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Analysis of Electrolysis
In this analysis of electrolysis, the somewhat optimistic assumption will be made that a separation factor of 7 can be obtained at a cell voltage of 2.1. At 95 percent current efficiency, the power consumption per gram-mole of water electrolyzed is then
|
Table 13.13 Separation factors in electrolytic heavy-water plants
*w/o, weight percent. * Predicted. |
of hydrogen produced.
Let us first consider the production of heavy water in a simple cascade of electrolytic cells, without recycle, as in Fig. 13.13. Such a cascade, used at Ems and Nangal, preconcentrates deuterium prior to final concentration by distillation of hydrogen. With a sufficient number of stages, such a cascade could be used to produce pure heavy water in low yield from natural water.
If the heads separation factor (3 is constant throughout such a simple cascade, the fraction of deuterium that may be recovered depends on the number of stages n and the overall enrichment ш in accordance with
/а-ы^Л"
r" V «“I /
as has been shown in Eq. (12.50).
As an example of the recovery of deuterium obtainable in a simple electrolytic cascade without recycle, production of heavy water containing 99.693 a/о deuterium from natural water containing 0.0149 a/о will be considered. The overall enrichment w is
A high, but attainable, overall separation factor of a = 7 will be used. A heads separation factor such as the one that would be used in an ideal recycle cascade of (3 = s/a = fl = 2.646 will be assumed. Then the number of stages n is given by
The recovery of deuterium, from Eq. (13.51), is
Г7 —(2,176,168)ms] 15
r = |——— —-—I = 0.00816 (13.54)
The reason for this low recovery, of course, is that most of the deuterium is carried off by the hydrogen produced during electrolysis, and only a small fraction is left in the residual water.
The maximum amount of heavy water that could be produced in this way as the by-product of 10,000 g-mol of hydrogen would be
(10,000X0.000149X0.00816) = 0.0122 g-mol (13.55)
or 0.244 g. The electric power consumption is 1180 kWh, or 4836 kWh/g D20. Because electric power costs of the order of $0.02/kWh, this corresponds to $100/g D20. It is evident that a profitable use must be made of the hydrogen, because the value of the heavy water is only a small fraction of the cost of power.
The recovery of deuterium can be increased substantially by burning deuterium-rich hydrogen from the upper stages of the plant and recycling the water to the electrolytic cells, as in Fig. 13.14. Figure 13.15 shows a generalized flow sheet for such a plant, with hydrogen from the lower stages being used as the principal plant product and with hydrogen from the upper stages being burned and recycled to increase recovery of heavy-water by-product. The principal variables in such a flow sheet are [46] 2
The increase in deuterium content per stage is measured by the heads enrichment factor /3, defined in terms of the atom fraction deuterium in the heads water leaving this stage xm and the atom fraction deuterium in the water leaving the next lower stage xm _ j, as
*m0 xm-1) xm — i(l xm)
In stages m — 1 and higher, the optimum enrichment per stage is that of an ideal cascade, in which
xm -1 — Ут+1 (13.57)
and P = >/a (13.58)
We shall use condition (13.58) to set the enrichment per stage in the lower stages in which hydrogen is not recycled, also. The total number of stages n is then given by Eq. (13.53).
As a specific example, we may consider a plant designed to produce 10,000 g-mol of hydrogen per minute, while recovering as a by-product as much heavy water as can be economically justified. The atom fraction D in feed water x0 will be taken as the natural value of 0.000149, and the atom fraction D in the heavy-water product xp will be taken as 0.99693 (to make the number of stages exactly 15.00). The deuterium content of hydrogen and water leaving the lower stages of this cascade is given in Table 13.14.
It evidently would not pay to bum and recycle hydrogen from stages 1 and 2, because it is no richer in deuterium than feed. To determine at which stage it would pay to begin to bum and recycle hydrogen, a number of alternative flow sheets have been worked out, with the most significant results summarized in the last four columns of Table 13.14. In the first case listed, hydrogen is burned and recycled on stage 3 and all higher stages, in the second case on stage 4 and higher, etc. In each case, the unbumed hydrogen production rate has been held constant at 10,000 mol. For each case there has been evaluated:
1. The deuterium recovery, from (13.51)
2. The moles of heavy water produced, P
3. The moles of hydrogen burned and recycled, H, the total tails flow of the recycle portion of the cascade, from (12.119)
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Table 13.14 Electrolytic plants for production of 10,000 mol of hydrogen, with heavy water as by-product (a = 7,P = y/Y, 15 stages)
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To determine which of these cases is best economically, it is necessary to set a value on the hydrogen that is burned and therefore lost. A representative value for hydrogen produced commercially by reforming naphtha is $1.50/1000 ft3; an electrolytic plant would probably not be built unless it could sell hydrogen for this figure. Because 0.5 mol of oxygen is consumed per mole of hydrogen burned, it is necessary to set a value on this, too. A value of $20/short ton, or $0.80/1000 ft3, will be used. The value of hydrogen and oxygen consumed is therefore $1.90/1000 ft3 or $1.59/kg-mol of hydrogen burned.
The next-to-the-last column of Table 13.14 gives AH/AP, the ratio of the additional hydrogen that must be made to the additional heavy water produced when hydrogen from an additional stage is burned and recycled. The last column gives the value of the additional hydrogen and the associated oxygen required to produce 1 kg of additional D20. This is obtained as ($1.59/2Q)(AH/AP). Because of the high value of $ 196/kg of incremental D20 made by burning hydrogen from stage 4, it is evident that it would not be economical to bum hydrogen from this stage. The incremental value of $74/kg for hydrogen from stage 5 is under the cost of heavy water in competing processes. Burning hydrogen from stage 5 to increase heavy-water production therefore might be justified.
The average cost of hydrogen and oxygen from stage 5 and higher burned to make heavy water in the most favorable case is
Although the need for efficient condensers and the complications of connecting electrolytic cells in series cascade would add something to the cost, it is evident that electrolysis provides a way of making small amounts of heavy water at a very low cost as a by-product of hydrogen and oxygen.
Figure 13.16 is a flow sheet for a plant for the case in which hydrogen from stage 5 and higher is burned and recycled. The fraction of deuterium in the feed that is recovered is only 0.238. This low recovery is characteristic of the electrolytic process when used as the sole means of concentrating deuterium. As a result, the amount of heavy water that could be produced by electrolysis alone, even at a large electrolytic plant, is small.
Although the recovery of heavy water is better than in the simple cascade without recycle,
|
% D |
0.0149 |
0.0394 |
0.1042 |
0.2752 |
0.725 |
1.89 |
4.86 99.19 |
99.693 |
|
Moles water |
10,000 |
2,745 |
753.0 |
206.93 |
78.53 |
30.18 |
11.70 0.492 |
0.3553 |
|
D20 |
1.49 |
1.082 |
0.78 5 |
0. 569 |
0569 |
0.570 |
0.569 0.488 |
0.3542 |
Figure 13.16 Optimum electrolytic cascade for production of 10,000 mol hydrogen and heavy — water by-product, a = 7; (3 = /T.
In Fig. 13.15, stages 1 to m-2 constitute a simple cascade, without recycle, and the remaining stages, from m — 1 to n, constitute an ideal, recycle cascade. We shall show how flow quantities may be derived for this flow sheet.
The deuterium content of water heads leaving stage m is
IF’xf + 1 — xF
The deuterium content of hydrogen tails from the same stage is
Compositions in Fig. 13.16 were obtained in this way.
The total amount of hydrogen formed from stages m to n is given by (12.119), for the total tails flow in the enriching section of an ideal cascade, with xm. x replacing zF. In the plant shown in Fig. 13.16, the total number of moles formed is
0,3553 99%y/T + 1) —VT [7 0.997 / 0.993 N yJT-) In VT [Уо.00725/ Vo.00313/
Hydrogen from stage m — 1 constitutes tails from the ideal cascade section, whose quantity relative to product is given by
Р{хр~хт_г)
xm — 2 Ут-І
In the plant shown in Fig. 13.16, the tails quantity is
The feed rate to stage 4 is W + P= 206.93.
In Fig. 13.15, the first m— 2 stages constitute a simple cascade, operated without recycle, with constant heads separation factor p. The recovery of deuterium from a simple cascade of m—2 stages operated at constant P is
(13.66)
from Eq. (12.48).
In the flow sheet of Fig. 13.16, the recovery of deuterium from the three stages of the simple cascade is
(13.67)
The number of moles of natural water fed to stage 1 required to get 206.93 mol of water
containing 0.2752 percent deuterium from stage 3 is then
„ (206.93X0.002752) _____
(0.38220X0.000149) ~ 10,000
6.2 Electrolytic Separation of Other Elements
Separation factors in electrolysis for other elements are much lower than for hydrogen. A few values that have been reported are listed in Table 13.15. These values are so low, and the cost of electric energy per unit electrolyzed is so high, that electrolysis is uneconomical for separating isotopes of any element other than hydrogen. Some concentration of 18 О takes place in an electrolytic deuterium plant.