准噶尔盆地永进油田特低渗储层分类评价研究

针对准噶尔盆地永进油田超深层、特低渗储层渗滤能力差,传统的储层分类评价难以细分界限的特点,引入毛管曲线分形维法和BP神经网络方法。储层岩石的孔隙结构是一种分形结构,可以用分形维数来定量描述其复杂程度。通过建立毛管压力曲线和孔隙大小分布的分形几何模型,计算了孔隙结构的分形维数,定量描述孔隙结构的复杂程度;用BP神经网络方法,经过反复实验和分析,输入5个节点数,即分形维和四条测井曲线系列(包括自然伽马、声波时差、深侧向和浅侧向电阻率),输出1个节点数,即一条深度连续的分形维曲线。网络预测值与实验值精度基本一致,根据上述方法原则求取了各井的分形维曲线,用以储层的精细分类及有效性评价。     

用分形方法研究负载型聚烯烃催化剂的表面形貌及其对聚合活性的影响

以Ｍｇ（ＯＥｔ）２和ＴｉＣｌ４作为钛镁体系聚乙烯催化剂的代表,在不同反应上制备了Ｔｉ－Ｍｇ体系负载型聚乙烯催化剂,并用扫描电镜（ＳＥＭ）技术对其亚微观结构进行研究,证实其具有分形特征。应用分形理论及其改进的盒子维法对催化剂的亚微观结构进行了详细的分析计算,给出了催化剂表面结构的分维数,结果发现,催化剂分维值Ｄｔ随着催化剂表面的不规则度及催化剂内部孔隙的增多而增大,而其聚合活性与催化剂表面分维值的关系较为复杂,只在适宜的催化剂分维值范围内,才可获得较高的聚合活性,研究证明了分维值可作为比较两个分形无规则度对象的表征参量。     

孔隙结构分形维数测试与应用研究进展

分维是描述分形的定量参数。储集层岩石的孔隙结构具有良好的分形特征,孔隙结构的分维可以定量描述孔隙结构的复杂程度。目前测量孔隙结构分维主要有四种方法：吸附法、离散法、散射法和压汞法。而分维的应用主要在五个方面：研究岩石的常规物性、成岩作用与沉积作用对分形的影响、粘性指进现象的研究、研究储层伤害与保护机理和对储层非均质性的研究。分形方法在孔隙结构中的应用不仅可以深化我们对孔隙结构的认识,还可以为孔隙结构中较复杂的问题提供新的工具。     

不同渗透率岩心一次进汞-退汞回路的分形特征

利用压汞法测得的毛细管压力曲线,比较分析了不同渗透率岩心的一次进汞-退汞回路的形态特征、变化规律及其孔隙分布特征。结合分形理论,分别用单分形段和多线性段拟合方法对中高渗透岩心和低渗透岩心的分形维数进行了拟合,阐述了分形维数作为量化指标与不同孔隙分布特征的关系。结果表明,中高渗透岩心水银以连续相退出岩心孔隙,进汞-退汞回路的分形特征曲线近于平行,计算的分形维数接近;而低渗透岩心退汞过程水银的连续性被破坏,大部分水银由于被孤立而形成残余饱和度,定量表现为分形特征曲线拟合的分形维数与岩心中较小孔隙的分形维数值接近。     

评测混凝土粗糙度的一种新方法及其分形表示

增加粗糙度是提高新老混凝土粘结性能的常用的方法.目前,国内外还没有相应的标准或规程对混凝土粗糙度的评测方法作出明确的规定,基于灌砂法的原理建立了一种新的混凝土表面粗糙度的评测方法-测试仪法.分别采用灌砂法、测试仪法对24个劈裂面进行测量分析,发现测试仪法是比灌砂法更先进更准确的测量粗糙度方法.利用分形理论,研究了分维值与粗糙度的关系,发现高差法分维值与粗糙度无正相关性,变步距法分维值与粗糙度有一定的正相关性.通过对两种分维值深入分析,综合利用高差法分维值和变步距法分维值,建立了测试仪法粗糙度与分维值的拟合公式.发现测试仪法粗糙度值随着测量步距的增大而减少,高差法分维值与其缩减系数有较好线性相关性,建立了拟合公式,达到了简化测量的目的.     

两种毛管压力模型对比的储层孔隙结构分形研究

基于多孔介质分形理论进行Li-Horne毛管压力模型和Brooks-Corey毛管压力模型的推导,证明Brooks-Corey毛管压力模型为Li-Horne毛管压力模型的一种特殊形式。并利用两种毛管压力模型对北部湾盆地不同渗透率岩样的压汞曲线进行拟合,获得孔隙大小分布指数来评价储层的非均质程度,由于Brooks-Corey模型适用于均质储层,而Li-Horne模型对于均质、非均质储层均适用,所以Li-Horne模型拟合结果好于Brooks-Corey模型。同时,根据Li-Horne模型推导出多孔介质孔隙分布的分形概率模型,其指数与分形维数有关,利用该模型计算的孔喉尺寸分布与压汞曲线获得的结果一致。     

球磨钢渣粒度分布的分形特征

应用分形几何理论,研究了转炉水淬钢渣在粉磨后的粒度分布特征.试验发现:(1)在双对数坐标下,钢渣微粉粒径的质量累积分数与粒径之间呈直线关系,这表明钢渣微粉粒度分布具有分形结构;(2)随着粉磨时间的延长,钢渣微粉的分维值不断增大,一定时间后,分维值的增大速度减缓;(3)分维值越小,钢渣越易破碎.因此,使用分维值可定量表征钢渣微粉的级配特征和均匀程度;同时分维值与钢渣微粉的比表面积之间满足良好的线性关系.     

三交北-临兴西区储层孔隙结构研究

三交北-临兴西区作为油气开发公司科研项目区块，其多层系含气特征表现明显，但储层岩性致密，物性差异大。针对该区储层致密，其孔隙、喉道极细小，毛管压力在油气运移中起着至关重要的作用，本次采用毛管压力法进行了孔隙结构研究，对储层的评价、气田的勘探开发具有很好的指导意义。     

海上低渗致密砂岩气藏渗流模型研究

结合压汞曲线来研究砂岩储层的分形维数,利用实验说明了致密气藏存在分形特性,通过推导计算了致密气藏分形维数,对于复杂的微小孔隙发育的砂岩孔隙结构,分形维数接近3.基于实验证实分形的基础上,考虑基质孔隙和裂缝存在分形特性,并考虑到致密气藏的应力敏感性,基于致密气在纳米级孔隙中的非达西流动特点,建立了新的分形致密气藏渗流模型,通过对模型进行求解的基础上研究了具有分形特性的致密气藏渗流规律.绘制并分析了不同参数影响下的压力动态典型曲线.通过分析表明,基质和裂缝分形参数都对压力动态产生影响,但影响的流动时期和阶段不同.传统的气藏模型是本文所建模型的特例.     

南京燕子矶下蜀黄土颗粒分形研究

根据分形理论,研究了南京燕子矶下蜀黄土粒度分形结构特征,发现在双对数坐标下粒径和粒度含量之间存在明显的线性关系,表明粒度组成具有分形结构.通过对燕子矶下蜀黄土颗粒分形的计算,发现其分维值介于2.4~2.6之间,随着黏粒含量的增大而增大,且与不均匀系数和曲率系数有良好的非线性关系.在此基础上,讨论了粒度分维所具有的工程地质意义.指出粒度分维揭示了不同土体工程地质性质差异的本质,可以作为土体分类的一个合理指标.     

Fractal Theory on Drying: A Review

Fractal geometry has been widely used in various dried materials and drying processes. This review summarizes the related studies and identifies the opportunities for future investigation. The application of fractal concept on drying can be categorized into describing microscopic and macroscopic structure of material in drying with fractal geometry and theoretical models with fractal theory for drying mechanism. And also, the capillary and network models for drying of capillary porous media are discussed and a fractal tortuous capillary model for drying of capillary porous media is proposed. From the selected examples, it is clear that the fractal theory has many advantages for identifying the complex structure of products and investigating drying mechanism. At last, some comments are made for the current investigations and also some prospects for the future development of this field are pointed out.     

Modeling changes of fractal pore structures in coal pyrolysis

Coal pyrolysis processes are numerically investigated in mathematically produced coal pore models which simulate real coal pores in the parameters of the porosity and fractal dimension. The simulations include FG-DVC chemical reaction model, gas molecular diffusion in pores, energy conservation model and coal swelling model. Numerical results are verified by experimental results qualitatively, and they revealed that both the porosity and volatile contents of the parent coal can affect the fractal dimension of the final char pores after pyrolysis linearly. A formula to predict the fractal dimension of char pores from its parent coal properties is obtained by curve fitting in numerous results.     

碳纳米管/PTFE复合材料磨损表面分形特性研究

基于分形理论和扫描电镜分析,采用双毯法计算了碳纳米管/PTFE复合材料磨损表面的三维分形维数。结果表明,基于Peleg-blanket法和磨损表面SEM图计算所得的分形维数,可以表征碳纳米管/PTFE复合材料磨损表面的形貌特征;随着填料含量的增加,复合材料磨损表面的分形维数依次减小;纯PTFE的分形维数最大,而5%碳纳米管/PTFE的分形维数最小,与复合材料磨损量的变化趋势相一致。     

Fractal analysis of pressure fluctuations in a three phase bubble column reactor operating at low pressure

Pressure fluctuations in a three phase bubble column reactor operating at relatively low pressure (92 KPa) have been analyzed by adopting the spectral and fractal analyses to get the engineering informations for the on-line control and fault diagnosis of the reactors. The mean value, standard deviation, skewness and kurtosis of the pressure fluctuations have been obtained. The local fractal dimension has been determined from the Pox diagram obtained by means of the rescaled range analysis of the pressure fluctuations based on the fractional Brownian motion. The local fractal dimension of pressure fluctuations has increased and thus the pressure fluctuation signals have become less persistent and irregular, with increases in the gas flow rate reaction temperature, particle size and solid content in the slurry phase. The local fractal dimension has been well correlated in terms of the operating variables.     

The effect of local residual stress on the fractal dimension of silicate glasses

Local residual stress caused by impacts, machining and indentation results in a decrease in strength in most materials that fail in a brittle manner. The ratio of the critical crack size, c, and the fracture mirror size, r, also is affected by the existence of local residual stress. The global fracture toughness of non-R curve materials is not affected by the local residual stress. The fractal dimension of the fracture surface as characterized by the fractal dimensional increment, D*, is directly related to the square of the fracture toughness. This paper addresses the question of the effect of the local residual stress on the fractal dimension of the fracture surface. We derive a relationship between the fractal dimensional increment and the c/r ratio for materials fractured with and without local residual stress. We then compare the prediction with two cases of experimental results. We show the fractal dimension remains constant with the change in the c/r ratio for local residual stress conditions.     

ANALYSIS OF PERMEABILITY FOR ELLIS FLUID FLOW IN FRACTAL POROUS MEDIA

This work studies the flow characteristics of Ellis fluid in saturated porous media. A fractal model is developed for the effective permeability of Ellis fluid flow in porous media based on the assumptions that porous media consist of a bundle of tortuous capillaries, whose size distribution and tortuosity follow the fractal scaling laws. The average flow velocity and the effective permeability for Ellis fluid flow in porous media are derived. The proposed fractal model does not contain any empirical constant, and every parameter in the model has clear physical meaning. The model predictions are compared with the measured data, and good agreement between them is obtained.     

Detection of the fractal character of compact adsorbed layers by the dropping mercury electrode

The development of compact adsorbed layers at the dropping mercury electrode is used for the detection of resulting changes in the geometry of the electrode-solution interface from Euclidean to fractal. A simple size scaling method of the Hg drop surface is applied, which focus on the time dependence of the drop area under conditions of constant adsorbate and base electrolyte concentration, constant potential and constant mercury flow rate.It is found that the slope of the log-log plots of capacitance or capacitance current against electrode surface area or electrode radius is increasing upon the formation of a compact adsorbed layer. Under equilibrium conditions the slope values of the linear log-log plots can be reasonably identified with the fractal dimension of the electrode/solution interface. However, due to the limited extent of the power-law range of the feature vs. scale relation, the size scaling method of the dropping mercury electrode can be used to probe fractal adsorbate films on a strictly qualitative level.     

Self-assembly and Fractal Feature of Chitosan and Its Conjugate with Metal Ions: Cu (II)/Ag (I)

In this paper, we investigated the self-assembly and fractal feature of chitosan and Ag (I), Cu (II)-chitosan due to the theoretical and practical importance of chitosan in biomedical engineering, biomaterials and environmental sciences etc. The self-assembly and fractal structures of chitosan and Ag (I), Cu (II)-chitosan were observed using atomic force microscope (AFM), and the fractal dimensions of chitosan and Ag (I)-chitosan were calculated. The results indicate that their fractal dimension is approximate 2 and relates with the accumulation degree: the fractal dimension decreases with the accumulation degree increases. In addition, a new self-assembly strategy was presented to study the lyotropic liquid crystals (LLC) of chitosan and the formation mechanism of LLC was primarily analyzed and discussed. All of these results are valuable for the structure/function relationship study of chitosan and useful for application in biomedical materials.     

Modeling of three-dimensional groundwater flow using the method to calculate fractal dimension

A three-dimensional finite-difference groundwater flow model was developed by the use of fractal theory. The model developed in this study can simulate the groundwater flow in fractured aquifers as well as in porous aquifers. The model was designed to be able to use other parameters, such as permeability, hydraulic conductivity, porosity and fractal dimension besides hydraulic parameters which are used in MODELOW. Methods which can calculate box fractal dimension used in the Baecher model and mass dimension used in Levy-Lee Fractal model were developed. The results of the model and MODFLOW agreed exactly in the case of the fractal dimension of 2.0 without regard to the use of a fractal equation. The fact that the drawdown along the distance from the well increases by increasing the fractal dimension shows the effect of fracture on groundwater flow.     

分形BET吸附模型

本文提出了一个改进的分形ＢＥＴ吸附模型。用此模型分析水在新型干燥剂上的吸附平衡和文献［８］中水在活性氧化铝上的平衡吸附数据。结果表明：所提出的模型能在整个相对蒸汽压力范围内描述水在吸附剂上的吸附平衡行为；脱附等温线与吸附等温线之间的差别可归结于吸附质的单层吸附。