Figure 12.23 shows the nomenclature to be used in describing the operation of an isotope separation plant during the transient period in which it is approaching steady-state performance. Figure 12.24 represents qualitatively the way tails and product flow rates and compositions will change with time during this transient period. Compositions are represented by a scale linear in In [x/(l -*)].

At time zero, all stages of the plant contain material of feed composition, zP. Initially the plant is operated with no feed supply and no tails or product withdrawal. As the plant operates, the fraction of desired isotope in material at the tails end of the plant decreases and the fraction of desired isotope in material at the product end increases. At time tx material at the tails end of the plant reaches the desired steady-state level xw. At this time tails withdrawal is started at such a rate W(t) as to keep the composition at this point constant at xw. Feed is supplied at a rate equal to tails withdrawal. At first, tails withdrawal is at a rate below the steady-state value W because the compositions elsewhere in the stripping section have not yet reached steady-state values. The tails rate increases and may temporarily exceed the steady-state value for a time, until product withdrawal can be started.

The fraction of desired isotope in material at the product end of the plant continues to increase, reaching the steady-state value yP at time t2. Product withdrawal is then started at such a rate P(t) as to keep product composition constant at yP. Feed is supplied at the rate P(t) + Wt). At first, product withdrawal is at a rate below the steady-state value P because the compositions elsewhere in the enriching section have not yet reached steady-state values. As time goes on, P(f) approaches P asymptotically.

The equilibrium, or start-up, time for product withdrawal tP is defined as the number of days of equivalent production lost during the approach to steady state. In Fig. 12.24, the area of the rectangle between the vertical line at tP and the horizontal line at unity equals the area between this horizontal line and the curve for P(t)/P. Mathematically,

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