The injection of supercritical CO2 through wells into deep brine reservoirs is a topic of interest for geologic carbon sequestration. The injected CO2 is predominantly immiscible with the brine and its low density relative to brine leads to strong buoyancy effects. The displacement of brine by CO2 in general is a multidimensional, complex nonlinear problem that requires numerical methods to solve. The approximations of vertical equilibrium and complete gravity segregation (sharp interface) have been introduced to reduce the complexity and dimensionality of the problem. Furthermore, for the radial displacement process considered here, the problem can be formulated in terms of a similarity variable that reduces spatial and temporal dependencies to a single variable. However, the resulting ordinary differential equation is still nonlinear and exact solutions are not available. The existing analytical solutions are approximations limited to certain parameter ranges that become inaccurate over a large portion of the parameter space. Here, I use a matched boundary extrapolation method to provide much greater accuracy for analytical/semi-analytical approximations over the full parameter range.