共查询到20条相似文献,搜索用时 15 毫秒
1.
Numerical Simulation of Single-Phase and Multiphase Non-Darcy Flow in Porous and Fractured Reservoirs 总被引:9,自引:0,他引:9
A numerical method as well as a theoretical study of non-Darcy fluid flow through porous and fractured reservoirs is described. The non-Darcy behavior is handled in a three-dimensional, multiphase flow reservoir simulator, while the model formulation incorporates the Forchheimer equation for describing single-phase or multiphase non-Darcy flow and displacement. The non-Darcy flow through a fractured reservoir is handled using a general dual-continuum approach. The numerical scheme has been verified by comparing its results against those of analytical methods. Numerical solutions are used to obtain some insight into the physics of non-Darcy flow and displacement in reservoirs. In addition, several type curves are provided for well-test analyses of non-Darcy flow to demonstrate a methodology for modeling this type of flow in porous and fractured rocks, including flow in petroleum and geothermal reservoirs. 相似文献
2.
A solution to the problem of shallow laminar water flow above a porous surface is essential when modeling phenomena such as erosion, resuspension, and mass transfer between the porous media and the flow above it. Previous studies proposed theoretical, experimental, and numerical insight with no single general solution to the problem. Many studies have used the Brinkman equation, while others showed that it does not represent the actual interface flow conditions. In this paper we show that the interface macroscopic velocity can be accurately modeled by introducing a modification to the Brinkman equation. A moving average approach was proved to be successful when choosing the correct representative elementary volume and comparing the macroscopic solution with the average microscopic flow. As the size of the representative elementary volume was found to be equal to the product of the square root of the permeability and an exponential function of the porosity, a general solution is now available for any brush configuration. Given the properties of the porous media (porosity and permeability), the flow height and its driving force, a complete macroscopic solution of the interface flow is obtained. 相似文献
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Numerical issues arising in computations of viscous flows in corners formed by a liquid–fluid free surface and a solid boundary are considered. It is shown that on the solid a Dirichlet boundary condition, which removes multivaluedness of velocity in the ‘moving contact‐line problem’ and gives rise to a logarithmic singularity of pressure, requires a certain modification of the standard finite‐element method. This modification appears to be insufficient above a certain critical value of the corner angle where the numerical solution becomes mesh‐dependent. As shown, this is due to an eigensolution, which exists for all angles and becomes dominant for the supercritical ones. A method of incorporating the eigensolution into the numerical method is described that makes numerical results mesh‐independent again. Some implications of the unavoidable finiteness of the mesh size in practical applications of the finite‐element method in the context of the present problem are discussed. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
5.
The volume-averaged equations are derived for convective flow in porous media. In the thermal energy equation viscous dissipation
is taken into account, and a suitable form is obtained which is valid when Brinkman effects are significant. 相似文献
6.
A New Model for Viscous Dissipation in Porous Media Across a Range of Permeability Values 总被引:3,自引:0,他引:3
In this paper a unified mathematical theory for the viscous dissipation term in the governing Brinkman equation is derived. This term has, unlike other models, the correct asymptotic behaviour in both the fully Darcy and Newtonian fluid flow limits. 相似文献
7.
Combined, forced, and free flow in a vertical circular duct filled with a porous medium is investigated according to the Darcy–Boussinesq
model. The effect of viscous dissipation is taken into account. It is shown that a thermal boundary condition compatible with
fully developed and axisymmetric flow is either a linearly varying wall temperature in the axial direction or, only in the
case of uniform velocity profile, an axial linear-exponential wall temperature change. The case of a linearly varying wall
temperature corresponds to a uniform wall heat flux and includes the uniform wall temperature as a special case. A general
analytical solution procedure is performed, by expressing the seepage velocity profile as a power series with respect to the
radial coordinate. It is shown that, for a fixed thermal boundary condition, i.e., for a prescribed slope of the wall temperature,
and for a given flow rate, there exist two solutions of the governing balance equations provided that the flow rate is lower
than a maximum value. When the maximum value is reached, the dual solutions coincide. When the flow rate is higher than its
maximum, no axisymmetric solutions exist.
E. Magyari is on leave from the Institute of Building Technology, ETH—Zürich. 相似文献
8.
M. Parvazinia V. Nassehi R. J. Wakeman M. H. R. Ghoreishy 《Transport in Porous Media》2006,63(1):71-90
Despite the widespread use of the Darcy equation to model porous flow, it is well known that this equation is inconsistent
with commonly prescribed no slip conditions at flow domain walls or interfaces between different sections. Therefore, in cases
where the wall effects on the flow regime are expected to be significant, the Darcy equation which is only consistent with
perfect slip at solid boundaries, cannot predict velocity and pressure profiles properly and alternative models such as the
Brinkman equation need to be considered. This paper is devoted to the study of the flow of a Newtonian fluid in a porous medium
between two impermeable parallel walls at different Darcy parameters (Da). The flow regime is considered to be isothermal and steady. Three different flow regimes can be considered using the Brinkman
equation: free flow (Da > 1), porous flow (high permeability, 1 > Da > 10−6) and porous flow (low permeability Da < 10−6). In the present work the described bench mark problem is used to study the effects of solid walls for a range of low to
high Darcy parameters. Both no-slip and slip conditions are considered and the results of these two cases are compared. The
range of the applicability of the Brinkman equation and simulated results for different cases are shown. 相似文献
9.
In this article we discuss the reduced basis method (RBM) for optimal control of unsteady viscous flows. RBM is a reduction method in which one can achieve the versatility of the finite element method or another for that matter and gain significant reduction in the number of degrees of freedom. The essential idea in this method is to define a reduced order subspace spanned by few basis elements and then obtain the solution via a Galerkin projection. We present several ways to define this subspace. Feasibility of the approach is demonstrated on two boundary control problems in cavity and wall bounded channel flows. Control action is effected through boundary surface movement on part of the solid wall. Application of RBM to the control problems leads to finite dimensional optimal control problems which are solved using Newton's method. Through computational experiments we demonstrate the feasibility and applicability of the reduced basis method for control of unsteady viscous flows. 相似文献
10.
Effects of Viscous Dissipation and Flow Work on Forced Convection in a Channel Filled by a Saturated Porous Medium 总被引:1,自引:3,他引:1
Fully developed forced convection in a parallel plate channel filled by a saturated porous medium, with walls held either at uniform temperature or at uniform heat flux, with the effects of viscous dissipation and flow work included, is treated analytically. The Brinkman model is employed. The analysis leads to expressions for the Nusselt number, as a function of the Darcy number and Brinkman number. 相似文献
11.
Velocity Measurements of a Free-Surface Turbulent Flow Penetrating a Porous Medium Composed of Uniform-Size Spheres 总被引:1,自引:0,他引:1
We present a laboratory experimental investigation of the interaction between the turbulent flow in an open channel and the
turbulent flow within its very permeable bed. The bed was composed of uniform-size spheres packed in a cubic pattern. Fluid
velocities were measured by Particle Image Velocimetry (PIV), which allowed us to investigate the spatial distribution of
the time-averaged flow properties in the zone where they are strongly affected by the geometry of the rough bed. We investigate
the effect of bed porosity on these flow properties by comparing the results of two experimental configurations: one with
an impermeable bed composed of a single layer of spheres and another with a permeable bed composed of five layers. For the
latter case, PIV measurements of velocities were also carried out inside two pores adjacent to the bed surface. This data
provides an insight into the mechanisms of momentum transfer between the turbulent open channel flow and the turbulent flow
within its very permeable bed. 相似文献
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V. M. Shapovalov S. V. Lapshina 《Journal of Applied Mechanics and Technical Physics》2003,44(2):198-203
The equations of the dynamics of a finitelength curved rod in a viscous flow are derived. The longitudinal stability of the rod against small deflections from a rectilinear form is studied for two types of flow (pure and simple shear). The minimum flexural rigidity of the rod that ensures rod stability for any orientation in the flow is found. The effective viscosity of a suspension filled with rectilinear discrete fibers is estimated. 相似文献
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The effects of viscous dissipation on unsteady free convection from an isothermal vertical flat plate in a fluid saturated
porous medium are examined numerically. The Darcy–Brinkman–Forchheimer model is employed to describe the flow field. A new
model of viscous dissipation is used for the Darcy–Brinkman–Forchheimer model of porous media. The simultaneous development
of the momentum and thermal boundary layers are obtained by using a finite difference method. Boundary layer and Boussinesq
approximation have been incorporated. Numerical calculations are carried out for various parameters entering into the problem.
Velocity and temperature profiles as well as local friction factor and local Nusselt number are shown graphically. It is found
that as time approaches infinity, the values of friction factor and heat transfer coefficient approach steady state. 相似文献
17.
The effect on the eruption process of water or steam injection into a volcanic conduit from an adjacent water-saturated stratum is studied. Both steady-state and unsteady processes are considered. The physical characteristics of these eruptions are identified. A mathematical model of such an eruption is proposed for the first time. 相似文献
18.
V. A. Babkin 《Fluid Dynamics》2002,37(4):587-593
Exact solutions are obtained for the following three problems in which the Brinkman filtration equations are used: laminar fluid flow between parallel plane walls, one of which is rigid while the other is a plane layer of saturated porous medium, motion of a plane porous layer between parallel layers of viscous fluid, and laminar fluid flow in a cylindrical channel bounded by an annular porous layer. 相似文献
19.
S. I. Martynov 《Fluid Dynamics》2002,37(6):889-895
Viscous flow past an infinite periodic array of rigid spheres is considered. The hydrodynamic interaction of all the particles in the array is taken into account. An analytical solution of the problem is proposed. The forces exerted by the fluid on the array particles are calculated and an expression for the velocity of fluid filtration through the array is obtained. The results are compared with the previous theoretical and experimental results. 相似文献
20.
A.V. Kuznetsov 《Flow, Turbulence and Combustion》1998,60(2):173-192
In this paper, the problem of fully developed forced convection in a parallel-plate channel partly filled with a homogeneous porous material is considered. The porous material is attached to the walls of the channel, while the center of the channel is occupied by clear fluid. The flow in the porous material is described by a nonlinear Brinkman–Forchheimer-extended Darcy equation. Utilizing the boundary-layer approach, analytical solutions for the flow velocity, the temperature distribution, as well as for the Nusselt number are obtained. Dependence of the Nusselt number on several parameters of the problem is extensively investigated. 相似文献