Fluid flow in a porous medium containing partially closed fractures

The model of Snow, in which a fracture is represented by two parallel channel walls, has frequently been used to study the flow of fluid in fractured reservoirs. Although this model gives important insight into the flow in fractures, very few naturally occurring fractures have smooth parallel faces. In this paper, a simple model of partially contacting and en-echelon fractures frequently found in geological materials is presented. In this model, a fracture is viewed as a planar region where separation and contact zones both exist. To analyse the fluid flow in a porous medium containing fractures of this type, a planar array of periodically spaced fracture segments is analysed. The flow through a single fracture is deduced by taking the limit as the spacing between neighbouring fractures becomes large. The hydraulic conductivity parallel to the fractures is found to be the parallel combination of the conductivity of the porous matrix and the system of parallel fractures, the individual fracture conductance being a series combination of the hydraulic conductance of the separation and contact zones. This interpretation enables the conductance of the contact zones to be evaluated and the results to be generalised to the case in which the material in the contact regions has a hydraulic conductivity different to that of the matrix. This may arise, for example, from grain-size reduction during fracturing or may result from a partial mineralisation or cementation of the fracture.     

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.     

THE TRANSIENT ELLIPTIC FLOW OF POWER-LAW FLUID IN FRACTAL POROUS MEDIA

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The behavior of naturally fractured reservoirs including fluid flow in matrix blocks

An alternative analytical solution to the system of equations for fluid flow through a double-porosity medium with a boundary condition of an equipotential surface is given in this paper. The problem is reduced to solving an integral equation. The solution is straight-forward, and involves only ordinary Bessel functions. Numerical results show that D, the ratio of matrix system permeability to fracture system permeability, has a strong effect on the two semilog straight lines characteristic of the pressure response in a double-porosity medium. As D increases from zero (the Warren-Root model) to one, the first semilog straight line moves closer to the second. This is similar to the effect of increasing ω, the ratio of storage capacity of the fracture system to total storage capacity, in the Warren-Root model which neglects the flow within matrix blocks.     

Aspects of geothermal well test analysis in fractured reservoirs

Several numerical experiments comparing the response of a fractured geothermal reservoir with that of a uniform reservoir are reported. A constant rate drawdown test followed by a buildup test is investigated for both an initially two-phase reservoir and an initially liquid reservoir which flashes during the test. Also, cold water injection into a two-phase reservoir is considered. In all cases the fracturing of the reservoir significantly changes the results for the uniform reservoir, and makes interpretation of the well test results more difficult.     

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.     

页岩气和致密砂岩气藏微裂缝气体传输特性

页岩气和致密砂岩气藏发育微裂缝,其开度多在纳米级和微米级尺度且变化大,因此微裂缝气体传输机理异常复杂.本文基于滑脱流动和努森扩散模型,分别以分子之间碰撞频率和分子与壁面碰撞频率占总碰撞频率的比值作为滑脱流动和努森扩散的权重系数,耦合这两种传输机理,建立了微裂缝气体传输模型. 该模型考虑微裂缝形状和尺度对气体传输的影响. 模型可靠性用分子模拟数据验证.结果表明:(1)模型能够合理描述微裂缝中所有气体传输机理,包括连续流动,滑脱流动和过渡流动;(2)模型能够描述不同开发阶段,微裂缝中各气体传输机理对传输贡献的逐渐变化过程;(3)微裂缝形状和尺度影响气体传输,相同开度且宽度越大的微裂缝,气体传输能力越强,且在高压和微裂缝大开度的情况下表现更明显.      

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.     

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.     

缝洞型多孔介质中多相流的有限体积法数值模拟

本文研究的碳酸盐岩油藏储集体属于缝洞型多孔介质.这类缝洞型多孔介质由裂缝、溶蚀孔洞和低孔隙度低渗透率的基岩组成.裂缝是空隙流体流动的主要通道;溶蚀孔洞大小从几厘米到数米不等,渗透率和孔隙度都很高,是流体主要的储集空间.由于缝洞型多孔介质空隙空间的复杂性和强非均质性,数值计算中基本控制方程的空间离散应采用非结构化网格的计算模型.本文采用有限体积法模拟缝洞型多孔介质中多相流体的流动,并给出了相应的单元中心格式有限体积法的计算公式.裂缝介质和溶洞介质中单元间多相流体的流动考虑为高速非达西流,其质量通量采用Forchheimer定律计算.非线性方程的离散选取全隐式格式,并采用Newton-Raphson迭代进行求解.通过两个二维模型注水驱油的数值模拟,验证了本文方法的有效性.     

Oscillatory Couette flow of rotating Sisko fluid

The oscillatory Couette flow of a magnetohydrodynamic （MHD） Sisko fluid between two infinite non-conducting parallel plates is explored in a rotating frame. The lower plate is fixed, and the upper plate is oscillating in its own plane. Using MATLAB, a numerical solution to the resulting nonlinear system is presented. The influence of the physical parameters on the velocity components is analyzed. It is found that the effect of rotation on the primary velocity is more significant than that on the secondary velocity. Further, the oscillatory character in the flow is also induced by rotation. The considered flow situation behaves inertialess when the Reynolds number is small.     

Discretizing two‐dimensional complex fractured fields for incompressible two‐phase flow

A method is introduced to discretize irregular and complex two‐dimensional fractured media. The geometry of the fractured media is first analysed by searching and treating the complex configurations. Based on that, the method generated a good mesh quality and allows for including finer grids. An incompressible two‐phase flow problem is solved to compare the developed method and a public method based on the approximation of a 1D fracture by the edges of a 2D finite element grid of the porous media. The comparison showed that the developed method (i) represents better the fractured domain by maintaining the geometric integrity of input surfaces and geologic data, (ii) provides, for sample and complex fractured domains, excellent and more accurate results, and (iii) is much less sensitive to the grid sizes. Furthermore, the method has to be more efficient than the other methods for transport problems and has to provide better predictable results; this is mainly based on point (ii) and because the method produces optimal triangular grids. Copyright © 2009 John Wiley & Sons, Ltd.     

A study on non-steady flow of upper-convected maxwell fluid in tube

The transient response of an upper-convected Maxwell fluid flow in a circular tube is analysed by variational approach of Kantorovich and the method of finite difference. The solution of the variational method is in agreement with the numerical results by the difference schemes. The results show that the method of Kantorovich is suitable for the study of non-steady flow of non-Newtonian fluids and the effect of elasticity of the fluid has an influence on the non-steady flow. project supported by National Natural Science Foundation of China     

Analytic Analysis for Oil Recovery During Counter-Current Imbibition in Strongly Water-Wet Systems

We study counter-current imbibition, where a strongly wetting phase (water) displaces non-wetting phase spontaneously under the influence of capillary forces such that the non-wetting phase moves in the opposite direction to the water. We use an approximate analytical approach to derive an expression for saturation profile when the viscosity of the non-wetting phase is non-negligible. This makes the approach applicable to water flooding in hydrocarbon reservoirs, or the displacement of non-aqueous phase liquid (NAPL) by water. We find the recovery of non-wetting phase as a function of time for one-dimensional flow. We compare our predictions with experimental results in the literature. Our formulation reproduces experimental data accurately and is superior to previously proposed empirical models.     

Laws of viscoplastic fluid flow in anisotropic porous and fractured media

In invariant tensor form, the laws of viscoplastic fluid flow are formulated for capillary and fractured media with a periodic microstructure that has orthotropic and transversely isotropic symmetry in the flow properties. An analysis of the laws of viscoplastic fluid flow in transversely isotropic and orthotropic porous and fractured media shows that in formulating the equations it is necessary to distinguish between the permeability tensor and the limiting gradient tensor, which may differ in the symmetry of the flow characteristics, and that the flow law is multivariant and admits one-, two-, and three-dimensional flows.     

Rotating electroosmotic flow of an Eyring fluid

A perturbation analysis is presented in this paper for the electroosmotic(EO) flow of an Eyring fluid through a wide rectangular microchannel that rotates about an axis perpendicular to its own. Mildly shear-thinning rheology is assumed such that at the leading order the problem reduces to that of Newtonian EO flow in a rotating channel, while the shear thinning effect shows up in a higher-order problem.Using the relaxation time as the small ordering parameter,analytical solutions are deduced for the leading-as well as first-order problems in terms of the dimensionless Debye and rotation parameters. The velocity profiles of the Ekman–electric double layer(EDL) layer, which is the boundary layer that arises when the Ekman layer and the EDL are comparably thin, are also deduced for an Eyring fluid. It is shown that the present perturbation model can yield results that are close to the exact solutions even when the ordering parameter is as large as order unity. By this order of the relaxation time parameter, the enhancing effect on the rotating EO flow due to shear-thinning Eyring rheology can be significant.     

Unsteady flow of a fourth-grade fluid due to an oscillating plate

The governing non-linear high-order, sixth-order in space and third-order in time, differential equation is constructed for the unsteady flow of an incompressible conducting fourth-grade fluid in a semi-infinite domain. The unsteady flow is induced by a periodically oscillating two-dimensional infinite porous plate with suction/blowing, located in a uniform magnetic field. It is shown that by augmenting additional boundary conditions at infinity based on asymptotic structures and transforming the semi-infinite physical space to a bounded computational domain by means of a coordinate transformation, it is possible to obtain numerical solutions of the non-linear magnetohydrodynamic equation. In particular, due to the unsymmetry of the boundary conditions, in numerical simulations non-central difference schemes are constructed and employed to approximate the emerging higher-order spatial derivatives. Effects of material parameters, uniform suction or blowing past the porous plate, exerted magnetic field and oscillation frequency of the plate on the time-dependent flow, especially on the boundary layer structure near the plate, are numerically analysed and discussed. The flow behaviour of the fourth-grade non-Newtonian fluid is also compared with those of the Newtonian fluid.     

Fully computerized evaluation of interferograms from fluid flow investigations

An interactive computerized system capable of evaluating interferograms, obtained for example in gas flow studies, has been developed. The program takes full advantage of the facilities offered by the Apple 2 microcomputer and is designed so that the user needs no previous knowledge of computers and/or software. The program is constructed of several main programs invoking other sub-programs; each program can be active at each step of the process and is menu driven. Thus, the user does not have to remember either the questions or their order of appearance.     

An investigation on internal thermal flow of non-Newtonian fluid

In the present paper an unsteady thermal flow of non-Newtonian fluid is investigated which is of the fiow into axisymmetric mould cavity. In the second part an unsteady thermal flow of upper-convected Maxwell fluid is studied, For the flow into mould cavity the constitutive equation of power-law fluid is used as a rheological model of polymer fluid. The apparent viscosity is considered as a function of shear rate and temperature. A characteristic viscosity is introduced in order to avoid the nonlinearity due to the temperature dependence of the apparent viscosity. As the viscosity of the fluid is relatively high the flow of the thermal fluid can be considered as a flow of fully developed velocity field. However, the temperature field of the fluid fiow is considered as an unsteady one. The governing equations are constitutive equation, momentum equation of steady flow and energy conservation equation of non-steady form. The present system of equations has been solved numerically by the splitting differen