore accessibility of CH₄ molecules. We note that these simulation predictions are based on rigid framework assumptions, and the results may vary if we consider the flexibility of the materials.

Fig. 2 Adsorption isotherms of CALF-20 at 298 K obtained from GCMC simulation: a. Simulated single-component CO₂ isotherm, compared with experimental isotherm data reported by Gopalsamy et al.,³⁶ and b. simulated single-component CH₄ isotherm.

Single component GCMC adsorption data of CALF-20 and its derivatives at three temperatures (273, 298, and 323 K) were fitted to the DSL model. The fitted DSL models show excellent agreement with the single-component GCMC simulation results across all materials. Fig. 3 presents the fitting results for CALF-20, while those for the remaining materials – SquCALF-20, FumCALF-20, BdcCALF-20, CubCALF-20, and TtdcCALF-20 – are provided in the SI (Fig. S3 and S4). According to the DSL parameters summarized in Table S1, all the adsorbent materials exhibited high CO₂ adsorption capacities, with TtdcCALF-20 showing the highest CO₂ uptake of approximately 12.3 mol kg⁻¹. However, TddcCALF-20 demonstrates one of the highest CH₄ uptakes (∼5.5 mol kg⁻¹), which may lead to a lower CH₄ recovery during adsorption/desorption cycles. In contrast, CALF-20, while showing a comparatively lower CO₂ uptake, shows the lowest CH₄ adsorption capacity (2.96 mol kg⁻¹) among all materials.

Fig. 3 Fitting results of a. CO₂ and b. CH₄ adsorption isotherms for CALF-20 using the dual-site Langmuir (DSL) model at 273 K, 298 K, and 323 K. Solid lines represent DSL fits, and open symbols denote the corresponding data points.

3. Binary mixture adsorption isotherms

The adsorption behavior of CO₂/CH₄ binary mixtures was analyzed at 298 K with both EDSL and IAST models. As shown in Fig. 4, IAST predictions show excellent agreement with GCMC data for CO₂, and the competitive adsorption behavior was reproduced with reasonable accuracy for CH₄. While some minor deviations at higher pressures for some derivatives were observed, we found that IAST is better at capturing the mixture isotherm behavior than the EDSL fittings (Fig. S5 and S6). All the materials showed higher adsorption of CO₂ than CH₄, indicating a clear preferential adsorption of CO₂ even under competitive mixture conditions. At elevated pressures, FumCALF-20 and TtdcCALF-20 exhibit the highest CO₂ uptakes, followed by BdcCALF-20. In contrast, SquCALF-20 shows comparatively lower CO₂ uptakes. For CH₄, CALF-20 presents the lowest uptake, whereas CubCALF-20, TtdcCALF-20, and BdcCALF-20 show relatively high CH₄ uptakes, which may adversely affect CH₄ recovery during cyclic operation of the process.

Fig. 4 Binary mixture (CH₄ : CO₂ = 50 : 50) adsorption isotherms at 298 K obtained from EDSL and IAST model predictions and GCMC simulations for six CALF-20 derivatives: a. CO₂ and b. CH₄.

The CO₂ selectivity and working capacity values under mixture conditions are calculated at the adsorption (1 bar) and desorption (0.1 bar) pressures (Table 5). FumCALF-20 and TtdcCALF-20 show the highest CO₂ working capacities, with values of 3.09 mol kg⁻¹ and 2.96 mol kg⁻¹, respectively, followed by CubCALF-20 (2.38 mol kg⁻¹) and BdcCALF-20 (2.20 mol kg⁻¹). In contrast, SquCALF-20 (1.44 mol kg⁻¹) and CALF-20 (1.36 mol kg⁻¹) show comparatively lower CO₂ working capacities. For CH₄, CALF-20 shows the lowest working capacity (0.031 mol kg⁻¹), followed by FumCALF-20 (0.184 mol kg⁻¹) and SquCALF-20 (0.192 mol kg⁻¹). In contrast, BdcCALF-20 (0.283 mol kg⁻¹), CubCALF-20 (0.283 mol kg⁻¹), and TtdcCALF-20 (0.313 mol kg⁻¹) show relatively higher CH₄ working capacities, indicating insufficient suppression of CH₄ adsorption. In terms of adsorption selectivity, CALF-20 presents the highest CO₂/CH₄ ratio (44.0), followed by FumCALF-20 (19.7), TtdcCALF-20 (11.0), CubCALF-20 (10.1), BdcCALF-20 (9.4), and SquCALF-20 (8.9). Table S2 in the SI compiles literature data for benchmark sorbents, including zeolites (13X, 5A), activated carbons, and carbon molecular sieves (CMSs). Conventional zeolites such as 13X and 5A typically exhibit CO₂/CH₄ selectivities in the range of ∼8–20 under similar conditions, whereas activated carbons and CMSs show lower to moderate selectivities of ∼3–12 depending on pore structure and preparation. The proposed CALF-20 derivatives achieve comparable or higher CO₂ selectivity while maintaining substantial working capacities under PSA-relevant conditions. This comparison highlights that CALF-20 derivatives are competitive with, and in some cases superior to, benchmark sorbents reported in the literature for biogas upgrading.

Table 5 Performance metrics based on isotherms: CO₂ and CH₄ working capacity (WC) and CO₂/CH₄ selectivity

Materials	WCCO2 (mol kg^−1)	WCCH4 (mol kg^−1)	Selectivityads	Selectivitydes
CALF-20	1.36	0.03	44.0	39.5
SquCALF-20	1.44	0.19	8.89	7.55
FumCALF-20	3.09	0.18	19.7	16.7
BdcCALF-20	2.20	0.28	9.35	8.63
CubCALF-20	2.38	0.28	10.1	9.61
TtdcCALF-20	2.96	0.31	11.0	8.92

---

4. Ternary mixture analyses

In practical biogas upgrading, it is important to describe the adsorption of other gas species, such as nitrogen (N₂). The composition of N₂ present in biogas stream strongly depends on the feedstock sources. For agricultural and wastewater sources, N₂ content is negligible, whereas landfill gas may contain up to ∼10% of N₂. To investigate the impact of N₂ in biogas separation, we conducted ternary GCMC simulations (CH₄ : CO₂ : N₂ = 50 : 40 : 10) at 298 K. The resulting data show negligible N₂ adsorption (see Fig. S7) across all the materials, validating our approach to treat the biogas as a binary CO₂/CH₄ mixture for all subsequent analyses.

5. Techno-economic analysis

The techno-economic performance of the optimized PVSA cycles was evaluated for CALF-20 and its five isoreticular derivatives. Table 6 summarizes the corresponding operating conditions, process performance indicators, and detailed cost breakdown obtained from the optimization. The feed composition was fixed at CO₂/CH₄ = 45/55, representing a typical biogas mixture, and a throughput of approximately 1333 Nm³ h⁻¹ has been reported in the literature for PSA biogas upgrading plants.⁶² This data highlights the distinct operating pressures, step durations, and equipment requirements among the materials, as well as their impact on CH₄ purity, recovery, and energy consumption.

Table 6 Optimized PVSA operating conditions, process indicators, and cost breakdown for CALF-20 and derivatives

	CALF-20	SquCALF-20	FumCALF-20	BdcCALF-20	CubCALF-20	TtdcCALF-20
Operating conditions
High pressure, PH (Pa)	176 395	495 891	161 700	103 693	128 475	258 309
Low pressure, PL (Pa)	49 959	41 323	36 758	18 942	37 356	30 678
Feed velocity, vF (m s^−1)	0.45	0.70	0.88	0.51	0.60	0.45
Heavy reflux ratio, βHR	0.36	0.48	0.09	0.06	0.16	0.32
Light reflux ratio, αLR	0.82	0.63	0.48	0.38	0.88	0.51
Adsorption time, tads (s)	209.16	61.88	121.35	134.17	321.43	162.42
Depressurization time, tdepres (s)	60.11	47.40	26.12	21.38	47.04	45.79
Pressurization time, tpres (s)	46.89	46.27	68.93	44.21	90.64	80.35
Column length, L (m)	3.99	3.14	5.21	5.01	4.34	4.22
Process performance indicators
CH4 purity (%)	98.03	97.80	97.13	97.77	98.08	97.22
CH4 recovery (%)	44.8	52.65	44.65	37.49	27.32	33.63
CH4 energy consumption (kWh kg^−1 CH4)	9.35	39.03	13.29	34.58	15.39	32.59
Train configuration
Number of columns per train, Ncol	3	3	3	3	3	3
Number of depressurization pumps per train, Nv,Dpres	1	1	1	1	1	1
Number of light reflux pumps per train, Nv,LR	1	1	1	1	1	1
Number of parallel trains, M	1	1	1	1	1	1
Cost performance
CH4 production cost, ($ per kg CH4)	4.313	6.121	4.802	6.863	7.029	7.249
EAC ($ per kg CH4)	0.081	0.188	0.146	0.114	0.113	0.133
Columns	0.0097	0.0054	0.0163	0.0178	0.0186	0.02
Compressors for feed	0.0267	0.0846	0.0374	0.0018	0.0204	0.0022
Compressors for heavy reflux	0.0011	0.0086	0.0008	0	0.0004	0
Vacuum pumps for depressurization	0.0079	0.0089	0.0209	0.0302	0.0211	0.0351
Vacuum pumps for light reflux	0.0029	0.0042	0.0113	0.0178	0.007	0.0219
Contingency and fee	0.0087	0.0201	0.0156	0.0122	0.0121	0.0142
Site developments, auxiliary buildings, off-site, and utilities	0.0241	0.0558	0.0434	0.0338	0.0337	0.0396
OPEX ($ per kg CH4)	4.232	5.933	4.656	6.749	6.916	7.116
Electricity	0.655	2.732	0.930	2.421	1.077	2.282
Adsorbent replacement	0.052	0.019	0.089	0.09	0.086	0.099
Labor	1.47	1.251	1.476	1.758	2.413	1.959
Supervisory	0.368	0.313	0.369	0.439	0.603	0.490
Maintenance	0.061	0.141	0.109	0.085	0.085	0.100
Operating supplies	0.012	0.028	0.022	0.017	0.017	0.020
Administrative overhead	0.285	0.256	0.293	0.342	0.465	0.382
Plant overhead	1.329	1.193	1.368	1.597	2.170	1.784

---

5.1. Cost performance. Fig. 5 shows the overall CH₄ production costs for CALF-20 and other derivatives. Although the CH₄ production costs of CALF-20 and FumCALF-20 are competitive relative to the other derivatives, they remain considerably higher than the established industrial production cost for biomethane, which typically ranges from $0.9 to $1.5 per kg of CH₄.⁶³ The total CH₄ production cost of this process is predominantly accounted for by operational expenditures (OPEX) while capital expenditures (EAC) account for only about 2–3% of the total cost.

Fig. 5 Breakdown of CH₄ production cost for six CALF-20 derivatives.

Fig. 6 shows the breakdown of the OPEX components. The analysis indicates that electricity, labor, and overhead emerged as the major cost contributors. Electricity accounts for a substantial portion of OPEX, reaching 40–50% in SquCALF-20, BdcCALF-20, and TtdcCALF-20. In contrast, CALF-20 and FumCALF-20 maintained much lower shares (<20%), which strongly suggests notable differences in energy efficiency between different materials. Labor was consistently the second-largest contributor, representing 20–35% of OPEX, reflecting the manpower required for cyclic operation and process control. Overhead costs were also considerable (20–30% in some cases), which may be associated with higher energy demand or operational complexity. In contrast, the contributions from adsorbent replacement, maintenance, and operating supplies were relatively minor, collectively accounting for less than 5–10% of OPEX. These results strongly indicate that the overall economics of PVSA processes are influenced more by operational efficiency than by capital investment. The breakdown of the capital expenditures (EAC) is provided in the SI (Fig. S8).

Fig. 6 Percentage contributions of OPEX to the methane production cost of six CALF-20 derivatives under cost-optimal PVSA operation. The absolute OPEX values (in $ per kg CH₄) are indicated above each bar.

Overall, CALF-20 and FumCALF-20 show relatively low total production costs, primarily due to their smaller shares of electricity consumption. This efficiency is attributed to their moderate CH₄ working capacities and high CO₂/CH₄ selectivities, which are partially reflected in their process-level energy requirements. In contrast, Bdc-, Cub-, and Ttdc-CALF-20 exhibit comparatively large CH₄ working capacities and lower CO₂ selectivities. This combination may lead to low desorption efficiency and results in less favorable economics. SquCALF-20, despite its low selectivity, achieves higher recovery and thus offers slightly better economic performance than some of the other derivatives, though it remains less competitive than CALF-20 or FumCALF-20. These findings highlight how the adsorption characteristics of the materials are reflected in the process-level energy efficiency and cost calculation, while the structural origins of such techno-economic differences are further discussed in the SI (section S13).

5.2. Operating conditions. Table 6 shows the optimized PVSA cycle with distinct operating conditions for different materials. The adsorption pressure (P_H) was highest for SquCALF-20 at 495 kPa, whereas the adsorption pressure for BdcCALF-20 is only 104 kPa. The desorption pressure (P_L) was highest for CALF-20 at approximately 50 kPa and lowest for TtdcCALF-20 at 30 kPa, indicating that lower desorption pressures increase vacuum load and electricity demand. These observations demonstrate the differences in CO₂ affinity and CH₄ desorption efficiency of different materials which are directly translated into the optimized adsorption and desorption pressures during cycle simulations. The feed velocity (v_F) was greatest for FumCALF-20 at 0.88 m s⁻¹, while TtdcCALF-20 exhibited the lowest value of 0.45 m s⁻¹. These differences are closely related to the overall throughput of the process and consequently affect both productivity and CH₄ production cost. The reflux ratios (heavy/light) also varied substantially: CubCALF-20 shows an extreme distribution (0.16/0.88), suggesting an operating condition more specialized for CO₂ removal rather than CH₄ recovery. In contrast, FumCALF-20 and CALF-20 show more balanced ratios of 0.48/0.48 and 0.36/0.82, respectively. The cycle step durations (adsorption, depressurization, and repressurization) also differed significantly among the materials. For example, CubCALF-20 requires the longest adsorption step of 321 s, which reduces throughput and penalizes productivity, whereas SquCALF-20 only requires 62 s, allowing for rapid cycle operation.

5.3. Train configuration. The optimization results show that all the materials converged to the same train configuration (Fig. S9). Each train required three adsorption columns, and only one vacuum pump was necessary for both the depressurization and light reflux steps. This outcome arises from the structural characteristics of the five-step modified Skarstrom cycle. Since adsorption, heavy reflux, and light reflux must be performed simultaneously, at least three columns are inherently required. In addition, under the optimized step time distributions, the adsorption step was consistently longer than the depressurization step, making it feasible to operate the depressurization stage with a single vacuum pump. The light reflux step could likewise be satisfied with a single pump. Therefore, while all the materials show substantial differences in process performance and CH₄ production cost, the same train configuration was obtained as an optimal configuration.

5.4. Process performance indicators. Under the optimized conditions, all the materials achieved CH₄ purities above 97%, thereby meeting the pipeline transport requirement (≥97%). However, substantial differences were observed in recovery. SquCALF-20 could reach the recovery of 52.7%, whereas CALF-20 and FumCALF-20 showed moderate recoveries of 44.8% and 44.7%, respectively. BdcCALF-20 achieved 37.5%, while CubCALF-20 and TtdcCALF-20 recorded the lowest recoveries of 27.3% and 33.6%, indicating potential disadvantages for practical deployment. Electricity consumption also varied sharply across the materials. CALF-20 and FumCALF-20 require only 9.35 and 10.3 kWh kg⁻¹ CH₄, respectively, highlighting their favorable economic performance. By contrast, SquCALF-20 demanded 39.3 kWh kg⁻¹ CH₄, while TtdcCALF-20 and BdcCALF-20 consume 32.6 and 34.6 kWh kg⁻¹ CH₄, more than three times higher than CALF-20. CubCALF-20 shows an intermediate consumption of 15.4 kWh kg⁻¹ CH₄, higher than CALF-20 but lower than the other high-cost materials. In summary, although all the materials met the purity constraint, their recoveries and energy demands varied significantly. Among all the adsorbents we evaluated, CALF-20 and FumCALF-20 emerged as economically competitive, combining moderate recovery with excellent energy efficiency. In contrast, SquCALF-20, despite its high recovery, accrued a high CH₄ production cost due to its elevated operational energy demands. CubCALF-20 and TtdcCALF-20 exhibited the least favorable combination, suffering from both low recovery and high operational energy demand. The results ultimately demonstrate that beyond meeting the purity requirement, recovery, energy efficiency, and ultimately the production (or separation) cost needs to be considered for ranking the overall economic viability of the adsorbent materials.

Conclusions

This study conducts a multi-scale computational investigation of CALF-20 and its isoreticular derivatives for biogas upgrading, integrating molecular simulations with PVSA process optimization, followed by techno-economic analyses. CALF-20 emerges as the most economically feasible, with >97% purity CH₄ production cost at $4.31 per kg of CH₄ and energy consumption of 9.35 kWh kg⁻¹ of CH₄. This performance stems from the material's low electricity demand and balanced CH₄ recovery, which originates from the material's selective adsorption of CO₂ over CH₄. The other materials, including SquCALF-20, CubCALF-20, TtdcCALF-20, and BdcCALF-20, suffer from excessive power consumption likely due to decreased selectivity between CO₂ and CH₄ due to the decreased number of preferential adsorption sites for CO₂ with ligand modulation. These effects allow CH₄ to co-adsorb with CO₂, leading to decreased CH₄ recovery and high energy costs. The findings indicate that the techno-economic outcomes are governed by the balance between recovery and energy efficiency, a key performance metric fundamentally rooted in the molecular-level adsorption characteristics of adsorbate molecules. We note that although all CALF-20 derivatives achieve CO₂/CH₄ separation, their economic performances remain uncompetitive compared to industrial benchmarks. Nevertheless, the evaluation workflow and methodology demonstrated in this work show strong potential to guide the discovery of more economically viable adsorbent materials for biogas upgrading in the future.

Conflicts of interest

There are no conflicts to declare.

Data availability

Simulation input files, optimized structures, and Python fitting codes for DSL models are available at: https://github.com/Chung-Research-Group/reproducible-workflows/tree/master/2025-biogas.

Supplementary information (SI): adsorption isotherm models and parameters, PVSA cycle description and equations, train design and techno-economic calculations, GCMC simulation results, isotherm fitting results, and molecular-level adsorption analyses. See DOI: https://doi.org/10.1039/d5me00131e.

Acknowledgements

This work was supported by a 2-year research grant from Pusan National University.

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