[burges]

The Ogata and Banks analytical solution of the ADE for a continuous source of infinite duration and a 1D domain with initial condition: C(x,0) = C, and BCs: C(0,t) = C, and C(x,t) = 0.

is given as:

C(x,t) = [erfc() + exp()erfc()]

where 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 of production and degradation of species obtained from the numerical solution of the ADE shows that specie production increases with time, whereas degradation (inversion of the production) reduces with time. However, the analytical equation above only matches the production (Ci = 0, Co > 0) but not the degradation (Ci > 0, Co = 0). 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.

[LuckyTran]

Abuse linearity. Define a new dynamic variable equal to K(x,t)=C(x,t)-Ci, re-cast the BC's and IC in terms of this new variable and you can make it work backwards. Basically, just do a substitution. As you've noticed, the solution only works for Ci=0 and Co>0 but not Ci>0 and Co=0. But it still works for Ki=0 and Ko>0 (which also satisfies your desire for Ci>0 and Co=0). =)