Pressure transient characteristics of non-uniform conductivity fractured wells in viscoelasticity polymer flooding based on oil-water two-phase flow

Polymer flooding in fractured wells has been extensively applied in oilfields to enhance oil recovery.In contrast to water,polymer solution exhibits non-Newtonian and nonlinear behavior such as effects of shear thinning and shear thickening,polymer convection,diffusion,adsorption retention,inaccessible pore volume and reduced effective permeability.Meanwhile,the flux density and fracture conductivity along the hydraulic fracture are generally non-uniform due to the effects of pressure distribution,formation damage,and proppant breakage.In this paper,we present an oil-water two-phase flow model that captures these complex non-Newtonian and nonlinear behavior,and non-uniform fracture characteristics in fractured polymer flooding.The hydraulic fracture is firstly divided into two parts:high-conductivity fracture near the wellbore and low-conductivity fracture in the far-wellbore section.A hybrid grid system,including perpendicular bisection(PEBI)and Cartesian grid,is applied to discrete the partial differential flow equations,and the local grid refinement method is applied in the near-wellbore region to accurately calculate the pressure distribution and shear rate of polymer solution.The combination of polymer behavior characterizations and numerical flow simulations are applied,resulting in the calculation for the distribution of water saturation,polymer concentration and reservoir pressure.Compared with the polymer flooding well with uniform fracture conductivity,this non-uniform fracture conductivity model exhibits the larger pressure difference,and the shorter bilinear flow period due to the decrease of fracture flow ability in the far-wellbore section.The field case of the fall-off test demonstrates that the proposed method characterizes fracture characteristics more accurately,and yields fracture half-lengths that better match engineering reality,enabling a quantitative segmented characterization of the near-wellbore section with high fracture conductivity and the far-wellbore section with low fracture conductivity.The novelty of this paper is the analysis of pressure performances caused by the fracture dynamics and polymer rheology,as well as an analysis method that derives formation and fracture parameters based on the pressure and its derivative curves.

Extraction Kinetics of Lanthanum in Chloride Medium by Bifunctional Ionic Liquid [A336][CA-12] Using a Constant Interfacial Cell with Laminar Flow

The extraction kinetics of La(III) from aqueous chloride solutions into n-heptane solutions of bifunctional ionic liquid extractant [A336][CA-12](tricaprylmethylammonium sec-octylphenoxy acetic acid) was investigated using a constant interfacial cell with laminar flow. The effects of stirring speed, temperature and specific interfacial area on the extraction rate were examined. The results indicate that mass transfer kinetics of La(III) is a mixed-controlled process influenced by interfacial reaction. On the basis of mass transfer kinetic results in the extraction of La(III) by [A336][CA-12], the extraction rate equation of La(III) is proposed in terms of pseudo-firstorder constants, which is supported by the measured thermodynamic equations. The mass-transfer kinetic model deduced from the rate controlling step is adequate to interpret the experimental data qualitatively.

EXTRACTION KINETICS OF RARE EARTH（Ⅰ） A Constant Interfacial Cell with Laminar Flow

A technique was developed to study mass trans fer process and inter facial reaction in two phases system. This constant inter facial cell with a laminar flow was made into a cubic structure. The two fluids were continuously recycled and mixed. The concentration of each liquid could be monitored by two different methods. This kind of structure made both flows near the inter face flow parallel to the inter face. The inter face was smooth and steady. The mass trans fer rate could be judged by the linear velocity of the flows. The technique can be used for the analyses of the control step in both phases near the inter face in a diffusion control process. A preliminary hydrodynamics and mass trans fer study on the cell was presented, which ensures the distinguishing between a diffusion and a chemical reaction control process. A simplified mass transfer equation,N =0.5303D 1 /2* (Ci- Cb)* (V / B) 1/2, was achieved.

Heat transfer in boundary layer stagnation-point flow towards a shrinking sheet with non-uniform heat flux

In this paper, the effect of non-uniform heat flux on heat transfer in boundary layer stagnation-point flow over a shrinking sheet is studied. The variable boundary heat fluxes are considered of two types： direct power-law variation with the distance along the sheet and inverse power-law variation with the distance. The governing partial differential equations （PDEs） are transformed into non linear self-similar ordinary differential equations （ODEs） by similarity transformations, and then those are solved using very efficient shooting method. The direct variation and inverse variation of heat flux along the sheet have completely different effects on the temperature distribution. Moreover, the heat transfer characteristics in the presence of non-uniform heat flux for several values of physical parameters are also found to be interesting.

Numerical simulation on rotordynamic characteristics of annular seal under uniform and non-uniform flows

Currently, the flow field of annular seals disturbed by the circular whirl motion of rotors is usually solved using computational fluid dynamics(CFD) to evaluate the five rotordynamic coefficients. The simulations are based on the traditional quasi-steady method. In this work, an improved quasi-steady method along with the transient method was presented to compute the rotordynamic coefficients of a long seal. By comparisons with experimental data, the shortcomings of quasi-steady methods have been identified. Then, the effects of non-uniform incoming flow on seal dynamic coefficients were studied by transient simulations. Results indicate that the long seal has large cross stiffness k and direct mass M which are not good for rotor stability, while the transient method is more suitable for the long seal for its excellent performance in predicting M. When the incoming flow is non-uniform, the stiffness coefficients vary with the eccentric directions. Based on the rotordynamic coefficients under uniform incoming flow, the linearized fluid force formulas, which can consider the effects of non-uniform incoming flow, have been presented and can well explain the varying-stiffness phenomenon.

Sedimentation motion of sand particles in moving water(Ⅰ):The resistance on a small sphere moving in non-uniform flow

In hydraulics,when we deal with the problem of sand particles moving relative to the surrounding water,Stokes'formula of resistance has usually been used to render the velocity of sedimentation of the particles.But such an approach has not been proved rigorously,and its accuracy must be carefully considered.In this paper,we discuss the problem of a sphere moving in a non-uniform flow field,on the basis of the fundamental theory of hydrodynamics.We introduce two assumptions:i)the diameter of the sphere is much smaller than the linear dimension of the flow field,and ii)the velocity of the sphere relative to the surrounding water is very small.Using these two assumptions,we solve the linearized Navier-Stokes equations and equations of continuity by the method of Laplace transform,and finally we obtain a formula for the resistance acting on a sphere moving in a non-uniform flow field.

Numerical investigation on flow and heat transfer characteristics of corrugated tubes with non-uniform corrugation in turbulent flow

Based on finite volume method, the pressure drop and heat transfer characteristics of one smooth tube and ten different axisymmetric corrugated tubes, including two with uniform corrugation and eight with non-uniform corrugation, have been studied. A physical model of the corrugated tube was built, then the numerical simulation of the model was carried out and the numerical simulation results were compared with the empirical formula.The results show that: the friction factor decreases with the increase of Reynolds number ranging from 6000 to 57000, the value of which in the corrugated tubes with non-uniform corrugation(tube 03–10) are smaller than those with uniform corrugation(tube 01–02). The geometry parameters of tube(01) have advantages on the heat transfer enhancement in low Reynolds number flow region(from 6000 to 13000) and tube(07–08)have advantages on the heat transfer enhancement in high Reynolds number flow region(from 13000 to 57000). The vortex, existed in each area between two adjacent corrugations called second flow region, is the root of the enhancement on heat transfer in the corrugated tubes. The effectiveness factor decreases with the increasing of Reynolds number and the performances of the corrugated tubes with pitch of 12.5 mm have advantages than these of 10 mm under the same corrugation geometric parameter.

Boundary Layer Flow of an Unsteady Dusty Fluid and Heat Transfer Over a Stretching Sheet with Non-Uniform Heat Source/Sink

An analysis has been carried out to study the effect of hydrodynamic laminar boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface in the presence of non-uniform heat source/sink. Heat transfer characteristics are examined for two different kinds of boundary conditions, namely 1) variable wall temperature and 2) variable heat flux. The governing partial differential equations are transformed to system of ordinary differential equations. These equations are solved numerically by applying RKF-45 method. The effects of various physical parameters such as magnetic parameter, dust interaction parameter, number density, Prandtl number, Eckert number, heat source/sink parameter and unsteadiness parameter on velocity and temperature profiles are studied.

A Computer Method of Steady Non-Uniform Gradually Varied Flow in Open Channel & in River

Most of water flow in open channel or in river belongs to steady non-uniform flow. The surface profiles are caused by changes of channel section. It is very important to analyze its computation. According to the regularity of its surface change, the suitable sectional dimensions of open channel or flood control work can be designed. Commonly, computation of non-uniform flow adopts the traditional methods by hand or by graphic method. The speed and precision of computation are restricted. In this paper, a software to calculate water surface profile is introduced. The software is put forward by using C++ .By means of interpolate method and dialogue between user and computer, we can calculate the water surface profile much more quickly and exactly.

Unsteady Non-Uniform Flow of Molten Metals in Rectangular Open Channels

In the metallurgical industries, it is very important to characterize the flow of molten metals in open channels given that they are transported through these devices to different plant sections. However, unlike the flow of water which has been studied since ancient times, the flow of molten metals in open channels has received little attention. The unsteady non-uniform flow of blast furnace molten pig iron in a rectangular open channel is analyzed in this work by numerical solution of the Saint-Venant equations. The influence of mesh size on the convergence of molten metal height is studied to determine the proper mesh and time step sizes. A sinusoidal inflow pulse is imposed at the entrance of the channel in order to analyze the propagation of the resulting wave. The influence of the angle of inclination of the channel and the roughness coefficient of the walls on the amplitude and the dynamic behavior of the height of the molten metal are analyzed. Phase portraits of the channel state variables are constructed and interpreted. Numerical simulations show that as the angle of inclination of the channel increases, the amplitude of the formed wave decreases. From 10 degrees onwards, the peak of the wave descends even below the initial height. On the other hand, the roughness coefficient affects the molten pig iron height profiles in an inverse way than the angle of inclination. The amplitude of the formed wave increases as the roughness coefficient increases.

基于Flowmaster软件的恒压泵系统流量调控的能耗分析

供水泵站通常采用阀门或变速(变频)调控来实现恒压供水,2种方式都涉及管路特性曲线或泵性能曲线的变化,这使得实际应用中能耗的定量计算比较繁琐.为此,借助Flowmaster流动系统仿真软件,以某恒压供水站为例,分别计算阀门调控和变速调控方式下泵系统性能的变化,并进行能耗对比分析,研究了恒压泵系统的转速和流量调节范围,为工程应用提供切实可行的计算方法.

Simulation of Variable Viscosity and Jeffrey Fluid Model for Blood Flow Through a Tapered Artery with a Stenosis

Non-Newtonian fluid model for blood flow through a tapered artery with a stenosis and variable viscosity by modeling blood as Jeffrey fluid has been studied in this paper. The Jeffrey fluid has two parameters, the relaxation time A1 and retardation time A2. The governing equations are simplified using the case of mild stenosis. Perturbation method is used to solve the resulting equations. The effects of non-Newtonian nature of blood on velocity profile, temperature profile, wall shear stress, shearing stress at the stenotsis throat and impedance of the artery are discussed. The results for Newtonian fluid are obtained as special case from this model.

Effect of viscous dissipation and heat source on flow and heat transfer of dusty fluid over unsteady stretching sheet

This paper investigates the problem of hydrodynamic boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface. The study considers the effects of frictional heating （viscous dissipation） and internal heat generation or ab- sorption. The basic equations governing the flow and heat transfer are reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformations. The transformed equations are numerically solved by the Runge-Kutta-Fehlberg-45 order method. An analysis is carried out for two different cases of heating processes, namely, variable wall temperature （VWT） and variable heat flux （VHF）. The effects of various physical parameters such as the magnetic parameter, the fluid-particle interaction pa- rameter, the unsteady parameter, the Prandtl number, the Eckert number, the number density of dust particles, and the heat source/sink parameter on velocity and temperature profiles are shown in several plots. The effects of the wall temperature gradient function and the wall temperature function are tabulated and discussed.

Robust design of natural laminar flow supercritical airfoil by multi-objective evolution method

Abstract A transonic, high Reynolds number natural laminar flow airfoil is designed and studied. The γ-θ transition model is combined with the shear stress transport （SST） k-w turbulence model to predict the transition region for a laminar-turbulent boundary layer. The non-uniform free-form deformation （NFFD） method based on the non-uniform rational B-spline （NURBS） basis function is introduced to the airfoil parameterization. The non-dominated sorting genetic algorithm-II （NSGA-II） is used as the search algo- rithm, and the surrogate model based on the Kriging models is introduced to improve the efficiency of the optimization system. The optimization system is set up based on the above technologies, and the robust design about the uncertainty of the Mach number is carried out for NASA0412 airfoil. The optimized airfoil is analyzed and compared with the original airfoil. The results show that natural laminar flow can be achieved on a supercritical airfoil to improve the aerodynamic characteristic of airfoils.

New Mechanism and Analytical Formula for Understanding the Gravity Constant <i>G</i>

The nature of gravitation and G is not well understood. A new gravitation mechanism is proposed that explains the origin and essence of the gravitational constant, G. Based on general relativity, the vacuum is considered to be a superfluid with measurable density. Rotating bodies drag vacuum and create a vortex with gradient pressure. The drag force of vacuum fluid flow in the arm of the vortex is calculated relative to the static vacuum and a value that is numerically equal to that of G is obtained. Using Archimedes’ principle, it is determined that G is the volume of vacuum displaced by a force equivalent to its weight which is equal to the drag force of the vacuum. It is concluded that the gravitational constant G expresses the force needed to displace a cubic metre of vacuum that weighs one kg in one second. Therefore, G is not a fundamental physical constant but rather is an expression of the resistance encountered by the gravitational force in the vacuum.

Heat Transfer with Viscous Dissipation in Couette-Poiseuille Flow under Asymmetric Wall Heat Fluxes

Analytical solutions of temperature distributions and the Nusselt numbers in forced convection are reported for flow through infinitely long parallel plates, where the upper plate moves in the flow direction with constant velocity and the lower plate is kept stationary. The flow is assumed to be laminar, both hydro-dynamically and thermally fully developed, taking into account the effect of viscous dissipation of the flowing fluid. Both the plates being kept at specified and at different constant heat fluxes are considered as thermal boundary conditions. The solutions obtained from energy equation are in terms of Brinkman number, dimensionless velocity and heat flux ratio. These parameters greatly influence and give complete understanding on heat transfer rates that has potentials for designing and analyzing energy equipment and processes.

Transient Pressure Behavior of a Well Located between a Constant Pressure Boundary and a Sealing Fault

Pressure transient analysis has been used to evaluate performance of a well located between one sealing fault and one constant pressure boundary. Type curves were generated by determining 1) dimensionless pressure and 2) rate of change of dimensionless pressure drop with respect to dimensionless time. When the well is located closer to the no flow boundary, both sets of type curves have three distinct slopes. These slopes characterize: 1) flow in an infinite reservoir, 2) presence of the no flow, and 3) the constant-pressure boundaries. When the well is closer to the constant pressure boundary, the type curves show two distinct slopes. These correspond to: 1) flow in an infinite reservoir, and 2) the presence of a constant pressure boundary. The type curves can be used to match actual pressure drawdown data and determine the drainage area and relative well location with respect to physical boundaries.

Analysis of one-dimensional consolidation of soft soils with non-Darcian flow caused by non-Newtonian liquid

Based on non-Darcian flow caused by non-Newtonian liquid, the theory of one-dimensional (1D) consolidation was modified to consider variation in the total vertical stress with depth and time. The finite difference method (FDM) was adopted to obtain numerical solutions for excess pore water pressure and average degree of consolidation. When non-Darcian flow is degenerated into Darcian flow, a comparison between numerical solutions and analytical solutions was made to verify reliability of finite difference solutions. Finally, taking into account the ramp time-dependent loading, consolidation behaviors with non-Darcian flow under various parameters were analyzed. Thus, a comprehensive analysis of 1D consolidation combined with non-Darcian flow caused by non-Newtonian liquid was conducted in this paper.

EFFECT OF THE MAGNETIC FIELD ON THE PULSATILE FLOW THROUGH A RIGID TUBE

This study presents the effect of the magnetic field with constant intensity on the pulsatile flow through a rigid tube. Basing on the experimental results, the influence of the magnetic field on the blood viscosity is considered The analytic solution of the pulsatile flow through a rigid tube under constant magnetic field intensitier and the effect of the magnetic field on the velocity distribution, flow and impedance in a rigid tube are given. this investigation is valuable for understanding the influence of the magnetic field on the blood circulation.

ON THE EFFECT OF REYNOLDS NUMBER ON VON KRMN'S CONSTANT

Fully developed turbulence measurements in pipe flow were made in the Reynolds number ranging from 10 x 10~3 to 350 x 10~3 with a hot-wire anemometer and a Pitot tube.Comparisons were made with the experimental results of previous work.The mean velocity profile and the turbulent intensity in the experiments in- dicate that for the mean velocity profile,in the fully developed turbulent pipe flow, von Kármán's constant κ is a function of Reynolds number,i.e.κ increases slowly with the Reynolds number.The empirical relationships could not be considered to be accurate enough to describe the fully developed turbulence over the whole Reynolds number range in pipe flow.