An overview on nonlinear porous flow in low permeability porous media

This paper gives an overview on nonlinear porous flow in low permeability porous media, reveals the microscopic mechanisms of flows, and clarifies properties of porous flow fluids. It shows that, deviating from Darcy's linear law, the porous flow characteristics obey a nonlinear law in a low-permeability porous medium, and the viscosity of the porous flow fluid and the permeability values of water and oil are not constants. Based on these characters, a new porous flow model, which can better describe low permeability reservoir, is established. This model can describe various patterns of porous flow, as Darcy's linear law does. All the parameters involved in the model, having definite physical meanings, can be obtained directly from the experiments.     

正交各向异性含液饱和多孔介质中应力波的传播

基于Biot的孔隙介质理论，研究了正交各向异性含液饱和多孔介质中应力波的传播特性．本文引入动态渗透率，导出了整个实频域内应力波传播的复特征方程及其解析解，给出了各种应力波成分的波速和衰减的解析表达武，计算了频散曲线和衰减曲线，并讨论了各类应力波之间的耦合关系及介质的各向异性对应力波传播的影响．     

A LGA model for fluid flow in heterogeneous porous media

A lattice gas automaton (LGA) model is proposed to simulate fluid flow in heterogeneous porous media. Permeability fields are created by distributing scatterers (solids, grains) within the fluid flow field. These scatterers act as obstacles to flow. The loss in momentum of the fluid is directly related to the permeability of the lattice gas model. It is shown that by varying the probability of occurrence of solid nodes, the permeability of the porous medium can be changed over several orders of magnitude. To simulate fluid flow in heterogeneous permeability fields, isotropic, anisotropic, random, and correlated permeability fields are generated. The lattice gas model developed here is then used to obtain the effective permeability as well as the local fluid flow field. The method presented here can be used to simulate fluid flow in arbitrarily complex heterogeneous porous media.     

Flux calculation at the interface between two rock types for two-phase flow in porous media

When simulating two-phase flow in porous media, one has to consider the case where there is a discontinuity in the medium. There relative permeabilities and capillary pressure functions may change and we address the problem of calculating the convective part of the numerical flux at the interface between the two rock types. Several solutions are compared.     

Nonlinear flow in fractured porous media

Conventional models of filtration in fractured porous bodies involve certain unwarrantable assumptions related to the definition of basic equations and the underestimation of a connection between the effective properties of a body and both the stress system and the pressure of a flowing fluid. A new theory is developed with the help of reconsidering those underlying assumptions and of a conception of the body being subject to elastic deformations. The theory is illustrated by means of studying a particular problem of stationary filtration.     

Mathematical model of two-phase fluid nonlinear flow in low-permeability porous media with applications

IntroductionItisasuccessfulexampleinadevelopmentstoryofscienceandtechnologyformechanicsoffluidsinporousmediatocombinewithengineeringtechnology .Fieldsinfluencedbythemechanicsinvolveddevelopmentofoil_gasandgroundwaterresources,controlonseawaterintrusionandsubsidenceandgeologichazards,geotechnicalengineeringandbioengineering ,andairlineindustry[1～ 7].Aproblemonnonlinearflowinlow_permeabilityporousmediaisbutonlyabasiconeindifferentkindsofengineeringfields,butalsooneoffrontlineresearchfieldsofmod…     

Plane steady-state incompressible fluid flow through a porous medium with a nonlinear resistance laws in the presence of a sink

Plane nonlinear fluid flows through a porous medium which simulate a sink located at the same distance from the roof and floor of the stratum for two nonlinear flow laws are constructed. The following flow laws are taken: a power law and a law of special form reducing to analytic functions in the hodograph plane.     

Streamline computations for porous media flow including gravity

In this paper we consider porous media flow without capillary effects. We present a streamline method which includes gravity effects by operator splitting. The flow equations are treated by an IMPES method, where the pressure equation is solved by a (standard) finite element method. The saturation equation is solved by utilizing a front tracking method along streamlines of the pressure field. The effects of gravity are accounted for in a separate correction step. This is the first time streamlines are combined with gravity for three-dimensional (3D) simulations, and the method proves favourable compared to standard splitting methods based on fractional steps. By our splitting we can take advantage of very accurate and efficient 1D methods. The ideas have been implemented and tested in a full field simulator. In that context, both accuracy and CPU efficiency have tested favourably.     

Finite element modelling of two-phase heat and fluid flow in deforming porous media

This paper details a finite element model which describes the flow of two-phase fluid and heat within a deforming porous medium. The coupled governing equations are derived in terms of displacements, pore pressures and temperatures, and details of the time-stepping algorithm and thermodynamic considerations are also presented. Two numerical examples are included for verification.     

The transient two-dimensional flow through double porous media

This paper presents the analytical solutions in Laplace domain for two-dimensionalnonsteady flow of slightly compressible liquid in porous media with double porosity by usingthe methods of integral transforms and variables separation.The effects of the ratio ofstorativities ω,interporosity flow parameter λ,on the pressure behaviors for a verticallyfractured well with infinite conductivity are investigated by using the method of numericalinversion.The new log-log diagnosis graph of the pressures is given and analysed.     

Rayleigh waves in orthotropic fluid-saturated porous media

In this paper, we are interested in the propagation of Rayleigh waves in orthotropic fluid-saturated porous media. This problem was investigated by Liu and Liu (2004). The authors have derived the secular equation of the wave but that secular equation is still in implicit form. The main aim of this paper is to derive explicit secular equation of the wave. By employing the method of polarization vector, the secular equations of Rayleigh waves in explicit form is obtained. This equation recovers the dispersion equation of Rayleigh waves propagating in pure orthotropic elastic half-spaces. Remarkably, the secular equation obtained is not a complex equation as the one derived by Liu and Liu, it is a really real equation.     

Global behavior of compressible three-phase flow in heterogeneous porous media

The homogenization method is used to analyze the equivalent behavior of a compressible three-phase flow model in heterogeneous porous media with periodic microstructure, including capillary effects. Asymptotic expansions lead to the definition of a global or effective model of an equivalent homogeneous reservoir. The resulting equations are of the same type as the points equations, with effective coefficients. The method allows the determination of these effective coefficients from a knowledge of the geometrical structure of the basic cell and its heterogeneities. Numerical computations to obtain the homogenized coefficients of the entire reservoir have been carried out via a finite element method.     

Compressibility and anisotropy effects in the processes of two-phase flow through a porous medium

Functions of the relative phase permeabilities which take into account the tensor nature of the relations between the absolute and phase permeabilities are constructed on the basis of experimental data. Problems of the displacement of gas by water and of water by gas in an orthotropic pore space are studied. The relative phase permeabilities obtained are compared with functions that depend only on the local saturation. The effect of the phase compressibility and the anisotropy of the absolute permeability tensor is considered.     

剧变截面圆管内渗流的数值计算方法

对于剧变截面圆管的渗流问题写出不可压缩渗流的基本方程组,对直接求解原始变量(速度和压力)的数值计算方法作出改进。先由非主流方向的运动方程计算压力,后由主流方向的运动方程计算主流方向的速度分量,再由连续性方程计算非主流方向的速度分量。这样可以避免在一般的求解原始变量方法中由连续性方程计算压力时出现的困难和麻烦。根据本方法和剧变截面圆管的特点,采用半交错不等距非正交贴体混合网格系。本文详细写出差分方程和迭代计算公式,对剧变截面圆管内的渗流算例进行数值计算。本方法的优点是简单和实用,在工程上具有较大的应用价值。     

Hydrodynamic stability of evaporation fronts in porous media

The stability of phase transition fronts in water flows through porous media is considered. In the short-wave approximation a linear stability analysis is carried out and a sufficient condition of hydrodynamic instability of the phase discontinuity is proposed. The problem of injection of a water-vapor mixture into a two-dimensional mixture-saturated formation is solved and its numerical solution is compared with an exact solution of the corresponding one-dimensional self-similar problem. It is discovered that, instead of the unstable discontinuities in the one-dimensional formulation, in the two-dimensional case a lengthy mixing zone with a characteristic scale that increases self-similarly with time is formed.     

Discretization limits of lattice-Boltzmann methods for studying immiscible two-phase flow in porous media

Digital images of porous media often include features approaching the image resolution length scale. The behavior of numerical methods at low resolution is therefore important even for well-resolved systems. We study the behavior of the Shan-Chen (SC) and Rothman-Keller (RK) multicomponent lattice-Boltzmann models in situations where the fluid-fluid interfacial radius of curvature and/or the feature size of the medium approaches the discrete unit size of the computational grid. Various simple, small-scale test geometries are considered, and a drainage test is also performed in a Bentheimer sandstone sample. We find that both RK and SC models show very high ultimate limits: in ideal conditions the models can simulate static fluid configuration with acceptable accuracy in tubes as small as three lattice units across for RK model (six lattice units for SC model) and with an interfacial radius of curvature of two lattice units for RK and SC models. However, the stability of the models is affected when operating in these extreme discrete limits: in certain circumstances the models exhibit behaviors ranging from loss of accuracy to numerical instability. We discuss the circumstances where these behaviors occur and the ramifications for larger-scale fluid displacement simulations in porous media, along with strategies to mitigate the most severe effects. Overall we find that the RK model, with modern enhancements, exhibits fewer instabilities and is more suitable for systems of low fluid-fluid miscibility. The shortcomings of the SC model seem to arise predominantly from the high, strongly pressure-dependent miscibility of the two fluid components.     

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 H.B.Jayaraman在20世纪80年代推导的悬链线索元有限元 法计算精度高，特别适用于精度要求比较高的大型索结构. 但是， 当索原长Lu的取值与悬索两节点之间的直线长度相近时，迭 代不易收敛，甚至发散. 提出了当该迭代不收敛时，应采用的迭 代策略. 计算结果表明，该方法准确，计算精度高，可供悬索结 构设计、施工时参考.     

Determination of permeability tensors for two-phase flow in homogeneous porous media: Theory

In this paper we continue previous studies of the closure problem for two-phase flow in homogeneous porous media, and we show how the closure problem can be transformed to a pair of Stokes-like boundary-value problems in terms of pressures that have units of length and velocities that have units of length squared. These are essentially geometrical boundary value problems that are used to calculate the four permeability tensors that appear in the volume averaged Stokes' equations. To determine the geometry associated with the closure problem, one needs to solve the physical problem; however, the closure problem can be solved using the same algorithm used to solve the physical problem, thus the entire procedure can be accomplished with a single numerical code.Nomenclature a a vector that maps V onto , m^-1. - A a tensor that maps V onto . - A area of the - interface contained within the macroscopic region, m². - A area of the -phase entrances and exits contained within the macroscopic region, m². - A area of the - interface contained within the averaging volume, m². - A area of the -phase entrances and exits contained within the averaging volume, m². - Bo Bond number (= (=(–)g²/). - Ca capillary number (= v/). - g gravitational acceleration, m/s². - H mean curvature, m^-1. - I unit tensor. - permeability tensor for the -phase, m². - viscous drag tensor that maps V onto V. - ^* dominant permeability tensor that maps onto v , m². - ^* coupling permeability tensor that maps onto v , m². - characteristic length scale for the -phase, m. - l characteristic length scale representing both and , m. - L characteristic length scale for volume averaged quantities, m. - n unit normal vector directed from the -phase toward the -phase. - n unit normal vector representing both n and n . - n unit normal vector representing both n and n . - P pressure in the -phase, N/m². - p superficial average pressure in the -phase, N/m². - p intrinsic average pressure in the -phase, N/m². - p –p , spatial deviation pressure for the -phase, N/m². - r ₀ radius of the averaging volume, m. - r position vector, m. - t time, s. - v fluid velocity in the -phase, m/s. - v superficial average velocity in the -phase, m/s. - v intrinsic average velocity in the -phase, m/s. - v –v , spatial deviation velocity in the -phase, m/s. - V volume of the -phase contained within the averaging volmue, m³. - averaging volume, m³. Greek Symbols V /, volume fraction of the -phase. - viscosity of the -phase, Ns/m². - density of the -phase, kg/m³. - surface tension, N/m. - (v +v ^T ), viscous stress tensor for the -phase, N/m².     

LBM simulation of fluid flow in fractured porous media with permeable matrix

To analyze and depict complicated fluid behaviors in fractured porous media with variably permeable matrix, an integrated discrete computational algorithm is proposed based on lattice Boltzmann method (LBM). This paper combines with the external force model and statistical material physics to effectively describe the feature changes while the fluid passes through the fractures within the permeable matrix. As an application example, a two dimensional rock sample is reconstructed using the digital image and characterized with different feature values at each LBM grid to distinguish pores, impermeable and permeable matrix by stating its local physical property. Compared with the conventional LBM, the results demonstrate the advantages of proposed algorithm in modeling fluid flow phenomenon in fractured porous media with variably permeable matrix.