The employment of 2D models to investigate the properties of 3D flows in porous media is ubiquitous in the literature. The limitations of such approaches are often overlooked. Here, we assess to which extent 2D flows in porous media are suitable representations of 3D flows. To this purpose, we compare representative elementary volume (REV) scales obtained by 2D and 3D numerical simulations of flow in porous media. The stationarity of several quantities, namely porosity, permeability, mean and variance of velocity, is evaluated in terms of both classical and innovative statistics. The variance of velocity, strictly connected to the hydrodynamic dispersion, is included in the analysis in order to extend conclusions to transport phenomena. Pore scale flow is simulated by means of a Lattice Boltzmann model. The results from pore scale simulations point out that the 2D approach often leads to inconsistent results, due to the profound difference between 2D and 3D flows through porous media. We employ the error in the evaluation of REV as a quantitative measure for the reliability of a 2D approach. Moreover, we show that the acceptance threshold for a 2D representation to be valid strongly depends on which flow/transport quantity is sought.

中文翻译：

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2D 建模在 3D 多孔介质中评估流动特性的适用性

使用 2D 模型来研究多孔介质中 3D 流动的特性在文献中无处不在。这种方法的局限性常常被忽视。在这里，我们评估多孔介质中的 2D 流动在多大程度上适合 3D 流动。为此，我们比较了通过多孔介质中流动的 2D 和 3D 数值模拟获得的代表性基本体积 (REV) 尺度。几个量的平稳性，即孔隙度、渗透率、速度的平均值和方差，是根据经典和创新统计来评估的。速度的变化与流体动力分散严格相关，被包括在分析中，以便将结论扩展到传输现象。孔隙尺度流动是通过格子玻尔兹曼模型模拟的。孔隙尺度模拟的结果指出，由于 2D 和 3D 流经多孔介质之间的巨大差异，2D 方法通常会导致结果不一致。我们使用 REV 评估中的误差作为 2D 方法可靠性的定量度量。此外，我们表明，二维表示有效的接受阈值很大程度上取决于所寻求的流量/传输量。