Immiscible thermo-viscous fingering in Hele-Shaw cells

Jackson, S.J.; Power, H.; Giddings, D.

Abstract

We investigate immiscible radial displacement in a Hele-Shaw cell with a temperature dependent viscosity using two coupled high resolution numerical methods. Thermal gradients created in the domain through the injection of a low viscosity fluid at a different temperature to the resident high viscosity fluid can lead to the formation of unstable thermo-viscous fingers, which we explore in the context of immiscible flows. The transient, multi-zone heat transfer is evaluated using a newly developed auxiliary radial basis function-finite collocation (RBF-FC) method, which locally captures variation in flux and field variable over the moving interface, without the need for ghost node extrapolation. The viscosity couples the transient heat transfer to the Darcy pressure/velocity field, which is solved using a boundary element - RBF-FC method, providing an accurate and robust interface tracking scheme for the full thermo-viscous problem.

We explore the thermo-viscous problem space using systematic numerical experiments, revealing that the early stage finger growth is controlled by the pressure gradient induced by the varying temperature and mobility field. In hot injection regimes, negative temperature gradients normal to the interface act to accelerate the interface, promoting finger bifurcation and enhancing the viscous fingering instability. Correspondingly, cold injection regimes stabilise the flow compared to isothermal cases, hindering finger formation. The interfacial mobility distribution controls the late stage bifurcation mode, with non-uniformities induced by the thermal diffusivity creating alternate bifurcation modes. Further numerical experiments reveal the neutral stability of the thermal effects on the fingering evolution, with classical viscous fingering dynamics eventually dominating the evolution. We conclude the paper with a mechanistic summary of the immiscible thermo-viscous fingering regime, providing the first detailed analysis of the thermal problem in immiscible flows.

Citation

Jackson, S., Power, H., & Giddings, D. (2019). Immiscible thermo-viscous fingering in Hele-Shaw cells. Computers and Fluids, 156, 621-641. https://doi.org/10.1016/j.compfluid.2017.04.004

• Journal Article Type: Article
• Acceptance Date: Apr 6, 2017
• Online Publication Date: Apr 7, 2017
• Publication Date: Oct 12, 2019
• Deposit Date: Apr 10, 2017
• Publicly Available Date: Apr 10, 2017
• Journal: Computers & Fluids
• Print ISSN: 0045-7930
• Electronic ISSN: 1879-0747
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 156
• Pages: 621-641
• DOI: https://doi.org/10.1016/j.compfluid.2017.04.004
• Keywords: Thermo-Viscous Fingering; Immiscible; RBF; BEM
• Public URL: https://nottingham-repository.worktribe.com/output/887594
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S004579301730124X
• Additional Information: This article is maintained by: Elsevier; Article Title: Immiscible thermo-viscous fingering in Hele-Shaw cells; Journal Title: Computers & Fluids; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.compfluid.2017.04.004; Content Type: article; Copyright: © 2017 Elsevier Ltd. All rights reserved.
• Contract Date: Apr 10, 2017