Although water distillation is no longer used for primary concentration of deuterium because of its high energy consumption, the principal features of water distillation plants for this purpose will be described briefly because they illustrate isotope separation principles so well.

Process requirements. Distillation of water for deuterium separation differs from all other industrial distillation processes in the extremely small difference in normal boiling point between the key components, 0.7°C between H2 О and HDO. This, coupled with the very low natural abundance of deuterium, leads to an extraordinarily high reboil vapor ratio, so that the heat consumption per unit of D20 product is enormous.

In fa<l — Хр)ІХр( 1 — Xp)] In o*

A rough idea of the requirements of the water distillation process may be derived from a representative separation factor of 1.05. The minimum number of theoretical plates (итіп) needed to enrich deuterium from the natural concentration of xp = 0.000149 atom fraction to product concentration of Xp = 0.998 is

The optimum number will be somewhat more than twice this, or around 700 plates.

The minimum consumption of steam per mole of heavy water produced is secured when an infinite number of plates is used, so that the outgoing steam depleted in deuterium may be in equilibrium with incoming feed.

From Eq. (12.80), the minimum molar ratio of steam flow rate G to product P is

For a practical plant, with a finite number of stages, around 200,000 mol of steam must be provided per mole of heavy water produced. Because of the small difference in boiling point between the two products, this large amount of heat flows through a relatively small temperature difference; in fact, the principal temperature differences are due to pressure drop across the column and temperature difference across reboiler and condenser heat exchange surface, rather than differences between the boiling points of the components. Economical operation requires that the large heat demand be supplied as nearly reversibly as possible, with the minimum practicable loss in availability. Reboil heat should be supplied with good thermodynamic efficiency, and column pressure drop should be minimized.

History of process. Despite these severe requirements, the water distillation process has been of interest because of its simple, conventional equipment. For primary concentration of deuterium from natural water, it received attention in Germany, where pilot-plant work was done by I. G. Farben during World War II [C3], and in the United States [M8], where most of the heavy water used by the Manhattan District was produced in this way.

Manhattan District plants. The water distillation plants of the Manhattan District were built to provide a simple and certain way of producing heavy water, although not necessarily at minimum cost. Because speed was more important than economy, it was not possible to explore fully developments that might have permitted more economical production. These plants are described briefly in this section; more detailed information has been given by Maloney and Ray [M8] and by Selak and Finke [S3].

Plants. Three water distillation plants were designed and built for the Manhattan District by

E. I. du Pont de Nemours and Company, Inc. These plants were located at Morgantown, West Virginia, Childersburg, Alabama, and Dana, Indiana. Parts of the plants were started up in June 1943, and concentrations reached steady-state values in June 1944. About 90 days were needed to reach steady state. The plants were shut down in October 1945 because of reduced demand and because of the high cost of their heavy water.

These distillation plants concentrated deuterium from 0.0143 a/о (atom percent) to 87 to 91 a/о. Further concentration to 99.8 percent was effected by electrolysis. The average recovery of D20 from the steam fed was only 1.94 percent; 360,000 mol of steam were, fed per mole of DjO produced.

The combined capacity of the three plants was 1.15 MT/month. The total production of

99.8 percent D2 was 20.7 MT.

The total cost of the plants was $14.5 million. The unit investment cost was therefore

$14,500,000

(1.15X12X1000)

The operating costs were as follows: Per month Per kg D2 0 Steam $295,000 $271 Other 127,000 117 Total $422,000 $388

Process. A simplified flow sheet of the process used at the Morgantown plant, the smallest and most efficient of the three, is shown in Fig. 13.3. This plant produced 254kg D20/month, with a deuterium recovery of 2.8 percent. The plant consists of an eight-stage cascade of distillation towers, with associated reboilers, condensers, and pumps. Summary data on the towers of each stage are given in Table 13.9.

The first stage consists of five parallel groups of two series-connected towers, of which one group, 1A and IB, are shown in Fig. 13.3. Feed for each 1A tower consists of condensate from the reboiler of the associated IB tower. Feed is introduced at the top of the 1A tower. Stripped vapor from the top plate is condensed in a barometric condenser, vented to a steam ejector that maintains a pressure of from 50 to 90 Torr at the top of the tower.

Slightly enriched water from the bottom of tower 1A is pumped to the top of tower IB, and vapor from the top of IB flows back to the bottom of 1A.

Most of the water at the bottom of IB, now enriched to 0.117 a/о deuterium, is converted to vapor in the reboiler and returned to IB, but around 12 percent is pumped ahead to the top of 2A. Vapor from the top of 2A is condensed in a condenser refrigerated with ammonia, to prevent loss of the now valuable water. This condenser is also vented to a steam ejector, which maintains a pressure of 130 Ton.

The second stage consists of two towers, 2A and 2B, connected in series, like each 1A and IB pair. The third and higher stages consist of single towers, of progressively decreasing diameter. Arrangements for reboiling water at the bottom of each tower and condensing and returning vapor at the top of the next stage are the same as at the bottom of 2B and the top of 3. The progressive decrease in tower diameter from the feed point to the product end is characteristic of an isotope separation plant.

As the water flows through the stages of the plant, it is enriched progressively in deuterium, until it reaches 89 a/о in the bottom product of the eighth and last stage.

Most of the steam for the plants at Morgantown and elsewhere was generated at 165 psia’’’ and throttled to 55 psia, the pressure at which it was used in the reboilers, even though steam at 22 psia would have sufficed to reboil the tower bottoms, where were at subatmospheric pressure. Because low-pressure, by-product steam was not available in the required amounts, it was necessary to generate steam solely for the water distillation plant. This was inefficient and added to the operating cost in these plants.

Towers. ToweTS of these plants over 18 in in diameter were of the plate type, with plates on 1-ft spaces. All the large towers used bubble caps, except 1A, which had tunnel caps. Towers 18 in in diameter and smaller were packed with |- by |-in ceramic rings.

Possible improvements. The designers of the Manhattan District plants recognized that two major improvements could be made in a future water distillation plant designed for economy rather than speed of construction. These were as follows:

1. More efficient utilization of heat than generating 150-psig steam solely for the distillation plant

2. The use of tower internals with greater capacity per unit volume than tunnel — or bubble-cap plates, to increase plant capacity for the same capital investment

More efficient utilization of heat. In the first-stage towers of the Manhattan District plants, where most of the heat was consumed, heat flowed from the tower bottom temperature of

^1 psia (pound force per square inch absolute) = 51.7 Torr = 0.06895 bar = 6895 Pa.

Waste condensate 0.0143% D 11,670 kg/h Figure 13.3 Morgantown water distillation plant.

Table 13.9 Towers of Morgantown water distillation plant Tower Number in parallel Diameter[44] No. of plates kg vapor/h Pressure, Torr a/o deuterium, bottom Top Bottom 1A 5 15 ft 80 (80,400) 67 238 IB 5 12 ft 90 80,400 238 536 0.117 2A 1 10.5 ft 72 (9,620) 129 340 2B 1 8 ft 83 9,620 340 645 1.04 3 1 3.3 ft 72 1,380 124 343 3.8 4 1 1.5 ft 72* 330 127 440 10.0 5 1 10 in 72t 85 127 340 11.5 6 1 10 in 72* 85 124 328 21.2 7 1 10 in 72* 90 124 333 56.4 8 1 10 in 72* 90 127 308 89 Total 18 757 92,070 tl ft= 12 in = 30.48 cm. * Number of theoretical plates in packed column.

195°F (10.5 psia)* to the tower top temperature of 111°F (1.3 psia). To transfer this heat through the reboilers, steam at 233°F (22 psia) was required. Because this heat is needed only at relatively low temperatures, it is very inefficient to obtain it by burning fuel under boilers, without making use of the heat at higher temperatures first. Two possible ways of providing low-temperature heat more efficiently are these:

1. Using 22-psia exhaust steam from the turbines of a power plant.

2. Using a vapor-recompression system

Examples of these two schemes are shown in Figs. 13.4 and 13.5. The turbine-exhaust scheme of Fig. 13.4 has two advantages over the vapor-recompression scheme of Fig. 13.5.

1. The cost of the condenser and steam jet ejector is less than that of the vapor compressor and feed-water preheater.

2. The power lost in the steam turbine plant is less than the power consumed by the vapor compressor. Although the theoretical power W lost by the turbine exhausting at 22 psia instead of at 1.3 psia is exactly the same as the power consumed by a compressor taking the same amount of steam from 1.3 to 22 psia, the actual turbine efficiency of E drops the turbine power lost to WE and the compressor efficiency of E? raises the power consumed by the compressor to W/E1.

The turbine exhaust scheme has the disadvantage of making the production rate of heavy water dependent on the production rate of power from the steam turbines.

Packed towers. After these plants were built, several improved types of tower internals were developed that have higher capacity per unit volume and lower pressure drop per theoretical

Figure 13.4 Water distillation tower reboiled by steam turbine exhaust.

plate than bubble-cap plates and are claimed to be more economical. The British Atomic Energy Research Establishment has developed a tower packing known as Spraypak [M4] for use especially in the water distillation process.

Distillation-cascade design principles. Some of the principles involved in designing an isotope separation plant for minimum cost will be illustrated by roughing out optimum conditions for a water distillation plant incorporating the two improvements noted above.

Design variables. The principal design variables in a water distillation plant are

1. The type of tower internals

2. The pressure p, Ton

3. The vapor velocity v, cm/s

4. The ratio of reboil vapor to product, G/P

Figure 13.S Water distillation tower reboiled by vapor recompression.

The best inemals and the optimum values of pressure, vapor velocity, and reboil vapor ratio are those that permit production of heavy water at minimum cost. The initial cost of the plant depends on a number of factors including the total number of towers, the total amount of reboiler and condenser surface, and the total volume of tower internals. The principal operating cost is for power, which is proportional to total loss in availability of steam as it flows through the towers. A complete minimum-cost analysis requires knowledge of the unit cost of all the important cost components and is beyond the scope of this book. Design for minimum volume of tower internals or minimum loss in availability due to tower pressure drop and for minimum cost of these two important contributors to total cost can be carried out without complete unit-cost data and will be discussed. Because the same choice of reboil vapor ratio minimizes the number of towers, their volume, and the loss of availability within them, this reboil vapor ratio is close to that which leads to minimum production cost. An equation for this optimum reboil vapor ratio will now be derived, and expressions will be developed for the total volume of towers and the total loss in availability in towers designed for the optimum ratio.

Enrichment equation. The differential equation for the increase in deuterium content x with distance z from the top of the tower is

А^=(а*-1М1-*)-^,-х) (13.12)

This equation is derived in a manner similar to (12.128); h is the height of a transfer unit, h dxjdz replaces dx/di, and G, the molar flow rate of steam, plays the role of the tails flow rate N.

Tower volume. At a point in the tower where the vapor velocity is v and the absolute pressure is p, the area A needed to accommodate a steam flow rate of G mol/s is

A=— (13.13)

where R is the gas constant and T the absolute temperature. The volume of tower dV needed to increase the deuterium content of the liquid by an amount dx is

dV A____________________ hRT/pv_____________

dx ~ dxjdz ~ [(a* — 1 )x(l — x)/G] — (P/G2XxP — x)

The steam flow rate that leads to minimum tower volume is that which makes this expression a minimum at every x, or

_ Щхр-х)
bopt (a*-iyx(i-x)

This is the tails flow rate for an ideal cascade. The details are the same as in deriving (12.132). At this optimum steam rate,

/dV = AhRT Pjxp-x)

V&/min pv(a* — 1)J X2(l — x)2

pv(a* — l)2

pv(a* — 1)’

In a tower in which h, T, p, v, and a* are held constant,

where Dpp, the separative capacity for the enriching section of an ideal cascade per unit

product rate, is given by

The factor 4hRT/pv(a* — l)2] gives the tower volume required for a plant performing 1 mol of separative work per second; it is a measure of the relative volume needed for different types of packing as a function of vapor velocity and pressure. When the design objective is to minimize tower volume, the type of packing and the velocity and pressure that minimize this factor should be selected.

Rate of loss of availability. In the scheme of Fig. 13.4 for reboiling a tower with low-pressure exhaust steam from a turbine, factors that reduce the power output of the turbine are (l)the temperature difference across the reboiler, which causes the turbine exhaust pressure to be higher than the tower bottom pressure, and (2) the steam pressure drop through the tower, which causes the tower bottom pressure to be higher than the tower top. We shall focus attention on the second of these inefficiencies and shall derive an expression for the reduction in turbine power caused by steam pressure drop through the tower.

If this were the only thermodynamic inefficiency, the loss in turbine power would equal the rate of loss of availability in the tower Q, given by

Q=T0 f (13.18)

where dS/dt is the rate of production of entropy in the tower and T0 is the temperature at which heat is rejected to cooling water. When liquid and vapor have the same temperature and when liquid-phase pressure changes are neglected, the rate of entropy production is simply that due to steam-pressure changes,

(13.19)

where Z is the height of the tower, and s is the entropy per mole of steam. If steam is treated as a perfect gas,

(13.20)

so that

The rate of availability loss per unit height is the integrand

dQ RTqG dp dz p dz

and the rate of availability loss per unit increase in deuterium content is

dQ dQ/dz_____________ (hRT0lp)(dp/dz)________

dx ~ dx/dz ~ [(a* — 1 )x(I — x)!G] -(P/G2 YxP-x)

The optimum steam rate, which makes this a minimum, is again given by (13.14), so that

(dQ 4hRT0 dp P(xp-x)

dx )min ~ (a* _ і fp dz xi(i-xf

4hRT0 dp (a*-l fp dzPDp’F

In a tower in which A, p, and a* are held constant, the minimum rate of loss of availability is obtained in the same way as the minimum volume (13.16) and is

The factor

4hRT0 dp («*-1 fp dz

gives the loss of turbine power in a plant performing 1 mol of separative work per second; it is a measure of the relative power consumption with different types of packing as a function of vapor velocity and pressure.

Costs for tower volume and power. The contribution of tower volume and availability loss to the cost of heavy water produced by the distillation of water in an ideal cascade may be evaluated when values are assigned to

/, the fractional charge against investment per year су, the unit cost of tower volume

cq, the unit cost of turbine work lost owing to tower pressure drop

. 4hRT ]c у————- 7 pita*-1)2

4hRT0 dp (a* — 1 Ур dz

The annual charge A for tower volume and power, then, is

where the numerical factor is the number of seconds per year. The contribution of tower volume and power to the unit cost of heavy water, in dollars per mole, is obtained by dividing the annual cost by the number of moles of heavy water produced per year, 3.15 X 107Acp:

jcv[4hRT/pv(a* — l)2] 4hRT0 dp) D^p_

3.15 X 107 CQ(a*-l fpdzxP

DPF may be obtained from (13.17). With xp = 0.000149 and xP = 0.998,

Dp, F

xp

Packing characteristics. We have shown that the optimum steam rate that leads to minimum tower volume and minimum power is that of the ideal cascade (13.14). The optimum type of packing, optimum pressure, and optimum vapor velocity is that which makes the expression in braces (1327) a minimum. We shall not attempt to evaluate a number of types of packing, but shall use Spraypak no. 37 packing as an example of the selection of optimum vapor velocity and pressure. This is the type of packing recommended by McWilliams and co-workers [M4] for a water distillation plant.

Figure 13.6 is a plot of the height of a transfer unit in feet, A, and the pressure drop per unit transfer unit in ton, A dp/dz, versus percent of flooding velocity, obtained from the data of McWilliams and co-workers [M4]. These data are for the system Нг O-HDO at total reflux and pressures of 420, 760, or 1245 Torr. Flooding velocities Vf reported by McWilliams et al. at

Figure 13.6 Characteristics of Spraypak no. 37 for H20-l DO, total reflux.

these three pressures are given in Table 13.10. For pressures below 420 Torr it will be assumed that the product v}p is constant at its value of 128.5 for 420 Torr and that h and h dpjdz have the same values as for 420 Torr shown in Fig. 13.6.

The following values will be assigned the parameters of the cost equation (13.27):

/ = 0.20/yr су = $0.002/cm3 cQ = $0.015/kWh

Table 13.10 Flooding velocities for Spraypak no. 37, system H20-D20, total reflux

Pressure p, Torr 420 760 1245

Temperature T, К 357.4 373.2 387.6

Vapor density p, g/cm3 (pM/RT) 0.000339 0.000588 0.000928

Flooding velocity, g/(cm2-s) [M4] 0.208 0.275 0.338

Vf, cm/s (above/p) 614 468 364

v}p, g/(cm-s2) 127.8 128.8 123.0

R = 62360 (Torr*cm3)/(ginol, K) (first term)

R = 0.000002310 kWh/(g-mol-K) (second term)

T = absolute temperature, K, corresponding to p, from Table 13.4 T0 = 310 К

a* — 1, from Table 13.4 h, cm, from Fig. 13.6 h dp/dz, Ton, from Fig. 13.6

v, vapor velocity, cm/s, and p, pressure, Ton, are independent variables

0.0213 hT 0.289 h^P (a*-l f Р» (a* —1 fpdz

With these values, Eq. (13.27) becomes

The first term gives the contribution of tower volume to the cost of heavy water; the second, the contribution of power.

Figure 13.7 represents these parts of the cost of heavy water from (13.29) as a function of vapor velocity, for pressures of 200, 420, 760, and 1245 Ton. Conditions that lead to minimum cost are listed in Table 13.11.

The above loss in availability is equivalent to 8.5 kWh/g D20. Because this takes account only of tower pressure drop, and does not include the loss in availability associated with temperature drop across heat exchange surface in reboilers and condensers, it is apparent that power consumption in water distillation is appreciably higher than in hydrogen distillation. The cost of $193/kg DjO covers only the cost of tower packing and power loss associated with tower pressure drop. If account were taken of the cost of tower shells and foundations,

reboilers, condensers, pumps, and other process equipment and other sources of power loss, the cost of producing heavy water by water distillation would be much greater than $215/kg, U. S. Energy Research and Development Administration (ERDA)’s charge in 1977 for heavy water made by the GS process.

Holdup and start-up time. McWilliams and co-workers [M4] have found that the holdup of Spraypak no. 37 under these conditions is about 4 lb water/ft3, or 0.064 g/cm3. Consequently, the total water holdup of the columns of a plant producing 1 g-mol of D20/s would be (0.064X1.02 X 1011 )/18 = 3.63 X 10® g-mol water. From Eqs. (13.17), (12.199), and (12.203), the average deuterium content of the water inventory of this plant is

. In [xP(l — xF)/xp( 1 — X/.)] — [{xP — Xp)/Xp( 1 — *F)]

Xg = ——————————————————————————————

Dp, fIxp

In [(0.998X0.999851)/0.000149X0.002)] — [(0.998 — 0.000149)/(0.998X0.999851)]

“ 6729

= 0.00209 atom fraction

The increase in D20 inventory during start-up of this plant would be

IE(xE ~xF) = 3.63 X 10® (0.00209 — 0.000149)

= 7.05 X 10s g-mol D20 (13.31)

The start-up time for this water distillation plant, evaluated from approximate Eq. (12.197), is

or 8.17 days.

The low holdup and low start-up time is another advantage of Spraypak compared with bubble-plate columns.

Squared-off cascade. The preceding treatment of a water distillation plant as an ideal cascade operated at uniform vapor velocity has required that the steam flow rate be varied continuously as its deuterium content changes and that the number of towers in parallel, or the tower area,
be changed continuously. On the other hand, a practical water distillation plant, like the Morgantown plant, will consist of a number of multiplate towers in parallel in the first group at the feed point, a smaller number in parallel in the second group at a higher deuterium content, a smaller number still or a smaller tower in the third group, and so on until at the product end a very small tower will suffice. A practical plant like this is characterized by uniform heads and tails flow over a large number of stages. Cohen [C9] has called such a plant a “squared-off’ cascade and has developed general equations for it.

Figure 13.8 compares the variation of tails flow rate with stage number in a squared-off cascade with the variation in an ideal cascade performing the same job of separation in the same number of stages. Because the total flow rate in an ideal cascade is the lowest possible, the area under the stepped curve of the squared-off cascade is greater than under the smoothly tapered curve of the ideal cascade.

Consider a squared-off cascade making product containing Xp fraction deuterium at the rate P. An equation giving the number of stages n12 needed in a section of the plant that enriches the deuterium content of water from хг to x2, with a uniform steam rate G, is obtained from Eq. (12.224):

1 , 1 +a

n ————— In ——

(a* — 1

b(x2 — Xi)

where a — —- ;— гтт—■—г— —————

(x2 + Xі + c) — 2x, x2 — 2cxp

P

G(a* — 1)

Figure 13.8 Steam flow rate versus stage number in ideal and squared — off cascades.

(a* —1 )x — (P/G)xp a* — 1 g — 1

the ratio of the steam rate to the minimum steam rate at Xi.

Because the number of stages in the portion of an ideal cascade whose overall separation is

a* — 1

CO is

the value of g that leads to the same number of stages in a square section as in an ideal cascade is given by

geo — 1

g~ 1

CO + 1 CO

This is close to the optimum value of g for a square cascade section, as will now be shown. The volume of the section is given by

hRT „ hRT G, gw-1

—- nG =——— г—- In——— —

pv pv a* — 1 g — 1

The optimum value of G for a section of a squared-off cascade is one that makes nG a minimum, with n given by (13.39).

We shall evaluate this optimum value and compare the minimum size of a section of a squared-off cascade with the portion of an ideal cascade performing the same job of separation. This will give us an idea of the penalty in increased equipment size paid by using practical towers with uniform vapor flow rates instead of the constantly changing flow rate of an ideal cascade.

hRT 4P pv (a*-i)2

*p(l ~*i) *l(l — Xp)

(*i>-*iXl -2xi) ~Xi)

The volume of the portion of an ideal cascade enriching deuterium from xt to x2 is

pv (a* — l)2 *1*2

With V from (13.45), Kideal from (13.47), n from (1339), and g defined by (13.41), there results

Figure 13.9 is a plot of К/КИеа1 against g, the ratio of the steam flow rate to the minimum at Xi for several values of the overall enrichment of the section (со = x2lx). Figure 13.9 shows (l)that the optimum steam rate in a square section is less than the optimum in an ideal cascade, and (2) that the penalty in using a squared-off cascade is less than 15 percent so long as the overall enrichment of a section is under 4. At x2/x2 = 4, the optimum steam rate is 1.35 times the minimum, at point A in the figure. In practice, a somewhat lower steam rate would be used in order to reduce the size of reboilers and condensers. A point around В might be chosen, at g= 125, where the number of stages in a square section is equal to the number in the portion of an ideal cascade with the same overall enrichment [cf. Eq. (13.44)]. The tower volume and power consumption at this condition are 1.156 times those of an ideal cascade, and costs are higher by the same factor.

Figure 13.9 Volume of square sec­tion relative to ideal cascade.

Figure 13.10 Example of Sulzer CY packing for water distillation columns. Diameter, 250 mm.

These equations for a squared-off cascade and those previously given for an ideal cascade were used to work out the variation of steam flow rate with stage number shown in Fig. 13.8 for an overall enrichment per section x2/xi =4 and a steam flow rate (?) 1.25 times the minimum. The following conditions have been assigned to each cascade:

P= 1 mol/h xP = 0.998 xF = 0.000149 a* = 1.04

The portion of each cascade up to x = 0.0093 has been shown.