FIGURE 8.9 Active zones at various times during adsorption and the breakthrough curve.

It is to be noted that by the nature of the process, the concentration at the bottom of the active zone as it moves through the column has to be at the limiting residual concentration. Thus, as long as ¿has not reached the bottom of the column, the effluent is the limiting residual concentration that a particular batch of carbon is capable of removing.

Figure 8.9b shows the movement of the active zone represented by the length S as it advances through the bed at various times. At the beginning of breakthrough, at which the lower end of S barely touches the bottom of the column, the total volume of treated water is represented by Vb. The shaded portion in the curve represents the total breakthrough mass of adsorbate before exhaustion. The total volume of wastewater treated at exhaustion is designated by V.

Determination of the length of the active zone. The length of the active zone represents a portion of bed that is no longer totally usable, since this is the particular length when breakthrough occurs. It is therefore important that this length be allowed for in design. To determine this length, perform a mass balance on the active zone during breakthrough. The total mass of pollutant that escaped removal from the beginning to the completion of breakthrough is

where the indices n and n + 1 refer to the volume or concentration that broke through S at a time step of At from tn to tn+1. Also, at the completion of breakthrough, the total mass of pollutant introduced into the influent of 8 is (Vx - Vb)[Co]. Thus, the mass of pollutants retained in the active zone Mr is

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