Modified Dubinin Astakhov Research Articles

Adsorption of HFO-1234ze(E) onto Steam-Activated Carbon Derived from Sawmill Waste Wood

This study utilizes waste Albizia lebbeck wood from a sawmill to prepare activated carbon adsorbents and explores their potential application in adsorption cooling systems with a novel hydrofluoroolefin (HFO) refrigerant characterized by a low global warming potential. Activated carbon was synthesized through a simple and green steam activation method, and the optimal carbon shows a specific surface area of 946.8 m2/g and a pore volume of 0.843 cm3/g. The adsorption isotherms of HFO-1234ze(E) (Trans-1,3,3,3-tetrafluoropropene) on the activated carbon were examined at 30, 40, and 50 °C up to 400 kPa using a customized constant-volume variable-pressure system, and significant adsorption of 1.041 kg kg−1 was achieved at 30 °C and 400 kPa. The experimental data were fitted using both the Dubinin–Astakhov and Tóth models, and both models provided excellent fit results. The D–A adsorption model simulated the net adsorption capacity at possible operating temperatures. The isosteric of adsorption was determined using the Clausius–Clapeyron and modified Dubinin–Astakhov equations. In addition, the specific cooling effect and coefficient of performance were also studied.

Modeling High-Pressure Hydrogen Uptake by Nanoporous Metal–Organic Frameworks: Implications for Hydrogen Storage and Delivery

Due to their very high porosity and superior textural properties, metal–organic frameworks (MOFs) are promising nanoporous materials for hydrogen storage by cryocompression. Herein, we investigated hydrogen adsorption on four commercial MOFs, namely, MIL53-Al, MOF-5, HKUST-1, and MOF-177, over a temperature range of 77 to 273 K and pressures up to 14 MPa. The modified Dubinin–Astakhov equation was used to fit the experimental adsorption data, and six parameters (m, nmax, α, β, P0, and Va) were obtained. We concluded that the parameters nmax and Va are related to the micropore volume, while α, β, m, and P0 are related to the average micropore size. Compared to hydrogen compression in an empty tank, the introduction of MOF-5 enhanced the volumetric hydrogen storage at 77 K and 10 MPa from 31 to 42 kg m–3. The released H2 capacities of MOFs from a loading pressure of 10 MPa to a discharge pressure of 0.5 MPa were determined for either isothermal discharge at 77 K or after temperature increase to 160 K. For MOF-5, the amount of usable hydrogen increased up to 10.6 wt % (40.8 mg cm–3) by pressure drop (from 10 to 0.5 MPa) and temperature increase (from 77 to 160 K).

Insight into the Adsorption of Methane on Gas Shales and the Induced Shale Swelling.

Shale gas resources are highly abundant in the world. They can provide sustainable energy supply and have the potential to reduce energy prices. Therefore, shale gas has become one of the most important resources for oil and gas exploration and production, especially in North America today. Adsorption and desorption of methane gas are some of the important physical and chemical processes involved in the accumulation, transport, and production of shale gas. The shale matrix will shrink or swell due to the desorption or adsorption of methane gas, which will impact the recovery of shale gas reservoirs. The main purpose of this investigation is to quantitatively ascertain how the adsorption of methane gas affects the volumetric changes of the shale matrix. Based on the adsorption potential theory, a modified Dubinin–Astakhov (D–A) equation was employed to describe the adsorption of supercritical methane gas on shale. Then, a coupled adsorption–strain model was established to investigate the volumetric strain of shale induced by the combined effects of methane gas adsorption and stress compression. The methane adsorption and the induced shale swelling were measured on a black shale sample from the Sichuan Basin at 303.15 K and pressure up to 10 MPa, and the proposed models were employed to interpret the experimental data. The results demonstrate that the proposed models show good applicability and provide a reliable prediction. The swelling moduli of shale samples were obtained by fitting the experimental data using the coupled adsorption–strain model. The results indicate that the swelling modulus of shale in this study is generally greater than that of coal. The calculated ratios of Young’s modulus to the swelling modulus do not show great variation from shale to shale in this study, which is similar to coal. This study can be incorporated into the numerical simulation of the production process of shale gas reservoirs.

Modified Dubinin-Astakhov Model for the Accurate Estimation of Supercritical Methane Sorption on Shales.

In order to evaluate the total shale gas-in-place (GIP) resources in deep formations, it is important to study the sorption of supercritical methane in shales. At present, the Dubinin–Astakhov model is used to describe sorption isotherms. However, it still has some shortcomings. The main objective of this study is to establish an optimized model for supercritical methane sorption in shales. A series of high-pressure methane sorption isotherms were measured at different temperatures (from 293 to 333 K) for shale samples collected in the Cengong block, Guizhou, China. The characteristics and causes of shale gas sorption capacity changes were analyzed. By comparing the fitting results of several conventional sorption models, the characteristics and applicable scope of these models are obtained. A four-parameter (V0, D, m, and ρa) modified supercritical D–A model was developed to accurately estimate the sorption of supercritical methane on shales based on Polanyi sorption potential theory. The results show that the sorption characteristic curve of methane on the shale surface under high pressure is obviously different from that under low pressure. The density of the sorption phase and the virtual saturated vapor pressure have a great influence on the fitting results of the sorption models. The density of the adsorption phase directly determines the ultimate sorption capacity of the shale sample. Also, the modified D–A model can improve the accuracy of the prediction of supercritical methane sorption on shales, and it can accurately describe the isothermal sorption law of gas in the supercritical state.

A critical analysis of transport models for refueling of MOF-5 based hydrogen adsorption system

This work presents a critical analysis of 2D model of refueling a hydrogen storage tank containing MOF-5 adsorbent under cryogenic and room temperature conditions. Three isotherm models, viz. Unilan, modified Dubinin–Astakhov DA and Tóth, were fitted with experimental data of hydrogen adsorption from the literature, and their effect on refueling of adsorbent bed is analyzed. The choice of isotherm has the greatest impact on predicting refueling behavior, for both flow-through and end-flow (i.e., batch) systems. A comparison between the ideal gas assumption and virial equation of state indicates that the former reasonably captures the overall behavior at lower computational cost. Analysis of the role of momentum balance, solved as full Navier–Stokes model and with Darcy’s approximation, indicates same hydrogen uptake in the adsorbent bed and only a minor difference in the predicted velocity profiles. Finally, effect of temperature-dependent physical properties of gas, adsorbent and walls is analyzed.

Application of the modified Dubinin-Astakhov equation for a better understanding of high-pressure hydrogen adsorption on activated carbons

Hydrogen storage in activated carbons (ACs) has proven to be a realistic alternative to compression and liquefaction. Adsorption capacities up to 5.8 wt% have indeed been obtained. The amount of adsorbed hydrogen depends on the textural properties of ACs, such as specific surface area and total pore volume. The modified Dubinin-Astakhov (MDA) equation proved to be a good analytical tool for describing hydrogen adsorption in a wide range of pressures and temperatures and for several adsorbents. The parameters of this model have been found to be somehow related to the textural properties of the adsorbent. Thus, we applied this model to understand better hydrogen adsorption on ACs over a wide range of pressures in relation to the textural properties of the ACs.We applied the MDA equation to evaluate also the isosteric heat of hydrogen adsorption, which was found to be in the range of 5–9 kJ mol−1. We compared the results obtained by applying the MDA equation with those obtained by both the sorption isosteric method and the Sips equation. This allowed finding the temperature dependence of the isosteric heat of adsorption, as well as its variation with respect to the textural properties of the ACs.

Analytical model and experimental investigation of the adsorption thermodynamics of coalbed methane

The study on adsorption thermodynamics is conducive to a deep understanding of the heat and mass transfer mechanism of coalbed methane in a coal seam. In this work, the analytical expressions of the isosteric heat for six adsorption models taking into account the temperature variations are directly derived according to Clausius–Clapeyron equation. Meanwhile, the adsorption content and adsorption heat at different pressures and temperatures are measured by the volumetric method of adsorption with a microcalorimetry system. It is found that the the adsorption heats obtained by different adsorption models exhibit different trends. The fitting quality of the experimental isotherms for different adsorption models affects the adsorption heat result. However, even if the models well fit the experimental isotherms, the theoretical adsorption heat values may be inconsistent. Furthermore, the calorimetric heats for all coal samples decreases with the increase in adsorption content in relation to the micropore distribution of coal. For all coal samples, the modified Dubinin–Astakhov (D–A) model can well fit the experimental isotherms and agree well with the results of calorimetric heats. By comparing the theoretical heat for different k values and the measured heat, the pseudo-saturation vapor pressure of the modified D–A model can be determined. Finally, by virtue of the isosteric heat of adsorption in a small temperature range, the adsorption isotherms at other adjacent temperatures are predicted successfully.

Adsorption system with heat pipe thermal control for mobile storage of gaseous fuel

Mobile storage of gaseous fuel is the design bottleneck in a commercialization of vehicles powered by natural gas and hydrogen. This paper is devoted to the questions of development of the system of effective accumulation and safe storage of natural gas in a coupled state by activated carbon fiber based on commercially available “Busofit TM-055”. Original experimental setup was developed for carrying out investigation of the processes of adsorption of gaseous fuel in the different carbon adsorbents and for simulation of gas charging/discharging of a storage vessel. The experimental data for methane equilibrium adsorption in a wide temperature range between 233 and 313 K and pressure up 5 MPa are obtained and analyzed from the standpoint of the theory of volume filling of micropores and the linearity of the adsorption isosteres. In the supercritical temperature region modified Dubinin–Astakhov equation are proposed for the prediction of the isotherms and isosteric heat of adsorption.In a second part, the basic settings of CFD model in terms of adsorption equilibrium, kinetics and coupled heat and mass transfer are described and results are discussed in regard to measures. The heat pipes are considered as a basic element of the thermal control for the storage vessels. A more detailed study of dynamic behavior of thermally controlled storage has been performed for constant mass flow rate and constant pressure of the methane at the inlet of the adsorber-vessel.

Isosteric heat of hydrogen adsorption on MOFs: comparison between adsorption calorimetry, sorption isosteric method, and analytical models

Isosteric heat of adsorption is an important parameter required to describe the thermal performance of adsorptive storage systems. It is most frequently calculated from adsorption isotherms measured over wide ranges of pressure and temperature, using the so-called adsorption isosteric method. Direct quantitative estimation of isosteric heats on the other hand is possible using the coupled calorimetric–volumetric method, which involves simultaneous measurement of heat and adsorption. In this work, we compare the isosteric heats of hydrogen adsorption on microporous materials measured by both methods. Furthermore, the experimental data are compared with the isosteric heats obtained using the modified Dubinin–Astakhov, Tóth, and Unilan adsorption analytical models to establish the reliability and limitations of simpler methods and assumptions. To this end, we measure the hydrogen isosteric heats on five prototypical metal–organic frameworks: MOF-5, Cu-BTC, Fe-BTC, MIL-53, and MOF-177 using both experimental methods. For all MOFs, we find a very good agreement between the isosteric heats measured using the calorimetric and isosteric methods throughout the range of loading studied. Models’ prediction on the other hand deviates from both experiments depending on the MOF studied and the range of loading. Under low-loadings of less than 5 mol kg−1, the isosteric heat of hydrogen adsorption decreases in the order Cu-BTC > MIL-53 > MOF-5 > Fe-BTC > MOF-177. The order of isosteric heats is coherent with the strength of hydrogen interaction revealed from previous thermal desorption spectroscopy measurements.

Reconstruction of adsorption potential in Polanyi-based models and application to various adsorbents.

The equilibrium Polanyi adsorption potential was reconstructed as ε = -RT ln(Ca(orH)/δ) to correlate the characteristic energy (E) of Polanyi-based models (qe = f[ε/E]) with the properties or structures of absorbates, where qe is the equilibriumn adsorption capacity, Ca(orH) is the converted concentration from the equilibrium aqueous concentration at the same activity and corresponds to the adsorption from the gas or n-hexadecane (HD) phase by the water-wet adsorbent, and "δ" is an arbitrary divisor to converge the model fitting. Subsequently, the modified Dubinin-Astakhov model based on the reconstructed ε was applied to aqueous adsorption on activated carbon, black carbon, multiwalled carbon nanotubes, and polymeric resin. The fitting results yielded intrinsic characteristic energies Ea, derived from aqueous-to-gas phase conversion, or EH, derived from aqueous-to-HD phase conversion, which reflect the contributions of the overall or specific adsorbate-adsorbent interactions to the adsorption. Effects of the adsorbate and adsorbent properties on Ea or EH then emerge that are unrevealed by the original characteristic energy (Eo), i.e., adsorbates with tendency to form stronger interactions with an adsorbent have larger Ea and EH. Additionally, comparison of Ea and EH allows quantitative analysis of the contributions of nonspecific interactions, that is, a significant relationship was established between the nonspecific interactions and Abraham's descriptors for the adsorption of all 32 solutes on the four different adsorbents: (Ea - EH) = 24.7 × V + 9.7 × S - 19.3 (R(2) = 0.97), where V is McGowan's characteristic volume for adsorbates, and S reflects the adsorbate's polarity/polarizability.

Performance comparison of adsorption isotherm models for supercritical hydrogen sorption on MOFs

Modeling of adsorption on porous material plays a crucial role in providing a better understanding of adsorption phenomena, isotherms, and isosteric heats, and predicting the thermodynamics of adsorption-based storage systems. In this work, the multicomponent potential theory of adsorption (MPTA) coupled with the modified Dubinin potential (MDP), the modified Dubinin–Astakhov (DA) model, and the Unilan model are compared for their effectiveness in nonlinear least square fitting of experimental hydrogen adsorption data on three prototypical metal–organic frameworks (MOFs) in two temperature ranges: 30K—room temperature (RT) for MOF-5, and 77K—RT for MOF-5, Cu-BTC, and MIL-101. The ability of each model to accurately describe excess adsorption is found to depend on the pore size and the energetic pore heterogeneity of MOFs, and the latter's relation to the assumptions used within each model. The simpler Langmuir-like Unilan model complies best with the monolayer type adsorption mechanism in MOFs with large pores and homogenous pore distribution, such as in MOF-5, while the pore filling models like modified DA and MPTA–MDP better represent the adsorption phenomena in MOFs with smaller pores and heterogeneous pore distributions, such as Cu-BTC and MIL-101. In the vicinity of hydrogen's critical temperature, adsorbed hydrogen inside the pores of MOF-5 undergoes a phase-transition to solid-like phase with densities higher than that of bulk solid hydrogen, which is attributed to the increased force field in the confined pores of MOF-5.

Lumped parameter model for charge–discharge cycle of adsorptive hydrogen storage system

We present a lumped parameter model for an adsorptive hydrogen storage system based on activated carbon. The model simply employs general mass balance and energy balance equations resulted from the fundamental conservation equations of thermodynamics. A modified Dubinin–Astakhov isotherm and a variable isosteric heat of adsorption are adopted in the lumped parameter model to improve validity for whole charge–discharge cycle. The lumped parameter model is implemented in Matlab/Simulink platform and applied to simulate charge–discharge cycle of the hydrogen storage system. Thermal averaging temperature is used to fill the gap between the multi-dimensional models, such as 0D model of Matlab/Simulink and 2D model of Comsol. The model is well validated by two sets of validation tests with the coolants of ice water and room temperature water respectively. The lumped parameter model is efficient and also accurate for predicting performance of adsorptive hydrogen storage system. Parametric studies are conducted to analyze the validity of the variable isosteric heat of adsorption, the practicality of heat transfer coefficient and the effect of hydrogen storage pressure.

Heat and mass transfer and fluid flow in cryo-adsorptive hydrogen storage system

Compared to room temperature adsorption, cryo-adsorptive hydrogen storage capacity has been greatly improved, and has become the central issue of the hydrogen storage research. Accurate simulation and optimization for cryo-adsorptive hydrogen storage has important guidance and application value to the experimental research, and the finite element software Comsol Multiphysics™ and system analysis software Matlab/Simulink™ can be used to simulate the cryo-adsorptive hydrogen storage. However, the computational fluid dynamics (CFD) software Fluent™ can provide more information on the heat and mass transfer and the fluid flow than above softwares. Based on the mass, momentum and energy conservation equations, this paper uses the modified Dubinin–Astakhov (D–A) adsorption isotherm model, linear driving force (LDF) model and dynamic thermal boundary condition which are implemented by means of CFD software Fluent to simulate the hydrogen adsorption processes of charging and dormancy in the case of liquid nitrogen cooling. We study the variations of temperature and pressure during the processes of charging and dormancy. The results show that the experimental data is in good agreement with the simulation results. We also analyze the effect of variable specific heat and anisotropic thermal conductivity on the heat and mass transfer and the fluid flow in cryo-adsorptive hydrogen storage system.

Long range structural and textural changes in [Zn(bdc)(ted)0.5] upon spontaneous dispersion of LiCl and hysteretic adsorption and desorption of carbon dioxide and hydrogen

A LiCl containing Zn(bdc)(ted)0.5 metal–organic framework (MOF) was prepared via an innocuous impregnation and thermal spontaneous dispersion process. The dispersion of the LiCl and crystallinity of the modified microporous framework were verified via standard and in situ high temperature X-ray diffraction (XRD). Pure component CO2 and H2 equilibrium adsorption–desorption analyses were performed on Zn(bdc)(ted)0.5 and (LiCl)[Zn(bdc)(ted)0.5] at 25 °C. The latter exhibited unexpected adsorption–desorption hystereses for both adsorbates and, according to XRD data, these were due to what appears to be a framework or pore contraction. Pore volumes estimated via a fit of desorption data with a Modified Dubinin–Astakhov model indicated that the LiCl containing material framework voids were at least 74% smaller as compared to the apohost. XRD patterns also indicated that the (LiCl)[Zn(bdc)(ted)0.5] structure expanded back to the apohost original state upon a nearly complete desorption of the CO2 adsorbate, suggesting that the apparent phase transition was reversible for this case. The overall adsorptive behavior of the (LiCl)[Zn(bdc)(ted)0.5] materials suggests that these could be suitable for gas capture applications under ambient conditions. For instance, the resulting average H2 heat of adsorption value is among the highest reported so far for a MOF.

Finite element simulation of heat and mass transfer in activated carbon hydrogen storage tank

A mathematical model of heat and mass transfer in activated carbon (AC) tank for hydrogen storage is proposed based on a set of partial differential equations (PDEs) controlling the balances or conservations of mass, momentum and energy in the tank. These PDEs are numerically solved by means of the finite element method using Comsol MultiphysicsTM. The objective of this paper is to establish a correct set of PDEs describing the physical system and appropriate parameters for simulating the hydrogen storage process. In this paper, we establish an axisymmetric model of hydrogen storage by adsorption on activated carbon, considering heat and mass transfer of hydrogen in storage tank during the charging process at room temperature (295K) and the pressure of 10MPa. To simulate the hydrogen storage process accurately, the heat capacity of adsorbed phase, the contact thermal resistance between the AC bed and the steel wall and the inertial resistance of high speed charging hydrogen gas are all taken into account in the model. The governing equations describing the hydrogen storage process by adsorption are solved to obtain the pressure changes, temperature distributions and adsorption dynamics in the storage tank. The pressure reaches a maximum value of 10MPa at about 240s. A small downward trend appears in the later stage of the charging process, which lasts 700s. The temperature distribution is highest in the center of the tank. The temperature history exhibits a rapid increase initially, followed by a steady decline. A modified Dubinin–Astakhov (D–A) model is used to represent the hydrogen adsorption isotherms. The highest hydrogen uptake is 10molH2/kg AC, at the entrance of hydrogen storage tank, where the temperature is lowest. The adsorption distribution at a given time is mainly determined by the temperature distribution, because the pressure is almost uniform in the tank. The adsorption history, however, is dominated by the pressure history because the pressure change is much larger than temperature change during the charging process of hydrogen storage.

Ion exchange and adsorption equilibrium studies on clinoptilolite, bentonite and vermiculite

In the present paper three natural minerals used in many industrial and environmental applications namely zeolite clinoptilolite and the clays bentonite and vermiculite are studied by utilising ion exchange and adsorption. In particular, the Dubinin–Astakhov adsorption isotherm is used modified by introducing a solubility-normalized adsorption potential for studying the ion exchange process. The equation, is applied in experimental isotherms in order to determine adsorption energy and heterogeneity parameter for the ion exchange of Pb 2+ in the natural minerals. The results indicate that the modified Dubinin–Astakhov adsorption isotherm represents the experimental data well and at the same time provides the heterogeneity parameter of the materials, which is an important adsorbent physical parameter as well as the adsorption energy. In order to deepen the study and link the results to the pore structure BET analysis is presented as well.

Volumetric hydrogen sorption capacity of monoliths prepared by mechanical densification of MOF-177

Bulk powdered MOF-177 is mechanically compressed to prepare monoliths with bulk densities more than three times its crystallographic density, and their excess and total gravimetric and volumetric hydrogen storage capacities are measured over a pressure range of 0–13 MPa at 77 K and room temperature. The maximum excess volumetric hydrogen storage capacity of these monoliths at ∼6 MPa and 77 K is 25.8 ± 1.2 g L−1, which is a 78% increase of that of powdered bulk MOF-177 and 80% of the theoretical maximum excess volumetric hydrogen storage capacity predicted on the basis of the material's crystallographic density. The monoliths show diminishing excess gravimetric capacity with increasing density which is attributed to their decreasing micropore volume, which in turn stems from the progressive collapse of MOF-177 crystals to an amorphous phase when they are subjected to densification. A modified Dubinin–Astakhov (DA) model is adapted to describe the excess gravimetric adsorption of samples with varying bulk densities. The total volumetric capacity of monoliths prepared from MOF-177 is 48.0 ± 2.1 g L−1 at 13 MPa and 77 K; if a complete storage system that does not reduce this capacity by more than 20% is designed, it can then meet the DOE 2015 volumetric system target at 77 K. Under the same conditions, it is easier to meet the DOE 2015 gravimetric system target of 5.5 wt% as the material's total gravimetric storage capacity is ∼10.3 ± 0.3 wt%.

Water Sorption Analysis on Vegetables Using Modified Dubinin–Astakhov Parameters

The parameters of a modified Dubinin–Astakhov (DA) equation were studied for six kinds of fresh vegetables. The equilibrium moisture content data were fitted to the modified DA equation under the condition that the limit of the moisture content of the adsorption space represented by M 0 was assumed to be roughly equal to the equilibrium moisture content at the relative humidity of 97.3%. Then we calculated other two DA parameters of n and A e . The former is the distribution index of the Weibull probability density function, and the latter is a characteristic energy. In addition, the logarithm of the value increased proportionally with the increase of the n value, and the A e value could be experimentally identified by the degree of the pore inside the vegetable. Moreover, we discussed the relationship between the DA parameter M 0 and the moisture content M m calculated with the monolayer adsorption capacity defined by a Brunauer–Emmett–Teller equation. As the results, the logarithm of M 0 approximately represented the direct proportion to that of M m among all tested vegetables. This showed the power low relationship between M 0 and M m , and the slope of the line could mean the fractal dimension of the moisture sorption space.

Adsorption equilibria of pure vapors and their binary mixtures on activated carbon Part I. Single-component equilibria

Absorption and desorption equilibria of three organic vapors on two kinds of activated carbon are investigated theoretically and experimentally. The application of the adsorption integral equation to microporous adsorbents is discussed. It is shown that the Dubinin theory of volume filling of micropores (TVFM) provides an improved method for describing the adsorption of organic vapors in the micropores of the carbon. From adsorption and desorption experiments, the transition from micropore filling to capillary condensation in mesopores can be observed. The corresponding adsorption potentials are related to a pore radius of about 1.6 nm. A modified Dubinin—Astakhov equation is proposed, which takes into account the end of micropore filling and the characteristic curves by means of a limiting potential A Gr. This equation describes the isothermal field of all six investigated systems very well in a wide temperature range (20 – 150 °C) with temperature-invariant parameters.