多孔介质自发渗吸关键问题与思考

多孔介质自发渗吸现象普遍存在于自然界和工业应用领域, 深入研究其微观流动机理及宏观渗流规律具有重要的科学和工程价值。由于受多孔介质物理属性、流体性质、边界条件等多种因素的影响, 自发渗吸机理及渗流规律难以厘清。目前, 已有众多物理实验、理论分析及数值模拟等方法对多因素影响下的自发渗吸过程进行了广泛而深入的研究。本文就该领域存在的关键问题及最新进展进行梳理分析并提出若干思考, 以期对多孔介质自发渗吸的理解和未来研究工作提供一定的借鉴。     

二维孔隙裂隙双重介质逾渗规律研究

在孔隙介质逾渗理论的基础上，将另外一个非常重要的渗透通道——裂隙引入到介质的逾渗研究中，提出了更为普遍的孔隙裂隙双重介质的逾渗研究方法.通过对二维平面孔隙裂隙双重介质的数值计算，得到了孔隙裂隙双重介质三个重要参数：孔隙率，裂隙分形维数、裂隙数量分布初值与逾渗概率的关系，给出了孔隙裂隙双重介质逾渗阈值的数学表达式，揭示了孔隙裂隙双重介质的逾渗规律. 关键词： 孔隙 裂隙 双重介质 逾渗 逾渗阈值     

变形双重介质分形油藏非达西流动分析

考虑与实际生产相符的介质的双重特性和分形特征,并考虑介质的变形,引入双重分形介质渗透率模数,建立应力敏感地层双重分形介质系统的流动方程.采用Douglas-Jones预估-校正法获得无限大地层定产量生产时变形双重分形介质模型的数值解和无限大地层定压生产时分形介质双孔模型的数值解,作出了典型的压力曲线图版.     

考虑相重新分布的双重介质分形油藏不稳定渗流压力动态特征

基于分形油藏渗流力学,针对存在井筒储集、表皮效应和井筒相重新分布影响下的不稳定渗流问题,建立双重介质分形油藏有效井径数学模型,并采用Douglas-Jones预估校正法求得无限大地层定产量生产条件下的非线性数值解.由数值解可知,该系统完整的压降曲线由四个流动区组成.最后分析各个分形参数、相重新分布参数和双重介质参数变化时压力的变化规律,做出典型压力曲线图版,为研究复杂渗流系统中相重新分布影响下的不稳定渗流规律提供参考.     

分支通道内液-液自发渗吸规律研究

自发渗吸过程中两相界面在分支通道内的破裂和汇合为强非稳态过程, 难以用经典理论及常规数值计算方法准确描述。本文采用格子玻尔兹曼方法研究孔隙结构分支通道基本单元内的液-液自发渗吸行为, 对比出入口通道大小、两相黏度差异对液-液自发渗吸行为的影响。入口通道的大小对两相界面破裂进入分支通道内的竞争自发渗吸行为起控制作用, 而两相流体黏度控制了自发渗吸整体行为。本研究为复杂孔隙结构内液-液自发渗吸行为定量表征提供研究基础。     

裂隙多孔介质双重逾渗模型的算法实现

简要介绍基于孔隙逾渗和裂隙逾渗叠加的双重逾渗模型,阐述模型的原理、算法及其实现过程.初步研究模型的分形特性,认为分形维数D是能够衡量模型连通性的重要参数.最后探讨模型的蒙特卡洛数值计算方法,兼顾计算精度与计算耗时,提出可操作的计算规模.     

不同边界条件下的渗吸驱动因素

建立不同边界条件下的渗吸数学模型, 分别研究在单一边界(OEO边界条件)和混合边界条件(TEO-OW边界条件)下重力和毛管压力对渗吸作用的驱动。结果表明: OEO边界条件下, 只存在逆向渗吸, 并且当开启端面在下端时, 重力抑制渗吸进行; 当开启端面在上端时, 重力促进渗吸进行; TEO-OW边界条件下, 同时存在逆向渗吸和同向渗吸, 对于逆向渗吸, 重力是阻力, 对于同向渗吸, 重力是动力, 当Bond数倒数较小时, 重力在渗吸作用中占主导地位, 当Bond数倒数较大时, 毛管力占主导地位。对比OEO开启端面在上端时和TEO-OW边界条件下重力和毛管力对渗吸作用的大小。结果显示, 在相同Bond数倒数下, OEO边界条件下重力作用的渗吸排油比例要高于TEO-OW边界条件下重力作用的渗吸排油比例。对比不同Bond数倒数下OEO和TEO-OW渗吸速度发现, 当Bond数倒数较小时, 重力起主导作用, OEO边界渗吸速度更快; 当Bond数倒数较大时, 毛管力起主导作用, TEO-OW边界条件渗吸速度更快。     

变形双重介质分形气藏非线性渗流理论模型及数值研究

以Warren-Root模型为基础,引入分形参数和压缩系数,考虑压力对具有分形特征的渗透率和孔隙度的影响,建立变形双重介质分形气藏渗流数学模型.应用高收敛和高精度的有限元法求解这类含有第二类边界条件的数学模型.利用压力曲线,压力导数,参数对压力的影响率详细分析了部分参数对压力的影响及在变形双重介质分形气藏渗流数学模型中所具有的独特意义.     

分形介质的传热与传质分析(综述)

本文论述了分形介质的分形理论和数学基础,并简要综述了用分形理论和方法研究分形介质的传热与传质特性(如多孔介质的渗透率、热导率以及池核态沸腾换热)方面目前所取得的研究进展,最后扼要展望了用分形理论和方法进一步研究分形介质的传热与传质的可能的若干课题和方向。     

多孔介质中卡森流体的分形分析

研究了非牛顿流体中的卡森流体在多孔介质中的流动特性.基于服从分形分布的弯曲毛细管束模型,运用分形几何理论推导出了该流体在多孔介质中流动的流量、流速、启动压力梯度和有效渗透率的分形解析解.模型中的每一个参数都有明确的物理意义,它将卡森流体在多孔介质中的流动特性与多孔介质的微结构参数有机联系起来.文中给出了卡森流体的流速、启动压力梯度和有效渗透率随着各影响因素的变化趋势,并进行了讨论.所得分形模型可以更深刻地理解卡森流体在多孔介质中流动的内在物理机理. 关键词： 多孔介质 卡森流体 分形     

颗粒介质尺度效应的抗剪试验及物理机理分析

针对颗粒介质力学特性的颗粒尺度效应研究,选用土矿物颗粒制备不同颗粒尺度的抗剪试样,进行一系列直剪快剪和三轴抗剪试验,测得了不同颗粒粒径和体分比试样的变形曲线及剪应力强度;基于颗粒间微观作用力与重力比值和胞元体模型,首次从微观和细观角度解释颗粒尺度效应的物理机理.结果表明,随着介质中粗颗粒的比例增加和粒径减小,介质变形特性增强,剪应力强度也随之提高;体分比对变形和强度特性的影响比粒径的影响更加显著.基于介质特性尺度效应物理机理分析,提出衡量介质颗粒聚集和摩擦效应的微重比判别参数以及应变梯度和变形协调微裂纹引起颗粒尺度效应的细观机理解释;文中提出的胞元体模型大大减少了颗粒物质体系的计算自由度,为工业和工程设计的计算建模提供一种可行途径.     

Tortuosity for streamlines in porous media

An analysis of tortuosity for streamlines in porous media is presented by coupling the circle and square models. It is assumed that some particles in porous media do not overlap and that fluid in porous media is incompressible. The relationship between tortuosity and porosity is attained with different configurations by using a statistical method. In addition, the tortuosity fractal dimension is expressed as a function of porosity. Those correlations do not include any empirical constant. The percolation threshold and tortuosity fractal dimension threshold of porous media are also presented as: c = 0.32, D T c = 1.07. The predicted correlations of the tortuosity and the porosity agree well with the existing experimental and simulated results.     

Fractal patterns of fluid domains for displacement processes in porous media

Percolation invasion displacement of a compressible defender is examined for two cases: when only the smallest accessible site is entered at each step and when all accessible sites less than the size given by a reducing back pressure are entered at each time step. Although the fractions of invading fluid are different, their scaling properties are equivalent. The effect of limited control of a back pressure in a real displacement and the effect of viscosity in a real time displacement are examined. In these cases the scaling properties of a percolation process at breakthrough are removed. As a result, one should expect that realistic displacement models will not have the singular properties usually attributed to percolation processes.     

单毛细管中赫切尔-巴尔克莱流体的分形分析

运用分形理论给出了非牛顿流体中的赫切尔-巴尔克莱流体在单毛细管中的渗流分形模型. 此模型将赫切尔-巴尔克莱流体的流量、流速、启动压力梯度和有效渗 透率与流体的流变特性、毛细管的结构参数联系起来, 并且不含经验常数, 每个参数都具有明确的物理意义, 所得分形模型更能体现出赫切尔-巴尔克莱流体流动的内在物理机理.     

Hydrocarbons imbibition for geometrical characterization of porous media through the effective radius approach

Surface energetic characterization of porous solids usually requires the determination of the contact angle. This quantity is deduced by imbibition experiments carried out in such media with high surface tension liquids. Now then, this methodology needs the geometrical characterization of the porous medium by means of the deduction of its effective radius. Normally, this is made by imbibition experiments with n-alkanes, liquids whose surface tension is low enough as to suppose their contact angles with the solid surface are null. However, this last procedure is not free from some criticisms. Among them, the possible influence of the imbibition velocity on the contact angle, the effect of the precursor liquid film ahead the advancing liquid front on the driving force that gives rise to the movement, or the dependence of the effective radius on the length of the hydrocarbon chain of the n-alkanes. In an attempt of going deeply in these questions, imbibition experiments with n-alkanes have been carried out in porous columns of powdered calcium fluoride. These experiments have consisted of the measurement of the increase in the weight of the columns caused by the migration of the liquids through their interstices. The analysis of their results has been carried out by means of a new procedure based on the study of the velocity profile associated to the weight increase. This analysis has permitted us to conclude that, at least in the calcium fluoride columns, the contact angle of the n-alkane is not influenced by the capillary rise velocity, it taking in fact a null value during the process. On the other hand, it has been also proved that the driving force of the movement is caused by the replacement of the solid-vapour interface by the solid-liquid interface that happens during the imbibition, which means that only the Laplace's pressure, and not the precursor liquid film, contributes to the development of the phenomenon. Finally, it has been compared the values of the effective radius associated to each n-alkane, similar values being found independently from the particular liquid employed in the experiments, fact that indicates that the porous solid can be considered as a bunch of cylindrical and parallel capillaries of the same radius.     

Conserved dynamics and interface roughening in spontaneous imbibition: A critical overview

Imbibition phenomena have been widely used experimentally and theoretically to study the kinetic roughening of interfaces. We critically discuss the existing experiments and some associated theoretical approaches on the scaling properties of the imbibition front, with particular attention to the conservation law associated to the fluid, to problems arising from the actual structure of the embedding medium, and to external influences such as evaporation and gravity. Our main conclusion is that the scaling of moving interfaces includes many crossover phenomena, with competition between the average capillary pressure gradient and its fluctuations setting the maximal lengthscale for roughening. We discuss the physics of both pinned and moving interfaces and the ability of the existing models to account for their properties. Received 17 February 1999 and Received in final form 24 November 1999     

掺杂NaCl水溶液结晶形貌的分形研究

水溶液结晶是研究分形形貌的重要实验之一。本文通过改变溶液浓度,溶质组分和结晶温度等宏观实验参数,用分形维数的方法研究了这些参数对结晶形貌的影响。指出在低浓度下的非平衡态中溶液结晶形貌具有分形结构;不同晶体的生长作用力相互竞争,混乱度最大的情况下形成的分形结构最凸出,生长作用力是影响晶体形貌的主要因素;同时,分子热运动也是影响结晶形貌的因素之一。