Miscible Hele-Shaw Displacements: A Three-Dimensional Framework Based on the Stokes Equations

加州大学圣巴巴拉分校CBET-0651498 E.Meiburg这项研究建立了一个新的框架，用于分析流动诱导弥散影响下的不稳定混相置换。该框架基于三维Stokes方程，采用非线性模拟和计算线性稳定性分析相结合的方法。因此，它取代了用有限有效性的简化色散模型来扩充低维Darcy方程的常见但有问题的方法。为了建立这个框架，研究集中在实验研究不稳定位移中经常使用的Hele-Shaw几何。这种几何形状与许多应用领域相关，从润滑问题、轴承流动和破碎岩石中的石油置换，到小型MEMS设备。与化学反应一样，可变密度位移以标称流动方向和重力矢量之间的任意角度进行处理。Stokes研究的结果随后被用来建立改进的基于Darcy的弥散模型，该模型能够捕捉Hele-Shaw几何结构中流动诱导弥散的影响。通过这种方式，这项研究有助于促进对流动诱导弥散对混相置换影响的理解。智力优势：二维和三维高分辨率斯托克斯流动模拟与计算线性稳定性分析相结合，为研究不稳定混相置换的复杂物理，特别是如何受流动诱导弥散影响提供了一套强大的工具。它们大大超过了迄今为止常见的基于达西的分析，后者必须通过经验分散模型来增强。新的框架被用来建立Hele-Shaw/Darcy类比的局限性，并生成广泛的Darcy结果的Hele-Shaw对应项。广泛的影响：对拟议工作产生的流动诱导弥散效应的高级理解增强了对多孔介质中传输过程的预测能力，并有助于设计和优化对石油和化工行业重要的各种流动过程。此外，该项目将对本科生和研究生进行大规模数值模拟概念的教育和培训，并将受益于他们与UCSB正在进行的计算科学和工程IGERT项目的联系。

CBET - 0651498 E. Meiburg, University of California-Santa BarbaraThis research establishes a new framework for analyzing unstable miscible displacements under the influence of flow-induced dispersion. This framework, based on the three-dimensional Stokes equations, employs both nonlinear simulations as well as computational linear stability analyses. It thus supersedes the common but questionable approach of augmenting the lower-dimensional Darcy equations with simplified dispersion models of limited validity.To establish this framework, the research focuses on the Hele-Shaw geometry frequently employed in experimental studies of unstable displacements. This geometry is relevant to numerous application areas, from lubrication problems, bearing flows, and oil displacements in fractured rocks, to small-scale MEMS devices. Variable density displacements are addressed with arbitrary angles between the nominal flow direction and the gravity vector, as are chemical reactions. The results from the Stokes investigation are subsequently employed to formulate improved Darcy-based dispersion models capable of capturing the effects of flow-induced dispersion in the Hele-Shaw geometry. In this way, this investigation contributes broadly towards advancing the understanding of the influence of flow-induced dispersion on miscible displacements.Intellectual merit: Two- and three-dimensional, high-resolution Stokes flow simulations combined with computational linear stability analyses provide a powerful set of tools for studying the complex physics of unstable miscible displacements, and in particular how these are affected by flow-induced dispersion. They go significantly beyond the Darcy-based analyses common to date, which have to be augmented by empirical dispersion models. The new framework is employed to establish the limitations of the Hele-Shaw/Darcy analogy, and to generate the Hele-Shaw counterparts of a wide range of Darcy results.Broader impact: The advanced understanding of flow-induced dispersion effects resulting from the proposed work enhances predictive capabilities for transport processes in porous media, and it aids in the design and optimization of a variety of flow processes of importance to the oil and chemical industries. Furthermore, the project will educate and train undergraduate and graduate students in the concepts of large-scale numerical simulations and will benefit from their association with an ongoing IGERT program in Computational Science and Engineering at UCSB.