压裂无环流无圈闭侵入渗流模型
Loopless non-trapping invasion percolation model for fracking
摘要：
水力压裂（压裂法）的最新发展使得能够从旧的低渗透性页岩中回收大量的天然气和石油。这些发展包括从低体积、高粘度流体注入到高体积、低粘度注入的变化。注入的流体引入了分布式损害，其提供了用于气体和油的提取的裂缝渗透性。为了模拟这一过程，我们利用一个无环的非捕获入侵渗透先前介绍的模型在一个强烈的无序介质中的最佳聚合物，并确定最小能量生成树的晶格。我们进行了数值模拟的二维正方形格子，并发现显着差异，从其他渗流模型。此外，我们发现，不断增长的裂缝网络满足Horton-Strahler和Tokunaga网络统计。与其他入侵渗流模型一样，我们的模型显示了爆发动力学，其中集群迅速扩展到一个连接的区域。我们引入了另一种定义的爆发是一个连续的系列开放的债券，其强度都低于一个特定的值。使用这个定义的突发，我们发现很好的协议与幂律频率面积分布。这些结果通常与在高容量压裂期间观察到的微震活动分布一致。
英文摘要：
Recent developments in hydraulic fracturing (fracking) have enabled the recovery of large quantities of natural gas and oil from old, low permeability shales. These developments include a change from low-volume, high-viscosity fluid injection to high-volume, low-viscosity injection. The injected fluid introduces distributed damage that provides fracture permeability for the extraction of the gas and oil. In order to model this process, we utilize a loopless non-trapping invasion percolation previously introduced to model optimal polymers in a strongly disordered medium, and for determining minimum energy spanning trees on a lattice. We performed numerical simulations on a 2D square lattice and find significant differences from other percolation models. Additionally, we find that the growing fracture network satisfies both Horton-Strahler and Tokunaga network statistics. As with other invasion percolation models, our model displays burst dynamics, in which the cluster extends rapidly into a connected region. We introduce an alternative definition of bursts to be a consecutive series of opened bonds whose strengths are all below a specified value. Using this definition of bursts, we find good agreement with a power-law frequency-area distribution. These results are generally consistent with the observed distribution of microseismicity observed during a high-volume frack.
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