Model reduction for fractured porous media: a machine learning approach for identifying main flow pathways
Model reduction for fractured porous media: a machine learning approach for identifying main flow pathways
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DOI：
10.1007/s10596-019-9811-7
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发表时间：
2019-06
影响因子：
2.5
通讯作者：
S. Srinivasan;S. Karra;J. Hyman;H. Viswanathan;G. Srinivasan
中科院分区：
文献类型：
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作者：
S. Srinivasan;S. Karra;J. Hyman;H. Viswanathan;G. Srinivasan
离散裂缝网络（DFN）常用于模拟裂缝性多孔介质中的流动和输运。在包含数千条裂缝的大型DFN上精确地求解流动和输运行为在计算上是昂贵的。这使得不确定性量化研究（如通过网络的旅行时间）在计算上难以处理，因为需要数百到数千次DFN模型的运行来获得预测的不确定性的界限。先前关于该主题的工作表明，可以通过考虑它的子网络（通常称为“骨干”子网络）来降低DFN的复杂性，该子网络的流量和传输特性随后被证明与整个网络相似。该技术相当于将网络的完整裂缝集划分为两个不相交的集，其中一个是骨干子网络，另一个是补充子网络。正是在这种背景下，我们提出了一种DFNs的系统约简技术，该技术通过随机森林分类器使用监督机器学习，从完整的骨折集合中选择主干子网络。我们发现训练后的分类器的样本内误差（精度和召回分数）是样本外误差的非常准确的指标，从而表明分类器可以很好地泛化到测试数据。此外，这种系统缩减技术产生的子网络小至整个DFN的12%，但仍能恢复整个网络的传输特性，如后期的峰值剂量和尾矿行为。最重要的是，子网络保持连接，它们的大小可以通过一个无量纲参数来控制。此外，随着子网络规模的增加，子网络突破曲线的kl -散度和ks -统计量也呈现出单调减小的物理现实趋势。通过这种技术获得的计算效率取决于子网的大小，但是对于小型子网可以预期大大减少计算时间，对于仅占整个网络10-12%的子网，可以节省多达90%的计算时间。
Discrete fracture networks (DFN) are often used to model flow and transport in fractured porous media. The accurate resolution of flow and transport behavior on a large DFN involving thousands of fractures is computationally expensive. This makes uncertainty quantification studies of quantities of interest such as travel time through the network computationally intractable, since hundreds to thousands of runs of the DFN model are required to get bounds on the uncertainty of the predictions. Prior works on the subject demonstrated that the complexity of a DFN could be reduced by considering a sub-network of it (often termed a “backbone” sub-network), one whose flow and transport properties were then shown to be similar to that of the full network. The technique is tantamount to partitioning the complete set of fractures of a network into two disjoint sets, one of which is the backbone sub-network while the other its complement. It is in this context that we present a system-reduction technique for DFNs using supervised machine learning via a Random Forest Classifier that selects a backbone sub-network from the full set of fractures. The in-sample errors (in terms of precision and recall scores) of the trained classifier are found to be very accurate indicators of the out-of-sample errors, thus exhibiting that the classifier generalizes well to test data. Moreover, this system-reduction technique yields sub-networks as small as 12% of the full DFN that still recover transport characteristics of the full network such as the peak dosage and tailing behavior for late times. Most importantly, the sub-networks remain connected, and their size can be controlled by a single dimensionless parameter. Furthermore, measures of KL-divergence and KS-statistic for the breakthrough curves of the sub-networks with respect to the full network show physically realistic trends in that the measures decrease monotonically as the size of the sub-networks increase. The computational efficiency gained by this technique depends on the size of the sub-network, but large reductions in computational time can be expected for small sub-networks, yielding as much as 90% computational savings for sub-networks that are as small as 10-12% of the full network.