For scrubbing with activated carbon, air is generally brought through a dry adsorption media, where the contaminant is adsorbed onto the media.
I would like to know what mathematical model is used for this process. I presume the rate of adsorption is proportional to the concentration of the contaminant, and can utilize a plugged flow reactor model - but the carbon has a finite amount of capacity it can adsorb. So, how does this change the equation? After t = 5 days if the first 0.1 mm is completely saturated, how would it take for a 1m long bed to reach breakthrough (i.e. detectable concentrations)? There has been rules of thumb used in industry (such as if the first 2/3 are saturation, change out the media), but I would like to see a more thorough mathematical derivation.
