The Ogata and Banks analytical solution of the convection-diffusion equation for a continuous source of infinite duration and a 1D domain:
C [mol/L] is the concentration,
x [m] is the distance,
R is the retardation factor,
D [m2/day] is the effective dispersion/diffusion,
v [m/day] is the flow velocity,
Ci [mol/L] is the initial concentration in the column, and
Co [mol/L] is the influent (or injected) concentration.
The time-evolution plot below shows two cases of specie production and degradation obtained from the numerical solution of equation (1) with the following parameters:
Production (red line):
Ci = 0 mol/L, Co = 1.2 mol/L, R = 1, D = 0.00048 m2/day, v = 0.24 m/day.
Degradation (green line):
Ci = 1 mol/L, Co = 0 mol/L, R = 1, D = 0.00048 m2/day, v = 0.24 m/day.
The analytical equation above matches (this is not shown in the plot) the production but not the degradation, whose curve is clearly an inversion of the production curve. So, I have been looking for the equivalent analytical expression that describes the degradation process (meaning that Ci would be contained therein). I am thus hoping that there is someone who may know this equation or could point me in the right direction. Thank you in advance.