A boundary element method for the solution of finite mobility ratio immiscible displacement in a Hele-Shaw cell.

In this paper, the interaction between two immiscible fluids with a finite mobility ratio is investigated numerically within a Hele-Shaw cell. Fingering instabilities initiated at the interface between a low-viscosity fluid and a high-viscosity fluid are analysed at varying capillary numbers and mobility ratios using a finite mobility ratio model. The present work is motivated by the possible development of interfacial instabilities that can occur in porous media during the process of C O₂ sequestration but does not pretend to analyse this complex problem. Instead, we present a detailed study of the analogous problem occurring in a Hele-Shaw cell, giving indications of possible plume patterns that can develop during the C O₂ injection. The numerical scheme utilises a boundary element method in which the normal velocity at the interface of the two fluids is directly computed through the evaluation of a hypersingular integral. The boundary integral equation is solved using a Neumann convergent series with cubic B-Spline boundary discretisation, exhibiting sixth-order spatial convergence. The convergent series allows the long-term nonlinear dynamics of growing viscous fingers to be explored accurately and efficiently. Simulations in low-mobility ratio regimes reveal large differences in fingering patterns compared with those predicted by previous high-mobility ratio models. Most significantly, classical finger shielding between competing fingers is inhibited. Secondary fingers can possess significant velocity, allowing greater interaction with primary fingers compared with high-mobility ratio flows. Eventually, this interaction can lead to base thinning and the breaking of fingers into separate bubbles. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]