多孔介质中流体的若干流动特性研究
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摘要
多孔介质广泛存在于自然界、工程材料、生物体和地下结构中,由于其微结构的复杂性,所以流体在多孔介质中的流动问题越来越受到人们的广泛关注。本文首先对多孔介质和分形的基本概念做了简要介绍,然后综述了分形几何理论基础。
第二部分采用几何分析法研究了二维和三维情况下的球形颗粒、立方体颗粒和板状颗粒多孔介质中流体流线的迂曲度,首先给出多孔介质的理想几何模型,通过分别考虑固体颗粒重叠时、不重叠时以及粒子的不同排列等情形时的流体流线,然后对这些理想代表性流线的迂曲度取几何平均和加权平均,最后推导出流体流过多孔介质的迂曲度解析表达式。本模型与实验数据和数值模拟结果均吻合很好,且迂曲度仅仅是孔隙率的函数,没有经验常数,因而有助于人们理解多孔介质中弯曲流线迂曲度的物理机理。
第三部分研究了幂律流体和宾汉姆流体在多孔介质中的流动。考虑到实际毛细管的弯曲性和毛细管管径的分形分布,给出了单毛细管中幂律流体的流量、水力传导系数和视粘度的分形表达式;给出了多孔介质中幂律流体的流量、流速、视粘度和有效渗透率的分形表达式;给出了多孔介质中宾汉姆流体的流量、流速和启动压力梯度的分形表达式且详细分析了启动压力梯度的影响因素。本模型将非牛顿流体与多孔介质的微结构参数有机联系起来,使我们更能深刻理解非牛顿流体在多孔介质中流动的内在机理。
第四部分研究了分形多孔介质中牛顿流体的平面径向和平行流动,考虑到实际毛细管的弯曲性和毛细管管径的分形分布,给出了径向和平行流动时的孔隙数目、孔隙率、流量、流速和渗透率的分形表达式;得到了分形多孔介质中微可压缩流体的压力分布方程;得到了无量纲的渗透率、压力和流速的解析表达式。分形多孔介质中径向和平行流动的压力分布方程在形式上与传统方法所得一致。
本文最后指出了采用分形理论和方法有可能解决的多孔介质其它输运性质参数的课题和方向。
Porous media exist everywhere in nature such as engineering materials, organs, oil and water reservoirs etc. Due to the structural complexity of porous media, the studies of flow behavior for fluid flow in porous media have steadily received much attention. First, we briefly introduce the concepts about porous media and fractal, and summarize the theory basis of fractal geometry.
In chapter 2, we focus on derivation of the tortuosity models for flow of Newtonian incompressible fluid in two- and three-dimensional porous media with spherical, cubic and plate-like particles by applying the geometrical method. We first present the ideal geometrical models of porous media to show the ideal and representative streamlines based on the assumption that some particles in porous media are unrestrictedly overlapped and hence of different configurations, then the average tortuosity is derived by geometrically and weightedly averaging these representative flow paths. The model predictions agree well with the available correlations obtained numerically and experimentally, they are expressed as a function of porosity with no empirical constant, and they are helpful for understanding the physical mechanism for tortuosity of flow paths in porous media.
In chapter 3, the power-law and Bingham fluid flow in porous media are studied. Based on the assumption that the porous medium consists of a bundle/set of tortuous streamlines/capillaries and on the fractal characteristics of pore size distribution in porous media, we develop the fractal expressions for flow rate, hydraulic conductivity and apparent viscosity for Power-law fluid flow in a single capillary, we develop the fractal expressions for flow rate, velocity, apparent viscosity and effective permeability for Power-law fluid flow in porous media, and develop the fractal expressions for flow rate, velocity and starting pressure gradient for Bingham fluid flow in porous media. The present models relate non-Newtonian fluids to the structural parameters of prous media, then the physical mechanism for non-Newtonian fluid flow in porous media is well understood.
In chapter 4, the plane-radial and plane-parallel flows for Newtonian fluid in fractal porous media are analyzed. Based on the same assumption as that in chapter 3, the expressions for porosity, flow rate, velocity and permeability for both radial and parallel flows are developed. The proposed expressions are expressed as a function of tortuosity, fractal dimension, maximum and minimum pore diameters, and there are no empirical constant and every parameter has clear physical meaning in the proposed expressions. The pressure distribution equations for slightly compressible fluid flow in fractal porous media for the plane-radial and plane-parallel flows are presented, and they are found to be formally the same as those obtained by the conventional method.
Finally, some possible research directions for future study are suggested regarding the other transport parameters in porous media.
第二部分采用几何分析法研究了二维和三维情况下的球形颗粒、立方体颗粒和板状颗粒多孔介质中流体流线的迂曲度,首先给出多孔介质的理想几何模型,通过分别考虑固体颗粒重叠时、不重叠时以及粒子的不同排列等情形时的流体流线,然后对这些理想代表性流线的迂曲度取几何平均和加权平均,最后推导出流体流过多孔介质的迂曲度解析表达式。本模型与实验数据和数值模拟结果均吻合很好,且迂曲度仅仅是孔隙率的函数,没有经验常数,因而有助于人们理解多孔介质中弯曲流线迂曲度的物理机理。
第三部分研究了幂律流体和宾汉姆流体在多孔介质中的流动。考虑到实际毛细管的弯曲性和毛细管管径的分形分布,给出了单毛细管中幂律流体的流量、水力传导系数和视粘度的分形表达式;给出了多孔介质中幂律流体的流量、流速、视粘度和有效渗透率的分形表达式;给出了多孔介质中宾汉姆流体的流量、流速和启动压力梯度的分形表达式且详细分析了启动压力梯度的影响因素。本模型将非牛顿流体与多孔介质的微结构参数有机联系起来,使我们更能深刻理解非牛顿流体在多孔介质中流动的内在机理。
第四部分研究了分形多孔介质中牛顿流体的平面径向和平行流动,考虑到实际毛细管的弯曲性和毛细管管径的分形分布,给出了径向和平行流动时的孔隙数目、孔隙率、流量、流速和渗透率的分形表达式;得到了分形多孔介质中微可压缩流体的压力分布方程;得到了无量纲的渗透率、压力和流速的解析表达式。分形多孔介质中径向和平行流动的压力分布方程在形式上与传统方法所得一致。
本文最后指出了采用分形理论和方法有可能解决的多孔介质其它输运性质参数的课题和方向。
Porous media exist everywhere in nature such as engineering materials, organs, oil and water reservoirs etc. Due to the structural complexity of porous media, the studies of flow behavior for fluid flow in porous media have steadily received much attention. First, we briefly introduce the concepts about porous media and fractal, and summarize the theory basis of fractal geometry.
In chapter 2, we focus on derivation of the tortuosity models for flow of Newtonian incompressible fluid in two- and three-dimensional porous media with spherical, cubic and plate-like particles by applying the geometrical method. We first present the ideal geometrical models of porous media to show the ideal and representative streamlines based on the assumption that some particles in porous media are unrestrictedly overlapped and hence of different configurations, then the average tortuosity is derived by geometrically and weightedly averaging these representative flow paths. The model predictions agree well with the available correlations obtained numerically and experimentally, they are expressed as a function of porosity with no empirical constant, and they are helpful for understanding the physical mechanism for tortuosity of flow paths in porous media.
In chapter 3, the power-law and Bingham fluid flow in porous media are studied. Based on the assumption that the porous medium consists of a bundle/set of tortuous streamlines/capillaries and on the fractal characteristics of pore size distribution in porous media, we develop the fractal expressions for flow rate, hydraulic conductivity and apparent viscosity for Power-law fluid flow in a single capillary, we develop the fractal expressions for flow rate, velocity, apparent viscosity and effective permeability for Power-law fluid flow in porous media, and develop the fractal expressions for flow rate, velocity and starting pressure gradient for Bingham fluid flow in porous media. The present models relate non-Newtonian fluids to the structural parameters of prous media, then the physical mechanism for non-Newtonian fluid flow in porous media is well understood.
In chapter 4, the plane-radial and plane-parallel flows for Newtonian fluid in fractal porous media are analyzed. Based on the same assumption as that in chapter 3, the expressions for porosity, flow rate, velocity and permeability for both radial and parallel flows are developed. The proposed expressions are expressed as a function of tortuosity, fractal dimension, maximum and minimum pore diameters, and there are no empirical constant and every parameter has clear physical meaning in the proposed expressions. The pressure distribution equations for slightly compressible fluid flow in fractal porous media for the plane-radial and plane-parallel flows are presented, and they are found to be formally the same as those obtained by the conventional method.
Finally, some possible research directions for future study are suggested regarding the other transport parameters in porous media.
引文
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