This paper describes computer modeling experiments for single adsorbate flow through a packed-bed adsorption reactor to examine the behavior of concentration "wave fronts" for aqueous and solid phases. Conclusions were: (1) The shape of thc wave front assumes a steady-state shape after development: (2) the wave front has constant velocity. (3) the solid-phase wave front is synoptic with the aqueous-phase wave front; (4) the wave-front velocity can be predicted from isotherm data; and (5) the adsorbate-concentration breakthrough curve can be calculated from wave-front data. These conclusions relate directly to design and operation. First, the length of the reactor can be calculated by wave-front velocity, which can be determined from isotherm data. Second, for pilot plant studies the major interest includes wave-front shape, length, and velocity. Third, in operation, the progress of the wave front should be monitored to predict the breakthrough