It is better you treat your fixed bed reactor under the assumption that it acts like a plug flow reactor and try to get the breakthrough curves by pilot plant runs, these curves are your plot of concentration vs.time and it will show the concentration profile within any given process time, then you can use the equation:
L=(tvc0)/p(Wsat-W0)
L=length of bulk bed
t=process time to reach a certain degree of reduction of c0
c0=initial concentration
p=density of bulk bed
Wsat=the concentration of solute on the packed bed at saturation
Wt=concentration of solute on packed bed at time, t