为提高多孔质材料渗透系数的理论计算精度, 本文基于分形理论建立了渗透系数求解模型, 并基于图像处理优化了分形维数的求解方法。首先, 利用扫描电子显微镜拍取4种多孔材料表面图像后, 使用盒维法求解分形维数并研究多孔材料图像大小和放大倍数对分形维数求解准确性的影响。其次, 基于气体Darcy定律、分形理论及修正的Hagen-Poiseulle气体方程建立了无修正系数的渗透系数求解方程, 从而完善了多孔材料分形理论计算公式。最后搭建渗透系数测量平台, 基于流动状态的判定结果, 验证了理论推导的正确性。结果表明: 图像越大、放大倍数越低, 分形维数越趋近于真实值; 通过建立材料的最大孔径、最小孔径、迂曲度及分形维数与渗透系数间的无经验参数的理论关系, 可使渗透系数理论计算值更加准确。通过对比渗透系数理论计算值及实验值可知, 误差值为5%～8%, 满足材料渗透系数测量的误差要求。本文研究为材料渗透系数的准确获取提供了新的途径。

To improve the theoretical calculation precision of permeability coefficient for porous material, solving model of permeability coefficient was established on the basis of fractal theory, and solving method of fractal dimension was optimized by image processing. Firstly, after photographing surface image of four kinds of porous materials with a scanning electron microscope, fractal dimension was solved by box dimension method and influence of image size and amplification factor of porous material on solving precision of fractal dimension was researched. Secondly, according to Darcy law, fractal theory and corrected Hagen-Poiseulle gas equation, solving equation of permeability coefficient without correction factor was established, resulting in calculation formula of fractal theory for porous material was improved. Finally measuring platform of permeability coefficient was established, and correctness of theoretical derivation was verified on the basis of judgment result of flow state. The result indicates: with increase of image size and decrease of amplification factor, fractal dimension approaches true value increasingly; theoretical calculation value of permeability coefficient is more accurate after theoretical relation without experience parameters of maximum diameter of hole, minimum diameter of hole, tortuosity, fractal dimension and permeability coefficient is established. Error value is 5%～8% through comparing theoretical calculation value of permeability coefficient and experiment value, which can satisfy error requirement of measuring for material permeability coefficient.This paper provides new ways of obtaining material permeability coefficient accurately.