粘性指进显示及其分维测量

考虑到液体驱油时粘性指进可能造成原油回采严重减少，利用图像采集系统对多孔介质中由粘性指进不稳定性导致的指进花样进行显示，测算其分维指数并研究聚合物浓度与分维的关系。     

多孔介质渗透率的一种新分形模型

多孔介质的渗流特性是油气藏工程、地下水资源利用、高放废物深地质处置等实际工程领域的热门研究问题．基于分形理论及多孔介质由一束面积大小不等的椭圆形毛细管组成的假设,本文建立了流体在分形多孔介质中渗流时的绝对渗透率及相对渗透率的分形渗透率模型．结果表明,绝对渗透率是最大和最小孔隙面积、分形维数、形状因子ε的函数,且当ε =1时,本文模型可以简化成Yu与Cheng模型;而非饱和多孔介质的相对渗透率与饱和度和多孔介质微结构参数有关．将本文提出的渗透率分形模型预测与实验测量数据及其他模型结果进行对比,显示它们整体吻合很好．     

聚合物流体渗流机理研究

聚合物流体在多孔介质中渗流的研究是近年来有重大进展的领域。本文介绍从力学与物理方法进行渗流机理研究的思路、主要结果和当前活跃的研究课题。流体的非牛顿性对复杂边界条件下均匀流体力学效应的影响已得到了较好的定量处理;揭示了拉伸流粘弹特性对渗流影响的机理,其定量描述则尚有待努力。进而讨论了石油工程中十分重要的非均一流体渗流的新进展,包括大分子效应与粘性指进效应及其分形描述。对于上述物理效应的综合考虑将使聚合物渗流力学研究进入新的阶段。      

一个简单易行的分形实验

用单位的Ｈｅｌｅ-Ｓｈａｗ实验装置,用不同的物系,以及不同的间距,进行了分形-粘性指进现象实验,并拍照记录下来．     

多孔介质输运性质的分形分析研究进展

首先对多孔介质输运性质的传统实验测量、解析分析和数值模拟计算研究进展作了扼要的评述.然后,着重综述采用分形理论和方法研究多孔介质输运性质分析解的理论、方法和所取得的进展.最后,指出采用分形理论和方法有可能解决其它尚未解决的有关多孔介质输运性质的若干课题和方向.      

幂律流体在多孔介质中径向渗流的分形模型

基于分形理论及毛细管模型,本文研究了非牛顿幂律流体在各向同性多孔介质中径向流动问题,推导了幂律流体径向有效渗透率的分形解析表达式．研究结果表明,幂律流体径向有效无量纲渗透率模型和Chang and Yortsos’s模型吻合很好;同时还得出幂律流体径向有效渗透率随孔隙率、幂指数的增加而增加,随迂曲度分形维数的增加而减少．     

分形在油气田开发中的应用

分形用于测井资料分析，为油藏描述提供了新的工具，使得利用油藏数值模拟来模拟复杂结构的油气藏变得更加便利；分形油藏上的试井分析解决了一些以前难以解释的问题；用分形来描述裂缝和孔洞结构，提高了酸化压裂的设计水平；用分形理论来描述两相流，揭示了部分粘性指进的触发机理．总之，分形理论在油气田开发中的应用，促进了渗流力学基础理论的发展．     

流体饱和标准线性粘弹性多孔介质中的平面波

研究了流体饱和不可压标准线性粘弹性多孔介质中平面波的传播和反射问题．在固相骨架小变形的假定下,得到了粘弹性多孔介质中波动方程的一般解,讨论了弥散关系和波的衰减特性．结果表明：在流体饱和不可压粘弹性多孔介质中,仅存在一个耦合纵波和一个耦合横波,纵波和横波的波速、衰减率等取决于孔隙流体与固相骨架间的相互作用以及固相骨架本身的粘性．同时,研究了半空间自由边界上入射波(纵波、横波)的反射问题。得到了非均匀反射波的波速、反射系数、衰减率等的表达式及其相关的数值结果．     

多孔介质自发渗吸研究进展

自发渗吸是发生在多孔介质里的一种常见自然现象, 存在于众多工程应用和自然科学领域, 多孔介质 中自发渗吸的基本静力学和动力学问题已成为当前国际研究的热点课题之一. 本文综述了传统理论研究中的 Lucas{Washburn(LW) 模型, Terzaghi 模型, Handy 模型, Mattax 和Kyte 无因次时间标度模型, Aronofsky 归 一化采收率标度模型以及近十年最新研究进展, 分析了渗吸机理判别参数研究, 简述了数值模拟研究及渗吸率 影响机理的实验研究现状, 总结了基于分形理论研究多孔介质自发渗吸的最新进展, 并展望了多孔介质以及裂 缝性双重多孔介质中牛顿流体和非牛顿流体自发渗吸研究的方向和课题.      

一维流体饱和粘弹性多孔介质层的动力响应

本文研究了不可压流体饱和粘弹性多孔介质层的一维动力响应问题。基于粘弹性理论和多孔介质理论,在流相和固相微观不可压、固相骨架服从粘弹性积分型本构关系和小变形的假定下,建立了不可压流体饱和粘弹性多孔介质层一维动力响应的数学模型,利用Laplace变换,求得了原初边值问题在变换空间中的解析解,并利用Laplace逆变换的Crump数值反演方法,得到原动力响应问题的数值解。数值研究了饱和标准线性粘弹性多孔介质层的动力响应,分析了固相位移、渗流速度、孔隙压力及固相有效应力等的响应特征。结果表明,与不可压流体饱和弹性多孔介质相同,不可压流体饱和粘弹性多孔介质中亦只存在一个纵波,并且固相骨架的粘性对动力行为有显著的影响。     

Simulation of multiphase flows in porous media

The ability to numerically simulate single phase and multiphase flow of fluids in porous media is extremely important in developing an understanding of the complex phenomena governing the flow. The flow is complicated by the presence of heterogeneities in the reservoir and by phenomena such as diffusion, dispersion, and viscous fingering. These effects must be modeled by terms in coupled systems of nonlinear partial differential equations which form the basis of the simulator. The simulator must be able to handle both single and multiphase flows and the transition regimes between the two. A discussion of some of the aspects of modeling dispersion and viscous fingering is presented along with directions for future work.The partial differential equation models are convection-dominated and contain important local effects. An operator-splitting technique is used to address these different effects accurately. Convection is treated by time stepping along the characteristics of the associated pure convection problem, and diffusion is modeled via a Galerkin method for single phase flow and a Petrov-Galerkin technique for multiphase regimes. ELLAM (Eulerian-Lagrangian Localized Adjoint Methods) are discussed to effectively treat the advection-dominated processes. Accurate approximations of the fluid velocities needed in the Eulerian-Lagrangian time-stepping procedure are obtained by mixed finite element methods. Adaptive local grid refinement techniques are then indicated to resolve important local phenomena around wells and large heterogeneities or to resolve the moving internal boundary layers which often govern the mass transfer between phases.     

LBM Simulation of Viscous Fingering Phenomenon in Immiscible Displacement of Two Fluids in Porous Media

This article presents the lattice Boltzmann simulation of viscous fingering phenomenon in immiscible displacement of two fluids in porous media. Such phenomenon generally takes place when a less viscous fluid is used to displace a more viscous fluid, and it can be found in many industrial fields. Dimensionless quantities, such as capillary number, Bond number and viscosity ratio between displaced fluid and displacing fluid are introduced to illustrate the effects of capillary force, viscous force, and gravity on the fluid behaviour. The surface wettability, which has an impact on the finger pattern, is also considered in the simulation. The numerical procedure is validated against the experiment about viscous fingering in a Hele-Shaw cell. The displacement efficiency is investigated using the parameter, areal sweep efficiency. The present simulation shows an additional evidence to demonstrate that the lattice Boltzmann method is a useful method for simulating some multiphase flow problems in porous media.     

Characterization of the crossover from capillary invasion to viscous fingering to fracturing during drainage in a vertical 2D porous medium

We experimentally studied the displacement of a viscous wetting fluid (water) by an inviscid non-wetting fluid (air) injected at the bottom of a vertical Hele-Shaw cell filled with glass microbeads. In order to cover a wide parameter space, the permeability of the porous medium was varied by using different bead size ranges and diverse air flow rates were generated by means of a syringe pump. A LED light table was used to back illuminate the experimental cell, allowing a high speed camera to capture images of the drainage process at equal time intervals. The invasion occurred in intermittent bursts. Image processing of the bursts and fractal analysis showed successive transitions from capillary invasion to viscous fingering to fracturing during the same experiment, dependent on the medium permeability, the air injection flow rate, and the vertical position in the cell. The interplay between the capillary, viscous and gravity forces determines the nature of the invasion pattern and the transitions, from capillary invasion to viscous fingering with decreasing fluid pressure on one hand and from viscous fingering to fracturing with decreasing effective overburden pressure on the other hand.     

Fully implicit finite difference pseudo‐spectral method for simulating high mobility‐ratio miscible displacements

A finite difference–pseudo‐spectral (FD–PS) algorithm is developed to simulate the viscous fingering instability in high mobility‐ratio (MR) miscible displacements. This novel algorithm uses the fully implicit alternating‐direction implicit (ADI) method combined with a Hartley based pseudo‐spectral method to solve the Poisson equation involving the streamfunction and the vorticity. In addition, under‐relaxation in the iterative evaluation of the streamfunction is adopted. The new code allowed to model successfully the viscous fingering instability for mobility‐ratios as high as 1800, and new non‐linear viscous fingering mechanisms are discovered. A systematic analysis of the effects of the MR, the Peclet number and the aspect ratio on the finger growth is conducted. It is found that the growth of the interfacial instability accelerates with increase in the MR and Peclet number. At larger values of these parameters the increased stiffness of the corresponding numerical problem caused significant increase in the computational time as it required finer grids and smaller time steps to capture the fine structures of the viscous fingers. Copyright © 2004 John Wiley & Sons, Ltd.     

Investigating the Temperature Dependency of Oil and Water Relative Permeabilities for Heavy Oil Systems

A look into the literature on the temperature dependency of oil and water relative permeabilities reveals contradictory reports. There are some publications reporting shifts in the water saturation range as well as variations in the relative permeability curves by temperature. On the other hand, some authors have blamed the experimental artifacts, viscous instabilities and fingering issues for these variations. We have performed core flooding experiments to further investigate this issue. Glass bead packs and sand packs were used as the porous media, and Athabasca bitumen with varying viscosities was displaced by hot water at differing temperatures. The unsteady-state method of relative permeability measurement was applied and the experimental data were history matched by a simulator that is tailor made to predict the relative permeabilities. The matches were obtained by varying the relative permeability correlation parameters. The results indicated that the initial water saturation has a direct relation with temperature, while residual oil saturation generally drops at higher temperatures. Although the water saturation range shifts, no direct and unique trend for either oil or water relative permeability is justified. The spread in relative permeabilities especially in the case of higher permeable cores suggests that viscous instabilities are present. As the same saturation shift happens by only changing the oil viscosity, the relative permeability variations with temperature can be attributed to oil to water viscosity ratio changes with temperature. Temperature dependency of relative permeabilities is more related to experimental artifacts, viscous fingering and viscosity changes than fundamental flow properties.     

Radial viscous fingering patterns in Hele-Shaw cells

Viscous fingering experiments were performed by injecting a liquid to radially displace a much more viscous liquid in a Hele-Shaw cell consisting of two parallel closely-spaced glass plates. Both smooth and etched plates were used to study the influence of plate roughness on the fingering mechanism. Effect of flow rate and interfacial tension was also demonstrated. The results show that symmetric dendritic finger patterns can form in the presence of anisotropy provided by an etched square network, for both miscible and immiscible fingers. Chaotic finger patterns can form both in a cell with smooth surfaces and in one having a network of randomly oriented channels etched on one plate. Due to interfacial tension, the immiscible finger patterns are less ramified than their miscible counterparts, are more sensitive to the flow rate and become compact as the flow rate decreases. Possible applications of two-phase displacement studies in Hele-Shaw cells are discussed, which include two-phase flow in porous media and acid fracturing of oil reservoirs.     

Pore-Scale Investigation of Two-Phase Flows in Three-Dimensional Digital Models of Natural Sandstones

The results of numerical simulation of the processes of two-phase flow through a porous medium in three-dimensional digital models of the porous space of three natural sandstone samples are given. The calculations are carried out using the lattice Boltzmann equations and the digital field gradient model over a wide range of the capillary numbers and the viscosity ratios of injected and displaced fluids. The conditions of flow through a porous medium with capillary fingering, viscous fingering and with stable displacement front are revealed.     

Viscosity-stratified flow in a Hele–Shaw cell

A hierarchy of mathematical models describing viscosity-stratified flow in a Hele-Shaw cell is constructed. Numerical modelling of jet flow and development of viscous fingers with the influence of inertia and friction is carried out. One-dimensional multi-layer flows are studied. In the framework of three-layer flow the interpretation of the Saffman–Taylor instability is given. A kinematic-wave model of viscous fingering taking into account friction between the fluid layers is proposed. Comparison with calculations on the basis of two-dimensional equations shows that this model allows to determine the propagation velocity of the viscous fingers.     

Unstable Displacement of Non-aqueous Phase Liquids with Surfactant and Polymer

In this paper, we study two-phase multicomponent displacement of two immiscible fluids in both homogeneous and heterogeneous porous media. In many applications such as enhanced oil recovery, fluid mixing and spreading can be detrimental to the efficacy of the process. Here, we show that when an initially immobile phase is being displaced by a finite-size slug of solvents (surfactant and polymer), viscous fingering significantly enhances mixing and spreading of solvents. These effects are similar to those caused by medium heterogeneity and lead to poor displacement efficiency. We first quantify the displacement efficiency subject to different mobility ratios, Peclet numbers, and levels of medium heterogeneity. We observe a non-monotonic behavior in displacement efficiency as a function of mobility ratio, indicating that although stable frontal interface is desirable, miscible viscous fingering on the rear interface will eventually disintegrate the solvents slugs and reduce the displacement efficiency. Then, we show that miscible viscous fingering developing on the rear interface of the chemical slug could be greatly suppressed when viscosity contrast is gradually decreased using exponential or linear functions, leading to 10% increase in displacement efficiency while using the same amount of chemicals. To elucidate this low displacement efficiency, we study the evolution of mixing, spreading, and interfacial length and show that while higher viscosity ratios are quite effective in mobilizing the initially immobile phase in 1D displacements, they are in fact detrimental in 2D unstable displacements since they enhance mixing and spreading of solvents.