煤炭自然发火存在明显的介尺度特性，应用介尺度科学理论将煤炭自然发火的微观反应机理与宏观变化特征相关联，有助于推进煤自燃领域的深入研究。首先分析了单煤颗粒、煤颗粒聚团及煤堆3个尺度的区别及相互联系，指出尺度之间正确的信息传递是多尺度模拟的前提，煤自燃领域尺度信息传递的主要方式是“尺度上联”。从数学建模角度提出煤颗粒聚团的本质就是煤堆的表征体元，以表征体元为最小单位的表征体元尺度数值模拟是一种忽略聚团内结构变化的基于宏观数学模型的计算方法，相对应的表征体元内考虑单煤颗粒相互影响的孔隙尺度数值模拟是一种基于微观数学模型的计算方法，由此明确了煤自燃研究中介尺度II所在的堆积态煤体层次的物理过程与数学概念。其次基于表征体元尺度的定义，考虑瞬时孔隙率和高温辐射换热特征，建立了连续性方程、动量守恒方程、能量守恒方程和浓度方程，简述了求解过程，指出需要由孔隙尺度模型获取的参数有孔隙率、渗透率、对流换热系数等。接着论述了基于格子玻尔兹曼方程、考虑内部孔隙结构的孔隙尺度微观模型，并用实例展示了采用工业CT技术获取煤岩体孔隙物理结构、3维数字重构及表征体元提取的步骤。最后利用不同尺度之间参数的本构关系，提出从孔隙尺度获取宏观控制方程中孔隙率、渗透率、惯性系数和对流换热系数的尺度上联方法，从数学上实现了孔隙尺度微观模型到表征体元尺度宏观模型之间的信息传递，从而完成了从孔隙尺度到表征体元尺度的多尺度物理建模和数学建模。

The coal spontaneous combustion has obvious mesoscale characteristics. The application of the mesoscale science and theory to correlate the microscopic reaction mechanism with the macroscopic properties of coal spontaneous combustion contributes to the in-depth study in the field of coal spontaneous combustion. Firstly,the physical process and the mathematical concept of the coal pile gradation in which the mesoscale II exists are made clear. The differ- ences and interrelationships among the three scales of single coal particle,particle cluster and coal pile are explained in detail. Specifically,multi-scale simulation depends on the reasonable information transfer among scales,which is mainly realized by upscaling method in the study of coal spontaneous combustion. From the point of view of mathemati- cal modeling,it is pointed out that the essence of coal particle cluster is the representative elementary volume (REV) of the coal pile. The REV scale simulation,whose minimum unit is REV,is based on macro-model,which ignores the structural changes in the cluster. Correspondingly,the pore scale simulation,which considers the interaction of individ- ual coal particles inside the REV,is based on micro-model. Secondly,based on the definition of the REV scale,the governing equations,including continuity,momentum,energy and concentration equations,which consider the effects of the transient porosity and high-temperature radiation,are built and the corresponding solving method is briefly de- scribed. Besides,it is pointed out that the parameters including porosity,permeability and heat transfer coefficient,etc. should be obtained from the pore scale simulation. Thirdly,the Lattice Boltzmann equations of pore scale simulation are discussed. A sample is employed to illustrate the procedures for the 3D digital reconstruction and the extraction of the REV. Finally,based on the constitutive relation of parameters between different scales,the upscaling method for obtai- ning parameters,such as porosity,permeability,inertia coefficient and convective heat transfer coefficient in macro- control equation,from the pore scale is proposed,which realizes the information transmission from the pore scale simu- lation with micro-model to the REV scale simulation with macro-model mathematically. Consequently,the multi-scale physical and mathematical modeling from pore scale to REV scale is completed.