The development of multi-scale computational tools to model multiple hydraulic fractures propagating in complex media.

在过去的十年里，全球能源格局发生了重大变化，这主要是由于一种通常被称为“水力压裂”的方法，该方法使从页岩气储层中提取碳氢化合物在经济上可行。这一过程已经通过一种新技术实现，该技术使得从水平威尔斯井产生多个水力裂缝（HF）成为可能。虽然水力压裂法一直存在争议，但由于碳氢化合物泄漏到地下水中的风险，这种新技术也可以通过在地热储层中创建裂缝网络来产生更清洁的能源。由于地壳顶部10公里处的能量是所有石油和天然气储量的5万倍，因此这项创新技术也具有产生清洁能源的巨大潜力。为了最小化压裂的环境风险并优化HF的放置，有必要具有可以模拟这些不断发展的HF的新配置的设计工具。然而，高频技术的这些重要发展已经使现场实践超出了当前的计算机模拟工具。现有的工具主要集中在模拟一个单一的HF在分段均匀的弹性介质中传播的演变。现在所需要的是模拟同时在复杂固体介质中传播并与预先存在的接头和故障相互作用的多个HF的能力。 即使是最简单的数学模型，一个单一的HF在均匀的弹性介质中传播涉及一个耦合系统的退化非线性积分偏微分方程与复杂的多尺度结构。这些方程还涉及一个奇异的自由边界问题，其中的前速度只能通过评估一个独特的限制。这种奇异的自由边界问题限制了HF模拟器对HF的建模，HF的传播由单个物理过程控制-通常是破碎岩石时释放的能量。在最近的一个重大突破（Peirce & Detournay，2008），我们开发了一个强大的和准确的数值技术，使用局部分析得到的尖端渐近解完全解决这类奇异自由边界问题。我们称之为隐式水平集算法（ILSA），我们已经用它来解决一些开放的问题。 该提案概述了一项雄心勃勃的研究计划，该计划利用创新的ILSA计划进一步开发一套新的计算工具，使工程师能够优化碳氢化合物生产，同时最大限度地减少水力压裂对环境的影响。这项研究计划已经引起了工业界的注意，并将为该领域的石油工程师提供新技术。建立这些稳健的设计工具可能会导致设计HF处理的监管要求，以使用最少的水实现最大的气体提取。对政策的潜在影响是巨大的。

The past decade has seen a significant change in the global energy landscape, largely due to a process commonly known as “fracking” that has made the extraction of hydrocarbons from shale gas reservoirs economically viable. This process has been enabled by a new technology that makes possible the generation of multiple hydraulic fractures (HFs) from horizontal wells. While fracking has been controversial, due to the risk of hydrocarbons leaking into groundwater, this novel technology can also be used to generate cleaner energy by creating fracture networks in geothermal reservoirs. Since the top 10 km of the earth’s crust holds 50,000 times as much energy as all oil and gas reserves, this innovative technology also has huge potential for generating clean energy. To minimize the environmental risk of fracking and to optimize the placement of HF, it is necessary to have design tools that can simulate these new configurations of evolving HF. However, these important developments in HF technology have put field practice beyond current computer simulation tools. Existing tools are primarily focused on simulating the evolution of a single HF propagating in a piece-wise homogeneous elastic medium. What is now required is the capacity to simulate multiple HF that simultaneously propagate in complex solid media and interact with pre-existing joints and faults.    Even the simplest mathematical model for a single HF propagating in a homogeneous elastic medium involves a coupled system of degenerate nonlinear integro-partial differential equations with a complex multi-scale structure. These equations also involve a singular free boundary problem, in which the front velocity can only be determined by evaluating a distinguished limit. This singular free boundary problem has limited HF simulators to the modeling of HF whose propagation is governed by a single physical process – typically the energy released when breaking the rock. In a recent significant breakthrough (Peirce & Detournay, 2008), we developed a robust and accurate numerical technique that uses the tip asymptotic solution obtained by local analysis to completely resolve this class of singular free boundary problem. We called this scheme the Implicit Level Set Algorithm (ILSA), which we have already used to solve a number of open problems.    This proposal outlines an ambitious research program that leverages the innovative ILSA scheme to further develop a novel set of computational tools that will enable engineers to optimize hydrocarbon production while minimizing the environmental impact of fracking. This program of research has already attracted the attention of industry and will provide new technology to petroleum engineers in the field. Establishing these robust design tools may result in regulatory requirements to design HF treatments to achieve maximal gas extraction using the least water. The potential impact for policy is considerable.