arXiv 2103.137092021-03physics.flu-dyn

非均质多孔介质中幂律流变流体流动的统计特性

On the statistical properties of fluid flows with transitional power-law rheology in heterogeneous porous media

Laurent Talon

摘要：

在这项工作中，我们研究非牛顿流体在非均质多孔介质中的流动。我们感兴趣的是呈现特定流变变化的流体：在一定剪切速率以下为牛顿流体，在一定剪切速率以上为幂律流体。由于多孔介质一般表现出强烈的空间非均匀性在大的地质尺度，我们研究这种不均匀性和流体的非线性流变学之间的相互作用。渗透率非均质与非线性流变之间的耦合对渗流有显著影响。我们特别关注速度场的统计特性（均值、方差、相关性等）。根据施加的平均压力梯度，三个宏观流态被确定。对于低或高的平均压力梯度，平均流率分别线性地或根据幂律增加。在后者的制度，我们观察到的速度场是更不均匀的剪切变稀流体比剪切增稠流体。这对应于剪切稀化流体的沟道效应。中间制度对应于一个渐进的和不均匀的局部流变变化。然后，根据压力梯度范围来表征该瞬态状态。并对流场进行了统计分析。流变阈值以上的区域的空间分布显示出有趣的统计特性。例如，它们表现出多尺度特征（分形），类似于其他临界系统（渗流，雪崩等）。更令人惊讶的是，即使一些统计特性是独立的参数，一个有趣的突然旋转的相关性被发现为一组特定的参数。这是通过使用问题的一些对称性来解释的。

英文摘要：

In this work, we study non-Newtonian fluid flow in heterogeneous porous media. We are interested in fluids presenting a specific change in rheology: Newtonian below a certain shear rate and power law above. Since porous media generally exhibit strong spatial heterogeneity at large geological scales, we study the interaction between such inhomogeneity and the nonlinear rheology of the fluid. The coupling between permeability heterogeneity and nonlinear rheology significantly affects the flow. We are particularly in the statistical properties of the velocity field (mean, variance, correlation, etc). Depending on the imposed mean pressure gradient, three macroscopic flow regimes are identified. For a low or high average pressure gradient, the average flow rate increases linearly or according to a power law, respectively. In the latter regime, we observe that the velocity field is more heterogeneous for shear-thinning fluids than for shear-thickening fluids. This is corresponding to a channeling effect of shear-thinning fluids. The intermediate regime corresponds to a progressive and inhomogeneous change of the local rheology. This transient regime is then characterized in terms of pressure gradient range. The flow field is also analyzed statistically. The spatial distribution of the regions above the rheology threshold shows interesting statistical properties. For instance, they exhibit multiscale characteristics (fractal), similar to other critical systems (percolation, avalanches, etc.). More surprisingly, even though some statistical properties are independent of the parameters, an interesting abrupt rotation of the correlations is found for a particular set of parameters. This is explained by using some symmetries of the problem.

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摘要：

英文摘要：

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