Abstract This article studies the individual contribution of each term in the Navier-Stokes-Darcy (Brinkman) equation to the fluid linear momentum balance and the consequences of opting for the Darcy or Brinkman equations in 3D reactive flow simulations of a vuggy carbonate. A two-scale continuum model was used to simulate the acidification of a carbonate sample using the Darcy and Brinkman equations. Rock heterogeneity is considered in the initial porosity and permeability fields, which are calculated directly from micro-CT images. Simulations showed that the Darcy equation predicts the acid breakthrough earlier in most cases. The convective acceleration term in the Brinkman equation plays an important role in describing the fluid momentum balance at high injection velocities, and this is a clear evidence against the use of the Darcy equation to model reactive flow in such conditions.

中文翻译：

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反应流中的 Brinkman 方程：每一项在碳酸盐酸化模拟中的贡献

摘要 本文研究 Navier-Stokes-Darcy (Brinkman) 方程中每一项对流体线性动量平衡的贡献，以及在 3D 孔状碳酸盐反应流模拟中选择 Darcy 或 Brinkman 方程的后果。两尺度连续模型用于使用 Darcy 和 Brinkman 方程模拟碳酸盐样品的酸化。在初始孔隙度和渗透率场中考虑了岩石非均质性，这些场是直接从显微 CT 图像计算出来的。模拟表明，达西方程在大多数情况下更早地预测了酸突破。Brinkman 方程中的对流加速项在描述高注入速度下的流体动量平衡方面起着重要作用，