基于Kozeny&mdash;Carman方程的渗透率分形模型

郑斌，李菊花

doi:10.11764/j.issn.1672-1926.2015.01.0193

天然气地球科学 >

2015 , Vol. 26 >Issue 1: 193 - 198

DOI: https://doi.org/10.11764/j.issn.1672-1926.2015.01.0193

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基于Kozeny—Carman方程的渗透率分形模型

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1.长江大学油气资源与勘探技术教育部重点实验室，湖北武汉 43010;2.长江大学石油工程学院，湖北武汉 430100

郑斌(1990-)，男，黑龙江绥化人，硕士研究生，主要从事油气田开发工程研究.E-mail：bin_zheng1990@163.com

收稿日期: 2014-05-20

修回日期: 2014-07-17

网络出版日期: 2015-01-10

基金资助

国家自然科学基金资助项目(编号：51204193)|中国石油股份公司重大科技专项(编号：2012E-3304)联合资助.

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A New Fractal Permeability Model for Porous Media Based on Kozeny-Carman Equation

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1.Key Laboratory of Exploration Technologies for Oil and Gas Resources,Yangtze University,Ministry  of Education,Wuhan 430100,China|2.Yangtze University,Petroleum Engineering,Wuhan 430100,China

Received date: 2014-05-20

Revised date: 2014-07-17

Online published: 2015-01-10

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摘要

Kozeny—Carman(KC)方程是渗流领域广泛应用于多孔介质渗透率预测的半经验公式，自该方程首次提出就不断地被修正并加以改进。应用分形理论，通过建立具有分形特征的毛管束模型，基于Posenille定律和达西公式分别确定了多孔介质的渗透率、孔隙度、比面的分形表达式，以经典的KC方程为基础，将三者的分形表达式相结合得出了全新的考虑比面影响的渗透率分形模型，同时得到了具有分形特征的KC常数。结果表明:多孔介质的渗透率是孔隙结构分形维数、迂曲度、宏观物性参数(孔隙度和比面)的函数，KC常数并不为固定值，而与毛细管的迂曲度、孔隙结构的分形维数等微观孔隙参数有着密切的联系。通过计算验证表明，相比于目前使用的KC方程，应用分形方法预测出的渗透率值与实际数值更加接近。

关键词： 分形; 渗透率; 孔隙度; 比面; Kozeny-Carman方程

本文引用格式

郑斌，李菊花 . 基于Kozeny—Carman方程的渗透率分形模型[J]. 天然气地球科学, 2015 , 26(1) : 193 -198 . DOI: 10.11764/j.issn.1672-1926.2015.01.0193

Abstract

Kozeny-Carman(KC)equation is a semi-empirical equation,which is widely used to predict permeability of porous media in the field of flow.Since the establishment of this equation,many new methods were adopted to increase its accuracy.In this paper,an analytical expression for the permeability in porous media using the fractal theory and capillary model was derived based on Posenille law and Darcy equation,which reflects the permeability,porosity,specific surface area relation.The new proposed model is expressed as a function of three properties of porous media considering the specific surface area from the classical KC equation.Meanwhile the fractalKC constant with no empirical constant is obtained.The result shows that permeability of porous media is the function of fractal dimension of pore structure,tortuosity,macroscopic petrophysical parameters(porosity and specific surface area).The KC constant is not constant and has close relationship with tortuosity,fractal dimension and microscopic pore structure parameters.It is concluded that the permeability calculated by using new fractal model is more accurate than that by other KC equations.

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Key words： Fractal; Permeability; Porosity; Specific surface; Kozeny-Carman equation

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