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.

CHAOTIC MOTIONS AND LIMIT CYCLE FLUTTER OF TWO-DIMENSIONAL WING IN SUPERSONIC FLOW

Based on the piston theory of supersonic flow and the energy method, the flutter motion equations of a two-dimensional wing with cubic stiffness in the pitching direction are established. The aeroelastic system contains both structural and aerodynamic nonlinearities. Hopf bifurcation theory is used to analyze the flutter speed of the system. The effects of system parameters on the flutter speed are studied. The 4th order Runge-Kutta method is used to calculate the stable limit cycle responses and chaotic motions of the aeroelastic system. Results show that the number and the stability of equilibrium points of the system vary with the increase of flow speed. Besides the simple limit cycle response of period 1, there are also period-doubling responses and chaotic motions in the flutter system. The route leading to chaos in the aeroelastic model used here is the period-doubling bifurcation. The chaotic motions in the system occur only when the flow speed is higher than the linear divergent speed and the initial condition is very small. Moreover, the flow speed regions in which the system behaves chaos axe very narrow.

Nonlinear aeroelastic analysis of a two-dimensional wing with control surface in supersonic flow

Based on the piston theory of supersonic flow and the energy method, a two dimensional wing with a control surface in supersonic flow is theoretically modeled, in which the cubic stiffness in the torsional direction of the control surface is considered. An approximate method of the cha- otic response analysis of the nonlinear aeroelastic system is studied, the main idea of which is that under the condi- tion of stable limit cycle flutter of the aeroelastic system, the vibrations in the plunging and pitching of the wing can approximately be considered to be simple harmonic excita- tion to the control surface. The motion of the control surface can approximately be modeled by a nonlinear oscillation of one-degree-of-freedom. The range of the chaotic response of the aeroelastic system is approximately determined by means of the chaotic response of the nonlinear oscillator. The rich dynamic behaviors of the control surface are represented as bifurcation diagrams, phase-plane portraits and PS diagrams. The theoretical analysis is verified by the numerical results.

Experimental and theoretical studies on two-dimensional vanadium carbide hybrid nanomaterials derived from V_(4)AlC_(3) as excellent catalyst for MgH_(2)

Hydrogen is considered one of the most ideal future energy carriers.The safe storage and convenient transportation of hydrogen are key factors for the utilization of hydrogen energy.In the current investigation,two-dimensional vanadium carbide(VC) was prepared by an etching method using V_(4)AlC_(3) as a precursor and then employed to enhance the hydrogen storage properties of MgH_(2).The studied results indicate that VC-doped MgH_(2) can absorb hydrogen at room temperature and release hydrogen at 170℃. Moreover,it absorbs 5.0 wt.%of H_(2) within 9.8 min at 100℃ and desorbs 5.0 wt.% of H_(2) within 3.2 min at 300℃.The dehydrogenation apparent activation energy of VC-doped MgH_(2) is 89.3 ± 2.8 kJ/mol,which is far lower than that of additive-free MgH_(2)(138.5 ± 2.4 kJ/mol),respectively.Ab-initio simulations showed that VC can stretch Mg-H bonds and make the Mg-H bonds easier to break,which is responsible for the decrease of dehydrogenation temperature and conducive to accelerating the diffusion rate of hydrogen atoms,thus,the hydrogen storage properties of MgH_(2) are remarkable improved through addition of VC.

A Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows

The present paper proposes a Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows based on the principle of weighted averaging zero skin-friction given by Haller （HALLER, G. Exact theory of unsteady separation for two-dimensional flows. Journal of Fluid Mechanics, 512, 257-311 （2004））. By analyzing the distribution of the finite-time Lyapunov exponent （FTLE） along the no-slip wall, it can be found that the periodic separation takes place at the point of the zero FTLE. This new criterion is verified with an analytical solution of the separation bubble and a numerical simulation of lid-driven cavity flows.

Experimental Investigation of Two-Dimensional Velocity on the 90°Double Bend Pipe Flow Using Ultrasound Technique

An experimental investigation was performed to investigate two-dimensional axial velocity field at downstream of the 90°double bend pipe with and without inlet swirling condition. The main objectives are to find separation region and observe the influence of inlet swirling flow on the velocity fluctuation using ultrasound technique. The experiments were carried out in the pipe at Reynolds number Re = 1 × 104. In case of inlet swirling flow condition, a rotary swirler was used as swirling generator, and the swirl number was setup S = 1. The ultrasonic measurements were taken at four downstream locations of the second bend pipe. Phased Array Ultrasonic Velocity Profiler (Phased Array UVP) technique was applied to obtain the two-dimensional velocity of the fluid and the axial and tangential velocity fluctuation. It was found that the secondary reverse flow became smaller at the downstream from the bend when the inlet condition on the first bend was swirling flow. In addition, inlet swirling condition influenced mainly on the tangential velocity fluctuation, and its maximum turbulence intensity was 40%.

A simplified two-dimensional boundary element method with arbitrary uniform mean flow

To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation（BIE） representation solves the two-dimensional convected Helmholtz equation（CHE） and its fundamental solution, which must satisfy a new Sommerfeld radiation condition（SRC） in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Green＇s kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole,dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation.

Corrigendum to“Atomic-scale electromagnetic theory bridging optics in microscopic world and macroscopic world”

The signs of the electric field markers in Figs.2 and 4 of the paper[Chin.Phys.B 32104211(2023)]have been corrected.These modifications do not affect the results derived in the paper.

Shale oil development techniques and application based on ternary-element storage and flow concept in Jiyang Depression,Bohai Bay Basin,East China

The ternary-element storage and flow concept for shale oil reservoirs in Jiyang Depression of Bohai Bay Basin,East China,was proposed based on the data of more than 10000 m cores and the production of more than 60 horizontal wells.The synergy of three elements(storage,fracture and pressure)contributes to the enrichment and high production of shale oil in Jiyang Depression.The storage element controls the enrichment of shale oil;specifically,the presence of inorganic pores and fractures,as well as laminae of lime-mud rocks,in the saline lake basin,is conducive to the storage of shale oil,and the high hydrocarbon generating capacity and free hydrocarbon content are the material basis for high production.The fracture element controls the shale oil flow;specifically,natural fractures act as flow channels for shale oil to migrate and accumulate,and induced fractures communicate natural fractures to form complex fracture network,which is fundamental to high production.The pressure element controls the high and stable production of shale oil;specifically,the high formation pressure provides the drive force for the migration and accumulation of hydrocarbons,and fracturing stimulation significantly increases the elastic energy of rock and fluid,improves the imbibition replacement of oil in the pores/fractures,and reduces the stress sensitivity,guaranteeing the stable production of shale oil for a long time.Based on the ternary-element storage and flow concept,a 3D development technology was formed,with the core techniques of 3D well pattern optimization,3D balanced fracturing,and full-cycle optimization of adjustment and control.This technology effectively guides the production and provides a support to the large-scale beneficial development of shale oil in Jiyang Depression.

THE TRANSIENT TWO-DIMENSIONAL FLOW THROUGH DOUBLE POROUS MEDIA

This paper presents the analytical solutions in Laplace domain for two-dimensional nonsteady flow of slightly compressible liquid in porous media with double porosity by using the methods of integral transforms and variables separation. The effects of the ratio of storativities to , interporosity flow parameter on the pressure behaviors for a vertically fractured well with infinite conductivity are investigated by using the method of numerical inversion. The new log-log diagnosis graph of the pressures is given and analysed.

An Improved Coupled Level Set and Continuous Moment-of-Fluid Method for Simulating Multiphase Flows with Phase Change

An improved algorithm for computing multiphase flows is presented in which the multimaterial Moment-of-Fluid(MOF)algorithm for multiphase flows,initially described by Li et al.(2015),is enhanced addressing existing MOF difficulties in computing solutions to problems in which surface tension forces are crucial for understanding salient flow mechanisms.The Continuous MOF(CMOF)method is motivated in this article.The CMOF reconstruction method inherently removes the"checkerboard instability"that persists when using the MOF method on surface tension driven multiphase(multimaterial)flows.The CMOF reconstruction algorithm is accelerated by coupling the CMOF method to the level set method and coupling the CMOF method to a decision tree machine learning(ML)algorithm.Multiphase flow examples are shown in the two-dimensional(2D),three-dimensional(3D)axisymmetric"RZ",and 3D coordinate systems.Examples include two material and three material multiphase flows:bubble formation,the impingement of a liquid jet on a gas bubble in a cryogenic fuel tank,freezing,and liquid lens dynamics.

SOLVING THE PROPAGATION OF ELECTROMAGNETIC WAVE IN A SIMPLE TWO-DIMENSIONALINHOMOGENEOUS MEDIUM BASED ON SYMPLECTIC GEOMETRICAL THEORY

A new symplectic geometrical high-frequency approximation method for solving the propagation of electromagnetic wave in the two-dimensional inhomogeneous medium is used in this paper. The propagating caustic problem of electromagnetic wave is translated into non-caustic problem by the coordinate transform on the symplectic space. The high-frequency approximation solution that includes the caustic region is obtained with the method combining with the geometrical optics. The drawback that the solution in the caustic region can not be obtained with geometrical optics is overcome by this method. The results coincide well with that of finite element method.

Three-Dimensional Numerical Simulation of Stably Stratified Flows over a Two-Dimensional Hill

Stably stratified flows over a two-dimensional hill are investigated in a channel of finite depth using a three-dimensional direct numerical simulation (DNS). The present study follows onto our previous two-dimensional DNS studies of stably stratified flows over a hill in a channel of finite depth and provides a more realistic simulation of atmospheric flows than our previous studies. A hill with a constant cross-section in the spanwise (y) direction is placed in a 3-D computational domain. As in the previous 2-D simulations, to avoid the effect of the ground boundary layer that develops upstream of the hill, no-slip conditions are imposed only on the hill surface and the surface downstream of the hill;slip conditions are imposed on the surface upstream of the hill. The simulated 3-D flows are discussed by comparing them to the simulated 2-D flows with a focus on the effect of the stable stratification on the non-periodic separation and reattachment of the flow behind the hill. In neutral (K = 0, where K is a non-dimensional stability parameter) and weakly stable (K = 0.8) conditions, 3-D flows over a hill differ clearly from 2-D flows over a hill mainly because of the three-dimensionality of the flow, that is the development of a spanwise flow component in the 3-D flows. In highly stable conditions (K = 1, 1.3), long-wavelength lee waves develop downstream of the hill in both 2-D and 3-D flows, and the behaviors of the 2-D and 3-D flows are similar in the vicinity of the hill. In other words, the spanwise component of the 3-D flows is strongly suppressed in highly stable conditions, and the flow in the vicinity of the hill becomes approximately two-dimensional in the x and z directions.

Cerebral blood flow volume measurements of the carotid artery and ipsilateral branches using two-dimensional phase-contrast magnetic resonance angiography

The optimal velocity encoding of phase-contrast magnetic resonance angiography （PC MRA） in measuring cerebral blood flow volume （BFV） ranges from 60 to 80 cm/s. To verify the accuracy of two-dimensional （2D） PC MRA, the present study localized the region of interest at blood vessels of the neck using PC MRA based on three-dimensional time-of-flight sequences, and the velocity encoding was set to 80 cm/s. Results of the measurements showed that the error rate was 7.0±6.0% in the estimation of BFV in the internal carotid artery, the external carotid artery and the ipsilateral common carotid artery. There was no significant difference, and a significant correlation in BFV between internal carotid artery ＋ external carotid artery and ipsilateral common carotid artery. In addition, the BFV of the common carotid artery was correlated with that of the ipsilateral internal carotid artery. The main error was attributed to the external carotid artery and its branches. Therefore, after selecting the appropriate scanning parameters and protocols, 2D PC MRA is more accurate in the determination of BFV in the carotid arteries.

Numerical Study of a Three-Dimensional Laminar Flow in a Rectangular Channel with a 180-Degree Sharp Turn

This study presents a numerical analysis of three-dimensional steady laminar flow in a rectangular channel with a 180-degree sharp turn. The Navier-Stokes equations are solved by using finite difference method for Re = 900. Three-dimensional streamlines and limiting streamlines on wall surface are used to analyze the three-dimensional flow characteristics. Topological theory is applied to limiting streamlines on inner walls of the channel and two-dimensional streamlines at several cross sections. It is also shown that the flow impinges on the end wall of turn and the secondary flow is induced by the curvature in the sharp turn.

Theory of Flexural Shear, Bending and Torsion for a Thin-Walled Beam of Open Section

Aspects of the general Vlasov theory are examined separately as applied to a thin-walled channel section cantilever beam under free-end end loading. In particular, the flexural bending and shear that arise under transverse shear and axial torsional loading are each considered theoretically. These analyses involve the location of the shear centre at which transverse shear forces when applied do not produce torsion. This centre, when taken to be coincident with the centre of twist implies an equivalent reciprocal behaviour. That is, an axial torsion applied concentric with the shear centre will twist but not bend the beam. The respective bending and shear stress conversions are derived for each action applied to three aluminium alloy extruded channel sections mounted as cantilevers with a horizontal principal axis of symmetry. Bending and shear are considered more generally for other thin-walled sections when the transverse loading axes at the shear centre are not parallel to the section = s centroidal axes of principal second moments of area. The fixing at one end of the cantilever modifies the St Venant free angular twist and the free warping displacement. It is shown from the Wagner-Kappus torsion theory how the end constrained warping generates an axial stress distribution that varies with the length and across the cross-section for an axial torsion applied to the shear centre. It should be mentioned here for wider applications and validation of the Vlasov theory that attendant papers are to consider in detail bending and torsional loadings applied to other axes through each of the centroid and the web centre. Therein, both bending and twisting arise from transverse shear and axial torsion applied to each position being displaced from the shear centre. Here, the influence of the axis position upon the net axial and shear stress distributions is to be established. That is, the net axial stress from axial torsional loading is identified with the sum of axial stress due to bending and axial stress arising from constrained warping displacements at the fixing. The net shear stress distribution overlays the distributions from axial torsion and that from flexural shear under transverse loading. Both arise when transverse forces are displaced from the shear centre.

AN EXPLORATION TO THE MODELLING OF TWO-DIMENSIONAL COMPLEX TURBULENT SHEAR FLOWS

The regions with shear stress and mean velocity gradient of opposite sign often exist in complex turbulent shear flows.In these cases,the eddy viscosity hypothesis breaks down.Hinze regards the,departure from eddy viscosity hypothesis as a result from transportation of mean momentum over distance by the large structures and arrives at a shear stress expression including the second order derivatives of the mean velocity.However,his expression greatly overestimates the shear stress.This implies that the flow particles are unlikely to have enough memory of the mean momentum over distance.By assuming the departure from eddy viscosity hypothesis as a result from transportation of the shear stress contained in smaller eddies over distance by the large structures,the present author has arrived at a new shear stress expression.The shear stress estimated so far is in good agreement with the experiments.

Flow体验理论对城郊乡村旅游开发的借鉴和启示——以南京市东郊句容市为例

在乡村振兴大背景下,乡村旅游蓬勃发展,尤其是城郊乡村旅游产品不断丰富,但还存在同质化、旅游者心流体验弱等问题亟待解决。本文以Flow※体验理论为指导,以南京市东郊句容市乡村旅游开发为研究对象,对其现状进行分析,从而提出目前日趋竞争激烈乡村旅游环境下城郊乡村旅游产品开发、创新的应对策略,以期对城郊乡村旅游发展起到指导和借鉴意义。

RESEARCH ON THE BLOCKING FLOW IN A TRANSPORTATION NETWORK──THE GENERAL CONCEPTS AND THEORY OF THE BLOCKING FLOW

Blockage is a kind of phenomenon occurring frequently in modern transportation network. This paper deals with the research work on the blocking now in a network with the help of network flow theory. The blockage phenomena can be divided intO local blockage and network blockage. In this paper, which deals mainly with the latter, the fundamental concepts and definitions of network blocking flow, blocking outset are presented and the related theorems are proved. It is proved that the sufficient and necessary condition for the emergence of a blocking now in a network is the existence of the blocking outset. The necessary conditions for the existence of the blocking outset in a network are analysed and the characteristic cutset of blockage which reflects the all possible situation of blocking nows in the network is defined.In the last part of the paper the mathematical model of the minimum blocking now is developed and the solution to a small network is given.

Simulation of two-dimensional interior ballistics model of solid propellant electrothermal-chem ical launch with discharge rod plasma generator

Instead of the capillary plasma generator(CPG),a discharge rod plasma generator(DRPG)is used in the30 mm electrothermal-chemical(ETC)gun to improve the ignition uniformity of the solid propellant.An axisymmetric two-dimensional interior ballistics model of the solid propellant ETC gun(2D-IB-SPETCG)is presented to describe the process of the ETC launch.Both calculated pressure and projectile muzzle velocity accord well with the experimental results.The feasibility of the 2D-IB-SPETCG model is proved.Depending on the experimental data and initial parameters,detailed distribution of the ballistics parameters can be simulated.With the distribution of pressure and temperature of the gas phase and the propellant,the influence of plasma during the ignition process can be analyzed.Because of the radial flowing plasma,the propellant in the area of the DRPG is ignited within 0.01 ms,while all propellant in the chamber is ignited within 0.09 ms.The radial ignition delay time is much less than the axial delay time.During the ignition process,the radial pressure difference is less than 5 MPa at the place 0.025 m away from the breech.The radial ignition uniformity is proved.The temperature of the gas increases from several thousand K(conventional ignition)to several ten thousand K(plasma ignition).Compare the distribution of the density and temperature of the gas,we know that low density and high temperature gas appears near the exits of the DRPG,while high density and low temperature gas appears at the wall near the breech.The simulation of the 2D-IB-SPETCG model is an effective way to investigate the interior ballistics process of the ETC launch.The 2D-IB-SPETC model can be used for prediction and improvement of experiments.