Tortuous Diffusion Path Research Articles

Long-term anticorrosion performance of a modifier-free Ni-graphene superhydrophobic coating

The inherent corrosion vulnerability of mild steel triggered by harsh environments significantly affects its service life and leads to economic losses. Superhydrophobic coatings have been developed to inhibit this issue, and the robustness and facile preparation processes of water-repellent surfaces are crucial for their application. Herein, this study investigated the long-term anticorrosion capability of a modification-free Ni-graphene superhydrophobic coating prepared on mild steel using electrodeposition. Immersion tests, electrochemical measurements, and surface analyses were conducted to verify its durability. The corrosion behavior of the as-prepared coating was characterized in two stages. In the initial stage, the air cushion between the hierarchical structures effectively reduced the direct contact area at the coating-electrolyte interface. Over an extended period, the graphene-embedded coating with refined grains exerted a durable shielding action by providing a tortuous diffusion path for the penetration of corrosive agents. Through in-depth exploration, the anticorrosion mechanism of the Ni-graphene superhydrophobic coating was synergistically determined by the superhydrophobic features endowed by the surface structure and the shielding effect provided by the inner structure, which offers potential guidance for addressing the demands for corrosion protection of mild steel in long-term service processes.

Designing tortuous gas diffusion path for hydrogen oxidation reaction and stability of solid oxide fuel cell: An engineered microstructural aspect in anode functional layer

Commercialization of solid oxide fuel cell (SOFC) is restricted due to long term performance degradation. SOFC is activated by diffusion of gasses through porous electrodes to the electrochemical active sites termed as triple phase boundary (TPB). Among all other parameters, tortuosity influences the functionality of TPB and is responsible for gas transport which relates its bulk diffusion and its migration through the porous electrode. The novelty of present research lies in designing of optimum tortuous gas diffusion path for effective hydrogen oxidation reaction through engineered morphology of anode functional layer. The study involves the fabrication of anode for planar SOFC using four configurations. Configuration A and B involves anode monolith synthesized through conventional route [(40 vol % Ni in dispersed-8 mol % Yttria stabilized zirconia (SZ)] and functional core-shell Ni@SZ. Configuration C (trilayer anode, TLA) is designed to have graded matrix with conventional Ni-SZ (fuel inlet side), 28 vol% Ni@SZ acting as active layer and 32 vol % Ni@SZ sandwiched in between. Configuration D consists of Ni@SZ as the active layer onto conventional Ni-SZ support. TLA is found to have minimum tortuosity (τ = 2) with maximum cell endurance for 2000 h (2.06–8.2 %/1000 h@800 °C under load). Ni@SZ with unimodal pore distribution is capable of reducing the activation barrier for charge migration (14 kJmol-1) compared to Ni-SZ (32 kJmol-1) with multimodal pores. This results in higher redox tolerance for Configuration B-D (4–7 % conductivity degradation/20 cycles) compared to Configuration A (27% conductivity degradation/20 cycles). Post mortem analyses of microstructure support the retention of core-shell morphology of Ni@SZ with lower deterioration.

Synergistic Enhancement of Electromagnetic Wave Absorption and Corrosion Resistance Properties of High Entropy Alloy Through Lattice Distortion Engineering

AbstractHigh entropy alloys (HEAs) are promising electromagnetic wave absorption (EMA) materials due to its designable crystal structure, variable electromagnetic properties, and excellent corrosion resistance. However, the impedance mismatch owing to the high electric and dielectric conductivity severely hinders the application of HEAs in the field of EMA. Herein, the lattice distortion of FeCoNiCu HEA is manipulated accurately by doping and annealing strategies to tailor the EMA properties. Significant lattice distortion is observed in the FeCoNiCuC0.37, which leads to a decrease in the electrical conductivity and the creation of abundant dipoles. Owing to the optimal impedance matching and boosted polarization loss, the FeCoNiCuC0.37 delivers a minimal reflection loss of −65.4 dB accompanied by an effective absorption bandwidth (EAB) of 6.81 GHz. After annealing at 200 °C, the EAB of the FeCoNiCuC0.37 is further increased to 7.99 GHz at 1.95 mm, which is better than that of most HEA‐based EMA absorbers reported so far. Moreover, it demonstrates excellent corrosion resistance owing to the more tortuous diffusion path of corrosive medium origin from lattice distortion. Thus, the study provides a new insight into designing high performance HEA‐based EMA materials with superior anti‐corrosion property by lattice distortion engineering.

Influence of hBN and MoS2 fillers on toughness and thermal stability of carbon fabric-epoxy composites

Hexagonal boron nitride (hBN) and molybdenum disulfide (MoS2) fillers of 2 to 8 wt.% influence on toughness, microhardness and thermal stability of carbon fabric-reinforced epoxy composite (CFREC) reported. Mode-I, mixed-mode I/II toughness and microhardness of CFREC improved due to the addition of hBN and MoS2 separately upto 6 wt.% filler loading. The epoxy matrix in CFREC modified by hBN and MoS2 strengthens the matrix, deflects the crack path and resists delamination. Toughness reduced beyond 6 wt.% filler addition due to agglomeration and poor fiber-filler-matrix bonding as revealed by the surface morphology of the fracture specimen. Thermal analysis reveals decomposition temperature at 25% weight loss increased from 395 to 430 °C and 395 to 411 °C due to 4 wt.% MoS2 and 4 wt.% hBN addition to CFREC respectively. Impermeable characteristics of MoS2 and hBN fillers caused tortuous diffusion path for gas molecules and delayed thermal decomposition.

3D hollow CoNi-LDH nanocages based MMMs with low resistance and CO2-philic transport channel to boost CO2 capture

Layered double hydroxide (LDH) bearing numerous hydroxyl groups shows high affinity with CO2 and is promising in mixed matrix membranes (MMMs) based CO2 capture. However, its non-porous structure limits the further improvement of CO2 permeability. In this work, 3D hollow CoNi-LDH nanocages were developed to construct low-resistance and CO2-philic transport channel in MMM by in-situ etching of ZIF-67 template. The resultant material exhibits hollow structure with cavity size of about 500 nm, mesopores and micropores from LDH stacking and ZIF-67 template. The outer layered CoNi-LDH nanosheets can attract more CO2 molecules by their abundant hydroxyl groups, resulting in an improvement in dissolution selectivity of CO2 over N2. Meanwhile, the tortuous gas diffusion paths originated from 2D nanosheet stacking can further enhance the CO2 selectivity over N2. Moreover, the hollow nanocages provide CO2 molecules with fast transport path, resulting in high CO2 permeability. As a result, compared with pure Pebax membrane and 2D LDH/Pebax MMM, all the 3D hollow CoNi-LDH/Pebax MMMs present enhanced CO2 permeability. The 3D hollow CoNi-LDH-2h/Pebax MMM performs the highest CO2 permeability of 135.49 Barrer, which are increased by 141.95% and 71.50% than those of the above two membranes, respectively. The selectivity of 3D hollow CoNi-LDH-2h/Pebax MMM is about 26.30% higher than that of the pure Pebax membrane. The present membrane presents comparable CO2 capture capacity in contrast with most reported Pebax based MMMs and surpasses the Robeson upper bond. Together with the good long-term stability, the 3D hollow CoNi-LDH nanocages are believed to be a promising candidate for MMMs to improve CO2 capture.

Synergy of superhydrophobic layer and amino-functionalized graphene/epoxy coating towards corrosion/wear resistance on Al alloy

The poor dispersity of graphene in epoxy (EP) coating is harmful to exerting its barrier effect, and the protective efficiency of onefold coating has some difficulty to meet the ever-increasing demands of corrosion protection on Al alloy. Herein, a multilayer protection system (FG-SH-EP) coating was composed of a top superhydrophobic (SH) coating and a bottom amino-functionalized graphene/epoxy (FG-EP) coating. The as-designed multilayer protection system shows good water-repellent (the water contact angle is over 150°). The lowest-frequency impedance of FG-SH-EP is increased by an order of magnitude, because SH surface strengthens the water resistance for early safeguard and FG builds tortuous diffusion path for corrosion media towards physical barrier effect. Additionally, the anti-wear ability of FG-SH-EP is improved by about four times compared to single EP coating. The excellent anti-corrosion/wear behaviors of FG-SH-EP are attributed to the synergistic protection effect of SH-EP and FG-EP. This work is helpful to promote the application of multilayer strategy in alloy protection field.

Multilayer structural epoxy composite coating towards long-term corrosion/wear protection

The corrosion-promotion effect caused by the high conductivity of graphene (G) cannot meet the requirement of long-term protection of G-containing coating under the increasingly complex working condition. Herein, a multifunctional epoxy (MF) composite coating with multilayer structure is constructed containing bottom nano-Al2O3/epoxy layer, intermediate G/epoxy layer, and top nano-SiO2/epoxy layer via a layer-by-layer (LBL) assembly method to improve the corrosion resistance, UV resistance, and tribological properties. MF composite coating exhibits an improved impedance value increased by 10 times and the excellent long-term chlorine resistance, mainly depending on the formation of tortuous diffusion path and avoiding the galvanic corrosion between G and metal substrate. Its wear rate (1.59 × 10−7 mm3/N·mm) is decreased by 73.54% compared with pure epoxy coating due to the lubrication effect of nanofillers and the increase of coating crosslinking density. Moreover, the improved UV aging resistance is reflected in the unchanged chemical structure after 30 days of exposure in UV irradiation, which is attributed to the absorption and reflection of UV light by the nanofillers. Therefore, the as-prepared multifunctional coating has great application prospects in materials protection.

Oxygen barrier properties of polyketone/EVOH blend films and their resistance to moisture

AbstractPolyketone (PK) has excellent chemical and mechanical properties, but its use in food packaging is limited due to its oxygen barrier properties being insufficient for high‐barrier film applications. To improve its oxygen barrier properties, PK has been blended with ethylene vinyl alcohol copolymer (EVOH), which is one of the highest oxygen barrier polymers in use today. The oxygen barrier properties under both dry and humid conditions, as well as the mechanical properties of PK/EVOH blend films were investigated in this study. These novel PK/EVOH blend films exhibited unusually low oxygen permeability values from 0.3 to 0.16 cc 20 μm m−2 day−1 atm−1 with increasing EVOH content from 30 to 70 wt%, which are even lower than those of the ideal laminar model that expresses the theoretical minimum permeability values attainable for blended barrier films. These high oxygen barrier properties of PK/EVOH blend films can conceivably be attributed to the combination of two dominant effects: a tortuous diffusion path through the EVOH domains in the PK matrix and hydrogen bonding interactions between PK and EVOH. Furthermore, in high‐humidity environments with retorting, the PK/EVOH blend films exhibited superior resistance to moisture over EVOH. Immediately after the retorting test, the oxygen permeability of the high‐barrier PK/EVOH blend films with an EVOH content of 30–40 wt% increased by less than 3× the pre‐retorting value, as opposed to 74× for EVOH. In addition, PK/EVOH blend films displayed superior stretching characteristics, with a breaking strain of over 300%, which are valuable for flexible packaging applications.

A Methodology for the Estimation and Modelling of the Obstruction Factor in the Expression for Mesopore Diffusion in Reversed-Phase Liquid Chromatography Particles

An experimental methodology for the determination of the obstruction factor in the expression for mesopore diffusion in Zorbax Eclipse Plus C18 reversed-phase particles is proposed. The method uses peak parking experiments conducted on particles that were previously stripped of their stationary phase by flushing the column with trifluoroacetic acid at a temperature of 60°C. Further using pure organic solvents as the mobile phase, any potential retention or surface diffusion effect is omitted. To avoid interference between the parked peaks and baseline disturbances typically occurring when switching on and off the flow, peak parking experiments were carried out in a set-up wherein two identical columns were used in parallel. This set-up allowed to maintain the flow through the detector at all times, by redirecting the flow from one column to the other during the peak parking experiments. Several tracer molecules (ionic and deuterated tracers) were compared and it was found that the use of deuterated molecules provides the best possible coverage of the accessible space of the mesopore volume. Interpreting the peak parking responses obtained with these tracers with a model based on the effective medium theory (EMT) subsequently provided an estimate of the value of the mesopore diffusion obstruction factor γmp. Taking the well-established pore hindrance factor F(λ) correction into account, the obtained experimental γmp-values are more in agreement with the tortuous and constricted diffusion paths one can expect in the void space within a structure resembling a monolithic skeleton with tetrahedral connectivity rather than in the void space formed by a packing of nanospheres. This is also more in line with the measured internal porosity values lying around εpz=0.5, whereas a packing of nanospheres would rather correspond to an εpz of 0.4. As such, the presented protocol provides a means to infer the internal mesopore structure of reversed-phase particles.

Modelling of 3D microstructure and effective diffusivity of fly ash blended cement paste

Accurate prediction of microstructural evolution and ionic diffusivity in fly ash blended cement paste is significant for practical application and durability design of blended cementitious materials. This paper presents an integrated modelling framework for simulating 3D microstructure and effective ionic diffusivity of blended cement paste with various fly ash replacement levels and water-to-binder (w/b) ratios. A voxel-based hydration model using cellular automaton-like evolution rules was developed to simulate 3D microstructural development of fly ash blended cement, based on which the effective diffusivity was simulated using a lattice Boltzmann (LB) model for diffusion considering the contributions of both capillary pores and gel pores in C–S–H gels to ionic diffusion. A series of experiments were conducted to characterise the morphology of Portland cement and fly ash, hydration process and pore structure of fly ash blended cement paste and measure the effective ionic diffusivity. The simulation results agree well with experimental data in terms of hydration heat, calcium hydroxide content, degree of hydration of fly ash, porosity, and effective diffusivity, which suggests that the developed microstructure-based LB model for diffusion can predict the ionic diffusivity of fly ash blended cement paste with high accuracy. The addition of fly ash can help reduce the ionic diffusivity of cement paste particularly after the capillary porosity depercolation occurs due to the more tortuous diffusion paths in the pozzolanic C–S–H gels.

The effect of hydrogen concentration on the fracture surface of medium Mn steels

To balance good strength and ductility, Medium Mn steels have been considered as the new generation materials used in automotives. However, they show delayed fracture, which is thought to relate to hydrogen. Therefore, in order to understand their mechanical properties with various hydrogen contents, it is very important to assess their safety. In this study, the effect of hydrogen on the mechanical properties of several medium Mn steels (MMSs) with different Mn content and treatments were investigated. For medium Mn steels, the stability of the retained austenite (RA) was examined and the hydrogen permeation test was performed. Austenite, as a barrier to hydrogen diffusion, leads to a tortuous diffusion path, which reduces the diffusion rate of hydrogen in MMSs. Increasing the Mn content increases the volume fraction of RA in the specimen. The stress-strain curves of MMSs were divided into three parts, determined by the stability and content of RA. Slow strain rate tensile tests with hydrogen charging were performed to investigate the behaviour of hydrogen diffusion and the mechanism of hydrogen embrittlement (HE). After the tests, the hydrogen content was measured and the fracture surface was observed and analysed. The phenomenon of HE in steels has been mainly explained based on the mechanisms of hydrogen-enhanced localised plasticity (HELP), hydrogen-enhanced decohesion (HEDE), and hydrogen assisted micro ovoid coalescence (HDMC). Due to the existence of hydrogen, fracture morphology changes from ductile mode to brittle mode. It was also found that under the same strain rate, tensile strength and elongation decrease gradually as hydrogen concentration increases, resulting in final failure.

Three-Dimensional Hierarchically Porous Graphene Fiber-Shaped Supercapacitors with High Specific Capacitance and Rate Capability.

Chemically converted graphene fiber-shaped supercapacitors (FSSCs) are highly promising flexible energy storage devices for wearable electronics. However, the ultralow specific capacitance and poor rate performance severely hamper their practical applications. They are caused by severe stacking of graphene nanosheets and tortuous ion diffusion path in graphene-based electrodes; thus, the ultralow utilization of graphene has been rarely carefully considered to date. Here, we address these issues by developing three-dimensional hierarchically porous graphene fiber with the incorporation of holey graphene for efficient utilization of graphene to achieve fast charge diffusion and good charge storage capability. Without deterioration in electrical but robust mechanical properties, the optimal graphene fiber shows ultrahigh specific capacitance of 220.1 F cm-3 at current density of 0.1 A cm-3 and boosted specific capacitance of 254.3 F cm-3 at 0.1 A cm-3 after nitrogen doping. Moreover, the nitrogen-doped 40% holey graphene hybrid fiber-assembled FSSC exhibits ultrahigh rate capability (96, 91, and 87% at current density of 0.5, 1.0, and 2.0 A cm-3, respectively, and 67% even at ultrahigh current density of 10.0 A cm-3) and excellent cycle stability (95.65% capacitance retention after 10 000 cycles). The contribution of three-dimensional interconnected hierarchically porous network to the enhanced electrochemical (EC) performance is semiquantitatively elucidated by Brunauer-Emmett-Teller and energy dispersive spectroscopy mapping. Our work gives insights into the importance of fully utilizing graphene and provides an efficient strategy for high EC performance in chemically converted graphene-based FSSCs.

Integrating multiple adsorption sites and tortuous diffusion paths into a metal–organic framework for C3H4/C3H6 separation

By integrating open metal sites, Lewis basic sites, and tortuous diffusion paths, a new metal–organic framework has been designed and synthesized, which exhibits high adsorption capacity and excellent selectivity for separating a C3H4/C3H6 mixture.

Contaminant Cation Effect on Oxygen Transport through the Ionomers of Polymer Electrolyte Membrane Fuel Cells

We characterized the effects of cobalt (Co2+) and other cation contaminants on the oxygen (O2) transport properties of the PFSA ionomer used in polymer electrolyte membrane fuel cells (PEMFCs) and gained insight into the mechanisms by which contaminant cations inhibit O2 transport. Such cations can be released by alloy catalysts and environmental conditions and pose a significant challenge to maintaining high current density performance with low platinum (Pt) loadings. We used a test cell capable of isolating the ionomer from the membrane electrode assembly (MEA), allowing for O2 transport resistance (RO2) measurements using a limiting current technique. We contaminated ionomer membranes with Li+, Na+, Ni2+, Co2+, and Ce3+ and found a general increase in RO2 for increased contamination levels and decreased water activity. In addition, our Co2+ results indicated distinct concentration-dependent regimes. The other cation-form ionomers allowed us to separate the impacts of ion pair strength, multivalency, and reduced water uptake. We believe that these factors cause a more compressed hydrophilic domain and tortuous O2 diffusion path, and a commensurate increase in RO2. Finally, we studied the impact of Co2+ on an operating PEMFC and found an increase in RO2consistent with the results of our isolated membrane tests.

Resistance Decay of Cu/Porous Low- ${k}$ Interconnect: Modeling and its Impact on Electromigration

It was found previously the resistance of Cu interconnect ( ${R}$ ) could decrease during baking and acceleration test, owing to moisture invasion through the nanoporous low- ${k}$ followed by moisture-induced oxidation of Ta-based liner and specularity recovery of the electron scattering at Cu/Ta interface. In this paper, a model is established to quantitatively interpret the underlying kinetics. It is shown that the model fits well with the experimentally observed hump-shaped temperature dependence of the R decay rate of Cu/porous SiCOH interconnects at 28-nm node at 170 °C~350°C. It reveals that the liner oxidation and resistance decay are controlled mainly by the migration of metal cation through the as-oxidized liner at the low temperatures but by the desorption/diffusion of the chemisorbed moisture in the low- ${k}$ at the high temperatures. Particularly, the model well reproduces the modest and unexpectedly significant low- ${k}$ -thickness dependence of the decay rate at the low and high temperatures, respectively, which indicates clearly the temperature-dependent influence of the tortuous diffusion path of moisture in the porous low- ${k}$ . The intimate relationship of Cu electromigration performance to such ${R}$ decay is also demonstrated.

Solid nanofoams based on cellulose nanofibers and indomethacin—the effect of processing parameters and drug content on material structure

The unique colloidal properties of cellulose nanofibers (CNF), makes CNF a very interesting new excipient in pharmaceutical formulations, as CNF in combination with some poorly-soluble drugs can create nanofoams with closed cells. Previous nanofoams, created with the model drug indomethacin, demonstrated a prolonged release compared to films, owing to the tortuous diffusion path that the drug needs to take around the intact air-bubbles. However, the nanofoam was only obtained at a relatively low drug content of 21wt% using fixed processing parameters. Herein, the effect of indomethacin content and processing parameters on the foaming properties was analysed. Results demonstrate that a certain amount of dissolved drug is needed to stabilize air-bubbles. At the same time, larger fractions of dissolved drug promote coarsening/collapse of the wet foam. The pendant drop/bubble profile tensiometry was used to verify the wet-foam stability at different pHs. The pH influenced the amount of solubilized drug and the processing-window was very narrow at high drug loadings. The results were compared to real foaming-experiments and solid state analysis of the final cellular solids. The parameters were assembled into a processing chart, highlighting the importance of the right combination of processing parameters (pH and time-point of pH adjustment) in order to successfully prepare cellular solid materials with up to 46 wt% drug loading.

A robust transparent encapsulation material: Silica nanoparticle-embedded epoxy hybrid nanocomposite

We report on the synthesis of a silica nanoparticle-embedded epoxy nanohybrid (SNP-EP nanocomposite), that can be used as a robust transparent encapsulation material for various applications. The SNP-EP nanocomposite is composed of a thermo-curable, bisphenol A-type epoxy polymer as a matrix and monodispersed silica nanoparticle (SNP) as a reinforcement, which can create tortuous diffusion path for moisture penetrants. SNP is synthesized via a base-catalyzed hydrolytic sol-gel condensation, and the surface of the SNP is modified with glycidyl and phenyl ligands to endure stable dispersion and chemical cross-linking with epoxy matrix. The SNP-EP nanocomposite exhibits significantly enhanced water vapor transmission rate of 1.52 g/m2 day and an optical transparency over 90% in the visible range with strong adhesion (5B). We introduce synthetic steps of the nanocomposite and discuss physical/chemical properties of the composite.

Solid cellulose nanofiber based foams – Towards facile design of sustained drug delivery systems

Control of drug action through formulation is a vital and very challenging topic within pharmaceutical sciences. Cellulose nanofibers (CNF) are an excipient candidate in pharmaceutical formulations that could be used to easily optimize drug delivery rates. CNF has interesting physico-chemical properties that, when combined with surfactants, can be used to create very stable air bubbles and dry foams. Utilizing this inherent property, it is possible to modify the release kinetics of the model drug riboflavin in a facile way. Wet foams were prepared using cationic CNF and a pharmaceutically acceptable surfactant (lauric acid sodium salt). The drug was suspended in the wet-stable foams followed by a drying step to obtain dry foams. Flexible cellular solid materials of different thicknesses, shapes and drug loadings (up to 50wt%) could successfully be prepared. The drug was released from the solid foams in a diffusion-controlled, sustained manner due to the presence of intact air bubbles which imparted a tortuous diffusion path. The diffusion coefficient was assessed using Franz cells and shown to be more than one order of magnitude smaller for the cellular solids compared to the bubble-free films in the wet state. By changing the dimensions of dry foams while keeping drug load and total weight constant, the drug release kinetics could be modified, e.g. a rectangular box-shaped foam of 8mm thickness released only 59% of the drug after 24h whereas a thinner foam sample (0.6mm) released 78% of its drug content within 8h. In comparison, the drug release from films (0.009mm, with the same total mass and an outer surface area comparable to the thinner foam) was much faster, amounting to 72% of the drug within 1h. The entrapped air bubbles in the foam also induced positive buoyancy, which is interesting from the perspective of gastroretentive drug-delivery.

Understanding Diffusion in Hierarchical Zeolites with House-of-Cards Nanosheets.

Introducing mesoporosity to conventional microporous sorbents or catalysts is often proposed as a solution to enhance their mass transport rates. Here, we show that diffusion in these hierarchical materials is more complex and exhibits non-monotonic dependence on sorbate loading. Our atomistic simulations of n-hexane in a model system containing microporous nanosheets and mesopore channels indicate that diffusivity can be smaller than in a conventional zeolite with the same micropore structure, and this observation holds true even if we confine the analysis to molecules completely inside the microporous nanosheets. Only at high sorbate loadings or elevated temperatures, when the mesopores begin to be sufficiently populated, does the overall diffusion in the hierarchical material exceed that in conventional microporous zeolites. Our model system is free of structural defects, such as pore blocking or surface disorder, that are typically invoked to explain slower-than-expected diffusion phenomena in experimental measurements. Examination of free energy profiles and visualization of molecular diffusion pathways demonstrates that the large free energy cost (mostly enthalpic in origin) for escaping from the microporous region into the mesopores leads to more tortuous diffusion paths and causes this unusual transport behavior in hierarchical nanoporous materials. This knowledge allows us to re-examine zero-length-column chromatography data and show that these experimental measurements are consistent with the simulation data when the crystallite size instead of the nanosheet thickness is used for the nominal diffusional length.

The impacts of microcosmic flow in nanoscale shale matrix pores on the gas production of a hydraulically fractured shale-gas well

Special nanoscale storage mechanisms and pore radii create complex shale gas transport mechanisms. Shale gas reservoir production performance evaluations are challenging due to difficulties associated with microcosmic flow mechanisms, such as Knudsen diffusion, surface diffusion, adsorption and desorption. A thorough understanding of the effects of these transport mechanisms on shale gas production can help to develop new and improved shale gas production prediction models. This paper derives a unified apparent permeability equation based on the Knudsen number and four flow regimes, incorporating viscous, slip, transition and free molecule flows. The new apparent-permeability model also considers the surface diffusion, adsorption layer and tortuous diffusion path. Fully coupled differential equations were developed for a hydraulic fracture and matrix system based on these microcosmic transport mechanisms and using the finite difference method. A sensitivity analysis was performed to investigate the impacts of several parameters on production, including the nanopore radii, Langmuir parameters and bottom-hole flow pressure. The simulation results demonstrate that the microcosmic flow mechanisms significantly impact shale gas production. Gas production increases as the Langmuir parameters increase, but the rate of the increase decreases over time. Knudsen diffusion and surface diffusion become more prominent as the pore radius and reservoir pressure decrease. The adsorption layer cannot be ignored at sufficiently small pore radii.