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

E. Meiburg， University of California-Santa barbara本研究建立了一个分析流动诱导分散影响下不稳定混相驱替的新框架。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。因此，它取代了用有限有效性的简化色散模型增加低维达西方程的常见但有问题的方法。为了建立这个框架，研究重点是在不稳定位移的实验研究中经常使用的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、裂缝岩石中的油位移到小型MEMS设备。变密度位移用标称流向和重力矢量之间的任意角度来处理，化学反应也是如此。Stokes研究的结果随后被用于制定改进的基于darcy的色散模型，该模型能够捕捉Hele-Shaw几何结构中流动诱导色散的影响。通过这种方式，这项研究对促进对流动引起的分散对混相驱替的影响的理解作出了广泛贡献。智力优势：二维和三维、高分辨率的Stokes流动模拟与计算线性稳定性分析相结合，为研究不稳定混相驱的复杂物理特性，特别是流体诱导色散对这些特性的影响，提供了一套强大的工具。它们大大超出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加以增强。新的框架被用来确定Hele-Shaw/Darcy类比的局限性，并产生广泛的Darcy结果的Hele-Shaw对应。更广泛的影响：对流动引起的分散效应的深入了解，提高了多孔介质中输送过程的预测能力，有助于设计和优化对石油和化学工业具有重要意义的各种流动过程。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计算科学与工程领域正在进行的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.