Contribution Of Surface Diffusion Research Articles

Large-Scale Analysis on Accelerated Aging of Pentaerythritol Tetranitrate (PETN) Powders in Detonators.

Pentaerythritol tetranitrate (PETN) has been used extensively in commercial detonators and other explosive applications for many decades. Here, we show the results of a comprehensive 1.5 year aging study of PETN in commercial detonators, addressing batch-to-batch variations, surface area changes, and comparisons of aged loose powders side-by-side with identically aged detonators. Function time analysis of the aged detonators has also been provided and discussed in the context of powder aging. This large-scale, statistically relevant study addresses long-standing questions on PETN aging without the complications from making comparisons between multiple batches of material. We have evaluated the aging time required to reach the maximum measured amount of PETN coarsening and estimated an activation barrier of ∼123 kJ mol-1, which is higher than literature values reported by Gee et al. It is possible that this discrepancy is due to the fact that that this study cannot quantify the relative contributions of surface diffusion versus sublimation processes. At the lower temperatures of 50 and 60 °C, we assume that surface diffusion dominates over sublimation processes, even at longer aging times. At the higher temperature of 75 °C, we assume that both surface diffusion and sublimation contribute at the early time points, which are included in the Arrhenius analysis for coarsening.

Kinetics of voids evolution during diffusion bonding of dissimilar metals on consideration of the realistic surface morphology: Modeling and experiments

A comprehensive model for analyzing the kinetics of void evolution and shrinkage during dissimilar diffusion bonding is proposed based on the sinusoidal profile. The model incorporates atom accumulation at void tip to determine the curvature radius of void neck, and integrates the local effect of surface diffusion to quantify the contribution of surface diffusion, thus avoiding the unrealistic void evolution observed in previous models. Furthermore, the model utilizes a combined diffusion coefficient for multicomponent alloys under the effect of stress and concentration gradients, to determine the interfacial diffusion coefficient for dissimilar joints. In contrast to previous models, the current model demonstrates significant improvements in predicted accuracy, efficiently depicting the realistic void evolution and interpreting the formation of various interfacial voids, which can be applied in various bonding cases, including for the dissimilar base metals with different surface conditions. Simulation results from bonding between austenitic steel and ferritic steel with different surface roughness reveal that interfacial voids predominantly form on the side of the base metal with the rougher bonding surface. Additionally, as surface roughness decreases, the prevailing surface source diffusion and interface source diffusion mechanisms promote void evolution and shrinkage, resulting in a significant reduction of the final bonding time. To achieve a high-quality bonding joint, it's suggested to place the smoother bonding surface on the higher creep-resistant base metal, which can accelerate the void closure process.

Insight into Adsorption Kinetics of Cs+, Rb+, Co2+, and Sr2+ on a Zeolites-Based Composite: Comprehensive Diffusional Explanation and Modelling

Kaolinite-rich soils were used to prepare zeolite-based composites via alkaline activation. The porous material was characterized by conducting XRD and microporosity measurements, as well as ESEM microscopy. The Weber and Morris (W-M) model was used for studying adsorption kinetics of radioactive cations on synthesized alkali-activated material. These investigations evidenced the effects of pore structure and the importance of the intrinsic characteristics of hydrated cations (ionic potential; hydrated radius; B-viscosity parameter; molar Gibbs energy of hydration of cation) on W-M kinetic rate constants. The application of diffusion-based models permitted us to assess the key diffusion parameters controlling successive diffusion regimes, and to reveal strong contributions of surface diffusion to adsorption kinetics during the course of the second and third kinetics stages of the W-M model. The magnitude of the surface diffusion coefficient was related to the capacity of hydrated cationic species to lose water molecules when penetrating brick pores. The HSDM model were tested for predicting radionuclide adsorption in a fixed-bed column. A breakthrough curve simulation indicated the predominance of the surface diffusion regime, which was in agreement with mathematical analysis of (batch) adsorption kinetics data. Ionic diffusion was linked to the characteristics of capillary porosity and connectivity of capillary pores in the composite, suggesting the generation of hydrated nuclides and their immobilization in the form of outer-sphere complexes.

Improved mathematical model of apparent permeability: A focused study on free and multilayer adsorptive phase flow

Apparent permeability is the quantification of gas transport in confined pore, which includes the pressure gradient-driven continuous flow (slip flow), the concentration gradient-driven molecular diffusion (Fick's diffusion, Knudsen diffusion) and the chemical gradient-driven surface diffusion. Molecular diffusion of free/adsorbed gas plays an important role in gas transfer, especially in nanopores. Most existing apparent permeability models simply define free gas diffusion as Knudsen diffusion, and surface diffusion as the diffusion of monolayer adsorbed molecules. However, the pore scale-dependent Knudsen diffusion, the molecular diffusion of free gas also includes the pore scale-independent Fick's diffusion. In addition, the empirical formula of surface diffusion coefficient derived from plug core diffusion experiment should be used cautiously, because there are other diffusion regimes involved in the diffusion process in multi-scale pores. In this work, the diffusion mechanisms of adsorbed/free gas were classified. A supercritical multilayer adsorption (SC-DA) model was obtained by fitting the adsorption data of homogeneous nano activated carbon, and the adsorption effect was applied to pore aperture change and surface diffusion, which is suitable for single/multilayer adsorption. Applying the improved surface diffusion flow and free gas diffusion flow into gas transport, a unified mathematical transport model was presented, from which the apparent permeability model was derived. Later, the improved model was verified using the experimental data from the micro-flow permeability of the nanofilms with regular size. Furthermore, the influence of each flow mechanism in nanopores was calculated and compared. The results showed that the gas transport in nanopores is dominated by molecular diffusion, but the contribution of surface diffusion in gas transfer is exaggerated if its diffusion coefficient is not chosen properly.

Bridge between mass transfer behavior and properties of bubbles under two-stage ultrasound-assisted physisorption of polyphenols using macroporous resin

Ultrasound is efficient to enhance various mass transfer processes. This study demonstrates that both ultrasound pretreatment and ultrasonication during adsorption promote the physisorption of polyphenols. The time to reach the adsorption equilibrium was shortened by more than 90 % when the resin diameter deceased from 592 μm to 60.23 μm in the intensive ultrasound pretreatment. The mass transfer mechanism of adsorption under mild sonication differs from that of adoption with intensive ultrasound pretreatment. Mild sonication during adsorption strengthens the influence of surface diffusion of polyphenols on intraparticle diffusion. In contrast, severe disruption of resin particles due to intensive ultrasound pretreatment weakens the surface diffusivity of polyphenols and reduces the contribution of surface diffusion. Also, the physics and sonochemistry of cavitation under sonication environments were explored. Under intensive and mild ultrasound treatments, the calculated bubble numbers were approximately 18789 L-1 and 6312 L-1, respectively. Moreover, a relationship was established between adsorption capacity from mass transfer modeling and bubble properties including the bubble collapse pressure, bubble number, processing time, and processing scale. This bridge between mass transfer behavior and properties of bubbles provides guidance and new insight for the design and scale-up of the ultrasound-assisted adsorption.

Experimental Study on the Liquid‐Phase Adsorption Equilibrium of n‐Butanol over Amberlyst™15 and Contribution of Diffusion Resistances

AbstractThis work investigates the liquid‐phase adsorption of n‐butanol on Amberlyst™15 in the temperature range 295–323 K at different initial adsorbate concentrations. The adsorbent was characterized by N2 physisorption, Fourier transform infrared adsorption of pyridine, scanning electron microscopy, and powder X‐ray diffraction. The data obtained confirmed an adsorbent structure with two porosity levels and amorphous polymer structure. The active sites in Amberlyst™15 are of Brønsted or Brønsted‐Lewis type. The liquid‐phase adsorption equilibrium constants were determined at different temperatures from slurry adsorber experiments. The thermodynamic state functions were estimated and are consistent thermodynamically with physical adsorption. The macropore diffusion coefficients of n‐butanol on Amberlyst™15 were estimated by using the moment technique, and the contribution of surface diffusion to the macropore diffusion coefficients was evaluated.

Transport Model for Gas and Water in Nanopores of Shale Gas Reservoirs

Because of the many nanoscale pores in shale gas reservoirs (SGRs), the fluid transport mechanisms in shale are complex. Also, previous research has shown that there exists water in the shale plays. Hence, two-phase gas-water transport model construction becomes very important so as to increase accuracy in numerical simulation work. However, most of the current study is still focused on single-phase gas transport. In this paper, based on the second slip model coupled with the fluid single-pipe flow equation, the Knudsen and surface diffusions, and combined with the fractal theory, the relative permeability model for gas-water in shale was constructed. The model reliability was proven by using the available two-phase gas-water relative permeability data. A sensitivity analysis has been carried out based on the proposed model. The results show that with the pressure decreasing, the relative permeability of gas increases. The increase of the pore size distribution fractal dimensions (Df) and fractal dimension (DT) caused the gas relative permeability (Krg) to increase. The Krg increases with the increase of Df and DT. The influence of the viscous slip flow, Knudsen diffusion, and surface diffusion are trade-offs, which are mainly controlled by water saturation (SW) and pressure (P). The Krg is extremely sensitive when P<1 MPa. Under low pressure and low water saturation, the effect of viscous slip flow is secondary. And its contribution increases gradually and becomes the main role with the increase of water saturation or pressure. The effect of the Knudsen diffusion is negligible when P>1 MPa and the water saturation SW>40%. However, it cannot be ignored under other conditions. The influence of surface diffusion reached 21.64%–72.78% when P<1 MPa and SW<10%. A surface diffusion contribution of less than 4.25% was obtained when P>1 MPa and SW>70%.

Impact of water film on methane surface diffusion in gas shale organic nanopores

When a shale pore radius is less than 10 nm, the contribution of surface diffusion to methane transport in shale multiscale pore structure will significantly increase. It is critical to understand whether the adsorbed water film in shale nanoscale organic pores is beneficial to multiscale methane transport. Thus, a model considering the effect of a water film on methane surface diffusion is established. Furthermore, the influences of a water film on different diffusion mechanisms are discussed. The results show that, first, when water molecule enters shale organic pores, an adsorption interface changes from gas-solid to gas-water, i.e., the fractional surface coverage of gas in the surface increases so the surface diffusion ability increases; second, when a pore radius is less than 6 nm, the overall diffusion capacity of methane in pores increases, even though a water film can decrease the slip flow and Knudsen diffusion. However, when a pore radius is 8–10 nm, the apparent permeability (Kapp) increases with pressure. Since a pore surface contains a water film, Kapp is not always greater than that for a pore surface without water film. Our investigation shows that the impact of fracturing fluid retention in shale multiscale pore structure is not always negative for methane multiscale transport if the volume of a fracturing fluid and shut-in time are reasonable.

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.

Influence of microgeometry of iron surface on the oxidation process – A comparison of multiscale geometric methods and their applicability

In this paper, an investigation of the effect of surface roughness on oxidation of polished, ground and sand-blasted samples made of iron exposed at 700 and 750 °C for 2 h in air is reported. Surface roughness was described by the 2D data sets obtained by contact profilometer and derived from microphotographs taken at three different magnifications: 100×, 200× and 500×. Surface roughness and curvature were measured by means of conventional and multiscale analysis. Oxidation behavior was analyzed in terms of mass change and SEM/BSE (scanning electron microscopy/backscattered electrons) observations. The oxidation kinetics was found to be influenced by initial surface roughness, however, its effect was different at 700 °C and 750 °C as the contribution of surface diffusion is greater at the lower temperature. It was also concluded that multiscale analysis can be successfully applied in describing surface roughness prior to high-temperature oxidation processes. The most adequate results were obtained from the data derived by contact profilometer and from microphotographs taken at the highest magnification.

Pore-scale investigation on coupled diffusion mechanisms of free and adsorbed gases in nanoporous organic matter

The long-term productivity of shale reservoirs is determined by shale gas diffusion properties in tight mudrocks, particularly in nanoporous organic matter (OM), within which the shale gas is mainly stored as free gas in the centers of pores and as adsorbed gas on pore surfaces. Although the multiple diffusion of free gas in porous media has been previously studied, the coupled diffusion mechanisms that involve both free and adsorbed gases as well as the contribution of surface diffusion induced by adsorbed gas, remain elusive. In this paper, a novel local coupled diffusivity lattice Boltzmann model (LCD-LBM), which considers both multiple diffusions of free gas and surface diffusion of adsorbed gas, is developed. The developed model allows prediction of the coupled diffusion mechanisms of free and adsorbed gases in the reconstructed nanoporous OM. The proposed model is validated by a molecular dynamic simulation result for shale gas diffusion in the nanoscale slit pore. The results show that OM diffusivity is in the magnitude order of 10−8 m2/s for an effective pore diameter of the OM ranging from 1 nm to 10 nm. The contribution of the adsorbed gas is prominent in the nanopores whose effective pore diameters are less than 2 nm. Furthermore, OM diffusivity is nearly independent of the gases diffusion direction and adsorbed gas molecules distribution pattern. The present work is conducted at the pore-scale, and thus it can be easily extended to evaluate the gas coupled diffusion mechanisms in other nanoporous materials.

An upscaled transport model for shale gas considering multiple mechanisms and heterogeneity based on homogenization theory

Because of the complex pore structure and multiple types of gas storage, the traditional Darcy permeability model is not valid for describing shale gas flow. In this paper, an upscaled transport model is established based on homogenization theory to consider multiple transport mechanisms and the heterogeneity of shale samples. This new transport model is employed to successfully explain pressure decay experimental data. The results show that absorbed gas cannot be ignored in pressure decay experiment and the pressure difference decreases rapidly when the absorbed gas is not considered. Then several critical conclusions have been drawn as follows. The permeability anisotropy for stochastic distribution model can be ignored and the effective permeability will be underestimated by double porosity model if surface diffusion dominates gas flow in shale reservoir. In addition, shale gas transport is dominated by Knudsen diffusion when the pore pressure is below 2 MPa and the contribution of surface diffusion increases as the pore pressure increases. The macroscopic effective permeability of the whole domain is dominated by the permeability of the connected phase; meanwhile, it can be influenced by the permeability of the disconnected phase. When the pore pressure is below 3.52 MPa, the effective permeability increases as the organic matter content (TOC) decreases. However, the effective permeability increases as the TOC increases when the pore pressure is above 3.52 MPa, which is different from traditionally believed when the relationship between the TOC and gas absorption capacity of the shale matrix is not considered. The effective permeability particularly increases at a high pore pressure as the Langmuir volume increases. In addition, the effective permeability increases as the Langmuir pressure decreases; however, this becomes apparent when the pore pressure is smaller.

Insight into mass transfer during ultrasound-enhanced adsorption/desorption of blueberry anthocyanins on macroporous resins by numerical simulation considering ultrasonic influence on resin properties

The mass transfer mechanism about ultrasonic enhancement of blueberry anthocyanin adsorption and desorption on macroporous resins were investigated. Ultrasound treatment led to the decrease of resin size, whereas average pore diameter, specific surface area, total pore volume were less affected. Then, the pore volume and surface diffusion model considering ultrasound-induced changes of particle size and surface area was employed to model anthocyanin adsorption process numerically. Generally, sonication enhanced external mass transfer coefficient (kL) and surface diffusion coefficient (Ds) during adsorption. The values of kL and Ds under sonication at 279 W/L and 20 °C were 7.578 × 10−2 cm/s and 2.000 × 10−9 cm2/s, which were 2.0% and 140.1% higher than the kL and Ds values under orbital agitation at 20 °C. Accordingly, anthocyanins penetrated into the interior of macroporous resins faster under sonication. The overall intraparticle diffusion for anthocyanin adsorption was dominated by pore volume diffusion with the contribution percentage higher than 50%. Sonication enhanced the contribution of surface diffusion to the overall diffusion, which was consistent with the increase of Ds with ultrasound energy. Moreover, a general diffusion model also incorporating the variations of particle size and surface area was utilized to model anthocyanin desorption process. The overall anthocyanin diffusivity increased with both ultrasound energy level and temperature. Anthocyanins distributed more homogenously inside resins under sonication at 279 W/L than under other treatments. This work could be a reference for the valorization of anthocyanins in food industry, especially juice and wine industries.

The adsorption kinetics of sodium dodecylbenzenesulfonate on activated carbon. Branched-pore diffusional model revisited and comparison with other diffusional models

The adsorption rate of sodium dodecylbenzenesulfonate (SDBS) on three commercial activated carbons (ACs) and an AC synthesized from almond shells was investigated in this study. The mechanisms controlling the overall adsorption rate of SDBS on ACs were found out by using the pore volume and surface diffusion model (PVSDM). The PVSDM showed that the intraparticle diffusion of SDBS in all ACs was mainly attributed to pore volume diffusion and surface diffusion. The surface diffusion coefficient, Ds, in all samples of ACs are influenced by the amount of surfactant adsorbed at equilibrium, qe, as well as the mean micropore width, L0. The contribution of surface diffusion to the overall intraparticle diffusion ranged from 45 to 70%, depending on the properties of AC. Moreover, the branched-pore diffusional model was revisited (BPDMR) assuming that the Fick diffusion is the only diffusion mechanism in the macropores and the diffusion in the micropores was represented by the micropore rate coefficient, KC. Besides, it was proposed that the parameter f representing the mass fraction of SDBS adsorbed on macropores, can be estimated from the textural properties of ACs. Three new strategies were proposed to analyze the experimental data using BPDMR model, and it was demonstrated that the macropore diffusivity in BPDMR is close to the molecular diffusivity of SDBS in water solution. The micropore rate constant, KC, ranged from 3.90 × 10−6 to 10.6 × 10−6 s−1 and was affected by textural characteristics of ACs. Both models predicted the global adsorption rate of SDBS on ACs satisfactorily.

Effect of Pore Shape on Nanoconfined Gas Flow Behavior: Implication for Characterizing Permeability of Realistic Shale Matrix

Good knowledge of nanoconfined gas flow behavior will significantly contribute to advance ultimate gas recovery from shale gas reservoirs. However, up to now, it has still been extremely challenging to have a clear understanding of the key issue. In particular, little attention is drawn to the effect of pore geometry on nanoconfined gas flow behavior. By means of developed experimental technology, realistic images reflecting pore characteristics can be obtained, which demonstrate that various pore shapes are exhibited in the shale matrix. To my knowledge, current related research is focused on gas transport through several conventional pore shapes, including circle, rectangle, and slit. As a result, the urgent issue, i.e., research on gas flow behavior through unconventional pore shapes, is highlighted. In this work, a model for gas transport through elliptical nanopores is established, which possesses an excellent varying-shape nature with changing aspect ratio (AR) and therefore covers lots of pore shapes and shares great application value. Both effects of gas slipperiness and surface diffusion are incorporated in this model. Moreover, the Langmuir isotherm is utilized to quantify the thickness of the adsorption layer of methane. When AR is equal to 1 and an infinite number, the proposed model can achieve excellent agreement compared with gas transport data through circular and slit-like nanopores. Results show that (a) the gas transport capacity will decrease with increasing AR value at a specific pressure point; (b) contribution of surface diffusion will become more prominent with higher AR value; (c) under different gas adsorption/desorption characteristics, there is no difference in gas transport capacity through nanopores with different ARs at high pressure and relatively large difference at low-pressure atmosphere; (d) current production prediction models or commercial software require consideration of the effect of various pore shapes to enhance application accuracy. In sum, the findings of this study can help in better understanding the methane flow feature through nanopores with various cross-sections, which further serve as the necessary theoretical attempt with regard to accurate characterization for flow capacity of a realistic shale matrix.

Gas transport in shale matrix coupling multilayer adsorption and pore confinement effect

Accurate prediction of gas transport in shale formations mainly consisting of micro- and nano-scale pores is a great challenge since most existing models only consider monolayer adsorption and the underlying multi-physics are either partially or completely overlooked. In this work, we have proposed a comprehensive single-component gas transport model integrating multilayer adsorption, surface diffusion, real gas effect, and pore confinement effect. The new analytical model is developed based on Bravo layer-sequence-model and then upscaled using an Effective Medium Approximation (EMA) method, where the generalized Brunauer-Emmett-Teller (BET) model, the modified Peng-Robinson equation of state (EoS) model, and the Sutton’s viscosity model are innovatively incorporated. The newly developed model has been successfully validated against simulation and experimental results with the assistance of an efficient iterative ensemble smoother (ES) algorithm. It is observed that the pore confinement effect is of importance when the pore size is smaller than 50 nm. The increase of gas viscosity due to the real gas effect is significant under reservoir conditions. The apparent permeability is found to increase greatly as the adsorption layer number increases, implying that the application of Langmuir model in existing gas transport models may substantially underestimate it. Given inorganic nanopores, the viscous flow is important at any pore sizes and the Knudsen diffusion plays a role in the pores that are less than 5 nm under reservoir conditions. As for organic nanopores, the contribution of surface diffusion is tangible when the pore size is below 150 nm and the Knudsen diffusion is negligible under high pressures.

Gas Mass Transport Model for Microfractures Considering the Dynamic Variation of Width in Shale Reservoirs

Summary Microfractures are commonly observed in shale reservoirs. During the shale gas–production process, stress sensitivity induces a change in the width of the microfractures, which is a significant factor that affects shale gas mass transport. By using research methods based on desorption theory and elastic–plastic mechanics, a shale gas mass transport model that considers the dynamic variations in the microfracture width is established in this paper. This model comprehensively fuses the surface diffusion model, slip flow model, Knudsen diffusion model, and cubic grid model. The reliability of this model is verified using molecular simulations, which do not include surface diffusion. The shale gas is considered as pure methane. Then, the different contributions of the gas mass transport mechanisms to the total mass transport are discussed in detail. The results demonstrate the following findings: (1) The studied flows are well–simulated by the proposed model. (2) Stress sensitivity results in a decrease in gas mass transport when the formation pressure exceeds 3.4 MPa, and the minimum value is approximately 0.45 times smaller than that when the width change is not considered. Moreover, stress sensitivity results in an increase in gas mass transport when the formation pressure is lower than 3.4 MPa, and the maximum value is approximately 4.5 times higher than that when the width change is not considered. (3) Shale gas mass transport is positively associated with the Young's modulus and Poisson's ratio, whereas it is negatively associated with the microfracture compressibility. When the formation pressure is less than 4 MPa, shale gas transport is positively correlated with the desorption capacity, whereas when the formation pressure exceeds 4 MPa, the effect of different desorption capacities on gas transport is nearly consistent. (4) When the microfracture width is at nanoscale and the reservoir pressure is lower than 15 MPa, surface diffusion has an obvious effect on the shale gas mass transport process. When the contribution of surface diffusion to the total shale gas mass transport is relatively small, the contributions of slip flow and Knudsen flow to shale gas mass transport exhibit the trend of “shifting each other.” When the surface diffusion contribution is larger, a reduction in its contribution leads to simultaneous initial increases in the contributions of slip flow and Knudsen flow to shale gas mass transport, and then these flows begin “shifting each other.”

A New Unified Gas-Transport Model for Gas Flow in Nanoscale Porous Media

SummaryA new unified gas-transport model has been developed to characterize single-component real-gas flow in nanoscale organic and inorganic porous media by modifying the Bravo (2007) model. More specifically, a straight capillary tube is characterized by a conceptual layered model consisting of a viscous-flow zone, a Knudsen-diffusion zone, and a surface-diffusion zone. To specify the contributions of the viscous flow and the Knudsen diffusion to the gas transport, the virtual boundary between the viscous-flow and Knudsen-diffusion zones is first determined using an analytical molecular-kinetics approach. As such, the new unified gas-transport model is derived by integrating the weighted viscous flow and Knudsen diffusion, and coupling surface diffusion. The model is also comprehensively scaled up to the bundles-of-tubes model considering the roughness, rarefaction, and real-gas effect. Nonlinear programming methods have been used to optimize the empirical parameters in the newly proposed gas-transport model. Consequently, the newly proposed gas-transport model yields the most accurate molar fluxes compared with the Bravo (2007) model and four other analytical models. One of the advantages of the new unified gas-transport model is its great flexibility, because the Knudsen number is included as an independent variable, which also endows the newly proposed model with the capability to cover the full-flow regimes. In addition, the apparent permeability has been mathematically derived from the new unified gas-transport model. A series of simulations has been implemented using methane gas. It is found through sensitivity analysis that apparent permeability is strongly dependent on pore size, porosity, and tortuosity, and weakly dependent on the surface-diffusivity coefficient and pore-surface roughness. The increased viscosity can reduce the total molar flux in the inorganic pores up to 66.0% under the typical shale-gas-reservoir conditions. The viscous-flow mechanism cannot be neglected at any pore sizes under reservoir conditions, whereas the Knudsen diffusion is found to be important when pore size is smaller than 2 nm and pressure is less than 35.0 MPa. The contribution of surface diffusion cannot be ignored when the pore size is smaller than 10 nm and the pressure is less than 15.0 MPa.

Strain rate dependence of the contribution of surface diffusion to bulk sintering viscosity

AbstractModeling of bulk sintering viscosity usually neglects the contribution of pore surface diffusion with respect to grain‐boundary diffusion. This approximation is questionable at the high densification rates used today in advanced fast sintering techniques. A two‐dimensional analysis of the problem shows that the influence of surface diffusion on bulk viscosity at high strain rate can be decomposed as the sum of two terms: a term linked to the change in pore surface curvature and a term linked to the change in grain‐boundary size. The computational procedure relies on the partition of pore profile evolution into a transient component accounting for non‐densifying phenomena and an asymptotic component accounting for strain‐rate‐controlled phenomena. The largest impact of surface diffusion is found to arise from the change in grain‐boundary size. It follows a transition from Newtonian viscosity at low strain rate to non‐Newtonian viscosity which, during densification, increases nearly linearly with strain rate. In some conditions, viscosity can then reach more than twice the value estimated when neglecting pore surface diffusion. Reversely, expansion is accompanied by a decrease in grain‐boundary size which causes a decrease in viscosity and can lead to grain separation at high strain rate.

Methane surface diffusion capacity in carbon-based capillary with application to organic-rich shale gas reservoir

Organic matter is widely distributed in organic-rich shale gas reservoir and has a large specific surface area to adsorb a significant quantity of methane molecules. In such nanoscale organic pores, the methane adsorbability and surface chemistries give rise to complex methane transport behaviours. Bulk state methane transports beyond continuum flow regime while surface diffusion for adsorbed methane plays a vital role in contributing to the total methane transport ability. In this study, we establish a methane surface diffusion model that considers the influence of confined pore space on methane adsorption, isosteric sorption heat and adsorbed methane coverage under high pressure. Grand canonical Monte Carlos simulations are carried out to estimate the adsorption isotherms of methane across a range of pore sizes and are applied to predict maximum methane concentration inside the adsorption layer volume. The contribution of surface diffusion on total methane transport ability in nanoscale confined pore space is investigated. Study results show that methane permeability for organic pores first decreases and then increases with the increase of pore size. Methane permeability for organic pore size less than 4 nm in relatively low pressure (<5 MPa) can be comparable to methane permeability for 20–25 nm inorganic pores. This can be attributed to the fact that the surface diffusion effect is enhanced in relatively low pressure and small pore sizes.