Understanding the dynamics of miscible viscous fingering is of paramount importance in a wide range of applications, from groundwater hydrology to enhanced oil recovery. In this work, we investigate the effect of precipitation and deposition of an initially dissolved component and the subsequent porosity and permeability variations on miscible viscous fingering in porous media. The commonly used stream function‐vorticity formulation does not allow for nonsolenoidality of the velocity vector, which is the case when the porosity field varies with time. This is why we develop a velocity‐vorticity formulation, making no further simplifications on the flow field. For numerical simulations, the governing equations are solved using the hybridization of pseudospectral and compact finite difference methods, and the time stepping is carried out through high‐order semi‐implicit schemes. Using our methodology, we tackle the problem of precipitation of an initially dissolved component through an infinitely fast and reversible reaction. It is found that the deposition of the formed precipitates in porous media results in more severe interfacial instabilities, the effect of which is attenuated as the viscosity ratio between the displacing and resident fluids increases. In addition, our results show that the formed precipitates are mostly concentrated around the interface where the two fluids actively mix. We also characterize the alterations of the local and global permeability fields, and interestingly, we find that the ultimate value of the overall permeability of the porous media scales linearly with the log‐viscosity ratio at any fixed deposition rate. It is worth mentioning that, without loss of generality, the developed methodology and analysis in this study are applicable to other forms of precipitation reactions (e.g., finite rate and irreversible) in porous media.

中文翻译：

---

原位形成沉淀及其随后沉积过程中多孔介质中粘性指状物的动力学

在从地下水水文学到提高采油率的广泛应用中，了解可混溶粘性指法的动力学至关重要。在这项工作中，我们调查了最初溶解的组分的沉淀和沉积以及随后的孔隙率和渗透率变化对多孔介质中可混溶粘性指状物的影响。常用的流函数涡度公式不允许速度矢量具有非电磁性，这是孔隙率场随时间变化的情况。这就是为什么我们开发速度涡度公式的原因，而没有进一步简化流场。对于数值模拟，使用伪光谱和紧凑有限差分方法的混合求解控制方程，时间步长是通过高阶半隐式方案进行的。使用我们的方法，我们通过无限快速和可逆的反应解决了最初溶解的组分沉淀的问题。发现形成的沉淀物在多孔介质中的沉积导致更严重的界面不稳定性，其影响随着驱替流体和驻留流体之间的粘度比增加而减弱。此外，我们的结果表明，所形成的沉淀物主要集中在两种流体有效混合的界面附近。我们还表征了局部和整体渗透率场的变化，有趣的是，我们发现，在任何固定沉积速率下，多孔介质总渗透率的最终值与对数黏度比呈线性比例关系。