We describe a method to simulate transient fluid flows in fractured media using an approach based on graph theory. Our approach builds on past work where the graph-based approach was successfully used to simulate steady-state fluid flows in fractured media. We find a mean computational speedup of the order of 1400 from an ensemble of a 100 discrete fracture networks in contrast to the $O\left({10}^4\right)$ speedup that was obtained for steady-state flows earlier. However, the transient flows considered here involve an additional degree of complexity that was not present in the steady-state flows considered previously with a graph-based approach, that of time marching and solution of the flow equations within a time-stepping scheme. We verify our method with an analytical test case and demonstrate its use on a practical problem related to fluid flows in hydraulically fractured reservoirs. By enabling the study of transient flows, we create an opportunity for a wide set of possibilities where a steady-state approximation is not sufficient, such as the example motivated by hydraulic fracturing that we present here. This work validates the concept that graphs are able to reliably capture the topological properties of the fracture network and serve as effective surrogates in an uncertainty-quantification framework.

中文翻译：

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使用图形在裂隙介质中进行瞬态流动建模

我们描述了一种基于图论的模拟裂隙介质中瞬态流体流动的方法。我们的方法建立在过去的工作基础上，其中基于图的方法已成功用于模拟裂隙介质中的稳态流体流动。与100个离散裂缝网络的集合相比，我们发现平均计算速度提高了1400量级。$Ø（{10}^4）$较早的稳态流获得的加速。但是，此处考虑的瞬态流涉及先前基于图形的方法所考虑的稳态流中不存在的其他复杂度，即时间步进和时间步长方案中的流方程解。我们通过分析测试案例验证了我们的方法，并证明了其在与水力压裂油藏中的流体流动有关的实际问题中的应用。通过对瞬态流进行研究，我们为稳态逼近不足的各种可能性创造了机会，例如，本文中以水力压裂为动力的示例。