A semi-analytical model for coupled flow in stress-sensitive multi-scale shale reservoirs with fractal characteristics

A large number of nanopores and complex fracture structures in shale reservoirs results in multi-scale flow of oil. With the development of shale oil reservoirs, the permeability of multi-scale media undergoes changes due to stress sensitivity, which plays a crucial role in controlling pressure propagation and oil flow. This paper proposes a multi-scale coupled flow mathematical model of matrix nanopores, induced fractures, and hydraulic fractures. In this model, the micro-scale effects of shale oil flow in fractal nanopores, fractal induced fracture network, and stress sensitivity of multi-scale media are considered. We solved the model iteratively using Pedrosa transform, semi-analytic Segmented Bessel function, Laplace transform. The results of this model exhibit good agreement with the numerical solution and field production data, confirming the high accuracy of the model. As well, the influence of stress sensitivity on permeability, pressure and production is analyzed. It is shown that the permeability and production decrease significantly when induced fractures are weakly supported. Closed induced fractures can inhibit interporosity flow in the stimulated reservoir volume (SRV). It has been shown in sensitivity analysis that hydraulic fractures are beneficial to early production, and induced fractures in SRV are beneficial to middle production. The model can characterize multi-scale flow characteristics of shale oil, providing theoretical guidance for rapid productivity evaluation.

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CON-TINUUM THEORIES (Ⅱ)—MICROMORPHIC CONTINUUM THEORY AND COUPLE STRESS THEORY

The purpose is to reestablish the balance laws of momentum, angular momentum and energy and to derive the corresponding local and nonlocal balance equations for micromorphic continuum mechanics and couple stress theory. The desired results for micromorphic continuum mechanics and couple stress theory are naturally obtained via direct transitions and reductions from the coupled conservation law of energy for micropolar continuum theory, respectively. The basic balance laws and equations for micromorphic continuum mechanics and couple stress theory are constituted by combining these results derived here and the traditional conservation laws and equations of mass and microinertia and the entropy inequality. The incomplete degrees of the former related continuum theories are clarified. Finally, some special cases are conveniently derived.

Effective-mass theory for coupled quantum dots grown on （11N）-oriented substrates

The electronic structures of coupled quantum dots grown on （11N）-oriented substrates are studied in the framework of effective-mass envelope-function theory. The results show that the all-hole subbands have the smallest widths and the optical properties are best for the （113）, （114）, and （115） growth directions. Our theoretical results agree with the available experimental data. Our calculated results are useful for the application of coupled quantum dots in photoelectric devices.

Dynamic coupled thermo-hydro-mechanical problem for heterogeneous deep-sea sediments under vibration of mining vehicle

Due to the influence of deep-sea environment,deep-sea sediments are usually heterogeneous,and their moduli of elasticity and density change as depth changes.Combined with the characteristics of deep-sea sediments,the thermo-hydro-mechanical coupling dynamic response model of heterogeneous saturated porous sediments can be established to study the influence of elastic modulus,density,frequency,and load amplitude changes on the model.Based on the Green-Lindsay generalized thermoelasticity theory and Darcy’s law,the thermo-hydro-mechanical coupled dynamic response model and governing equations of heterogeneous deep-sea sediments with nonlinear elastic modulus and density are established.The analytical solutions of dimensionless vertical displacement,vertical stress,excess pore water pressure,and temperature are obtained by means of normal modal analysis,which are depicted graphically.The results show that the changes of elastic modulus and density have few effects on vertical displacement,vertical stress,and temperature,but have great effects on excess pore water pressure.When the mining machine vibrates,the heterogeneity of deep-sea sediments has great influence on vertical displacement,vertical stress,and excess pore water pressure,but has few effects on temperature.In addition,the vertical displacement,vertical stress,and excess pore water pressure of heterogeneous deep-sea sediments change more gently.The variation trends of physical quantities for heterogeneous and homogeneous deep-sea sediments with frequency and load amplitude are basically the same.The results can provide theoretical guidance for deep-sea mining engineering construction.

Antiplane shear crack in a prestressed elastic medium based on the couple stress theory

A prestressed elastic medium containing a mode-Ⅲcrack is studied by means of the couple stress theory(CST).Based on the CST under initial stresses,a governing differential equation along with a mixed boundary value problem is established.The singularities of the couple stress and force stress near the crack tips are analyzed through the asymptotic crack-tip fields resulting from the characteristic expansion method.To determine their intensity,a hypersingular integral equation is derived and numerically solved with the help of the Chebyshev polynomial.The obtained results show a strong size-dependence of the out-of-plane displacement on the crack and the couple stress intensity factor(CSIF)and the force stress intensity factor(FSIF)around the crack tips.The symmetric part of the shear stress has no singularity,and the skew-symmetric part related to the couple stress exhibits an r^(-3/2)singularity,in which r is the distance from the crack tip.The initial stresses also affect the crack tearing displacement and the CSIF and FSIF.

Insight into coupled Ni-Co dual-metal atom catalysts for efficient synergistic electrochemical CO_(2)reduction

The development of highly active,selective,and stable electrocatalysts can facilitate the effective implementation of electrocatalytic CO_(2)conversion into fuels or chemicals for mitigating the energy crisis and climate problems.Therefore,it is necessary to achieve the goal through reasonable material design based on the actuality of the operational active site at the molecular scale.Inspired by the stimulating synergistic effect of coupled heteronuclear metal atoms,a novel Ni-Co atomic pairs configuration(denoted as NiN_(3)?CoN_(3)-NC)active site was theoretically screened out for improving electrochemical CO_(2)reduction reaction(CO_(2)RR).The structure of NiN_(3)?CoN_(3)-NC was finely regulated by adjusting Zn content in the precursors Zn/Co/Ni-zeolite imidazolate frameworks(Zn/Co/Ni-ZIFs)and pyrolysis temperature.The structural features of NiN_(3)?CoN_(3)-NC were systematically confirmed by aberration-corrected HAADF-STEM coupled with 3D atom-overlapping Gaussian-function fitting mapping,XAFS,and XRD.The results of theoretical calculations reveal that the synergistic effect of Ni-Co atomic pairs can effectively promote the*COOH intermediate formation and thus the overall CO_(2)RR kinetic was improved,and also restrained the competitive hydrogen evolution reaction.Due to the attributes of Ni-Co atomic pairs configuration,the developed NiN_(3)?CoN_(3)-NC with superior catalytic activity,selectivity,and durability,with a high turnover frequency of 2265 h^(-1)at-1.1 V(vs.RHE)and maximum Faradaic efficiency of 97.7%for CO production.This work demonstrates the great potential of DACs as highly efficient catalysts for CO_(2)RR,provides a useful strategy to design heteronuclear DACs,exploits the synergistic effect of multiple metal sites to facilitate complex CO_(2)RR catalytic reactions,and inspires more efforts to develop the potential of DACs in various fields.

Guest Review:Potential theory method for 3D crack and contact problems of multi-field coupled media: A survey

This paper presents an overview of the recent progress of potential theory method in the analysis of mixed boundary value problems mainly stemming from three-dimensional crack or contact problems of multi-field coupled media. This method was used to derive a series of exact three dimensional solutions which should be of great theoretical significance because most of them usually cannot be derived by other methods such as the transform method and the trial-and-error method. Further, many solutions are obtained in terms of elementary functions that enable us to treat more complicated problems easily. It is pointed out here that the method is usually only applicable to media characterizing transverse isotropy, from which, however, the results for the isotropic case can be readily obtained.

Analysis and engineering of coupled cavity waveguides based on coupled-mode theory

The analytical expression for the transmission spectra of coupled cavity waveguides （CCWs） in photonic crystals （PCs） is derived based on the coupled-mode theory （CMT）. Parameters in the analytical expression can be extracted by simple numerical simulations. We reveal that it is the phase shift between the two adjacent PC defects that uniquely determines the flatness of the impurity bands of CCWs. In addition, it is found that the phase shift also greatly affects the bandwidth of CCWs. Thus, the engineering of the impurity bands of CCWs can be realized through the adjustment of the phase shift. Based on the theoretical results, an interesting phenomenon in which a CCW acts as a single PC defect and its impurity band possesses a Lorentz lineshape is predicted. Very good agreement between the analytical results and the numerical simulations based on transfer matrix method has been achieved.

Complete leaky mode coupling in dual-core photonic crystal fibre based on the coupled-mode theory

This paper theoretically investigates the dependence of leaky mode coupling between inner core fundamental mode and outer core defect mode on phase and loss matching in pure silica dual-core photonic crystal fibres with the multi-pole method. The complete mode coupling can take place when both the phase and loss matching conditions are satisfied at the avoided anti-crossing wavelength. It shows the influences of cladding structure parameters including the diameters of cladding air holes d1, diameters of outer core holes d2 and hole to hole pitch A on the characteristics of leaky modes coupling. The coupled-mode theory is used to analyse the mode transition characteristics and the complete coupling can be clearly indicated by comparing the real and imaginary parts of propagation constant of the leaky modes.

A High-Precision Calculation of Bond Length and Spectroscopic Constants of Hg2 Based on the Coupled-Cluster Theory with Spin-Orbit Coupling

Based on the two-component relativistic effective core potential and matched basis sets cc-pwcvnz-pp （n=Q, 5）, combining the completed basis-set extrapolation of electronic correlation energy and the fourth-order polynomial fitting technique, the bond length and spectroscopic constants of Hg2 are studied by the coupled cluster theory with spin-orbit coupling. Spin-orbit coupling is included in the post Hartree-Fock procedure, i.e., in the coupled- cluster iteration, to obtain more reliable theoretical results. The results show that our theoretical values agree with the experimental values very well and will be helpful to understand the spectral character of Hg2.

Comparative Analysis of Characteristics of the Coupled and Decoupled Parallel Mechanisms

The existence of coupling makes the parallel mechanism possess some special advantages over the serial mechanism, while it is just the coupling that brings about the parallel mechanism some limitations, such as complex workspace, high nonlinear relationship between input and output, difficulties in static and dynamic analysis, and the development of control system, which restricts its application fields. The decoupled parallel mechanism is currently one of the research focuses of the mechanism fields, while the study on the different characteristics between the deeoupled and coupled parallel mechanisms has not been reported. Therefore, this paper performs the systematic comparative analysis of the 3-RPUR and the 3-CPR parallel mechanisms. The features of the two mechanisms are described and their movement forms are analyzed with screw theory. The inverse and forward displacement solutions are solved and the Jacobian matrices are obtained. According to the Jacobian matrices and by using the theory of physical model of the solution space, the workspace, dexterity, velocity, payload capability, and stiffness of the mechanisms are analyzed with plotting the indices atlases. The research results prove that the effects of the coupling on the parallel mechanism are double-side, and then the adoption of the decoupled parallel mechanism should be determined by the requirements of the concrete application situation. The contents of this paper should be useful for the type synthesis and practical application of the parallel mechanism.

Train–track coupled dynamics analysis:system spatial variation on geometry,physics and mechanics

This paper aims to clarify the influence of system spatial variability on train–track interaction from perspectives of stochastic analysis and statistics.Considering the spatial randomness of system properties in geometry,physics and mechanics,the primary work is therefore simulating the uncertainties realistically,representatively and efficiently.With regard to the track irregularity simulation,a model is newly developed to obtain random sample sets of track irregularities by transforming its power spectral density function into the equivalent track quality index for representation based on the discrete Parseval theorem,where the correlation between various types of track irregularities is accounted for.To statistically clarify the uncertainty of track properties in physics and mechanics in space,a model combining discrete element method and finite element method is developed to obtain the spatially varied track parametric characteristics,e.g.track stiffness and density,through which the highly expensive experiments in situ can be avoided.Finally a train–track stochastic analysis model is formulated by integrating the system uncertainties into the dynamics model.Numerical examples have validated the accuracy and efficiency of this model and illustrated the effects of system spatial variability on train–track vibrations comprehensively.

Size dependent free vibration analysis of functionally graded piezoelectric micro/nano shell based on modified couple stress theory with considering thickness stretching effect

Higher-order shear and normal deformation theory is used in this paper to account thickness stretching effect for free vibration analysis of the cylindrical micro/nano shell subjected to an applied voltage and uniform temperature rising.Size dependency is included in governing equations based on the modified couple stress theory.Hamilton’s principle is used to derive governing equations of the cylindrical micro/nano shell.Solution procedure is developed using Navier technique for simply-supported boundary conditions.The numerical results are presented to investigate the effect of significant parameters such as some dimensionless geometric parameters,material properties,applied voltages and temperature rising on the free vibration responses.

Formulation of thermo-hydro-mechanical coupling behavior of unsaturated soils based on hybrid mixture theory

Thermo-Hydro-Mechanical （THM） coupling pro- cesses in unsaturated soils are very important in both theoretical researches and engineering applications. A coupled formulation based on hybrid mixture theory is derived to model the THM coupling behavior of unsaturated soils. The free-energy and dissipative functions for different phases are derived from Taylor＇s series expansions. Constitutive relations for THM coupled behaviors of unsaturated soils, which include deformation, entropy change, fluid flow, heat conduction, and dynamic compatibility conditions on the interfaces, are then established. The number of field equations is shown to be equal to the number of unknown variables; thus, a closure of this coupling problem is established. In addition to modifications of the physical conservation equations with coupling effect terms, the constitutive equations, which consider the coupling between elastoplastic deformation of the soil skeleton, fluid flow, and heat transfer, are also derived.

Linear and nonlinear torsional free vibration of functionally graded micro/nano-tubes based on modified couple stress theory

The linear and nonlinear torsional free vibration analyses of functionMly graded micro/nuno-tubes （FGMTs） are analytically investigated based on the couple stress theory. The employed non-classical continuum theory contains one material length scale parameter, which can capture the small scale effect. The FGMT model accounts for the through-radius power-law variation of a two-constituent material. Hamilton＇s principle is used to develop the non-classical nonlinear governing equation. To study the effect of the boundary conditions, two types of end conditions, i.e., fixed-fixed and fixed-free, are considered. The derived boundary value governing equation is of the fourthorder, and is solved by the homotopy analysis method （HAM）. This method is based on the Taylor series with an embedded parameter and is capable of providing very good approximations by means of only a few terms, if the initial guess and the auxiliary linear operator are properly selected. The analytical expressions are developed for the linear and nonlinear natural frequencies, which can be conveniently used to investigate the effects of the dimensionless length scale parameter, the material gradient index, and the vibration amplitude on the natural frequencies of FGMTs.

Complex dynamics analysis of impulsively coupled Duffing oscillators with ring structure

Impulsively coupled systems are high-dimensional non-smooth systems that can exhibit rich and complex dynamics.This paper studies the complex dynamics of a non-smooth system which is unidirectionally impulsively coupled by three Duffing oscillators in a ring structure.By constructing a proper Poincare map of the non-smooth system,an analytical expression of the Jacobian matrix of Poincare map is given.Two-parameter Hopf bifurcation sets are obtained by combining the shooting method and the Runge-Kutta method.When the period is fixed and the coupling strength changes,the system undergoes stable,periodic,quasi-periodic,and hyper-chaotic solutions,etc.Floquet theory is used to study the stability of the periodic solutions of the system and their bifurcations.

Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic micro-plate based on surface stress and modified couple stress theories using differential quadrature method

The size-dependent effect on the biaxial and shear nonlinear buckling analysis of an isotropic and orthotropic micro-plate based on the surface stress, the modified couple stress theory （MCST）, and the nonlocal elasticity theories using the differential quadrature method （DQM） is presented. Main advantages of the MCST over the classical theory （CT） are the inclusion of the asymmetric couple stress tensor and the consideration of only one material length scale parameter. Based on the nonlinear von Karman assumption, the governing equations of equilibrium for the micro-classical plate consid- ering midplane displacements are derived based on the minimum principle of potential energy. Using the DQM, the biaxial and shear critical buckling loads of the micro-plate for various boundary conditions are obtained. Accuracy of the obtained results is validated by comparing the solutions with those reported in the literature. A parametric study is conducted to show the effects of the aspect ratio, the side-to-thickness ratio, Eringen＇s nonlocal parameter, the material length scale parameter, Young＇s modulus of the surface layer, the surface residual stress, the polymer matrix coefficients, and various boundary conditions on the dimensionless uniaxial, biaxial, and shear critical buckling loads. The results indicate that the critical buckling loads are strongly sensitive to Eringen＇s nonlocal parameter, the material length scale parameter, and the surface residual stress effects, while the effect of Young＇s modulus of the surface layer on the critical buckling load is negligible. Also, considering the size dependent effect causes the increase in the stiffness of the orthotropic micro-plate. The results show that the critical biaxial buckling load increases with an increase in G12/E2 and vice versa for E1/E2. It is shown that the nonlinear biaxial buckling ratio decreases as the aspect ratio increases and vice versa for the buckling amplitude. Because of the most lightweight micro-composite materials with high strength/weight and stiffness/weight ratios, it is anticipated that the results of the present work are useful in experimental characterization of the mechanical properties of micro-composite plates in the aircraft industry and other engineering applications.

MECHANISM OF WATER-SOIL COUPLED ACTION DURING MINING SUBSIDENCE

This paper,on the basis of the scientific research of engineering geological exploration in a mining area,systematically studies the reasons and influence factors of consolidation and deformation of the saturated soil included in the thick loose water-bearing overburden due to mining subsidence,and analyses the dissipation of hyperstatic pore water pressure during the change of original stress and strain state of the soil. Again,by means of the coupled model based on Cambridge model and Biot's three-dimensional consolidation theory,adopting a great many physico-mechanical parameters measured in various soil layers,the paper analyses the consolidation and deformation of saturated soil affected by mining subsidence with elasto-plastic finite element method.Thus,the research not only reveals the regulation of stress,strain,displacement and hyperstatic pore water pressure dissipation in overlying soil mass,but also opens up a new direction and way for the research of mining subsidence.

Investigation of block foundations resting on soil-rock and rock-rock media under coupled vibrations

In the present study,the dynamic response of block foundations of different equivalent radius to mass（R;/m） ratios under coupled vibrations is investigated for various homogeneous and layered systems.The frequency-dependent stiffness and damping of foundation resting on homogeneous soils and rocks are determined using the half-space theory.The dynamic response characteristics of foundation resting on the layered system considering rock-rock combination are evaluated using finite element program with transmitting boundaries.Frequencies versus amplitude responses of block foundation are obtained for both translational and rotational motion.A new methodology is proposed for determination of dynamic response of block foundations resting on soil-rock and weathered rock-rock system in the form of equations and graphs.The variations of dimensionless natural frequency and dimensionless resonant amplitude with shear wave velocity ratio are investigated for different thicknesses of top soil/weathered rock layer.The dynamic behaviors of block foundations are also analyzed for different rock-rock systems by considering sandstone,shale and limestone underlain by basalt.The variations of stiffness,damping and amplitudes of block foundations with frequency are shown in this study for various rock—rock combinations.In the analysis,two resonant peaks are observed at two different frequencies for both translational and rotational motion.It is observed that the dimensionless resonant amplitudes decrease and natural frequencies increase with increase in shear wave velocity ratio.Finally,the parametric study is performed for block foundations with dimensions of 4 m × 3 m × 2 m and 8m×5m×2m by using generalized graphs.The variations of natural frequency and peak displacement amplitude are also studied for different top layer thicknesses and eccentric moments.

Nonlinearity analysis of piezoelectric micromachined ultrasonic transducers based on couple stress theory

This paper studies the static deformation behavior of a piezoelectric micromachined ultrasonic transducer （PMUT） actuated by a strong external electric field. The transducer membrane consists of a piezoelectric layer, a passive layer and two electrode layers. The nonlinearities of the piezoelectric layer caused by electrostriction under a strong electric field are analyzed. Because the thickness of the transducer membrane is on the microscale, the size dependence of the deformation behavior is evaluated using the couple stress theory. The results show that the optimal ratio of the top electrode diameter and the membrane diameter is around 0.674. It is also found that this optimal value does not depend on any other parameters if the thicknesses of the two electrodes are negligible compared with those of the piezo- electric and passive layers. In addition, the nonlinearities of the piezoelectric layer will become stronger along with the increase of the electric field, which means that softening of the membrane stiffness occurs when a strong external electric field is applied. Meanwhile, the optimal thickness ratio for the passive layer and the piezoelectric layer is not equal to 1.0 which is usually adopted by previous researchers. Because there exists size dependence of membrane deforma-tion, the optimal value of this thickness ratio needs to be greater than 1.0 on the microscale.