Viscous Fingering of Reversible Reactive Flows in Porous Media
The dynamics of viscous fingering instability of miscible displacements in a homogeneous porous medium are examined in the case of flows that involve reversible chemical reactions between the displacing and displaced fluid. The flows are modeled using the continuity equation, Darcy’s law, and volume-averaged forms of the convection-diffusion-reaction equation for mass balance of a bi-molecular reaction. Numerical simulations were carried out using a Hartley transform based pseudo-spectral method combined with semi-implicit finite-difference time-stepping algorithm. The results of the simulations allowed to analyze the mechanisms of fingering instability that result from the dependence of the fluids viscosities on the concentrations of the different species, and focused on different flow scenarios. In particular, the study examined the effects of varying important parameters namely the Damkohler number that represents the ratio of the hydrodynamic and chemical characteristic time scales, and the chemical reversibility coefficient, and analyzed the resulting changes in the finger structures. The results are presented for flows with an initially stable as well as initially unstable front between the two reactants.
KeywordsFluid mechanics Homogeneous porous media Hydrodynamics Miscible displacements Reversible chemical reaction Stability Viscous fingering
H. Alhumade acknowledges financial support from the Ministry of higher education in Saudi Arabia. The authors would like also to acknowledge WestGrid for providing computational resources.
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