王镜惠　梅明华　刘娟　王华军

摘      要：为了提供有效的煤岩渗透率计算方法，基于分形理论推导了煤样渗透率计算模型，提出了相应参数的获取方法，基于高压压汞实验获得的毛管压力数据和实验测得的相应煤样的渗透率数据验证了计算方法的正确性，并基于该方法利用数值模拟的方法分析了煤样渗透率的主要影响因素。结果表明，分形理论的煤岩渗透率计算方法能够有效预测煤岩渗透率，平均误差仅为6.84%;煤岩分形维数、迂曲度和最大孔隙半径对渗透率具有重要影响，煤岩渗透率随着分形维数和迂曲度增加而降低，随最大孔隙半径增加而增加。

关  键  词：分形理论;高煤阶;煤岩;渗透率;计算方法

中图分类号：TQ021.4       文献标识码： A      文章编号：1671-0460（2020）07-1356-05

Research and Application of the Permeability Calculation

Method for High-rank Coal Rock Based on Fractal Theory

WANG Jing-hui1a， MEI Ming-hua2， LIU Juan1b， WANG Hua-jun2

（1. a.School of Chemistry and Chemical Engineering;1b. School of life Science，Yulin University， Yulin Shaanxi 719000， China;

2. The Second Gas Production Plant of PetroChina Changqing Oilfield Branch Company， Shaanxi Yulin719000， China;

Abstract： In order to provide effective calculation method of the coal rock permeability， the permeability calculation model of coal samples was deduced based on the fractal theory， and the acquisition approach of corresponding parameters was proposed. The correctness of the calculation method was verified based on the capillary pressure data from high-pressure mercury injection experiments， and the main influencing factors of the coal sample permeability were analyzed based on the permeability calculation model. The results showed that the permeability calculation method of high-rank coal rock based on the fractal theory could effectively predict the permeability， and the average error was only 6.84%. The fractal dimension， tortuosity and maximum pore radius of coal rock had important influence on its permeability. And the permeability of high-rank coal rock decreased with the increase of fractal dimension and tortuosity， and increased with the increase of maximum pore radius.

Key words： Fractal theory; High coal rank; Coal rock; Permeability; Calculation method

煤層气储层渗透率对开展煤层气储层评价，实现煤层气井高产稳产具有重要意义^[1]。煤层气储层一般需要通过压裂提供渗透率^[2]，但煤层原始渗透率对煤层气开发起决定性作用。煤层气储层为低孔低渗储层，孔隙结构复杂，煤样制取难度较大且渗透率测试较难，迫切需要有效的渗透率计算模型。许多学者对致密砂岩储层渗透率预测进行了研究，如邓浩阳等研究了基于致密砂岩储层孔隙结构参数，利用多元回归的方法建立渗透率计算模型^[3];张涛等建立了致密砂岩储层绝地渗透率计算模

型^[4];范宜仁等基于三组分法建立了致密砂岩岩心核磁共振渗透率表征新模型^[5];而对于煤岩渗透率的研究则多为实验测试，缺乏成熟的计算方法，刘帅帅等以鄂尔多斯盆地东缘柳林矿区南部4号煤层为研究对象，研究了有效应力对煤储层不同方向渗透率的影响^[6]。……