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.

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.

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.

Calculation of the Coupling Coefficient of Twin-Core Fiber Based on the Supermode Theory with Finite Element Method

Currently, coupled mode theory (CMT) is widely used for calculating the coupling coefficient of twin-core fibers (TCFs) that are used in a broad range of important applications. This approach is highly accurate for scenarios with weak coupling between the cores but shows significant errors in the strong coupling scenarios, necessitating the use of a more accurate method for coupling coefficient calculations. Therefore, in this work, we calculate the coupling coefficients of TCFs using the supermode theory with finite element method (FEM) that has higher accuracy than CMT, particularly for the strong coupling TCF. To investigate the origin of the differences between the results obtained by these two methods, the modal field distributions of the supermodes of TCF are simulated and analyzed in detail.

THE COUPLING DYNAMICAL MODELING THEORY OF FLEXIBLE MULTIBODY SYSTEM

Based on the deformation theory of elastic beams, the coupling effect between the coupling displacements of a point on the middle line of beam and large overall motion is presented. The 'coupling matrix library' and Jourdain's variation principle and single direction recursive formulation method are used to establish the general coupling dynamical equations of flexible multibody system. Two typical examples show the coupling effect between coupling displacements and large overall motion on the dynamics of flexible multibody system consisting of beams.

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.

Gravitational constant in f(R) theories of gravity with non-minimal coupling between matter and geometry

We study the effect of the non-minimal coupling between matter and geometry on the gravitational constant in the context of f(R) theories of gravity on cosmic scales. For a class of f(R) models,the result shows that the value of the gravitational constant not only changes over time but also has the dampened oscillation behavior.Compared with the result of the standard ACDM model, the consequence suggests that the coupling between matter and geometry should be weak.

Numerical Simulation of Gear Heat Distribution in Meshing Process Based on Thermal-structural Coupling

The thermal balance state of high-speed and heavy-load gear transmissionsystem has an important influence on the performance and failure of geartransmission and the design of gear lubrication system. Excessive surfacetemperature of gear teeth is the main cause of gluing failure of gear contactsurface. To investigate the gear heat distribution in meshing processand discuss the effect of thermal conduction on heat distribution,a finiteelement model of spur gear is presented in the paper which can representgeneral involute spur gears. And a simulation approach is use to calculategear heat distribution in meshing process. By comparing with theoreticalcalculation, the correctness of the simulation method is verified, and theheat distribution of spur gear under the condition of heat conduction isfurther analyzed. The difference between the calculation results with heatconduction and without heat conduction is compared. The research hascertain reference significance for dry gear hobbing and the same type ofthermal-structural coupling analysis.

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.

Some recent advances in 3D crack and contact analysis of elastic solids with transverse isotropy and multifield coupling

Significant progress has been made in mixed boundary-value problems associated with three-dimensional（3D） crack and contact analyses of advanced materials featuring more complexities compared to the conventional isotropic elastic materials.These include material anisotropy and multifield coupling,two typical characteristics of most current multifunctional materials.In this paper we try to present a state-of-the-art description of 3D exact/analytical solutions derived for crack and contact problems of elastic solids with both transverse isotropy and multifield coupling in the latest decade by the potential theory method in the spirit of V.I.Fabrikant.whose ingenious breakthrough brings new vigor and vitality to the old research subject of classical potential theory.We are particularly interested in crack and contact problems with certain nonlinear features.Emphasis is also placed on the coupling between the temperature field（or the like） and other physical fields（e.g.,elastic,electric,and magnetic fields）.We further highlight the practical significance of 3D contact solutions,in particular in applications related to modern scanning probe microscopes.

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.

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.

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.

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.

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.

Size-dependent thermoelastic initially stressed micro-beam due to a varying temperature in the light of the modified couple stress theory

The bending of the Euler-Bernoulli micro-beam has been extensively modeled based on the modified couple stress(MCS)theory.Although many models have been incorporated into the literature,there is still room for introducing an improved model in this context.In this work,we investigate the thermoelastic vibration of a micro-beam exposed to a varying temperature due to the application of the initial stress employing the MCS theory and generalized thermoelasticity.The MCS theory is used to investigate the material length scale effects.Using the Laplace transform,the temperature,deflection,displacement,flexure moment,and stress field variables of the micro-beam are derived.The effects of the temperature pulse and couple stress on the field distributions of the micro-beam are obtained numerically and graphically introduced.The numerical results indicate that the temperature pulse and couple stress have a significant effect on all field variables.

A Size-Dependent Functionally Graded Higher Order Plate Analysis Based on Modified Couple Stress Theory and Moving Kriging Meshfree Method

A size-dependent computational approach for bending,free vibration and buckling analyses of isotropic and sandwich functionally graded(FG)microplates is in this study presented.We consider both shear deformation and small scale effects through the generalized higher order shear deformation theory and modified couple stress theory(MCST).The present model only retains a single material length scale parameter for capturing properly size effects.A rule of mixture is used to model material properties varying through the thickness of plates.The principle of virtual work is used to derive the discrete system equations which are approximated by moving Kriging interpolation(MKI)meshfree method.Numerical examples consider the inclusions of geometrical parameters,volume fraction,boundary conditions and material length scale parameter.Reliability and effectiveness of the present method are confirmed through numerical results.

Design and application of a new kind of rolling coupling

Based on Hertz theory of elastic contact and the design theory of ball bearings, a new type of rolling coupling was designed. The two halves of the rolling coupling can be moved relatively by a small axial force when a great moment is exerted on it. The rolling coupling was used to connect the principal axis and the decelerator of continuous extrusion machine and it can greatly decrease the harmful axial forces on the continuous machine. The engineering formulas for the contact stress and distance of apporach of the rolling elements were deduced and the method for designing the rolling couplings was proposed. The formulas for the forces exerted on the rolling element were verified by the experiment.

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.