  This study outlines a model for injected fluid flow in a vertically confined
porous aquifer with mechanical dispersion. Existing studies have investigated
the behaviour and geometry of immiscible fluid flow in this setting, where the
injected fluid displaces the resident fluid, forming a sharp interface between
the two. The present study extends analytical solutions to include mechanical
dispersion of the interface. The solutions are inverted to solve for time as a
function of position (r,z), giving each position in the aquifer an intersection
time corresponding to the moment the travelling interface intersects a point of
interest. The set of (r0,z0) positions which share an intersection time are
treated as dummy variables that represent an 'effective surface' and are
integrated over to solve for the velocity field within the aquifer. Using this
velocity field, the concentration profile resulting from mechanical dispersion
can be found analytically.It is shown that the concentration of the injected
fluid smoothly decays around the position of the interface from immiscible
solutions, allowing for the injected fluid to be present in detectable
quantities beyond the extent of these interfaces. This concentration spread
should be considered in defining outer boundaries on fluids in injection well
applications such as carbon capture and storage or groundwater applications.
