Simulation of uncompressible fluid flow through a porous media

Recently, a great interest has been focused for investigations about transport phenomena in disordered systems. One of the most treated topics is fluid flow through anisotropic materials due to the importance in many industrial processes like fluid flow in filters, membranes, walls, oil reservoirs, etc. In this work is described the formulation of a 2D mathematical model to simulate the fluid flow behavior through a porous media (PM) based on the solution of the continuity equation as a function of the Darcy’s law for a percolation system; which was reproduced using computational techniques reproduced using a random distribution of the porous media properties (porosity, permeability and saturation). The model displays the filling of a partially saturated porous media with a new injected fluid showing the non-defined advance front and dispersion of fluids phenomena.     

Numerical modeling of fluid flow in anisotropic fractured porous media

A model of double porosity in the case of an anisotropic fractured porous medium is considered (Dmitriev, Maksimov; 2007). A function of fluid exchange between the fractures and porous blocks depending on flow direction is given. The flow function is based on the difference between the pressure gradients. This feature enables one to take into account anisotropic properties of filtration in a more general form. The results of numerical solving a model two-dimensional problem are presented. The computational algorithm is based on a finite-element space approximation and explicit-implicit time approximations.     

Computational homogenization and nonlinear effects in heterogeneous fluid saturated porous media

For the two-scale modelling of deforming fluid-saturated porous structure we apply the asymptotic homogenization approach to the fluid-structure interaction problem involving linear elastic porous skeleton and the Newtonian compressible fluid. The sensitivity analysis of effective coefficients depending on the geometrical configuration is used to introduce a weakly nonlinear formulation which enables to capture influences of the deformation on the material properties. The paper is devoted to the comparison of the linear and the weakly nonlinear models (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non-linear laws of fluid flow through anisotropic porous media

Non-linear laws of fluid flow through anisotropic porous media are written out in invariant tensor form for all crystallographic point symmetry groups. The equations, as is customary in seepage theory [1, 2], are represented by expressions containing the seepage velocity up to and including the third degree. Expressions defining non-linear flow resistances are given and it is shown that, when one transfers from linear to non-linear seepage laws, the symmetry group of the flow properties may change. For example, the isotropic flow properties manifested in Darcy's law may become essentially anisotropic in a non-linear law and display asymmetry, that is, they may be different along one straight line in the positive and negative directions. It is shown that, compared with linear seepage laws for anisotropic media, when flow properties may be defined by just four essentially different types of equation, in non-linear laws the appearance of anisotropy is highly diversified and the number of distinct types of equation increases considerably.     

Thermomechanical effects in the flow of a fluid in porous media

This paper deals with analysis, by methods of extended thermodynamics, of the thermomechanical effects which arise in the flow of a weakly viscous fluid in a porous medium. Under the hypothesis that the fluid fills all the interstices among the powder and that the size of the powder grains and of the interstices is much lower than a suitable characteristic length, linearized field equations are written, which include, in a natural way, terms which take into account the Dufour, Soret, and virtual mass effects. As a limiting case when the evolution time of the heat flux goes to infinite and no entropy flux is carried, the flow of liquid helium II in a porous medium is obtained.     

Simulation of filtrational gas combustion processes in nonhomogeneous porous media

A one-dimensional two-temperature model of a combustion front moving with filtration of a fuel gaseous mixture in chemically inert porous media with discontinuous thermophysical parameters is investigated from numerical standpoint. From the algorithmic viewpoint, the emphasis is on new applications of two-level explicit and semi-implicit difference schemes with moving adaptive grids. From the angle of physical features of the processes under consideration, the bulk of attention is focused on aspects of combustion front stabilization, which is important in some technical applications.     

Homogenization of the acoustic equations for a porous long-memory viscoelastic material filled with a viscous fluid

We consider the system of linear differential and integro-differential equations describing small vibrations in an ?-periodic combined medium consisting of a porous long-memory viscoelastic material and a viscous fluid filling the pores. By using the two-scale convergence method, we construct the system of homogenized equations and prove the convergence of solutions of the original problems to the solution of the homogenized problem as ? ?? 0.     

Experimental evaluation of phase velocities and tortuosity in fluid saturated highly porous media

In the current contribution, we present a novel method for the determination of the high frequency tortuosity parameter, α_∞ in high porous media. Therefore, time-domain measurements of ultrasonic signals are performed with a transmission technique. Aluminium foams with different pore fluids will be under the scope of experimental investigation. Finally, the experimental results are compared with analytical wave propagation tests. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

李群方法在渗流力学的应用

试图用李群方法来分析流体及渗流的运动规律.对于流形上流体、渗流力学方程的研究,物理空间的流动中的拓扑结构只要具有李群的性质,便可以此来进行流动分析.这是将李群理论直接、直地应用于渗流力学的一种方法.李群方法将众多求解特定类型的渗流微分方程方法统一到共同的概念之下.李群无穷小变换方法为寻找微分方程的闭合形式的解提供的广泛的应用,补充了求解渗流力学方程的数学物理技巧.     

Three-dimensional finite/infinite elements analysis of fluid flow in porous media

Fluid flow in naturally fractured porous media can always be regarded as an unbounded domain problem and be better solved by finite/infinite elements. In this paper, a three-dimensional two-direction mapped infinite element is generated and combined with conventional finite elements and one direction infinite element to simulate poroelasticity. Therefore, the entire semi-infinite domain can be included in the numerical analysis. Both single- and dual-porosity porous media are considered. For the purpose of validation, we compare the results of finite/infinite elements with those of finite elements under two extreme boundary conditions. The comparison indicated that mapped infinite element is an appropriate approach to model fluid flow in porous media and provides an intermediate solution.     

Simulation of a compositional model for multiphase flow in porous media

In this article, we consider the simulation of a compositional model for three‐dimensional, three‐phase, multicomponent flow in a porous medium. This model consists of Darcy's law for volumetric flow velocities, mass conservation for hydrocarbon components, thermodynamic equilibrium for mass interchange between phases, and an equation of state for saturations. A discretization scheme based on the block‐centered finite difference method for pressures and compositions is developed. Numerical results are reported for the benchmark problem of the third comparative solution project (CSP) organized by the society of petroleum engineers (SPE). © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005.     

Synchronization effects in rotors partly filled with fluid

In fluid-filled rotors self-excited vibrations occur induced by a surface wave of the fluid. A characteristic property is the instability over the full range of angular velocity above the Eigenfrequency of the system. A possible explanation is the occurrence of synchronization effects between fluid and rotor. The behaviour of rotors partly filled with fluid was mostly studied under the aspect of stability in steady-state conditions. For non-steady-state investigations, discrete models with reduced number of degrees of freedom and reasonable ability to model the system behaviour are desirable due to the complexity of fluid modelling. This paper analyses a simple minimal model and shows synchronization effects between fluid and rotor model. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A conforming mixed finite-element method for the coupling of fluid flow with porous media flow

Salim Meddahi ^{We consider a porous medium entirely enclosed within a fluidregion and present a well-posed conforming mixed finite-elementmethod for the corresponding coupled problem. The interfaceconditions refer to mass conservation, balance of normal forcesand the Beavers–Joseph–Saffman law, which yieldsthe introduction of the trace of the porous medium pressureas a suitable Lagrange multiplier. The finite-element subspacesdefining the discrete formulation employ Bernardi–Raugeland Raviart–Thomas elements for the velocities, piecewiseconstants for the pressures and continuous piecewise-linearelements for the Lagrange multiplier. We show stability, convergenceand a priori error estimates for the associated Galerkin scheme.Finally, we provide several numerical results illustrating thegood performance of the method and confirming the theoreticalrates of convergence.}     

The fluid flow through porous media. Regularity of the free surface

The fluid flow through an earth dam separating two water reservoirs of different levels gives rise to a free boundary problem. In [1] we have proved the existence of a solution to this problem. In this paper we show that the free boundary is regular.     

Refraction of a fluid at an interface between two anisotropic porous media

Zusammenfassung In dieser Arbeit wird die Strömung über eine Grenzfläche zwischen zwei anisotropen porösen Körpern betrachtet.     

Vorticity transport in a viscoelastic fluid in the presence of suspended particles through porous media

We consider the transport of vorticity in an Oldroydian viscoelastic fluid in the presence of suspended magnetic particles through porous media. We obtain the equations governing such a transport of vorticity from the equations of magnetic fluid flow. It follows from these equations that the transport of solid vorticity is coupled to the transport of fluid vorticity in a porous medium. Further, we find that because of a thermokinetic process, fluid vorticity can exist in the absence of solid vorticity in a porous medium, but when fluid vorticity is zero, then solid vorticity is necessarily zero. We also study a two-dimensional case.     

Analytic solution for heat transfer of a third grade viscoelastic fluid in non-Darcy porous media with thermophysical effects

An analytic approximate solution is presented for the natural convective dissipative heat transfer of an incompressible, third grade, non-Newtonian fluid flowing past an infinite porous plate embedded in a Darcy–Forchheimer porous medium. The mathematical model is developed in an $(x\text{,}y)$ coordinate system. Using a set of transformations, the momentum equation is rendered one-dimensional and a partly linearized heat conservation equation is derived. The viscoelastic formulation presented by Akyildiz [Akyildiz FT. A note on the flow of a third grade between heated parallel plates. Int J Non-Linear Mech 2001;36:349–52] is adopted, which generates lateral mass and viscoelastic terms in the heat conservation equation, as well as in the momentum equation. A number of special cases of the general transformed model are discussed. A homotopy analysis method (HAM) is implemented to solve, with appropriate boundary conditions, the coupled third-order, second degree ordinary differential equation for momentum and the second-order, fourth degree heat conservation equation.     

Traveling waves in porous media with phase-dependent damping

We consider a simple model for the fluid flow in a porous medium. The model consists of a hyperbolic system of balance laws, which take into account phase changes and allow for metastable states thanks to the introduction of an equilibrium pressure. A damping term is included as well, which depend not only on the velocity but also on the phase of the fluid; in particular, it vanishes in the vapor phase. The existence and uniqueness of traveling waves is proved in several important cases.