Permeability Variation Research Articles

Research on the Pore Evolution of Oil Shale under Different Thermal Treatment Temperatures Using NMR and FE-SEM Methods

Underground in situ pyrolysis for oil shale extraction is currently significant; the evolutions in microstructure, porosity, and permeability parameters are essential factors in evaluating the productivity of oil shale after pyrolysis. With the underground oil shale reservoir core, obtained from Jimsar Sag in the Junggar Basin in China, as the research object, the samples were subjected to the treatment at different high temperatures (400°C, 500°C, 600°C, and 700°C). The NMR and FE-SEM experiments on oil shale samples were conducted; the T 2 relaxation spectra, pore size distribution, and porosity and permeability variation were analyzed; and the relationships between movable fluid saturation and porosity and permeability were established, respectively. The results showed that when the thermal treatment temperature increased, the porosity and permeability of oil shale rose continuously but showed different laws. With the temperature being lower than 400°C, the porosity increased slowly, and the growth rate of porosity increased rapidly when the thermal treatment temperature was higher than 500°C. In the pyrolysis temperature range of 25°C~400°C, the growth rate of permeability was relatively slow. With the continuously enhancing temperature (500°C~600°C), the growth rate of permeability accelerated rapidly. When the temperature continued to rise (700°C), the increase of permeability began to slow down. There is a nonlinear correlation between porosity and movable fluid saturation and an approximately linear correlation between permeability and movable fluid saturation. The findings showed that 600°C was the suitable temperature for the pyrolysis of oil shale.

EFFECT OF CHANGE IN THE COEFFICIENT OF PERMEABILITY ON CONSOLIDATION CHARACTERISTICS OF CLAYS

The settlement rate and pore water pressure dissipation rate are mainly controlled by the permeability of soil. Both laboratory and field tests show that the permeability is varied during the loading and consolidation process. It is known that consolidation process is accompanied by decrease in void ratio which leads to decrease in the coefficient of permeability. The importance of the decrease of the coefficient of permeability on the time rate of settlement and pore water pressure needs to be investigated.This paper takes into account the change in coefficient of permeability during consolidation and studies its effect on consolidation characteristics of a clay layer. The finite element method is used in the analysis and the package Geo-Slope is adopted through coupling the programs SIGMA/W and SEEP/W. The relationship between the applied pressure and permeability was determined experimentally for three samples.It was concluded that the effect of permeability is clear at later times of consolidation due to decrease in void ratio and hence slower dissipation of pore water pressure. Taking into account variable permeability leads to longer times of consolidation. At later times (after 400 days), the excess pore water pressure predicted for the case of variable permeability is greater thanconventional case by about (10 – 12) %.

Effect of different injection fluids scenarios on swelling and migration of common clays in case of permeability variations: a micromodel study

Swelling and migration of present clays make damage to the oil reservoirs due to low salinity waterflooding (LSWF) can induce serious problems in the case of oil recovery improvement and researchers are trying to solve this problem. The purpose of this work is to investigate the mechanism of two phenomena of swelling and migration clays in the porous media of a reservoir rock by injecting a different composition of LSWF using a glass micromodel and providing the appropriate composition and pattern of injection with the removal of damage. Proper water flooding design, application of efficient swelling inhibitors, and migration control are among the most important methods to overcome the problem of formation damage due to swelling and migration of clays. A series of static (bulk or bottle test) and dynamic tests were carried out using a micromodel with a coating of kaolinite and montmorillonite clays in the vicinity and injection of different low salt water compositions. The type and amount of these clays were selected based on the results of XRD and SEM mineralogical tests on real reservoir rock, FW and diluted FW, SW and diluted SW, solution of 1% zirconium oxychloride in 20 times diluted seawater (SI), and composition of nanofluid MgO, SiO2, and Al2O3 in 20 times diluted. In the studies conducted by the micromodel, only the images taken were used in the analysis of the mechanisms, but here, the input and output pressures of the micromodel were recorded with high-precision pressure transmitters, and by using the differential pressure, the permeability was calculated and the formation damage index was introduced. The overlap of the interpretation of the captured images and the changes of the numerical parameter of the damage index in all stages of injection of smart water composition was considered to evaluate the simultaneous and separate mechanisms of swelling and migration of clays. The results of the experiments in this research show that clay swelling has destructive effects on permeability, and migration due to the transfer of clays from the porous medium can have promising effects on reducing the damage index in some conditions. And it is necessary to use the swelling control compound during the flooding process, but the migration inhibitor compound is not always suitable. Gradual reduction of salinity is also introduced as a pattern to prevent swelling damage or clay migration.In general, in this study, the best design and fluid engineering for smart water injection with the least damage in the micromodel scale was presented.

Modified diffuse interface fluid model and its consistent energy-stable computation in arbitrary domains

Binary fluid flows in irregular domains are common phenomena in natural and industrial fields. To describe these physical processes, we herein present a novel fluid flow-coupled two-material model reflecting different wetting conditions on an arbitrary fluid-solid interface. A modified ternary Cahn–Hilliard (CH) diffuse interface model is adopted to capture the fluid-fluid interface. One of three components is fixed for all time to represent the profile of complex domains. By considering the contact angle condition on solid-fluid interface and equilibrium interface assumption, an extra wetting term is derived. To treat the fluid flow in domains with solid obstacles, we consider the entire system as a porous medium with variable permeability and add a large penalty term into the incompressible Navier–Stokes (NS) equations. It can be proven that the proposed modified Cahn–Hilliard–Navier–Stokes (CHNS) system satisfies the energy dissipation law (energy stability). Based on the scalar auxiliary variable (SAV) approach with appropriate correction techniques, the linear and consistent energy-stable scheme is developed. We introduce the numerical implementation and estimate the discrete version of energy stability in detail. The proposed method can be implemented on regular Cartesian grids with the absence of explicit boundary treatment. Moreover, the calculations are totally decoupled in each time step. Extensive numerical experiments not only indicate the expected accuracy and stability but also show the superior performance in arbitrary domains with different wetting conditions.

Effects of Coal Permeability Anisotropy on Gas Extraction Performance

To investigate gas flow characteristics in coal seams with strong anisotropy, a coupled anisotropic dual-porosity model was established. Effects of permeability anisotropy on variations in gas pressure, gas extraction volume and effective extraction areas were analyzed. Furthermore, mechanisms of crustal stress, initial gas pressure, ultimate adsorption strain and Langmuir volume constant on permeability anisotropy and extraction amount were studied. Results show that permeability anisotropy could result in an elliptical pressure drop zone around production boreholes. Changes in effective gas extraction areas are divided into three stages: slow growth in an elliptical shape, rapid growth with a superposition effect and steady growth in a funnel shape. Permeability isotropy enables faster reaching of stage III than the anisotropy case. As the vertical stress increases, gas pressure distribution around boreholes gradually changes from an ellipse with horizontal direction as long axis to a circle. Larger initial gas pressure could bring consistently higher gas production in the initial and middle extraction stages, and a faster decrease in the late phase. When gas pressure is 2.5 MPa, the peak daily gas production in initial extraction stage is about three times higher than that in the late phase. Ultimate adsorption strain is positively correlated with permeability change. This relationship becomes more significant with a longer extraction time. In contrast, permeability variation is inversely proportional to the Langmuir volume constant in the initial extraction stage. However, these factors are directly proportional in the late stage. The order of significance of each factor’s effect on permeability is crustal stress > ultimate adsorption strain > initial gas pressure > Langmuir volume constant. Moreover, initial gas pressure has the most significant effect on gas extraction volume, while Langmuir volume constant has the least significant impact. Results could provide a theoretical reference for extraction borehole design and drainage parameter setting to improve extraction performance.

A theoretical solution to investigate long-term behavior of pressurized tunnels in severe squeezing conditions

In this paper, an analytical-numerical method is presented to study the long-term behavior of pressurized tunnels. In this regard, the pressurized tunnel construction is simplified into three stages: tunnel excavation, installation of the lining, and applying the internal water pressure. The rock mass around the tunnel is assumed to obey the viscoelastic Burgers model and to have a permeability that is variable over time in any location. The tunnel lining is elastic and has constant permeability. To derive the equations, the coupled hydro-mechanical interactions are simulated and solved simultaneously to find out the tunnel displacements and lining pressures. After verifying the proposed method, a parametric study is conducted, and the influences of various parameters such as rock mass rheological parameters, the ratio of rock mass permeability to lining permeability, variation of rock mass permeability over time and distance, and magnitude of the internal water pressure are investigated. The obtained results show the significance of considering variable permeability on the tunnel performance. As well, the Maxwell shear modulus is the most influencing parameter among Burgers model parameters.

A coupled bio-chemo-hydro-wave model and multi-stages for MICP in the seabed

As an environmentally friendly technology, the microbially induced calcite precipitation (MICP) has been gradually applied for the seabed reinforcement. However, there are few models for the simulation of the MICP process in marine environment. A coupled bio-chemo-hydro-wave model for MICP in the seabed was proposed in this paper. This model can capture the bacterial behaviour (growth, decay, attachment, diffusion), the evolutions of chemical substances (urea, calcium, ammonium, calcium carbonate), and the variations of porosity and permeability. It is indicated that (1) distributions of the bacteria and chemical substances show obvious heterogeneity, and are related to the injection rate and injection time; (2) The calcium carbonate content, porosity, and permeability are significantly affected by the initial bacterial concentration, injection rate, injection time and cementing solution concentration. The reduction ratios of porosity and permeability show significant linear increasing trend with the increase of calcium carbonate content; (3) Although MICP process increases the vertical excess pore pressure gradient in the shallow seabed, the seabed can remain stable under the large waves due to the increasing of soil weight and inner cohesive force.

Bionic octopus structure Inspired Stress-Driven reconfigurable microwave absorption and multifunctional compatibility in infrared stealth and De-icing

Constructing intelligent materials with self-adjustable microwave absorption, infrared stealth and de-icing performances has been of great importance to make the devices and equipment adapt to the variable electromagnetic environment. However, the concurrent achievement of desired microwave absorption, timely switching and multifunctional compatibility is the key issue to be urgently resolved but still remains an enormous challenge. Inspired by the flexible octopus tentacles biomorph, the bionic structure of carbon foam coated by Fe3C particles (CCF) is synthesized via an in-situ carbothermal reduction. Wherein, the carbon foams serve as the basic octopus tentacle skeleton and the magnetic Fe3C particles act as suckers on the surface, providing both sufficient dielectric and magnetic loss by regulating N-defects elaborately. As a result, the CCF hybrids reveal obviously compressive-sensitive microwave absorption characteristics, accompanied by tremendous variations of permittivity and permeability. Moreover, the excellent cyclic mechanical stability, high thermal management and de-icing properties are also explored, which reveals the great potential for multifunctional applications as smart microwave absorbers in multifunctional fields.

Impact of supercritical CO2 exposure time on the porosity and permeability of dry and wet shale: The influence of chemo-mechanical coupling effects

CO2 storage in shale formation is a potential way to reduce CO2 emissions for carbon neutrality. The variation of permeability in shale triggered by CO2-shale interaction plays an important role in CO2 sequestration. The effect of supercritical CO2 (ScCO2) exposure times (0, 10, 20, 30, 40 days) on the porosity and permeability evolution of dry and wet shale samples was investigated herein. Results show that the porosity and permeability of both dry shale and wet shale increased first and then decreased over exposure time, and there is an inflection point. The porosity and permeability evolution of shale is controlled by the chemical-mechanical coupling effects. The dissolution of mineral induced by ScCO2 exposure increases the porosity and permeability of shale. The mechanical weakening induced by ScCO2 exposure enhances the pores compressibility of shale, makes the porosity and permeability decrease at stressed condition. In the early stage, the chemical effect is dominant, after the time of inflection point, the mechanical weakening effect is dominant. The inflection time of wet shale is earlier than that of dry shale, indicating that the chemical effect dominant stage in wet shale is shorter than that in dry shale. This can be attributed to that the water promoted the chemical reaction and enhanced the weakening of mechanical properties, then shortened the chemical corrosion dominated stage. Our findings suggest that ScCO2-shale interaction can contribute to the decrease in porosity and permeability of shale with the increase of ScCO2 exposure time, and hence adversely affecting the shale gas recovery and the continue injectivity of CO2. Thus, the time dependent chemical-mechanical coupling effects should be considered in evaluating the shale gas production and CO2 storage capacity.

Anisotropic Evolution of Effective Stress and Pore Pressure during Coalbed Methane Drainage

Summary The anisotropy and dynamic variation in permeability of gas-adsorbing coals have a significant influence on fluid flow behavior in the cleat system. The assumption of a constant anisotropy coefficient (the ratio between permeability components in orthogonal directions) has been traditionally made to simplify the seepage-stress coupling analytical model. In this approach, the pressure drop of the coalbed is separated into desorption and nondesorption areas. To evaluate the effective stress, pore pressure, permeability distribution, and variable anisotropy coefficient more accurately, analytical formulas were developed that consider elastic mechanics and methane sorption. The results show that the anisotropy coefficient can be dynamic when cleat compressibility anisotropy exists. Pressure contours are a set of ellipses that increase in eccentricity from the near-wellbore area to the pressure drop boundary, leading to corresponding anisotropy changes in effective stress and permeability. The gas desorption-related matrix shrinkage effect causes a discontinuous pressure drop gradient at the boundary between desorption and nondesorption areas, resulting in nonsmooth pressure drop curves. The pressure gradient difference changes with the radius of the desorption area and is nonisotropic, with the high-permeability direction showing a greater difference than the low-permeability direction. These results indicate that the dynamic anisotropy coefficient has a significant impact on coalbed drainage and extraction. Compared to previous mathematical models, which assumed permeability isotropy or constant anisotropy coefficient in cleat systems, the proposed model provides a more accurate method to evaluate pressure and permeability distribution.

A comparative investigation of the effect of gas type on foam strength and flow behavior in tight carbonates

Foam generation technique has been practically applied to overcome gas mobility issue during enhanced oil recovery (EOR) processes. Incorporated with the utilized gas, the capability of foaming agent to generate persistent foam determines the flow performance under reservoir conditions. In this study, we first identified the surfactants with excellent phase behavior and foaming properties and, second, evaluated their bulk foam performance with different gases, including N2, CO2, and hydrocarbon gas (CH4) under high-pressure and high-temperature conditions. In bulk, the foam generated with the high-density gas, i.e., CO2, exhibited the greatest foamability but the lowest foam stability. With amidoamine oxide-based surfactant, CH4-foam was found to be more stable than N2-foam, while the opposite was observed for sulfobetaine-based surfactant. The most effective surfactant was later used to perform flow experiments on two tight carbonate rocks, including Minnesota Norther Cream Buff and Edwards limestone, with permeabilities of ∼0.8 and 16 mD, respectively. The core-flooding experiments showed that the optimum quality of CO2-foam was lower than that of N2- and CH4-foams. For a given flow rate and fixed foam quality, the steady-state strength followed the descending order of CH4-, N2-, and CO2-foam. However, in general, the difference in foam strength between N2- and CH4-foams was insignificant when the total flow rate was varied. We also found that the variation in rock permeability had a greater effect on the strength of the CO2-foam compared to those generated with N2 and CH4. In the presence of oil, the shear-thinning behavior of all foams was found more prominent. The increase in oil saturation had a more adverse effect on the strength of N2- and CH4-foams, particularly in the higher permeability rock. The results indicated that the foam strength, which is key in the effectiveness of foam EOR applications, is greatly influenced by several factors such as gas density, gas solubility in water, the presence of oil, and rock permeability.

Influence of Oyster Shell Pyrolysis Temperature on Sediment Permeability and Remediation

Permeability is an important aspect of sediment remediation. It is well-known that oyster shells can be used for sediment remediation, however the influence of pyrolysis temperature on sediment permeability remains unknown. In this study, we examined sediment permeability and remediation using crushed oyster shells of less than 5 mm in size that were pyrolyzed at 350 °C (POS350) and 600 °C (POS600) for six hours. Based on the results of the variable head permeability test, POS600 has greater sediment permeability than POS350. In addition, POS600 has greater than POS350 to reduce dissolved inorganic nitrogen (DIN; NH3-N, NO2-N, and NO3-N) and phosphate (PO4-P) from organically enriched sediment because of its higher Ca2+ elution. In conclusion, pyrolysis of oyster shells at 600 °C is more effective than pyrolysis at 350 °C. This finding is true because the transformation of CaCO3 to CaO, which is the source of Ca2+, stimulates pore water flow. Based on these findings, it can be concluded that pyrolyzed oyster shells are beneficial for increasing sediment permeability, thereby helping in the remediation of sediments.

In-field measurement and numerical modelling of air leakage in concrete: From laboratory specimen to structural full-scale

This work estimates air leakage through concrete porosity for structures by using data obtained in field combined with stochastic finite element (SFE) modelling. For this purpose, a methodology is proposed to evaluate permeability under representative over-pressurization conditions based on in-field measurements under vacuum. This makes it possible to investigate the air leakage through the inner wall of a 1:3 scaled nuclear vessel named the VeRCoRs mock-up. Measurements are made for over 80 points scattered on the external face of the inner wall of the structure. Based on the data collected, a statistical analysis quantifies the spatial variation of permeability and contributes to the building of an SFE model of air leakage at the structural scale. Measured and predicted data are in good agreement on the service life of the structure. This shows the relevance of combining in-field measurements during an operational phase and the SFE modelling for better evaluation of the structural performance. The lessons learnt from the present work could be useful for the assessment of all structures with durability or mechanical issues that induce a continuous loss of tightness.

Spin-Current-Driven Permeability Variation for Time-Varying Magnetic Metamaterials

We study permeability ($\ensuremath{\mu}$) variation of a lithographically prepared magnetic meta-atom consisting of $\mathrm{Ta}$/Py/$\mathrm{Pt}$ trilayers by means of spin-torque ferromagnetic resonance (ST FMR). With an injection of a direct current up to $\ifmmode\pm\else\textpm\fi{}20\phantom{\rule{0.2em}{0ex}}\mathrm{mA}$ together with an alternating current in GHz frequencies, the meta-atom under external magnetic fields shows significant changes in position and width of ST FMR signals due to a massive spin-current injection. This leads to the spin-current-driven $\ensuremath{\mu}$ variation, which is verified by analytical calculation based upon the experimentally obtained resonance field and Gilbert-damping parameter. The present study paves a way to time-varying spintronic metamaterials with a high modulation frequency for realizing microwave sources toward the post-fifth-generation mobile-communication system.

Magnetic Resonance Imaging of Mouse Cerebral Cavernomas Reveal Differential Lesion Progression and Variable Permeability to Gadolinium.

Cerebral cavernous malformations, also known as cavernous angiomas, are blood vessel abnormalities comprised of clusters of grossly enlarged and hemorrhage-prone capillaries. The prevalence in the general population, including asymptomatic cases, is estimated to be 0.5%. Some patients develop severe symptoms, including seizures and focal neurological deficits, whereas others remain asymptomatic. The causes of this remarkable presentation heterogeneity within a primarily monogenic disease remain poorly understood. We established a chronic mouse model of cerebral cavernous malformations, induced by postnatal ablation of Krit1 with Pdgfb-CreERT2, and examined lesion progression in these mice with T2-weighted 7T magnetic resonance imaging (MRI). We also established a modified protocol for dynamic contrast-enhanced MRI and produced quantitative maps of gadolinium tracer gadobenate dimeglumine. After terminal imaging, brain slices were stained with antibodies against microglia, astrocytes, and endothelial cells. These mice develop cerebral cavernous malformations lesions gradually over 4 to 5 months of age throughout the brain. Precise volumetric analysis of individual lesions revealed nonmonotonous behavior, with some lesions temporarily growing smaller. However, the cumulative lesional volume invariably increased over time and after about 2 months followed a power trend. Using dynamic contrast-enhanced MRI, we produced quantitative maps of gadolinium in the lesions, indicating a high degree of heterogeneity in lesional permeability. MRI properties of the lesions were correlated with cellular markers for endothelial cells, astrocytes, and microglia. Multivariate comparisons of MRI properties of the lesions with cellular markers for endothelial and glial cells revealed that increased cell density surrounding lesions correlates with stability, whereas denser vasculature within and surrounding the lesions may correlate with high permeability. Our results lay a foundation for better understanding individual lesion properties and provide a comprehensive preclinical platform for testing new drug and gene therapies for controlling cerebral cavernous malformations.

Studying the Favorable Zone for Pressure-Relief Gas Extraction by Combining Numerical Investigation and On-Site Application

Gas extraction in the pressure-relief area using the depressurization effect of seam mining is an effective way to solve coal-mine gas problems. In this paper, we performed numerical modelling of the 204 working face via FLAC 3D, by which the stress variation of the rock mass and associated permeability evolution during the working face advancement were investigated. Furthermore, the favorable gas extraction zone for pressure relief was proposed based on the gas extraction performance of the on-site boreholes. The results show that: (1) gas extraction varies with the evolution of the three zones of the overlying rock and the associated permeability variation, which becomes stable when the height of the three zones remains unchanged; (2) the favorable zone for gas extraction of the 204 working face ranges from 13 m to 19 m of Dv, in which the gas extraction of on-site boreholes are located, presents better performance than other areas; (3) the gas extraction volume of the optimized gas extraction scheme rises to 77.46 m3/min with a 77.26% gas extraction rate, eliminating gas overrun in the working face and upper corner and increasing the advancement speed to 6.4 m/d. The on-site verification confirms the numerical simulation scope, more accurately determining the favorable zone for gas extraction. This may provide a reliable approach for improving the pressure-relief gas extraction performance and reducing the associated engineering costs.

Porosity and permeability estimation using seismic wave velocity along Yangtze River embankment

Although porosity and permeability are essential parameters for slope stability, estimating the spatial porosity and permeability variation of slope site is difficult because of complexity of petrophysical modeling. The differential effective medium (DEM) and self-consistent approximation (SCA), which used to calculate elastic modulus of porous materials, are applied to link seismic wave velocity to porosity and permeability. The shear-wave velocity structure is gathered through a near surface Rayleigh-wave survey, and the porosity and permeability profiles are further estimated. The results are cross validated by the borehole data and poroelastic relation. The petrophysical structure of the Yangtze River embankment may further reflect hydrological properties of laminated layers, which bear relatively large porosity and permeability in some area. The results show that the porosity and permeability profiles based on SCA are more reliable with respecting to the borehole data. The relationship between seismic velocity and porosity and permeability is established and validated, favoring a sound basis for further hydrological interpretation of seismic data. Furthermore, some geotechnical suggestions are put forward during the flood seasons in correspondence to the natural hazard mitigation.

Assessment of the deep oil and gas bearing potential onshore in the west of Azerbaijan (Tarsdallar area)


 
 
 The Tarsdeller oil and gas field, which has a brachyoanthicline structure, is the most promising area of the oil-gas region (OGR) in the Kura-Gabirri interfluve. Goal: Based on the reservoir characteristics of rock samples obtained from exploration wells drilled in the area adjacent to the field, petrophysical models have been compiled, reflecting the spatial variation in porosity and permeability of oil-containing reservoirs. Objects: Consideration of the petrophysical properties of core samples taken in the study area made it possible to confirm the oil and gas potential of deep-seated reservoirs. Methods: This analyzed the values and variation of petrophysical properties by depth, age and various physical factors. The observed wide range of changes in the reservoir properties of rocks in the study area is mainly due to tectonic changes, lithological heterogeneity of the sedimentary complex, differences in the depth of bedrocks, as well as the complexity of tectonic conditions. As a result, to predict the oil and gas content in deep reservoirs of the same structures, it is advisable to use the methods of exploration geophysics, as well as the results of changes inthe reservoir characteristics of rocks, determined by petrophysical data. At the same time, it is most expedient to focus on the study of Paleogene-Cretaceous tectonics for the search for oil and gas objects using prospecting and exploration (preferably aerial-photo-space) works at the field. Results: Models made in 3D format illustrate the predicted oil and gas potential and patterns of distribution of productive horizons involved in the geological structure of oil and gas deposits, along the depths and stratigraphic units. It is shown that although the permeability of the rocks in the area is low, the porosity values are favorable for the industrial accumulation of hydro-carbons. Fractured carbonate reservoirs of the Upper Cretaceous are the most promising among the Mesozoic sediments in the OGRbetween the Kura and Gabirri rivers. Deep-seated structural uplifts complicated by large-amplitude fractures are recommended as the priority targets for further geological exploration. However, the real potential of the Eocene deposits, which are widespread in the NGR between the Kura and Gabirri rivers, remains unexplored by deep drilling. This is due, on the one hand, to the incomplete opening of the Eocene section in the structures prepared for deep drilling, structural-tectonic and lithofacies features, as well as insufficient knowledge of drilling for oil and gas, and on the other hand, poor development of promising intervals of the section.
 
 

Modeling Approaches to Permeability of Coal Based on a Variable-Order Fractional Derivative

In the past decades, many permeability models have been proposed to characterize the coal permeability evolution in the elastic state. Considering that the coal near the mining working face is often in the plastic or post-peak failure state, it is significant to characterize the coal permeability evolution in the plastic and post-peak failure stages for safe mining. In this study, two permeability models are developed using a variable-order fractional derivative to characterize the coal permeability evolution during the whole process of elastic, plastic, and post-peak failure stages. The results indicate that both models have the ability to better describe the coal permeability evolution during the whole process in areas near the mining working face. In addition, the physical and mechanical interpretation of the variable-order function is given as an indicator of fracture development, indicating the sensitivity of stress variation to coal fracture development. Moreover, the relationships among the effective stress, damage variable, and post-peak permeability of coal are discussed.

Multiple upscaling procedures for gas transfer in tight shale matrix-fracture systems

Multiple upscaling schemes for gas transfer in nanoporous media, microporous matrix, core-scale matrix, and centimeter-scale matrix-fracture systems are investigated. An Open Multi-Processing (OpenMP)-based parallelized multi-scale numerical solver for micro-gaseous flow in composite microporous media is developed by coupling the pore-scale multiple-relaxation-time lattice Boltzmann method (MRT-LBM) and representative elementary volume (REV)-scale LBM model. The permeability of the microporous matrix is calculated through hundreds of pore-scale simulations for gas transfer in nanoporous media, before being imported into the REV-scale LBM to predict the core-scale matrix permeability. It is followed by the investigations of the variations of core-scale permeability with the heterogeneous spatial distribution of organic matter aggregates, mineral aggregates, interparticle pores, and microfractures. The parallel and sequential gas transfer processes in a larger shale system containing the tight matrix and hydraulic fractures are studied and analyzed. The results reveal several new insights: 1) the microscale spatial distribution of multiple constituents has relatively little effect on the core-scale permeability; 2) an ultra-large local pressure gradient occurs in a thin boundary layer of tight shale matrix, which is shown to be proportional to the square root of the permeability ratio, resulting in considerable flow characteristic velocity in the matrix; 3) the in-situ matrix-fracture transfer satisfies a sequential transport process due to a long equilibration time delay between the tight matrix and fractures; 4) the observed high production rate for tight shale may be caused by the ultra-large local pressure gradient in the matrix (and not by a large apparent permeability as commonly assumed). The results also reveal some anomalous phenomena for multiscale gas transfer in tight shale formations.