Calculating the effective permeability of sandstone with multiscale lattice Boltzmann/finite element simulations
Calculating the effective permeability of sandstone with multiscale lattice Boltzmann/finite element simulations
复制标题
通过多尺度晶格玻尔兹曼/有限元模拟计算砂岩的有效渗透率
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
J. Fredrich
中科院分区：
文献类型：
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作者：
Joshua A. White;R. Borja;J. Fredrich
格子玻尔兹曼（LB）方法是模拟复杂多孔介质中单个孔隙中流体流动的一种有效方法。LB方法处理复杂边界条件的方便性，加上算法固有的并行性，使其成为解决亚连续尺度流动问题的一种优雅方法。然而，当前计算资源的现实可能会限制这些模拟的大小和分辨率。一个主要的研究重点是开发方法升级微尺度技术用于工程利益的宏观问题。在本文中，我们提出了一个混合，多尺度框架模拟通过多孔介质的扩散。我们使用有限元（FE）方法来解决在宏观尺度上的连续边界值问题。每个有限元被视为一个子细胞和分配的渗透率从亚连续模拟使用LB方法计算。这个框架使我们能够有效地找到一个宏观尺度的解决方案，同时仍然保持有关微观异质性的信息。作为这些模拟的输入，我们使用同步加速器计算的砂岩3D显微断层图像，样品分辨率为3.34 μm。我们讨论这些模拟的预测能力，以及实施问题。我们还量化了连续（达西）尺度的下限，以及确定混合LB-FE模拟的最佳代表性基本体积。
The lattice Boltzmann (LB) method is an efficient technique for simulating fluid flow through individual pores of complex porous media. The ease with which the LB method handles complex boundary conditions, combined with the algorithm’s inherent parallelism, makes it an elegant approach to solving flow problems at the sub-continuum scale. However, the realities of current computational resources can limit the size and resolution of these simulations. A major research focus is developing methodologies for upscaling microscale techniques for use in macroscale problems of engineering interest. In this paper, we propose a hybrid, multiscale framework for simulating diffusion through porous media. We use the finite element (FE) method to solve the continuum boundary-value problem at the macroscale. Each finite element is treated as a sub-cell and assigned permeabilities calculated from subcontinuum simulations using the LB method. This framework allows us to efficiently find a macroscale solution while still maintaining information about microscale heterogeneities. As input to these simulations, we use synchrotron-computed 3D microtomographic images of a sandstone, with sample resolution of 3.34 μm. We discuss the predictive ability of these simulations, as well as implementation issues. We also quantify the lower limit of the continuum (Darcy) scale, as well as identify the optimal representative elementary volume for the hybrid LB–FE simulations.