Unary and Binary Dynamic Column Breakthrough Experiments with Carbon Dioxide and Nitrogen Imaged by X-ray Computed Tomography.

Unary and Binary Dynamic Column Breakthrough Experiments with Carbon Dioxide and Nitrogen Imaged by X‑ray Computed Tomography - PMC Skip to main content An official website of the United States government Here's how you know Here's how you know Search Log in Primary site navigation Search Log in Search PMC Full-Text Archive Search in PMC Journal List User Guide As a library, NLM provides access to scientific literature. Inclusion in an NLM database does not imply endorsement of, or agreement with, the contents by NLM or the National Institutes of Health. Learn more: PMC Disclaimer | PMC Copyright Notice Langmuir . 2026 May 21;42(21):14716–14732. doi: 10.1021/acs.langmuir.6c00250 Unary and Binary Dynamic Column Breakthrough Experiments with Carbon Dioxide and Nitrogen Imaged by X‑ray Computed Tomography David Büchner 1 , Ronny Pini 1, * Author information Article notes Copyright and License information 1 Department of Chemical Engineering, Imperial College London, London SW7 2AZ, U.K. * Email: r.pini@imperial.ac.uk . Received 2026 Jan 15; Accepted 2026 May 14; Revised 2026 May 11; Collection date 2026 Jun 2. © 2026 The Authors. Published by American Chemical Society This article is licensed under CC-BY 4.0 PMC Copyright notice PMCID: PMC13235649  PMID: 42165198 Abstract This study extends the digital adsorption (DA) methodi.e., adsorption experiments augmented with X-ray computed tomography (XCT)from unary systems with strongly adsorbing CO 2 to unary systems with weakly adsorbing N 2 and to binary systems involving both species. Using this method, equilibrium adsorption isotherms on commercial activated carbon and zeolite 13X were measured for both gases at 294.15 K between 0.1 and 9 bar. Our analysis shows that X-ray attenuation by the bulk phase must be considered for weak adsorbates, while it is relevant only at elevated pressures for strong adsorbates. Unary dynamic column breakthrough (DCB) experiments with N 2 showed that, with a correction factor, the DA method can describe the transient progression of the internal adsorbed phase under near-isothermal, equilibrium-controlled conditions quantitatively. In binary CO 2 –N 2 DCB experiments, the direct determination of adsorbed amounts requires local composition data; however, when complemented by a one-dimensional DCB model, the experimental results are shown to capture dynamic adsorption behavior, including fast N 2 and slower CO 2 uptake, as well as a thermally enhanced roll-up. These results demonstrate that XCT provides valuable insight into dynamic adsorption processes and that, with care, the DA method can also be applied to weakly adsorbing systems. Introduction Adsorption-based gas separation and purification play a vital role in chemical processing and environmental sustainability. , Among their diverse applications, carbon capture, utilization, and storage (CCUS) has emerged as a critical strategy for mitigating postcombustion CO 2 emissions, which requires efficient separation of CO 2 from flue gas components such as N 2 . − Achieving such separations relies not only on the design of the adsorption process but also on the selection of appropriate adsorbent materials. A wide range of candidatesincluding porous carbons, metal–organic frameworks, and zeoliteshas been investigated for CO 2 capture. Among these, zeolite 13X is often used as a benchmark adsorbent for bone-dry or moisture-controlled gas streams due to its high CO 2 -N 2 selectivity, low cost, and established commercial use in other separation processes. , Designing and optimizing adsorption processes typically relies on dynamic column breakthrough (DCB) experiments, which provide transient outlet concentration, flow, and local temperature data, from which competitive loadings and kinetic parameters can be derived. − However, conventional DCB analysis yields only column-averaged information, masking local effects arising from packing heterogeneities, flow maldistribution, or thermal gradients. Recent advances also show that both experimental artifacts in breakthrough measurements, such as those arising from adsorbent shaping and pressure-drop effects, and model-based factors, including temperature-dependent kinetics and isotherm selection, can systematically bias breakthrough interpretation and derived uptake values. , These limitations are particularly significant for multicomponent systems such as CO 2 -N 2 compositions, where both mass and heat transfer strongly influence breakthrough behavior and apparent selectivity. − A well-known manifestation of such coupling is the roll-up phenomenon, where the outlet concentration of a weakly adsorbing species temporarily exceeds its inlet value. , The classical, equilibrium-driven roll-up originates from the displacement of the weaker adsorbing component by a stronger one. Subsequent studies have shown that thermal effects can profoundly modify or even dominate this behavior. Li et al. reported a dual-mode roll-up in CO 2 –H 2 O systems, where a detached thermal front propagated ahead of the adsorption wave. Pirngruber et al. observed a coupled but still distinct thermal wave in CO 2 –CH 4 mixtures, while Ahn et al. demonstrated that even modest temperature rises can amplify the magnitude of the equilibrium roll-up without producing a separate thermal front. These studies show that, although thermal and equilibrium effects are coupled, they can give rise to distinct roll-up behaviors depending on whether heat effects form an independent wave or merely enhances equilibrium displacement. Despite these insights, direct experimental observation of such phenomena inside an operating adsorption column remains challenging, as conventional breakthrough setups provide only outlet-averaged responses. Recent experimental methods using X-ray computed tomography (XCT) have opened new opportunities to visualize adsorption phenomena within packed beds. This development has been supported by the substantial expansion and maturation of laboratory and synchrotron X-ray imaging facilities over recent decades, which has made advanced XCT approaches increasingly practical to integrate into materials-focused research. , Building on this foundation, the digital adsorption (DA) method leverages XCT imaging to measure changes in X-ray attenuation associated with gas adsorption, enabling the measurement of spatially resolved adsorption loading and isotherms , and the reconstruction of three-dimensional maps of microstructural material properties, such as specific surface area and micropore volume. Applied to CO 2 adsorption on activated carbon, the DA method has demonstrated the capability to capture internal concentration profiles and dynamic wave propagation during breakthrough experiments. Despite this promise, the method has not yet been extended to other gases or multicomponent systems, where differences in adsorption strength and density changes pose additional challenges for quantitative interpretation. The present study addresses this gap by extending the DA method to unary and binary gas systems involving N 2 and CO 2 on zeolite 13X and activated carbon. For weakly adsorbing species such as N 2 , the contribution of the bulk gas phase to the overall XCT signal is significant and must be accurately accounted for. Here, a correction approach is introduced to isolate the adsorbed-phase contribution and enable quantitative comparison with conventional DCB results. The methodology is then applied to explore competitive adsorption in CO 2 –N 2 systems, providing spatially and temporally resolved insights into the interplay between equilibrium and thermal effects during DCB experiments. These results demonstrate that XCT offers a powerful means to probe the internal dynamics of complex adsorption processes, serving as a complementary diagnostic tool, advancing both experimental characterization and model validation for next-generation gas separation technologies. Materials and Methods Digital Adsorption Method The DA method has been successfully used to measure adsorption isotherms as well as internal 1-D profiles of the adsorbed amount during DCB experiments. At this point, a brief summary of the DA method is provided, including the central equations. XCT is a well-established technology in medicine and various scientific and engineering applications. At its core lies its capability to measure localized attenuation, i.e., the linear attenuation coefficient, which is dependent on the density and atomic number of the matter. Three-dimensional maps of the local attenuation are obtained through rotating either the X-ray source and the detector array around the sample or through rotating the sample in place, while keeping the X-ray source and detector fixed. The series of two-dimensional projections from various angles is then mathematically processed to create a three-dimensional cross-sectional image of the sample. While with some X-ray scanners the output quantity is a grayscale value, or the linear attenuation coefficient directly, in a medical XCT scanner, as used in this study, the common output quantity is the so-called CT number in Hounsfield units (HU). The CT number can be understood as a precalibrated quantity, where the calibration is obtained through the application of a linear transformation of the mass attenuation coefficient, such that the CT number of air and water correspond to −1000 HU and 0 HU, respectively. Under the assumption of a constant and narrow X-ray energy spectrum above 100 kV and within a limited density range, the calibration against known fluids also allows for the approximation of the CT number as a linear function of the fluid’s mass density ρ C T ( ρ ) = a ρ + b 1 where a and b are fluid dependent calibration coefficients. Fundamentally, this equation suggests that the CT number of any given voxel can be obtained through linearly combining the contribution of all components, i.e., differently dense materials, to the total attenuation. In other words, by subtracting two XCT images, the change of the CT number of a given voxel can be directly correlated to a change of density in the respective voxel. This is the concept at the core of the DA method, which calculates the excess adsorbed amount by relating it to the change of density between a well-registered reference and a subsequent image taken after adsorption has occurred. The reference image is acquired prior to the adsorption experiment, with the bed in a fully regenerated condition and under a known inert atmosphere, for example, helium. In this case, the total CT number has contributions from the solid phase (adsorbent), the bulk gas phase, and the adsorbed phase. Assuming the solid phase remains unchanged in both the reference and subsequent image, its contribution cancels out when the difference image is calculated. As a result, the total change in CT number of a voxel at time t and located at X = [ x , y , z ] can be used to calculate an excess adsorption term H ex ( t , X , θ) with θ­( t , X ) = [ p ( t , X ), T ( t , X ), y ( t , X )] defining the thermodynamic state through pressure p , temperature T , and gas-phase composition y , for every voxel or volume element. H e x ( t , X ; θ ( t , X ) ) = C T ® ( t , X ; θ ( t , X ) ) − C T ® ( X ; θ * ) − ϕ t o t ( X ) ( C T g ( θ ( t , X ) ) − C T g ( θ * ) ) 2 The first part of the right-hand side of the equation is the difference between the CT number measured during the adsorption experiment C T ® ( t , X ; θ ( t , X ) ) and a reference scan C T ® ( X ; θ * ) , acquired at a known reference thermodynamic state θ*. To obtain the change in CT number due to adsorption, the second term representing the change of CT number of the gas phase, composed of the total porosity ϕ tot ( X ) = ϕ b ( X ) + ϕ p ( X ), and CT number of the adsorptive gas CT g (θ­( t , X )) and CT number of the gas at the reference state CT g (θ*), is subtracted. Subtracting this term effectively emulates the corrections for free space and buoyancy that are applied in conventional volumetric and gravimetric measurement systems, respectively. ϕ b and ϕ p refer to the bed’s and the particle’s porosity, respectively. The excess in CT number can then be transferred into an excess adsorbed mass per unit volume m e x ( t , X ; θ ( t , X ) ) = H e x ( t , X ; θ ( t , X ) ) / a ( θ ( t , X ) ) 3 where a (θ­( t , X )) is the previously introduced calibration coefficient. Further, the excess adsorbed amount η ex in moles adsorbed per kilogram of adsorbent can be obtained via the expression η e x ( t , X ; θ ( t , X ) ) = m e x ( t , X ; θ ( t , X ) ) ρ b e d ( X ) M m ( θ ( t , X ) ) 4 with ρ bed ( X ) being the bulk density of the bed and M m (θ­( t , X )) the effective molar mass of the adsorbate. Digital Adsorption MethodConsiderations for Static and Dynamic Measurements with Single- and Multi-Component Systems As of now, the DA method has only been applied to systems with CO 2 as a single adsorptive gas, using pure helium at atmospheric conditions as the reference state. , In static isotherm measurements employing the DA method, as performed by Joss et al., the bulk gas phase is in equilibrium throughout the bed. Under these conditions, the thermodynamic state becomes independent of time and spatial location, such that θ­( t , X ) = θ eq where θ eq denotes the equilibrium adsorption state. Furthermore, since equilibrium in the gas phase, and consequently in the adsorbed phase, requires temporal invariance, the expression for the excess CT number simplifies to H e x ( X ; θ e q ) = C T ® ( X ; θ e q ) − C T ® ( X ; θ * ) − ϕ t o t ( X ) ( C T g ( θ e q ) − C T g ( θ * ) ) 5 The CT number at adsorption equilibrium, C T ® ( X ; θ e q ) , and at the reference state, C T ® ( X ; θ * ) , can be measured directly as absolute values using XCT. Similarly, the local total porosity ϕ tot ( X ) can either be measured through XCT or an average porosity measured and assumed uniform across the bed. The gas-phase CT numbers at adsorption equilibrium, CT g (θ eq ), and at the reference state, CT g (θ*) can be determined through the respective calibration measurements. Consequently, in this static formulation, all quantities appearing in eq can be explicitly determined. In case of a single adsorptive component, the effective molar mass in eq reduces to the molar mass of this component. This enables accurate measurements of unary excess adsorption isotherms using the DA method. Using eq , the excess in CT number can be directly extended to any system with multiple adsorptive gases (multicomponent system). The gas-phase CT numbers at equilibrium, CT g (θ eq ), must then be obtained through XCT measurements of the respective mixture, or, assuming ideal gas behavior and linear density–CT response, they can be estimated as C T g = ∑ i ω i C T g , i 6 with the mass fraction ω i and gas CT number CT g, i of (pure) component i . Further, under the assumption of a linear density–CT response, the calibration curves eq are expected to collapse onto a single linear curve, with a ≈ 1. , Therefore, a total excess adsorbed mass can be calculated through eq . Because it does not discriminate between the individual components in the mixture, this total excess adsorbed mass would correspond to the mass measured with traditional gravimetric adsorption isotherm measurements of mixtures. In a DCB experiment, the bed is not in thermodynamic and adsorption equilibrium until full breakthrough is achieved. The temperature and concentration of the gas phase, as well as the amount, composition, and temperature of the adsorbed phase, vary with time and location. As a result, eq can not be simplified further. While both C T ® ( t , X ; θ ( t , X ) ) and C T ® ( X ; θ * ) can still be measured in absolute terms, the calculation of the CT number of the bulk gas phase CT g (θ­( t , X )) would require knowledge of its local and instantaneous composition. This information is not directly accessible in a continuous way through experimental measurements. Pini et al. suggest that CT g (θ­( t , X )) ≈ CT g (θ*) if the DCB experiment is conducted at the same temperature and pressure as the reference state. This assumption allows removing the contribution of the bulk gas phase to the overall CT number change in eq . Under these conditions, the evolution of the total excess adsorbed amount can be estimated in both single- and multicomponent DCB experiments. Digital Adsorption MethodBulk Gas Correction Neglecting the effect of gas phase composition on the total CT number change, as done in Pini et al., has been shown to yield accurate results for DCB experiments involving a single, strongly adsorbing gas such as CO 2 . However, as demonstrated in the Results section of this study, this assumption is no longer valid for weakly adsorbing gases, for which the bulk gas phase contribution becomes non-negligible and must be explicitly accounted for. To address this limitation, a general correction approach is proposed here. To this end, we reformulate the bulk gas term in eq as ϕ t o t ( X ) ( C T g ( θ ( t , X ) ) − C T g ( θ * ) ) ≈ S ( t , X ) ϕ t o t ( X ) ( C T g ( θ e q ) − C T g ( θ * ) ) 7 where S ( t , X ) is the local correction factor, and CT g (θ eq ) the CT number of the gas phase after equilibrium has been achieved, i.e., the state corresponding to the inlet feed composition in a DCB experiment. The term (CT g (θ eq ) – CT g (θ * )) is therefore a constant value which is scaled to mimic the transient change of the bulk gas concentration throughout the bed. The correction factor is computed as S ( t , X ) = C T ® ( t , X ; θ ( t , X ) ) − C T ® ( X ; θ * ) C T ® ( X ; θ e q ) − C T ® ( X ; θ * ) 8 and is defined such that S = 0 when C T ® ( t , X ; θ ( t , X ) ) = C T ® ( X ; θ * ) (no adsorption) and S = 1 when C T ® ( t , X ; θ ( t , X ) ) = C T ® ( X ; θ e q ) (equilibrium achieved). Between these limits, S ( t , X ) interpolates linearly. While this method should, in principle, be applicable to single- and multicomponent systems, it still relies on the assumption that the bulk-gas phase concentration front moves with the same velocity and exhibits the same dispersion as the adsorbed-phase. Experimental Setups The experimental setup used for the isotherm measurements is shown in Figure a. The central part of the custom-made column is a PEEK tube (Ensinger Ltd., TECAPEEK natural), housing the adsorbent bed. The length, inner, and outer diameters of the packed bed are 273 mm, 30 mm, and 50 mm, respectively. PEEK was selected because of its beneficial radiolucent properties, which prevent imaging artifacts and thereby enable more accurate imaging results. At both ends of the tube, a small recess accommodates two disks, one sieve-like and one with a conical diameter increase, designed to ensure proper confinement of the bed and optimized gas distribution. Both disks are securely pressed into the PEEK tube using custom-made caps, which also serve as connection points for peripheral sensors and gas supply lines. This design ensures a tight seal while maintaining optimal gas flow and diffusion into the bed. The caps have an additional round and oval elongation, used to locate them in a custom-made column holder, which in turn is horizontally fixed onto the scanner bed. The pressure was measured using two pressure transmitters (Keller UK, PA-23SY), and one thermocouple (TC Ltd., Ultrafine wired K type) which was attached to the outside of the column about 50 mm into the bed. Pressure and temperature are continuously recorded with a data logger (Pico Technology Ltd., TC-08). A vacuum pump was attached to the outlet side of the column to obtain pressures below 1 bar. Isotherms were measured on two microporous adsorbent materials, zeolite 13X rods (Sigma-Aldrich, diameter ≈1.6 mm, batch MKCS3238) and activated carbon rods (Sigma-Aldrich, Norit RB3, diameter ≈3 mm, batch BCCJ6516). The feed gases were supplied by BOC at their respective CP grade, Helium 99.999%, CO 2 99.995%, and N 2 99.9992%. 1. Open in a new tab Flow-diagrams of the experimental setup used for the adsorption isotherm measurments (a) and dynamic column breakthrough experiments (b). V valve, RV relief valve, PT pressure transducer, VP vacuum pump, MFC mass flow controller, MFM mass flow meter, TC thermocouple. Figure b depicts the experimental setup used to conduct the DCB experiments. The same adsorption column, pressure transmitter, and data logger, as in the previously described setup for the isotherm measurements, were used. Four thermocouples (TC Ltd., Ultrafine wired K type) were routed axially along the bed center, inside a polyethylene tube (3.2 mm outer diameter). At about 1/8, 3/8, 5/8, and 7/8 of the bed length L , respectively, the thermocouple nodes were moved through a hole out of the tube and fixed to its outside. The exact locations of the thermocouple junctions with respect to the bed inlet were determined through visual inspection of the X-ray images for each experiment. The inlet flow rate was prescribed using a mass flow controller (Alicat Scientific, MC-500SCCM-D), while the outlet flow conditions were recorded through one CO 2 analyzer (Gas Sensing Solutions Ltd., SprintIR-R) and one mass flow meter (Alicat Scientific, M-1 SLPM-D). The three DCB experiments were conducted on zeolite 13X rods (Sigma-Aldrich, diameter ≈1.6 mm, batch MKCS3238) using the same CP grade gases purchased from BOC. Experimental Procedure: Isotherm Measurements Four separate isotherm measurement experiments, one with each adsorbent material and gas, were conducted at ambient temperature (approximately 294.15 K) using dry adsorbents. The activated carbon rods were regenerated overnight at 423.15 K, while the zeolite 13X rods were regenerated at 563.15 K, to ensure the removal of moisture and any potential contaminants. Following regeneration, the adsorbents were packed into the vertically placed PEEK column. A continuous flow of helium was maintained throughout the packing process to avoid exposure to air. Between the four experiments, the column was thoroughly emptied and cleaned to prevent cross-contamination between the adsorbents. After packing, the column was positioned in the column holder, which was premounted and aligned to the scanner bed. A controlled helium atmosphere at 2 bar was established, and two initial scans, referred to as “reference scans”, were acquired. Subsequently, the column was not moved for the entire experiment. The gas adsorption isotherm measurements were performed in two distinct modes: adsorption and desorption. During the adsorption mode, the outlet side of the column was sealed, and the pressure was incrementally increased to 1, 3, 5, 7, and 9 bar. The pressure was controlled using a gas pressure regulator, and after each adjustment and an initial adsorption period of 15 min, the inlet was closed. The system was then allowed to equilibrate until the pressure and temperature had stabilized for a minimum of 30 min. Upon reaching equilibrium, two X-ray scans, referred to as “adsorption scans”, were acquired. This procedure was repeated for each pressure step. During the desorption phase, the inlet side of the column remained sealed, and pressure was gradually reduced to 2, 1, 0.8, 0.6, 0.4, and 0.2 bar by opening the outlet valve to a vacuum pump. Once the desired pressure was achieved, the outlet valve was closed, and the system, similar to the experiments in adsorption mode, was allowed to equilibrate, i.e., a stabilization of pressure and temperature was observed for at least 30 min. Subsequently, two “desorption scans” were acquired. This process was repeated for each pressure step during desorption. X-ray imaging was conducted using a Toshiba Aquilon 64 Scanner set to a tube voltage of 120 kV and a current of 200 mA. Images were reconstructed with an x × y × z resolution of 0.117 × 0.117 × 1 mm, without the application of additional filtering. The complete length of the packed bed was scanned, with a field of view in the x – y plane of 59.9 mm. The scanning time for a complete scan was approximately 10 s. After completion of the measurements, the adsorbent was removed from the column, regenerated under the same conditions as prior to the experiment, and weighted using a laboratory scale. The bed volume of 1.929 × 10 –4 ± 1.29 × 10 –6 m 3 and measured mass m was used to compute the bulk density of the bed ρ bed and subsequently the average total porosity, defined as ϕ tot,avg = 1 – ρ bed /ρ s , where ρ s is the skeletal density of the adsorbent, which was assumed from literature. Since pore volume is not used in the modeling or interpretation in this study, no further pore-structure characterization was required. The calculated values are summarized in Table . During the postprocessing, a cylindrical section, with a diameter corresponding to the column diameter and length of 100 mm, was segmented to determine the adsorbed amount. The total time for completing one full adsorption isotherm measurement across all pressure points was approximately 12 h. Image analysis and data processing were performed using custom Python scripts developed in-house. 1. Material and Bed Properties of the Adsorption Isotherm Measurements. parameter zeolite 13X activated carbon m [kg] 0.121 ± 0.001 0.087 ± 0.001 ρ bed [kg/m 3 ] 627.3 ± 6.673 450.8 ± 6.0 ρ s [kg/m 3 ] 2567 ± 40 2160 ± 340 ϕ tot,avg [-] 0.7557 ± 0.01426 0.7913 ± 0.1250 CT s [HU] 2222 ± 189 984 ± 1193 Open in a new tab a Value taken from the literature. Experimental Procedure: Dynamic Column Breakthrough Experiments Three DCB experiments were conducted at ambient temperature (approximately 294.15 K) and into the ambient atmosphere (approximately 0.99 bar). After regenerating the zeolite 13X rods at 563.15 K overnight, the adsorbent was packed into the vertically placed PEEK column while a helium purge was maintained. Each experiment was performed on a freshly regenerated and newly packed bed of the same zeolite 13X rods. After packing each bed, the column was moved into the preinstalled column holder, and a helium purge (100 sccm, standard cubic centimeters per minute, referenced to 25 °C and 1 atm) was maintained until the temperature at all of the four thermocouple nodes had converged to and remained at room temperature for at least 1 h. After the equilibrated state of the bed was obtained, two repeated X-ray scans, referred to as the “reference scan”, were acquired. Subsequently, at time t = 0 s, the DCB experiment was initiated through the application of a step change in the inlet flow gas composition. For the three DCB experiments, the total mass flow rate was 100 sccm, while the inlet gas composition varied (unary CO 2 , unary N 2 , and a binary mixture of 50 vol % CO 2 and 50 vol % N 2 ). The system delay was corrected by measuring the gas holdup volumes upstream and downstream of the packed bed using repeated isopropanol displacement measurements, yielding 9.6 cm 3 and 9.4 cm 3 , respectively. The overall dead volume of 19 cm 3 , therefore, corresponds to 8.9% of the system volume, which is well below the upper limit of approximately 20–30%, beyond which dead-volume effects begin to significantly distort the breakthrough front shape and residence-time interpretation. For the present CO 2 on zeolite 13X system, which is strongly adsorbing, transient reductions in the outlet volumetric flow can in principle amplify downstream dead-volume effects. , However, the detector was located closely downstream of the packed bed and the downstream dead volume was limited to 9.4 cm 3 , ensuring that dead-volume effects on the measured breakthrough response remained limited. At a volumetric flow rate of 100 sccm, the inlet volume corresponds to a dead time of 5.76 s, which was used to temporally align the DCB with the corresponding XCT measurements. Accordingly, the first CT scan was acquired at t = 0 s, corresponding to 5.76 s after the initiation of the DCB experiment. In the case of the unary CO 2 and N 2 experiments, subsequent scans were taken at 300 and 60 s intervals, respectively. After the initial breakthrough was observed through an increase of the outlet flow rate, the lengths of the scanning intervals were partially increased. During the binary CO 2 -N 2 experiment, the initial scanning interval was reduced to 45 s, necessary to track the fast-moving N 2 front, and was then increased to 900 s until the first CO 2 breakthrough was observed. The DCB experiments were considered complete after the outlet flow rate was equal to the inlet flow rate, and all four temperature measurements had converged to room temperature. DCB Modeling A one-dimensional DCB model, developed and described previously by Ward et al., was employed to simulate the transient adsorption experiments. The model simulates the behavior of a compressible, nonisothermal gas mixture containing three components: CO 2 , N 2 , and He, with He acting as an inert, nonadsorbing component. The pressure drop along the column is calculated using Darcy’s law, and the gas and solid phases are assumed to remain in thermal equilibrium throughout the column. Mass transfer into the solid phase is represented by a linear driving force (LDF) model under macropore diffusion control. The associated intraparticle diffusion rate constant was calculated through k = 15 ϕ p D m τ p r p 2 , with the particle porosity ϕ p , molecular diffusivity D m , and particle tortuosity τ p assumed from literature and summarized in Table . The core of the model comprises coupled mass and energy balances, including overall and component mass balances for the fluid phase, component mass balances for the solid phase, and energy balances for both the column and wall. These balances account for advection and longitudinal dispersion in the gas phase, as well as heat released by adsorption and heat exchange between the gas, column wall, and surroundings, through conduction and convection. The Supporting Information file provides the corresponding partial differential equations and boundary conditions (Section 1). The equations are discretized in space using a semi-implicit finite-volume scheme. Time integration for the unary simulations was performed using MATLAB’s ode15s solver with the mass-matrix approach, while for the binary case, ode23t was found to be more efficient and therefore used. 2. Physical Parameters and Properties of the DCB Model. parameter value units Geometric dimensions column length, L 0.273 [m] inner column diameter, D in 0.03 [m] outer column diameter, D out 0.05 [m] thermocouple diameter, D TC 0.0032 [m] Feed conditions feed pressure, p F 100,000 [Pa] feed temperature, T F 294.15 [K] Ambient conditions ambient temperature, T ∞ 294.15 [K] Physical properties of bed/adsorbent particle porosity, ϕ p 0.5751 [-] particle diameter, D p 1.6 × 10 –3 [m] particle tortuosity, τ p 3 [-] molecular diffusivity, D m 1.5 × 10 –5 [m 2 s –1 ] heat capacity of adsorbent, C p,s 1070 [J kg –1 K –1 ] thermal conductivity of adsorbent, k s 0.63 [J m –1 K –1 s –1 ] Physical properties of gas/adsorbate CO 2 N 2 CO 2 -N 2 molar mass of gas, M m,g 0.044 0.028 [kg mol –1 ] density of gas, ρ g × 10 5 1.87 1.249 1.594 [kg m –3 ] dynamic viscosity of gas, μ g × 10 5 1.48 1.76 1.6 [kg m –1 s –1 ] heat capacity of gas, C p,g 846 1040 921 [J kg –1 K –1 ] heat capacity of adsorbate, C p,a 846 1040 921 [J kg –1 K –1 ] thermal conductivity of gas, k g 0.0168 0.026 0.0211 [J m –1 K –1 s –1 ] effective thermal conductivity, k z 0.0474 0.070 0.05813 [J m –1 K –1 s –1 ] Physical properties of column wall density of column wall, ρ W 627.3 [kg m –3 ] heat capacity of column wall, C p,W 1100 [J kg –1 K –1 ] thermal conductivity of column wall, k W 0.27 [J m –1 K –1 s –1 ] Open in a new tab All parameters describing the physical properties of the modeled system are summarized in Tables and . To reflect the decreased cross-sectional area due to the rod housing of the thermocouples, an adjusted equivalent diameter D e = 2 ( D i n / 2 ) 2 − ( D T C / 2 ) 2 was used as the inner column diameter in the simulation. At the given conditions, and in contrast to Ward et al. who used a stainless steel column, the model was found to be sensitive to both inside and outside heat transfer coefficients. Accordingly, both were fitted to obtain the optimal match of the model solution for each of the three DCB experiments. The optimizations were carried out using MATLAB’s genetic algorithm function ga , with the following cost function to be minimized for the optimization parameter h in (inner heat transfer coefficient) and h out (outer heat transfer coefficient). J T ( h o u t , h i n ) = 1 n T C n p , T ∑ j = 1 n T C ∑ i = 1 n p , T ( T T C , j s i m ( h o u t , h i n , t i ) − T T C , j exp ( t i ) ) 2 9 The cost function J T represents the mean squared error between the experimentally measured temperatures, T TC,j , and the corresponding simulated temperatures, T TC,j . The summation is carried out over all measurement times t i for each thermocouple j , with a total of n p,T time points and n TC thermocouples distributed along the axial positions. As multiple and sufficiently high local temperature readings were obtained, it was not considered necessary to include the flow rate response in the cost function. Results and Discussion CT Number Change due to Adsorption As part of the isotherm measurements using the DA method, four sets of 3D XCT scans at respective total pressures were acquiredone set for CO 2 and N 2 adsorption, and for activated carbon and zeolite 13X, respectively. Since the isotherm measurements were performed at constant temperature and with pure adsorptive gases, the thermodynamic state θ reduces to a single variable, namely the pressure p , in the following analysis. As can be seen in Table , the average total difference in CT number C T ® ( p e q ) − C T ® ( p * ) ranges from 0.5148 HU and 0.5946 HU at 0.1 bar for N 2 adsorption on activated carbon and zeolite 13X, respectively, to 133.0 HU and 152.9 HU at 9 bar for CO 2 adsorption on the same adsorbents. Calibration measurements were conducted to obtain the explicit relationship CT g ( ρ ) = aρ + b for each adsorptive. The parameters a and b were fitted for He, CO 2 , and N 2 measurements, respectively, and are reported in the Supporting Information (Section 2). The calculated bulk gas contribution during the adsorption experiments −ϕ tot (CT g ( p eq ) – CT g ( p * )) is provided for selected pressures in the right column of Table (the value in parentheses refers to % contribution to the value C T ® ( p e q ) − C T ® ( p * ) ). When comparing this relative share R ( p ), it is apparent from Table and more clearly Figure , that different behaviors are observed for the CO 2 and N 2 data sets. For CO 2 adsorption, R ( p ) increases nonlinearly but monotonically, rising from below 1% at vacuum pressures to just under 10% at 9 bar, for both adsorbents. In contrast, for N 2 adsorption, R ( p ) decreases from above 25% at low vacuum pressures, reaches a local minimum of about 17% near 1 bar, and then increases similarly to the CO 2 adsorption curve, to just above 25% at 9 bar, for both adsorbents. 3. Excess CT Attenuation from Static Unary Adsorption Experiments. H ex C T ® ( p e q ) − C T ® ( p * ) –ϕ tot ( CT g ( p eq ) – CT g ( p * )) Activated carbon CO 2 0.1 bar 11.0401 11.1866 0.1466 (1.3%) 1 bar 43.9251 45.3844 1.4593 (3.2%) 9 bar 121.123 133.0229 11.8999 (8.9%) Activated carbon N 2 0.1 bar 0.3463 0.5148 –0.1686 (26%) 1 bar 4.5429 5.4728 –0.9298 (17.3%) 9 bar 20.5357 27.95 –7.4143 (25.7%) Zeolite 13X CO 2 0.1 bar 75.2359 75.3931 0.1572 (0.2%) 1 bar 114.7692 116.1269 1.3577 (1.2%) 9 bar 141.3743 152.9365 11.5622 (7.6%) Zeolite 13X N 2 0.1 bar 0.4402 0.5949 0.1546 (32.8%) 1 bar 3.9844 4.8652 0.8808 (17%) 9 bar 20.8139 28.0074 7.1935 (26.5%) Open in a new tab 2. Open in a new tab Ratio R ( p ) = ϕ t o t ( C T g ( p e q ) − C T g ( p * ) ) / ( C T ® ( p e q ) − C T ® ( p * ) ) as a function of pressure, p eq , for zeolite 13X (a) and activated carbon (b). Circles correspond to the measured values, and the dashed lines to the explicit analytical solution derived from the DSL isotherm parametrization. Relative Contribution of Bulk Gas to CT Number Changes The contrasting behavior of R ( p ) for CO 2 and N 2 adsorption shown in Figure arises from the relative magnitudes and growth rates of the CT number contributions from adsorption and the bulk gas phase. As shown in Table , the total CT change C T ® ( p e q ) − C T ® ( p * ) is substantially larger for CO 2 than for N 2 , reaching over 150 HU at 9 bar compared to only a few tens of HU for N 2 . In this system, CT g ( p *) is constant, while CT g ( p eq ) increases linearly with pressure. Consequently, the bulk gas contribution −ϕ tot ( X )­( CT g ( p eq ) – CT g ( p * )) is linear with a slope that can be exactly calculated from the total porosity and gas properties. For CO 2 , this linear bulk gas contribution is small compared to the total CT change, producing a monotonic, slowly increasing R ( p ) from below 1% to roughly 10%. For N 2 , the bulk gas contribution is comparable to the total CT change at low pressures, giving initial R ( p ) values above 25%. As adsorption increasingly contributes to the total CT signal, the relative share of the bulk gas decreases, creating a local minimum near 1 bar. At higher pressures, the total CT change due to adsorption continues to increase but begins to saturate, i.e., its slope decreases, while the bulk gas contribution remains linear with constant slope. Consequently, the numerator slope exceeds that of the denominator, causing R ( p ) to increase again, eventually approaching the same trend as for CO 2 . From a mathematical point of view, this behavior can be explained by expressing the relative contribution as A ( p ) = C T ® ( p e q ) − C T ® ( p * ) , ⁣ B ( p ) = − ϕ t o t ( X ) ( C T g ( p e q ) − C T g ( p * ) ) 10 where R ( p ) = B ( p )/ A ( p ). The observed minimum in R ( p ) occurs where the relative growth rate of the total CT change equals that of the bulk gas contribution d d p ln ⁡ A ( p ) = 1 B ( p ) d B d p 11 which provides a compact analytical condition for the pressure p min at which R ( p ) reaches its minimum. Through this formulation, the pressure p min can be determined numerically from the measured total CT change. Alternatively, if the excess CT change H ex ( p ) = A ( p ) + B ( p ) is expressed via an adsorption isotherm model such as the DSL model, p min can be calculated explicitly from the known model parameters, providing a direct connection between the adsorption behavior and the observed minimum in the relative bulk-gas contribution. The complete derivations and the explicit formulation to calculate p min are provided in the Supporting Information (Section 6). The explicit stationary condition was solved numerically using the Newton method. For N 2 adsorption, analytical solutions were obtained, yielding p min ≈ 96.3 kPa for zeolite 13X and p min ≈ 71.3 kPa for activated carbon, in excellent agreement with the minima observed in the measured R ( p ) curves shown in Figure . In contrast, no solution was found for CO 2 adsorption on either adsorbent, consistent with the monotonic increase of R ( p ) in the experimental data. Overall, for CO 2 adsorption, the relative bulk-gas contribution R ( p ) increases monotonically but remains very small at typical measurement pressures (e.g., 3.2% for activated carbon and 1.2% for zeolite 13X at 1 bar), allowing the bulk-gas contribution to be safely neglected in the total CT number change, as done in previous studies. In contrast, N 2 adsorption exhibits a nonmonotonic behavior in R ( p ), with a distinct minimum at intermediate pressures and substantially higher contributionsroughly an order of magnitude larger than for CO 2 . While Joss et al. argue that the bulk-gas term may be neglected at low pressures, this approximation is only robust for strongly adsorbing systems. For nitrogen and other weakly adsorbing systems, the bulk-gas contribution remains significant relative to the adsorption signal and must therefore be explicitly included when deriving excess adsorption from CT number changes using the DA method. Equilibrium Adsorption Isotherms Measurements Equations – were applied to obtain the molar excess adsorbed amounts per unit mass of adsorbed at each isotherm point. Figure shows the measured isotherm as empty circles, with the error bars expressing the respective uncertainty, i.e., one standard deviation. Uncertainties were determined through the classic rules of image noise calculation and error propagation as described in detail in the Supporting Information (Section 3–5). 3. Open in a new tab Equilibrium excess adsorption isotherms of CO 2 and N 2 on zeolite 13X, (a,b), and activated carbon (c,d) at 294.15 K, respectively. Excess adsorption amounts have been calculated within a 100 mm thick section of the adsorbent column, equivalent to a total volume of roughly 70 685 mm 2 or total mass of 44.42 and 31.87 g of zeolite 13X and AC, respectively. Selected literature data at similar temperatures (±4 K) is for zeolite 13X ,,− and activated carbon ,,,− indicated by the crosses. The isotherm measurements with their respective uncertainties are also provided in tabular form in the Supporting Information (Section 7). The uncertainty associated with the CO 2 isotherms remains fairly constant and below 2% and 4% for zeolite 13X and activated carbon, respectively. As reported in Joss et al., the error on the estimated bed density, which propagates through into the total bed porosity, is dominating the overall uncertainty. This error is the same for CO 2 and N 2 adsorption. However, as the excess amount adsorbed is smaller in the case of N 2 adsorption on both adsorbent materials, the relative uncertainty of the N 2 isotherms is higher. It ranges from 52% and 92% at the lowest vacuum pressure, to 2% and 6% at high pressures, for zeolite 13X and activated carbon, respectively. All four isotherms exhibit the characteristic features of a type I adsorption isotherm. The CO 2 isotherms, in particular, illustrate the distinction between an adsorbent with a predominantly uniform micropore structure and strong ion–quadrupole interactions, such as zeolite 13X, and one where a broader pore size distribution, together with dispersion-driven physisorption, governs adsorption, as is typical for activated carbons. The CO 2 isotherm of zeolite 13X displays a steep uptake at low pressures, reaching 2.8 mol·kg –1 at 0.1 bar, followed by an early saturation plateau at higher pressures. In contrast, the CO 2 isotherm of activated carbon increases more gradually and continues to rise appreciably over the entire pressure range. While the N 2 isotherms on both adsorbents also exhibit a convex type I shape, the curvature is less pronounced than for CO 2 , approaching a more linear behavior over the investigated pressure range. The equilibrium capacities are considerably lower, reaching only 1.3 mol·kg –1 on zeolite 13X and 1.8 mol·kg –1 on activated carbon at 9 bar. This behavior reflects the weaker interactions of N 2 with the adsorbent surface of zeolite 13X. As a result, the uptake on zeolite 13X is strongly suppressed compared to CO 2 , whereas activated carbon, with its broader distribution of micro- and meso-pores, accommodates N 2 more effectively and thus exhibits a higher overall capacity. To obtain explicit formulations of the adsorption isotherms, the dual-site Langmuir (DSL) model was employed for both CO 2 and N 2 isotherms. The DSL model is required to account for the stronger adsorption affinity and the presence of distinct adsorption sites arising from the heterogeneous pore structure of the adsorbents. The DSL isotherm model is described through q * = q s 1 b 1 c 1 + b 1 c + q s 2 b 2 c 1 + b 2 c 12 with the equilibrium absolute amount adsorbed q * expressed as a function of concentration c , and the temperature independent saturation capacities q s 1 and q s 2 and adsorption equilibrium constants b 1 and b 2 for each of the two sites, respectively. The adsorption equilibrium constant for each site i is temperature dependent and follows the van’t Hoff equation b i = b 0 , i exp ( − Δ U i / R T ) 13 where b 0, i is the reference equilibrium constant, and Δ U i the change of internal energy due to adsorption. Assuming ideal gas behavior ( c = p / RT ), the DSL isotherm model is directly expressed as a function of partial pressure instead of molar concentration. Typically, the six parameters q s 1 , q s 2 , b 0,1 , b 0,2 , Δ U 1 , and Δ U 2 are fitted to experimental data of at least four isotherms. However, as in this work, isotherms could only be measured at one specified temperature (room temperature), it is not meaningful to fit the change of internal energy Δ U i . Instead, from literature, typical values were fixed, ,, and the remaining four parameters fitted against the CO 2 isotherm measurements. For thermodynamic consistency, the sum of the saturation capacities was then fixed for the respective adsorbent, q s 1 , C O 2 + q s 2 , C O 2 = q s 1 , N 2 + q s 2 , N 2 . Subsequently, ω, b 0,1 and b 0,2 were fitted against the N 2 isotherm measurements, whereby q s 1,N 2 = ω· q s 1,CO 2 and q s 2,N 2 = (1 – ω)· q s 1,CO 2 . The fitting was conducted using the curve fit function of the scipy Python package, which employs a nonlinear least-squares method. It is noted that while the DA method measures excess adsorbed amount, the DSL model defines an absolute adsorbed amount. As this work focuses on the lower-pressure region, the difference between the two is assumed negligible. The fitted isotherms parameters are summarized in Table and the resulting isotherms at measurement conditions are shown as dashed lines in Figure . The four fitted isotherm show an overall good agreement with the measured excess adsorbent amounts. In the case of the CO 2 and N 2 isotherms on the zeolite 13X, the model prediction is well within the estimated uncertainties of the measurements. This is mostly also true for the N 2 isotherm on activated carbon, while for the CO 2 isotherm, a consistent under-prediction of the excess adsorbed amount is observed. 4. Langmuir Isotherm Parameter. adsorbent parameter CO 2 N 2 zeolite 13X q s 1 [mol/kg] 2.98 2.309 q s 2 [mol/kg] 2.444 3.115 b 0,1 [m 3 /mol] 3.588 × 10 –7 1.13 × 10 –6 b 0,2 [m 3 /mol] 1.31 × 10 –8 5.26 × 10 –8 Δ U 1 [J/mol] –36 600 –18 981 Δ U 2 [J/mol] –35 700 –18 582 activated carbon q s 1 [mol/kg] 0.88 7.647 q s 2 [mol/kg] 8.041 1.274 b 0,1 [m 3 /mol] 1.822 × 10 –6 7.924 × 10 –7 b 0,2 [m 3 /mol] 1.297 × 10 –6 4.994 × 10 –6 Δ U 1 [J/mol] –28 630 –14 807 Δ U 2 [J/mol] –20 370 –17 501 Open in a new tab a From literature Ward et al. 2022. b From literature Park et al. 2019. c From literature Pini et al. 2021. Comparison of CO 2 and N 2 Adsorption Isotherms The DA method provides reliable adsorption measurements across a range of pressures and adsorbates. For CO 2 , it yields low uncertainties on both zeolite 13X and activated carbon, demonstrating good reproducibility and consistency with prior work using the DA approach. For N 2 , the relatively small excess uptakes at low pressures naturally lead to larger relative uncertainties, reflecting the intrinsic challenges of accurately quantifying weakly adsorbing gases. , Other studies on these adsorbents, using conventional volumetric or gravimetric techniques, further support the expected adsorption behavior and variability. , Overall, these results highlight that the DA method can produce meaningful and reproducible adsorption data while addressing the experimental challenges inherent to weakly interacting adsorbates. The observed shapes of the CO 2 and N 2 isotherms align well with the structural characteristics of the adsorbents. Zeolite 13X, with its uniform micropore structure, exhibits the steep initial uptake and early saturation typical of type I behavior, whereas activated carbon, possessing a broader and more evenly distributed range of micro- and mesopores, shows a more gradual adsorption increase across the pressure range. In addition to the excess adsorption isotherms measured with the DA method, Figure shows various isotherms at similar temperatures (294.15 ± 4 K) measured with volumetric and gravimetric methods for the same adsorbent materials. For zeolite 13X, the literature data set used for comparison consists entirely of binder-formed samples, including spherical beads, ,, cylindrical beads, and extruded pellets. The activated carbons included (Chemviron, BPL 3 × 10, AC, 2GA-H2J, Norit R1, RB2 and RB3 ,, ) are also commercial formed materials. Both the CO 2 and N 2 isotherms obtained in this study fall well within the range covered by literature data, which is expected given the normal variation in adsorption capacity among binder-formed zeolite 13X samples and between different commercial activated carbons. While Joss et al. demonstrated the capability of the DA method to resolve CO 2 isotherms on zeolite 13X and activated carbon at pressures above 1 bar, this work successfully extends the method’s applicability to vacuum pressures and the more weakly adsorbing N 2 . It should be noted that all measurements were performed at a single temperature, and the internal energy of adsorption was assumed from literature values. ,, Conducting adsorption experiments at multiple temperatures would provide a more rigorous determination of thermodynamic properties and further validate the DA method, particularly for weakly interacting gases. DCB Experiments: Conventional Output and Model Fitting In total, three DCB experiments were conducted following the previously described procedure. Figure shows the conventionally measured DCB outputtransient outlet flow rates and temperatures at the specified locationsfor unary CO 2 (a,b), unary N 2 (c,d), and a 50 vol % CO 2 –50 vol % N 2 mixture (e,f), respectively. The experimental measurements are represented by the red full line in the flow rate response, and the colored square symbols in the temperature plots. Time is nondimensionalised using the residence time t r = V bed / f in , where V bed is the volume of the empty column (m 3 ) and f in the inlet flow rate (m 3 /s). Since the inlet flow rate was identical in all three experiments, the reference time is the same as well in all three experiments ( t r = 135.6 s). For the two unary DCB experiments, the model results were optimized by fitting the inner and outer heat transfer coefficients to the first and fourth temperature measurements, using the defined cost function, eq . These two were chosen as they provided the most consistent data, whereas including all four measurements was found to overconstrain the optimization. For the binary experiment, the optimization was based on the first and third temperature measurements, as the fourth exhibited an inconsistency shortly before the onset of the large temperature spike. The obtained optimal heat transfer coefficients are summarized in Table . The evaluation of the cost function, i.e. mean squared error in temperature, for the optimal pair of heat transfer coefficients yields J T = 1.176 K 2 , 0.01991 K 2 , and 2.424 K 2 for the unary CO 2 , unary N 2 , and binary CO 2 –N 2 DCB experiments, respectively. Considering the outside heat transfer coefficients, the value obtained for the unary CO 2 DCB experiment is within or near the upper end of the range expected for natural convection and minimal forced convection in a laboratory environment. , However, the value of 28.2 W·m –2 and 26.26 W·m –2 obtained for the unary N 2 and binary CO 2 –N 2 experiment, respectively, lie well outside this physically plausible range. This indicates that they likely reflect parameter compensation in the model and possible inaccuracies in temperature sensing rather than a true physical external heat transfer coefficient. The inside heat transfer coefficient is not readily approximated through physical correlations; however, the obtained values are within the range of inside heat transfer coefficients used in CO 2 DCB models in literature. , 4. Open in a new tab Flow rate and temperature measurements from three dynamic column breakthrough experiments with 100 sccm CO 2 (top row), 100 sccm N 2 (middle row), and a binary CO 2 -N 2 mixture at 50/50 with a total flow rate of 100 sccm (bottom row). Experimental and model outlet flow rates are represented by solid red and dashed blue lines, respectively. Temperatures at approximately one, three, five, and seven-eighths of the column length L are shown in red, blue, yellow, and green, respectively (experimental data as square symbols; model predictions as solid lines). 5. Fitted Inside and Outside Heat Coefficients. CO 2 flow rate [sccm] N 2 flow rate [sccm] h out W/m 2 K h in W/m 2 K 100 - 9.248 15.77 - 100 27.99 53.30 50 50 23.13 8.171 Open in a new tab In Figure , the model results are shown as blue dashed lines for the flow rate response and as solid colored lines for the temperature profiles. In the two binary experiments, peak temperatures recorded by the second and third thermocouples were lower than those of the first and fourth, in contrast to the gradual decrease predicted by the model. The consistent relative differences between peaks suggest imperfect calibration of the middle thermocouples. However, since the absolute deviations are small and only the outer thermocouple data were used for model fitting, this is acceptable within the scope of this work. The flow rate response curves show excellent agreement in breakthrough time and shape between experiments and model predictions for both binary cases, confirming the validity of fitting heat transfer coefficients using multiple temperature measurements. A noteworthy deviation is a small increase in flow rate just before the sudden jump, observed in the CO 2 DCB experiment. This coincides with a slight temperature rise at the last thermocouple prior to the sharp increase. This premature breakthrough suggests minor gas channeling, which can occur near the wall where the bed density is reduced. The ratio of the column to particle diameter (18.75) is close to 20, which is considered sufficient to minimize near-wall effects, and above 10, the minimum value recommended by Wilkins et al. However, these thresholds do not account for a solid rod (thermocouples) along the center of the bed, which is reducing the bed density further, and thus promotes channeling, despite the sufficient bed to particle diameter radius. The model prediction for the binary CO 2 –N 2 DCB experiment shows overall good agreement regarding the location and magnitude of the slower temperature front caused by CO 2 adsorption. The model predicts a faster propagation of the sharp temperature front than observed experimentally, with peak temperatures occurring increasingly ahead of the measurements over time. Additionally, the simulated temperature rise is more abrupt, whereas the experimental data show a slower, gradual increase before the sharp jump. A plot of the temperature profiles with a restricted time axis up to N 2 breakthrough, provided in the Supporting Information file (Section 8), shows that the model significantly underpredicts the temperature rise from N 2 adsorption at the three downstream thermocouples. At the first thermocouple, the model additionally predicts a temporary temperature drop between the local N 2 peak and the onset of CO 2 adsorption, whereas the experiments show a continued increase with a temporarily lower gradient. The mismatch before N 2 breakthrough is attributed to the small temperature rise during N 2 adsorption and its short duration relative to the overall experiment. Consequently, the cost function used for model fitting is dominated by the larger temperature increase during CO 2 adsorption, causing the model to underpredict the N 2 -related temperature changes. With regard to the conventional flow rate output, for this experiment, absolute and component flow rates could not be determined through calibration, as only the CO 2 concentration was measured, and the composition of the CO 2 –N 2 –He mixture is therefore unknown. Instead, the experimental flow rate was normalized by the absolute flow rate measured at the end of the experiment. The flow rate response shows good agreement with regard to N 2 breakthrough time. The intermediate plateau observed between N 2 and CO 2 breakthrough is slightly higher in the experimental measurements than in the model, which can be attributed to the noncalibrated measurements. A clear difference between experimental measurements and model predictions is present in the CO 2 breakthrough response. The model predicts a considerably earlier initial breakthrough and a more dispersed breakthrough curve. Only when converging to the input flow rate do the curves start to overlap well again. This difference is in line with the previous observation of faster advancing temperature peaks in the model. Unary DCB Experiments: Spatially Resolved Internal Amount Adsorbed Next to the conventional DCB measurements, the DA method was employed to measure the internal amount adsorbed at regular time intervals. Figure a shows 13 1-dimensional profiles of the amount adsorbed measured throughout the unary CO 2 DCB experiment. Each circular symbol represents the amount adsorbed averaged over a 2 mm slice of the bed. As demonstrated in a similar experiment by Pini et al., the shape of the internal profiles closely resembles that of the previously introduced flow rate breakthrough curve. Furthermore, the color scheme clearly illustrates the advancement of the adsorbed CO 2 front through the bed over the course of the experiment. Discarding the first and last 10 mm of the bed, the average amount adsorbed at the close of the experiment is 4.138 mol/kg, which is slightly below the 4.266 mol/kg measured during the DA isotherm measurements at the same conditions. The sliced-averaged adsorbed amount has a standard deviation of 0.0517 mol/kg, which matches the estimated method’s uncertainty of 0.0517 mol/kg. However, the observed maximum deviation of ±0.161 mol/kg is ≈3.1× the standard deviation and far exceeds the method’s uncertainty, indicating that these variations likely arise from heterogeneities inherent in random packings, as previously suggested by Pini et al. As solid lines, the figure also shows the internal profiles of the adsorbed amount of CO 2 obtained from the model fitted to the temperature measurements. Comparison with the experimental profiles at the same relative time indicates great consistency. However, the model-predicted front of the adsorbed phase initially lags slightly behind the experimentally measured one, before propagating at a higher velocity and eventually surpassing the experimental profiles. This deviation is likely attributable to the thickness effect within the packingspecifically, a locally reduced bulk density near the inlet and outlet , which in the experiments facilitates a more rapid penetration speed of the front and may also reflect small inaccuracies introduced through temperature-based parameter fitting. 5. Open in a new tab Internal adsorbed amount profiles obtained through the application of the DA method to the unary CO 2 (a) and N 2 (b) DCB experiments. Symbols indicate the experimental values averaged over a 2 mm section along the bed axis, and the solid curves show the DCB model predictions derived from parameters fitted to the conventional temperature measurements. Times are represented by the color code with respect to the residence time. Figure b shows the progression of the adsorbed-phase front during the unary N 2 DCB experiment. The excess adsorbed amount was calculated from the XCT images using the DA method with the previously introduced correction factor. The average CT number at equilibrium, C T ® ( X ; θ e q ) , and the CT number difference C T ® ( X ; θ e q ) − C T ® ( X ; θ * ) at τ = 4.5 are −210.6 HU and 5.0 HU, respectively. Assuming complete exchange of He with N 2 in the bulk phase, the CT number contribution CT g (θ eq ) – CT g (θ*) was calculated to be 1.153 HU, based on the CT number gas calibration measurements provided in the Supporting Information (Section 2). The one-dimensional profiles clearly show that introducing the correction factor produces the expected behavior; that is, no significant N 2 adsorption occurs ahead of the adsorbed-phase front, while at saturation the level of excess adsorbed amount agrees well with the values obtained from the DA isotherm measurements. The average adsorbed amount at saturation in the N 2 DCB experiment is 0.2206 mol/kg, slightly lower than the value obtained from the isotherm measurements under identical conditions (0.2458 mol/kg), which marginally exceeds the estimated method’s uncertainty (0.0144 mol/kg). This difference can be attributed to the presence of thermocouple tubing in the column, which reduces the effective adsorbent mass while the same bed density is applied, leading to a slight underestimation of the calculated adsorbed amount. The maximum deviation and standard deviation for N 2 are ±0.0716 mol/kg and 0.0156 mol/kg, respectively, both notably smaller than the corresponding values for CO 2 . This supports the interpretation that the observed deviations primarily arise from inherent heterogeneities in the local bed density. Since the total amount of N 2 adsorbed is considerably smaller than that of CO 2 , these density variations produce a proportionally weaker amplification of the adsorbed-phase fluctuations. The internal profiles at corresponding times obtained from the model are again depicted as solid lines in the Figure. For the N 2 DCB experiment, the predicted one-dimensional profiles of the adsorbed amount are in good agreement with the experimental data, consistent with the unary CO 2 DCB case. A minor deviation is observed at later relative times: while the experimental profiles show that the adsorbed-phase front remains relatively constant in shape, the model predicts an increasingly dispersed front, leading to a gentler slope. DCB Behavior of Weakly Adsorbing Components As shown by the preceding results, the change in bulk gas composition contributes substantially to the overall variation in CT number for weakly adsorbing systems. In the case of nitrogen, the contribution from the bulk gas phase was found to be at least 17%. While this effect can be readily accounted for in static isotherm measurements using the DA method, it cannot be directly quantified in DCB experiments, where the local composition of the bulk gas phase is difficult to measure experimentally. To address this limitation, the present study introduces a correction factor that incorporates the CT number variation associated with changes in the bulk gas phase. This correction exploits the linear mixing behavior of X-ray attenuation in low-Z gas mixtures, for which the CT number scales linearly with bulk gas density and composition. In the present formulation, the scaling factor S further assumes that variations in bulk gas composition scale linearly with the local adsorbed amount, which strictly holds only for linear adsorption isotherms. The validity of this assumption, in the case of the here studied unary N 2 DCB experiment, is supported by the internal profiles of the relative amount adsorbed and the mole fraction of nitrogen at discrete times obtained with the DCB model (shown in the Supporting Information , Section 8), which exhibit an almost perfect overlap. This observation indicates that the conducted experiment was equilibrium-controlled and operated near isothermal conditions. The good agreement between the internal profiles obtained through the DA method and the model therefore demonstrates that, with the introduction of the correction factor, the DA method can also be applied to study the internal dynamics of more weakly adsorbing systems, provided that the system is equilibrium-controlled, near isothermal, and exhibits a near linear adsorption isotherm. For systems exhibiting strongly nonlinear isotherms, the definition of the scaling factor could, in principle, be improved by explicitly incorporating the corresponding isotherm parametrization. Breakthrough Curve Reconstruction from Internal Adsorption Profiles The internal adsorbed amount at given times can further be used as an alternative way to obtain the conventional breakthrough curve. For this purpose, a molar balance is calculated to obtain the molar outlet flow rate ṅ o u t ( t i ) = ṅ i n − ṅ a d s ( t i ) 14 at time t i , where ṅ i n is the molar inlet flow rate, and ṅ a d s ( t i ) the molar adsorption rate. The instantaneous adsorption rate can be calculated through ṅ a d s ( t i ) = m b ( η̅ e x ( t i ) − η̅ e x ( t i − 1 ) ) t i − t i − 1 15 were η̅ e x is the total amount adsorbed in the bed, and m b the total mass of adsorbent in the bed. The conversion between volumetric flow rate f in sccm and molar flow rate ṅ in mol s –1 is carried out assuming ideal-gas behavior at standard conditions (298.15 K and 1 atm), yielding ṅ = 6.83 × 1 0 − 7 f . Figure shows the breakthrough curve obtained through molar balance calculations, utilizing the DA measurements of the unary CO 2 DCB experiment. Although the experimental data results in somewhat oscillating values, it can be seen that the molar balance approach reproduces the breakthrough curve accurately. The breakthrough time is in excellent agreement with the time predicted by the model, and the tail of the breakthrough curve is well captured. However, because of the low sampling rate, i.e., the long time between two consecutive XCT scans, the initial sharp rise of the flow rate at breakthrough is only captured through two measurement points. For the same reason, no meaningful curve was obtained through this approach when applied to the unary N 2 DCB experiment. In this case, the scanning interval is too large in relation to the overall duration of the experiment, i.e., too few points are available to reproduce the breakthrough curve. 6. Open in a new tab Breakthrough curve of the unary CO 2 DCB experiment, calculated through the molar balance approach. The red crosses and the dashed blue line represent the experimental and model data, respectively. Binary DCB Experiment: Spatially Resolved Internal Profiles The correction factor method could in principle, also be applied to the binary CO 2 -N 2 DCB experiment to calculate a total (excess) adsorbed mass via the DA method. However, this would require additional considerations of the bulk gas phase contribution, because of the development of multiple transitions, i.e., from the reference state to a pure N 2 composition (to yield a difference of 1.153 HU) and to a 50/50 CO 2 -N 2 composition (to yield an additional difference of 0.313 HU). These two stages would need to be reflected in the correction factor, which could be defined to have an intermediate state. Alternatively, as it has been done in the unary CO 2 DCB experiment, the second smaller change to the CO 2 -N 2 mixture could be neglected. However, for clarity the correction factor has not been applied to the binary experiment and the local absolute change in CT number Δ C T ® = C T ® ( t , X ; θ ( t , X ) ) − C T ® ( X ; θ * ) -and thus density is reported instead. For eight discrete time steps, i.e., XCT scans acquired throughout the binary DCB experiment, Figure shows a 3-dimensional visualization of the packed bed, with the left upper quarter of the cylindrical cross-section cut out. The multisequential color code, applied to the local CT number difference, Δ C T ® , was defined such that the two stages of the experiment are clearly distinguishable. Starting from a regenerated bed at t / t r = 0.4, a first change in CT number (transitioning from dark red to yellow-red grains) is observed, progressing continuously through the bed and corresponding to the fast-moving N 2 adsorption front. This front reaches the end of the column at t / t r = 7.7, in agreement with the N 2 breakthrough time determined from the measured response in the gas flow rate. Subsequently, the slower-moving CO 2 -rich adsorption front (dark blue-green grains) advances through the bed until it reaches the column end at t / t r = 94.1, which likewise agrees well with the experimentally observed time of initial CO 2 breakthrough, i.e. the second step increase in flow rate seen in Figure e. The thermocouple array is clearly visible as the region of no to low CT number difference along the core of the packed bed. 7. Open in a new tab Three-dimensional visualization of the local CT number differences Δ C T ® = C T ® ( t , X ; θ ( t , X ) ) − C T ® ( X ; θ * ) at different relative times during the CO 2 -N 2 DCB experiment. The flow direction is from the upper left to the lower right end of the bed. For better visualization, the column axis is scaled by 1/2 and the voxel resolution convoluted with a 2 × 2 × 2 mm kernel. To facilitate a quantitative analysis of the binary DCB experiment, one-dimensional profiles of the slice-averaged CT number difference Δ C T ® are shown in Figure a. A simple 4 mm moving average convolution was applied to reduce the imaging noise while also preserving relevant details. The color code to indicate the relative time was again chosen in such a way that the time until N 2 breakthrough and from N 2 to the breakthrough of the feed gas mixture are captured by a transition from dark red to yellow, and yellow to dark purple, respectively. The logarithmic scaling of the y -axis promotes the clear recognition of the two phases of the binary DCB experiment. In the first phase, which is associated with the time until N 2 breaks through, the CT number difference continuously increases from 0 HU to 4.469 HU. Assuming that only N 2 has been adsorbed and that helium in the bulk gas phase has been completely replaced by nitrogen, application of the DA method yields an adsorbed amount of 0.222 mol/kg. This value is in good agreement with those obtained during the unary DCB experiment and from the isotherm measurements. In the second phase of the experiment, the CT number difference increases further to a considerably higher level of 99.85 HU. This increase is associated with the adsorption of CO 2 . The DCB model predicts a CO 2 mole fraction of 99.9% in the adsorbed phase after complete breakthrough, supporting the assumption of a pure CO 2 adsorbed phase. Under these conditions, and for a bulk gas phase with a 50/50 N 2 –CO 2 composition, the DA method yields an excess adsorbed amount of CO 2 of 3.671 mol/kg. This value lies between the previously measured equilibrium adsorbed amounts 3.637 mol/kg and 3.940 mol/kg, corresponding to partial CO 2 pressures of 0.38 and 0.56 bar, respectively. The minor reduction can likely be attributed to the reduced cross-sectional area as well as wall effects around the TC, which reduce the packed bed density and therefore adsorption capacity. 8. Open in a new tab (a) Full CT number difference range; (b) range corresponding to the fast-moving N 2 front; and (c) range corresponding to the slow-moving CO 2 -rich front. Experimental data (symbols) were smoothed using a 4 mm moving-average convolution along the bed axis. Solid curves in (b,c) represent DCB model predictions based on parameters fitted to conventional temperature measurements. Times are represented by the color code with respect to the residence time of the total flow rate. Figure b,c present the same internal profiles, with the y -axes scaled linearly and cropped to the ranges corresponding to N 2 and CO 2 adsorption, respectively. The CT number difference Δ C T ® was reverse-calculated from the output of the model calibrated for the binary DCB experiment to enable a quantitative comparison with the experiments. The local and instantaneous adsorbed amounts of N 2 and CO 2 were individually converted into excess CT numbers using eqs and and summed up to obtain H ex ( t , X ; θ­( t , X )). The CT number change associated with variations in the gas-phase composition CT g (θ eq ) – CT g (θ*) was determined using the local and instantaneous composition of the gas phase, the gas–CT number calibrations reported in the Supporting Information (Section 2), and the gas mixture CT number definition, ( eq ). Using the local CT number changes from adsorption and gas-phase composition and applying the rearranged eq , yielded the model-predicted total CT number change, which is shown as solid lines in the figures for each relative time. The model accurately reproduces the CT number difference of the N 2 plateau (4.61 HU) and the final equilibrium state after CO 2 breakthrough (101.2 HU). During the first phase [ Figure b], the profiles reconstructed from the model output are flatter than the experimental ones, indicating a less dispersed N 2 front in the experiment. In the second phase [ Figure c], the model captured the overall shape of the profiles somewhat better, although the initial increase was less steep. As the profiles approached saturation, agreement with the experimental data improved. The increase in CT number difference predicted by the model occurred earlier than observed experimentally. This suggests a faster and more dispersed CO 2 propagation through the bed in the simulation, which is supported by the deviation of the flow rate response curve. The binary CO 2 –N 2 DCB experiment therefore highlights the ability of XCT to capture complex adsorption dynamics. Although the DA method cannot be applied to resolve the two adsorbing components independently, since this would require knowledge of the local and instantaneous composition of the adsorbed phase, direct analysis of the CT number differences can still be interpreted. The sequential N 2 and CO 2 fronts are clearly resolved, and the CT number changes provide a powerful and effective means to visualize and interpret dynamic behavior in the adsorbed phase throughout the DCB experiment. Next to capturing the two steps of the binary DCB experiments, the one-dimensional profiles of the CT number difference also reveal an intermediate reduction of the CT number difference, as seen in Figure a. The profiles are only shown for four, i.e., every third, relative times to not clutter the figure and highlight the intermediate reductions. While some variation is observed around the mean CT number difference of the plateau (4.469 HU; standard deviation: 0.2801 HU), the observed dip clearly exceeds this variability and increases with relative time. To quantify this behavior, Figure b presents the minimum value of the dipaveraged over a 3 mm thick slice centered at the local minimumrelative to the plateau mean. A distinct trend is evident, with the relative reduction in CT number difference increasing from approximately 10% to 35% over time. Profiles of the total CT number difference reconstructed from the model output, indicated by the red line in Figure c, show a comparable reduction, though it is notably smaller and decreases marginally from around 2.1% to 1.4% throughout the second phase of the experiment. The CT number difference of the bulk gas phase, relative to the regenerated state, increases only minimally when N 2 is displaced by CO 2 . 9. Open in a new tab CT number difference profiles, Δ C T ® = C T ® ( t , X ; θ ( t , X ) ) − C T ® ( X ; θ * ) , capturing a transient reduction in Δ C T ® (i.e., N 2 desorption) occurring ahead of a second increase in Δ C T ® , which is associated with the initial CO 2 adsorption during the binary CO 2 –N 2 DCB experiment. (a) Experimental profiles at selected relative times (every third time point) to highlight the evolving dip. (b) Minimum value of the dip, averaged over a 3 mm slice at the local minimum, plotted relative to the plateau mean (experiment: 4.469 HU, model: 4.61 HU). (c) Model-reconstructed CT number difference profiles at t / t ref = 34.4, showing the contributions of the two adsorbed components and bulk gas. Thermally Enhanced Nitrogen Roll-Up during Binary DCB The present observation, a local reduction in CT number and thus adsorbed amount before the arrival of the strongly adsorbing component, is reminiscent of thermally influenced roll-up phenomena previously reported in the literature. Li et al. described a dual-mode roll-up in CO 2 –H 2 O systems, where a thermal wave detached from the main concentration front and propagated further ahead, producing early desorption of the weaker component. Pirngruber et al. observed a similar but more tightly coupled behavior for CO 2 –CH 4 breakthrough experiments, in which the thermal wave advanced slightly ahead of, yet remained linked to, the equilibrium-displacement front. Ahn et al., in contrast, reported an enhancement of the classical roll-upthat is, thermal effects modifying the magnitude and shape of the equilibrium-driven roll-up without forming a distinct, preceding thermal wave. The behavior observed here most closely aligns with this latter case: a thermally assisted desorption of N 2 that amplifies the classical single-mode roll-up rather than generating a fully separated thermal front. This interpretation is supported by the experimental data. The reduction of the CT number ahead of the CO 2 adsorption wave by 10% and 35% corresponds to adsorbed amounts of 0.1944 mol/kg and 0.1255 mol/kg, respectively, assuming the bulk gas phase is pure N 2 . Using the fitted dual-site Langmuir isotherm for N 2 on zeolite 13X at atmospheric pressure, these reductions translate to local temperature increases of approximately 9 K (303.15 K) and 29.5 K (323.65 K), the latter of which coincides with the measured peak temperatures at the four thermocouples (328.1–324.4 K from first to fourth position). A closer inspection of the total flow-rate response curves ( Figure ) further supports this view. While the flow rate remains elevated between N 2 and CO 2 breakthroughs, reflecting the equilibrium-displacement-induced roll-up, a pronounced enhancement immediately following N 2 breakthrough indicates an additional thermally driven contribution. Moreover, the small dip observed just before CO 2 breakthrough corresponds to the arrival of the thermal frontand thus of the region already depleted in adsorbed N 2 at the column outlet. Taken together, these observations indicate that the phenomenon corresponds to a thermally enhanced single-mode roll-up, rather than a fully detached dual-mode wave. It is also consistent with the observation that thermally induced desorption increases over the course of the experiment: as heat accumulates in the bed, more energy is transported downstream, enhancing desorption in the later regions of the column. However, these experimental findings contrast with the model predictions, which, while reproducing a roll-up, show only limited evidence of thermal enhancement. Notably, Wilkins et al. do not explicitly report the roll-up in terms of flow rate, as they found it experimentally difficult to measure, nor do they indicate observing a thermally enhanced roll-up. Their careful treatment of nonisothermal behavior should, in principle, capture such effects. Nevertheless, it must therefore be assumed that the heat effects are not fully captured by the model. While the temperature profile is generally well reproduced in magnitude, differences remain. The experiment shows a more gradual initial rise before steeper gradients, whereas the model predicts a more abrupt increase. Moreover, the poor fit of the N 2 temperature wave suggests that the heat transfer coefficients may not be constant, but instead vary with local temperature and flow rate. While the collective interpretation of the experimental results, point toward the presence of a thermally enhanced roll-up, further experiments, for example with a bed initially saturated with CO 2 at a lower concentration, which is then purged with a pure CO 2 front could potentially provide clarity, as in this case the DA method could be used to accurately calculate the adsorbed amount, and prove the desorption of N 2 . Furthermore, it could be investigated what definition and parameters of the models would need to be modified to reproduce the thermally enhanced roll-up. 10. Open in a new tab Breakthrough response (total flow rate) of the binary CO 2 –N 2 DCB experiment, showing the enhanced roll-up phenomenon of the weakly adsorbing nitrogen. Conclusion This study successfully extended the DA method, i.e., the augmentation of adsorption experiments with XCT, from unary systems with strongly adsorbing CO 2 to unary and binary systems with weakly adsorbing N 2 . Using the DA method, adsorption isotherms of CO 2 and N 2 on commercial activated carbon and zeolite 13X were accurately measured, and the role of the bulk gas phase in interpreting CT number changes was quantified, demonstrating the necessity of fully accounting for it. A unary DCB experiment with N 2 on zeolite 13X showed that, with a suitable correction factor, the DA method can reliably track the transient progression of the internal adsorbed phase under near-isothermal, equilibrium-controlled conditions. Limitations were encountered in a binary CO 2 –N 2 system, where the adsorbed amount could not be directly determined without knowledge of the local adsorbed-phase composition; nonetheless, complementation with a one-dimensional DCB model highlighted that XCT can provide valuable insights into complex dynamic phenomena. Both fast N 2 and slower CO 2 adsorption stages were well captured, and a local reduction in CT number ahead of CO 2 adsorption indicated a thermally enhanced roll-up, i.e., N 2 desorption driven by propagated heata phenomenon rarely observed due to measurement challenges. These findings highlight that XCT can be meaningfully utilized to improve our understanding of complex dynamic adsorption processes and, in doing so, can inform the development of more accurate process models. Building on this capability, the present study lays the groundwork for extending the DA method to cyclic adsorption processes, where measurements of internal loading profiles could provide experimental access to phenomena that are currently accessible only through simulations. Supplementary Material la6c00250_si_001.pdf (1.7MB, pdf) Acknowledgments DB is supported through the Departmental PhD Scholarship from the Department of Chemical Engineering, Imperial College London. The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.langmuir.6c00250 . Equations of the one-dimensional dynamic adsorption model; gas density–CT number calibration; X-ray noise estimation for gas density calibration and packed-bed measurements; uncertainty analysis; condition for the extremum of R ( p ); equilibrium adsorption isotherm data; additional temperature and internal profile data from dynamic column breakthrough experiments ( PDF ) The authors declare no competing financial interest. References Sircar S.. Applications of Gas Separation by Adsorption for the Future. Adsorpt. Sci. Technol. 2001;19:347–366. doi: 10.1260/0263617011494222. [ DOI ] [ Google Scholar ] Pullumbi P., Brandani F., Brandani S.. Gas separation by adsorption: technological drivers and opportunities for improvement. Curr. Opin. Chem. Eng. 2019;24:131–142. doi: 10.1016/j.coche.2019.04.008. [ DOI ] [ Google Scholar ] Chao C., Deng Y., Dewil R., Baeyens J., Fan X.. Post-combustion carbon capture. Renew. Sustain. Energy Rev. 2021;138:110490. doi: 10.1016/j.rser.2020.110490. [ DOI ] [ Google Scholar ] Gabrielli P., Gazzani M., Mazzotti M.. The Role of Carbon Capture and Utilization, Carbon Capture and Storage, and Biomass to Enable a Net-Zero-CO2 Emissions Chemical Industry. Ind. Eng. Chem. Res. 2020;59:7033–7045. doi: 10.1021/acs.iecr.9b06579. [ DOI ] [ Google Scholar ] Zanco S. E., Joss L., Hefti M., Gazzani M., Mazzotti M.. Addressing the Criticalities for the Deployment of Adsorption-based CO2 Capture Processes. Energy Procedia. 2017;114:2497–2505. doi: 10.1016/j.egypro.2017.03.1407. [ DOI ] [ Google Scholar ] Raganati F., Miccio F., Ammendola P.. Adsorption of Carbon Dioxide for Post-combustion Capture: A Review. Energy Fuels. 2021;35(16):12845–12868. doi: 10.1021/acs.energyfuels.1c01618. [ DOI ] [ Google Scholar ] Ganiyu S. A.. Review of zeolitic-based sorbents for CO2 capture: Insights into functional modifications economic feasibility and machine learning-enhanced strategies. Chem. Eng. J. Adv. 2025;23:100818. doi: 10.1016/j.ceja.2025.100818. [ DOI ] [ Google Scholar ] Boot-Handford, M. E. ; et al. Carbon capture and storage update, Apple Academic Press, 2014, pp 145–200. [ Google Scholar ] Wilkins N. S., Rajendran A., Farooq S.. Dynamic column breakthrough experiments for measurement of adsorption equilibrium and kinetics. Adsorption. 2021;27:397–422. doi: 10.1007/s10450-020-00269-6. [ DOI ] [ Google Scholar ] Hofman P. S., Rufford T. E., Chan K. I., May E. F.. A dynamic column breakthrough apparatus for adsorption capacity measurements with quantitative uncertainties. Adsorption. 2012;18:251–263. doi: 10.1007/s10450-012-9398-y. [ DOI ] [ Google Scholar ] Ruthven, D. M.

Principles of Adsorption and Adsorption Processes; Dynamics of Adsorption ColumnsSingle-Transition Systems, John Wiley & Sons: New York, 1984; Chapter 8.8, pp 220–231. [ Google Scholar ] Alhashem H., Sengupta D., Bose S., Wang X., Sha F., Islamoglu T., Farha O. K.. Effective Strategy toward Obtaining Reliable Breakthrough Curves of Solid Adsorbents. ACS Appl. Mater. Interfaces. 2024;16:5093–5102. doi: 10.1021/acsami.3c15859. [ DOI ] [ PubMed ] [ Google Scholar ] Esquivel G. C., Shafeeyan M. S., Nava C. O. R., Cabello-Robles J. J., Botello M. T. H., García-Martínez J. C.. Carbon dioxide adsorption modeling to determine breakthrough curves in a fixed bed: isotherm and temperature effects. Int. J. Chem. React. Eng. 2024;22:1395–1408. doi: 10.1515/ijcre-2024-0117. [ DOI ] [ Google Scholar ] Wilkins N. S., Rajendran A.. Measurement of competitive CO2 and N2 adsorption on Zeolite 13X for post-combustion CO2 capture. Adsorption. 2019;25:115–133. doi: 10.1007/s10450-018-00004-2. [ DOI ] [ Google Scholar ] Avijegon G., Xiao G., Li G., May E. F.. Binary and ternary adsorption equilibria for CO2/CH4/N2 mixtures on Zeolite 13X beads from 273 to 333 K and pressures to 900 kPa. Adsorption. 2018;24:381–392. doi: 10.1007/s10450-018-9952-3. [ DOI ] [ Google Scholar ] Rajagopalan A. K., Rajendran A.. The effect of nitrogen adsorption on vacuum swing adsorption based post-combustion CO2 capture. Int. J. Greenhouse Gas Control. 2018;78:437–447. doi: 10.1016/j.ijggc.2018.09.002. [ DOI ] [ Google Scholar ] Hsieh J. S., Turian R. M., Tien C.. Multicomponent liquid phase adsorption in fixed bed. AIChE J. 1977;23:263–275. doi: 10.1002/aic.690230308. [ DOI ] [ Google Scholar ] Kapoor A., Yang R. T.. Roll-up in fixed-bed, multicomponent adsorption under pore-diffusion limitation. AIChE J. 1987;33:1215–1217. doi: 10.1002/aic.690330717. [ DOI ] [ Google Scholar ] Li G., Xiao P., Xu D., Webley P. A.. Dual mode roll-up effect in multicomponent non-isothermal adsorption processes with multilayered bed packing. Chem. Eng. Sci. 2011;66:1825–1834. doi: 10.1016/j.ces.2011.01.023. [ DOI ] [ Google Scholar ] Pirngruber G. D., Hamon L., Bourrelly S., Llewellyn P. L., Lenoir E., Guillerm V., Serre C., Devic T.. A method for screening the potential of MOFs as CO2 adsorbents in pressure swing adsorption processes. ChemSusChem. 2012;5:762–776. doi: 10.1002/cssc.201100716. [ DOI ] [ PubMed ] [ Google Scholar ] Ahn H., Chun C., Park M., Ahn I. S., Lee C. H.. Thermal effects on the breakthrough curve of a hydrogen ternary system at a fixed bed. Sep. Sci. Technol. 2001;36:2121–2145. doi: 10.1081/SS-100105909. [ DOI ] [ Google Scholar ] Pini R., Joss L.. See the unseen: applications of imaging techniques to study adsorption in microporous materials. Curr. Opin. Chem. Eng. 2019;24:37–44. doi: 10.1016/j.coche.2019.01.002. [ DOI ] [ Google Scholar ] Burnett T. L., Withers P. J.. Completing the picture through correlative characterization. Nat. Mater. 2019;18:1041–1049. doi: 10.1038/s41563-019-0402-8. [ DOI ] [ PubMed ] [ Google Scholar ] Maire E., Withers P. J.. Quantitative X-ray tomography. Int. Mater. Rev. 2014;59:1–43. doi: 10.1179/1743280413y.0000000023. [ DOI ] [ Google Scholar ] Pini R.. Multidimensional quantitative imaging of gas adsorption in nanoporous solids. Langmuir. 2014;30:10984–10989. doi: 10.1021/la502582c. [ DOI ] [ PubMed ] [ Google Scholar ] Joss L., Pini R.. Digital Adsorption: 3D Imaging of Gas Adsorption Isotherms by X-ray Computed Tomography. J. Phys. Chem. C. 2017;121:26903–26915. doi: 10.1021/acs.jpcc.7b09836. [ DOI ] [ Google Scholar ] Joss L., Pini R.. 3D Mapping of Gas Physisorption for the Spatial Characterisation of Nanoporous Materials. ChemPhysChem. 2019;20:524–528. doi: 10.1002/cphc.201801148. [ DOI ] [ PubMed ] [ Google Scholar ] Pini R., Joss L., Hosseinzadeh Hejazi S. A.. Quantitative imaging of gas adsorption equilibrium and dynamics by X-ray computed tomography. Adsorption. 2021;27:801–818. doi: 10.1007/s10450-020-00268-7. [ DOI ] [ Google Scholar ] Wellington S. L., Vinegar H. J.. X-Ray Computerized Tomography. J. Pet. Technol. 1987;39:885–898. doi: 10.2118/16983-PA. [ DOI ] [ Google Scholar ] Malek A., Farooq S., Rathor M., Hidajat K.. Effect of velocity variation due to adsorption-desorption on equilibrium data from breakthrough experiments. Chem. Eng. Sci. 1995;50:737–740. doi: 10.1016/0009-2509(94)00245-M. [ DOI ] [ Google Scholar ] Rajendran A., Kariwala V., Farooq S.. Correction procedures for extra-column effects in dynamic column breakthrough experiments. Chem. Eng. Sci. 2008;63:2696–2706. doi: 10.1016/j.ces.2008.02.023. [ DOI ] [ Google Scholar ] Ward A., Pini R.. Efficient Bayesian Optimization of Industrial-Scale Pressure-Vacuum Swing Adsorption Processes for CO2 Capture. Ind. Eng. Chem. Res. 2022;61(36):13650–13668. doi: 10.1021/acs.iecr.2c02313. [ DOI ] [ Google Scholar ] Delgado J. A., Águeda V. I., Uguina M. A., Sotelo J. L., Brea P., Grande C. A.. Adsorption and diffusion of H2, CO, CH4, and CO2 in BPL activated carbon and 13X zeolite: Evaluation of performance in pressure swing adsorption hydrogen purification by simulation. Ind. Eng. Chem. Res. 2014;53:15414–15426. doi: 10.1021/ie403744u. [ DOI ] [ Google Scholar ] Park Y., Ju Y., Park D., Lee C. H.. Adsorption equilibria and kinetics of six pure gases on pelletized zeolite 13X up to 1.0 MPa: CO2, CO, N2, CH4, Ar and H2. Chem. Eng. J. 2016;292:348–365. doi: 10.1016/j.cej.2016.02.046. [ DOI ] [ Google Scholar ] Cavenati S., Grande C. A., Rodrigues A. E.. Adsorption Equilibrium of Methane, Carbon Dioxide, and Nitrogen on Zeolite 13X at High Pressures. J. Chem. Eng. Data. 2004;49:1095–1101. doi: 10.1021/je0498917. [ DOI ] [ Google Scholar ] McEwen J., Hayman J. D., Yazaydin A. O.. A comparative study of CO2, CH4 and N2 adsorption in ZIF-8, Zeolite-13X and BPL activated carbon. Chem. Phys. 2013;412:72–76. doi: 10.1016/j.chemphys.2012.12.012. [ DOI ] [ Google Scholar ] Schell J., Casas N., Pini R., Mazzotti M.. Pure and binary adsorption of CO 2, H 2, and N 2 on activated carbon. Adsorption. 2012;18:49–65. doi: 10.1007/s10450-011-9382-y. [ DOI ] [ Google Scholar ] Millward A. R., Yaghi O. M.. Metal-organic frameworks with exceptionally high capacity for storage of carbon dioxide at room temperature. J. Am. Chem. Soc. 2005;127:17998–17999. doi: 10.1021/ja0570032. [ DOI ] [ PubMed ] [ Google Scholar ] Dreisbach F., Staudt R., Keller J. U.. High Pressure Adsorption Data of Methane, Nitrogen, Carbon Dioxide and their Binary and Ternary Mixtures on Activated Carbon. Adsorption. 1999;5(3):215–227. doi: 10.1023/a:1008914703884. [ DOI ] [ Google Scholar ] Rufford T. E., Watson G. C., Saleman T. L., Hofman P. S., Jensen N. K., May E. F.. Adsorption equilibria and kinetics of methane + nitrogen mixtures on the activated carbon Norit RB3. Ind. Eng. Chem. Res. 2013;52:14270–14281. doi: 10.1021/ie401831u. [ DOI ] [ Google Scholar ] Park D., Ju Y., Kim J. H., Ahn H., Lee C. H.. Equilibrium and kinetics of nitrous oxide, oxygen and nitrogen adsorption on activated carbon and carbon molecular sieve. Sep. Purif. Technol. 2019;223:63–80. doi: 10.1016/j.seppur.2019.04.051. [ DOI ] [ Google Scholar ] Kapoor A., Ritter J. A., Yang R. T.. An Extended Langmuir Model for Adsorption of Gas Mixtures on Heterogeneous Surfaces. Langmuir. 1990;6:660–664. doi: 10.1021/la00093a022. [ DOI ] [ Google Scholar ] Broom D. P.. Challenges in characterizing adsorbents for gas storage and separation. Adsorption. 2024;30(7):1565–1591. doi: 10.1007/s10450-023-00424-9. [ DOI ] [ Google Scholar ] Mohammad S., Fitzgerald J., Robinson R. L., Gasem K. A.. Experimental uncertainties in volumetric methods for measuring equilibrium adsorption. Energy Fuels. 2009;23:2810–2820. doi: 10.1021/ef8011257. [ DOI ] [ Google Scholar ] Pini R.. Interpretation of net and excess adsorption isotherms in microporous adsorbents. Microporous Mesoporous Mater. 2014;187:40–52. doi: 10.1016/j.micromeso.2013.12.005. [ DOI ] [ Google Scholar ] Singh V. K., Kumar E. A.. Measurement of CO2 adsorption kinetics on activated carbons suitable for gas storage systems. Greenhouse Gases:Sci. Technol. 2017;7:182–201. doi: 10.1002/ghg.1641. [ DOI ] [ Google Scholar ] Churchill S. W., Chu H. H.. Correlating equations for laminar and turbulent free convection from a horizontal cylinder. Int. J. Heat Mass Transfer. 1975;18:1049–1053. doi: 10.1016/0017-9310(75)90222-7. [ DOI ] [ Google Scholar ] Holman, J. P.

Heat transfer McGraw-Hill series in mechanical engineering, 9th ed.; McGraw-Hill: New York, 2002. [ Google Scholar ] Knox J. C., Ebner A. D., Levan M. D., Coker R. F., Ritter J. A.. Limitations of Breakthrough Curve Analysis in Fixed-Bed Adsorption. Ind. Eng. Chem. Res. 2016;55:4734–4748. doi: 10.1021/acs.iecr.6b00516. [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] Richardson, J. F. ; Harker, J. H. ; Backhurst, J. R. ; Coulson, J. M. . Coulson and Richardson’s Chemical Engineering, Particle Technology and Separation Processes, 5 th ed.; Butterworth-Heinemann: Oxford, Vol. 2, 2002. [ Google Scholar ] von Seckendorff J., Hinrichsen O.. Review on the structure of random packed-beds. Can. J. Chem. Eng. 2021;99:S703–S733. doi: 10.1002/cjce.23959. [ DOI ] [ Google Scholar ] Delgado J. M.. A critical review of dispersion in packed beds. Heat Mass Tran. 2006;42:279–310. doi: 10.1007/s00231-005-0019-0. [ DOI ] [ Google Scholar ] Associated Data This section collects any data citations, data availability statements, or supplementary materials included in this article. Supplementary Materials la6c00250_si_001.pdf (1.7MB, pdf) Articles from Langmuir are provided here courtesy of American Chemical Society ACTIONS View on publisher site PDF (5.0 MB) Cite Collections Permalink RESOURCES Similar articles Cited by other articles Links to NCBI Databases Follow NCBI NCBI on X (formerly known as Twitter) NCBI on Facebook NCBI on LinkedIn NCBI on GitHub NCBI RSS feed Connect with NLM NLM on X (formerly known as Twitter) NLM on Facebook NLM on YouTube National Library of Medicine 8600 Rockville Pike Bethesda, MD 20894 Web Policies FOIA HHS Vulnerability Disclosure Help Accessibility Careers NLM NIH HHS USA.gov Back to Top

Related documents

• Prevalencia de cálculos pulpares en dientes permanentes en el sector posterior. Análisis tomográfico computarizado de haz cónico en el Centro Radiográfico X Ray. Periodo 2020-2023#1041277
• Materials Experiment and Analysis Database: Sample imaging and alignment measurements containing 2 files performed on plate containing Co,Mn,V,Zr annealed at 535.0C to add O on 2014-12-08 from Run 20141207.181005#674752
• Tratamiento de revelador agotado del proceso de impresión digital de CtP (Computer-to-Plate) por medio de oxidación parcial con dióxido de titanio (Tio2) mediante fotocatálisis en un reactor fotocatalítico con luz UV#1002003
• Materials Experiment and Analysis Database: X-ray fluorescence analysis in which 0 sub-analyses are performed on plate(s) containing C, Sn,Fe,Cu,Mn,Co,Ta annealed at 400.0C to add O on 2017-01-15 from Analysis 20170115.142648#294044
• Carbon Dioxide Investigation#872507