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Three-Dimensional Crack Propagation Algorithms Based on Universal Meshes and their Application to Fracking

基于通用网格的三维裂纹扩展算法及其在压裂中的应用

基本信息

批准号：
1662452
负责人：
Adrian Lew
金额：
$ 48.81万
依托单位：
Stanford University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-08-01 至 2021-12-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1662452&HistoricalAwards=false
关键词：
Three Dimensional Crack Propagation Algorithms

项目摘要

Accurate prediction of when and how a crack will grow and propagate through a rock formation is an important yet unsolved problem in engineering. Crack growth and prediction models guide the design of strategies to frack oil and gas reservoirs and to inject fracking fluids and waste water back underground, and help assess the resulting seismicity. Crack growth models are also used in evaluating the stability of reservoirs for carbon sequestration, and in the engineering of geothermal reservoirs. Additionally, they play an important role in developing understanding of geophysical phenomena, such as volcanic eruptions and fracture of glaciers. This award supports fundamental research to formulate and implement numerical algorithms and methods to simulate the propagation of cracks through structures and underground rocks. The outcomes of this project will reduce the predictive uncertainty to the understanding of the physics and the structure of the rock being fractured. It will alleviate or remove uncertainties associated with the computational methods. By improving the way such predictions are made, the project has the potential to impact energy production and associated concerns for years to come. Additionally, this project will train a graduate student in an area in which experts are highly sought, as well as involve undergraduate students from predominantly underrepresented minority institutions, training and exposing them to research in engineering. To attain control of the numerical errors associated with simulating the propagation of cracks, this project will combine three novel developments. First, the formulation of a robust algorithm to deform a single background mesh of tetrahedra so that it exactly meshes every cracked geometry obtained as the fracture propagates in three dimensions. Such mesh is called a universal mesh. Second, the formulation of a class of numerical methods that enable the computation of stress intensity factors along a crack front with high-order of accuracy. Third, the creation of an algorithm to compute convergent evolution of brittle and hydraulic fractures in three dimensions. Working jointly, the universal mesh algorithm and the high-order method should enable the computation of very accurate crack evolutions without constant re-meshing around the crack front.

准确预测裂纹在岩石中的扩展时间和方式是工程中一个重要而尚未解决的问题。裂缝增长和预测模型指导了压裂油气藏和将压裂液和废水注入地下的策略设计，并有助于评估由此产生的地震活动。裂缝增长模型也用于评估碳封存储层的稳定性，以及地热储层的工程设计。此外，它们在加深对火山爆发和冰川断裂等地球物理现象的了解方面发挥着重要作用。该奖项支持基础研究，制定和实施数值算法和方法，以模拟裂缝通过结构和地下岩石的传播。该项目的成果将减少预测的不确定性，以了解物理和岩石的结构被破碎。它将减轻或消除与计算方法相关的不确定性。通过改进这种预测的方式，该项目有可能影响未来几年的能源生产和相关问题。此外，该项目还将在一个非常需要专家的领域培训一名研究生，并让来自代表性不足的少数民族院校的本科生参与，培训他们并使他们接触工程研究。为了控制与模拟裂纹扩展相关的数值误差，该项目将结合联合收割机三个新的发展。首先，制定一个强大的算法来变形一个单一的背景网格的四面体，使它精确地网格每个裂缝的几何形状获得的裂缝在三维传播。这种网格称为通用网格。第二，制定了一类数值方法，使沿沿着裂纹前缘的应力强度因子的计算具有高的精度。第三，建立了计算三维脆性和水力裂缝收敛演化的算法。共同工作，通用网格算法和高阶方法应该能够计算非常精确的裂纹演化，而无需围绕裂纹前缘不断重新网格化。

项目成果

期刊论文数量（7）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Analysis of a method to compute mixed-mode stress intensity factors for non-planar cracks in three-dimensions

DOI：
10.1051/m2an/2023001
发表时间：
2023-01
期刊：
ESAIM: Mathematical Modelling and Numerical Analysis
影响因子：
0
作者：
Benjamin E. Grossman‐Ponemon;M. Negri;A. Lew
通讯作者：
Benjamin E. Grossman‐Ponemon;M. Negri;A. Lew

Logarithmic Growth of Dikes From a Depressurizing Magma Chamber

减压岩浆室中岩墙的对数增长

DOI：
10.1029/2019gl086230
发表时间：
2020
期刊：
Geophysical Research Letters
影响因子：
5.2
作者：
Grossman‐Ponemon, Benjamin E.;Heimisson, Elías R.;Lew, Adrian J.;Segall, Paul
通讯作者：
Segall, Paul

Numerical analyses of crack path instabilities in quenched plates