基于密度差驱动流的非线性瓦斯吸附研究:实验与数值解算

煤瓦斯吸附规律及其数学表征是进行煤层瓦斯含量评估、煤层气产出预测、突出危险性判别的理论基础。在理论描述煤瓦斯吸附时,经典菲克扩散模型仅考虑了吸附瓦斯量的变化,忽略了煤基质孔隙空间内的游离瓦斯,并且煤的孔隙尺度分布广泛,不同尺度孔隙中气体流动机制应有差异,因此仅采用菲克扩散解释瓦斯吸附行为可能不够有效。为对煤瓦斯非线性吸附过程进行精确表征,首先进行了不同尺度煤块在不同初始压力下的瓦斯变压吸附实验,得到瓦斯吸附量随时间的变化曲线;根据菲克模型的推导过程,将吸附瓦斯与游离瓦斯一并计为瓦斯密度,提出基于密度差驱动流的瓦斯非线性吸附数学模型(密度模型);其次,利用有限差分法编制了求解代码分别对菲克模型与密度模型进行了数值解算;最后将两种模型的解算结果与实验结果进行对比,发现:菲克模型计算的瓦斯吸附曲线一定程度上偏离实验曲线,而密度模型的计算曲线与实验曲线吻合良好。结果表明密度模型能更加精确的描述瓦斯非线性吸附。

Investigation of non-linear gas adsorption in coal based on density-gradient driven flow:Experiments and numerical solutions

Coal gas adsorption and its mathematical characterization plays a theoretical basis to estimate coal seam gas content,forecast coalbed gas production,classify the coal/gas outburst.When theoretically describing coal gas absorption,only considering adsorbed gas to compute gas content in coal and only involving Fick’s mass influx may lead to an erroneous prediction due to the pore size in coal ranging widely and it should be a multi-mechanism process in multi-scale pores.In order to theoretically characterize the gas adsorption process in high accuracy,a series of experiments were conducted under different initial pressures with different grain size samples,and the changing curves of the gas adsorption amount with time were obtained.Following this,recalling to the derivation of Fick model,the concept of gas density was employed to compute gas content consisting of adsorbed gas and free gas,the non-linear gas adsorption model (Density model) was proposed with an assumption that the gas transport in coal was density-gradient driven flow,and the numerical model of Density model was presented by using the finite difference method.Numerical code to solve the two models was developed independently.Afterward the two sets of simulated results obtained by numerical solving the Fick model and Density model were compared to the measured date,and it shows Density model owns a higher accuracy over Fick model in terms of modeling gas adsorption,implying the proposed Density model may be more effective in describing the non-linear gas transport behaviors in coal.