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

CBET - 0651498 E. Meiburg，University of California-Santa Barbara本研究建立了一个新的框架来分析流动诱导弥散影响下的不稳定混相驱。这个框架，三维斯托克斯方程的基础上，采用非线性模拟以及计算线性稳定性分析。因此，它取代了常见的，但有问题的方法，增加低维达西方程与简化的色散模型的有限validity.To建立这个框架，研究的重点是Hele-Shaw几何经常采用的不稳定位移的实验研究。这种几何形状与许多应用领域有关，从润滑问题，轴承流动和断裂岩石中的油位移到小规模MEMS器件。变密度位移与标称流动方向和重力矢量之间的任意角度进行处理，如化学反应。斯托克斯调查的结果，随后制定改进的达西为基础的色散模型能够捕捉到的影响，在Hele-Shaw几何形状的流动诱导的色散。通过这种方式，这项调查有助于广泛推进流动诱导的分散对混相displacement.Intellectual优点的影响的理解：二维和三维，高分辨率斯托克斯流模拟与计算线性稳定性分析相结合，提供了一个强大的工具，用于研究不稳定混相位移的复杂物理，特别是这些是如何受到流动诱导的分散。他们远远超出了达西为基础的分析常见的日期，这必须由经验色散模型增强。新的框架被用来建立Hele-Shaw/Darcy类比的局限性，并产生了广泛的Darcy结果的Hele-Shaw对应物。从所提出的工作中对流动引起的弥散效应的深入理解增强了多孔介质中输运过程的预测能力，并且它有助于对石油和化学工业重要的各种流动过程的设计和优化。此外，该项目将教育和培训大规模数值模拟概念的本科生和研究生，并将受益于他们与UCSB正在进行的IGERT计算科学与工程项目的联系。

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.