https://orcid.org/0009-0006-6082-0010
Figures
Abstract
Adsorbed natural gas (ANG) technology represents a viable option for energy storage solutions. However, the enhancement of the storage performance is constrained by the thermal effect inherent to conformable ANG storage tanks for small dual-fuel ships. This research had developed a COMSOL numerical model for a 200 L conformable ANG storage tank packed with HKUST-1 to simulate the thermal effects resulting from the charging flow rates and temperature, charging modes. Based on the numerical calculation results, the effects of these charging conditions on the storage performance of the conformable storage tank were analyzed and evaluated. The findings suggested that the heat generated throughout the charging process was a crucial factor affecting both the cumulative storage amount and temperature fluctuations within the ANG system. Furthermore, the study revealed that a combination of low charging temperature and cyclic charging significantly mitigated the adverse effect of thermal effects, thereby improving charging efficiency, and enhancing the overall storage performance of the conformable ANG storage tank.
Citation: Yang B, Lu J, Sun Y (2025) Effect of charging conditions on the storage performance of a conformable adsorbed natural gas tank packed with HKUST-1. PLoS One 20(12): e0336677. https://doi.org/10.1371/journal.pone.0336677
Editor: Nayan Ranjan Singha, Maulana Abul Kalam Azad University of Technology West Bengal, INDIA
Received: April 21, 2025; Accepted: October 29, 2025; Published: December 2, 2025
Copyright: © 2025 Yang et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: The research data of this paper are uploaded to the Zenodo database (DOI:10.5281/zenodo.15879766).
Funding: This research project was sponsored by Natural Science Foundation of Fujian Provincial (2023J01905), Young and Middle-aged Scientific Research Project of Fujian Province (JAT210300). Innovation and Entrepreneurship Project for University Students in Fujian Province (S202310399052).
Competing interests: The authors have declared that no competing interests exist.
1. Introduction
Natural gas, with its high calorific value, low carbon dioxide emissions and sustainability attributes, is internationally recognized as a clean energy [1]. The utilization of natural gas as a fuel for small dual-fuel ships can reduce carbon emissions, thereby contributing to the mitigation of the greenhouse effect. Natural gas application upon vessels still faces many restrictions [2]. Among these, lack of effective storage technology is one of the crucial technical issues. ANG technology offers the advantage of storing natural gas at low pressures and ambient temperatures [3]. The conformable ANG storage tanks, due to their compact design and ease of use, can be applied as storage tanks for small dual-fuel ships [4]. However, the thermal effect within adsorption system exhibited greater prominence as the charging process progressed, which in turn impedes the improvement of storage performance, and poses challenges for the effective storage of natural gas.
Currently, in order to weaken the thermal effect within ANG adsorbent system, the primary strategies focused on adding heat transfer structures to adsorbent beds and improving the thermal conductivity of the adsorbents. The known heat transfer structures include honeycomb fins [5], 3D printed metal grids [6], and heat transfer fins affixed to the outer wall of storage tanks [7]. Moreover, the structure of conformable ANG storage tanks also served as a measure to enhance heat transfer, facilitating the mitigation of thermal effects in adsorbent beds. As the size of conformable storage tanks increased, the thermal effect of adsorbent beds became evident during the charging process [3]. Nano porous carbon, noted for its high thermal conductivity [8] and MOFs [9,10], characterized by their high specific surface area and pore volume, are regarded as ideal adsorbents for ANG. Adding specific proportions of expanded graphite [5] or graphene oxide [11], etc. into the adsorbents could improve their thermal conductivity. These approaches aimed to improve charging efficiency by facilitating the heat exchange between the interior and exterior of adsorbent beds. Furthermore, the natural gas flow acted as a heat carrier [12], during the cyclic charging, it transferred heat into and out of the adsorbent bed, thereby promoting heat exchange within and around ANG tanks. This mechanism represented another technological approach for managing thermal effects and improving the storage performance. Based on existing literatures [13–15], simulation studies on small-scale ANG storage systems primarily focused on two-dimensional axisymmetric models, which were not applicable to the modeling of a conformable ANG storage tank. Therefore, considering its compact structure, a three-dimensional model needed to be established for numerical analysis.
Given the preceding considerations, it is necessary to construct a three-dimensional model to research the effect of cyclic charging under various conditions on the storage performance of conformable ANG storage tanks. This research focused on a modular, flat-designed ANG storage tank unit. The thermal conductivities of the adsorbent bed in both the longitudinal and transverse directions of its three-dimensional model were calculated. Charging/discharging tests and numerical simulation verification by filling activated carbon SAC-02 (with a BET specific surface area 1550 m2·g-1) in a vessel with a capacity of approximately 1 L were conducted. Considering the challenges associated with performing tests directly on a 200 L ANG tank in practical applications, the validated model was scaled up to its actual size. Subsequently, HKUST-1 known for its excellent methane adsorption performance, was selected as the adsorbent [6]. A quantitative analysis and evaluation were performed regarding the effects of cyclic charging under different conditions on the storage performance of the conformable tank packed with HKUST-1, focusing on main aspects such as cumulative charging amount, charging duration and efficiency.
2. Methodology
2.1. Experimental
The conformable ANG storage tank enhanced the utilization of external space, as illustrated in Fig 1. The test rig for a conformable ANG vessel was presented in Fig 2. In order to provide fuel for about 10 minutes, the vessel with a net capacity of approximately 1L was designed, which constituted a unit of the conformable ANG storage system. Additionally, four T-shaped thermocouples were arranged within the storage vessel to monitor temperature fluctuations at the upper, middle and lower sections, as depicted in Fig 3. Methane, the adsorbate in this study, was a flammable and explosive gas. Prior to conducting the tests, it was necessary to perform leak detection. Nitrogen with a purity of 99.99% was introduced into the system until the pressure reached 3.5 MPa, ensuring that the pressure change within the system was less than 0.2% after 24 h. The coconut shell activated carbon SAC-02 used in this study was produced by Ning de Xin Sen Company in Fujian. After being dried at 150°C for 24 h in a vacuum drying oven, the activated carbon was placed into the ANG vessel. Stainless steel strainers were installed at both ends of the vessel to prevent powder from being expelled. Finally, a pump with a vacuum level of 0.054 Pa was employed to evacuate the system for 12 h, simultaneously removing the impurity gases within the system. Detailed procedures for the tests could be referred to the literature [16].
2.2. Numerical simulations
The numerical simulation of the charging process was conducted using COMSOL software. The model equations were discretized utilizing the control volume integral method. The adsorption equilibrium for methane upon the adsorbent could be formulated as
The effects of both the viscous resistance and inertial resistance of the methane could be expressed as follows [17]
The energy conservation equation throughout the adsorption and desorption of methane on porous adsorbents could be formulated as
The effective heat capacity of the transient term was expressed as follows
During the adsorption process, assuming that no heat was generated in the adsorbent system, i.e., an isothermal charging process, whose charging efficiency was 1. The charging efficiency served as a measure of the thermal effect strength of the adsorbent system and
was defined as follows
The adsorbent bed utilized both longitudinal and transverse thermal conductivities by [18]
The heat generated throughout the charging process consisted of adsorption heat and compression heat, that’s
The modified D-A equation was utilized to compute the excess adsorption amount, that’s [19]
The mass transfer resistance was characterized by a linear driving force equation, that’s [20]
2.3. Model grids division and initial conditions
Considering the symmetry of the vessel, a quarter model was established. The COMSOL was utilized to automatically divide the grids. The results of the grid independence study were presented in Fig 4. Four progressively refined mesh divisions were evaluated, revealing that the computed mean temperature curves of the adsorbent bed were essentially coincident. Consequently, in order to reduce computation time, the fine mesh with a grid number of 4603 was selected.
The simulations were conducted based on the following assumptions:(1) The porosity of adsorbent particles was uniform; (2) The gas phase, adsorbent, and adsorption phase were in thermal equilibrium; (3) Methane gas exhibited laminar flow behavior at the storage vessel’s inlet and outlet.
Six points (A1-A6) were set to monitor temperature fluctuations, which were A1 (0, −0.025, 0.17), A2 (0, −0.025, 0.0925), A3 (0, −0.025, 0.003), A4 (0, 0.00625, 0.17), A5 (0, 0.00625, 0.0925) and A6 (0, 0.00625, 0.003), as illustrated in Fig 5. The cyclic charging process was simulated with the following setup. The bottom of the vessel was designated as the outlet, as depicted in Fig 5. Once the pressure within the adsorbent system attained the preset value, ventilation commenced at the outlet. At this moment, the adsorbent system maintained the preset pressure, and the charging process was still ongoing. The simulation process was set with a step size of 1 s and a relative tolerance of 1e-4. The initial pressure within the model was 0 Pa, and both the initial and ambient temperature were all 298 K. The density of methane was calculated as an ideal gas, with a specific heat capacity of 2222 J·kg-1·K-1, a thermal conductivity of 0.0332 W·m-1·K-1, and a dynamic viscosity of 1.087e-5 Pa·s. These parameters for the vessel wall were 7840 kg·m-3, 502 J·kg-1·K-1, and 13.78 W·m-1·K-1 respectively.
3. Results and discussion
3.1. Verification of the numerical model
Methane charging and discharging verification tests were performed using a vessel containing the activated carbon SAC-02. The physical characteristics and fitting parameters for the D-A equation related to the SAC-02 were presented in Table 1. A typical flow rate corresponding to the actual operating conditions of the ship power plant was adopted for model validation tests. The vessel was packed with about 310 g of SAC-02. The experimental data of the flow rate was recorded using a MFC. The fitting sectioned functions for this charging and discharging mass fluxes were presented in Table 2.
Figs 6a-6b illustrated a comparison of the experimental data with the simulated values regarding pressure variations and mean temperature fluctuations. The simulated values represented the average of results obtained from multiple repetitions of simulations conducted under identical conditions. All mean relative errors remained below 5%, falling within the acceptable limits. This result suggested that the developed numerical model was accurate and appropriate for simulations and predictive researches.
3.2. Effect of charging conditions upon the storage performance
The thermal effects of the adsorbent system containing HKUST-1 were evaluated through a numerical model based on a storage tank with a net capacity of about 200 L. Table 3 displayed the physical properties of HKUST-1. The experimental results regarding the excess adsorption of methane on HKUST-1 were analyzed using nonlinear fitting through the D-A equation, and the parameters derived from this equation for HKUST-1 were listed in Table 3.
3.2.1. Effect of different charging flow rates.
With the rise in charging flow rate, the peak value of the mean temperature rose significantly, and the moment to reach the peak temperature was clearly advanced, so the charging duration to reach the target pressure was shortened in Fig 7. This was mainly due to the charging flow rate increasing, the heat within the adsorbent system couldn’t be transmitted in time, thereby leading to a rapid rise in temperature. From the D-A equation, it could be inferred that the instantaneous adsorption amount would decrease at this time. Therefore, the cumulative charging amount decreased from 1329.6 g to 1259.4 g, reducing around by 5.3%. In contrast, assuming no heat generation during the isothermal charging process, the temperature remained constant, resulting in an isothermal cumulative charging amount of 1468.2 g, which remained unchanged. Since the denominator remained constant while the numerator decreased, the charging efficiency correspondingly declined from 90.6% to 85.8%. Furthermore, under the same target pressure, a higher charging flow rate indicated a shorter charging duration, which decreased by 77.5%, as detailed in Table 4.
3.2.2. Effect of different charging temperatures.
Based on the findings from the previous section, it was evident that a mass flux of 8.7024e-3 kg·m-2·s-1 for charging resulted in both the maximum cumulative charging amount and charging efficiency of the adsorbent bed. Consequently, this section utilized this mass flux for further investigation. When charging at different temperatures, the mean temperature fluctuations exhibited a consistent trend, as shown in Fig 8. The maximal mean temperature within the adsorbent system at a charging temperature of 193 K was about 1.4% lower than that at room temperature, while the cumulative charging amount increased by 3.3% approximately. Due to the same charging flow rate, the time taken for the adsorbent bed to reach the same pressure was essentially consistent across different charging temperatures. A lower charging temperature significantly decreased the mean temperature of the adsorbent bed. According to the D-A equation, this would improve both the accumulated charging amount and isothermal charging amount, while also cause an increase in the temperature difference between the interior and exterior of the adsorbent bed, and lead to a decrease in the charging efficiency. This relationship was illustrated in the data presented in Table 5.
3.2.3. Effect of different charging modes.
As depicted in Fig 9, after attaining the peak temperature, the mean temperature within the adsorbent system could be decreased rapidly during cyclic charging. After reaching the maximum temperature, the curve exhibited a swift decline to room temperature. During the cyclic charging(C) process, meanwhile after the pressure of the adsorbent bed attaining 3.5 MPa, the cumulative charging amount continued to increase, showing a growth of about 9.0%, which was significantly higher than that of charging mode(A). This was primarily attributable to that the temperature of the adsorbent bed continuously decreased, and methane was constantly adsorbed. Under the charging mode(A), charging ceased once the pressure reaching 3.5 MPa. As a result, the temperature declined faster than other modes, and the cumulative charging amount remained consistent. As cyclic charging(C) at 298 K, the charging efficiency was 96.9%, very close to that of the isothermal charging, the heat of adsorption and compression generated by the adsorbent bed was transferred rapidly by the gas flow, showing that the thermal effects had been weakened to a very low level. In contrast, charging mode (B), characterized by continuous charging without circulation, maintained the pressure at 3.5 MPa, leading to the continuous generation of heat and gradual temperature fluctuations, whose charging efficiency was slightly lower than that of cyclic charging (C), as detailed in Table 6.
3.2.4. Effect of charging modes combined with different charging flow rates and temperatures.
The mean temperature within the adsorption system under the charging condition Ⅲ declined significantly faster than that in other cases, with the corresponding cumulative charging amount reaching the maximum of 1638.3 g, as listed in Table 7. In comparison, when charging under condition Ⅴ, the mean temperature decline was only slower than that under condition Ⅲ. Under condition Ⅰ, the mean temperature was the highest and decreased at the slowest rate. The cumulative charging amount at condition Ⅴ was about 6.6% lower than that at condition Ⅲ. Moreover, the cumulative charging amount at condition Ⅲ was approximately 23.3% higher than that at condition Ⅰ in room temperature, the maximum mean temperature at condition Ⅰ reaching 309.8 K. The fluctuations of the mean temperature and cumulative charging amount at conditions Ⅱ and Ⅳ were relatively close, as shown in Fig 10. The charging flow rate determined the inflection points of each curve in Fig 10. Compared to the charging flow rate, cyclic charging and cryogenic intake were two crucial factors that could significantly reduce the mean temperature, while simultaneously enhancing the cumulative charging amount in the adsorption system, which approaching isothermal charging efficiencies as listed in Table 7.
Fig 11 demonstrated that at the moment charging completed, these charging conditions had a notable effect on the temperature at the inlet region within the adsorption system, with minimal impact upon that of the center region instead, where temperature was nearly uniform at about 314 K. Over time, compared to other conditions, cyclic charging combined with cryogenic intake could transfer heat and cool the adsorbent bed rapidly, progressively reduce the temperature within the entire adsorption system, achieving the goal of improving charging efficiency.
4. Conclusion
COMSOL was utilized to carry out numerical simulations to explore the storage performance of the conformable ANG tank. This research primarily analyzed and discussed the impact of various charging conditions upon the storage performance of the large-scale conformable adsorption system containing HKUST-1. Only methane was considered as the main component of natural gas, whereas in reality, natural gas also contains minor amounts of ethane, propane, butane and so on. The discussion on the impact of low-temperature factors on simulation results in the model was limited. Future researches could focus on the charging characteristics of multi-component natural gas in ANG. The following conclusions had been drawn:
- 1) Increasing the charging flow rate negatively impacted both the enhancement of cumulative charging amount and efficiency. Specifically, the cumulative charging amount decreased from 1329.6 g to 1259.4 g, representing a reduction of approximately 5.3%. Additionally, the charging efficiency declined from 90.6% to 85.8%.
- 2) Employing a lower charging temperature could enhance the cumulative charging amount, while resulting in a slight reduction in the charging efficiency. For instance, when using a charging temperature of 193 K compared to the room temperature, the peak of the mean temperature experienced a reduction of about 1.3%, while the cumulative charging amount rose by around 3.4%. Furthermore, as the charging temperature decreased, the charging efficiency of the adsorbent bed exhibited a minor downward trend.
- 3) Cyclic charging optimized the charging process, making it more close to an isothermal process, significantly mitigating the thermal effect within the adsorbent system, and achieving greater cumulative charging amount and efficiency. Notably, cyclic charging could largely influence the temperature fluctuations in the inlet region of the adsorbent system, while having less effect on that in the central region. The optimal charging conditions were as follows: a flow rate of 1.6566e-2 kg·m-2·s-1, a temperature of 213 K, and the implementation of cyclic charging, with a maximum cumulative charging amount of 1638.3 g and a charging efficiency of up to 94.7%.
References
- 1. Memetova A, Tyagi I, Karri RR, Kumar V, Tyagi K, Suhas, et al. Porous carbon-based material as a sustainable alternative for the storage of natural gas (methane) and biogas (biomethane): A review. Chemical Eng J. 2022;446:137373.
- 2. Wang Y, Cao Q, Liu L, Wu Y, Liu H, Gu Z, et al. A review of low and zero carbon fuel technologies: Achieving ship carbon reduction targets. Sustainable Energy Technol Assessments. 2022;54:102762.
- 3. Patil KH, Sahoo S. Charge characteristics of adsorbed natural gas storage system based on MAXSORB III. J Natural Gas Sci Eng. 2018;52:267–82.
- 4. Prosniewski MJ, Rash TA, Knight EW, Gillespie AK, Stalla D, Schulz CJ, et al. Controlled charge and discharge of a 40-L monolithic adsorbed natural gas tank. Adsorption. 2018;24(6):541–50.
- 5. Zhao G, Zheng Q, Zhang X, Zhang W. Adsorption equilibrium and the effect of honeycomb heat exchanging device on charge/discharge characteristic of methane on MIL-101(Cr) and activated carbon. Chinese J Chemical Eng. 2020;28(7):1964–72.
- 6. Grande CA, Kaiser A, Andreassen KA. Methane storage in metal-organic framework HKUST-1 with enhanced heat management using 3D printed metal lattices. Chemical Eng Res Design. 2023;192:362–70.
- 7. Chaudhary A, Gautam, Sahoo S. Thermal management and optimization of the reactor geometry for adsorbed natural gas storage systems subjected to free convection and radiative environment. J Natural Gas Sci Eng. 2023;109:1–20.
- 8. Men’shchikov IE, Shkolin AV, Strizhenov EM, Khozina EV, Chugaev SS, Shiryaev AA, et al. Thermodynamic Behaviors of Adsorbed Methane Storage Systems Based on Nanoporous Carbon Adsorbents Prepared from Coconut Shells. Nanomaterials (Basel). 2020;10(11):2243. pmid:33198162
- 9. Kayal S, Sun B, Chakraborty A. Study of metal-organic framework MIL-101(Cr) for natural gas (methane) storage and compare with other MOFs (metal-organic frameworks). Energy. 2015;91:772–81.
- 10. Sun B, Kayal S, Chakraborty A. Study of HKUST (Copper benzene-1,3,5-tricarboxylate, Cu-BTC MOF)-1 metal organic frameworks for CH4 adsorption: An experimental investigation with GCMC (grand canonical Monte-carlo) simulation. Energy. 2014;76:419–27.
- 11. Wang H, Zheng Q, Zhang X, Wu M. Development of HKUST-1 composites for methane storage by adsorption through incorporation and carbonization. Results Eng. 2023;18:101098.
- 12. Ubaid S, Zacharia R, Xiao J, Chahine R, Bénard P, Tessier P. Effect of flowthrough cooling heat removal on the performances of MOF-5 cryo-adsorptive hydrogen reservoir for bulk storage applications. Int J Hydrogen Energy. 2015;40(30):9314–25.
- 13. Prado DS, Amigo RCR, Paiva JL, Silva ECN. Analysis of convection enhancing complex shaped adsorption vessels. Applied Thermal Engineering. 2018;141:352–67.
- 14. Mirzaei S, Shahsavand A, Ahmadpour A, Garmroodi Asil A, Arami-Niya A. Dynamic simulation and experimental performance of an adsorbed natural gas system under variable charging conditions. Applied Thermal Eng. 2022;206:118067.
- 15. Chaudhary A, Gautam, Sahoo S. Thermal management and optimization of the reactor geometry for adsorbed natural gas storage systems subjected to free convection and radiative environment. Gas Sci Eng. 2023;109:104851.
- 16.
Wang H. Structure improvement and heat transfer enhancement of typical MOFs based on adsorbed natural gas (ANG) (In Chinese). Xiamen: Jimei University. 2023.
- 17. Mota JPB, Rodrigues AE, Saatdjian E, Tondeur D. Charge dynamics of a methane adsorption storage system: Intraparticle diffusional effects. Adsorption. 1997;3(2):117–25.
- 18. Delahaye A, Aoufi A, Gicquel A, Pentchev I. Improvement of hydrogen storage by adsorption using 2‐D modeling of heat effects. AIChE Journal. 2002;48(9):2061–73.
- 19. Richard MA, Bénard P, Chahine R. Gas adsorption process in activated carbon over a wide temperature range above the critical point. Part 1: modified Dubinin-Astakhov model. Adsorption, 2009, 15(1): 43–51.
- 20. Xiao Y, Qiu S, Zhao Q, Zhu Y, Godiya CB, He G. Numerical simulation of low-concentration CO2 adsorption on fixed bed using finite element analysis. Chinese Journal of Chemical Engineering. 2021;36:47–56.
- 21.
Wang ZH. Adsorption equilibrium of methane on typical adsorption materials (In Chinese). Xiamen: Jimei University; 2018.