18.08.2015   NUCLEAR CHEMICAL ENGINEERING

Total Flow Rates

The total interstage flow rate of heads or tails is a measure of the size of the separation plant. In a distillation plant, for example, the total volume of column internals is proportional to the total interplate vapor flow rate. In a gaseous diffusion plant, the total amount of power expended in pumping gas from one stage to the next is proportional to the total heads flow rate.

An expression for the total flow rate of heads or tails in stripping or enriching section may be derived by summing the appropriate Eq. (12.106) or (12.107). For example, the total heads flow rate in the stripping section J$ is

^ "S nS

/s — 2 Mi = J=г £ 05′-1)+(!-**) 2 O-rt

Я, jfS-1

,P*—*

/=i

ns in this equation may be eliminated by (1254), with the result

, W L. „..^Mi-^Wi-^f)] fcF-xwXl ~2zf) /s = s—ГІ t1 -*y(P+1)]———————————————

(?F-*w)P* -(P1 + 1M)

*rO-*fX0-i) і

The total tails flow rate in the enriching section is obtained from (12.106):

„ V „ p I>K0 + 1) —/3) In [ур(1-гр)1гр{1 — yp)}

Ke= l NUl Щ—————————

i=ns ‘

(yr-zp) №2-(fi2 + lУ*р]}

2fQ~zf) 0-1 (

and the total heads flow rate in the enriching section is

Zf(l ~xw) XH’Cl -*f)

(12.121)

Terms in yp—zp and zp—хщ have canceled out because of the material-balance relations (12.52) and (12.53). Also, because of these material-balance relations, (12.121) may be written

output

input

(12.122)

This result is of great importance for isotope separation plants. It states that the total flow in the plant is the product of two factors, the first a function only of the heads separation factor 0, and the second a function only of the flow rates and composition of feed, product, and tails.

The first factor is a measure of the relative ease or difficulty of the separation; it is large when 0 is close to unity and small when /3 differs markedly from unity. The second factor is a measure of the magnitude of the job of separation; it is proportional to the throughput, and is large when product and tails differ substantially in composition from feed, and small when these compositions are nearly equal. The second factor has been termed the separative capacity, because it is a measure of the rate at which a cascade performs separation. It equals the sum of two output terms, each the product of an output flow rate and a function of the corresponding output condition, minus an input term that is the product of the feed rate and a function of the input condition. The separative capacity is discussed in more detail in Sec. 10.

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