Equilibrium Time for Isotope Separation Plants

One of the most striking aspects of plants for producing heavy water or is the long time they must be operated when first started before it is possible to withdraw enriched material of specified product composition from them. This is because the amount of desired isotope held up in the plant may represent many days or even months of normal production, and at start-up the plant must be run without product withdrawal for a time sufficient to produce the plant s working inventory of desired isotope. The purpose of this section is to derive approximate relations that may be used to estimate the so-called equilibrium, or start-up, time of an isotope 

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 t material at the tails end of the plant reaches the desired steady-state level x. At this time tails withdrawal is started at such a rate R (r) as to keep the composition at this point constant at Xj i. 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 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 Une and the curve for P t)jP. Mathematically, 

Atom Molar fraction flow desired Streom rote component 

---