Solute transport in porous media is affected by several factors. The heterogeneous structure of the permeability field is a key factor controlling the spreading and mixing behaviors of a solute cloud. On the other hand, other factors such as the viscosity contrast between the dissolved solute and the ambient fluid can also play an important role. Although both these mixing mechanisms (field heterogeneity and viscosity contrast) have been acknowledged and studied, more investigations are needed in order to better characterize the effect of the variation of both the degree of viscous fingering and the level of disorder of the porous medium. This work aims to explore the impact of field heterogeneity and viscosity contrast on the transport behavior of an inert solute in a two-dimensional flow field. To achieve this, we performed high-resolution numerical simulations based on the spectral method to solve coupled flow and transport equations for a given range of viscosity contrast and log-permeability variance. We analyze the degree and rate of mixing, contour length of the solute cloud, spatial statistics of the concentration field, and arrival times at a control plane to characterize spreading and mixing in the domain. Through the use of numerical simulations, we provide a quantitative separation of the impacts of fingering and heterogeneity and we parametrize the concentration probability distribution function. We find that the interplay among viscous fingering, high-permeability channeling, and low-permeability stagnation at small scales create important features in the spreading and mixing characteristics. In particular, our results indicate that at early times viscosity contrast has a more significant impact on mixing than permeability heterogeneity, and the effect of viscosity contrast on early and late arrival times at a control plane is enhanced by increasing levels of permeability heterogeneity; on the other hand, heterogeneity reduces the peak concentration at a control plane and causes larger solute cloud spreading when the solute is more viscous than the ambient fluid compared to when the solute is less viscous. Moreover, we find that the concentration cumulative distribution function of the solute cloud can be described as a beta distribution for the range of viscosity contrast and permeability heterogeneity considered.

中文翻译：

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渗透率异质性和粘度对比对溶质混合的相对影响

多孔介质中的溶质传输受多种因素影响。渗透场的非均质结构是控制溶质云扩散和混合行为的关键因素。另一方面，其他因素，例如溶解的溶质和周围流体之间的粘度对比，也可以发挥重要作用。尽管这两种混合机制（场异质性和粘度对比）都已得到承认和研究，但还需要更多的研究来更好地表征粘性指状程度和多孔介质无序程度变化的影响。本工作旨在探讨场异质性和粘度对比对二维流场中惰性溶质输运行为的影响。为了达成这个，我们基于光谱方法进行了高分辨率数值模拟，以解决给定范围的粘度对比度和对数渗透率方差的耦合流动和传输方程。我们分析混合的程度和速率、溶质云的轮廓长度、浓度场的空间统计以及到达控制平面的时间，以表征域中的扩散和混合。通过使用数值模拟，我们提供了对指法和异质性影响的定量分离，并对浓度概率分布函数进行了参数化。我们发现粘性指法、高渗透率通道和小规模低渗透率停滞之间的相互作用在传播和混合特性中产生了重要的特征。特别是，我们的结果表明，在早期，粘度对比对混合的影响比渗透率非均质性更显着，并且通过增加渗透率非均质性水平，粘度对比对控制平面上早晚到达时间的影响得到增强；另一方面，当溶质比周围流体更粘稠时，与溶质粘稠度较低时相比，异质性会降低控制平面的峰值浓度并导致更大的溶质云扩散。此外，我们发现溶质云的浓度累积分布函数可以描述为考虑的粘度对比度和渗透率非均质性范围的β分布。并且通过增加渗透率非均质性水平来增强粘度对比对控制平面的早到晚到达时间的影响；另一方面，当溶质比周围流体更粘稠时，与溶质粘稠度较低时相比，异质性会降低控制平面的峰值浓度并导致更大的溶质云扩散。此外，我们发现溶质云的浓度累积分布函数可以描述为考虑的粘度对比度和渗透率非均质性范围的β分布。并且通过增加渗透率非均质性水平来增强粘度对比对控制平面的早到晚到达时间的影响；另一方面，当溶质比周围流体更粘稠时，与溶质粘稠度较低时相比，异质性会降低控制平面的峰值浓度并导致更大的溶质云扩散。此外，我们发现溶质云的浓度累积分布函数可以描述为考虑的粘度对比度和渗透率非均质性范围的β分布。当溶质比周围流体更粘稠时，与溶质粘稠度较低时相比，异质性降低了控制平面的峰值浓度并导致更大的溶质云扩散。此外，我们发现溶质云的浓度累积分布函数可以描述为考虑的粘度对比度和渗透率非均质性范围的β分布。当溶质比周围流体更粘稠时，与溶质粘稠度较低时相比，异质性降低了控制平面的峰值浓度并导致更大的溶质云扩散。此外，我们发现溶质云的浓度累积分布函数可以描述为考虑的粘度对比度和渗透率非均质性范围的β分布。