不等厚分形复合油藏不稳定渗流问题的数学模型及压力特征

将分形几何理论与渗流理论相结合,推导不等厚横向非均质油藏不稳定渗流的试井分析数学模型.储集层模型由m(m≥2)个环绕中心的环形区域组成,在不同的环形区域内,储集层和流体的性质不同,其孔隙度和渗透率可以具有不同的分形分布;地层厚度也可以不同,但在同一区域内看作近似不变.考虑井筒储存和表皮效应影响,建立了此类分形复合油藏模型的不稳定渗流有效井径数学模型.针对典型的3类外边界条件,应用Laplace变换求得拉氏空间的解析解;制作了2类两区复合油藏模型的典型压力曲线,分析了压力动态特征和参数影响.分形指数对晚期的压力动态有很大影响压力曲线开始时合并为一,随着时间的增加而发散;分形指数值愈大(表明分形网络越扭曲复杂,地层的连通性越差),直线愈陡,反之愈平缓.地层厚度的变化对典型曲线也有一定的影响,晚期压力随着厚度增大(第二区逐渐变厚)而逐步减小.不等厚横向非均质油藏、均质复合油藏及分形油藏均是此模型的特例,其建模方法可以推广到双重介质分形复合油藏.图1参6(向开理摘)     

Roughness signature of tribological contact calculated by a new method of peaks curvature radius estimation on fractal surfaces

This paper proposes a new method of roughness peaks curvature radii calculation and its application to tribological contact analysis as characteristic signature of tribological contact. This method is introduced via the classical approach of the calculation of radius of asperity. In fact, the proposed approach provides a generalization to fractal profiles of the Nowicki's method [Nowicki. Wear Vol. 102, p. 161–176, 1985] by introducing a fractal concept of curvature radii of surfaces, depending on the observation scale and also numerically depending on horizontal lines intercepted by the studied profile. It is then established the increasing of the dispersion of the measures of that lines with that of the corresponding radii and the dependence of calculated radii on the fractal dimension of the studied curve. Consequently, the notion of peak is mathematically reformulated. The efficiency of the proposed method was tested via simulations of fractal curves such as those described by Brownian motions. A new fractal function allowing the modelling of a large number of physical phenomena was also introduced, and one of the great applications developed in this paper consists in detecting the scale on which the measurement system introduces a smoothing artifact on the data measurement. New methodology is applied to analysis of tribological contact in metal forming process.     

古潜山灰岩裂缝分布的分形特征

相似维数对于定量评价储层裂缝平面分布的非均质性和裂缝的发育程度，是一种实用性很强的非线性统计方法，并对平面上裂缝发育程度具有很强的定量描述能力。裂缝发育的线性分布曲线表明，裂缝分布具有分形几何特征。运用变尺度分形统计方法，统计了储层裂缝发育区平面分布的相似维数，理论和实际资料都证实该充填空间能力较差，裂缝发育程度不是很强，这与目前该油气藏的地质特征及产能情况比较吻合。     

一种基于小波变换结合反向迭代修正的VQ图象压缩编码方法

将反向迭代法引入对ＶＱ（矢量量化）编码误差进行修正，从而使建立在小波变换基础上的ＶＱ编码方法的重建图象质量得到改善，使信噪比（ＳＮＲ）提高了３～８ｄＢ。对于与训练集内样本相差较大的图象在压缩比相同的条件下，改善重建图象的效果尤为明显。     

Fractal model to predict the crack roughness effect on the local bending compliance of circular shafts

In this paper the local compliance due to a transverse fractal crack in a shaft under pure bending is investigated. In a fractal crack, the surface is considered irregular and it is characterized by the presence of nonuniformities at different scales. Therefore, the crack surface can be modeled as a fractal surface with fractal dimension D. An analytical model for the compliance coefficient is presented with and without the effect of the surface roughness. The results obtained shows that as the dimension of the fractal surface increases the compliance increases as well. It is shown that this behavior conforms well with existing experimental results.     

a-Si:H簿膜的晶化与分形结构的形成

利用透射电子显微镜(TEM)观测a-Si:H 薄膜在不同温度下生长的分形结构。实验方法为原位动态技术。对分形结构的TEM形貌像用Sandbox方法计算了其分形维数。450℃时,形成具有类似分叉状的分形结构,分形线数d_f=1.69;800℃时,形成岛状分形结构,分形维数d_f=1.76。实验结果表明,分形结构的形成与薄膜物性的变化相联系。文中还对分形结构与a =Si:H 薄膜晶化的关系进行了讨论。     

Floc rupture and turbulence: a framework for analysis

The paper focuses on the physical character of flocs. This is developed through analysis of the impact of hydrodynamic stress on floc size. Theory is developed on the basis of an energy criterion which balances the turbulent kinetic energy against the energy expenditure associated with rupture. For turbulence, the kinetic energy per unit volume is moulded by the velocity scale (νε)^1/4 and the d/η ratio in which ν, ε, η refer to the kinematic viscosity, the rate of energy dissipation per unit mass and the Kolmogorov length, respectively. The distance scale, d, is equivalent to the maximum floc size. In its most rudimentary form, floc structure is based on the model S∝k?/d³ in which k is the number of bonds broken and ? the potential energy expenditure per bond broken. With appropriate development, this transforms to S=S₀(d/d₀)^D−3 in which d₀ is the primary particle size, D the fractal dimension, and S₀ is a scaling factor controlling the mechanical strength. From the energy criterion, analytical expressions are derived for d in the form d=γε^−m/2 in which γ and m are constants. Beside the proposal of models for S, a valuable advance is the development of rupture theory for the whole domain of d/η. Theory is examined using a number of published data sets in which there exists knowledge of parameters γ, m and D. The paper demonstrates how the model can be used as an analytical tool for dissecting the factors which control S₀. The theory establishes a framework which can be developed further, and applies to flows containing fractal aggregates in both industry and the natural environment.     

Strkuctured-light Image Compression Based on Fractal Theory

The method of fractal image compression is introduced which is applied to compress the line structured-light image.Based on the self-similarity of the structured-light image, we attain satisfactory compression ratio and higher peak signal-to-noise ratio (PSNR).The experimental results indicate that this method can achieve high performance.     

快速覆盖式分形压缩算法

提出了一种覆盖式分形压缩方法,并给出了相应快速搜索算法.该方法采用四连通扩充的方式,在给定误 差范围内,尽可能地合并规则Range分区,从而减少所需迭代变换的数目.为减少存储Range分区信息所需的字 节,在存储压缩映射时,根据Range分区多边形的边数调整存储顺序,对于那些复杂的Range分区,只记录其外接 矩形框信息.在解码时,采用一种覆盖式绘制方法,可以完全恢复原Range分区情形.通过对Lenna,图象的实验表 明,在恢复图象的信噪比为29.63dB时,可以达到41倍的压缩倍数.     

分形层次及码尺与分辨率的关系

提出了在分形研究中，用计算机进行图像分析时，分形层次和码尺与图像采样分辨率之间的关系。码尺的改变只能通过改变输入的分辨率，同时输入分辨率的选择要综合考虑分形自身的层次要求、输入方法以及测量的要求。给出了实验验证。