随着对以页岩为代表的微纳结构多孔介质研究的深入，对其孔隙结构的表征要求逐渐精细化、标准化、原理清晰化。以页岩为例，准确表征其内部的孔隙结构，是获取储层内部页岩气储存状态、流动特征及岩石力学性质的基本依据。页岩为代表的多孔介质其孔隙结构具有复杂的特性，微纳尺度的孔隙结构衍生出复杂形态的连通结构；低孔隙结构又使得岩石渗透率较低；致密的骨架使得页岩整体仍具有一定的强度。因而对页岩孔隙结构的表征需要采取吸附试验、扫描电镜观测等手段进行。其中应用最广泛的是低温气体吸附试验法。在低温下测出多孔介质吸附气体体积随相对压力的变化曲线，即吸附等温线。并利用吸附理论进行曲线计算，可以得到样品的孔隙率、比表面积、孔径分布等参量，但物理吸附方法也存在诸多不足，它是一种非直观的表征分析方法，表征结果很大程度上依赖于吸附原理的假设，例如其假设为单一的圆柱孔或者狭缝孔，均不符合实际情况，而其多层吸附结构的假设，也越来越多人提出怀疑。此外，吸附是一个很复杂的过程，运用分子动力学对微纳尺度的吸附过程进行计算模拟可以看到该过程中还有大量的细节值得进一步研究，以BET、BJH等方法为基础的一些简化吸附模型，仍然有深入探讨的必要性。扫描电镜观测一种应用于微观平面结构的直观观测技术，利用扫描电镜显微成像技术得到多孔介质剖面的直观图像，由此可观测各成分的平面形态和结构特征，借助数字图像处理技术实现对其结构形态的定量表征，得到孔隙率、孔径分布、孔形态参数、甚至比表面积等参量。基于扫描电镜的图像处理方法也存在着一些问题尚待解决：例如从二维剖面提取的孔隙结构参数是否与三维结构等价；图像区域取多大才能具有代表性；在4nm分辨率下，所有微孔和部分介孔都无法观测统计等等。

本文对当前表征多孔介质的技术进行了分析整理，提出了改进的模型和技术，取得了较好的成果。利用Langmuir单层吸附理论，重新修正BET多层吸附模型，提出多层独立吸附模型——MIA模型，并对模型参数进行了物理和数值上的深入探究。BET模型仅能利用30%测试数据（分压在0.05至0.35区段），造成在微孔和大孔区域的失准，而MIA模型则进行全段拟合，测试数据得到了充分利用，更充分地表征微孔、介孔和大孔比表面积值。测试结果表明，MIA模型对测出比表面比BET模型高出20%以上；基于经典BJH模型思想，利用毛细凝聚原理和多层吸附膜原理，提出了微分BJH模型并进行了简化分析，得到了求解孔径分布的简单、清晰并且准确的方法。利用该方法，可为解释微纳尺度多孔介质中假峰提供一种思路，并将求解孔径分布的过程极大地简化。进一步地，由于常规孔径分布求解方案仅能假设为单一孔形态进行求解，并不能代表实际情况，而不同孔形内，介质储存、输运性质有着较大的差别。本文利用Kelvin方程、多层吸附原理和表面张力增强效应（TSE），对圆柱孔、狭缝孔和墨水瓶孔的吸附过程进行分析，构建了各自孔形下的基本吸附等温线。由于对不同孔径的孔的等温线与孔数目分布函数之积的积分，为形状孔的总孔径分布，而对不同形状孔的总孔径分布进行叠加，则得与实测等温线相当的等温线预测值。该并利用线性插值和离散化分析，将该过程转化为矩阵求解，即可得各形状孔的孔数目分布，进而可得其孔径分布。同时，利用扫描电镜，对多孔介质进行了显微成像，进行了样品的直观观测，并设计了数字图像处理算法，实现了对多孔介质扫描电镜图像孔隙率、孔径分布等特征参数的有效提取。利用MatLab编写了提取程序并封装成了相应软件，在页岩孔隙结构特征参数提取上得到了较好地应用，能够有效地识别出其中有机质、无机质、有机孔、无机孔、裂缝，使得这项定性观测技术实现了较为全面的定量化描述。最后，由于扫描电镜观测的是多孔介质的平面结构参数，本文还进一步地通过严格的数学推导和数值实验，提出了三维孔隙结构参数与平面孔隙结构参数的对应关系，得到平面的面孔率与样品孔隙率在测试样品具有足够代表性下完全等效的。本文针对多孔介质的表征技术提出或改进了系列技术和理论，应用这些技术和理论，多孔介质微纳尺度的孔隙结构表征有更清晰的原理、更准确的结果和更便捷的手段。为我们研究以页岩为代表的多孔介质微观性质提供有效的帮助。

With the development of the research on micro nano porous media represented by shale, the characterization of pore structure is required to be more refined, standardized and clear. Taking shale as an example, the accurate characterization of its internal pore structure is the basis for obtaining the internal shale gas storage state, flow characteristics and rock mechanical properties. As a representative porous media, shale has complex across scales structure, but the rock permeability is relatively low because of low porosity and the compact skeleton makes the shale certain strength. The characterization of shale pore structure needs both adsorption test and SEM observation. Adsorption test is the most widely used method is low temperature gas. At low temperature, the curve of adsorption gas volume with relative pressure, i.e. adsorption isotherm, was measured. The parameters such as porosity, specific surface area and pore size distribution can be obtained by using adsorption theory. However, there are many shortcomings in physical adsorption method. It is a non-intuitive characterization analysis method, and the characterization results largely depend on the assumption of adsorption principle, such as the assumption of a single cylindrical hole or slit hole, which is not in line with the actual situation. In addition, adsorption is a very complex process, and using molecular dynamics to calculate and simulate the micro and nano scale adsorption process, we can see that there are a lot of details in the process that are worth further study. Some simplified adsorption models based on BET, BJH and other methods are still necessary to be further discussed. Scanning electron microscope observation is a kind of direct viewing technology applied to the micro plane structure. The image of the porous medium section is obtained by using the scanning electron microscope micro imaging technology, from which the plane shape and structure characteristics of each component can be observed. The quantitative characterization of its structure shape can be realized by means of digital image processing technology, and the porosity, pore size distribution, pore shape parameters and even specific surface can be obtained. There are still some problems to be solved in the image processing method based on SEM. We don`t know exactly whether the pore structure parameters extracted from 2D section are equivalent to 3D structure, and how large the image area is to be representative. Moreover, all micropores and some mesopores cannot be observed and counted under 4nm resolution.

In this paper, the current technologies of characterizing porous media are under discussion, and the improved models and technologies are presented. Based on Langmuir's single-layer adsorption theory, the BET multi-layer adsorption model is revised by proposing the multi-layer independent adsorption model MIA model, and the physical and numerical parameters of the model are explored. The BET model can only use 30% of the experiment data (the relative pressure between 0.05 to 0.35), resulting in the inaccuracy in the microporous and macroporous space, while the MIA model can fit the full section, so all the test data are fully used. Therefore, the specific surface area of microporous, mesoporous and macroporous are all taken into account. The test results show that the MIA model are 20% higher than BET model in surface area. Being accordance with BJH model, based on the principle of capillary coacervation and multilayer adsorption membrane effect, a differential BJH model (DBJH) is proposed and estimated. A simple, clear and accurate method to solve the pore size distribution is obtained. DBJH model offers a novel perspective of the origin of false peaks in micro and nano scale porous media, and simplifies the process of solving pore size distribution greatly. Furthermore, because the conventional solution of pore size distribution can only be assumed to be a single pore shape, it does not represent the actual structure, but there are great differences in the storage and transport properties of media in different pore shapes. In this paper, Kelvin equation, multi-layer adsorption principle and surface tension enhancement effect (TSE) are combined to analyze the adsorption process of cylindrical holes, slit holes and ink bottle holes, and the basic adsorption isotherms of their respective hole shapes are constructed. The curve accumulation of the integral of the product of isotherm function and the quantity distribution function of holes with different apertures is the distribution of the total apertures of the holes with different shapes, the predicted value of the isotherm corresponding to the measured isotherm can be obtained by superposing the distribution of the total apertures of the holes with different shapes. By using linear interpolation and discretization analysis, the process of functional calculation can be transformed into matrix solution, and then the distribution of the number of holes in each shape can be obtained. At the same time, scanning electron microscope is used to image the porous media and observe the samples directly, and digital image processing algorithm is designed to effectively extract the porosity, pore size distribution and other characteristic parameters of the SEM image of the porous media. Using MatLab to write the extraction program and package it into the corresponding software, it has been well applied in shale pore structure feature parameter extraction, and can effectively identify organic matter, inorganic matter, organic hole, inorganic hole and fracture, which makes the qualitative observation technology achieve a more comprehensive quantitative description. Finally, because the plane structure parameters of porous media are observed by SEM, the corresponding relationship between the three-dimensional pore structure parameters and the plane pore structure parameters is proposed through strict mathematical derivation and numerical experiments, and the plane face rate and the sample pore rate are completely equivalent under the enough representativeness of the test sample. This paper puts forward or improves a series of technologies and theories for characterization of porous media. With these technologies and theories, the characterization of porous media micro and nano scale pore structure has clearer principles, more accurate results and more convenient means, which provides effective help for us to study the micro properties of porous media represented by shale.