Gas Adsorption Behavior Research Articles

Computational study on the effect of steric hindrance in functionalised Zr-based metal-organic frameworks on hydrocarbon storage and separation

ABSTRACT Light hydrocarbon gases, such as methane, ethane, propane, ethylene, and propene, are commonly used in manufacturing processes as raw material or energy fuel. Traditionally, these gases are mainly separated by cryogenic distillation, which requires massive amounts of energy because of high-pressure and low-temperature operating conditions. Many studies have shown that metal–organic frameworks (MOFs) are potential materials for gas storage and separation because of their unique properties, such as high surface area, nontoxicity, and large gas storage capacity. UiO-66 and its modified materials are considered ideal candidates for gas storage and separation and have attracted increased attention since they can be easily synthesized and are thermally and chemically stable. In this study, we used grand canonical Monte Carlo (GCMC) to simulate and understand the gas adsorption behaviour of UiO-66 and its variants, including UiO-66-NO2, UiO-66-NH2, UiO-66-Br, and UiO-66-(CH3)2, for pure light hydrocarbon gases and their binary mixtures. The adsorption isotherm and adsorption site energy distribution are analysed and discussed to identify the best candidate for gas adsorption and separation. It is found that the modified form of UiO-66-NH2 has good selectivity, large gas storage potential, and high working capacity compared to UiO-66. Further insight into favourable gas adsorption positions is discussed.

Synthesis, structural and sorption characterization of a Hofmann compound, Ni(3-methy-4,4′-bipyridine)[Ni(CN)4

Acetone extraction of crystalline Ni(CN)4-based metal organic framework Ni(3-Methy-4,4′-bipyridine)[Ni(CN)4] which has dimethyl sulfoxide “DMSO” as guest molecules (nicknamed Ni-BpyMe(D) followed by evacuation yielded the guest-free crystalline framework, (Ni-BpyMe(A)). Ni-BpyMe(A) was determined to be orthorhombic, Pmma, a = 12.6025(4) Å, b = 7.3324(3) Å, c = 11.3095(4) Å, V = 1045.07 (2) Å3 and Z = 2. The structure of Ni-BpyMe(A) consists of a 3-D net built from extended 2-D [Ni(CN)4] groups. These layers are connected to each other via the BpyMe ligands at the six-fold coordinated Ni1 site while Ni2 has a four-fold coordination environment. While forming infinite square nets, the [Ni(CN)4] chains progress in a zig-zag fashion along the ab-direction; they can be projected along a or b directions. Another feature of this structure is that instead of locating the –CH3 group in one position of the pyridine ring as expected, it appears to be in two mirror-related positions on the same pyridine ring. The structure represents an average of two configurations which gives rise to the pseudosymmetry. The methyl group is distributed equally among each side of the pyridine ring; therefore, the occupancy of the methyl group is 50%. The compound exhibits a Type-I sorption characteristic. The absence of a hysteresis loop indicates that it is not likely a flexible MOF. A comparison of the structure of Ni-BpyMe(A) with the previously reported structure of Ni-BpyMe(D) with DMSO as guest molecules revealed a different structure (Monoclinic P2/n) as a result of significant increase in the bipyridyl dihedral angle from 34.87° to 90.00° after removal of the guest molecules in the pores. The change in ring orientation of the BpyMe ligands stabilize the pore structure against collapse. The structural change is relevant to gate opening behaviors observed in other MOFs although no gating behavior was indicated in the gas adsorption behavior.

Thermodynamic Analysis of CH4/CO2/N2 Adsorption on Anthracite Coal: Investigated by Molecular Simulation

The interpretation of gas adsorption behavior on a coal surface is an important theoretical basis for gas injection to enhance the recovery of coalbed methane. In order to further explore the adsor...

Utilization of zeolite as a potential multi-functional proppant for CO2 enhanced shale gas recovery and CO2 sequestration: A molecular simulation study of the impact of water on adsorption in zeolite and organic matter

We proposed to use zeolites as multi-functional proppants for enhanced shale gas recovery and CO2 sequestration in our previous paper and studied the competitive adsorption of CO2 and CH4 in silicalite-1 and kerogen organic matter. It is proved that CO2 released from proppants can be preferentially adsorbed by kerogen and replace the adsorbed CH4. In the present paper, we aim at studying the impact of water on the gas adsorption capacity and selectivity of CO2 over CH4 since water can significantly alter gas adsorption behaviors in zeolites and organic matter. We carry out grand canonical Monte Carlo simulations of water adsorption and the competitive adsorption of a CO2, CH4, and water mixture in silicalite-1 and in kerogen. It is found that water is less favored in both adsorbents but could suppress the adsorption of CO2 and CH4 when the water content is high, it can also enhance CO2/CH4 selectivity under some circumstances. Kerogen shows a stronger preference for adsorbing CO2 over CH4 under most conditions; thus, the replacement process of CO2 and CH4 with water present can still happen in the positive direction.

Outstanding Performance of Transition-Metal-Decorated Single-Layer Graphene-like BC6N Nanosheets for Disease Biomarker Detection in Human Breath.

In the present work, we report highly sensitive and selective nanosensors constructed with metal-decorated graphene-like BC6N employing nonequilibrium Green’s function (NEGF) formalism combined by density functional theory (DFT) toward multiple inorganic and sulfur-containing gas molecules (NO, NO2, NH3, CO, CO2, H2S, and SO2) as disease biomarkers from human breath. Monolayer sheets of pristine BC6N and Pd-decorated BC6N were evaluated for their gas adsorption properties, electronic property changes, sensitivity, and selectivity toward disease biomarkers. The pristine BC6N nanosheets exhibited sharp drops in the bandgap when interacted with gases such as NO2 while barely affected by other gases. However, the nanosecond recovery time and low adsorption energies limit the gas sensing applications of the pristine BC6N sheet. On the other hand, the Pd-decorated BC6N-based sensor underwent a semiconductor to metal transition upon the adsorption of NOx gas molecules. The conductance change of the sensor’s material in terms of I–V characteristics revealed that the Pd-decorated BC6N sensor is highly sensitive (98.6–134%) and selective (12.3–74.4 times) toward NOx gas molecules with a recovery time of 270 s under UV radiation at 498 K while weakly interacting with interfering gases in exhaled breath such as CO2 and H2O. The gas adsorption behavior suggests that metal-decorated BC6N sensors are excellent candidates for analyzing pulmonary disease and cardiovascular biomarkers, among other ailments of the stomach, kidney, and intestine.

CO2 and CH4 adsorption on periodic mesoporous organosilica: A DFT study

Periodic mesoporous organosilicas (PMO) were proposed as potential adsorbents for CO2/CH4 adsorption-separation due to their strong interactions with CO2 and low affinity for CH4. Herewith, we present a comprehensive density functional theory (DFT) study about the binding properties of CO2 and CH4 with the pore walls of different PMO materials. The calculations considered the M06−2X DFT exchange-correlation functional, and cluster models of the walls of the PMO materials with organic bridges based on phenylene (Ph-), biphenylene (Bph-), pyridine (Py-) and bipyridine (Bpy-) fragments or on mixtures of Ph/Py- and Bph/Bpy- moieties. All materials showed stronger interactions with CO2 than with CH4, which suggests they are potentially selective for CO2 over CH4. From the calculated data it is demonstrated that the PMO materials with phenylene moieties establish more favorable contacts with CO2 than those found in their counterparts with bridges based on the homologous heteroaromatic nitrogen compounds, viz. pyridine. Independently of the size of the organic bridge, both phenylene- and biphenylene- PMO materials showed similar CO2 adsorption behavior. The presence of bipyridine-bridges improved the CO2 adsorption behavior only when mixed with biphenylene moieties. The adsorption behavior of CO2 gas can be directly related to the SiOH···OCO distance, i.e., the adsorption strength increases with the decrease of this distance. In the case of the CH4 adsorption, the least favorable adsorptions were determined for PMO materials with pyridine and phenylene/pyridine bridges.

The Determination of Pore Shape and Interfacial Barrier of Entry for Light Gases Transport in Amorphous TEOS-Derived Silica: A Finite Element Method.

The interfacial barrier of entry for light gas transport in a nanopore was a crucial factor to determine the separation efficiency in membrane technologies. To examine this effect, amorphous silica was prepared by sol-gel process, and its characterization results revealed that the commonly used cylindrical pore shape failed to represent the adsorption behavior of gases, but instead the pore shape had to be represented by a slit pore model. A finite element method (FEM) was developed to analyze the interfacial resistance by integrating a Lennard-Jones (LJ) potential over the layer area. It was found that the strong repulsion/attraction at the pore interface could be paired with the motion energy of guest molecules to predict the ideal selectivity between gases, thereby providing a solution to preliminarily screen the separation performance among a host of membrane candidates.

Ammonia gas sensing properties and density functional theory investigation of coral-like Au-SnSe2 Schottky junction

This paper introduces a coral-like Au-modified SnSe2 nanocomposite prepared by a simple hydrothermal method. The pure- and Au-modified SnSe2 film sensors were prepared on the substrate with interdigitated electrodes by drop coating. The compositions, morphologies and microstructures of the as-synthesized nanomaterials were observed using transmission electron microscopy (TEM), X-ray diffraction (XRD), scanning electron microscopy (SEM) and X-ray photoelectron spectroscopy (XPS). The Au-modified SnSe2 nanocomposite has a coral-like morphology assembled from many irregular and very thin nanosheets. The gas performances of the film sensors at room temperature were tested through a series of experiments. The experimental results demonstrated that the Au-modified SnSe2 nanocomposite film sensor had excellent response characteristics, extremely short response/recovery time, outstanding gas selectivity and stability towards ammonia gas compared with the pure one. In addition, the first-principle density functional theory (DFT) was employed to simulate the effect of Au modification on gas adsorption behavior, clarifying the internal mechanism of gas sensing by combining with Au-SnSe2 Schottky junction. These results verified that the Au-modified SnSe2 film sensor is a high-performance candidate for enhanced ammonia gas sensing properties at room temperature.

Two porous Ni-MOFs based on 2,4,6-tris(pyridin-4-yl)-1,3,5-triazine showing solvent determined structures and distinctive sorption properties toward CO2 and alkanes.

By regulating the solvent used for synthesis, two porous Ni-MOFs, namely {[Ni3(BTC)2(TPT)2/3(H2O)4.08(MeOH)0.92]·2DMF·0.5H2O·0.5MeOH}n (1) and {[Ni3(BTC)2(TPT)2(H2O)6]·6DMF}n (2) (H3BTC = 1,3,5-benzenetricarboxylic acid, TPT = 2,4,6-tris(pyridin-4-yl)-1,3,5-triazine, DMF = N,N-dimethylformamide, and MeOH = methanol) were obtained. Compound 1 reveals a rigid 3D framework, while compound 2 shows a flexible 3-fold interpenetrated framework. Compound 1 exhibits a selective adsorption of CO2 due to the sieving effect of the rigid framework containing two types of cages with small apertures. Noteworthily, the flexible compound 2 displays an obviously guest-induced structural transformation. The desolvated compound 2 reveals a much higher capacity toward CO2 and n-C4H10 than those of N2 CH4, C2H6 and C3H8.

Thermal decarboxylation for the generation of hierarchical porosity in isostructural metal-organic frameworks containing open metal sites.

The effect of metal-cluster redox identity on the thermal decarboxylation of a series of isostructural metal–organic frameworks (MOFs) with tetracarboxylate-based ligands and trinuclear μ3-oxo clusters was investigated. The PCN-250 series of MOFs can consist of various metal combinations (Fe3, Fe/Ni, Fe/Mn, Fe/Co, Fe/Zn, Al3, In3, and Sc3). The Fe-based system can undergo a thermally induced reductive decarboxylation, producing a mixed valence cluster with decarboxylated ligand fragments subsequently eliminated to form uniform mesopores. We have extended the analysis to alternative monometallic and bimetallic PCN-250 systems to observe the cluster's effect on the decarboxylation process. Our results suggest that the propensity to undergo decarboxylation is directly related to the cluster redox accessibility, with poorly reducible metals, such as Al, In, and Sc, unable to thermally reduce at the readily accessible temperatures of the Fe-containing system. In contrast, the mixed-metal variants are all reducible. We report improvements in gas adsorption behavior, significantly the uniform increase in the heat of adsorption going from the microporous to hierarchically induced decarboxylated samples. This, along with Fe oxidation state changes from 57Fe Mössbauer spectroscopy, suggests that reduction occurs at the clusters and is essential for mesopore formation. These results provide insight into the thermal behavior of redox-active MOFs and suggest a potential future avenue for generating mesoporosity using controlled cluster redox chemistry.

Molecular engineering in a family of pillared-layered metal-organic frameworks for tuning gas adsorption behavior.

In this work, inspired by a water-assisted three-dimensional supramolecular structure 1, we use a mixed-ligand strategy to form a 3D pillared-layered matrix by the introduction of linear ligands to compete against the water molecules. The resulting analogue microporous MOFs of 2-H, 2-F and 2-N, decorated with different functional groups, similarly show the CO2 uptake. Thanks to the negligible N2 adsorption capacity, enhanced selective adsorption towards CO2 is achieved in compound 2-N. That is, we present here an alternative plan for the high CO2 selective adsorption performance. In addition, the structure stability and moderate affinity for CO2 of these microporous MOFs endow them with excellent reusability.

Modeling Non-isothermal Transport Behavior of Real Gas in Deformable Coal Matrix

This work presents a coupled thermo-hydraulic–mechanical (THM) model to study real gas flow behavior in a deformable coal matrix. The matrix encompasses multiple pore sizes ranging from nanometers to micrometers, and promotes various complex, inter-related mass transport mechanisms. In this model, the adsorbed gas layer at the interface between the solid matrix and the free gas phase is considered as an independent phase. Gas adsorption/desorption and diffusion process are defined separately for individual phase, which are then interacted via mass exchange between the phases. The Knudsen number based flow regimes are adopted to describe bulk gas transport in the matrix of varying pore sizes, and the adsorbed phase transport is described by surface diffusion mechanisms. The thermal effect on gas adsorption and transport behavior is investigated. In addition, the mechanical behavior is included to consider the stress dependency of the porosity and intrinsic permeability of porous rocks. The validity of the proposed model is achieved by comparing numerical solutions with published experimental data. Numerical simulations were performed to investigate the real gas transport processes in a coal matrix of multiple pore sizes. The simulated results show that the times to reach pressure equilibrium and adsorption equilibrium are not the same, and they depend on the pore size, pressure, and surface diffusion. The time required to reach equilibrium is reduced significantly with an increase of pore sizes. Diffusion coefficients in the porous matrix are not constant but vary with pressure and pore sizes, which is important for accurate estimation of coalbed gas production or carbon sequestration.

High performance novel nanoadsorbents derived - natural cellulose fibers for superior CO2 adsorption and CO2 / CH4 separation

ABSTRACT Currently dioxide carbon and methane as the most important greenhouse gases are constantly being emitted to the atmosphere. Thus, to reduce the detrimental effects resulting from these gases, they must be captured and separated. In this regard, novel and low- cost nanoadsorbents based on cotton pulp, jute, and kenaf as carbon fibers were successfully synthesized and fabricated. In order to provide a micro-mesoporous structure, cotton pulp, jute, and kenaf as carbon fibers were carbonized at 600°C and then activated with KOH/C (named CP-AC, J-AC, and K-AC samples). The physicochemical properties of the fabricated nanoadsorbents were characterized by BET, FTIR, XRD, and ESEM analyses. Compared to the other nanoadsorbents used, J-AC nanoadsorbent displayed an enhanced CO2 adsorption capacity at the pressure of 1 bar (5.7 mmol/g) and 35 bar (18.4 mmol/g). The fabricated nanoadsorbents created a high surface area (up to 1978 m2/g) with a pore volume of up to 0.95 cm 3/g. Several isotherm models were utilized to investigate the adsorption behavior of gases. It was found that Dual site Langmuir-Freundlich model better fitted the experimental data. The ideal adsorbed solution theory (IAST) was employed to calculate the adsorption selectivity and with the results revealing a considerable CO2/CH4 selectivity. The results also indicated that the fabricated nanoadsorbents at low pressures compared to the nanoadsorbent used in the literature have higher adsorption capacity for CO2. To summarize, the synthesized nanoadsorbents provided an excellent adsorption capacity. Thus, they could be considered for CO2 and CH4 adsorption.

Crystallizing Atomic Xenon in a Flexible MOF to Probe and Understand Its Temperature-Dependent Breathing Behavior and Unusual Gas Adsorption Phenomenon.

Flexible metal-organic frameworks (MOFs) hold great promise as smart materials for specific applications such as gas separation. These materials undergo interesting structural changes in response to guest molecules, which is often associated with unique adsorption behavior not possible for rigid MOFs. Understanding the dynamic behavior of flexible MOFs is crucial yet challenging as it involves weak host-guest interactions and subtle structural transformation not only at the atomic/molecular level but also in a nonsteady state. We report here an in-depth study on the adsorbate- and temperature-dependent adsorption in a flexible MOF by crystallizing atomic gases into its pores. Mn(ina)2 shows an interesting temperature-dependent response toward noble gases. Its nonmonotonic, temperature-dependent adsorption profile results in an uptake maximum at a temperature threshold, a phenomenon that is unusual. Full characterization of Xe-loaded MOF structures is performed by in situ single-crystal and synchrotron X-ray diffraction, IR spectroscopy, and molecular modeling. The X-ray diffraction analysis offers a detailed explanation into the dynamic structural transformation and provides a convincing rationalization of the unique adsorption behavior at the molecular scale. The guest and temperature dependence of the structural breathing gives rise to an intriguing reverse of Xe/Kr adsorption selectivity as a function of temperature. The presented work may provide further understanding of the adsorption behavior of noble gases in flexible MOF structures.

Crystalline Naphthylene Macrocycles Capturing Gaseous Small Molecules in Chiral Nanopores.

A series of chiral naphthylene macrocycles, [n]cyclo-epi-naphthylenes ([n]CeNAPs), possessing epi-linkages were synthesized by one-pot macrocyclization. With chiral (R)- or (S)-1,1'-linkages embedded in binaphthyl precursors, the macrocycles were assembled in polygonal structures possessing chiral hinges as corners. Among four chiral [n]CeNAP variants, [8]CeNAP with eight naphthylene panels formed robust columnar assemblies in crystals. The nanoporous crystals maintained a columnar assembly structure even after the removal of encapsulated solvent molecules, and their gas adsorption behavior was thoroughly investigated. Gas adsorption, including state-of-the-art in situ crystallographic analyses, revealed accurate atomic-level structures of the nanopores trapping gaseous N2 molecules in chiral C2 arrangements. With macrocycles as basic frameworks, functional nanopores may be exploited for chiral small-molecule alignments.

Adsorption and absorption of supercritical methane within shale kerogen slit

Gas storage in shale primarily includes three forms: free gas in the fractures or macropores, adsorbed gas upon the kerogen surface, and absorbed gas in the kerogen matrix. However, current techniques cannot distinguish the adsorbed and absorbed gas, which restrict the understanding of gas storage and transport mechanisms through shale kerogen. On the basis of the grand canonical Monte Carlo (GCMC) simulations, we propose a technique to determine the independent adsorption and absorption isotherms of methane within slit-shaped shale kerogen under supercritical conditions. We observe that if the pore pressure is higher than ~3.5 MPa, the absorption amount is much smaller than that of adsorbed gas; however, at lower pressures, the absorption capacity is superior to that of the adsorption. Meanwhile, the ratio between adsorption and absorption quantities continuously increases with pressure. We probe the underlying mechanisms and study the effect of slit aperture, temperature, as well as moisture on gas adsorption and absorption capacity. Enlarging the slit aperture increases the adsorbed gas contents but shows only a negligible effect on the absorption capacity. Heating facilitates the escapement of gas molecules, thus leading to the inhibition of both adsorption and absorption capacities. Water molecules occupying the adsorption site on the slit surface impedes methane adsorption, but the absorption capacity within the kerogen matrix remains unchanged. This work elucidates the gas adsorption and absorption behavior in shale kerogen and sheds light on the storage and transport of hydrocarbons in nanoporous materials.

Experimental investigation of methane adsorption and desorption in water-bearing shale

Methane adsorption and desorption in shale can significantly be affected by water due to the water-bearing depositional environment of shale and the application of hydraulic fracturing technology in shale gas production. The characteristics of shale gas adsorption and desorption are comprehensively affected by the temperature, pressure, and especially, the water content in the reservoir. To further explore the impact of water on shale gas adsorption and desorption, the adsorption-desorption experiments of methane in water-bearing shale at different temperatures and different pressures are performed. Afterward, the adsorption behavior and desorption hysteresis are characterized by employing the Langmuir model and Langmuir+λ model. Finally, the ways of the pressure, temperature, and water combinedly affect shale gas adsorption behavior and desorption hysteresis are analyzed. The results show that adsorption and desorption of methane in the water-bearing shale are irreversible, which are consistent with the Langmuir model and the Langmuir+λ model, respectively. An increase in temperature will reduce adsorption and promote desorption, as an increase in temperature essentially enhances the thermal movement of methane molecules. Water lowers the adsorption and desorption of methane in shale, as the water molecules occupy the adsorption sites in organic pores and clay mineral pores in different ways. However, the effect of temperature and water content on adsorption is closely related to the pressure. The lower the pressure, the more significant the effect of temperature and water content. The combined effect analysis demonstrates that the impact of water on methane adsorption in shale is much more significant than that of the temperature. Still, desorption is simultaneously affected by both temperature and water content. As the pressure decreases in the desorption process, the desorption rate is dominantly affected by water when the pressure is lower than 8 MPa, and the desorption rate is aggressively affected by temperature when the pressure is at above 8 MPa. Cited as : Li, A., Han, W., Fang, Q., Memon, A., Ma, M. Experimental investigation of methane adsorption and desorption in water-bearing shale. Capillarity, 2020, 3(3), 45-55, doi: 10.46690/capi.2020.03.02

Kinetic and thermodynamic studies on gas adsorption behaviour of natural fibres

Gas adsorption properties of key natural fibres were investigated through monitoring the adsorption process of ammonia onto wool and cotton by time-resolved infrared spectroscopy. It was found that Langmuir isotherm model best described ammonia adsorption onto wool and cotton, indicating monolayer adsorption. The adsorption capacity of wool and cotton for ammonia was found to be 7.948 × 10−5 mol g−1 and 3.066 × 10−5 mol g−1, respectively. Adsorption diffusion was found to be the rate limiting step for wool in the initial adsorption stage, following the Dumwald–Wagner model. For cotton, adsorption reaction process was found to be the rate limiting step for the whole adsorption, following the pseudo-second-order model. The activation energy values of ammonia adsorption were calculated to be 26.50 kJ mol−1 for wool and 30.43 kJ mol−1 for cotton, which demonstrates that ammonia adsorption onto fibres requires energy. The study could promote developing textile products for odour control.

Pristine and palladium-doped perovskite bismuth ferrites and their nitrogen dioxide gas sensor studies

Undoped and palladium-doped perovskite bismuth ferrite nitrogen dioxide (NO2) gas sensors (BiFeO3 i.e. BFO and Pd-BiFeO3 i.e. Pd-BFO) are successfully synthesized via an easy and low-cost sol–gel process. The Pd-doping in BFO is confirmed through an X-ray diffraction data, field emission scanning electron microscopy images, energy-dispersive X-ray spectroscopy analysis, and its influence on the structure, morphology, surface area, and the NO2 gas sensor performance of the BFO sensor has been examined and explored. Moreover, the plausible gas sensing response mechanism of Pd-BFO film sensor has also been proposed. The nanocubes embedded into a uniformly distributed upright standing nanoplates facilitate better gas adsorption and diffusion behavior on providing an excellent NO2-sensing performance with good sensitivity, excellent selectivity, better response (90 s)/recovery (110 s), and noticeable repeatability under a fixed 100 ppm NO2 gas concentration level at an optimized low operating temperature i.e. 150 °C.

A multiscale approach for simulation of shale gas transport in organic nanopores

Gas flow behaviors in shale are significantly complicated because of the inherent complexity and heterogeneity of shale formations. Revealing the gas transport characteristic is critical for achieving high efficiency of shale gas exploitation. In this work, a multiscale approach combined molecular simulation and lattice Boltzmann method has been proposed for investigating gas transport in shale organic nanopores. Firstly, the characteristic of adsorbed gas in shale nanopore was obtained by molecular simulation. Then, the adsorption properties were integrated to develop a lattice Boltzmann model, which can capture slippage and surface diffusion effects in shale nanopores. By employing this proposed multiscale model, the effects of pressure, temperature and pore size on shale gas adsorption and transport characteristics in organic nanopore were studied. Numerical results show pore size and pressure have great influences on gas adsorption behaviors. The gas apparent permeability tends to increase with the increment of temperature and decrease of pressure. Moreover, the influences of pore size and pressure on surface diffusion permeability were examined. Numerical results indicate the contribution of surface diffusion to overall apparent permeability tends to be enhanced in small pore and low pressure. However, this influence will be greatly weakened with the increasing pore size.