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

University Of California-Santa Barbara, Santa Barbara CA

Investigators

Abstract

CBET - 0651498 E. Meiburg, University of California-Santa Barbara This 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.