Zhu Jiujiang, Ma Jingsheng
School of Civil Engineering, Wuyi University, Jiangmen, Gunagdong Province, China.
Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh, UK.
Sci Rep. 2018 Apr 11;8(1):5826. doi: 10.1038/s41598-018-24151-2.
A gray lattice Boltzmann model has previously been developed by the authors of this article to simulate fluid flow in porous media that contain both resolved pores and grains as well as aggregates of unresolved smaller pores and grains. In this model, a single parameter is introduced to prescribe the amount of fluid to be bounced back at each aggregate cell. This model has been shown to recover Darcy-Brinkman flow but with effective viscosity and permeability correlated through the model parameter. In this paper, we prove that the model parameter relates to the fraction of the solid phase of a sub-pore system for a specific set of bounce-back conditions. We introduce an additional parameter to the model, and this enables flow simulation in which cases with variable effective viscosity and permeability can be specified by selecting the two parameters independently. We verify and validate the model for layered channel cases and mathematically analyze fluid momentum and energy losses for the single- and two-parameter models to explain the roles of the parameters in their conservation. We introduce a strategy to upgrade our model to an isotropic version. We discuss the fundamental differences between our model and the Brinkman body-force LBM scheme.
本文作者此前已开发出一种灰色格子玻尔兹曼模型，用于模拟多孔介质中的流体流动，该多孔介质包含已解析的孔隙和颗粒以及未解析的较小孔隙和颗粒的聚集体。在该模型中，引入了一个单一参数来规定在每个聚集体单元处反弹回的流体量。该模型已被证明可以恢复达西 - 布林克曼流动，但有效粘度和渗透率通过模型参数相关联。在本文中，我们证明了对于特定的一组反弹条件，模型参数与子孔隙系统的固相分数相关。我们在模型中引入了一个额外参数，这使得能够进行流动模拟，在这种情况下，可以通过独立选择这两个参数来指定具有可变有效粘度和渗透率的情况。我们针对分层通道情况验证并确认了该模型，并对单参数和双参数模型的流体动量和能量损失进行了数学分析，以解释参数在其守恒中的作用。我们引入了一种将模型升级为各向同性版本的策略。我们讨论了我们的模型与布林克曼体力格子玻尔兹曼方案之间的根本差异。
