新疆石油地质

新疆石油地质 ›› 2010, Vol. 31 ›› Issue (2): 167-170.

• 油藏工程 • 上一篇    下一篇

粗糙颗粒碳酸盐岩三维酸蚀分形数学模型

李小刚1, 杨兆中1, 苏建政2, 刘长印2, 张汝生2   

  1. 1.西南石油大学,成都 610500;
    2.中国石化 勘探开发研究院,北京 100083
  • 收稿日期:2009-10-22 修回日期:2009-12-14 发布日期:2020-09-17
  • 作者简介:李小刚(1981-),男,四川仁寿人,讲师,博士,油气田开发,(Tel)028-83045166(E-mail)swpuadam@126.com.
  • 基金资助:
    国家科技重大专项协作课题(2008ZX05005-06);四川省青年科技基金前期资助项目(06ZQ026-045)

Fractal Mathematic Model for 3D Acid Corrosion of Rough Carbonate Rock Particles

LI Xiao-gang1, YANG Zhao-zhong1, SU Jian-zheng2, LIU Chang-yin2, ZHANG Ru-sheng2   

  1. 1. Southwest Petroleum University, Chengdu, Sichuan 610500, China;
    2. Research Institute of Petroleum Exploration and Development, Sinopec, Beijing 100083, China
  • Received:2009-10-22 Revised:2009-12-14 Published:2020-09-17

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摘要： 酸化压裂作为碳酸盐岩油气藏的重要增产措施,其增产效果与酸岩反应过程有密切联系。前人的酸岩反应数学模型未考虑岩石颗粒表面的分形特征和酸液对岩石颗粒的三维溶蚀,与实际酸岩反应过程存在明显差异。首先运用分形几何方法对粗糙颗粒的面积、体积等形状特征量进行规范表征,然后以化学反应动力学、传质理论为基础,建立岩石颗粒三维酸蚀分形数学模型,进而分析完全溶蚀时间、溶蚀率等反应特征参数的变化趋势。研究表明:碳酸盐岩颗粒表面分形维数对颗粒完全溶蚀时间的影响很显著,而且分形维数越高,完全溶蚀时间越长;溶蚀时间并非随着颗粒当量半径、氢离子主体量含量增加而单调递增或递减;当相对反应时间一定时,分形维数越高,颗粒溶蚀率越高。

关键词: 分形, 数学模型, 碳酸盐岩, 酸化, 压裂

Abstract: Acid fracturing as an important stimulation technology for carbonate reservoir is closely related with reaction process of acidrock reaction process in effectiveness. The previous acid-rock reaction models have failed to describe fractal feature of rock particle surface and 3D corrosion of acidic liquid on the grain, so there are obvious differences compared with such a real reaction process. This paper conducts regular characterization of the area and volume of rough rock particles by method of fractal geometry, develops the fractal mathematic model of 3D acid corrosion of rough carbonate rock particles on the basis of chemical reaction kinetics and mass transfer theory, and analyzes the variation trends of total corrosion time and corrosion rate of carbonate rocks. The study shows that the effect of fractal dimension of carbonate rock particle on the total corrosion time is remarkable, and the larger the fractal dimension, the longer the total corrosion time; moreover, such a time is not increasing or decreasing monotonously with the increases of rock equivalent radius and main concentration of hydrogen ion content. For a certain relative reaction time, the larger the fractal dimension, the higher the particle corrosion rate.

Key words: fractal, mathematic model, carbonate rock, acid fracturing

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