Micro/Nano-pore Network Analysis of Gas Flow in Shale Matrix

Impact of Pressing Time on the Microstructure of Two Types of Goat Cheeses and Its Relationship With Sensory Attributes

The objective of this study was to study the impact of pressing time on the microstructure of goat cheese and its relationship with sensory attributes. The microstructure of the artisanal cheeses was performed by scanning electron microscopy and image analysis. The validation of the microstructural complexity was carried out experimentally with sensory attributes. The pressing time influenced the microstructural parameters Feretmax, Geodiam, and τ and the cheese type influenced the parameters Feretmax, Geodiam, and Geoelong. The correlation values between microstructural complexity and sensory attributes were 0.85 and 0.84 for fresh cheeses and matured cheeses, respectively. The pressure times of 12 and 18 h resulted in cheese microstructures with the highest complexity in terms of Feretmax, Geodiam, Geoelong, and τ parameters. The obtained results are supported by the correlation values between microstructural complexity and sensory attributes.

Shale pore characteristics and their impact on the gas-bearing properties of the Longmaxi Formation in the Luzhou area

Deep shale has the characteristics of large burial depth, rapid changes in reservoir properties, complex pore types and structures, and unstable production. The whole-rock X-ray diffraction (XRD) analysis, reservoir physical property parameter testing, scanning electron microscopy (SEM) analysis, high-pressure mercury intrusion testing, CO2 adsorption experimentation, and low-temperature nitrogen adsorption-desorption testing were performed to study the pore structure characteristics of marine shale reservoirs in the southern Sichuan Basin. The results show that the deep shale of the Wufeng Formation Longyi1 sub-member in the Luzhou area is superior to that of the Weiyuan area in terms of factors controlling shale gas enrichment, such as organic matter abundance, physical properties, gas-bearing properties, and shale reservoir thickness. SEM is utilized to identify six types of pores (mainly organic matter pores). The porosities of the pyrobitumen pores reach 21.04-31.65%, while the porosities of the solid kerogen pores, siliceous mineral dissolution pores, and carbonate dissolution pores are low at 0.48-1.80%. The pores of shale reservoirs are mainly micropores and mesopores, with a small amount of macropores. The total pore volume ranges from 22.0 to 36.40 μL/g, with an average of 27.46 μL/g, the total pore specific surface area ranges from 34.27 to 50.39 m2/g, with an average of 41.12 m2/g. The pore volume and specific surface area of deep shale gas are positively correlated with TOC content, siliceous minerals, and clay minerals. The key period for shale gas enrichment, which matches the evolution process of shale hydrocarbon generation, reservoir capacity, and direct and indirect cap rocks, is from the Middle to Late Triassic to the present. Areas with late structural uplift, small uplift amplitude, and high formation pressure coefficient characteristics favor preserving shale gas with high gas content and production levels.

The curvature effect on the distribution behavior of nonpolar atoms in nano-confined space

The chemical and physical properties of nonpolar atoms are obviously affected by confinement. A curvature-based theoretical model for helium particles distributed in carbon nanotubes is proposed by considering the L-J pair potential and the Boltzmann distribution. The potential gap formed by the non-bonded interaction between a helium atom and a carbon nanotube surface leads to a layered structure distribution with high density near the surface. By assuming adsorption as a competition between the potential gap and the thermal energy, the desorption critical temperature is discussed for helium adsorbed on the layer, which is confirmed to be a monotonic decreasing function of nanotube diameter. The helium atom distribution relations between the nanotube diameter, temperature and the potential gap obtained from molecular dynamics simulations are consistent with the curvature-based model predictions. The adsorption ratio is defined by the numbers of particles adsorbed on the near surface layered structure over total particle numbers, which decreases with the increase of temperature and carbon nanotube diameter. The curvature-based model is further confirmed by studying krypton and argon atoms in the appendix. This work provides a simple model to predict the distribution behavior and reveals the curvature effect on the distribution and adsorption of non-polar atoms confined in nano-space, which could be important for a better understanding of the chemical and physical properties of gas storage in the nano-confined space.

Micro X-ray fluorescence reveals pore space details and spatially-resolved porosity of rock-based microfluidic devices

Characterization of microscopic details of the fabric of mudstones and shales (i.e., structure and composition) is important to understand their storage and transport properties. Current characterization methods struggle to probe reliably multiple scales of interest (e.g., pore and fracture) and measure properties at the finest resolution under representative in situ conditions. Micro X-ray fluorescence (μXRF) is a high-performance imaging technique that produces elemental images at sub-10 μm spatial resolution and could offer insight into a diversity of shale properties, such as mineral composition, porosity, and in situ pressure gradients. This study designed and carried out a porosity mapping protocol using model and real-rock microfluidic devices and contrast fluids. Etched silicon micromodels with real-rock pore network patterns served as ideal models to establish a proof of concept. Measurements were performed on a novel μXRF microscope not powered by synchrotron radiation. We registered the μXRF datasets with the binary rock masks used for micromodel fabrication and applied segmentation algorithms to compare porosities. We assessed expected advantages and limitations through a sensitivity analysis and beam study. μXRF is an important new imaging technique for microfluidic applications.

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.

Supramolecular dynamic binary complexes with pH and salt-responsive properties for use in unconventional reservoirs

Hydraulic fracturing of unconventional reservoirs has seen a boom in the last century, as a means to fulfill the growing energy demand in the world. The fracturing fluid used in the process plays a substantial role in determining the results. Hence, several research and development efforts have been geared towards developing more sustainable, efficient, and improved fracturing fluids. Herein, we present a dynamic binary complex (DBC) solution, with potential to be useful in the hydraulic fracturing domain. It has a supramolecular structure formed by the self-assembly of low molecular weight viscosifiers (LMWVs) oleic acid and diethylenetriamine into an elongated entangled network under alkaline conditions. With less than 2 wt% constituents dispersed in aqueous solution, a viscous gel that exhibits high viscosities even under shear was formed. Key features include responsiveness to pH and salinity, and a zero-shear viscosity that could be tuned by a factor of ~280 by changing the pH. Furthermore, its viscous properties were more pronounced in the presence of salt. Sand settling tests revealed its potential to hold up sand particles for extended periods of time. In conclusion, this DBC solution system has potential to be utilized as a smart salt-responsive, pH-switchable hydraulic fracturing fluid.

Impact of de-ionized water on changes in porosity and permeability of shales mineralogy due to clay-swelling

Hydraulic fracturing is widely applied for economical gas production from shale reservoirs. Still, the swelling of the clay micro/nano pores due to retained fluid from hydraulic fracturing causes a gradual reduction of gas production. Four different gas-bearing shale samples with different mineralogical characteristics were investigated to study the expected shale swelling and reduction in gas permeability due to hydraulic fracturing. To simulate shale softening, these shale samples were immersed in deionized (DI) water heated to 100 °C temperature and subjected to 8 MPa pressure in a laboratory reactor for 72 hours to simulate shale softening. The low-temperature nitrogen adsorption and density measurements were performed on the original and treated shale to determine the changes in micro and nano pore structure. The micro and nano pore structures changed, and the porosity decreased after shale treatment. The porosity decreased by 4% for clayey shale, while for well-cemented shale the porosity only decreased by 0.52%. The findings showed that the initial mineralogical composition of shale plays a significant role in the change of micro and nano pores and the pore structure alteration due to retained fluid from hydraulic fracturing. A pore network model is used to simulate the permeability of shale used in this study. To define pore structure properties, specific factors such as porosity, pore size, pore throat distribution, and coordination number were used. Furthermore, the anisotropy characteristics of shale were integrated into the model via a coordination number ratio. Finally, the change in permeability due to shale softening was determined and compared with untreated with the progress of shale softening. The simulation showed that the permeability of Longmaxi shale could decrease from 3.82E–16 m2 to 4.71E–17 m² after treatment.

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.

A Triple Pore Network Model (T-PNM) for Gas Flow Simulation in Fractured, Micro-porous and Meso-porous Media

In this study, a novel triple pore network model (T-PNM) is introduced which is composed of a single pore network model (PNM) coupled to fractures and micro-porosities. We use two stages of the watershed segmentation algorithm to extract the required data from semi-real micro-tomography images of porous material and build a structural network composed of three conductive elements: meso-pores, micro-pores, and fractures. Gas and liquid flow are simulated on the extracted networks and the calculated permeabilities are compared with dual pore network models (D-PNM) as well as the analytical solutions. It is found that the processes which are more sensitive to the surface features of material, should be simulated using a T-PNM that considers the effect of micro-porosities on overall process of flow in tight pores. We found that, for gas flow in tight pores where the close contact of gas with the surface of solid walls makes Knudsen diffusion and gas slippage significant, T-PNM provides more accurate solution compared to D-PNM. Within the tested range of operational conditions, we recorded between 10 and 50% relative error in gas permeabilities of carbonate porous rocks if micro-porosities are dismissed in the presence of fractures.

Numerical Issues for Solving Eu-type Generalized Hydrodynamic Equations to Investigate Continuum-rarefied Gas Flows

Eu-type generalized hydrodynamic equations have been derived from the Boltzmann kinetic theory and applied to investigate continuum and/or rarefied gas flows. This short communication first reports detailed and important issues in the use of the mixed discontinuous Galerkin method to solve Eu-type generalized hydrodynamic equations in multidimensions. Three major issues are reported. These include the treatment of solid boundary conditions for the nonlinear constitutive equations, a slope limiter to maintain high accuracy and avoid unphysical oscillations, and the computational efficiency compared with that of the particle method. In addition, we implement the present model to a rigid problem, which includes gas flows around the NACA0018 airfoil, a sharp wedge, a sphere and a three-dimensional Apollo configuration.

Deep-Subsurface Pressure Stimulates Metabolic Plasticity in Shale-Colonizing Halanaerobium spp

Bacterial Halanaerobium strains become the dominant persisting microbial community member in produced fluids across geographically distinct hydraulically fractured shales. Halanaerobium is believed to be inadvertently introduced into this environment during the drilling and fracturing process and must therefore tolerate large changes in pressure, temperature, and salinity. Here, we used a Halanaerobium strain isolated from a natural gas well in the Utica Point Pleasant formation to investigate metabolic and physiological responses to growth under high-pressure subsurface conditions. Laboratory incubations confirmed the ability of Halanaerobium congolense strain WG8 to grow under pressures representative of deep shale formations (21 to 48 MPa). Under these conditions, broad metabolic and physiological shifts were identified, including higher abundances of proteins associated with the production of extracellular polymeric substances. Confocal laser scanning microscopy indicated that extracellular polymeric substance (EPS) production was associated with greater cell aggregation when biomass was cultured at high pressure. Changes in Halanaerobium central carbon metabolism under the same conditions were inferred from nuclear magnetic resonance (NMR) and gas chromatography measurements, revealing large per-cell increases in production of ethanol, acetate, and propanol and cessation of hydrogen production. These metabolic shifts were associated with carbon flux through 1,2-propanediol in response to slower fluxes of carbon through stage 3 of glycolysis. Together, these results reveal the potential for bioclogging and corrosion (via organic acid fermentation products) associated with persistent Halanaerobium growth in deep, hydraulically fractured shale ecosystems, and offer new insights into cellular mechanisms that enable these strains to dominate deep-shale microbiomes.IMPORTANCE The hydraulic fracturing of deep-shale formations for hydrocarbon recovery accounts for approximately 60% of U.S. natural gas production. Microbial activity associated with this process is generally considered deleterious due to issues associated with sulfide production, microbially induced corrosion, and bioclogging in the subsurface. Here we demonstrate that a representative Halanaerobium species, frequently the dominant microbial taxon in hydraulically fractured shales, responds to pressures characteristic of the deep subsurface by shifting its metabolism to generate more corrosive organic acids and produce more polymeric substances that cause "clumping" of biomass. While the potential for increased corrosion of steel infrastructure and clogging of pores and fractures in the subsurface may significantly impact hydrocarbon recovery, these data also offer new insights for microbial control in these ecosystems.

Gaseous flow through heterogeneous, partially connected networks of pipes

Simulations of flow of an ideal gas through heterogeneous simple cubic pipe networks with different pipe radius distributions and variable bond coordination numbers were performed. Networks with monomodal and bimodal radius distributions were constructed. A very wide range of Knudsen numbers was achieved. Flow simulations of purely viscous gases and incompressible liquids were also carried out for comparison. The permeability to gas in the purely viscous regime was larger than the permeability to an incompressible liquid. Based on a variety of computational tests, this result was likely not a numerical artifact. The simulated macroscopic flow behavior differed from the underlying single pipe model, depending on the radius distribution, network connectivity and magnitude of the externally applied pressure gradient, and was compatible with the Klinkenberg analysis only when the maximum Knudsen number used in each simulation was lower than 1. In this condition, the Klinkenberg coefficient was nearly proportional to the inverse of the network hydraulic radius while the effect of the radius distribution was weak and that of the network connectivity essentially negligible. The bimodal simulations displayed a typical percolation behavior, with the Klinkenberg coefficient remaining constant as long as the large pipe population was connected.

Rapid migration of CO2-rich micro-fluids in calcite matrices

The transport of supercritical fluids is a determining factor for several geological processes and fundamental in predicting natural resource accumulation and distribution. Calcite, ubiquitous in most geological environments, may contain supercritical CO2 trapped under the form of fluid inclusions that may move through grain boundaries affecting the rock physical properties. However, despite macroscopic evidence for this process, until recent it was not possible to characterize this process at the nano-scale due to the difficulty of such observations. In this study, we report nanometer-scale observations on calcite crystal surfaces and demonstrate that stress with absence of visible deformation produces fluid leakage from fluid inclusions. Atomic Force Microscopy scanning experiments on freshly cleaved calcite crystals containing visible fluid inclusions revealed the spontaneous formation of nanometer-scale hillocks on flat crystal terraces in only a few minutes, without evidence of surface dissolution. The fact the hillocks formed on flat surface in a short time was unexpected and suggests deposition of material from the inner crystal to the surface through small-scale fluid migration. We estimated the rate of this fluid mobility is by several orders of magnitude higher than the diffusion rate through vacancies estimated in calcite crystals showing that CO2-rich fluids through micro-pore and nano-pore spaces is in reality much higher than previously assumed using current predictive models.

Hierarchical integration of porosity in shales

Pore characterization in shales is challenging owing to the wide range of pore sizes and types present. Haynesville-Bossier shale (USA) was sampled as a typical clay-bearing siliceous, organic-rich, gas-mature shale and characterized over pore diameters ranging 2 nm to 3000 nm. Three advanced imaging techniques were utilized correlatively, including the application of Xe⁺ plasma focused ion beam scanning electron microscopy (plasma FIB or PFIB), complemented by the Ga⁺ FIB method which is now frequently used to characterise porosity and organic/inorganic phases, together with transmission electron microscope tomography of the nano-scale pores (voxel size 0.6 nm; resolution 1-2 nm). The three pore-size scales each contribute differently to the pore network. Those <10 nm (greatest number), 10 nm to 100 nm (best-connected hence controls transport properties), and >100 nm (greatest total volume hence determines fluid storativity). Four distinct pore types were found: intra-organic, organic-mineral interface, inter-mineral and intra-mineral pores were recognized, with characteristic geometries. The whole pore network comprises a globally-connected system between phyllosilicate mineral grains (diameter: 6-50 nm), and locally-clustered connected pores within porous organic matter (diameter: 200-800 nm). Integrated predictions of pore geometry, connectivity, and roles in controlling petrophysical properties were verified through experimental permeability measurements.

A Unified Framework for Modeling Continuum and Rarefied Gas Flows

The momentum and heat transport in rarefied gas flows is known to deviate from the classical laws of Navier and Fourier in Navier-Stokes-Fourier (NSF) equations. A more sophisticated Nonlinear Coupled Constitutive Model (NCCM) has been derived from the Boltzmann equation to describe gaseous and thermal transport both in continuum and rarefied gas flows. We first develop a unified numerical framework for modeling continuum and rarefied flows based on the NCCM model both in two and three dimensions. Special treatment is given to the complex highly nonlinear transport equations for non-conserved variables that arise from the high degree of thermal nonequilibrium. For verification and validation, we apply the present scheme to a stiff problem of hypersonic gas flows around a 2D cylinder, a 3D sphere, and the Apollo configuration both in continuum and rarefied situations. The results show that the present unified framework yields solutions that are in better agreement with the benchmark and experimental data than are the NSF results in all studied cases of rarefied problems. Good agreement is observed between the present study and the NSF results for continuum cases. The results show that this study provides a unified framework for modeling continuum and rarefied gas flows.

Pore-Scale Simulation and Sensitivity Analysis of Apparent Gas Permeability in Shale Matrix

Extremely low permeability due to nano-scale pores is a distinctive feature of gas transport in a shale matrix. The permeability of shale depends on pore pressure, porosity, pore throat size and gas type. The pore network model is a practical way to explain the macro flow behavior of porous media from a microscopic point of view. In this research, gas flow in a shale matrix is simulated using a previously developed three-dimensional pore network model that includes typical bimodal pore size distribution, anisotropy and low connectivity of the pore structure in shale. The apparent gas permeability of shale matrix was calculated under different reservoir pressures corresponding to different gas exploitation stages. Results indicate that gas permeability is strongly related to reservoir gas pressure, and hence the apparent permeability is not a unique value during the shale gas exploitation, and simulations suggested that a constant permeability for continuum-scale simulation is not accurate. Hence, the reservoir pressures of different shale gas exploitations should be considered. In addition, a sensitivity analysis was also performed to determine the contributions to apparent permeability of a shale matrix from petro-physical properties of shale such as pore throat size and porosity. Finally, the impact of connectivity of nano-scale pores on shale gas flux was analyzed. These results would provide an insight into understanding nano/micro scale flows of shale gas in the shale matrix.

A Comprehensive Model for Real Gas Transport in Shale Formations with Complex Non-planar Fracture Networks

A complex fracture network is generally generated during the hydraulic fracturing treatment in shale gas reservoirs. Numerous efforts have been made to model the flow behavior of such fracture networks. However, it is still challenging to predict the impacts of various gas transport mechanisms on well performance with arbitrary fracture geometry in a computationally efficient manner. We develop a robust and comprehensive model for real gas transport in shales with complex non-planar fracture network. Contributions of gas transport mechanisms and fracture complexity to well productivity and rate transient behavior are systematically analyzed. The major findings are: simple planar fracture can overestimate gas production than non-planar fracture due to less fracture interference. A “hump” that occurs in the transition period and formation linear flow with a slope less than 1/2 can infer the appearance of natural fractures. The sharpness of the “hump” can indicate the complexity and irregularity of the fracture networks. Gas flow mechanisms can extend the transition flow period. The gas desorption could make the “hump” more profound. The Knudsen diffusion and slippage effect play a dominant role in the later production time. Maximizing the fracture complexity through generating large connected networks is an effective way to increase shale gas production.

A novel method for correcting scanline-observational bias of discontinuity orientation

Scanline observation is known to introduce an angular bias into the probability distribution of orientation in three-dimensional space. In this paper, numerical solutions expressing the functional relationship between the scanline-observational distribution (in one-dimensional space) and the inherent distribution (in three-dimensional space) are derived using probability theory and calculus under the independence hypothesis of dip direction and dip angle. Based on these solutions, a novel method for obtaining the inherent distribution (also for correcting the bias) is proposed, an approach which includes two procedures: 1) Correcting the cumulative probabilities of orientation according to the solutions, and 2) Determining the distribution of the corrected orientations using approximation methods such as the one-sample Kolmogorov-Smirnov test. The inherent distribution corrected by the proposed method can be used for discrete fracture network (DFN) modelling, which is applied to such areas as rockmass stability evaluation, rockmass permeability analysis, rockmass quality calculation and other related fields. To maximize the correction capacity of the proposed method, the observed sample size is suggested through effectiveness tests for different distribution types, dispersions and sample sizes. The performance of the proposed method and the comparison of its correction capacity with existing methods are illustrated with two case studies.