A semi-analytical pressure and rate transient analysis model for inner boundary and propped fractures exhibiting dynamic behavior under long-term production conditions

The loss of hydrocarbon production caused by the dynamic behavior of the inner boundary and propped fractures under long-term production conditions has been widely reported in recent studies.However,the quantitative relationships for the variations of the inner boundary and propped fractures have not been determined and incorporated in the semi-analytical models for the pressure and rate transient analysis.This work focuses on describing the variations of the inner boundary and propped fractures and capturing the typical characteristics from the pressure transient curves.A generalized semi-analytical model was developed to characterize the dynamic behavior of the inner boundary and propped fractures under long-term production conditions.The pressure-dependent length shrinkage coefficients,which quantify the length changes of the inner zone and propped fractures,are modified and incorporated into this multi-zone semi-analytical model.With simultaneous numerical iterations and numerical inversions in Laplace and real-time space,the transient solutions to pressure and rate behavior are determined in just a few seconds.The dynamic behavior of the inner boundary and propped fractures on transient pressure curves is divided into five periods:fracture bilinear flow(FR1),dynamic PFs flow(FR2),inner-area linear flow(FR3),dynamic inner boundary flow(FR4),and outer-area dominated linear flow(FR5).The early hump during FR2 period and a positive upward shift during FR4period are captured on the log-log pressure transient curves,reflecting the dynamic behavior of the inner boundary and propped fractures during the long-term production period.The transient pressure behavior will exhibit greater positive upward trend and the flow rate will be lower with the shrinkage of the inner boundary.The pressure derivative curve will be upward earlier as the inner boundary shrinks more rapidly.The lower permeability caused by the closure of un-propped fractures in the inner zone results in greater upward in pressure derivative curves.If the permeability loss for the dynamic behavior of the inner boundary caused by the closure of un-propped fractures is neglected,the flow rate will be overestimated in the later production period.

Effect of diagenetic variation on the static and dynamic mechanical behavior of coral reef limestone

Coral reef limestone at different depositional depths and facies differ remarkably on the textural and mineralogical characteristics,owing to the complex sedimentary diagenesis.To explore the effects of pore structure and mineral composition associated with diagenetic variation on the mechanical behavior of reef limestone,a series of quasi-static and dynamic compression tests along with microscopic examinations were performed on the reef limestone at shallow and deep burial depths.It is revealed that the shallow reef limestone(SRL)is classified as a porous aragonite-type carbonate rock with high porosity(55.3±3.2)%and pore connectivity.In comparison,the deep reef limestone(DRL)is mainly composed of dense calcite-type calcium carbonate with low porosity(4.9±1.6)%and pore connectivity.The DRL strengthened and stiffened by the tight grain framework consistently displays much higher values of the dynamic compressive strength,elastic modulus,brittleness index,and specific energy absorption than those of the SRL.The gap between two types of limestone further increases with an increase in strain rate.It appears that the failure pattern of SRL is dominated by the inherent defects like weak bonding interfaces and growth lines,revealed by the intricate fracturing network and mixed failure.Likewise,although the preexisting megapores in DRL may affect the crack propagation on pore tips to a certain distance,it hardly alters the axial splitting failure of DRL under impacts.The stress wave propagation and attenuation in SRL is primarily controlled by the reflection and diffusion caused by plenty mesopores,as well as an energy dissipation in layer-wise pore collapse and adjacent grain crushing,while the stress wave in DRL is highly hinged on the insulation and diffraction induced by the isolated megapores.This process is accompanied by the energy dissipation behavior of inelastic deformation resulted from the pore-emanated microcracking.

Experimental and numerical study on dynamic mechanical behaviors of shale under true triaxial compression at high strain rate

High-energy gas fracturing of shale is a novel,high efficacy and eco-friendly mining technique,which is a typical dynamic perturbing behavior.To effectively extract shale gas,it is important to understand the dynamic mechanical properties of shale.Dynamic experiments on shale subjected to true triaxial compression at different strain rates are first conducted in this research.The dynamic stress-strain curves,peak strain,peak stress and failure modes of shale are investigated.The results of the study indicate that the intermediate principal stress and the minor principal stress have the significant influence on the dynamic mechanical behaviors,although this effect decreases as the strain rate increases.The characteristics of compression-shear failure primarily occur in shale subjected to triaxial compression at high strain rates,which distinguishes it from the fragmentation characteristics observed in shale under dynamic uniaxial compression.Additionally,a numerical three-dimensional Split Hopkinson Pressure Bar(3D-SHPB),which is established by coupling PFC3D and FLAC3D methods,is validated to replicate the laboratory characteristics of shale.The dynamic mechanical characteristics of shale subjected to different confining stresses are systematically investigated by the coupling PFC3D and FLAC3D method.The numerical results are in good agreement with the experimental data.

THE ASYMPTOTIC BEHAVIOR AND OSCILLATION FOR A CLASS OF THIRD-ORDER NONLINEAR DELAY DYNAMIC EQUATIONS

In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existence of eventually positive solutions having upper bounds and tending to zero.Third,we obtain new oscillation criteria by employing the Potzsche chain rule.Then,using the generalized Riccati transformation technique and averaging method,we establish the Philos-type oscillation criteria.Surprisingly,the integral value of the Philos-type oscillation criteria,which guarantees that all unbounded solutions oscillate,is greater than θ_(4)(t_(1),T).The results of Theorem 3.5 and Remark 3.6 are novel.Finally,we offer four examples to illustrate our results.

Experimental study and numerical simulation of the impact of under-sleeper pads on the dynamic and static mechanical behavior of heavy-haul railway ballast track

Laying the under-sleeper pad(USP)is one of the effective measures commonly used to delay ballast degradation and reduce maintenance workload.To explore the impact of application of the USP on the dynamic and static mechanical behavior of the ballast track in the heavy-haul railway system,numerical simulation models of the ballast bed with USP and without USP are presented in this paper by using the discrete element method(DEM)-multi-flexible body dynamic(MFBD)coupling analysis method.The ballast bed support stiffness test and dynamic displacement tests were carried out on the actual operation of a heavy-haul railway line to verify the validity of the models.The results show that using the USP results in a 43.01%reduction in the ballast bed support stiffness and achieves a more uniform distribution of track loads on the sleepers.It effectively reduces the load borne by the sleeper directly under the wheel load,with a 7.89%reduction in the pressure on the sleeper.Furthermore,the laying of the USP changes the lateral resistance sharing ratio of the ballast bed,significantly reducing the stress level of the ballast bed under train loads,with an average stress reduction of 42.19 kPa.It also reduces the plastic displacement of ballast particles and lowers the peak value of rotational angular velocity by about 50%to 70%,which is conducive to slowing down ballast bed settlement deformation and reducing maintenance costs.In summary,laying the USP has a potential value in enhancing the stability and extending the lifespan of the ballast bed in heavy-haul railway systems.

Nonlinear Dynamics Behaviors of a Rotor Roller Bearing System with Radial Clearances and Waviness Considered

A rotor system supported by roller beatings displays very complicated nonlinear behaviors due to nonlinear Hertzian contact forces, radial clearances and bearing waviness. This paper presents nonlinear bearing forces of a roller bearing under four-dimensional loads and establishes 4-DOF dynamics equations of a rotor roller bearing system. The methods of Newmark-β and of Newton-Laphson are used to solve the nonlinear equations. The dynamics behaviors of a rigid rotor system are studied through the bifurcation, the Poincar è maps, the spectrum diagrams and the axis orbit of responses of the system. The results show that the system is liable to undergo instability caused by the quasi-periodic bifurcation, the periodic-doubling bifurcation and chaos routes as the rotational speed increases. Clearances, outer race waviness, inner race waviness, roller waviness, damping, radial forces and unbalanced forces-all these bring a significant influence to bear on the system stability. As the clearance increases, the dynamics behaviors become complicated with the number and the scale of instable regions becoming larger. The vibration frequencies induced by the roller bearing waviness and the orders of the waviness might cause severe vibrations. The system is able to eliminate non-periodic vibration by reasonable choice and optimization of the parameters.

Quasi-static and dynamic tensile behaviors in electron beam welded Ti-6Al-4V alloy

The quasi-static and dynamic tensile behaviors in electron beam welded（EBW） Ti-6Al-4V alloy were investigated at strain rates of 10-3 and 103 s-1,respectively,by materials test system（MTS） and reconstructive Hopkinson bars apparatus.The microstructures of the base metal（BM） and the welded metal（WM） were observed with optical microscope.The fracture characteristics of the BM and WM were characterized with scanning electronic microscope.In Ti-6Al-4V alloy joint,the flow stress of WM is higher than that of BM,while the fracture strain of WM is less than that of BM at strain rates of 103 and 10-3 s-1,respectively.The fracture strain of WM has apparent improvement when the strain rate rises from 10-3 to 103 s-1,while the fracture strain of BM almost has no change.At the same time,the fracture mode of WM alters from brittle to ductile fracture,which causes improvement of the fracture strain of WM.

One-dimensional dynamic compressive behavior of dry calcareous sand at high strain rates

Calcareous sand has distinct characteristics in comparison with silica sand, such as dynamic behavior at high strain rates(HSRs). This is closely related to pile driving, aircraft wheel loading and mining activities. To understand the response of calcareous sand at HSRs, a series of dynamic tests is performed using the split Hopkinson pressure bar(SHPB) with steel sleeve, including 6 validation tests of bar-against-bar and 16 comparative tests relevant to the relative density and strain rate of calcareous and silica sands.The apparent dynamic stiffness of calcareous sand is approximately 10% of that for silica sand due to different particle shapes and mineral compositions. The axial stress-strain response of silica sand is mainly governed by the deformation of individual grain and soil skeleton, and particle crushing. However, porous calcareous sand shows yielding and strain-hardening responses that are always followed by particle crushing. As the applied loading increases, the particle crushing of calcareous sand develops from local instability to whole breakage. Calcareous sand has lower viscous flow effects compared with silica sand at HSRs.

DYNAMIC BEHAVIOR OF A CRACKED FLEXIBLE ROTOR SUPPORTED ON JOURNAL BEARINGS

The dynamic behavior of a cracked flexible rotor supported on three kinds ofjournal bearings is presented. Numerical experiments show that nonsynchronous responseswill happen due to the rotor crack, and the amplitudes of the nonsynchronous componentsbecome larger with the increase of crack. On the other hand, the fluid forces of journalbearings can suppress the nonsynchronous response. The (1/2) × or (3/2) × harmoniccomponent rarely appears for small crack near the rotating speed ratio Ω = 2Ωc or Ω =(2/3)Ωc. In the case of supercritical rotating speed, the additional 0× harmonic component is increased as the crack increases. The bearing parameters affect greatly the occur-rence of the nonsynchronous responses by means of exerting innuence on the critical spedand the stabi1ity of the system.

Dynamic changes of behaviors, dentate gyrus neurogenesis and hippocampal miR-124 expression in rats with depression induced by chronic unpredictable mild stress

The depression-like behavior phenotype,neurogenesis in the dentate gyrus and miR-124 expression in the hippocampus are the focus of current research on the pathogenesis of depression and antidepressant therapy.The present study aimed to clarify the dynamic changes of depression-like behavior,dentate gyrus neurogenesis and hippocampal miR-124 expression during depression induced by chronic stress to reveal pathological features at different stages of depression and to further provide insight into depression treatment.Chronic unpredictable mild stress depression models were established by exposing Sprague-Dawley rats to various mild stressors,including white noise,thermal swimming,stroboscopic illumination,soiled cages,pairing with three other stressed animals,cold swimming,tail pinch,restraint and water and food deprivation.Chronic unpredictable mild stress model rats underwent dynamic observation from 1 to 8 weeks and were compared with a control group(normal feeding without any stressors).To observe changes in the depression-like behavior phenotype during chronic unpredictable mild stress-induced depression,a sucrose preference test was used to evaluate the degree of anhedonia.An open-field test was used to evaluate locomotor activity and anxiety status.Compared with the control group,chronic unpredictable mild stress rats lost weight but did not have a depression-like behavioral phenotype at 1-4 weeks.Chronic unpredictable mild stress rats presented decreased sucrose preference and locomotor activity at 5-8 weeks.In addition,chronic unpredictable mild stress rats did not have significant anxiety-like behavior during 1-8 weeks of modeling.To observe neurogenesis dysfunctions and changes in neuronal number in the dentate gyrus during chronic unpredictable mild stress-induced depression,markers(DCX and DCX/BrdU)of neural proliferation and differentiation and the neuronal marker NeuN were assessed by immunofluorescence.Compared with the control group,neurogenesis and the neuronal number in the dentate gyrus did not change from 2 to 6 weeks;however,neural proliferation and differentiation in the dentate gyrus decreased,and the number of neurons decreased until the eighth week in the chronic unpredictable mild stress group.Real-time quantitative reverse transcription polymerase chain reaction assays and fluorescence in situ hybridization were used to measure the expression of hippocampal miR-124 during chronic unpredictable mild stress-induced depression.The results showed that the expression of hippocampal miR-124 was unchanged during the first 4 weeks but increased from 5 to 6 weeks and decreased from 7 to 8 weeks compared with the control group.These findings indicate that during chronic unpredictable mild stress-induced depression,the behavioral phenotype,miR-124 expression in the hippocampus,neurogenesis in the dentate gyrus and neuronal numbers showed dynamic changes,which suggested that various pathological changes occur at different stages of depression.All experimental procedures and protocols were approved by the Experimental Animal Ethics Committee of Guangzhou University of Chinese Medicine of China in March 2015.

Dynamic Tensile Behavior and Constitutive Modeling of TC21 Titanium Alloy

The dynamic tensile behaviors of a newly developed Ti-6 Al-2 Sn-2 Zr-3 Mo-1 Cr-2 Nb-Si alloy（referred as TC21 in China） over a wide range of strain rates from quasi-static to dynamic regimes(0.001-1 200 s-1) at different temperatures were experimentally investigated. A split Hopkinson tension bar apparatus and a static material testing system were utilized to study the stress-strain responses under uniaxial tension loading condition. The experimental results indicate that the tensile behavior of TC21 titanium alloy is dependent on the strain rate and temperature. The values of initial yield stress increase with increasing strain rate and decreasing temperature. The effects of strain rate and temperature on the initial yield behavior are estimated by introducing two sensitivity parameters. The phenomenological-based constitutive model, Johnson-Cook model, is suitably modified to describe the rate-temperature dependent constitutive behavior of TC21 titanium alloy. It is observed that the modified model is in good agreement with the experimental data subjected to the investigated range of strain rates and temperatures.

DYNAMIC RHEOLOGICAL BEHAVIOR OF POLYPROPYLENE FILLED WITH ULTRA-FINE POWDERED RUBBER PARTICLES

Dynamic rheological characteristics of polypropylene (PP) filled with ultra-fine full-vulcanized powdered rubber (UFPR) composed of styrene-butadiene copolymer were studied through dynamic rheological measurements on an Advanced Rheometric Expansion System (ARES). A specific viscoelastic phenomenon, i.e. 'the second plateau', appeared at low frequencies, and exhibits a certain dependence on the amount of rubber particles and the dispersion state in the matrix. This phenomenon is attributed to the formation of aggregation structure of rubber particles. The analyses of Cole-Cole diagrams of the dynamic viscoelastic functions suggest that the heterogeneity of the composites is enhanced on increasing both particle content and temperature.

Dynamic Behavior Analysis of Finger Seal Based on Equivalent Dynamic Model

Finger seal is a new technology developed for gas path sealing in gas turbine engine.It has been paid attention to its good sealing performance and lower manufacture cost.The vibration behavior of finger seal is not be considered in performance analysis for the contact finger seal with compliant geometric configuration,then this will influence the reliability of the performance analysis and the parametric design of a finger seal.According to the dynamic character of finger seal,the harmonic vibration and free vibration models of a repetitive section of a two-layer finger seal that contains one high and one low finger seal are established separately.The dynamic behavior of finger seal in different working conditions is obtained based on the dynamic response analysis of finger＇s vibrations.The dynamic low hysteresis and low wear terms based on the equivalent dynamic model of finger seal are put forward,which can be used to predict the dynamic behavior of finger seal.As an example,the dynamic behaviors of an 8-layer finger seal and a 10-layer finger seal were predicted,and the validity of the prediction was demonstrated by the leakage test results of these two finger seals.The work presented here not only could make the dynamic analysis of finger seal with complicated structure simple and easy especially for multi-layer finger seal system,but also suggest a useful method for designing the finger seal with good dynamic behavior by means of different seal layers assembly.

QUALITATIVE ANALYSIS OF DYNAMICAL BEHAVIOR FOR AN IMPERFECT INCOMPRESSIBLE NEO-HOOKEAN SPHERICAL SHELL

The radial symmetric motion problem was examined for a spherical shell composed of a class of imperfect incompressible hyper-elastic materials, in which the materials may be viewed as the homogeneous incompressible isotropic neo-Hookean material with radial perturbations. A second-order nonlinear ordinary differential equation that describes the radial motion of the inner surface of the shell was obtained. And the first integral of the equation was then carded out. Via analyzing the dynamical properties of the solution of the differential equation, the effects of the prescribed imperfection parameter of the material and the ratio of the inner and the outer radii of the underformed shell on the motion of the inner surface of the shell were discussed, and the corresponding numerical examples were carded out simultaneously. In particular, for some given parameters, it was proved that, there exists a positive critical value, and the motion of the inner surface with respect to time will present a nonlinear periodic oscillation as the difference between the inner and the outer presses does not exceed the critical value. However, as the difference exceeds the critical value, the motion of the inner surface with respect to time will increase infinitely. That is to say, the shell will be destroyed ultimately.

Dynamic Analysis of Hydrodynamic Behavior of A Flatfish Cage System Under Wave Conditions

This paper presents a simulation model based on the finite element method. The method is used to analyze the motion response and mooring line tension of the flatfish cage system in waves. The cage system consists of top frames, netting, mooring lines, bottom frames, and floats. A series of scaled physical model tests in regular waves are conducted to verify the numerical model. The comparison results show that the simulated and the experimental results agree well under the wave conditions, and the maximum pitch of the bottom frame with two orientations is about 12o. The motion process of the whole cage system in the wave can be described with the computer visualized technology. Then, the mooring line tensions and the motion of the bottom frame with three kinds of weight are calculated under different wave conditions. According to the numerical results, the differences in mooring line tensions of flatfish cages with three weight modes are indistinct. The maximum pitch of the bottom frame decreases with the increase of the bottom weight.

Dynamic Behaviors of A Marine Riser Under Two Different Frequency Parametric Excitations

The marine risers are often subjected to parametric excitations from the fluctuation top tension. The top tension on the riser may fluctuate with multiple frequencies caused by irregular waves. In this paper, the influence between different frequency components in the top tension on the riser system is theoretically simulated and analyzed. With the Euler-Bernoulli beam theory, a dynamic model for the vibrations of the riser is established. The top tension is set as fluctuating with time and it has two different frequencies. The influences from the fluctuation amplitudes, circular frequencies and phase angles of these frequency components on the riser system are analyzed in detail. When these two frequencies are fluctuating in the stable regions, the riser system may become unstable because ω1+ω2≈2Ωn. The fluctuation amplitudes of these frequencies have little effect on the components of the vibration frequencies of the riser. For different phase angles, the stability and dynamic behaviors of the riser would be different.

THE DYNAMICAL BEHAVIOR OF FULLY DISCRETE SPECTRAL METHOD FOR NONLINEAR SCHRODINGER EQUATION WITH WEAKLY DAMPED

Nonlinear Schrodinger equation (NSE) arises in many physical problems. It is a very important equation. A lot of works studied the wellposed, the existence of solution of NSE etc. And there are many works studied the numerical methods for it. Recently, since the development of infinite dimensional dynamic system the dynamical behavior of NSE has been investigated. The paper [1] studied the long time wellposedness, the existence of universal attractor and the estimate of Lyapunov exponent for NSE with weakly damped. At the same time it was need to study the large time new computational methods and to discuss its convergence error estimate, the existence of approximate attractors etc. In this pape we study the NSE with weakly damped (1.1). We assume,where 0【λ【2 is a constant. If we wish to construct the higher accuracy computational scheme, it will be difficult that staigh from the equation (1.1). Therefore we start with (1. 4) and use fully discrete Fourier spectral method with time difference to

Experimental and numerical investigations on the tensile mechanical behavior of marbles containing dynamic damage

To investigate the degradation mechanism of static tensile mechanical behaviors of marble containing dynamic damage,multiple impact loading tests were performed on the disc marble samples,and then static Brazilian tests were conducted for the damaged samples.Besides,coupling modeling technology of finite difference method(FDM)—discrete element method(DEM)was used to carry out the numerical investigation.The results show that after multiple impacts,more white patches appear on the surface,and some microcracks,macro-fractures as well as pulverized grains are found by optical microscopic.The static tensile strength decreases with the increase of the dynamic damage variable characterized by the ultrasonic wave velocity of sample.The interaction between grains in the damaged sample becomes intense in the subsequent static loading process,causing a relatively large strain.The volume of the fragments falling off around the loading points becomes larger as impact number increases.As the dynamic damage increases,the absorbed energy of sample during the static loading first decreases and then tends to be stable.Both the stress concentration and the breakage of the force chains are the root causes of the degradation of the static tensile strength.

Dynamic behavior of bridge-erecting machine subjected to moving mass suspended by wire ropes

The dynamic behavior of a bridge-erecting machine, carrying a moving mass suspended by a wire rope, is investigated. The bridge-erecting machine is modelled by a simply supported uniform beam, and a massless equivalent ＂spring-damper＂ system with an effective spring constant and an effective damping coefficient is used to model the moving mass suspended by the wire rope. The suddenly applied load is represented by a unitary Dirac Delta function. With the expansion method, a simple closed-form solution for the equation of motion with the replaced spring-damper-mass system is formulated. The characters of the rope are included in the derivation of the differential equation of motion for the system. The numerical examples show that the effects of the damping coefficient and the spring constant of the rope on the deflection have significant variations with the loading frequency. The effects of the damping coefficient and the spring constant under different beam lengths are also examined. The obtained results validate the presented approach, and provide significant references in the design process of bridgeerecting machines.

Dynamic Mechanical Behavior of a Novel Polymeric Composite Damping Material

The dynamic mechanical behavior of a novel polymeric composite damping material has been investigated in this article. The composite consists of chlorinated polyethylene （CPE）, N,N-dicyclohexyl-2-benzothiazolylsufenamide （DZ）, 4,4＇-thio-bis（3-methyl-6-tert-buthylphenol） （BPSR） and vapor-grown carbon fiber （VGCF）. It is found that either the position or the intensity of damping peak can be controlled by changing the composition of CPE/DZ/BPSR composite. Within a certain composition region, damping peak maximum depends on CPE/DZ ratio, whereas damping peak position is controlled by BPSR content. Moreover, the improvement of storage modulus can be achieved by incorporation of VGCF. These results may imply that a damping material possessing both good damping properties and high strength can be designed and obtained.