We investigate the impact of sub-grid scale horizontal lamination on the migration of the CO${}_2$ plume during geologic sequestration. A new physics-based model that includes the effects of capillary and viscous forces is used to obtain effective flow-rate dependent capillary pressure and relative permeability functions. For this purpose a macroscopic capillary number is derived that accurately describes the viscous-capillary force balance. The model is based on the fractional flow approach and is implemented in an extended radial Buckley-Leverett solution. This provides an easy way to investigate the impact of mm to m scale laminae on the frontal advance of the plume. Our work shows that at injection rates and volumes commonly used at geologic sequestration sites, capillary number dependency is important during the initial phase of the injection period. At later stages, the use of a capillary limit solution will be a valid approximation, even close to the injection well.

我们研究了亚网格规模水平层压对CO迁移的影响${}_{\mathrm{2个}}$地质封存过程中出现羽状流。一种新的基于物理学的模型，其中包括毛细作用力和粘性力的作用，用于获得有效的流速相关的毛细作用压力和相对渗透率函数。为了这个目的，导出了宏观的毛细管数，其准确地描述了粘性-毛细作用力的平衡。该模型基于分数流方法，并在扩展的径向Buckley-Leverett解决方案中实现。这提供了一种简单的方法来研究毫米级到微米级薄片对羽流前沿的影响。我们的工作表明，在地质封存点通常使用的注入速率和体积下，毛细管数依赖性在注入期的初始阶段很重要。在以后的阶段，使用毛细管极限溶液将是有效的近似值，