Three fixed-bed adsorbers containing 10,000 lb of granules of activated carbon (b = 30 lb/ft3) each are to be used

Three fixed-bed adsorbers containing 10,000 lb of granules of activated carbon (ρb = 30 lb/ft3) each are to be used to treat 250gpm of water containing 4.6 mg/L of 1, 2-dichloroethane (D) to reduce the concentration to less than 0.001 mg/L. Each carbon bed has a height equal to twice the diameter. Two beds are to be placed in series so that when Bed 1 (the lead bed) becomes saturated with D at the feed concentration, that bed is removed. Bed 2 (the trailing bed), which is partially saturated at this point, depending upon the width of the MTZ, becomes the lead bed, and previously idle Bed 3 takes the place of Bed 2. While Bed 1 is off-line, its spent carbon is removed and replaced with fresh carbon. The spent carbon is incinerated. The equilibrium adsorption isotherm for D is given by q = 8c0.57, where q is in mg/g and c is in mg/L. Once the cycle is established, how often must the carbon in a bed be replaced? What is the maximum width of the MTZ that will allow saturated loading of the lead bed?