水饱和树状分支网络的分形电导率模型

IF 3.3 3区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractals-Complex Geometry Patterns and Scaling in Nature and Society Pub Date : 2023-08-09 DOI:10.1142/s0218348x23500755

Huaizhi Zhu, Boqi Xiao, Yidan Zhang, Huan Zhou, Shaofu Li, Yanbin Wang, Gongbo Long

{"title":"水饱和树状分支网络的分形电导率模型","authors":"Huaizhi Zhu, Boqi Xiao, Yidan Zhang, Huan Zhou, Shaofu Li, Yanbin Wang, Gongbo Long","doi":"10.1142/s0218348x23500755","DOIUrl":null,"url":null,"abstract":"Electrical conductivity is an important physical property of porous media, and has great significance to rock physics and reservoir engineering. In this work, a conductivity model including pore water conductivity and surface conductivity is derived for water-saturated tree-like branching network. In addition, combined with Archie’s law, a general analytical formula for the formation factor is presented. Through the numerical simulation of the analytical formula above, we discuss the impact of some structural parameters ([Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] in tree-like branching network on the resistance, conductivity and formation factor. The results show that the total resistance [Formula: see text] is proportional to [Formula: see text], [Formula: see text], and inversely proportional to [Formula: see text], [Formula: see text]. The relation between conductivity and porosity in this model is contrasted with previous models and experimental data, and the results show considerable consistency at lower porosity. It is worth noting that when [Formula: see text], the conductivity and porosity curve of this model overlap exactly with those plotted by the parallel model. The fractal conductance model proposed in this work reveals the operation of the current in the tree-like branching network more comprehensively.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":" ","pages":""},"PeriodicalIF":3.3000,"publicationDate":"2023-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A FRACTAL ELECTRICAL CONDUCTIVITY MODEL FOR WATER-SATURATED TREE-LIKE BRANCHING NETWORK\",\"authors\":\"Huaizhi Zhu, Boqi Xiao, Yidan Zhang, Huan Zhou, Shaofu Li, Yanbin Wang, Gongbo Long\",\"doi\":\"10.1142/s0218348x23500755\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Electrical conductivity is an important physical property of porous media, and has great significance to rock physics and reservoir engineering. In this work, a conductivity model including pore water conductivity and surface conductivity is derived for water-saturated tree-like branching network. In addition, combined with Archie’s law, a general analytical formula for the formation factor is presented. Through the numerical simulation of the analytical formula above, we discuss the impact of some structural parameters ([Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] in tree-like branching network on the resistance, conductivity and formation factor. The results show that the total resistance [Formula: see text] is proportional to [Formula: see text], [Formula: see text], and inversely proportional to [Formula: see text], [Formula: see text]. The relation between conductivity and porosity in this model is contrasted with previous models and experimental data, and the results show considerable consistency at lower porosity. It is worth noting that when [Formula: see text], the conductivity and porosity curve of this model overlap exactly with those plotted by the parallel model. The fractal conductance model proposed in this work reveals the operation of the current in the tree-like branching network more comprehensively.\",\"PeriodicalId\":55144,\"journal\":{\"name\":\"Fractals-Complex Geometry Patterns and Scaling in Nature and Society\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":3.3000,\"publicationDate\":\"2023-08-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fractals-Complex Geometry Patterns and Scaling in Nature and Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s0218348x23500755\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0218348x23500755","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}

引用次数: 0

摘要

电导率是多孔介质的一个重要物理性质，对岩石物理和油藏工程具有重要意义。在这项工作中，导出了一个包括孔隙水电导率和表面电导率的水饱和树状分支网络的电导率模型。此外，结合阿尔奇定律，给出了地层因素的一般分析公式。通过对上述解析公式的数值模拟，我们讨论了树状分支网络中的一些结构参数（[公式：见正文]、[公式：看正文]、]公式：见文本]、[方程式：见文本][公式：见图文本]、]方程式：见案文]、]对电阻、电导率和形成因子的影响。结果表明，总电阻[公式：见正文]与[公式：见正文]，[公式：看正文]，与[公式：见正文]，【公式：见文本】成反比。将该模型中的电导率与孔隙率之间的关系与以前的模型和实验数据进行了对比，结果表明，在较低的孔隙率下，电导率与孔隙率的关系相当一致。值得注意的是，当[公式：见正文]时，该模型的电导率和孔隙度曲线与平行模型绘制的曲线完全重叠。本文提出的分形电导模型更全面地揭示了树状分支网络中电流的运行。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A FRACTAL ELECTRICAL CONDUCTIVITY MODEL FOR WATER-SATURATED TREE-LIKE BRANCHING NETWORK

Electrical conductivity is an important physical property of porous media, and has great significance to rock physics and reservoir engineering. In this work, a conductivity model including pore water conductivity and surface conductivity is derived for water-saturated tree-like branching network. In addition, combined with Archie’s law, a general analytical formula for the formation factor is presented. Through the numerical simulation of the analytical formula above, we discuss the impact of some structural parameters ([Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] in tree-like branching network on the resistance, conductivity and formation factor. The results show that the total resistance [Formula: see text] is proportional to [Formula: see text], [Formula: see text], and inversely proportional to [Formula: see text], [Formula: see text]. The relation between conductivity and porosity in this model is contrasted with previous models and experimental data, and the results show considerable consistency at lower porosity. It is worth noting that when [Formula: see text], the conductivity and porosity curve of this model overlap exactly with those plotted by the parallel model. The fractal conductance model proposed in this work reveals the operation of the current in the tree-like branching network more comprehensively.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Fractals-Complex Geometry Patterns and Scaling in Nature and Society 数学-数学跨学科应用

CiteScore

7.40

自引率

23.40%

发文量

319

审稿时长

>12 weeks

期刊介绍： The investigation of phenomena involving complex geometry, patterns and scaling has gone through a spectacular development and applications in the past decades. For this relatively short time, geometrical and/or temporal scaling have been shown to represent the common aspects of many processes occurring in an unusually diverse range of fields including physics, mathematics, biology, chemistry, economics, engineering and technology, and human behavior. As a rule, the complex nature of a phenomenon is manifested in the underlying intricate geometry which in most of the cases can be described in terms of objects with non-integer (fractal) dimension. In other cases, the distribution of events in time or various other quantities show specific scaling behavior, thus providing a better understanding of the relevant factors determining the given processes. Using fractal geometry and scaling as a language in the related theoretical, numerical and experimental investigations, it has been possible to get a deeper insight into previously intractable problems. Among many others, a better understanding of growth phenomena, turbulence, iterative functions, colloidal aggregation, biological pattern formation, stock markets and inhomogeneous materials has emerged through the application of such concepts as scale invariance, self-affinity and multifractality. The main challenge of the journal devoted exclusively to the above kinds of phenomena lies in its interdisciplinary nature; it is our commitment to bring together the most recent developments in these fields so that a fruitful interaction of various approaches and scientific views on complex spatial and temporal behaviors in both nature and society could take place.