Shale gas permeability upscaling from the pore-scale
Shale gas permeability upscaling from the pore-scale
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DOI：
10.1063/5.0020082
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发表时间：
2020-10-01
影响因子：
4.6
通讯作者：
Wu, Lei
中科院分区：
文献类型：
--
作者：
Germanou, Lefki;Ho, Minh Tuan;Wu, Lei
大量页岩样品的有效渗透率为页岩气生产提供了有用的见解。然而，由于计算成本高，样品图像中缺乏孔隙连通性，直接对大岩石样品中的气体流动进行孔隙尺度模拟是不可行的，因此只能通过放大尺度来确定。虽然Brinkman公式被广泛应用于常规岩石的渗透率提升，但如何在这种粗尺度模型中选择有效粘度尚不清楚。此外，它在页岩中的应用很少，因为页岩中的稀疏化效应很重要，因此传统的Navier-Stokes方程不适用于页岩，而且它的准确性还没有得到评估。本研究旨在解决上述两个问题，通过比较几种含裂缝的二维和三维随机多孔介质的Brinkman解与Stokes方程和Boltzmann方程的精细解(分别针对连续介质和稀薄气体流动)。结果表明，在Brinkman模型中，用流体粘度代替有争议的有效粘度，对所考虑的情况可以得到准确的结果。此外，Brinkman模型能够很好地预测页岩中稀薄气体流动的宏观数量，因为误差小于7%，而忽略稀薄效应会导致有效渗透率被严重低估(在所研究的情况下，最高可达90%)。尽管多孔介质的非均质性和各向异性增加了Brinkman模型计算有效渗透率的误差，但总的来说，从这个粗尺度模型中提取的有效渗透率要好于细尺度模型。
The effective permeability of large shale samples provides useful insights into shale gas production. However, its determination can only be achieved through upscaling, since the direct pore-scale simulation of gas flows in large rock samples is not feasible due to the high computational cost and absence of pore connectivity in sample images. Although the Brinkman formulation is widely used in the permeability upscaling of conventional rocks, how to choose the effective viscosity in this coarse-scale model is not clear. Moreover, its application in shale rocks, where the rarefaction effects are important so that the conventional Navier-Stokes equations are inadequate, is rare, and its accuracy has not been assessed. This study aims to address the above two problems, by comparing the Brinkman solutions of several two-dimensional and three-dimensional random porous media containing fractures with the fine-scale solutions of the Stokes and Boltzmann equations (for continuum and rarefied gas flows, respectively). It is found that the use of the fluid viscosity in the Brinkman model, instead of the controversial effective viscosity, leads to accurate results for the cases considered. Additionally, the macroscopic quantity in rarefied gas flows in shale rocks is well predicted by the Brinkman model for a wide range of gas rarefaction, since the error is found to be less than 7%, while neglecting the rarefaction effects leads to significant underestimation of effective permeability (up to 90% in the cases studied). Although heterogeneity and anisotropy of the porous medium increase the error of the effective permeability derived from the Brinkman model, generally speaking, the effective permeability extracted from this coarse-scale model compares favorably to its fine-scale counterpart.