We investigate the immiscible displacement (drainage) of a wetting fluid in a porous medium by a nonwetting fluid using multi–graphics processing unit (GPU) lattice Boltzmann simulations with the aim of better understanding the pore‐scale processes involved in the geological sequestration of CO₂. Correctly resolving the dynamics involved in multiphase flow in permeable media is of paramount importance for any numerical scheme. Generally, the average fluid flow is assumed to be at low Reynolds numbers Re_av. Hence, by neglecting inertial effects, this immiscible displacement should be characterized by just two dimensionless numbers, namely, the capillary number Ca_av and the viscosity ratio, which quantify the ratio of the relevant forces, that is, the viscous and capillary forces. Our investigation reveals that inertial effects cannot be neglected in the range of typical capillary numbers associated with multiphase flow in permeable media. Even as the average Ca_av and Re_av decrease away from the injection point, inertial effects remain important over a transient amount of time during abrupt Haines jumps, when the nonwetting phase passes from a narrow restriction to a wider pore space. The local Re_l at the jump sites is orders of magnitude higher than the average Re_av, with the local dynamics being decoupled from the externally imposed flow rate. Therefore, a full Navier‐Stokes solver should be used for investigating pore‐scale displacement processes. Using the Ohnesorge number to restrict the parameter selection process is essential, as this dimensionless number links Ca_av and Re_av and reflects the thermophysical properties of a given system under investigation.

中文翻译：

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与地质封存相关的排水位移模式的孔隙模型

我们使用多图形处理单元（GPU）格子Boltzmann模拟研究非润湿流体在多孔介质中的润湿流体的不混溶位移（排水），目的是更好地了解参与CO地质隔离的孔隙尺度过程₂。正确解决渗透介质中多相流动所涉及的动力学问题对于任何数值方案都是至关重要的。通常，假定平均流体流量处于低雷诺数R e _{a v}。因此，通过忽略惯性效应，这种不混溶的位移应仅由两个无量纲数来表征，即毛细管数C a _{a v}粘度比，它量化了相关力的比值，即粘性力和毛细力。我们的研究表明，在可渗透介质中与多相流相关的典型毛细管数范围内，惯性效应不可忽略。即使当平均Ç一个_一个v和- [R Ë_一个v降低从注射点离开，惯性效应突然海恩斯期间保持在一段短暂的量重要跳跃，当非润湿相从窄限制到更宽孔隙空间通过。跳跃点的局部R e _l比平均R e _{a v}高几个数量级，局部动力学与外部施加的流速脱钩。因此，应使用完整的Navier-Stokes求解器来研究孔尺度位移过程。使用奥内佐格数限制参数选择过程是必不可少的，因为这量纲数链接Ç一个_一个v和- [R Ë_一个v，并反映给定系统的所研究的热物理性质。