Real Gas Research Articles

Numerical Investigation of Two-Phase Shock Waves in CO2 Flows Using a Modified Hertz–Knudsen Model

Abstract Understanding the complex behavior of two-phase shocks in CO2 flows is essential for a variety of applications, including carbon capture and storage () and transcritical refrigeration cycles. This study presents a comprehensive numerical investigation of two-phase shock waves using the multispecies user-defined real gas model in Ansys Fluent. The simulations are performed for de-Laval nozzles, exploring the two-phase shock features for three-dimensional (3D), two-dimensional (2D), and two-dimensional axisymmetric geometries. The nonequilibrium condensation, subsequent evaporation, and denucleation occurring across the shock are modeled through a set of user-defined scalar transport equations implemented within Ansys Fluent. The two-phase computational fluid dynamics (CFD) simulations are carried out in proximity to the critical point where real gas effects are relevant. The CO2 real gas properties are computed using an in-house Python code and integrated into the solver via user-defined functions as external look-up tables. This study provides valuable insights into the physical processes underlying two-phase shocks in CO2 flows and their sensitivity to geometric variations and thermodynamic conditions. The findings contribute to the development and modification of predictive models and optimized designs for systems involving two-phase CO2 flows. The results highlight the influence of geometry configurations and thermodynamic conditions on shock location and intensity, providing comparisons for shock waves occurring in two-phase flows and supercritical single-phase flows.

Shock wave propagation in a real gas with or without gravitational field in the presence of magnetic field and monochromatic radiation via group invariance method

PurposeThis article aims to find the similarity solutions for the one-dimensional motion of spherical symmetric shock wave in non-ideal gas influenced by the azimuthal magnetic field and monochromatic radiation in the presence or absence of gravitational field. This paper also aims to study the effects of physical parameters on the strength of shock wave, and on the flow variables in the flow-field region behind the shock front.Design/methodology/approachThe Roche model is used to describe the gravitational field effects due to a massive nucleus at the point of symmetry. To derive the similarity solutions, the Lie group symmetry method has been used. Also, the numerical solutions to the present problem are obtained by using Rung–Kutta method of the fourth order with the use of Mathematica software. The effects of variation in the parameter of non-idealness of the gas, the gravitation parameter, the strength of the ambient magnetic field and the adiabatic index of the gas on the shock wave, and on the flow variables is discussed. A comparative study between with and without gravitational field is also, made.FindingsFor different choices of the arbitrary constants that appeared in the solution of infinitesimal generators, we have obtained seven distinct cases of similarity solutions. In the absence of the gravitational field, the similarity solution exists to the power and exponential law shock paths, but in the presence of gravitational field, the similarity solution exists to the power law shock path case only. In the absence of gravitational field, the shock strength is enhanced in the exponential law shock path case in comparison to the power law shock path case. It is found that the shock wave decays with an increase in the value of the adiabatic exponent, the strength of magnetic field, non-idealness of the gas or gravitational parameter.Research limitations/implicationsThe consideration of medium under the influence of gravitational field due to a heavy nucleus at the center and presence of magnetic field decrease the shock strength. This result may be helpful in designing space vehicle and jet engine.Practical implicationsThe result of the present study may be used in the analysis of data from the measurements by space craft in the solar wind and in neighborhood of the Earth’s magnetosphere.Social implicationsThe obtained results may be used for mankind.Originality/valueThe study of spherical shock wave propagation influenced by monochromatic radiation and azimuthal magnetic field in a non-ideal gas with or without gravitational field has yet to be discussed by any authors by using the Lie group symmetry method. In this article, we have discussed all possible cases of similarity solutions using the Lie group symmetry method, which is not studied by anyone as known to us.

Study on the real gas effect on the windward side of an inflatable reentry capsule

In this paper, the reentry flow field of an inflatable reentry capsule was numerically simulated using the air 9-component chemical nonequilibrium model and the ideal gas hypothesis model. The difference in the calculation results of the two methods was investigated, the manifestation of the real gas effect was studied, and the reasons for the difference between the real gas effect of the inflatable reentry capsule and the real gas effect of the rigid reentry capsule were explored. The results show that compared with the ideal gas hypothesis, the real gas effect makes the shock wave position closer to the wall, the air temperature after the shock wave decreases, and the wall heat flux density decreases; at 83 km, the specific heat ratio of the gas after the shock wave is higher than 1.4, and the air undergoes a dissociation reaction, while at 73 km, the real gas effect is weaker, the specific heat ratio of the air after the shock wave remains at 1.4, and the air still exists in the form of molecules; the main reason for the difference in the strength of the real gas between the inflatable reentry capsule and the rigid reentry capsule in the same altitude range is that the drag-to-weight ratio of the inflatable reentry capsule is larger than that of the rigid reentry capsule, and the speed decreases faster after entering the atmosphere, and the speed is lower at the same altitude.

Modelling pressure dynamics of oil–gas two-phase flow in double-porosity media formation with permeability-stress sensitivity

Pressure dynamics can reflect the basic characteristics of fluid flow through underground porous formation. In this research, the oil–gas two-phase flow model for a double-porosity media formation with permeability-stress sensitivity was first established for three kinds of outer boundaries. The unified governing equation was deduced by utilizing the H function. The nonlinear mathematical model in consideration of permeability-stress sensitivity was linearized by implementing the canonical perturbation transformation and then solved by using the Laplace transformation. After that, a sequence of typical log–log curves of pressure dynamics influenced by various model parameters were plotted and analyzed. These curves reflect the typical characteristic of a V shape caused by the inter-porosity fluid flow from matrix toward natural fractures. Oil saturation and permeability-stress sensitivity coefficient have much influence on the pressure dynamics. Ultimately, the established model of oil–gas two-phase flow was validated through a well-test fitting interpretation for a real condensate gas well in a sandstone formation. This research can offer insights into the pressure dynamics dominated by the oil–gas two-phase flow in naturally fractured formations and the permeability-stress sensitivity effect.

Numerical simulation of shock attenuation with real gas effects and a turbulent boundary layer in the expansion tube

AbstractThe influence of real gas effects and a turbulent boundary layer on shock wave attenuation in the expansion tube is studied by numerically solving the axisymmetric compressible Navier–Stokes equations with an adaptive mesh refinement technique. Numerical simulation results reveal that the ideal gas assumption is not applicable to the expansion tube, and the turbulent boundary layer plays a major role in decreasing the shock wave speed in the acceleration tube of the expansion tube. Shock wave attenuation is attributed to the turbulent boundary layer decreasing the pressure behind the shock wave. The numerical simulations that include the real gas effects and the development of turbulent boundary layers qualitatively agree with analytical solutions in the shock tube, and they show good agreement with the experimental results, especially for the shock speed in the acceleration tube of the expansion tube. Both effects should be considered in the numerical simulation model aimed to support experiments in expansion tubes.

A Static/Dynamic Coupled Harmonic Balance Method for Dry Friction Systems Containing Rigid Body Modes

Abstract A harmonic balance method for under-constrained dry friction systems containing rigid body modes (HBM-RBM) is proposed. This method aims to overcome the encountered obstacle when applying the harmonic balance method to turbine blades damped by underplatform dampers. The inspiration for HBM-RBM comes from the free interface modal synthesis method. The key innovation involves deriving the elastic inversion of the singular stiffness matrix through the elimination of rigid body modes. In this way, the general HBM framework can be adopted, and the frequency response of under-constrained dry friction systems can be solved in a static/dynamic coupled manner. The accuracy and efficiency are both verified on a lumped parameter model and a finite element model of turbines with UPDs from a real gas turbine. A comparative study between the HBM-RBM and the commonly adopted way of imposing artificial grounding springs (HBM-AGS) is conducted. Results demonstrate that the HBM-RBM holds a significant advantage over HBM-AGS, as it eliminates the need for artificial grounding springs (AGS) and avoids the necessity for numerous trial cases to determine AGS stiffness.

Study of Neural Network Architectures for Determining Gas Concentrations by Spectra

A study of a number of neural networks of different architectures for determining gas concentrations from spectra obtained using an optical emission gas analyzer, which measures the spectrum of electromagnetic radiation emitted by gases when excited by an electric discharge, is presented. The neural network is trained on data from the optical spectroscopy laboratory and is able to predict gas concentrations from spectra at high speed. The research concerned the deep neural network architectures with convolutional and recurrent layers. Convolutional layers highlight the features of the spectra, while recurrent layers take into account the consistent structure of the data. The quality of the neural network is evaluated by the R2 coefficient of determination, and the comparison between networks by the RMSE indicator between the predicted and real gas concentrations.

A Three-Dimensional Model of a Spherically Symmetric, Compressible Micropolar Fluid Flow with a Real Gas Equation of State

In this work, we analyze a spherically symmetric 3D flow of a micropolar, viscous, polytropic, and heat-conducting real gas. In particular, we take as a domain the subset of R3 bounded by two concentric spheres that present solid thermoinsulated walls. Also, here, we consider the generalized equation of state for the pressure in the sense that the pressure depends, as a power function, on the mass density. The model is based on the conservation laws for mass, momentum, momentum moment, and energy, as well as the equation of state for a real gas, and it is derived first in the Eulerian and then in the Lagrangian description. Through the application of the Faedo–Galerkin method, a numerical solution to a corresponding problem is obtained, and numerical simulations are performed to demonstrate the behavior of the solutions under various parameters and initial conditions in order to validate the method. The results of the simulations are discussed in detail.

An Experimental Study on the Effects of Nonuniform Vane Spacing on Forced Response Reduction in a Mistuned Rotor Blisk in a Multistage Axial Compressor

Abstract Stators with nonuniform vane spacing (NUVS) are known to effectively reduce the forced response of adjacent rotors by spreading the primary engine order (EO) excitation at a certain speed to a series of weaker excitations at nearby EOs over a wider speed range. To be used in a real gas turbine engine, it is essential to know the forced response vibratory reduction that can be achieved for a specific NUVS configuration at different operating conditions. The classical estimation method to predict the blade response reduction is to quantify the reduction of the forcing function at a potential resonance crossing by conducting a circumferential Fourier analysis of the asymmetric flow field. However, besides excitation reduction, the blade forced response also depends on other factors, such as damping and blade-to-blade interactions due to mistuning. To study the blade forced response reduction in a realistic environment, a comprehensive experimental study was conducted in the Purdue three-stage axial research compressor at three different loading conditions. The vibratory response of the first torsion (1 T) mode forced response of rotor 2 was measured by strain gages (SGs) for two different upstream stator 1 configurations: the symmetric 38-vaned stator 1 configuration and the NUVS stator 1 configuration with 18–20 vane halves. As expected, the strong 38EO-1T response from the symmetric stator reduced to a series of weaker responses from 35EO to 41EO in the NUVS configuration. The overlap of adjacent EO responses caused considerable beating phenomena in the blade SG time–history data. There was substantial blade-to-blade variation in blade response for both symmetric and asymmetric stator 1 configurations due to the inherent nonintentional mistuning in the rotor 2 blisk. This, in turn, causes a large blade-to-blade variation in the reduction factors. While higher responding blades tend to have larger reduction factors, some blades show almost no forced response reduction when switching to the NUVS stator. In addition, the reduction factors for each blade and the maximum reduction factor for the whole blisk also change significantly with loading conditions. The measured reduction factors and the peak response EO are not well predicted by the classical estimation method. This indicates that both damping and mistuning effects need to be considered in the NUVS reduction factor prediction.

Software for CO2 Storage in Natural Gas Reservoirs

The paper presents a simulation-based approach for optimizing CO2 injection into depleted gas reservoirs, with the goal of enhancing underground CO2 storage. The research employs a two-dimensional dynamic reservoir model, developed using Darcy’s law, to describe gas flow in a pressure-homogeneous porous medium, along with real gas equations. The model integrates the Du Fort–Frenkel and finite-difference methods to accurately simulate the behavior of CO2 during injection and storage. Real data from an operational gas storage facility were used to calibrate the model. CO2sim v1 software, specifically developed for this purpose, simulates CO2 injection cycles and quiescence phases, enabling the optimization of storage capacity and energy efficiency. The reservoir model, based on the engineering of the geological structure, is discretized into approximately 16,000 cells and solved using the finite-difference method, allowing for rapid simulation of CO2 injection and quiescence processes. The average computation time for a 150-day cycle is approximately 5 min. Simulation results indicate that increasing the number of injection wells and carefully controlling the injection rates significantly improves the distribution of CO2 within the reservoir, thereby enhancing storage efficiency. Additionally, appropriate well placement and prolonged quiescence periods lead to better CO2 dispersion, increasing the storage potential while reducing energy costs. The study concludes that further development of the software, along with comprehensive technical and economic assessments, is required to fully optimize CO2 storage on a commercial scale.

Performance and failure modes of thermal barrier coatings deposited by EB-PVD on blades under real service conditions in gas turbine

Thermal barrier coatings (TBCs) with a double columnar crystal structure of CoCrAlY/YSZ, prepared using electron beam physical vapor deposition (EB-PVD), were applied to turbine blades and tested in real gas turbine conditions. This study investigates their failure mechanisms under both actual operating conditions and simulated external loads, using three-point bending tests. The performance of full-sized, TBC-coated blades was analyzed through finite element modeling, while the thermomechanical and mechanical properties of the coatings after service were measured to support the simulation and provide insights into the failure processes. A new degradation mode, characterized by penetration cracking, was observed in the EB-PVD coatings. This behavior is linked to the columnar grain structure of YSZ and CoCrAlY, lower operational temperatures, and the reduced thickness of the YSZ layer. Surface cracks in the YSZ coating primarily occurred in regions with large curvature, where stress concentrations are higher. This study offers new insights into the failure modes of TBCs under real gas turbine operating conditions.

Deeper insights into the devolatilization mechanism of biomass fixed-bed gasification under various atmospheres

In recent years, biomass oxy-fuel gasification has prompted increased interest for its ability to produce a gas with low tar content and to assist in carbon reduction. It is noteworthy that the type of atmosphere is a crucial factor influencing the devolatilization process in biomass gasification and the specific mechanisms by which an oxy-fuel atmosphere influences the devolatilization process remain inadequately explored. This work aimed to investigate the effect of various reaction atmospheres on devolatilization behavior, reaction kinetics, intermediate product formation, and biochar functional groups (BFGs) evolution. In comparison to an inert atmosphere, the oxy-fuel atmosphere facilitated the release of volatiles, and enhanced energy self-sustainability within the devolatilization system. The presence of O2 and CO2 promoted the generation of potential anhydrosugars while suppressing the formation of phenolic compounds. The synergistic effect present in the oxy-fuel atmosphere augments the exothermic effect and promotes the release of volatile and alkane gases during the devolatilization process. Furthermore, as oxygen concentrations increased in the reaction atmosphere, the sequential response of BFGs primarily followed the order: C-O → aromatic ring → C-OH/C–H/COO– → C=O. Moreover, advanced characterization analyses revealed that the oxy-fuel environment was more effective in promoting the aromatization and pore structure of biochar than an inert atmosphere. Collectively, these findings have substantial implications for reaction modeling in biomass fixed-bed gasification under real gas atmospheres and guide future research on tar control strategies.

A thermodynamics-based coupled model for multi-phase flowback in deformable dual-porosity shale gas reservoirs

Over the past decades, there has been growing interest in modelling multi-phase flowback in shale gas reservoirs during hydraulic fracturing, primarily due to the significant risk of groundwater pollution. However, the lack of fully coupled simulations and a unified theoretical model has hindered the study of coupled adsorptive hydro-mechanical behaviour and its influence on fluid flowback prediction. In this paper, we have extended the non-equilibrium thermodynamics-based Mixture Coupling Theory to derive the constitutive relationship and governing equation for adsorptive multi-phase fluid flows in deformable dual-porosity media. Helmholtz free energy density has been used to establish the relationship between solids and fluids. The interaction of adsorptive fluids in the pore and fracture space has been fully considered, leading to a new form of constitutive equation, which obtained the molecular adsorptive effect on the rock by introducing adsorption entropy production. The proposed governing equations determine the fully coupled evolution of solid deformation and multi-phase flow, with the consideration of adsorption as well as pore and fracture porosity change. Numerical simulation is then performed to study the flowback of a real shale gas well and the influence of coupled behaviour on model prediction. The simulation shows that the flowback flux is mainly by the fracture (more than 99.9 %) and the overall cumulative volume is 2427.1 m3 within 225 h which accounts for about 5.3 % of the total injected fracturing fluid, and the sensitivity analysis reveals that the manual fracture porosity is the most sensitive factor to the cumulative flowback. This work provides new insights into the flowback process of shale reservoirs in a fully coupled view and the proposed theoretical tool should contribute to the modelling of other adsorptive multi-phase flow problem in deformable dual-porosity media such as carbon storage and coalbed methane production.

A study of the electrostatic properties of the interiors of low-mass stars: Possible implications for the observed rotational properties

Context. In the partially ionized material of stellar interiors, the strongest forces acting on electrons and ions are the Coulomb interactions between charges. The dynamics of the plasma as a whole depend on the magnitudes of the average electrostatic interactions and the average kinetic energies of the particles that constitute the stellar material. An important question is how these interactions of real gases are related to the observable stellar properties. Specifically, the relationships between rotation, magnetic activity, and the thermodynamic properties of stellar interiors are still not well understood. These connections are crucial for understanding and interpreting the abundant observational data provided by space-based missions, such as Kepler/K2 and TESS, and the future data from the PLATO mission. Aims. In this study, we investigate the electrostatic effects within the interiors of low-mass main sequence (MS) stars. Specifically, we introduce a global quantity, a global plasma parameter, which allows us to compare the importance of electrostatic interactions across a range of low-mass theoretical models (0.7 − 1.4 M⊙) with varying ages and metallicities. We then correlate the electrostatic properties of the theoretical models with the observable rotational trends on the MS. Methods. We use the open-source 1D stellar evolution code MESA to compute a grid of main-sequence stellar models. Our models span the log g − Teff space of a set of 66 Kepler main-sequence stars. Results. We identify a correlation between the prominence of electrostatic effects in stellar interiors and stellar rotation rates. The variations in the magnitude of electrostatic interactions with age and metallicity further suggest that understanding the underlying physics of the collective effects of plasma can clarify key observational trends related to the rotation of low-mass stars on the MS. These results may also advance our understanding of the physics behind the observed weakened magnetic braking in stars.

Legacy ICS Cybersecurity Assessment Using Hybrid Threat Modeling—An Oil and Gas Sector Case Study

As security breaches are increasingly widely reported in today’s culture, cybersecurity is gaining attention on a global scale. Threat modeling methods (TMM) are a proactive security practice that is essential for pinpointing risks and limiting their impact. This paper proposes a hybrid threat modeling framework based on system-centric, attacker-centric, and risk-centric approaches to identify threats in Operational Technology (OT) applications. OT is made up of software and hardware used to manage, secure, and control industrial control systems (ICS), and its environments include factories, power plants, oil and gas refineries, and pipelines. To visualize the “big picture” of its infrastructure risk profile and improve understanding of the full attack surface, the proposed framework builds on several threat modeling methodologies: PASTA modeling, STRIDE, and attack tree components. Nevertheless, the continuity and stability of vital infrastructure will continue to depend heavily on legacy equipment. Thus, protecting the availability, security, and safety of industrial environments and vital infrastructure from cyberattacks requires operational technology (OT) cybersecurity. The feasibility of the proposed approach is illustrated with a case study from a real oil and gas production plant control system where numerous significant cyberattacks in recent years have targeted OT networks more frequently as hackers realized the possibility of disruption due to insufficient OT security, particularly for outdated systems. The proposed framework achieved better results in detecting threats and severity in the design of the case study system, helping to increase security and support cybersecurity assessment of legacy control systems.

A plethora of novel solitary wave solutions related to van der Waals equation: a comparative study

In this article, we explore exact solitary wave solutions to the van der Waals equation which is crucial for numerous applications involving a variety of physical occurrences. This system is used to define the behavior of real gases taking into consideration finite size of molecules and also has some applications in industry for granular materials. The model is studied under the effect of fractional derivatives by employing two different definitions: β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document}, and M-truncated. Further, new extended direct algebraic method is employed to construct the solitary wave solutions for the model. The solutions transmit several novel solutions, such as dark-singular, dark–bright, singular-periodic and dark solutions, and this method establishes the conditions required for the formation of these structures. To show the comparative analysis between two different fractional operators, results are graphically represented in the form of 2-dimensional and 3-dimensional visualizations.

Exploring explainable ensemble machine learning methods for long-term performance prediction of industrial gas turbines: A comparative analysis

In today's modern life, where electricity demand is one of the fundamental necessities, gas turbines play a pivotal role in meeting this demand. As such, it is imperative to address the challenges faced in the field. Current models often rely on simplifying assumptions, neglecting the intricate relationships between variables. This limitation leads to reduced accuracy and reliability, ultimately affecting the overall efficiency of gas turbine systems. Furthermore, the complexity of gas turbine behavior, coupled with the scarcity of comprehensive datasets, exacerbates the problem.To address these challenges, this research aimed to develop an advanced model capable of accurately forecasting real gas turbine behavior. The proposed approach leveraged ensemble decision trees, robust preprocessing techniques, and rigorous evaluation using an extensive dataset spanning from 2011 to 2015. The training and validation phases were conducted on data from 2011 to 2014, with the 2015 dataset reserved for evaluation.The results demonstrated that the bagging structure outperformed the boosted structure, exhibiting lower complexity and higher reliability. Remarkably, the bagging approach with only 30 estimators achieved a superior root mean square error of 1.4176, outperforming the boosted trees with 200 learners. The model effectively captured the overall gas turbine performance, though it encountered limitations in certain specific operating ranges.To further investigate the model's behavior, an evaluation was conducted to assess the effects of the input variables on the output power. While the interpretability of the results posed some challenges, the overall findings were deemed acceptable and provide valuable insights for optimizing gas turbine performance. The significance of this research lies in its potential to inform decision-making and enhance the efficiency of gas turbine systems, ultimately contributing to the reliable and sustainable supply of electricity.

Water-retaining slurry washcoat for high-loading and robust CuMnOx structured catalyst toward durable monoxide oxide purification from real flue gas

Structured catalysts play key roles in many industries with the advantages of low pressure drop and efficient mass transfer. The copper-manganese oxide (CuMnOx) as a cost-effective catalyst has been widely applied in gas purification, but still lack efficient structured catalyst due to the challenge in controlling its slurry and coating quality. In this work, this challenge was addressed by introducing the water-retaining agent (WRA) into slurry with sophisticatedly designed conditions. The effects of the type and dosage of WRA, pH value, and temperature on slurry properties including viscosity, stability, and water-retention were systematically studied, and the slurry property-coating quality relationship was correlated. The preferred slurry and coated layer could be segregated into sub-millimeter-sized water-retaining regions where catalyst and binder particles were well dispersed and connected. After slow release of water and organic during drying and calcination, the CuMnOx structured catalyst with uniform, defect-free and dense coating was obtained, showing high loading (>160 kg/m3), great mechanical strength (powder shedding rate < 1 wt%), and no blockage for practical use. The robustness of the structured catalysts was validated by a scale-up preparation of 2 m3 volume amount for CO purification from real ore-sintering flue gas in a steel plant, which achieved the CO catalytic efficiency maintaining over 90 % for more than 1440 h. This work showcases an efficient strategy for structured catalyst preparation and expands the gas purification application of the industrially-favored CuMnOx.

Supercritical hydrothermal combustion and enhanced degradation characteristics of phenol

Supercritical hydrothermal combustion is a green combustion technology that produces flames in supercritical water (SCW), which can realize efficient disposal of aqueous wastes. In this study, the typical pollutant phenol is investigated through tubular reactor experiments and mechanism analysis to explore its hydrothermal combustion properties and enhanced degradation effects on refractory species. The results show that 3.06 and 3.41 wt% phenol can be self-ignited in the tubular reactor with a critical preheating temperature of 460 °C. Methanol could improve the ignition and burnout characteristics of phenol. As the COD ratio of methanol was greater than 0.35, the ignition temperature of phenol was reduced to 420 °C, with TOC removal rate achieving 99.9%. At 460 °C, phenol positively influenced the heat release during combustion of phenol/methanol. In oxidation of phenol/ammonia, 1.61 wt% phenol resulted in the reaction temperature rising by around 62.0 °C, allowing a NH4-N removal rate of 92.8% through its synergistic kinetic and thermal effects. Whereas, the nitrogen-containing intermediates from ammonia inhibited phenol oxidation. Finally, a mechanism-based kinetics model for oxidation of phenol in SCW was developed by means of real gas properties and sensitive reaction step modifications, which was viable for simulating the ring-opening path of phenol.

A hydraulic-mechanical coupled triple porosity fractal model considering action mechanisms and gas transport mechanisms in carbon-hydrogen reservoirs

The shale formation, a common carbon-hydrogen reservoir, has numerous nanoscale pores that facilitate multiple gas transport mechanisms, including viscous flow, slip flow, Knudsen diffusion, and surface diffusion. Additionally, various action mechanisms involving effective stress, real gas effect, gas adsorption and desorption, and fracture-pore characteristics significantly influence gas transport. In this study, we conceptualize shale as a triple porosity medium comprising organic matrix, inorganic matrix, and microfractures. For each system, its hydraulic-mechanical coupled model with action mechanisms and gas transport mechanisms is derived based on fractal theory. After validating the model with Barnett and Marcellus data, the evolution of apparent permeability and gas pressure is studied, as well as the influences of pore fractal features, the real gas effect, and the number of hydraulic fractures on gas extraction. Simulation results indicate that, in comparison to organic matrix, inorganic pore fractal features exert a more noticeable effect on cumulative production. The real gas effect is critical in gas transport and reservoir reserve estimation; disregarding this effect results in a 17.4% underestimation of cumulative gas production by the 1600th day. Fracture interference attenuates the improvement in cumulative production gains from increased hydraulic fracture numbers.