Author(s)

S. Jackson, D. Stevens, H. Power, D. Giddings

Abstract

In this work, the interaction between two immiscible fluids with a finite mobility is investigated numerically in a Hele-Shaw cell, simulating conditions found during the injection and lateral spreading of supercritical CO2 in a deep subsurface aquifer. A two-phase numerical method is presented that uses a direct boundary element approach to compute the normal velocity at the interface between two fluids in a 2-D Hele-Shaw cell, through the evaluation of a hypersingular integral. The resulting second kind Fredholm equation is solved numerically using a truncated convergent Neumann series. Utilising cubic B-Spline surface geometry and function interpolation, the numerical scheme exhibits 6th order spatial convergence and a computational cost that scales with O(N2). This allows the long term non-linear dynamics of a growing CO2–brine interface to be explored accurately and efficiently, revealing large differences with previous single-phase models and interface capturing techniques.

Keywords

boundary element method, viscous fingering, finite mobility ratio, Hele-Shaw flow, hypersingular integral, interface tracking