Mathematical model and numerical solution of constant pressure adsorption of gas in coal particles
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摘要: 为了研究瓦斯在煤粒中的流动机理，开展了4组不同初始压力下的煤粒瓦斯定压吸附实验，提取了累计瓦斯吸附量随时间变化的实验数据。基于压力梯度驱动的达西理论和游离瓦斯密度梯度驱动的新扩散模型，建立2种煤粒瓦斯定压吸附数学模型，并利用有限差分法对数学模型进行了数值解算，得到了煤粒内部累计吸附量的模拟数据。将2种模拟结果与实验数据对比分析发现，数值计算结果与实验相吻合，验证了数值模拟的准确性；两者中的关键比例系数随压力呈现不同的变化趋势，透气性系数随压力呈负相关，微孔道扩散系数不随压力而改变；证明了新提出的游离瓦斯密度梯度驱动的扩散模型比达西定律更适合用来描述煤粒中的瓦斯运移规律。Abstract: In order to study the flow mechanism of gas in coal particles, four groups of constant pressure adsorption experiments were carried out at different initial pressures, and the experimental data of cumulative gas adsorption volume content with time were extracted. Based on Darcy theory driven by pressure gradient and new diffusion model driven by the density gradient of free gas, two kinds of mathematical models of gas adsorption at constant pressure were established, and the adsorption process was numerically solved by VB program code, and the simulation data of cumulative adsorption volume content inside coal particles were obtained. By comparing and analyzing the two kinds of simulation results with the experimental data, it is found that numerical calculation results are consistent with the experimental data, thus verifying the accuracy of the numerical simulation. In addition, the key proportional coefficients in the two models with the change of pressure are different. The permeability coefficient is negatively correlated with the pressure, and the microchannel diffusion coefficient does not change with the pressure. It is concluded that the diffusion model driven by the density gradient of free gas is more suitable to describe the gas migration law in coal particles than Darcy's law and Fick's law.
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表 1 模拟参数取值
Table 1. Simulation parameter value
参数 取值 来源 孔隙率f 0.058 实测 温度T/K 308.150 实测 吸附常数a/(m3·t-1) 15.625 实测 吸附常数b/(MPa-1) 0.779 实测 煤视密度ρs/(g·m-3) 1.432×106 实测 标准情况下瓦斯密度ρc/(g·m-3) 717 通用 透气性系数λ/(m2·MPa-2·d-1) 10-5~10-7 程序试算 微孔道扩散系数Km/(g·MPa-1·m-1·s-1) 10-7~10-9 程序试算 
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