碳酸盐岩酸蚀蚓孔分形模型及酸化参数优化

Fractal Model of Carbonate Acidized Wormhole and Acidizing Parameter Optimization

张合文 邹洪岚 鄢雪梅 崔明月 蒋卫东

ZHANG Hewen ZOU Honglan YAN Xuemei CUI Mingyue JIANG Weidong

中国石油勘探开发研究院, 北京 海淀 100083

Research Institute of Petroleum Exploration and Development, Haidian, Beijing 100083, China

碳酸盐岩基质酸化的主要特征是形成酸蚀蚓孔，蚓孔在欧氏空间上被认为是无序和杂乱无章的，采用经典数学方法对蚓孔进行实验模拟和数学描述难度较大，但准确描述酸蚀蚓孔的穿透深度对施工参数的优化和提高酸化效果具有重要意义。基于此目的，首先完成了多组岩芯酸化流动实验，采用CT扫描得到了蚓孔的真实形态，引入“盒维数”计算方法，对实验得到蚓孔的分形性进行了验证，并求取了不同蚓孔形态的Hausdorff分形维数。结果表明，实验得到的酸蚀蚓孔具有较好的分形性，且分形维随着溶蚀形态的变化而不同，范围在1.19~1.98，最优排量对应的分形维数在1.6左右。其次，将室内实验和分形几何数学方法相结合，建立了酸蚀蚓孔等效长度分形计算模型，并对影响蚓孔等效长度的因素进行了敏感性分析。

Carbonate matrix acidizing mainly features acid wormholes that are deemed to be unordered and disorganized in Euclidean space. It is difficult to conduct experimental simulations and mathematically describe wormholes using classic mathematical methods; however, an accurate description of the penetration depth of acid wormholes is of significance for construction parameter optimization and acidizing effect improvement. To this end, multiple groups of core acidification flow simulation tests were carried out first in this study, using CT scanning to determine the true forms of the wormholes. The term "box dimension" was introduced to verify the wormhole fractal properties and to calculate the Hausdorff fractal dimensions of different wormhole forms. Test results indicate that the wormholes in this test featured favorable fractal properties; fractal dimensions varied from 1.19-1.98 as solution features changed; and the dimension corresponding to the optimum capacity was approximately 1.6. Moreover, a combined method of laboratory testing and fractal geometry was employed to establish a fractal calculation model for the equivalent length of acidized wormholes, and to conduct a sensitivity analysis of factors affecting the wormhole's equivalent length.

10.11885/j.issn.1674-5086.2015.08.06.02