Page 117 - Analysis, Synthesis and Design of Chemical Processes, Third Edition

From Figure 3.3, it can be seen that the limiting case for overlapping occurs when the step taking the
longest time (here, the tray drying step in TD-301, which takes 4 h to complete) repeats itself without a
waiting time between batches. The time to complete n batches using this limiting overlapping scheme is
given by

(3.2)

where T is the minimum total (overlapping) time, and [max (t )] is the maximum individual time step for
i
O
the batch process. The subscript O denoting overlapping will be dropped, and T will be used as the total
processing time from this point on. For the example, T = (8–1)(4.0) + (14.5) = 42.5 h.

Comparing Figures 3.1 and 3.3, the use of overlapping sequencing reduces the processing time
significantly (from 116 to 42.5 h) and makes much better use of the equipment; specifically, the equipment
is operated for a higher fraction of time in the overlapping scheme compared with the nonoverlapping
scheme.

In batch operations, the concept of cycle time is used to refer to the average time required to cycle
through all necessary steps to produce a batch. The formal definition is found by dividing the total time to
produce a number of batches by the number of batches. Thus, from Equations (3.1) and (3.2),

(3.3)

(3.4)