Permeability Shale Gas Research Articles

Experimental Investigation on the Evolution of Physicochemical Properties and Dissolution Mechanism of High-Siliceous Shale with Acid Treatment

Summary The investigation of the influence of acidification conditions on the modification patterns of shale and the mechanisms of shale acidification processes is an indispensable aspect of further development within the field of shale acidizing theory. Prior research on shale acidizing has predominantly used hydrochloric acid (HCl) and carbonate-rich shale, which has restricted the scope of application for shale acidizing techniques and has not thoroughly examined the reaction kinetics of acid-rock interactions under reservoir conditions. This study focuses on siliceous shale, utilizing hydrogen fluoride (HF) in rotating disk experiments to assess the kinetic parameters of acid-rock reactions under varying acidification conditions, including duration, concentration, temperature, bedding direction, and acid flow velocity. Key influencing factors such as time, temperature, concentration, and experimental methods were selected for a comprehensive analysis, incorporating mineral composition [X-ray diffraction (XRD) and scanning electron microscopy with energy dispersive spectroscopy (SEM-EDS)], microstructure (SEM), pore medium characteristics [mercury intrusion porosimetry (MIP) and low-temperature nitrogen adsorption (LNA)], surface morphology (3D laser scanning), and nanoindentation testing (NIT). The findings confirm the positive role of acid treatment in enhancing the permeability of shale oil and gas and in softening the reservoir rock, while also indicating potential negative impacts on hydrocarbon extraction, such as the formation of precipitated byproducts and the exfoliation of rock layers. This paper investigates the patterns of influence of HF acidizing parameters on siliceous shale and elucidates the mechanisms of action in shale acidification transformations, thereby providing a theoretical foundation for the modification of shale oil and gas reservoirs.

The roles of different migration mechanisms in the transport of H2O–CH4 gas mixture in shales

Studying the roles of different migration mechanisms in shale matrix gas transport is beneficial for shale gas extraction and CO2 sequestration. The roles of different transport mechanisms in shale H2O–CH4 gas mixture transport were investigated considering their contributions to fluid flux. A permeability model coupling multiple gas migration mechanisms was developed by combining the pore network-related effective medium approximation, which was validated using process data from simultaneous H2O–CH4 transport in shales. The results showed that the gas transport mechanisms dominating methane and water vapor migration in shale differed. Slip flow and Knudsen diffusion contributed approximately 99% to methane migration. Water vapor surface diffusion as well as slip flow and Knudsen diffusion primarily contributed to the water vapor permeability before and after a time point, respectively. Water vapor and methane permeability generally decreased with time. The equilibrium water vapor and methane permeabilities ranged from 2.7699×10−22–12.312×10−22 m2 and 0.2640×10−21–4.9036×10−21 m2, respectively. The methane surface diffusion permeability increased slowly with time before approaching methane monolayer adsorption (before ∼100 s). An increase in relative humidity (approximately 300–3600 s) can promote the transport of water vapor. Water vapor and methane adsorption, especially the condensation of adsorbed water, could largely explain the decrease in shale gas permeability.

Novel methodology to couple decline curve analysis with CFD reservoir simulations for complex shale gas reservoirs

AbstractShale reservoirs are highly complex and are difficult to study using conventional reservoir simulation tools. This study introduces a novel methodology for estimating production from complex shale gas reservoirs by coupling decline curve analysis (DCA) with computational fluid dynamics (CFD) simulations. The proposed method uses exponential DCA to analyze production data from a dual porosity–permeability shale gas transport model. These complexities include fracture characteristics, geomechanical properties, nanopore confinement effects, and multiple flow mechanisms contributing to the total production performance. The shale gas transport model is validated through historical production data from Marcellus shale. The new methodology also tests fracture characteristics. It shows that increased porosity and permeability will increase the recoverable reserves but will have varying effects on the decline rate. The paper demonstrates the advantages of the proposed methodology over conventional reservoir simulation tools. It provides insights into the factors affecting shale gas production performance through the inclusion of the complexities of an unconventional shale gas reservoir. The paper provides a proof of concept on the particular reservoir of which the field data is provided—Barnett and Marcellus Shale.

Study on the multifractal characterization and seepage of the shale matrix: A case study of the Longmaxi Formation in southwestern Sichuan Basin, China

The pore structure and heterogeneity of shale significantly impact the occurrence and permeability of shale gas. Studying these aspects is beneficial for exploring and developing shale gas. In this study, organic-rich shale from the Longmaxi Formation in the Luzhou-Changning area was selected as the research subject. Experiments, including spontaneous imbibition, pressure saturation, and nuclear magnetic resonance, were conducted to characterize the pore structure and heterogeneity of the shale in this area. Using multifractal theory, we analyzed and discussed the multifractal characteristics of pores with different connectivities in relation to permeability. The results indicate that the T2 cutoff value (T2f) of the shale is greater than the T2c value, suggesting that the pore size of connected pores exceeds that of pores retaining bound water. The sizes of connected pores primarily range from 1 to 30 nm, predominantly between 1 and 10 nm. Significant differences were observed in the multifractal spectrum functions under dry, spontaneous imbibition, and water-saturated conditions, reflecting varying degrees of heterogeneity. The multifractal parameters differ, with higher ΔD values under water-saturated conditions, indicating that pores with weaker connectivity enhance the overall heterogeneity of the shale when saturated. Conversely, lower ΔD values under dry conditions suggest less heterogeneity in pores containing bound water. Total organic carbon (TOC) and clay content were identified as the main factors influencing the development of connected pores. Based on these findings, a discriminant 3D diagram correlating permeability with porosity, tortuosity, and multifractal parameters (D0-Dmax) of strongly connected pores was established for the Luzhou-Changning area. This diagram serves as an effective tool for evaluating the flow capacity of shale reservoirs and offers guidance for identifying sweet spots within the reservoir.

Comparative Study on Flow Characteristics in Deep Marine and Marine-Continental Transitional Shale in the Southeastern Sichuan Basin, China.

Permeability is a significant characteristic of porous media and a crucial parameter for shale gas development. This study focuses on deep marine and marine-continental transitional shale in the southeastern Sichuan area using the gas pulse decay testing method to systematically analyze the gas permeability, stress sensitivity, and gas transport mechanisms of shale under different pressure conditions and directions. The results show that the porosity and gas permeability of the deep marine shale are greater compared to those of the marine-continental transitional shale. The elevated fluid pressure in the deep marine shale offers superior conditions for the preservation of nanopores, while the high quartz content provides advantageous conditions for fluid transport in nanopore channels. The permeability and stress sensitivity of the deep marine shale are greater than those of the marine-continental transitional shale, and the stress sensitivity is greater in the perpendicular bedding direction than in the parallel bedding direction, possibly related to the mineral composition of shale and the compaction it has undergone. The flow mechanism of the deep marine shale is transition flow and Knudsen flow, while that of the marine-continental transitional shale is transition flow. The deep marine shale possesses smaller nanopore sizes and a higher quantity of micropores, which create advantageous conditions for gas transport within nanopores. During the process of extracting shale gas, the extraction of gas causes a decrease in pore pressure and an increase in effective stress, resulting in a reduction in permeability. However, when the pore pressure reaches a specific value, the enhanced slippage effect leads to an increase in permeability, which is advantageous for gas extraction. In the later stage of shale gas well production, intermittent production plans can be developed considering the strength of the slippage effect, leading to a significant improvement in production efficiency.

Analytical Model of Shale Gas Permeability Based on the Pore Size Distribution from FE-SEM and Image Analysis

Analytical Model of Shale Gas Permeability Based on the Pore Size Distribution from FE-SEM and Image Analysis

A multi-layer nanocased model to explain the U-shaped evolution of shale gas permeability at constant confining pressure

Understanding the evolution of shale permeability is critical in efficiently recovering gas from shale reservoirs. Two representative profiles of permeability evolution are typically experimentally observed under constant confining pressure and incremented gas pressure – “U-shape” with increasing gas pressure but sometimes absent the second upright limb of the “U” at high gas pressures. Current models fail to address these two different profiles, potentially leading to inappropriate explanation of experiment observations or inaccurate predictions of gas production. In order to determine the mechanistic reason, a multi-layer nanocased model, in which transmissive nanotubes are embedded within a cylindrical sheath of matrix, is proposed. In the model, permeability evolution is defined as a function of the evolving nanotube radius within a total matrix radius. The ensemble structure governs the transition from local deformation of the nanotube wall to the global deformation of the matrix sheath, particularly as sorbing/swelling gas gradually permeates the sheath wall. The finite element method is employed to calculate permeability evolution from an initial equilibrium state to final equilibrium. We develop a series of permeability evolution curves that match various experimental profiles. Contrasting observed permeability responses are attributed to the competition between nanotube strain and matrix global strain. The former term enlarges the nanotube radius while the latter term swells the matrix declining the permeability value. Therefore, when the matrix global strain dominates at late time, permeability decreases. Conversely, a permeability recovery stage is barely observed in the late stage because in most cases global swelling dominates the permeability evolution and an extended observational period is necessary before this swelling appears. This is also the reason why the observed final permeability ratio is rarely greater than unity. A small nanotube radius or a large adsorption strain favors a significant decrease in permeability. When the nanotubes are located within the inorganic matrix, the permeability profile conforms to poro-elastic theory and the decreasing permeability stage is barely apparent or absent. The proposed model thus provides insight into the controls on permeability evolution in shales and the controlling impact of shale matrix properties by considering the inhomogeneities of the shale matrix.

Principal characteristics of marine shale gas, and the theory and technology of its exploration and development in China

The exploration and development theory and technology of marine shale gas with shallow burial depth of 3500 m in South China has become mature after more than 10 years of practice. In order to continuously promote the exploration and development of shale gas in China, based on the research results of many scholars, combined with production practice, the main characteristics of marine shale gas in China and the main theory and technology of exploration and development are further summarized. The results show that: (1) The basic characteristics of marine shale gas in southern China are marine deep-water shelf deposition, and organic-rich shale is distributed continuously in a large area; The organic matter is stored in situ after high thermal maturity gas generation, and the gas content of shale is affected by late tectonic activity; The reservoir space is dominated by nano-scale pores, and the reservoir is super-tight and ultra-low permeability, which has no natural productivity without well stimulation; Bedding and natural fracture affect the productivity of shale gas wells; The mechanical properties of shale rock determine the effect of horizontal wells. In the early stage of well production, the production rate is high and the decline is fast, while in the middle and late stage, the rate is low but the production cycle is long. (2) Based on the above characteristics, the theory of “sweet spot” and “sweet interval” of shale gas and the theory of effective development of artificial gas reservoir are established, that is, the sedimentary and tectonic interaction forms the “sweet area” or “sweet spot” of marine shale gas. Gas productivity is determined by geological and engineering factors, so the “sweet spot” must be found to develop. By constructing artificial gas reservoir through “making an artificial high permeability area, and reconstructing a seepage field”, the effective development of ultra-tight and low permeability shale gas reservoirs can be realized. It is the most effective technique for shale gas development to accurately create “transparent geological body” of reservoirs based on geology-engineering integrated evaluation technology and establish artificial gas reservoir through multi-stage fracturing technology. (3) The overpressure area in the southern Sichuan Basin is the “sweet area” for shale gas development. The “sweet interval” of the lower Silurian Longmaxi Formation with a thickness of 3–5 m and high brittle-rich organic matter is the optimal “golden target” for horizontal wells. (4) The development leapfrog from the first generation to the second generation has been realized by the key technology of multi-stage fracturing of horizontal wells. The EUR per well of Upper Ordovician Wufeng Formation and Longmaxi Formation in southern Sichuan has increased from 0.5 × 108 m3 in the initial stage to 1.0 × 108–1.2 × 108 m3 at present with a buried depth of shallower than 3500 m. (5) The effective area favorable for shale gas development in southern Sichuan is 2.0 × 104 km2, and it is estimated that the proven geological reserves of shale gas can reach 10 × 1012 m3. It is preliminarily predicted that the shale gas production in China will exceed 300 × 108 m3 in 2025 and reach 400 × 108 m3 in 2035.

Prediction of the shale gas permeability: A data mining approach

One of the most important parameters affecting shale gas extraction is the gas permeability of shale. Because there are many influencing factors and the mechanism of interaction is complex, it is difficult to accurately predict the gas permeability of shale. In this paper, a new machine learning model is proposed by combining Mind Evolutionary Algorithm (MEA) and Adaptive Boosting Algorithm-Back Propagation Artificial Neural Network (ADA-BPANN), which predicted the gas permeability of cement mortar with different moisture contents under different stress conditions based on the results of 616 laboratory gas permeability experiments. This is the first time that a combination of MEA and ADA-BPANN algorithms has been used to predict shale gas permeability. Compared to the traditional machine learning algorithms such as Particle Swarm Optimization Algorithm (PSO) and Genetic Algorithm (GA) optimized ADA-BPANN. The excellent performance of MEA optimized ADA-BPANN has been verified. This novel algorithm has higher prediction accuracy, shorter training time, and can avoid problems such as local optimization and overfitting. Secondly, the sensitivity of the parameters is analysed by using the novel model, and the results show that the parameter with the greatest influence on gas permeability is relative moisture content, followed by confining pressure, seepage pressure and confining pressure loading/unloading stage. The present research shows that the MEA optimized ADA-BPANN model has great potential for estimating the stress-dependent gas permeability of shale with different moisture contents. It is very helpful for the shale gas exploitation.

Prediction of gas production rate from shale gas reservoirs using a micro–macro analysis

Shale gas has become one of the important contributors to the global energy supply. The declining pattern of the gas production rate with time from an unconventional gas reservoir is due to the depletion of shale gas stored in the nanovoids of the shale formation. However, there are only limited ways to predict the variation of the gas production rate with time from an unconventional gas reservoir. This is due to the multiple transport mechanisms of gas in nano-scale pores and changes in shale gas permeability with pressures in nano-scale pores, which is impacted by the pore structure of the shale. In this study, the permeability-pressure (K-p) relationship for different shales (Eagle Ford, Haynesville, Longmaxi and Opalinus) were determined using an equivalent anisotropic pore network model (PNM). This PNM has REV-scale shale gas flow in randomly generated nanovoids and their connection in the shale matrix, and the multiphase flow of shale gas including viscous flow, slip flow and Knudsen diffusion. These predicted K-p correlations were then used in a finite element model (FEM) to predict the variation of the gas production rate with time (flux-time curves) at the macroscale. The simulation results show that the flux-time curves can be simplified to two linear segments in logarithmic coordinates, which are influenced by the fracture length and initial gas pressure. The predicted results using the PNM-FEM were validated by comparing them with the reported field test data. The method described in this study can be used to upscale the gas transport process from micro- to macroscale, which can provide a predictive tool for the gas production in shales.

Lattice Boltzmann modeling of gaseous microflow in shale nanoporous media

Gaseous microflow in nanoporous media of ultratight shale strata was reexamined. Hundreds of nanoscale pore network samples of the Wufeng and Longmaxi shale matrix were reconstructed by ultra-precise FIB-SEM experiments and the Quartet Structure Generation Set (QSGS) method. An OpenMP-based, high-performance, parallelized MRT-LBM model to predict shale gas flow in reconstructed nanoporous media was developed accordingly. The MRT-LBM model was validated against the analytical solutions, molecular dynamics simulations, and discrete velocity method. The MRT-LBM accurately predicted gaseous microflow in the continuum, slip, and early transition flow regimes. Using this solver, extensive pore-scale simulations of the gas transport in nanoscale pore networks were performed to study the effects of pore heterogeneity and slippage effects on the apparent permeability of shale gas. It has been known that gas slippage and Knudsen diffusion dramatically improve gas flow in a single capillary. Hence, permeability models based on a bundle of capillaries followed the increasing gas flow predictions. However, our modeling results revealed that gas slippage is suppressed by pore tortuosity, wall curvature, and surface roughness. The proportionality factor of the Klinkenberg model decreases with increasing tortuosity and decreasing porosity. We develop an apparent permeability model appropriate for low-porosity and large-tortuosity shale nanoporous media, with a corrected proportionality factor.

Study on Flow Model and Flow Equation of Shale Gas Based on Microflow Mechanism

Shale gas storage and permeability space is between nanometers and micrometers and has strong multiscale characteristics, resulting in highly complicated shale gas flow. Therefore, the development of shale gas needs to clarify the seepage mechanism of shale gas and establish a flow model and flow equation that can analyze shale gas flow. In this paper, based on the single nanotube model, combined with the Weiyuan-Changning shale gas demonstration zone of the target layer of the Longmaxi formation shale core high-pressure mercury pore throat test results, the contribution of seepage, diffusion, transition flow, and free molecular flow to shale gas flow was calculated. The contribution of seepage and diffusion is over 95%, and seepage and diffusion are the main flow pattern. Then, a shale gas seepage and diffusion coupled flow model and coupled flow equation were established. A method for calculating shale permeability and diffusion was proposed using the relationship between flow pressure and shale gas velocity. Finally, shale gas flow experiment analysis was carried out to verify that the established shale gas flow model and flow equation can describe the shale gas flow well. The result shows that the flow rate of shale gas is composed of seepage flow rate and diffusion flow rate. The seepage flow rate is proportional to the pseudopressure difference and proportionate to the low-pressure squared difference. The diffusion velocity is proportional to the difference in shale gas density, and the pressure difference in low pressure is proportional. As the pressure of a shale gas reservoir decreases, the proportion of diffusion flow increases. The research results enrich the understanding of shale gas flow; it also has particular reference significance to the development of shale gas reservoirs.

Pore structure alteration and permeability enhancement of shale under cyclic thermal impacts

Cyclic thermal impact technology can effectively modify shale reservoirs and improve reservoir fracture networks while removing water phase traps to increase shale gas permeability. Therefore, an experiment on the cyclic thermal impacts of shale was conducted to investigate the alteration of pore structure and permeability of shale before and after cyclic thermal impacts. The results indicated that, under the thermal impact temperature of 300 °C, pores were continuously generated and expanded in the shale. With the increase in thermal impacts, the cumulative porosity of shale gradually increases, and the growth trend is a logarithmic function of the number of thermal impacts. The permeability of shale can be increased effectively through cyclic thermal impacts, and it increases logarithmically with the number of thermal impacts indicates the importance of multiple injection heat treatments in the process of improving the permeability of shale reservoirs.

Experimental Research on the Effect of Ultrasonic Waves on the Adsorption, Desorption, and Seepage Characteristics of Shale Gas.

Shale gas reservoirs are tight reservoirs with ultralow porosity and ultralow permeability, and their matrix pores are mostly nanoscale. In addition, matrix particles and organic pore surfaces adsorb shale gas. These problems cause the production per well of shale gas to be lower than that of conventional natural gas. The use of hydraulic fracturing technology to exploit shale gas can achieve a good production increase effect. However, using this technology has some limitations caused by technical characteristics and geological conditions. Therefore, new technologies for shale gas exploitation need to be explored. In this study, we propose a method to improve the flow characteristics of shale gas by using ultrasonic waves to increase shale gas production and perform experimental tests to research the actual effect of this method. The lithology, mineral composition, pore structure, specific surface area, and pore size distribution of shale samples are tested. Then, the attenuation characteristics of ultrasonic waves propagating in shale are analyzed. Finally, the effect of ultrasonic waves on the adsorption, desorption, and seepage of shale gas is explored. Results show that the Langmuir adsorption isotherm can describe the adsorption characteristics of shale gas under the action of ultrasonic waves. The gas adsorption constant decreases with increasing ultrasonic wave power. The ultrasonic waves accelerate the gas desorption rate, significantly increase the desorption volume, and prolong the time taken to reach desorption equilibrium. They also increase the permeability of shale gas, and the growth is proportional to the power of the ultrasonic waves. These results indicate that the permeability of shale gas has a power function relationship with the effective stress under ultrasonic waves.

An anisotropic pore-network model to estimate the shale gas permeability

The permeability of shale is a significant and important design parameter for shale gas extraction. The shale gas permeability is usually obtained based on Darcy flow using standard laboratory permeability tests done on core samples, that do not account for different transport mechanisms at high pressures and anisotropic effects in shales due to nano-scale pore structure. In this study, the permeability of shale is predicted using a pore network model. The characteristics of pore structure can be described by specific parameters, including porosity, pore body and pore throat sizes and distributions and coordination numbers. The anisotropy was incorporated into the model using a coordination number ratio, and an algorithm that was developed for connections of pores in the shale formation. By predicting hydraulic connectivity and comparing it with several high-pressure permeability tests, the proposed three-dimensional pore network model was verified. Results show that the prediction from the anisotropic pore network model is closer to the test results than that based on the isotropic pore network model. The predicted permeability values from numerical simulation using anisotropic pore network model for four shales from Qaidam Basin, China are quite similar to those measured from laboratory tests. This study confirmed that the developed anisotropic three-dimensional pore network model could reasonably represent the natural gas flow in the actual shale formation so that it can be used as a prediction tool.

Shale gas permeability upscaling from the pore-scale

The effective permeability of large shale samples provides useful insights into shale gas production. However, its determination can only be achieved through upscaling, since the direct pore-scale simulation of gas flows in large rock samples is not feasible due to the high computational cost and absence of pore connectivity in sample images. Although the Brinkman formulation is widely used in the permeability upscaling of conventional rocks, how to choose the effective viscosity in this coarse-scale model is not clear. Moreover, its application in shale rocks, where the rarefaction effects are important so that the conventional Navier–Stokes equations are inadequate, is rare, and its accuracy has not been assessed. This study aims to address the above two problems, by comparing the Brinkman solutions of several two-dimensional and three-dimensional random porous media containing fractures with the fine-scale solutions of the Stokes and Boltzmann equations (for continuum and rarefied gas flows, respectively). It is found that the use of the fluid viscosity in the Brinkman model, instead of the controversial effective viscosity, leads to accurate results for the cases considered. Additionally, the macroscopic quantity in rarefied gas flows in shale rocks is well predicted by the Brinkman model for a wide range of gas rarefaction, since the error is found to be less than 7%, while neglecting the rarefaction effects leads to significant underestimation of effective permeability (up to 90% in the cases studied). Although heterogeneity and anisotropy of the porous medium increase the error of the effective permeability derived from the Brinkman model, generally speaking, the effective permeability extracted from this coarse-scale model compares favorably to its fine-scale counterpart.

Effect of gas adsorption-induced pore radius and effective stress on shale gas permeability in slip flow: New Insights

Abstract Shale, a heterogeneous and extremely complex gas reservoir, contains low porosity and ultra-Low permeability properties at different pore scales. Its flow behaviors are more complicated due to different forms of flow regimes under laboratory conditions. Flow regimes change with respect to pore scale variation resulting in change in gas permeability. This work presents new insights regarding the change of pore radius due to gas adsorption, effective stress and impact of both on shale gas permeability measurements in flow regimes. From this study, it was revealed that the value of Klinkenberg coefficient has been affected due to gas adsorption-induced pore radius thickness impacts and resulting change in gas permeability. The gas permeability measured from new proposed equation is provides better results as compare to existing equation. Adsorption parameters are the key factors that affect radius of shale pore. Both adsorption and effective stress have an effect on the pore radius and result gas permeability change. It was found that slip effect enhances the apparent gas permeability and also changes with effective stress; therefore, combine impact of slip flow and effective stress is very important as provides understanding in evolution of apparent permeability during shale gas production.

A Flow - Solid Coupling Permeability Model of Shale Gas Reservoir Based on Dual Media

The study of shale gas seepage mechanism can provide theoretical basis for the production capacity evaluation and prediction of shale gas reservoir. The shale gas permeability model is an important part of the theoretical research of shale gas seepage. In this paper, the spring system model is applied to the shale reservoir, and the shale reservoir is simplified as the ideal dual porosity medium model. By analyzing and considering the influence of adsorption layer, diffusion, seepage, matrix deformation and slippage, the dual porosity permeability model of shale gas under various factors is given. In addition, the model is compared with the Civan permeability model and permeability experiment to verify its rationality. The results show that the model proposed in this paper is reasonable and reliable. The model has certain theoretical and practical significance for perfecting the theory of shale gas seepage flow.

New theoretical model to calculate the apparent permeability of shale gas in the real state

Although many studies have been conducted to investigate the mechanisms of shale gas transport through a single nanopore, the mechanisms are not yet well understood. In this study, a theoretical model was developed to calculate the apparent permeability of shale gas in a real state through a single nanopore, and the apparent permeability of a bundle of nanopores was derived. Second, to improve the reliability of the newly developed model, two models for gas deviation factor and viscosity were selected based on 278 data points, and the models for surface diffusion coefficient were also discussed. Third, the validity of the developed model was investigated using two sets of experimental data from the literature. Finally, the effects of gas state, pore radius, temperature, adsorption parameters and pore radius distribution on apparent permeability were systematically analyzed. The results show that the developed model is capable of determining the apparent permeability of shale gas transport through a single nanopore and describing the migration process of shale gas. The Chen & Yang model, Dranchuk & Abou-Kassem model and Sutton model are selected to calculate the surface diffusion coefficient, gas deviation factor and viscosity, respectively. The effects of pore radius, temperature, and adsorption parameters are more remarkable at low pressures than at high pressures. In addition, the surface diffusion of shale gas in a single nanopore cannot be ignored, but it can be ignored in a shale core with large pores under reservoir conditions. Large pores in the shale core control the apparent permeability.

A permeation model of shale gas in cylindrical-like kerogen pores at geological conditions

Understanding the diffusion and permeation behavior of shale gas at geological depths is significantly important to exploration of shale gas, while the permeation mechanism of shale gas in shale gas reservoir is closely related to the confined fluid behavior at mesoscopic scale and cannot be described by traditional Fick or Knudsen diffusion models. In this work, we use the dual control volume grand canonical molecular dynamics method to systematically investigate the permeation processes of shale gas in cylindrical -like kerogen pores represented by the carbon nanotube at different geological depths, and hundreds of simulation data in different pressures, temperatures and pore diameter are obtained. By analyzing these simulated data, we propose a new permeation model to describe the permeability of shale gas in cylindrical-like kerogen pores at geological depths. The new model can satisfactorily reproduce the extrapolation testing data of permeability of shale gas, and perfectly bridge the gap between macroscopic Fick model and microscopic Knudsen model, which provides a useful guidance and reference for exploration of shale gas.