不同粒径与压力下煤粒瓦斯吸附数学模型研究
Study on mathematical model of coal particles gas adsorption under different particle sizes and pressures
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摘要: 采用煤粒进行瓦斯吸附实验是研究煤基质瓦斯流动机理的基本手段。为探究煤粒形状对煤体瓦斯吸附规律的影响，设计煤粒瓦斯恒温定压吸附实验，得到4种粒度的煤样在不同瓦斯压力下的吸附特征。基于煤基质游离瓦斯密度梯度扩散理论，分别建立圆柱形和球形煤粒瓦斯定压吸附数学模型，并通过有限差分法进行编程解算，后用实验数据来验证模拟结果。发现将煤粒视作球形和圆柱形得到的模拟结果均与实验结果匹配程度较高，证明了煤基质游离瓦斯密度梯度扩散理论的准确性和可靠性；煤样粒径增加时，微孔道扩散系数增大；瓦斯吸附压力对微孔道扩散系数的影响较小，微孔道扩散系数摆脱对瓦斯吸附压力和吸附时间的依赖；相对来说，煤粒的形状对瓦斯吸附数学模型的预测精度影响不大，但2种模型的微孔道扩散系数存在显著差异；当瓦斯吸附压力与煤样粒径固定时，圆柱形煤粒的微孔道扩散系数大于球形煤粒的微孔道扩散系数，约为2倍，主要是由于2种形状有效扩散截面积的差异性。Abstract: Gas adsorption experiment with coal particles is a basic means to study the gas flow mechanism of coal matrix. In order to explore the influence of coal particle shape on coal gas adsorption law, a constant temperature and pressure adsorption experiment was designed to obtain the adsorption characteristics of coal samples with four particle sizes under different gas pressures. Based on the gradient diffusion theory of free gas density in coal matrix, the mathematical models of constant pressure adsorption of cylindrical and spherical coal gas were established respectively, and solved by finite difference method, and the simulation results were verified by experimental data. It is found that the simulation results obtained by considering the coal particles as spherical or cylindrical have a good match with the experimental results, which proves the accuracy and reliability of the gradient diffusion theory of free gas density in coal matrix. The diffusion coefficient increases with the increase of coal particle size. The influence of gas adsorption pressure on the diffusion coefficient of micropore is small, and the diffusion coefficient of difference of surface area between the two shapes.
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