A semi-analytical model for coupled flow in stress-sensitive multi-scale shale reservoirs with fractal characteristics

A large number of nanopores and complex fracture structures in shale reservoirs results in multi-scale flow of oil. With the development of shale oil reservoirs, the permeability of multi-scale media undergoes changes due to stress sensitivity, which plays a crucial role in controlling pressure propagation and oil flow. This paper proposes a multi-scale coupled flow mathematical model of matrix nanopores, induced fractures, and hydraulic fractures. In this model, the micro-scale effects of shale oil flow in fractal nanopores, fractal induced fracture network, and stress sensitivity of multi-scale media are considered. We solved the model iteratively using Pedrosa transform, semi-analytic Segmented Bessel function, Laplace transform. The results of this model exhibit good agreement with the numerical solution and field production data, confirming the high accuracy of the model. As well, the influence of stress sensitivity on permeability, pressure and production is analyzed. It is shown that the permeability and production decrease significantly when induced fractures are weakly supported. Closed induced fractures can inhibit interporosity flow in the stimulated reservoir volume (SRV). It has been shown in sensitivity analysis that hydraulic fractures are beneficial to early production, and induced fractures in SRV are beneficial to middle production. The model can characterize multi-scale flow characteristics of shale oil, providing theoretical guidance for rapid productivity evaluation.

Multi-scale Fractal Characteristics of Atmospheric Boundary-Layer Turbulence

The turbulence data are decomposed to multi-scales and its respective fractal dimensions are computed. The conclusions are drawn from investigating the variation of fractal dimensions. With the level of decomposition increasing, the low-frequency part extracted from the turbulence signals tends to be simple and smooth, the dimensions decrease; the high-frequency part shows complex, the dimensions are fixed, about 1.70 on the average, which indicates clear self-similarity characteristics.

Multi-scale pore fractal characteristics of differently ranked coal and its impact on gas adsorption

Well-developed pores and cracks in coal reservoirs are the main venues for gas storage and migration.To investigate the multi-scale pore fractal characteristics,six coal samples of different rankings were studied using high-pressure mercury injection(HPMI),low-pressure nitrogen adsorption(LPGA-N2),and scanning electron microscopy(SEM)test methods.Based on the Frankel,Halsey and Hill(FHH)fractal theory,the Menger sponge model,Pores and Cracks Analysis System(PCAS),pore volume complexity(D_(v)),coal surface irregularity(Ds)and pore distribution heterogeneity(D_(p))were studied and evaluated,respectively.The effect of three fractal dimensions on the gas adsorption ability was also analyzed with high-pressure isothermal gas adsorption experiments.Results show that pore structures within these coal samples have obvious fractal characteristics.A noticeable segmentation effect appears in the Dv1and Dv2fitting process,with the boundary size ranging from 36.00 to 182.95 nm,which helps differentiate diffusion pores and seepage fractures.The D values show an asymmetric U-shaped trend as the coal metamorphism increases,demonstrating that coalification greatly affects the pore fractal dimensions.The three fractal dimensions can characterize the difference in coal microstructure and reflect their influence on gas adsorption ability.Langmuir volume(V_(L))has an evident and positive correlation with Dsvalues,whereas Langmuir pressure(P_(L))is mainly affected by the combined action of Dvand Dp.This study will provide valuable knowledge for the appraisal of coal seam gas reservoirs of differently ranked coals.

PARAMETER IDENTIFICATION PROBLEM OF THE FRACTAL INTERPOLATION FUNCTIONS

Parameter identification problem is one of essential problem in order to model effectively experimental data by fractal interpolation function.In this paper,we first present an example to explain a relationship between iteration procedure and fractal function.Then we discuss conditions that vertical scaling factors must obey in one typical case.

Analysis of Multi-Scale Fractal Dimension for Image Interpolation

This article presents a novel image interpolation based on rational fractal fimction. The rational function has a simple and explicit expression. At the same time, the fi＇actal interpolation surface can be defined by proper parameters. In this paper, we used the method of ＇covering blanket＇ combined with multi-scale analysis; the threshold is selected based on the multi-scale analysis. Selecting different parameters in the rational function model, the texture regions and smooth regions are interpolated by rational fractal interpolation and rational interpolation respectively. Experimental results on benchmark test images demonstrate that the proposed method achieves very competitive performance compared with the state-of-the-art interpolation algorithms, especially in image details and texture features.

A Method Determining Vertical Scaling Parameters of Fractal Interpolation

A method determining vertical scaling parameters of fractal interpolation is given in this paper. By computer experiments, it is clear that this method is very effective.

Microstructure Characterization of Bubbles in Gassy Soil Based on the Fractal Theory

The microscopic characterization of isolated bubbles in gassy soil plays an important role in the macroscopic physical properties of sediments and is a key factor in the study of geological hazards in gas-bearing strata.Based on the box-counting method and the pore fractal features in porous media,a fractal model of bubble microstructure parameters in gassy soil under different gas con-tents and vertical load conditions is established by using an industrial X-ray CT scanning system.The results show that the fractal di-mension of bubbles in the sample is correlated with the volume fraction of bubbles,and it is also restricted by the vertical load.The three-dimensional fractal dimension of the sample is about 1 larger than the average two-dimensional fractal dimension of all the slices from the same sample.The uniform porous media fractal model is used to test the equivalent diameter,and the results show that the variation of the measured pore diameter ratio is jointly restricted by the volume fraction and the vertical load.In addition,the measured self-similarity interval of the bubble area distribution is tested by the porous media fractal capillary bundle model,and the fitting curve of measured pore area ratio in a small loading range is obtained in this paper.

Analysis of synergistic influence of multi-scale design parameters on nearly-zero energy office blocks performance based on architectural morphological classification and parametric modeling

Design parameters at different scales in the pre-design phase could significantly impact both building energy consumption and photovoltaic(PV)power generation potential.However,existing studies often overlook the synergistic effects of design parameters across multiple scales(block-building-facade scales)when evaluating these aspects.This paper aims to propose a workflow for the assessing building energy consumption and PV power generation potential of office blocks applicable in the pre-schematic design phase considering the synergistic influence of multi-scale design parameters,using building typology and parametric modelling approach.The study proposed a multi-scale design parameter classification system combined with parametric modelling.The study investigated 80 office blocks in Wuhan as the study case,which were classified into array type and enclosed type.Correlation analysis and multiple regression equations were used to quantify the single versus synergistic effects of different scale design parameters.Results suggest that focusing solely on a single scale during the pre-design stage is typically inadequate for understanding building energy potential.In contrast,multi-scale synergistic analysis boosts energy use intensity(EUI)by 7.56%and net energy use intensity(NEUI)by 33.96%.Under multi-scale synergistic conditions,the EUI of array type is more influenced by the building design parameters,while the NEUI is effected by the balance of multi-scales design parameters.While the EUI of enclosed types exhibit balanced effects across multi-scale design parameters,with NEUI results aligning closely with PV power generation potential.Multiple regression equations highlight building density and shape factor as key influencers for both array and enclosure layouts.This study offers designers a flexible and scalable workflow for evaluating building energy consumption and PV power generation potential in the pre-design phase.The findings can guide nearly-zero energy urban block planning to achieve a balance between energy supply and demand.

Fractal structures in a generalized square map with exponential terms

Fractal structures in a generalized squared map with exponential terms are expanded in this paper. We describe how complex behaviors can arise as the parameters change. The appearances of different kinds of fractal structures, in both the attractive and the divergent regions, and most interestingly, on small regular islands embedded in the chaotic region, are manifested to have a variety of extraordinary geometries in the parameter plane.

A smart productivity evaluation method for shale gas wells based on 3D fractal fracture network model

The generation method of three-dimensional fractal discrete fracture network(FDFN)based on multiplicative cascade process was developed.The complex multi-scale fracture system in shale after fracturing was characterized by coupling the artificial fracture model and the natural fracture model.Based on an assisted history matching(AHM)using multiple-proxy-based Markov chain Monte Carlo algorithm(MCMC),an embedded discrete fracture modeling(EDFM)incorporated with reservoir simulator was used to predict productivity of shale gas well.When using the natural fracture generation method,the distribution of natural fracture network can be controlled by fractal parameters,and the natural fracture network generated coupling with artificial fractures can characterize the complex system of different-scale fractures in shale after fracturing.The EDFM,with fewer grids and less computation time consumption,can characterize the attributes of natural fractures and artificial fractures flexibly,and simulate the details of mass transfer between matrix cells and fractures while reducing computation significantly.The combination of AMH and EDFM can lower the uncertainty of reservoir and fracture parameters,and realize effective inversion of key reservoir and fracture parameters and the productivity forecast of shale gas wells.Application demonstrates the results from the proposed productivity prediction model integrating FDFN,EDFM and AHM have high credibility.

Dense Fractal Networks, Trends, Noises and Switches in Homeostasis Regulation of Shannon Entropy for Chromosomes’ Activity in Living Cells for Medical Diagnostics

We analyze correlations and patterns of oxidative activity of 3D DNA at DNA fluorescence in complete sets of chromosomes in neutrophils of peripheral blood. Fluorescence of DNA is registered by method of flow cytometry with nanometer spatial resolution. Experimental data present fluorescence of many ten thousands of cells, from different parts of body in each population, in various blood samples. Data is presented in histograms as frequency distributions of flashes in the dependence on their intensity. Normalized frequency distribution of information in these histograms is used as probabilistic measure for definition of Shannon entropy. Data analysis shows that for this measure of Shannon entropy common sum of entropy, i.e. total entropy E, for any histogram is invariant and has identical trends of changes all values of E (r) = lnr at reduction of rank r of histogram. This invariance reflects informational homeostasis of chromosomes activity inside cells in multi-scale networks of entropy, for varied ranks r. Shannon entropy in multi-scale DNA networks has much more dense packing of correlations than in “small world” networks. As the rule, networks of entropy differ by the mix of normal D 2 and abnormal D > 2 fractal dimensions for varied ranks r, the new types of fractal patterns and hinges for various topology (fractal dimension) at different states of health. We show that all distributions of information entropy are divided on three classes, which associated in diagnostics with a good health or dominants of autoimmune or inflammatory diseases. This classification based on switching of stability at transcritical bifurcation in homeostasis regulation. We defined many ways for homeostasis regulation, coincidences and switching patterns in branching sequences, the averages of Hölder for deviations of entropy from homeostasis at different states of health, with various saturation levels the noises of entropy at activity of all chromosomes in support regulation of homeostasis.

The Hierarchy Model of Seismicity:Its Empirical Relationships and Fractal Natures

Starting from a simple hierarchy model of seismicity,some empirical relationships of seismicity and the fractal natures of its time and space and of the source size of earthquakes have been derived in this paper.From the results,some conclusions can be drawn as follows.First,the coefficient b in the Gutenberg-Richter relationship is equal to 2bt where bt is the coefficient in the empirical relationship between the magnitude and average epicentral distance,and b is also equal to the coefficient bi in the empirical relationship between the magnitude and average time interval.Second,the fractal dimension values of the average epicentral distance,the average time interval,and the source size are 2,1,and 26,respectively.

基于分形理论的新型电力系统规划场景生成方法

新型电力系统中的新能源占比不断提高,源荷不确定性使得新型电力系统的规划边界难以确定,因此有必要提出适应新型电力系统的规划场景生成方法。分析净负荷数据的分形特征,并提出规划场景生成方法的总体框架;在提出净负荷时间序列盒维数计算方法的基础上,利用盒维数的时移不变性提出规划场景初始点的预测方法;对分形插值算法进行细化,并提出基于初始点的规划场景生成方法。以某地区实际净负荷数据为例进行分析,验证了所提方法的有效性和可行性。

基于改进SFS算法的锚杆钻臂参数整定研究

针对锚杆钻臂井下自动控制过程中存在的环境恶劣、地质复杂等特殊工况,需着重考虑PID的参数选取,为此采用随机分形搜索算法(SFS)对PID参数进行整定。由于随机分形搜索算法存在局部搜索能力不足、易陷入局部最优等问题,在面对机械臂待整定参数多及参数间耦合严重时,其整定效果不佳。因此,引入混沌初始化、正余弦策略、自适应K值选取策略以提高算法的局部搜索能力以及全局搜索速度;采用柯西、差分定向变异策略使算法跳出局部最优。通过标准测试函数测试表明改进后的随机分形搜索算法收敛速度及精度均有一定提高。最后通过锚杆钻臂参数整定仿真实验表明:改进后随机分形搜索算法整定的PID参数总体适应度值提高21%;各关节的量化指标表示改进后随机分形搜索算法跳出了局部最优,提高了整体寻优精度与速度。

一维条码检测技术中分形理论应用分析

本研究基于一维条码检测技术截取150个典型反射率曲线段计算统计容量维数(D_(c))及缺陷度(Defects),选取边缘比率(ER)、边缘线段数量(LS)及波峰谷数量(FG)作为指标,采用主成分分析法计算反射率曲线段的复杂度。经统计,D_(c)区间范围为[1.00,1.42],平均值为1.18;Defects的区间范围为[0,0.0227],平均值为0.0055,D_(c)与复杂度的相关性显著,相关系数0.51。实验结果表明,Defects对于条码符号印制质量情况的评判主要集中于“最大”缺陷处,对于细微缺陷的描述不到位,D_(c)对于条码符号印刷质量的缺陷能够补充描述细节缺陷的情况,可作为一维条码符号印制品的质量检测的有效技术工具。

陕北黄土区不同植被下深剖面土壤的分形特征

[目的]探究不同植被下深剖面土壤分形特征及其与土壤理化性质和水力学参数的关系,为植被恢复和农业生产提供重要的参考依据。[方法]以陕西省神木六道沟流域为研究区域,采集该区域4种植被(草地、杏树、油松、柠条)下>13 m深剖面土壤样品,测定土壤颗粒组成、含水率以及有机碳含量等,计算土壤分形维数,分析不同植被下深剖面土壤的分形特征。[结果](1)该区土壤黏粒、粉粒及砂粒含量分别为15%,40%和45%,不同植被下土壤颗粒组成的差异显著(p<0.05)。(2)整个剖面上4个样地的分形维数无显著差异(p>0.05),在1—2 m土层深度内,植被类型对土壤分形维数的影响显著(p<0.05),且油松及草地样地的分形维数大于其他两个样地。(3)土壤分形维数与黏粒含量及土壤水力参数(θ_(r),n和K_(sat))的相关性显著(p<0.05),但与有机碳和含水率相关性不显著(p>0.05)。[结论]土壤分形维数主要受土壤细小颗粒影响,且对土壤水力性质具有一定的指示作用,油松及草地对土壤结构改善作用最佳。

A New Characteristic Parameter of Frequency Distribution—Fractal Structure Factor

A large amount of data can be obtained by measuring any matter or any phenomenon, and the calculation of characteristic parameter of frequency distribution and simulation of a frequency distribution curve will be made using these data. A new characteristic parameter of frequency distribution-fractal structure factor is suggested for this purpose, and its calculative method and application are given here.

MULTI-SCALE NUMERICAL MODEL FOR SIMULATING CONCRETE MATERIAL BASED ON FRACTAL THEORY

A new multi-scale numerical model is presented using the fractal theory and adopting FEM to simulate the failure of concrete.The relation between the fractal box dimension in large scale and the damage to concrete in small scale is deduced.And the evolutionary process of elastic modulus and strength in small scale is given.Consequently,the multi-scale numerical model is proposed to describe the constitutive relation of concrete between small scale and large scale.A two-dimensional static analysis of a concrete block is performed by using this model and the calculation result is discussed.The propagation of cracks of the concrete block is also studied.

路用集料形貌特征参数分析与性能评价

沥青路面的长期抗滑性能取决于集料的抗磨光/耗性能,准确快速计算集料的形貌特征十分重要。本文引入一种新型高抗滑路用集料——88#煅烧铝矾土,采用Image-Pro-Plus 6.0(IPP)、IBM SPSS Statistics 26.0(SPSS)等数字图像处理软件对集料形貌特征进行分析评价。同时对不同磨光次数下集料形貌特征参数的变化进行灰熵关联分析,得到各集料形貌特征参数与其磨光值(PSV)的灰熵关联度。结果表明,采用IPP软件能够准确获得各集料的形貌特征参数,并且,相较于传统路用集料,88#煅烧铝矾土具有更加丰富的棱角特性及较高的粗糙度。通过灰熵关联分析得到,分形维数与PSV之间的相关性最显著。

黄河下游冲积平原试验区土壤水分特征曲线的传递函数研究

黄河下游冲积平原区是我国重要的粮食生产基地和工业集聚地,该地区土壤水力学参数的获取,对于保障用水安全和指导农业生产具有重要意义。为建立黄河下游冲积平原区的土壤水分特征曲线传递函数(PTFs),以河南省兰考县闫楼乡作为黄河下游冲积平原试验区,基于多元非线性逐步回归和单因素扰动方法,建立了包气带土壤水分特征曲线的PTFs,并分析了影响因素敏感性。研究结果显示,实测土壤水分特征曲线以及土壤理化性质参数呈现较强变异性,所建立的PTFs精度良好,具备应用推广价值。多元回归结果表明,土壤颗粒组成是本文PTFs的主要影响因素,其中黏粒含量对PTFs最为敏感,砂粒含量次之,粉粒含量最弱。在其余5个土壤理化特性中,对PTFs的相对敏感的因素是pH值和分形维数。研究表明,土壤物理化学性质与土壤水分特征曲线模型参数的关系复杂,并非一般线性或单调关系。尽管土壤物理化学性质参数可以提高PTFs精度,但土壤颗粒组成是影响土壤水分运动的根本原因,其作为构建PTFs的关键因素不可忽略。在实际应用中,PTFs使用者可根据所掌握数据的实际情况,结合影响因素敏感性,决定影响因素的取舍。