含瓦斯煤粒前期扩散理论模型及解析解

Theoretical Model of Early Diffusion in Coal Particles Containing Methane and Its Analytical Solution

为了研究瓦斯前期扩散规律,在假设煤粒瓦斯前期扩散系数近似恒定的基础上,根据球坐标系表示的Fick第二定律,建立了数学模型,并运用数学物理方法推导出了其解析解。采用新模型与经典模型分别对不同吸附平衡瓦斯压力、煤级、粒度和破坏类型的扩散实验数据进行了数值计算,结果表明:新模型能够适合不同实验条件的前期扩散规律,比经典模型更加符合实验结果;采用新模型计算得到的扩散系数普遍比经典模型要高;当煤粒均值度趋近趋于1时,新模型与经典模型计算结果趋同;扩散系数与瓦斯压力、煤级、粒度和破坏程度正相关,前期扩散源占比与破坏类型、瓦斯压力呈正相关,而与粒度、煤级负相关。

In order to study the early gas diffusion laws, on the basis of assuming that the pre-diffusion coefficient of coal particle methane is constant, according to the second law of Fick in the spherical coordinate system, the mathematic model was established, and its analytical solution was obtained by mathematical and physical method. The new model and the classical model are applied to calculate the methane diffusion experimental data under different equilibrium pressure, coal ranks, particle sizes and deformed coal, respectively. The results show that： the new model could describe the early diffusion more exactly than the classical model. Generally, the diffusion coefficients calculated by the new model are more than that by the classical model. When the uniformity of coal particles approaches to 1, the new model would agree with the classical model. The diffusion coefficient has a positive correlation with equilibrium pressure, coal rank, particle size and deformed type, and the methane amount in early diffusion stage has a positive correlation with the deformed type and equilibrium pressure, but a negative correlation with particle size and coal rank.