Abstract In unconventional reservoirs, as the effective pore size becomes close to the mean free path of gas molecules, gas transport in porous media begins to deviate from Darcy’s law. The objective of this study is to explore the similarities of gas flows in nanochannels and core samples as well as those simulated by direct simulation BGK (DSBGK), a particle-based method that solves the Bhatnagar-Gross-Krook (BGK) equation. Due to difficulties in fabrication and experimentation, previous study on gas flow experiments in nanochannels is very limited. In this work, steady-state gas flow was measured in reactive-ion etched nanochannels with a controlled channel size on a sillicon wafer. A core-based permeability measurement apparatus was used to perform steady-state gas flow measurements on carbonate and shale samples. Klinkenberg permeability was obtained under varying pore pressures but constant temperature and effective stress. Methane was used in nanofluidic and rock experiments, making them directly comparable. Results from both experiments were then compared to gas flow simulations by DSBGK method carried out on several independently constructed geometry models. DSBGK uses hundreds of millions of simulated molecules to approximate gas flow inside the pore space. The intermolecular collisions are handled by directly integrating the BGK equation along each molecules trajectory, rather than through a sampling scheme like that in the direct simulation Monte-Carlo (DSMC) method. Consequently, the stochastic noise is significantly reduced, and simulation of nano-scale gas flows in complex geometries becomes computationally affordable. The slippage factors obtained from these independent studies varied across three orders of magnitude, yet they all appear to collapse on a single scaling relation where the slippage factor in the slip flow regime is inversely proportional to the square root of intrinsic permeability over porosity. Our correlation could also fit the data in the literature, which were often obtained using nitrogen, after correcting for temperature and gas properties. This study contributes to rock characterization, well testing analysis as well as the understanding of rarefied gas transport in porous media.

中文翻译：

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来自纳米流体、岩石和孔隙尺度模拟的纳米多孔介质中气体滑移的比例定律

摘要 在非常规油气藏中，随着有效孔径接近气体分子平均自由程，多孔介质中的气体输运开始偏离达西定律。本研究的目的是探索纳米通道和核心样品中气体流动的相似性，以及通过直接模拟 BGK (DSBGK) 模拟的气体流动的相似性，BGK (DSBGK) 是一种求解 Bhatnagar-Gross-Krook (BGK) 方程的基于粒子的方法。由于制造和实验上的困难，以前对纳米通道中气流实验的研究非常有限。在这项工作中，在硅晶片上具有受控通道尺寸的反应离子蚀刻纳米通道中测量稳态气流。使用基于岩心的渗透率测量装置对碳酸盐和页岩样品进行稳态气流测量。Klinkenberg 渗透率是在不同孔隙压力但恒定温度和有效应力下获得的。甲烷被用于纳米流体和岩石实验，使它们具有直接可比性。然后将两个实验的结果与通过 DSBGK 方法在几个独立构建的几何模型上进行的气流模拟进行比较。DSBGK 使用数亿个模拟分子来近似孔隙空间内的气体流动。分子间碰撞是通过沿每个分子轨迹直接积分 BGK 方程来处理的，而不是通过直接模拟蒙特卡罗 (DSMC) 方法中的采样方案来处理。因此，随机噪声显着降低，复杂几何形状的纳米级气流模拟在计算上变得负担得起。从这些独立研究中获得的滑移因子在三个数量级之间变化，但它们似乎都在单一比例关系上崩溃，其中滑移流状态中的滑移因子与孔隙度的固有渗透率的平方根成反比。在校正温度和气体特性后，我们的相关性还可以拟合文献中的数据，这些数据通常是使用氮气获得的。这项研究有助于岩石表征、试井分析以及对多孔介质中稀薄气体输运的理解。然而，它们似乎都在单一比例关系上坍塌，其中滑流状态中的滑移因子与孔隙度的固有渗透率的平方根成反比。在校正温度和气体特性后，我们的相关性还可以拟合文献中的数据，这些数据通常是使用氮气获得的。这项研究有助于岩石表征、试井分析以及对多孔介质中稀薄气体输运的理解。然而，它们似乎都在单一比例关系上坍塌，其中滑流状态中的滑移因子与孔隙度的固有渗透率的平方根成反比。在校正温度和气体特性后，我们的相关性还可以拟合文献中的数据，这些数据通常是使用氮气获得的。这项研究有助于岩石表征、试井分析以及对多孔介质中稀薄气体输运的理解。