Page 184 - Adsorption Technology & Design, Elsevier (1998)

170 Design procedures

6.7.4 Bed depth service time (BDST)
As for the empty bed contact time method, the BDST method is also used
extensively by the water industry and can be applied to other industrial
situations. The assumption is that the adsorption rate is proportional to both
the residual adsorbent capacity and the remaining adsorbate concentration.
The relationship between the service time, t, the linear velocity, u, the depth
of adsorbent bed, L, the rate constant, k, the adsorptive capacity, N0 (mass
per unit volume), the influent concentration, co, and the concentration at
breakthrough, Cb is given by the following equation in which dimensionally
consistent units must be used:
No red )]
t- , L-~ln -1 (6.55)
cou kNo ('~b

The critical bed depth is the theoretical depth of adsorbent that is just
sufficient to prevent the effluent concentration from exceeding Cb at zero
time and clearly is equal to the mass transfer zone length MTZL described
above. The critical bed depth may be calculated by substituting t = 0 into
equation (6.55):

MTZL - k~lo In - 1 (6.56)

As shown in Figure 6.10, the adsorptive capacity of the system, No, and the
rate constant, k, can be obtained from the slope and intercept, respectively,
of a plot of t against L, which, according to equation (6.55), should be a
straight line. The raw data for the BDST plot are obtained from a small-scale
or pilot-scale experiment using at least three columns in series, in the
manner shown in Figure 6.7. The total bed depth and flow velocity should
approximate to those values which are anticipated for the full-scale unit.
From the breakthrough curves, the breakthrough points, tb, expressed as
service time, are plotted against bed depth in the form of Figure 6.10.
Service times at different bed depths can be obtained either from the graph
or from equation (6.55). The selection of an acceptable service time with its
corresponding bed depth may be based on judgement, on experience or
following a full economic evaluation which yields the lowest annual cost
taking both capital investment and operating costs into account.
Faust and Aly (1987) describe how the BDST model can be used to
calculate design information for flowrates other than that used to derive the
original BDST plot. The slope, a, of the original plot is defined as follows:

No
slope = a = (6.57)
cou