UNSTEADY FLOW OF NON-NEWTONIAN VISCO-ELASTIC FLUID IN DUAL-POROSITY MEDIA WITH THE FRACTIONAL DERIVATIVE

The fractional order derivative was introduced to the seepage flow research to establish the relaxation models of non-Newtonian viscoelastic fluids in dual porous media. The flow characteristics of non-Newtonian viscoelastic fluids through a dual porous medium were studied by using the Hankel transform, the discrete Laplace transform of sequential fractional derivatives and the generalized Mittag-Leffler function. Exact solutions were obtained for arbitrary fractional order derivative. The long-time and short-time asymptotic solutions for an infinite formation were also resulted. The pressure transient behavior of non-Newtonian viscoelastic fluids flow through an infinite dual porous media was studied by using Stehfest's inversion method of the numerical Laplace transform. It shows that the characteristics of the fluid flow are appreciably affected by the order of the fractional derivative.     

INVESTIGATION OF THE FLOW IN FRACTAL RESERVOIR INCLUDING THE EFFECTS OF QUADRATIC GRADIENT TERM

According to the assumption of slightly compressible fluid, the quadratic gradient term in the nonlinear partial differential equations for the traditional well-test model is usually neglected. The linear partial differential equation is thus established. It is known that neglecting the quadratic gradient term results in errors for long-time well tests. A nonlinear flow model for fractal medium is constructed and the quadratic gradient term is considered. The exact solutions of the fractal reservoir models are obtained by Laplace transform and Weber transform in a constant-rate and constant-pressure production for an infinitely large system. This paper addresses the variation of pressure with fluid compressibility coefficient and fractal reservoir parameters. The plots of the typical pressure curves are constructed, and the results can be applied to well-test analysis.     

THE SIMILAR STRUCTURE OF SOLUTIONS IN FRACTAL MUITILAYER RESERVOIR INCLUDING A QUADRATIC GRADIENT TERM

When the classical nonlinear partial differential equations are used to model the fractal reservoir, based on the assumption of low compressibility fluids, the effects of the quadratic gradient term are ignored, which would be questionable for mixed gas reservoirs and low permeability reservoirs. To consider the influence of the wellbore storage, the nonlinear mathematical flow model of the fractal multilayer reservoir is built in this paper, with three kinds of outer boundaries (infinite boundaries, constant pressure boundaries and closed boundaries). Using the Laplace transform method, the solutions for the dimensionless reservoir pressure and the bottom hole pressure in the Laplace space are obtained. An analysis shows that the solutions involve similar structures even for three different kinds of outer boundaries, and can be unified as a continuous fraction. The unified expression would make it more convenient to analyze the formation parameters, which greatly facilitates the development of the well test analysis software.     

THE PRESSURE TRANSIENT ANALYSIS OF DEFORMATION OF FRACTAL MEDIUM

The assumption of constant rock properties in pressure-transient analysis of stress-sensitive reservoirs can cause significant errors in the estimation of temporal and spatial variation of pressure. In this article, the pressure transient response of the fractal medium in stress-sensitive reservoirs was studied by using the self-similarity solution method and the regular perturbation method. The dependence of permeability on pore pressure makes the flow equation strongly nonlinear. The nonlinearities associated with the governing equation become weaker by using the logarithm transformation. The perturbation solutions for a constant pressure production and a constant rate production of a linear-source well were obtained by using the self-similarity solution method and the regular perturbation method in an infinitely large system, and inquire into the changing rule of pressure when the fractal and deformation parameters change. The plots of typical pressure curves were given in a few cases, and the results can be applied to well test analysis.     

THE STRUCTURAL FLOW IN PIPE CONTAINING POROUS MEDIUM SATURATED WITH POWER-LAW FLUID

In this article,the method of volume averaging of flow in porous media and averaging theorem was employed to the Navier-Stokes equations.The total drag force per unit volume was considered as the bulk damping resistance due to the porous structure(i.e.,the Darcy resistance)and the resistance due to the inertia force(i.e.,the Forchheimer resistance),then the Brinkman-Forchheimer extended Darcy model was obtained from average momentum equation.The structural flow in a pipe containing porous medium saturated with power law fluid was applied in the present study.A new theoretical analysis of fully developed non-Darcy flow in a pipe containing a fibrous medium saturated with power law fluid was conducted.Using the integration method,the boundary layer solutions were obtained for flow core velocity and its radius.These theoretical solutions were used to analyze the effects of the Darcy number and inertia parameter on the axial velocity profile in the porous medium pipe.     

RADICAL FLOW IN POROUS MEDIA WITH DISPERSION AND ADSORPTION

The radical transport of chemical concentration in porous media with dispersion and adsorption was studied in this paper. Using Langmuir‘s adsorption model, the numeri cal equation of concentration transport was derived. The flows with and without adsorption were simulated and analyzed. Comparison of the obtained solution with the known analytical solution for flow without adsorption shows the presented numerical method is correct and effective, which can be used in reservoir engineering     

THE ANALYSIS OF THE STEADY FLOW IN THE FLOW CHAMBER

A flow chamber whose length and width are far larger than its own height was widely used to study cell's mechanical behavior in vitro , especially the cell's adhesion property. The paper analyzed the flow field of the flow chamber in detail, and gave the analytical expressions of the velocity, pressure and shear stress when the fluid flowed in and out the chamber through a small crevice. Then, full and clear discussion of flow field was made. Also the velocity field was measured by an Ultrasonic Doppler Velocity-metre. It was found that the experimental values coincided with the theoretical values. These results were important to study the cell's mechanical behavior in vitro .     

ANALYSIS OF PULSATILE FLOW IN THE PARALLEL-PLATE FLOW CHAMBER WITH SPATIAL SHEAR STRESS GRADIENT

The Parallel-Plate Flow Chamber (PPFC), of which the height is far smaller than its own length and width, is one of the main apparatus for the in-vitro study of the mechanical behavior of cultured vascular Endothelical Cells (ECs) exposed to fluid shear stress. The steady flow in different kinds of PPFC has been extensively investigated, whereas, the pulsatile flow in the PPFC has received little attention. In consideration of the characteristics of geometrical size and pulsatile flow in the PPFC, the 3-D pulsatile flow was decomposed into a 2-D pulsatile flow in the vertical plane, and an incompressible plane potential flow in the horizontal plane. A simple method was then proposed to analyze the pulsatile flow in the PPFC with spatial shear stress gradient. On the basis of the method, the pulsatile fluid shear stresses in several reported PPFCs with spatial shear stress gradients were calculated. The results were theoretically meaningful for applying the PPFCs in-vitro, to simulate the pulsatile fluid shear stress environment, to which cultured ECs were exposed.     

NUMERICAL ANALYSIS OF THE NON-NEWTONIAN BLOOD FLOW IN THE NON-PLANAR ARTERY WITH BIFURCATION

A numerical analysis of non-Newtonian fluid flow in non-planar artery with bifurcation was performed by using a finite element method to solve the three-dimensional Navier-Stokes equations coupled with the non-Newtonian constitutive models, including Carreau, Cross and Bingham models. The objective of this study is to investigate the effects of the non-Newtonian properties of blood as well as curvature and out-of-plane geometry in the non-planar daughter vessels on the velocity distribution and wall shear stress. The results of this study support the view that the non-planarity of blood vessels and the non-Newtonian properties of blood are of important in hemodynamics and play a significant role in vascular biology and pathophysiology.     

EXACT SOLUTION FOR SPHERICAL FLOW AND TRANSIENT BEHAVIOR OF PRESSURE WITH CONSIDERATION OF EFFECTS OF QUADRATIC-GRADIENT TERM

1 .　ＩＮＴＲＯＤＵＣＴＩＯＮＰｒｅｓｓｕｒｅｄｉｓｔｒｉｂｕｔｉｏｎｓａｒｏｕｎｄ ｐｒｏｄｕｃｔｉｏｎａｎｄｉｎ ｊｅｃｔｉｏｎｗｅｌｌｓａｒｅｏｆｇｒｅａｔｉｍｐｏｒｔａｎｃｅｉｎｈｙｄｒｏｌｏｇｙａｎｄｐｅｔｒｏｌｅｕｍｒｅｓｅｒｖｏｉｒｅｎｇｉｎｅｅｒｉｎｇ .Ｂｅｃａｕｓｅｏｆｔｈｅｐｒｅｓ ｅｎｃｅｏｆｔｈｅｑｕａｄｒａｔｉｃｐｒｅｓｓｕｒｅ ｇｒａｄｉｅｎｔｔｅｒｍ ,ｔｈｅｐａｒ ｔｉａｌｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｄｅｓｃｒｉｂｉｎｇｔｈｅｐｒｅｓｓｕｒｅｄｉｓｔｒｉ ｂｕ…     

THEORY OF FLUID-SOLID COUPLED FLOW THROUGH FRACTURED LOW-PERMEABILITY OIL RESERVOIR AND ITS APPLICATIONS

ＢＲＩＥＦＩＮＴＲＯＤＵＣＴＩＯＮＯＦＴＨＥＰＡＰＥＲ :　Ｔｈｅｆｒａｃｔｕｒｅｄｌｏｗ ｐｅｒｍｅａｂｉｌｉｔｙｏｉｌｒｅｓｅｒｖｏｉｒｗｉｌｌｂｅａｍａ ｊｏｒｆｕｔｕｒｅｅｎｅｒｇｙｓｏｕｒｃｅａｓｃｏｎｖｅｎｔｉｏｎａｌｏｉｌｐｒｏｄｕｃｔｉｏｎｒａｔｅｓｇｒａｄｕａｌｌｙｄｅｌｉｎｅ .Ｄｕｒｉｎｇｔｈｅｗａｔｅｒ ｆｌｏｏｄｄｅｖｅｌ ｏｐｍｅｎｔｏｆｔｈｉｓｋｉｎｄｏｆｏｉｌｒｅｓｅｒｖｏｉｒ,ｔｈｅｉｎｔｅｒａｃｔｉｏｎｂｅｔｗｅｅｎｆｌｕｉｄｆｌｏｗａｎｄｒｏｃｋ ｍａｓｓｄｅｆｏｒｍ…     

不稳定渗流浸润线计算在梦山水库的应用

以江西省新建县梦山水库为例,阐述了均质土坝(设计前)和砼心墙坝(设计后)的不稳定渗流浸润线计算的过程,并对计算结果进行了分析.     

ANALYSIS OF EDL EFFECTS ON THE FLOW AND FLOW STABILITY IN MICROCHANNELS

The effects of the Electrical Double Layer (EDL) on the liquid mean flow and the flow stability in microchannels are investigated by solving the Poisson-Boltzmann equation. The models of the traditional streaming Electrical Current Balance (ECB) and the newly introduced streaming Electrical Current Density Balance (ECDB) are applied to determine the electrical streaming current. The numerical results show that the electrical streaming current backflow in the ECB model near the wall can be removed by using the ECDB model, which is suitable to study the effects of the EDL on the mean flow and the flow stability in microchannels. The flow is found more unstable if the ECDB model is applied.     

A STUDY ON TRANSIENT FLUID FLOW OF HORIZONTAL WELLS IN DUAL-PERMEABILITY MEDIA

To adopt horizontal wells in dual media reservoirs,a good understanding of the related fluid flows is necessary.Most of the recent studies focus on dual porosity media instead of dual permeability media.In this article,through both integral transformation and sink-source superposition,a new Laplace-domain solution is obtained for the slightly-compressible fluid flow in the 3-D dual-permeability media in which the horizontal well is operating in a constant rate of production.Major asymptotic characteristics of diagnosis curves of dimensionless downhole pressure are analyzed by the limited analysis.Effects of parameters of dual-permeability media including mobility ratio κ,storativity ratio ω and inter-porosity flow parameter κ on the downhole pressure are studied by using the Laplace numerical inversion.The new solution obtained in this article includes and improves the previous results and then can be used as a basis for either pressure transient analysis or formation behavior evaluation for the typical reservoir with horizontal wells.     

ANALYSIS OF TWO-PHASE FLOW PRESSURE BUILDUP DATA FROM WELL IN AN INFINITE MULTIWELL RESERVOIR

A general method has been developed for analyzing two-phase flow pressure buildup data from a well located in a system of both production and injection wells completed in an infinite muhiwell reservoir. The analysis technique assumes that the tested well has established its own drainage area before shut-in and a linear reservoir pressure trend dominates the well pressure behavior at the instant of shut-in. And for the two-phase flow problems the horizontal saturation gradients are assumed to be negligible. The entire pressure rcsponse, whether or not conventional semilog straight lines exist, can be analyzed and the Injection-Production Ratio （IPR）, the total fluid （oil/water） mobility, the average drainage-area pressure, and also the skin factor can be calculated much easily. The validity and applicability of the method are demonstrated by a field example. The technique by using the type curves for analyzing the pressure-buildup data is also presented here.     

STOCHASTIC ANALYSIS OF UNSATURATED FLOW WITH THE NORMAL DISTRIBUTION OF SOIL HYDRAULIC CONDUCTIVITY

Stochastic approaches are useful to quantitatively describe transport behavior over large temporal and spatial scales while accounting for the influence of small-scale variabilities. Numerous solutions have been developed for unsatu-rated soil water flow based on the lognormal distribution of soil hydraulic conductivity. To our knowledge, no available stochastic solutions for unsaturated flow have been derived on the basis of the normal distribution of hydraulic conductivity. In this paper, stochastic solutions were developed for unsaturated flow by assuming the normal distribution of saturated hydraulic conductivity ( K,). Under the assumption that soil hydraulic properties are second-order stationary, analytical expressions for capillary tension head variance (σh2) and effective hydraulic conductivity (Kii*) in stratified soils were derived using the perturbation method. The dependence of σh2 and K," on soil variability and mean flow variables (the mean capillary tension head and its temporal and sp     

A MATHEMATICAL MODEL OF THE FLOW FROM THE OUTLET IN DAMS

1 .　ＩＮＴＲＯＤＵＣＴＩＯＮＦｒｅｅｊｅｔｆｒｏｍａｎｏｕｔｌｅｔｉｎａｄａｍｉｓａ ｐｏｐｕｌａｒｍｅａｎｓｏｆｄｉｓｃｈａｒｇｉｎｇｆｌｏｏｄｉｎｈｙｄｒａｕｌｉｃｅｎｇｉｎｅｅｒｉｎｇ ,ｗｈｉｃｈｈａｓｍａｎｙｍｅｒｉｔｓ ,ｓｕｃｈａｓｅｃｏｎｏｍｉｃｉｎｖｅｓｔｍｅｎｔ,ｓｉｍｐｌｅｓｅｎｇｉｎｅｅｒｉｎｇｓｔｒｕｃｔｕｒｅｓａｎｄａｗｉｄｅｓｕｉｔａｂｉｌｉｔｙｆｏｒｂｏｔｈｔｈｅｆｌｏｗｒａｔｅａｎｄｔｈｅｗａｔｅｒｄｅｐｔｈｄｏｗｎｓｔｒｅａｍ .Ｔｈｅｆｅａｔｕｒｅｏｆｔｈｉｓｆｌ…     

ANALYSIS OF TWO-PHASE FLOW PRESSURE BUILDUP DATA FROM A WELL IN AN INFINITE MULTIWELL RESERVOIR

NOMENCLATURE A1———drainage area of the tested well ( Well 1) At———total reservoir drainage area B———two-phase formation volume factor C———wellbore storage coefficient Cf———rock compressibility fator Co———oil compressibility fator Cw———water compressibility fator Ct———compressibility fator K———reservoir permeability m———slope of a semilog straight line m1———slope defined by Eq.(12) p-———average reservoir pressure-pD———di mensionless average drainag…     

三峡工程对库区水流水质影响预测

利用开发的三峡水库整体一维水流水质数学模型，对三峡水库建成前后的水流水质变化趋势进行预测分析。重点介绍三峡工程建成后，库区水流条件巨大变化对污染物输移转化特性和水质分布的影响。预测结果表明，三峡工程建成后，三斗坪水位175m条件下，回水区断面平均流速比建库前减小4倍左右，平均有机污染物自净降解速率和大气复氧速率比天然河道状况减小1倍。由于污染物在库区滞留时间成倍延长，有机污染物排入水库后的自净降解总量较天然河道状况增大，因而，建库后加水区内断面平均有机污染物浓度较天然河道状况明显下降，但是，断面平均溶解氧浓度与天然河道状况相比也明显降低，对于守恒类污染物，建库前后水质变化不大。因此，三峡工程对库区水质影响有利也有弊。