Abstract This work investigates upscaling of capillary pressure curves for modeling gravity segregation under the influence of capillary heterogeneity. We consider two flowing phases driven by gravity and capillary forces and seek the saturation spatial and temporal variation until equilibrium is reached. Existing upscaling methods, found in the literature, are applied to a number of cases. Resulting saturation solutions are compared to fine-scale simulations and the different methods are evaluated, showing in general that the popular capillary limit method produces the best results. However, a large number of cases are found to have significant errors. This leads to the conclusion that all existing methods are often inadequate and developing new methods should be considered. We therefore propose a new optimization-based upscaling method. Using this approach it is shown that capillary pressure can be upscaled to Brooks-Corey type functions and produce accurate upscaled simulations matching the fine-scale solutions. Optimization upscaling is computationally demanding and requires the fine-scale simulations for minimizing an objective function. However, it is shown that the upscaled curves can be applied to different permeability realizations to calculate ensemble average saturation solutions.

中文翻译：

---

用于重力毛细管驱动流数值模拟的毛细管压力曲线放大

摘要 这项工作研究了在毛细管非均质性影响下模拟重力偏析的毛细管压力曲线的放大。我们考虑由重力和毛细管力驱动的两个流动相，并寻求饱和空间和时间变化，直到达到平衡。在文献中发现的现有放大方法适用于许多情况。将得到的饱和度解决方案与精细模拟进行比较，并对不同的方法进行评估，通常表明流行的毛细管极限方法会产生最好的结果。但是，发现大量案例存在重大错误。由此得出结论，所有现有方法通常都不够充分，应考虑开发新方法。因此，我们提出了一种新的基于优化的放大方法。使用这种方法表明，毛细管压力可以放大到 Brooks-Corey 类型函数，并产生与精细解匹配的精确放大模拟。优化升级在计算上要求很高，并且需要精细的模拟来最小化目标函数。然而，结果表明放大的曲线可以应用于不同的渗透率实现来计算集合平均饱和度解。