Abstract Gas adsorption volume has long been recognized as an important parameter for coalbed methane (CBM) resource assessment as it determines the overall gas capacity of coal. As the industrial standard practice, Langmuir volume (VL) is used to describe the gas adsorption volume. Another important parameter, Langmuir pressure (PL), is typically overlooked because it does not directly relate to the resource estimation. However, PL defines the slope of the adsorption isotherm and the ability of a well to attain the critical desorption pressure in a significant reservoir volume, which is critical to plan the initial water depletion rate for a CBM well. Qualitatively, both VL and PL are related to the fractal pore structure of coal, but the intrinsic relationships among fractal pore structure, VL, and PL are not well studied and quantified due to the complex pore structure of coal. In this study, a series of experiments were conducted to measure the fractal dimensions of coal and their relationship to methane adsorption capacity. The thermodynamic model of the gas adsorption on heterogonous surfaces was revisited, and the theoretical models that correlate the fractal dimensions with the Langmuir constants were proposed. Applying the fractal theory, adsorption capacity ( V L ) is proportional to a power function of specific surface area and fractal dimension, and the slope of the regression line contains information on the molecular size of the adsorbed gas. We also found that P L is linearly correlated with sorption capacity, which is defined as a power function of total adsorption capacity ( V L ) and a heterogeneity factor (ν). This implies that PL is not independent of VL, instead, a positive correlation between V L and P L has been noted elsewhere (e.g., Pashin [1]). In the Black Warrior Basin, Langmuir volume is positively related to coal rank (Pashin, 2010; Kim, 1977) [1,2], and Langmuir pressure is inversely related to coal rank. It was also found that P L is negatively correlated with adsorption capacity and fractal dimension. A complex surface corresponds to a more energetic system, which results in an increase in the number of available adsorption sites and adsorption potential, which raises the value of V L and reduces the value of P L .

中文翻译：

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煤的朗缪尔吸附体积和压力之间的内在关系：实验和热力学模型研究

摘要 瓦斯吸附量长期以来被认为是煤层气资源评价的重要参数，因为它决定了煤的整体瓦斯容量。作为工业标准做法，朗缪尔体积 (VL) 用于描述气体吸附体积。另一个重要参数，朗缪尔压力 (PL)，通常被忽视，因为它与资源估计没有直接关系。然而，PL 定义了吸附等温线的斜率以及井在重要储层体积中达到临界解吸压力的能力，这对于规划 CBM 井的初始耗水率至关重要。定性地，VL和PL都与煤的分形孔隙结构有关，但分形孔隙结构VL、由于煤的复杂孔隙结构，PL 和 PL 没有得到很好的研究和量化。在这项研究中，进行了一系列实验来测量煤的分形维数及其与甲烷吸附能力的关系。重新审视了气体在异质表面吸附的热力学模型，并提出了将分形维数与朗缪尔常数相关联的理论模型。应用分形理论，吸附容量 (VL) 与比表面积和分形维数的幂函数成正比，回归线的斜率包含有关吸附气体分子大小的信息。我们还发现 PL 与吸附容量线性相关，吸附容量定义为总吸附容量 (VL) 和异质性因子 (ν) 的幂函数。这意味着 PL 并不独立于 VL，相反，VL 和 PL 之间的正相关已在别处注意到（例如，Pashin [1]）。在 Black Warrior 盆地，Langmuir 体积与煤阶呈正相关（Pashin，2010；Kim，1977）[1,2]，而 Langmuir 压力与煤阶呈负相关。还发现PL与吸附容量和分形维数呈负相关。复杂的表面对应于能量更高的系统，这导致可用吸附位点和吸附势的数量增加，从而提高了 VL 值并降低了 PL 值。Kim, 1977) [1,2]，Langmuir 压力与煤级成反比。还发现PL与吸附容量和分形维数呈负相关。复杂的表面对应于能量更高的系统，这导致可用吸附位点和吸附势的数量增加，从而提高了 VL 值并降低了 PL 值。Kim, 1977) [1,2]，Langmuir 压力与煤级成反比。还发现PL与吸附容量和分形维数呈负相关。复杂的表面对应于能量更高的系统，这导致可用吸附位点和吸附势的数量增加，从而提高了 VL 值并降低了 PL 值。