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．     

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.      

考虑损伤作用计算多孔介质有效应力研究

多孔介质的变形表现为黏弹塑性,其中,弹性变形体现为本体变形;黏性变形体现为结构变形;塑性变形体现为损伤变形.在原有有效应力理论的基础上结合损伤力学的基本原理,研究多孔介质有效应力的性质.在原假设多孔介质颗粒可压缩的前提下,假定部分颗粒可发生局部破坏,并且在颗粒破坏后,有效应力将有所增加,相应的骨架承载能力将有微小程度增强.采用损伤有效应力参与计算将能更加准确地描述多孔介质复杂的变形性质.     

岩土介质的分形孔隙和分形粒子

岩土介质是晶粒状材料,存在大量的孔隙。这些孔隙的存在严重地影响岩土介质的力学、物理和化学性能。大量的研究表明,岩土介质的孔隙几何从原子尺度到晶粒尺寸范围内均表现出分形特征。目前分形几何已被广泛应用来研究岩土的孔隙率,输运特性和渗透性等等。本文从5个方面来讨论岩土介质的分形孔隙和分形粒子:①分形几何简介;②孔隙介质的分形模型;③岩土介质的分形孔隙特性和它们的分形量测方法;④岩土的分形粒子;⑤水土保持估计中的分形毛细管模型。      

弹塑性多孔介质流固耦合新理论:混合耦合理论

在全球气候变化和双碳政策的大背景下,多孔介质中固体的变形和流体的输运问题变得尤为重要。然而,在多孔介质中建立流固耦合模型仍面临的挑战之一是需要考虑跨越宏观尺度到纳米尺度的耦合作用。本文利用基于非平衡热力学的混合耦合理论,提出了一个弹塑性多孔介质流固耦合新模型,在同一个理论框架内研究了弹性变形、塑性变形和液体渗流之间跨尺度的耦合,考虑了耗散过程中的熵产,并利用Helmholtz自由能来连接宏观尺度上的力学变形和纳米尺度上的液体输运之间的相互作用。在应力-应变关系中采用了弹塑性刚度系数以反映塑性的影响。同时,经典的达西定律扩展为考虑固体的塑性变形。通过与文献中模型的比较,验证了该模型的有效性。最后,数值分析表明在多孔介质的流固耦合中塑性变形具有比较显著的影响。     

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多孔介质的变形表现为黏弹塑性,其中,弹性变形体现为本体变形;黏性变 形体现为结构变形;塑性变形体现为损伤变形. 在原有有效应力理论的基础上结合损伤力学 的基本原理,研究多孔介质有效应力的性质. 在原假设多孔介质颗粒可压缩的前提下,假定 部分颗粒可发生局部破坏,并且在颗粒破坏后,有效应力将有所增加,相应的骨架承载能力 将有微小程度增强. 采用损伤有效应力参与计算将能更加准确地描述多孔介质复杂的变形性 质.     

基于物理界面的双重介质有限裂隙渗流模型

基于连续介质或者离散裂隙假设,含裂隙的多孔介质渗流问题有多种数学力学模型。受物理界面的启发,提出一种新的有限裂隙连续介质力学模型,可以为宏观裂隙-多孔介质内的流体输运问题等提供近似计算方案。该模型属于一类双重介质模型,将曲面上低维度的流场转化为三维空间的流场,并且与连续的多孔介质的流场耦合,在数学上表示为统一的输运控制方程和初始边界条件。这个近似模型为不方便实施高维度-低维度耦合求解的数值计算方法提供新的模拟思路,如光滑粒子流体动力学等无网格粒子类方法。     

多孔介质——自由流界面应力跳跃条件下流动特性解析解

对非对称多孔介质--自由流复合通道内多孔介质内部及多孔介质与自由流体界面处复杂质量、动量输运特性进行研究. 在多孔介质区采用Brinkman-extended Darcy模型并结合速度连续,剪切应力跳跃的界面条件对此复合通道内流体的传递现象进行求解,提出了考虑界面应力跳跃时非对称复合通道各区域流体运动速度及摩擦系数的解析式,分析了界面应力跳跃系数,达西数及无量纲多孔层偏心厚度对流体速度及摩擦系数的影响. 结果表明:改变界面性质可在一定条件下明显控制各区域流体速度分布;在达西数、多孔层偏心厚度一定情况下,界面应力系数的增大会使界面流速减小,而使流体摩擦系数增大,特别是界面应力系数小于0的情况下变化更明显,此时若不考虑界面应力系数则会造成较大误差. 当界面应力系数及多孔层偏心厚度均为较小负数值时,改变多孔层偏心厚度对界面速度的影响要大于改变界面应力系数的情况;而当界面应力系数及多孔层偏心厚度为较大正数值时,情况则相反. 较大达西数下,界面应力系数及多孔层偏心厚度对流体摩擦系数的影响均较大,继续减小达西数至一定程度时,界面应力系数对流体摩擦系数的影响可忽略不计而认为只与多孔层偏心厚度相关,且对较大多孔层偏心厚度更敏感.      

沸腾换热的分形分析

研究沸腾换热过程是安全、高效地利用能源的基础.简要评述了沸腾换热(池内沸腾、流动沸腾、临界热流密度和纳米流体沸腾换热)的研究进展;详细论述了采用分形理论和方法研究沸腾换热分析解的理论和方法;指出了采用分形理论和方法有可能解决其它尚未解决的有关沸腾换热的若干课题和方向.      

不可压饱和粘弹性多孔介质固结问题的Gurtin型变分原理

基于多孔介质理论,在固相骨架和孔隙流体微观不可压,固相骨架小变形且满足线性粘弹性积分型本构关系的假定下,利用卷积积分的性质,本文首先建立了以固相骨架位移、孔隙流体相对速度和孔隙流体压力为宗量的流体饱和粘弹性多孔介质固结问题的一个Gurtin型变分原理.其次,利用Lagrange乘子法解除相关的变分约束条件,建立了流体饱和粘弹性多孔介质固结问题的若干广义Gurtin型变分原理,包括第三类的Hu-Washizu型变分原理.最后,简单讨论了等价初边值问题的相应变分原理.这些Gurtin型变分原理的建立不仅丰富了饱和粘弹性多孔介质的相关理论,而且为相关数值模拟方法,如有限元法、无网格法等的建立奠定了理论基础.     

A Hierarchical Sampling for Capturing Permeability Trend in Rock Physics

Among all properties of reservoir rocks, permeability is an important parameter which is typically measured from core samples in the laboratory. Due to limitations of core drilling all over a reservoir, simulation of rock porous media is demanded to explore more scenarios not seen in the available data. One of the most accurate methods is cross correlation based simulation (CCSIM) which recently has broadly applied in geoscience and porous media. The purpose of this study is producing realizations with the same permeability trend to a real sample. Berea sandstone sample is selected for this aim. Permeability results, extracted from smaller sub-samples of the original sample, showed that classic Kozeny–Carman permeability trend is not suitable for this sample. One reason can be due to lack of including geometrical and fractal properties of pore-space distribution in this equation. Thus, a general trend based on fractal dimensions of pore-space and tortuosity of the Berea sample is applied in this paper. Results show that direct 3D stochastic modeling of porous media preserves porous structure and fractal behavior of rock. On the other hand, using only 2D images for constructing the 3D pore structures does not reproduce the measured experimental permeability. For this aim, a hierarchical sampling is implemented in two and three steps using both 2D and 3D stochastic modeling. Results showed that two-step sampling is not suitable enough, while the utilized three-step sampling occurs to be show excellent performance by which different models of porous media with the same permeability trend as the Berea sandstone sample can be generated.     

On the Permeability of Fractal Tube Bundles

The permeability of a porous medium is strongly affected by its local geometry and connectivity, the size distribution of the solid inclusions, and the pores available for flow. Since direct measurements of the permeability are time consuming and require experiments that are not always possible, the reliable theoretical assessment of the permeability based on the medium structural characteristics alone is of importance. When the porosity approaches unity, the permeability?Cporosity relationships represented by the Kozeny?CCarman equations and Archie??s law predict that permeability tends to infinity and thus they yield unrealistic results if specific area of the porous media does not tend to zero. The aim of this article is the evaluation of the relationships between porosity and permeability for a set of fractal models with porosity approaching unity and a finite permeability. It is shown that the tube bundles generated by finite iterations of the corresponding geometric fractals can be used to model porous media where the permeability?Cporosity relationships are derived analytically. Several examples of the tube bundles are constructed, and the relevance of the derived permeability?Cporosity relationships is discussed in connection with the permeability measurements of highly porous metal foams reported in the literature.     

Study of the effect of capillary pressure on the permeability of porous media embedded with a fractal-like tree network

In this paper, the analytical expressions for permeability of (both saturated and unsaturated) porous media embedded with a fractal-like tree network are presented based on fractal theory and technique when the capillary pressure is taken into account. Both the dimensionless effective permeability and the relative permeability of the composites, which are defined as porous media embedded with a fractal-like tree network in this work, are derived and found to be a function of saturation, the capillary pressure and microstructural parameters of the networks. The relative permeabilities predicted by the present fractal model are compared with the available experimental data and a fair agreement between them is found.     

A Fractal Model for Oil Transport in Tight Porous Media

Tight porous media are mainly composed of micro/nano-pores and throats, which leads to obvious microscale effect and nonlinear seepage characteristics. Based on the capillary bundle model and the fractal theory, a new nonlinear seepage equation was deduced, and a further fractal permeability model was obtained for oil transport in tight porous media by considering the effect of the boundary layer. The predictions of the model were then compared with experimental data to demonstrate that the model is valid. This model clarifies the oil transport mechanisms in tight porous media: the effective permeability is no longer a constant value and is governed by properties of tight porous media and oil. Furthermore, parameters influencing effective permeability were analyzed. The model can accurately present the seepage characteristics of the oil in tight porous media and provide a reliable basis for the development of unconventional reservoirs.     

Effect of an Inserted Porous Layer Located at a Wall of a Parallel Plate Channel on Forced Convection Heat Transfer

A theoretical study is performed on heat and fluid flow in partially porous medium filled parallel plate channel. A uniform symmetrical heat flux is imposed onto the boundaries of the channel partially filled with porous medium. The dimensional forms of the governing equations are solved numerically for different permeability and effective thermal conductivity ratios. Then, the governing equations are made dimensionless and solved analytically. The results of two approaches are compared and an excellent agreement is observed, indicating correctness of the both solutions. An overall Nusselt number is defined based on overall thermal conductivity and difference between the average temperature of walls and mean temperature to compare heat transfer in different channels with different porous layer thickness, Darcy number, and thermal conductivity ratio. Moreover, individual Nusselt numbers for upper and lower walls are also defined and obtained. The obtained results show that the maximum overall Nusselt number is achieved for thermal conductivity ratio of 1. At specific values of Darcy number and thermal conductivity ratio, individual Nusselt numbers approach to infinity since the value of wall temperatures approaches to mean temperature.     

STUDY ON ANALYSIS METHOD OF “THREE BOX” IN HEAT AND MASS TRANSFER PROCESS OF RESERVOIR MEDIA

油藏多孔介质孔隙组成及结构变化多样,一些特性参数很难全部获得,精确描述和分析困难;另外,多孔介质内渗流过程水力条件和作用机理复杂,存在热流固耦合作用,目前的一些分析方法和研究模型具有一定的局限性.提出了油藏多孔介质的表征单元体（representative elementary volume,REV）描述表征方法;基于表征单元体建立了多孔介质的黑箱模型、灰箱模型和白箱模型,据此提出了多孔介质的“黑箱→灰箱→白箱”分析过程.基于黑箱模型和灰箱模型推导了REV导热系数计算公式、给出了REV热质传递过程的热平衡方程.结合中国油藏热采情况,对多孔介质导热系数变化规律和蒸汽驱热质传递特性进行了分析,得到了一些有意义的结果.该工作为多孔介质热质传递过程分析提供了新思路和新方法.     

油藏多孔介质热质传递“三箱”分析模型研究

油藏多孔介质孔隙组成及结构变化多样,一些特性参数很难全部获得,精确描述和分析困难;另外,多孔介质内渗流过程水力条件和作用机理复杂,存在热流固耦合作用,目前的一些分析方法和研究模型具有一定的局限性.提出了油藏多孔介质的表征单元体（representative elementary volume,REV）描述表征方法;基于表征单元体建立了多孔介质的黑箱模型、灰箱模型和白箱模型,据此提出了多孔介质的“黑箱→灰箱→白箱”分析过程.基于黑箱模型和灰箱模型推导了REV导热系数计算公式、给出了REV热质传递过程的热平衡方程.结合中国油藏热采情况,对多孔介质导热系数变化规律和蒸汽驱热质传递特性进行了分析,得到了一些有意义的结果.该工作为多孔介质热质传递过程分析提供了新思路和新方法.