Analysis of characteristics of pressure curve in gas-condensate wells

This paper utilizes a flow equation with a sink item that describes the characteristics of pressure-time chart when the pressure is higher than the maximum condensate pressure.We have established a sink item to show the influence of accumulation of condensate liquid according to Duhamet Principle of Superposition,and introduced two coefficients for it:condensing strength R_D and condensing relaxation timeλ_D.This paper gives the principle and the quantitative expression of the well pressure influenced by condensate function in the flow equation.An analytical solution for an infinite system is obtained(constant rate).These results can be used to analyse the unsteady flow test of constant production.     

Darcy Flow in a Wavy Channel Filled with a Porous Medium

Flow in channels bounded by wavy or corrugated walls is of interest in both technological and geological contexts. This paper presents an analytical solution for the steady Darcy flow of an incompressible fluid through a homogeneous, isotropic porous medium filling a channel bounded by symmetric wavy walls. This packed channel may represent an idealized packed fracture, a situation which is of interest as a potential pathway for the leakage of carbon dioxide from a geological sequestration site. The channel walls change from parallel planes, to small amplitude sine waves, to large amplitude nonsinusoidal waves as certain parameters are increased. The direction of gravity is arbitrary. A plot of piezometric head against distance in the direction of mean flow changes from a straight line for parallel planes to a series of steeply sloping sections in the reaches of small aperture alternating with nearly constant sections in the large aperture bulges. Expressions are given for the stream function, specific discharge, piezometric head, and pressure.     

Slow steady flows of a conducting fluid at large Hartmann numbers

We consider slow steady flows of a conducting fluid at large values of the Hartmann number and small values of the magnetic Reynolds number in an inhomogeneous magnetic field. The general solution is obtained in explicit form for the basic portion (core) of the flow, where the inertia and viscous forces may be neglected. The boundary conditions which this solution must satisfy at the outer edges of the boundary layers which develop at the walls are considered. Possible types of discontinuity surfaces and other singularities in the flow core are examined. An exact solution is obtained for the problem of conducting fluid flow in a tube of arbitrary section in an inhomogeneous magnetic field.The content of this paper is a generalization of some results on flows in a homogeneous magnetic field, obtained in [1–8], to the case of arbitrary flows in an inhomogeneous magnetic field. The author's interest in the problems considered in this study was attracted by a report presented by Professor Shercliff at the Institute of Mechanics, Moscow State University, in May 1967, on the studies of English scientists on conducting fluid flows in a strong uniform magnetic field.     

Oscillatory flow of second grade fluid in cylindrical tube

The unsteady oscillatory flow of an incompressible second grade fluid in a cylindrical tube with large wall suction is studied analytically. Flow in the tube is due to uniform suction at the permeable walls, and the oscillations in the velocity field are due to small amplitude time harmonic pressure waves. The physical quantities of interest are the velocity field, the amplitude of oscillation, and the penetration depth of the oscillatory wave. The analytical solution of the governing boundary value problem is obtained, and the effects of second grade fluid parameters are analyzed and discussed.     

Wave processes in an elastic half-plane impacted by a blunt-nosed rigid body

The problem of unsteady deformation of an elastic half-plane is considered whose surface is impacted, at an initial instant, by a blunt-nosed rigid body, which generates diverging unsteady elastic waves and deforms the medium. The corresponding initial-boundary-value problem is formulated whose solution is constructed for the early stage of the interaction. The integral Laplace transform in the time variable and the integral Fourier transform in the one of the spatial variables are used. The solution of the problem is obtained in terms of the transforms and a formal solution is constructed in terms of the original functions. For a body with a fixed contact region, an analytical expression of the normal stress at an arbitrary point of the half-plane as a function of time is obtained. For a body shaped as an obtuse-angled wedge, analytical expressions of the normal stress and displacement at an arbitrary point at the symmetry axis of the problem are obtained. Calculations are performed and used to analyze the characteristic features of the wave processes in the medium as functions of time, the surface distance, and the mechanical properties of the material.     

A Study of the Time Constant in Unsteady Porous Media Flow Using Direct Numerical Simulation

We consider unsteady flow in porous media and focus on the behavior of the coefficients in the unsteady form of Darcy’s equation. It can be obtained by consistent volume-averaging of the Navier–Stokes equations together with a closure for the interaction term. Two different closures can be found in the literature, a steady-state closure and a virtual mass approach taking unsteady effects into account. We contrast these approaches with an unsteady form of Darcy’s equation derived by volume-averaging the equation for the kinetic energy. A series of direct numerical simulations of transient flow in the pore space of porous media with various complexities are used to assess the applicability of the unsteady form of Darcy’s equation with constant coefficients. The results imply that velocity profile shapes change during flow acceleration. Nevertheless, we demonstrate that the new kinetic energy approach shows perfect agreement for transient flow in porous media. The time scale predicted by this approach represents the ratio between the integrated kinetic energy in the pore space and that of the intrinsic velocity. It can be significantly larger than that obtained by volume-averaging the Navier–Stokes equation using the steady-state closure for the flow resistance term.     

Propagation of unsteady waves in an elastic layer

We consider a plane problem of propagation of unsteady waves in a plane layer of constant thickness filled with a homogeneous linearly elastic isotropic medium in the absence of mass forces and with zero initial conditions. We assume that, on one of the layer boundaries, the normal stresses are given in the form of the Dirac delta function, the tangential stresses are zero, and the second boundary is rigidly fixed. The problem is solved by using the Laplace transform with respect to time and the Fourier transform with respect to the longitudinal coordinate. The normal displacements at an arbitrary point are obtained in the form of finite sums.     

On unsteady unidirectional flows of a second grade fluid

Some properties of unsteady unidirectional flows of a fluid of second grade are considered for flows produced by the sudden application of a constant pressure gradient or by the impulsive motion of one or two boundaries. Exact analytical solutions for these flows are obtained and the results are compared with those of a Newtonian fluid. It is found that the stress at the initial time on the stationary boundary for flows generated by the impulsive motion of a boundary is infinite for a Newtonian fluid and is finite for a second grade fluid. Furthermore, it is shown that initially the stress on the stationary boundary, for flows started from rest by sudden application of a constant pressure gradient is zero for a Newtonian fluid and is not zero for a fluid of second grade. The required time to attain the asymptotic value of a second grade fluid is longer than that for a Newtonian fluid. It should be mentioned that the expressions for the flow properties, such as velocity, obtained by the Laplace transform method are exactly the same as the ones obtained for the Couette and Poiseuille flows and those which are constructed by the Fourier method. The solution of the governing equation for flows such as the flow over a plane wall and the Couette flow is in a series form which is slowly convergent for small values of time. To overcome the difficulty in the calculation of the value of the velocity for small values of time, a practical method is given. The other property of unsteady flows of a second grade fluid is that the no-slip boundary condition is sufficient for unsteady flows, but it is not sufficient for steady flows so that an additional condition is needed. In order to discuss the properties of unsteady unidirectional flows of a second grade fluid, some illustrative examples are given.     

Viscoelastic layer under the action of a moving load

Recently, problems concerning the dynamic behavior of imperfect continuous media under various types of actions have been widely investigated. The method of Laplace transformation is very convenient for describing physical processes concerning unsteady phenomena. In viscoelastic media two complications are added: the representation of the properties of a medium depending on time, and the inversion of the obtained solutions containing this additional complication. Certain approximate methods of inversion in the analysis of viscoelastic stresses are discussed in [1]. In [2, 3] a discussion is given for an effective method of constructing the solution of unsteady problems for finite and for infinite imperfect media using auxiliary functions, and a solution is presented for a half-space. Making use of the idea of the inversion of transforms, discussed in [4], in [5] a solution is obtained and a complete picture is presented for the dynamics of the variation of the stress field in a viscoelastic half-space. In the present study we consider the action of a normal moving load that is suddenly applied to the free surface of a viscoelastic layer. By Laplace and Fourier integral transformations we obtain a solution in the form of a uniformly converging series based on longitudinal and transverse waves reflected in the layer. By means of inverting the transforms by the method discussed in [4, 5], we obtain an exact solution for the stress field in the medium under investigation. We consider the special case of a viscoelastic medium of Boltzmann type, for which we obtain a numerical realization of the solution on a digital computer.     

Time‐domain BEM solution of convection–diffusion‐type MHD equations

The two‐dimensional convection–diffusion‐type equations are solved by using the boundary element method (BEM) based on the time‐dependent fundamental solution. The emphasis is given on the solution of magnetohydrodynamic (MHD) duct flow problems with arbitrary wall conductivity. The boundary and time integrals in the BEM formulation are computed numerically assuming constant variations of the unknowns on both the boundary elements and the time intervals. Then, the solution is advanced to the steady‐state iteratively. Thus, it is possible to use quite large time increments and stability problems are not encountered. The time‐domain BEM solution procedure is tested on some convection–diffusion problems and the MHD duct flow problem with insulated walls to establish the validity of the approach. The numerical results for these sample problems compare very well to analytical results. Then, the BEM formulation of the MHD duct flow problem with arbitrary wall conductivity is obtained for the first time in such a way that the equations are solved together with the coupled boundary conditions. The use of time‐dependent fundamental solution enables us to obtain numerical solutions for this problem for the Hartmann number values up to 300 and for several values of conductivity parameter. Copyright © 2007 John Wiley & Sons, Ltd.     

Cascade aerodynamic gust response including steady loading effects

To predict the unsteady convected gust aerodynamic response of a cascade comprised of arbitrary thick and cambered aerofoils in an incompressible, inviscid, flow field, a complete first-order model is formulated. The flow is analysed by considering a periodic flow channel. The velocity potential is separated into steady and unsteady harmonic components, each described by a Laplace equation. The strong dependence of the unsteady aerodynamics on the steady effects of aerofoil and cascade geometry and incidence angle is manifested in the coupling of the unsteady and steady flow fields through the unsteady boundary conditions. Analytical solutions in individual grid elements of a body-fitted computational grid are then determined, with the complete solution obtained by assembly of these local solutions. The validity and capabilities of this model and solution technique are then demonstrated by analysing the steady and unsteady aerodynamics of both theoretical and experimental cascade configurations.     

Plane incompressible fluid flow past an array of arbitrary profiles vibrating with arbitrary phase shift

We consider the problem of the vibration of an array of arbitrary profiles with arbitrary phase shift. Account is taken of the influence of the vortex wakes. The vibration amplitude is assumed to be small. The problem reduces to a system of two integral Fredholm equations of the second kind, which are solved on a digital computer. An example calculation is made for an array of arbitrary form.A large number of studies have considered unsteady flow past an array of profiles. Most authors either solve the problem for thin and slightly curved profiles or they consider the flow past arrays of thin curvilinear profiles [1].In [2] a study is made of the flow past an array of profiles of arbitrary form oscillating with arbitrary phase shift in the quasi-stationary formulation. The results are reduced to numerical values. Other approaches to the solution of the problem of unsteady flow past an array of profiles of finite thickness are presented in [3–5] (the absence of numerical calculations in [3, 4] makes it impossible to evaluate the effectiveness of these methods, while in [5] the calculation is made for a symmetric profile in the quasi-stationary formulation).     

Unsteady unidirectional micropolar fluid flow

This paper considers the unsteady unidirectional flow of a micropolar fluid, produced by the sudden application of an arbitrary time dependent pressure gradient, between two parallel plates. The no-slip and the no-spin boundary conditions are used. Exact solutions for the velocity and microrotation distributions are obtained based on the use of the complex inversion formula of Laplace transform. The solution of the problem is also considered if the upper boundary of the flow is a free surface. The particular cases of a constant and a harmonically oscillating pressure gradient are then examined and some numerical results are illustrated graphically.     

Unsteady hydromagnetic pipe flow at small Hartmann number

Summary In this paper we have studied the problem of the unsteady flow of an electrically conducting incompressible viscous fluid through a circular pipe under the influence of a uniform applied transverse magnetic field when the walls are non-conducting. It has been assumed that the velocity vanishes on the non-conducting walls and initially the fluid is at rest. The velocity field and the induced magnetic field are calculated by an iteration procedure and have been found up to second order terms inM (Hartmann number) which is taken to be small. We have also neglected the term involving (= 4/) the self inductance of the fluid, which is valid for small values ofM.Since the pressure gradient is not necessarily a constant in unsteady flow, we have assumed it to be an arbitrary function of time. A particular case when the pressure gradient is an exponential function of time has also been investigated in detail. For a constant pressure gradient the curves for the velocity field and the induced magnetic field have been drawn (at different values of Hartmann number and time). It has been found that for small values of time the fluid is accelerated near the centre in contrast to the case of a non-conducting fluid.     

SH波作用下界面任意形状孔洞附近的动应力集中

采用Green函数和复变函数法求解了平面SH波在界面任意形状孔洞上的散射问题.首先,取含有任意形状凹陷的弹性半空间,在其水平表面上任意一点承受时间谐和的反平面线源荷载作用时的位移场作为Green函数.然后,按契合方式构造出界面任意形状孔洞对SH波的散射模型,利用所得Green函数按界面位移连续条件建立求解问题的定解积分方程组,求解界面孔附近的动应力集中系数.最后,给出了界面上椭圆孔和方孔边缘动应力集中系数的数值结果,并讨论了不同介质参数和孔洞形状对孔附近动应力集中系数的影响.     

Prediction of oscillating thick cambered aerofoil aerodynamics by a locally analytic method

A complete first-order model and locally analytic solution method are developed to analyse the effects of mean flow incidence and aerofoil camber and thickness on the incompressible aerodynamics of an oscillating aerofoil. This method incorporates analytic solutions, with the discrete algebraic equations which represent the differential flow field equations obtained from analytic solutions in individual grid elements. The velocity potential is separated into steady and unsteady harmonic parts, with the unsteady potential further decomposed into circulatory and non-circulatory components. These velocity potentials are individually described by Laplace equations. The steady velocity potential is independent of the unsteady flow field. However, the unsteady flow is coupled to the steady flow field through the boundary conditions on the oscillating aerofoil. A body-fitted computational grid is then utilized. Solutions for both the steady and the coupled unsteady flow fields are obtained by a locally analytic numerical method in which locally analytic solutions in individual grid elements are determined. The complete flow field solution is obtained by assembling these locally analytic solutions. This model and solution method are shown to accurately predict the Theodorsen oscillating flat plate classical solution. Locally analytic solutions for a series of Joukowski aerofoils demonstrate the strong coupling between the aerofoil unsteady and steady flow fields, i.e. the strong dependence of the oscillating aerofoil aerodynamics on the steady flow effects of mean flow incidence angle and aerofoil camber and thickness.     

Determination of bottom pressure in river flow over an obstacle

Free-surface flow in natural watercourses was investigated using two-dimensional incompressible fluid equations written for a longitudinal vertical plane. Within the framework of similarity theory, expanding the unknown variables in power series of given structure reduces the problem to a sequence of ordinary differential equations for which an analytical solution is obtained. The solution reproduces the spatial pattern of the flow over the bottom surface of arbitrary geometry. The results of calculation of the pressure field near an underwater pipeline are presented which can be used in the stability analysis of pipeline-bottom soil systems in the case of scouring.     

Nonequilibrium adsorption of an isobar series of radionuclides

The one-dimensional problem of transport at a constant velocity of an isobar series of radio-active elements by an inactive carrier gas through a semiinfinite porous médius is investigated. A system of equations is given for an isobar series of N elements with consideration of their nonequilibrium adsorption. The analytical solution was obtained for a series of two elements with an arbitrary time dependence of the entry concentration of the leading element. The solution of the system was investigated in the case when the boundary condition for the leading element of the series was assigned in the form of a delta function. The case of equilibrium adsorption is examined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 145–149, May–June, 1976.In conclusion, the authors thank A. N. Gudkov for discussing the work.     

Stationary flow of a conducting liquid in a rectangular channel with two nonconducting walls and two walls having an arbitrary conductivity parallel to an external magnetic field

The flow of a conducting liquid in a channel of rectangular cross section with two walls (parallel to the external magnetic field) having an arbitrary conductivity, the other two being insulators, is considered. The solution of the problem is presented in the form of infinite series. The relationships obtained are used for numerical calculations of the velocity distribution and the distribution of the induced magnetic field over the cross section for several modes of flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkostt i Gaza, No. 5, pp. 46–52, September–October, 1970.     

Magnetohydrodynamic mixed convection in a vertical channel

The problem of combined free and forced convective magnetohydrodynamic flow in a vertical channel is analysed by taking into account the effect of viscous and ohmic dissipations. The channel walls are maintained at equal or at different constant temperatures. The velocity field and the temperature field are obtained analytically by perturbation series method and numerically by finite difference technique. The results are presented for various values of the Brinkman number and the ratio of Grashof number to the Reynolds number for both equal and different wall temperatures. Nusselt number at the walls is determined. It is found that the viscous dissipation enhances the flow reversal in the case of downward flow while it counters the flow in the case of upward flow. It is also found that the analytical and numerical solutions agree very well for small values of ε.