A New Analytical Approximation for the Flow into a Well in a Finite Reservoir

A new approach is presented for the pressure calculation around a horizontal well or a partially penetrating vertical well in a finite height reservoir. The new method matches the asymptotic solutions close to- and far from the well. To this end, the reservoir is divided into two distinct volumes with ellipsoidal and elliptically cylindrical symmetry, respectively. Comparison with other techniques shows that the new expressions yield excellent results. The method is also applicable to reservoirs containing one elliptical, vertical or horizontal fracture, and can be used with account of a zone of altered permeability around the well or fracture due to formation damage or stimulation.     

Nonlinear Schrdinger equation with combined power-type nonlinearities and harmonic potential

This paper discusses a class of nonlinear Schrdinger equations with combined power-type nonlinearities and harmonic potential. By constructing a variational problem the potential well method is applied. The structure of the potential well and the properties of the depth function are given. The invariance of some sets for the problem is shown. It is proven that, if the initial data are in the potential well or out of it, the solutions will lie in the potential well or lie out of it, respectively. By the convexity method, the sharp condition of the global well-posedness is given.     

Nonlinear Schrodinger equation with combined power-type nonlinearities and harmonic potential

This paper discusses a class of nonlinear Schrodinger equations with combined power-type nonlinearities and harmonic potential.By constructing a variational problem the potential well method is applied.The structure of the potential well and the properties of the depth function are given.The invariance of some sets for the problem is shown.It is proven that,if the initial data are in the potential well or out of it,the solutions will lie in the potential well or lie out of it,respectively.By the convexity method,the sharp condition of the global well-posedness is given.     

Wall shape effects on multiphase flow in channels

Two-fluid flow is examined analytically and numerically for increased flow rates through a channel with surface roughness or branching or both. The viscosity and density ratios of the fluids are of order unity. There is much concern in terms of applications as well as fluid dynamical phenomena in configurations where one fluid is present only as a thin layer near an outer wall, leaving the other fluid occupying the channel core and part of a viscous wall layer. The interactive dynamics in both regions is studied and numerical and asymptotic analyses are performed. The major situations examined are: the flow to two symmetrically bifurcating daughters and the flow in a single channel over a rough wall, as well as a combination of the two situations. The principal phenomena of interest are conditions for flow reversal, the presence of upstream influence and the trajectories of the injected fluid as the density or viscosity ratio varies. Special relatively thin or thinning wall layers are produced when the core fluid viscosity increases or when the fluid travels downstream into a daughter vessel.     

Deformation, stress state and thermodynamic force for a growing void in an elastic–plastic material

The growth of a spherical void in an elastic–plastic body, subjected to external pressure or tension and a gas pressure as well as a surface stress at the void surface, is investigated. The deformation, strain and stress state in the full body is presented. In addition, the local and global energy terms are calculated. Finally the total thermodynamic force on the void surface as well as the total dissipation are evaluated and compared allowing the calculation of the mechanical contribution to void growth due to diffusion of vacancies generated by plastification or irradiation.     

Method of Selective Injection of Chemical Reactants into a Inhomogeneous Layered Reservoir

The unsteady process of homogeneous compressible fluid flow through a porous weakly deformable inhomogeneous layered reservoir is considered in the absence of a hydrodynamic connection between the layers. A method of selective injection of chemical reactants into high- or low-permeability parts of the reservoir based on fluid injection at a rate determined by the intensity of the well-bore crossflows after the shutting-in of the well is proposed. This method makes it possible to inject a fixed quantity of reactant, determined by the reservoir system parameters and the well operating regime, into the high- or, conversely, low-permeability layers.     

TWO－PHASE FLOW FOR A HORIZONTAL WELL PENETRATING A NATURALLY FRACTURED RESERVOIR WITH EDGE WATER INJECTION

ＴＷＯ－ＰＨＡＳＥＦＬＯＷＦＯＲＡＨＯＲＩＺＯＮＴＡＬＷＥＬＬＰＥＮＥＴＲＡＴＩＮＧＡＮＡＴＵＲＡＬＬＹＦＲＡＣＴＵＲＥＤＲＥＳＥＲＶＯＩＲＷＩＴＨＥＤＧＥＷＡＴＥＲＩＮＪＥＣＴＩＯＮＧｕｏＤａｌｉ（郭大立）ＬｉｕＣｉｑｕｎ（刘慈群）（Ｒｅｃｅｉｖｃ...     

Two-phase flow for a horizontal well penetrating a naturally fractured reservoir with edge water injection

This paper examines the two-phase flow for a horizontal well penetrating a naturally fractured reservoir with edge water injection by means of a fixed streamline model. The mathematical model of the vertical two-dimensional flow or oil-water for a horizontal well in a medium with double-porosity is established, and whose accurate solutions are obtained by using the characteristic method. The saturation distributions in the fractured system and the matrix system as well as the formula of the time of water free production are presented. All these results provide a theoretical basis and a computing method for oil displacement by edge water from naturally fractured reservoirs.     

A Review of Speckle Pattern Fabrication and Assessment for Digital Image Correlation

As a carrier of deformation information, the speckle pattern, or more exactly the random intensity distributions, which could be naturally occurred or artificially fabricated onto test samples’ surface, plays an indispensable role in digital image correlation (DIC). It is now well recognized that the accuracy and precision in DIC measurements not only rely on correlation algorithms, but also depend highly on the quality of the speckle pattern. Considering the huge diversity in test materials, spatial scales and experimental conditions, speckle pattern fabrication could be a challenging issue facing DIC practitioners. To obtain good speckle patterns suitable for DIC measurements, some key issues of fabrication methods and quality assessment of speckle patterns must be well addressed. To this end, this review systematically presents the speckle pattern classification and fabrication techniques for various samples and scales, as well as some typical quality assessment metrics.     

Critical damping for well oscillations. A theoretical investigation

The oscillations of water in a well in a leaky aquifer might be subcritically or supercritically damped. The theory of well oscillations has turned out to be a special case of a general theory of damped motion of pendulums. In the case of a well in a leaky aquifer, the criterion for critical damping is a simple power expression that relates the leakage factor and the storativity of the aquifer and where the exponent is a function of the transmissivity of the aquifer. If the damping is critical and the leakage is extremely small, so the storativity has to be. If the aquifer is non leaking, the damping cannot be supercritical.     

TWO－PHASE FLOW FOR A HORIZONTAL WELL PENETRATING A NATURALLY FRACTURED RESERVOIR WITH EDGE WATER INJECTION

ＴＷＯ－ＰＨＡＳＥＦＬＯＷＦＯＲＡＨＯＲＩＺＯＮＴＡＬＷＥＬＬＰＥＮＥＴＲＡＴＩＮＧＡＮＡＴＵＲＡＬＬＹＦＲＡＣＴＵＲＥＤＲＥＳＥＲＶＯＩＲＷＩＴＨＥＤＧＥＷＡＴＥＲＩＮＪＥＣＴＩＯＮＧｕｏＤａｌｉ（郭大立）ＬｉｕＣｉｑｕｎ（刘慈群）（Ｒｅｃｅｉｖｅ...     

AN UPPER BOUND ON RANDOM BUFFETING FORCES CAUSED BY TWO-PHASE FLOWS ACROSS TUBES

This paper investigates the random buffeting excitation forces that apply to tubes in two-phase cross-flows. The spectral magnitude of these forces is studied with the help of a database that includes most of the available experimental data on direct or indirect force measurements. Different fluid mixtures, namely steam–water, air–water and various types of Freon, as well as different thermohydraulic or geometrical situations are included in the database. Using a formalism similar in principle to that used successfully in the modelling of buffeting in single-phase flows, the scaling of the data is undertaken. While dynamic pressure, viscosity or surface tension are found not to be relevant parameters, gravity forces allow us to define appropriate dimensionless spectra for all cases. The meaning of these parameters as well as the effects of flow regimes or fluid mixtures are discussed. Finally, an upper bound on the magnitude of these forces, which is of practical applicability, is proposed.     

Friedrichs systems for systems of wave equations and shear waves in a three-dimensional elastic medium

This paper considers a two-dimensional hydraulic model which describes gas or oil flow to a horizontal well with hydraulic fractures and takes into account the reservoir geometry and fluid flow between the reservoir and the well. A computational algorithm is proposed, and calculations for gas and oil reservoirs are performed. A comparison of the calculation results and the solutions of the corresponding problems in a three-dimensional formulation show that the calculations using the approximate hydraulic model yield reasonably accurate results.     

Hydraulic model for oil and gas reservoirs

This paper considers a two-dimensional hydraulic model which describes gas or oil flow to a horizontal well with hydraulic fractures and takes into account the reservoir geometry and fluid flow between the reservoir and the well. A computational algorithm is proposed, and calculations for gas and oil reservoirs are performed. A comparison of the calculation results and the solutions of the corresponding problems in a three-dimensional formulation show that the calculations using the approximate hydraulic model yield reasonably accurate results.     

均匀流量假设下分枝水平井的产能公式

将分枝水平井视为垂直裂缝，在均匀流量假设下，利用复变函数理论推导出了当分枝数分别为1和2时的分枝水平井产能公式。证明了在均匀流量假设下垂直裂缝相当的折算半径与导流能力为无限大的相比减少12％。     

Spin-up and wrapping of cryogenic helium bubble around dewar well from rest in microgravity

Time dependent animation of spherically shaped bubble sitting at one-side of the dewar container, which is spin-up from rest to certain rotating speed of interests, has been investigated. Time dependent deformation of bubble with or without a completion of wrapping around the inner well of the rotating dewar, are numerically studied and simulated. Some similarity parameters are considered for a completion of bubble wrapping around the dewar well. Illustrative examples show that the degree of the completion of bubble wrapping around the dewar well increases with increasing container rotating speed and Weber number.     

Generating line spectra from experimental responses. Part II: Storage and loss functions

A computer algorithm is described which allows the determination of a discrete distribution of relaxation times from simulated or smoothed storage or loss modulus data, or of retardation times from simulated or smoothed storage or loss compliance data. The distributions faithfully reproduce the input data and are suitable for data storage as well as for generating any other response curves.     

A Well in a ??Target?? Stratum of a Two-Layered Formation: The Muskat?CRiesenkampf Solution Revisited

Explicit analytical solutions are obtained in terms of hydraulic head (pressure) and Darcian velocity for a steady Darcian flow to a point/line sink and array of sinks with refraction of streamlines on a horizontal interface between two layers of constant hydraulic conductivities. The sinks are placed in a ??target?? layer between a constant potential plane and interface. An equipotential surface, encompassing the sink represents a horizontal or vertical well, is reconstructed as a quasi-cylinder or quasi-sphere. The method of electrostatic images and theory of holomorphic functions are employed for obtaining series expansion solutions of two conjugated Laplace equations. If the conductivity of the ??target?? layer is less than that of the super/sub-stratum, then there is a minimum of the flow rate into the well of a given size. Applications to agricultural drainage and surface DC-electrical resistivity surveying are discussed.     

Chaotic thresholds for the piecewise linear discontinuous system with multiple well potentials

In this paper we investigate the bifurcations and the chaos of a piecewise linear discontinuous (PWLD) system based upon a rig-coupled SD oscillator, which can be smooth or discontinuous (SD) depending on the value of a system parameter, proposed in [18], showing the equilibrium bifurcations and the transitions between single, double and triple well dynamics for smooth regions. All solutions of the perturbed PWLD system, including equilibria, periodic orbits and homoclinic-like and heteroclinic-like orbits, are obtained and also the chaotic solutions are given analytically for this system. This allows us to employ the Melnikov method to detect the chaotic criterion analytically from the breaking of the homoclinic-like and heteroclinic-like orbits in the presence of viscous damping and an external harmonic driving force. The results presented here in this paper show the complicated dynamics for PWLD system of the subharmonic solutions, chaotic solutions and the coexistence of multiple solutions for the single well system, double well system and the triple well dynamics.