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The Physical Chemistry of Water

and Aqueous Solutions

3-1 INTRODUCTION

It is the purpose of this chapter to review in an elementary fashion some selected

physicochemical topics of direct concern to the technology of water-cooled reactors. Data are

presented on materials and systems of interest. Included are:

(a)

Chemical thermodynamics of light water, and some metal-water systems

(b)Electrical properties of water and dilute solutions of electrolytes

(c)Behavior of concentrated solutions of interest in reactor and steam generator

technology

(d)Some consideration of the supercritical state of water.

3-2 CHEMICAL THERMODYNAMICS OF WATER AND METAL-WATER

SYSTEMS

The major area of interest in the chemical thermodynamics for water reactor systems is that of

waters-material reactions. Most metals of interest are unstable with respect to water and their

utilization in water-containing systems depends on the kinetics of the reactions. In many

cases, because of the protection afforded by the product of the reaction, the rates of the

reaction are sufficiently slow to permit practical application of the materials. This aspect ofwater-material systems is treated in the chapters of corrosion. However, when more than one

corrosion product can be formed, the conditions of thermodynamic stability of the variousoxides can be of practical significance and merit attention.

The stability of a chemical system with respect to a possible reaction is measured by the

change in free energy for the reaction between reactants and products. For pure condensed

phases, the standard state is the material in its natural state at the temperature of interest. For

liquids (of high vapor pressure) and gases, the standard state is the vapor at unit fugacity

(ideal pressure). Tables of heat and standard free energy of formation for oxides of interest in

water reactor technology have been summarized in convenient form by Coughlin1. From the

fundamental relationship

KRTF ln (3.1)

the activities or fugacities of the phases at equilibrium can be calculated.

Thus, for the reaction

H2OH2+ O2

the equilibrium constant is

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2

OH

HO

ef

ffK

2

22

2/1

For the very small degrees of dissociation of pure water. which occur at the temperatures of

interest, we write

222222H OOH PfPf

where the fugacity is then equal to the partial pressure, for the gases. Water does not behave

as an ideal gas, and a correction is required. Define asf/P, me ratio of fugacity-to-partial

pressure for pure water.

Thus,

OH22 Pf OH (3.2)

Broch2has computed for saturated water vapor (and therefore the saturated liquid) up to thecritical point, and his data may be used in the calculations. He finds log (sat)

-1= 300P0.618,

withPin pounds per square inch.

Thus, Eq. (3.2) is written

e

OsatH

OOK

P

PP

2

222

(3.3)

or

OsatHe

O PKP 22

3

2 2 (3.4)

and

32

22 2

OsatHe

O PK

P (3.5)

for the dissociation of pure water. Although this treatment is not entirely exact, further

refinements are neither warranted nor possible with existing data on mixtures of steam and

gases.

For metal reactions, similar equations are derived. Thus, for the reaction

NiO = Ni + O2 (3.6)

2

2

O

NiO

ONi

e Pa

faK

(3.7)

since the solid phases have unit activity, and the fugacity of the gas maybe taken equal to its

partial pressure.

Thus,

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2

2 eO KP (3.8)

If the equilibrium partial pressure of oxygen from NiO [Eq. (3.8)] is greater than the

equilibrium partial pressure of 0 1 from pure water [Eq. (3.5)] at a given temperature, then Ni

would be stable in pure water at that temperature. This implies that the ratio of water-to-nickel

is very large; i.e., the composition does not change with a small increment of reaction. Forsuch comparisons, curves of the equilibrium partial pressure of oxygen for pure water, water

containing added hydrogen, water containing added oxygen, and various oxides of interest,

have been computed and are plotted in Fig. 3.1. The curves for heavy water (D2O) would be

little different from that of light water (H2O) and are not included on the chart.

Note from Fig. 3.1 that silver is thermodynamically stable with respect to pure water over the

whole temperature range covered, and, except at relatively low temperature (

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effect of the oxygen predominates. Moreover, the chart assumes that the composition of the

liquid phase is not changed by the reactions proceeding toward equilibrium.

3-3 ELECTROCHEMICAL PROPERTIES OF WATER AND DILUTE

SOLUTIONS

Heterogeneous reactor water chemistry is, except for the special case of chemical control,

mainly restricted to that of pure water, or solutions sufficiently dilute (10-4M) as to behave in

essentially an ideal manner. Accordingly, in contrast to conventional boiler water chemistry, it

was desirable and possible almost from the very beginning to consider the chemistry of the

coolant in terms of actual properties lit the temperatures of interest. With the gradual decrease

in the concentrations of treatment chemicals, a similar approach is now possible in

conventional boiler plants and, in particular, in supercritical systems. Measurements in both

areas of application are still most conveniently made at low temperatures. However, the

properties of water and solutions over the whole temperature range are required so that

measurements at low temperature can provide information on the high-temperature properties.

Aside from analytical measurements of the amounts of specific elements, the most importantdata are those pertaining to the pH and conductance of the coolant. In this connection,

therefore, the ionic equilibria and conductivity properties in water and dilute solutions of

specific solutes are of importance.

3-3.1 Acid-base Equilibria of Dilute Solutions

With respect to acid and base equilibria, a substance is classified as an acid if it has a

tendency to lose a proton, and as a base if it has a tendency to gain a proton. The relationship

between an acid and a base may then be written

A H+ + B (3.9)

Acid Proton Base

The acid and base are conjugate to one another. Since free protons cannot be expected to exist

in solution to any significant extent, the acidic or basic properties of a solute cannot be

realized unless the solvent itself possesses acid or basic properties, i.e., can accept or donate

protons. Thus, the general case for significant acid or basic solutions must be written

2121 ABBA (3.10)

where Al and Bl and A2 and B2 are the conjugate acid and bases of the solute and solvent,

respectively.

Water can act as both a proton acceptor and a proton donor (amphiprotic) and therefore its

solutions can show both acidic and basic properties. In heterogeneous water reactor systems,interest is confined largely to pure water and basic solutions, and these will be discussed in

detail.

Water dissociates to solvated protons and hydroxyl ions

OHOHO2H 32 (3.11)

with similar reaction for heavy water. The equilibrium for this reaction is written

w

OH

OHOHK

a

aa

2

2

3 (3.12)

For dilute solutions, up to 10-4M, the activities are nearly equal to the molal concentrations m,

and the water activity is essentially constant. We may write, therefore.

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mH+mOH-= Kw (3.13)

and the constant K.._will apply for all conditions consistent with the above qualifications.

Measurements of K"" have been made by a variety of methods. Agreement at low

temperatures is quite good, including measurements based on the conductance of water. Very

few measurements are available at temperatures> 200 F. Those of Noyes et al.3 are most

definitive. even though they are over 50 years old. Table 3.1 and Fig. 3.2 present three sets ofdata for the molal ion product of pure

Table 3.1Molal Ion Product of Water

Temp., FKw10

14

Jones4Temp., F

Kw1014

Noyes et al.3

Kw1014

Harned and

Owen5

75 0.90 64.4 0.64 0.57

200 43 212 55 54.6

300 208 313 268 222

400 500 424 645 403480 645 583 340 308

540 628

water including a compilation from various sources by Jones4and the data of Noyes et al.3

Harned and Owen5present three relationshipsfor the variation of Kw, with temperature, and

the values for their Eq. (15-3-7a), shown here as Eq. (3.14), are included in Table 3.1 and Fig.

3.2.

TT

Kw 0170607.00875.699.4470

log (3.14)

The agreement between the various estimates is reasonably good.

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Fig. 3.2. Molal ion product of water.

Some possibility exists that the experimental results of Noyes et al.3may be in error. (See

comment by Wright et al.6)

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The bases of interest in water reactor technology are KOH, LiOR, and NH 4OH. NaOH is not

ordinarily utilized because of problems resulting from activation of 23Na to 24Na. NH,OH is a

weak base. LiOH has been shown experimentally6to be associated at high concentrations, and

the same is probably true for KOH at high temperatures. At the normal concentrations of

interest (10-4M), however, only the dissociation of NH4OH need be taken into account in

computing solution pH. The dissociation constants for NH4OH and LiOH are presented inTable 3.2 and Fig. 3.3, respectively. Table 3.2 also presents KA for the HSO4

- ion. The

calculated pH at high temperature of pure water, dilute solutions of ammonia, and strong

bases, are plotted in Fig. 3.4, where SB is molal concentration of added base. In Fig. 3.4, the

point for K2SO4, at 560 F, indicates that a 0.5 10-4M solution of K2SO4is more alkaline at

that temperature than a solution of NH3which has a pH at 75F of 10.0{11.1 ppm NH3).

Table.3.2Dissociation Constants: KB-NH4OH and LiOH; KA-HSO4-: Molal Units

NH4OH LiOH HSO4-

Temp., F KB106 Jones4 KB10

6 Wright6 KB, Wright KA 106, a

75 17.9120 21.9 0.135

160 19.1 0.0731

200 15.0 16.1 0.0804

240 12.4 0.0502 880

280 10.2 0.0348

300 7.80 300

320 7.37 0.0500

360 5.18 0.0467

400 2.83 3.42 0.0502 42.0

440 2.19 0.0320

480 1.13 1.30 0.0305 10.0520 0.84 0.0234

540 0.43

560 0.35 2.00aData from W. L Marshall and E. V. Jones. Reactor Chemistry Division Annual Progress

Report For Period Ending Jan. 31, 1965,ORNL-3789, p. 148, Oak Ridge National

Laboratory; alsoJ.Phys. Chem,. 70, 12(December 1966).

The dissociation equilibria are calculated from the following equations:[M

+] + [H

+] = [OH

-] (3.15)

(Condition of Electroneutrality)

[H+][OH

-] =Kw (3.16)

(Dissociation of Water)

[M+] + [MOB] = [B] (3.17)

(Material Balance for Base)

B

-

MOH

OHMK

(3.18)

(Dissociation of Base)

The [ ] represent molal concentrations.

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Fig. 3.3. Dissociation constantsKB. for NH4OH and LiOH.

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Fig. 3,4. pH of solutions of strong bases (SB), NH3, and pure water.

A value of pH is assumed, defining [H+]. From this, one calculates [OH-] from Eq. (3.16), and

[M+] then from Eq. (3.15). For completely dissociated bases, [M] = [B]. For incompletely

dissociated bases, [MOH] is then calculated by substituting the values of [M +] + [OH-] in Eq.

(3.18); [B] is then calculated from Eq. (3.17). For univalent weak bases,

H

1HH

BBK

KK ww (3.19)

The calculations involve only simple arithmetic and are used to generate data for cross

plotting to give the results in more convenient form. More detailed calculations have been

reported (Meek, 13Chap. 6).

3-3.2 Slightly Soluble Metal Oxides or Bases

Another group of dilute solutions of extreme importance in water reactor technology is that ofthe saturated solutions of the corrosion product oxides. Jones7 has determined the

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concentration of metals in equilibrium with corroding Ni-CrFe alloy 600. His results, as

tabulated by Cheng,8 are presented in Table 3.3. An electropolished Incoloy-600 autoclave

was operated for 1500 h at 550 F (288C) at the starting coolant conditions shown in the left-

hand column. For the data of the other temperatures shown, the autoclave was equilibriated

for one day at the temperature of interest. An additional test was run (see Table 3.4) to

determine the effect of short-term changes in water chemistry after previous exposure for1500 h to a different chemistry, all at 340 F. The composition of the Incoloy-600 used for the

autoclaves is given in Table 3.5. Jones7 found that the "solubility" decreases with time, and

generally reaches a fairly steady state after 1500 h. The various metals are not found in the

water in proportion to their composition in the alloy, and the solubilities of the various

elements vary with temperature and solution pH. The short-term tests, Table 3.4, indicate that

the measured solubility is primarily dependent on the final water chemistry, not that of the

previous period of exposure. Although these data are of limited validity as solubility data,

they provide some idea of the effect of alkaline additives and of temperature on the solubility

of the various metals, which should be useful in considering ionic transport of corrosion

products.

The data as tabulated by Cheng8represent the temperature effect quite well, but include agreat deal of scatter for the effect of pH. A better representation of the solution composition at

550 F is presented in Fig. 3.5 from the original data7for samples after about 1000 h of

constant-temperature operation. The pH is that of the solution at 550 F.

Table 3.3Solubilities of Incoloy-600 Corrosion Producs, Corros ion , Ref. 8)

[one-day run after ~1500h at 550 F (288 C)]

Element Water Temperature, F (C)

Water pH ppb 75(24) 200(93) 350(177) 450(232) 550(288) 650/343)

Ammoniatedand

HydrogenSaturated at

Room

Temperature

8.5 Iron 1.0 9.0 20.5 9.5 2.7 1.58.5 Nickel 14.4 10.9 10.9 9.0 4.5 1.0

8.5 Chromium

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Element Water Temperature, F (C)Water pH ppb 75(24) 200(93) 350(177) 450(232) 550(288) 650/343)

Lithiated

and

HydrogenSaturated at

Room

Temperature

10.5 Iron 0.6 1.2 1.5 1.1 1.2 1.7

10.5 Nickel 3.6 0.8 1.4 4.2 1.6 0.3

10.5 Chromium

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Fig. 3.5 Solubility of Inconel corrosion products in 550 F hydrogenated water.

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Fig. 3.6 Solubility of Co

2+

in water at 680 F (saturated) (Ref. 9).

The apparatus was supplied with solutions of Co(OH)2obtained by passing solutions of CoCl2

through an anion exchanger. The solution was concentrated by evaporation and the pH

adjusted by adding NaOH. The solubility (as Co2+) at low chloride concentrations was found

to vary from about 0.1 ppm at pH of 8.5 and below, corresponding to that of Co 2++ CoOH++

Co(OH)2, to about 0.0055 mg liter at a pH of 10.5 and above, corresponding to the solubility

of Co(OH)2. At a pH of 7, the solubility was dependent on the chloride ion concentration,

decreasing from about 0.1 ppm Co2+at 0.5 ppm Cl to about 0.05 ppm Co2+at 2.5 ppm Cl,

indicating the possible formation of a basic salt CoOHCl. The resules of Mingulina et al. 9at

680F, pH 10,0.008 ppm, are to be compared with those of Jones7at 600F-pH 10 with LiOH,

less than 0.1 ppb.Sweeton et al.10have reported measurements of the solubility of Fe from Fe3O4over a range

of temperatures in dilute acidic and basic solutions, saturated at room temperature with 1 atm

H2pressure. They write, as the general dissolution reaction,

Ob)H3

4(Fe(OH)(g)H

3

1b)H(2(s)OFe

3

12

b)(2

b243

They have interpreted their data in terms of three values of b corresponding to three soluble

forms for the iron; namely,

Fe + b = 0

Fe(OH)+ b = 1Fe(OH)3

- b = 3

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for each of which a solubility product is defined

31

2H

2

2

H

Fe(OH)

PK

b

b

bb

WritingKbas a function of temperature as

R

DTBTAK

303.2

)1(ln/log

They have correlated all their data to these models.

The data and the correlations indicate the expected response of the solubility of Fe3O4to the

pH of the solution. The following illustrative solubility data are calculated from the

correlations:

Solubility of Fe from Fe3O4

ppb

Temperature C/FBase concentration 300/572 260/500 200/392

10- M 8.3 4.6 3.5

0M 16 32 89

In alkaline solution, 10-4M, the solubility is regular in the temperature interval, whereas in

untreated water the solubility is strongly retrograde. Addition of base decreases the solubility,

as expected, with the effect being greatest at the lower temperature.

3-3.3 Electrical Conductivity of Aqueous Solutions

By virtue of its high dielectric constant and relatively low viscosity, water provides a highly

conducting medium for ionic solutes (electrolytes). Hydrogen ions (protons) and hydroxyl

ions, have exceptionally high mobilities in water through proton transfer mechanisms. The

specific conductance of pure water is, however, quite low (as shown in Fig. 3.7) because of

the low population of the conducting ions in pure water.

The conductance of solutions (defined as the reciprocal of resistance in ohms) is expressed in

terms of the specific conductanceK, which is the conductance in reciprocal ohms of 1 cm) of

solution between parallel electrodes 1 cm apart.

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Fig. 3.7. Conductance of water and some solutions.

The conductance of that volume of solution containing one equivalent of ions between similar

electrodes is called the equivalent conductance , which is related to the specific conductance by

C

1000

where C is the concentration of the solute in equivalents per liter. In all cases, the observedconductance is corrected by subtracting the conductance of the pure solvent. Experimentally, it isobserved that the equivalent conductance is a function of concentration. The value of at infinitedilution, termed 0is a unique property of the solute; it is an additive property of the conductance at

infinite dilution of the individual ions (Kohlrausch's law of the independent migration of ions). Table

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3.6 lists the ion conductances at infinite dilution at 25C (o+, o

-) of a number of ions of interest, from

which 0for a variety of salts can be obtained.

Table 3.6Ion Conductance. at Infinite Dilution at 25 C, ohms-1, cm2equiv-1

Cation o+ Anion o-

H+ 349.82 OH- 197.6

Tl+ 7.4.4 Br- 78.4

K+ 73.52 Cl- 76.8

NH4+ 73.4 NO3

- 71.44

Na+ 50.11 HCO3- 44.5

Li+ 38.69 SO4- 79.8

Ba + 63.64

Ca + 59.50

Sr+ 59.96

Mg+

53.06

3-3.3.1 Effect of Temperature and Concentration on the Conductivity of Solutions

The conductivity of dilute solutions of 1:1 electrolytes. as a function of concentration and temperatureis adequately represented by the Debye-Hckel-Onsager Equation

C 00 (3.19)

Table 3.7 presents values of and for water as a function of temperature. 0must be determinedexperimentally and is a function of both pressure and temperature. The pressure dependence atordinary temperatures is quite small up to 5000 psi and need not be considered further for reactor

applications.

Table 3.7Debye-Hckel-Onsager Conductivity Equation Parameters

Temperature, F

64.4 0.2261 50.50

77.0 0.2289 60.10

122. 0.2406 99.75

167 0.2549 146.5

212 0.2723 201.0

262.4 0.3016. 266.6

284 0.3139. 298.0

312.8 0.3318 340.0

424.4 0.4254 523.5

500 0.5272 650.8

537.8 0.6013 737.3

582.8 0.7269 870.0

Johnston11

showed that the variation of 0 with temperature was fairly well represented by theequation

nk 0 (3.20)

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where k and nare empirical constants and the solution (solvent) viscosity. Values for n for

some electrolytes in water are

NaCl = 0.94

NH4OH = 0.71

KCl = 0.86

LiOH = 0.75

In general, electrolytes with a high value of 0at room temperature have lower values of n

than electrolytes with lower room temperature values of 0. Figure 3.7 shows the variation of

0for a number of electrolytes over the temperature range of interest, including H-OH. These

data were obtained from the summary of Wright et al.6and were extrapolated in part by using

the 0-relationship. Shown also is the calculated specific conductance of H2O. Quist ct al.12

have, in a similar fashion, prepared a compilation of limiting ionic conductance at high

temperatures, presented in Table 3.8.

Table 3.8Limiting Equivalent Conductances of Several Ions

at Temperatures to 400 C (Ref. 12)ohms-1cm2equiv-1

Temperature, C H+ Li+ Na+ K+ NH4+ OH- Cl-

100 (1 atm) 364 156 151 195 206 447 211

200 (0.865 g/cm ) 824 329 304 364 394 701 391

300 (0.7125 g/cm ) 894 562 459 504 579 821 561

400 (0.8 g/cm ) 945 440 455 520

A useful application of these data is the calculation of the diffusion coefficient for the

infinitely dilute solution. From the Nernst Formula,

00

00

21

2110-2

ZZ

ZZ108.93/sec)(cm

TD

For the dilute solutions normally of interest in reactor technology, the difference between

and 0is not ordinarily greater than about 1.5 %, as expressed by the Debye-Hckel-Onsager

Equation. However, at the higher temperatures, ion-pair formation can be significant for some

electrolytes. Bjerrum13 provided a method of analysis of the formulation of ion pairs in

completely ionized electrolytes. The association is expressed as an equivalent dissociation

constantKDIdefined by

AC

ACKDI (3.21)

Experimental data are available for a number of electrolytes of interest. These are summarized

in Table 3.9 taken from Wright et al.6

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Table 3.9Ion Association-KDI(Ref. 6)

Electrolyte Temperature, C KDI

NaCl 281 0.22

306 0.093

KCl 281 0.49

306 0.12

HCk 260 0.12

306 0.035

NaOH 218 0.55

The utilization of supercritical water in conventional power technology is now widespread.

Correspondingly, interest has increased in the application of the supercritical cycle to power

reactor technology, both in thermal14 and breeder15 reactors. Studies have been reported of

heat transfer and corrosion for nuclear application of the supercritical water cycle.16 In

connection with this potential application, it is pertinent to review briefly the physicochemical

properties of supercritical water. For power-cycle application, interest is limited to the regionbelow 5000 psi. Franckl7 has presented a comprehensive review of the properties of

supercritical water as a solvent for electrolytes, covering most of the pertinent available

literature. In general, the significant properties, such as dielectric constant and viscosity, are

strongly dependent on density which, in turn, is strongly dependent on pressure. The density

of water in the region of interest in reactor technology is shown in Fig. 3.23. At the higher

densities, the dielectric constant is sufficiently high so that significant ionization and

conductance of electrolytes results. Equivalent conductances of the order of 1000 to 1200

mho's are observed. At lower densities (low dielectric constant) most salts are incompletely

ionized, but dissociation becomes more complete at the higher densities. Water shows an

increasing degree of dissociation at higher densities at high temperature. In the region of

interest for power applications (under 5000 psia), most of these effects are not substantial. It is

necessary, however, to bear in mind that there is a continuity in the properties of water in this

region.

3-4 CONCENTRATED SOLUTIONS

The behavior of concentrated solutions of electrolytes is of concern in water reactor

technology because of possible concentration at boiling heat transfer surfaces, where

concentration of solutes can lead to the persistence or formation of other phases. The concern

is primarily related to the interaction between the solution and the material with which it is in

contact, although, as noted later (Chap. 6), the concentration process of itself can be

significant in the case of nuclear poisons. The interaction with metals and their oxide surfacesis influenced by the specific nature of the ions and their concentration. The latter can be

limited by solubility, volatility, and pressure-temperature relationships for the solutions.

Specific effects of the ions are considered in Chap. 8; the latter considerations are treated

here.

An ideal solute dissolved in water produces a vapor-pressure lowering, described by Raoult's

Law,

1

0

11 NPP (3.22)

This equation can be rearranged to

20

11

0

11

0

1 1 NPNPPP (3.23)

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and

20

1

1

0

1 NP

PP

(3.24)

That is, the relative vapor-pressure lowering is proportional to the mol fraction of solute. For

completely dissociated solutes in water, the mol fraction of ions must be used for N2 in the

ideal case, but departures from ideality are to be expected.

Considering evaporation as an isobaric process, it will be limited by concentration so that both

the thermal (temperature) and material (vapor pressure) exchanges cease. Thus, the required

conditions for equilibrium are that the solution concentrates until its vapor pressure at the

prescribed temperatureP1Tis equal to the total applied pressure , assuming that T is greater

than the saturation temperature of the pure solvent at the pressure . The solution vapor-

pressure curve is limited by solubility or critical phenomena, of which the former is of

primary concern in current water reactors.

3-4.1 Strong BasesThe vapor pressures of solutions of NaOH and LiOH at the temperatures of interest have been

reported l8 and are listed in Table 3.10.

The more concentrated solutions of LiOH produce only about one third the vapor-pressure

lowering of the equivalent amount of NaOH. More dilute solutions show a lesser deviation.

This is probably related to the association of Li+ and OH- ions. In further contrast to NaOH

and KOH, the solubility of LiOH, as shown in Fig. 3.8, is also quite limited. Figure 3.9 shows

the equilibrium superheat of solutions of NaOH and LiOH as a function of concentration at

2000 psia.

The precision of available data does not justify distinction in pressure for the range shown.

Note that a superheat of only 5 F corresponds to a concentration of about 1.25 M for both

NaOH and LiOH. A solution at these concentrations and temperatures would be quite

aggressive and undesirable 10 most metallic materials.

It is evident that where such conditions exist in reactors, local concentration must be limited

by mass transfer considerations rather than thermodynamic equilibria. That this has been

successfully achieved will be evident later in discussions of corrosion under heat transfer

conditions. It is also evident from Fig. 3.9 that LiOH solutions cannot exist at a superheat in

excess of about 8.4 ~F at 2000 psi. As a solution evaporates, the equilibrium T does not

increase as the concentration increases with evaporation above about 4 M. At 6.25 M, the

solubility limit is reached, and the solution would disappear by evaporation of water and

precipitation of LiOH. Quite similar behavior will be exhibited by all salts of relatively lowsolubility and low vapor-pressure lowering, although, as will be evident later, it is unusual for

a strong base.

The behavior of nonvolatile solutes on concentration merits further consideration in another

connection. In superheat reactors (relatively low pressure, high temperature), entrained boiler

water will contain solutes whose behavior is a function of the vapor pressures of their

saturated solutions, shown quite generally in Fig. 3.10, modified from a figure of Keevil.19

The vapor pressure of the saturated solution is plotted here against temperature. Consider

water droplets containing NaCl entrained in steam being superheated al 1500 psi. As shown

by the intersection of the 1500-psi isobar and the vapor-pressure curve of saturated solutions

of NaCl, up to a surface temperature of 655 F the surface would be covered by solutions of

NaCl. At temperatures above 655 F, the solutions would dry out.

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Table 3.10Vapor-Pressure Depression Data for Lithium and Sodium Hydroxide Solutions of Equivalent Concentrationsa

LiOH NaOH LiOH NaOH LiOH NaOH

ConcentrationGrams per 100 Grams H2O 5 5 8.4 10 10 15.6 15 15 25

Weight Percent 4.76 4.76 7.83 8.59 8.59 13.5 13.04 13.04 20.0Molality 2.09 1.25 2.09 3.92 2.35 3.92 6.25 3.75 6.25

Vapor-Pressure Depression (P), psi

248 F 1 1.2 1.95 1 2.25 4 4 3.6 6.7

320 F 4.5 3.6 6.3 3 7.15 11.5 7 11.2 18.8

392 F 12.5 9 14.5 13 16 27 18 26 44

482 F 35.5 25 38 34 42.5 69 50 67 107

572 F 73 52 83 74 93 147 90 144 226

662 F 120 98 158 140 177 280 137 275 433aNaOH data calculated from vapor-pressure data in the International Critical Tables; LiOH data calculated from smooth curves in Figs. 3, 4 and5 of Report BMI-1329.18bSaturated, approximately.

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Fig. 3.8. Solubility of lithium hydroxide in water (Ref. 18).

Fig. 3.9. Superheat of solutions of NaOH and LiOH at 2000 psia.

The fate of the solute is determined by its volatility, to be discussed in the next section. The

behavior of KCl would be quite similar except that the solutions would persist to about 700F.

The behavior of alkalis (except LiOH) is quite different. The vapor pressure of the saturated

solution reaches a maximum at quite low temperatures. Thus, as the solution is heated the

solute is concentrated until it is in equilibrium, but it does not dry out. As noted earlier,

lithium hydroxide solutions would dry out at even lower temperatures than either NaCl or

KCl.

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Fig. 3.11. pH of sodium orthophosphate solutions having various mol ratios of sodium-to-

phosphate (Combustion. Ref. 22).

Even the use of the modified form of coordinated phosphate control does not ensure the

complete absence of free caustic. Concentrated phosphate solutions can react with iron oxide

to form sodium iron phosphate, leaving behind a more alkaline solution than that originally

present.

3-5 SOLUTE VOLATILITY-SOLUBILITY IN STEAM

There are many potential circumstances in water reactor technology where the volatility of a

solute into steam or the solubility in steam or supercritical fluid can be a matter of concern for

design or operation. The materials of interest range in volatility from very high values, as with

NH3, to very low values, such as corrosion product or salt impurities. It will be convenient to

discuss these two classes separately.

3-5.1 High Volatility Materials

3-5.1.1 NH3

Because of its volatility, NH3 is attractive as a source of alkalinity in reactor and boilertechnology. In a simple (single-stage) evaporation process the limiting concentration ratio will

not exceed the reciprocal of the distribution constant, vapor to liquid. NH3 is quite stable,

thermally, at the temperature of concern in reactor technology, but is subject to radiolysis (see

Chap. 4). Morpholine and cyclohexylamine are also used in conventional boiler technology as

a source of basicity in the condensing portion of the steam cycle. Jones23 has reported

experimental determinations of the distribution coefficient for NH3at various concentrations

and high temperatures.

The equilibrium is between un-ionized ammonia in the liquid and NH3in the vapor. Thus,

[NH3]

l[NH

3]v (3.25)

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and

D3

3

NH

NHK

l

v

The relationship between [NH3]l, identical to [NH4OH], and NH3, the total ammonia

concentration in solution, is readily derived by the method of Eqs. (3.15) to (3.18). Write

[NH4+] as NH3and [NH4OH] as (1 -1)NH3. The relationship is

HK

K1

11

W

B

(3.26)

Where [H+] is obtained from Eq. (3.19).

Various values of are assumed from which NH3is calculated, and a curve of vs NH3

constructed.KDis then given by

D3

3

NH-1NH Kv

(3.27)

The apparent distribution coefficient is, therefore,

'

DD

3

3 -1NH

NHKKv

(3.28)

Figure 3.12 showsKDfor NH3as a function of temperature for water at saturation pressure.

3-5.1.2 Iodine

Radioisotopes of iodine of considerable biological significance are formed in nuclear fissionin high yield. The chemical behavior of iodine, and particularly its volatility, are matters of

considerable practical importance in nuclear power plant design and operation. The chemistry

of iodine-water systems is quite complex. Thus, iodine reacts in water (hydrolyzes) to form

hydriodic and hypoiodous acid,

I2+ H2OHI + HIO (3.29)

Hypoiodous acid, in turn, can disproportionate to iodic acid and iodine. Thus,

5HIOHIO3+ 2I2+ 2H2O (3.30)

The hydrolysis reaction increases with temperature and pH, and is inversely proportional tothe concentration of iodine. Dilute solutions, less than -10-5M, are extensively hydrolyzed

even in neutral solution. Volatility is contributed by both I2and HIO (a weak acid), since the

degree of dissociation of HIO will decrease with increasing pressure. The apparent KD

defined as

l

v

2

2

IHIHIO

IHIO

is a complex function of temperature and pH.

Styrikovich et al.24have published the results of a series of determinations of the distribution

of iodine compounds between steam and water, as a function of pressure (temperature) andlow temperature pH (pH0), for saturated steam.

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Fig. 3.12. Distribution coefficientKDof undissociated ammonia, saturated water, and steam

vs temperature (J. Phys. Chem., Ref. 23).

The measurements were made over a range of total iodine concentrations of 1 to 100 mg/kg,

but are reported for concentrations of 10-4M (25.4 ppm). Figure 3.13 shows the effect of

pressure and pH, on the apparent distribution coefficient KD at low and intermediate

pressures. The curves reflect the hydrolysis with increasing pH, decreasing the volatilization

of the I2 and increasing volatility at higher pressures in the high pH0 region, reflecting theincreased volatilization from HIO. Figure 3.14 shows the apparent distribution coefficient KDfor HIO at 425 and 1000 psi. Here, the coefficients show maxima at a value of pH0of about

8.5, reflecting the amphoteric nature of HIO, which is the major species present. The true

distribution coefficient of HIO would be twice the value of KD at 1000 psi, assuming that

hydrolysis of I2 was practically complete, and dissociation of HIO negligible at that

temperature.

Note from Fig. 3.13 that at low pressure, such as in evaporators, and low pH, neutral or lower,

the apparent distribution coefficient of iodine is extremely high, of the order of 610-3 or

greater, and that this is reduced to about 410-5at a pH 10. Ordinarily, iodine derived from

high-temperature water reactors is present largely as iodide, which will have a very lowvolatility except at very low pH values.

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Fig. 3.13.KDvalues of iodine at low pressures (Ref. 24).

Any treatment that reduces the iodide to iodine will, of course, have adverse effect on iodine

retention.

Figure 3.14 indicates that at 1000 psi and pH 7 the apparent distribution coefficient for iodine

is about 10-3. It is expected, as noted later, that values ofKDof the order of 10-4or less are to

be expected from boiling reactor waters at this pressure because of the reduced state of the

iodine (I-).

Fig. 3.14.KD values of hypoiodous acid as a function of pH0, 71 kg/cm

2pressure (o)and at

30 kg/cm2pressure (0) (Ref. 24).

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3-5.2 Low Volatility Solutes

3-5.2.1 General Considerations

All salts and oxides are to some extent soluble in steam or supercritical water. The degree of

solubility is a complex: function or the nature of the material and the density and temperatureof the water phase. In general, the solubility increases with the density at constant

temperature. The problems created by this solubility in power cycles are a function of the

parameters of the cycle and the characteristics of the particular solute system. With the

continued trend to higher temperatures and pressures in steam power cycles, difficulties have

been encountered in this area, and a considerable body of information on systems of

importance has been developed.

A difficulty experienced in conventional power technology is the deposition in the turbine of

solutes volatilized with steam in the boiler-silica, NaOH, Na2SO4, and copper oxides being

the major sources. Control of the problem has been achieved primarily by reducing the

quantities of these solutes entering the unit and, additionally, in the case of silica, by reducingits volatilization tendencies by optimum adjustment of the boiler water alkalinity. Transport of

solutes by carryover of water into the steam can also be a major source of difficulty, and must

be controlled mechanically by separation devices and steam washing.

In addition to the turbine fouling problem, difficulties can be encountered from deposits in the

heat generation system and chemical attack of the transported solutes on the materials of

construction in all parts of the system. The situation is quite complex because some of the

solutes can react with each other or with water, forming less soluble or more volatile

compounds which are then separated in the flow system (chlorides, carbonates). The behavior

of mixtures of salts can therefore vary from practically independent action to complex

interactions.

With few exceptions, current non-nuclear steam power generation is carried out at pressures

up to 3500 psi and temperature of the steam up to 1050 to 1100 F. Nuclear superheat

generation equipment currently projected is confined to the subcritical region, but

considerable interest also exists in the supercritical cycle. 14,15

3-5.2.2 Phase Relationships

Power technology is concerned with initially dilute solutions, which, by evaporation, can form

concentrated solutions of highly soluble solutes. Consideration must therefore be given to the

whole concentration range in many applications. This has already been done for the liquid

phase of selected solutes at subcritical temperatures.The phase relationships for water-solute systems, for the most part, fall into two extreme

classes. Figure 3.15 shows a system where a continuous series of solutions and critical

compositions is formed between water and the solute. NaCl and KCl form systems of this

type. Figure 3.16 shows a system where limited solubility and critical compositions exist

between the two components. Silica, the metal oxides, and Na2SO4 form systems of this type.

The detailed phase diagrams for the two types of systems are shown in Fig. 3.17 for NaCl and

in Fig. 3.18 for SiO2.

The sodium chloride diagram is considered first. It consists of three domains: the liquid

solution phase; the vapors in equilibrium with this liquid, sub- and transcritical: and the vapor

in equilibrium with solid sub- and transcritical. LineA-B is the composition of the saturatedliquid phase. Line C-D is the critical composition. LineE-F is the composition of the vapor in

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equilibrium with the saturated solution A-B. The isobars G-H are the compositions in

equilibrium with solutions between the saturation line A-B and the critical line C-D in the

transcritical region.

Fig. 3.15. Nonintersecting critical and solubility curves.

Fig. 3.16. Intersecting critical and solubility curves.

The isobarsI-J are the vapors in equilibrium with the unsaturated solutions in the subcritical

(water) region. The isobarsK-L arc the compositions of the vapor in equilibrium with solid

salt over the whole pressure range.

In low solubility systems, SiO2-H2O (Fig. 3.18), the unsaturated system extends only minutely

past the critical temperature of water. Thus, there is no transcritical two-phase liquid-vaporregion.

It is advantageous to consider separately the data on volatilization from solutions, and of

solute solubility in steam.

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Fig. 3.17. Phase equilibrium diagrams for system NaCl-H2O (Ref. 33)

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Fig. 3,18. Phase equilibrium diagram for SiO2-H2O (Ref. 33).

These data have been correlated by semiempirical relationships derived by considering the

solubility process as a solvation reaction. Consider

x(solid) + m(H2O)(x mH2O) (3.31)vapor vapor

representing a solute molecule reacting with mwater molecules to form a complex soluble in

the vapor phase. The equilibrium constant for this reaction is defined by the equations

000 STHF (3.32a)

eKRTF ln0 (3.32b)

m

x

mx

e

v

v

aa

aK

OH

OH

2

2

(3.33c)

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If we define the activity of the vapor as proportional to its density , that of the dissolved

solute complex (x mH2O) as equal to the concentration of the solute in the vapor phase, and

that of the pure solid phase as unity, then

Constantlnln0

R

HmC vvv (3.33)

This equation provides a reasonably satisfactory description of solute solubilities over

restricted ranges of temperature and density.

Considering unsaturated solutions (liquid and vapor) in equilibrium with each other, the

activity of the pure solute in equilibrium with each phase must be given by

m

e

mx

xaK

aa

OH

OH

2

2 (3.34)

Since the two phases are in equilibrium, axmust be the same. Thus,

l

m

e

mx

v

m

e

mx

aK

a

aK

a

OH

OH

OH

OH

2

2

2

2 (3.35)

As above, assuming m is the same for both phases, we can then write

R

vlS

RT

Hm

C

C vl

l

v

l

v ),(lnln00

,

(3.36a)

At the critical point, the enthalphy and entropy terms vanish; the compositions must be equal.

For a restricted range of temperatures and densities, not too far from the critical, we can write

m

l

v

l

v

CC

(3.36b)

This equation has been used by Styrikovich and Martynova25 to correlate the distribution of

solutes between steam and water, with application to boiling water reactors. Figure 3.19 from

Styrikovich and Martynova25 indicates that, for many solutes, the simplified equation is

obeyed over a substantial range of pressures. In general, those materials that are weak

electrolytes in water -Al2O3, B2O3, SiO2- have high distribution coefficients and low values of

m of the order of 1 to 2. Strong electrolytes, such as NaOH and NaCl, have low distribution

coefficients and high values of m of the order of 4.

At high concentrations of solute there are effects due to the amphoteric nature of some of theweak electrolytes, and departures from strong electrolyte behavior.

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Fig. 3.19.KD, distribution of solutes between water and steam (Ref. 25)

The effect of pH is illustrated by the data for Co2+ at 680F as shown in Fig. 3.20. The

volatility data reflect the solubility behavior as shown in Fig. 3.6. Cobalt occurs only in the

form Of Co(OH)2at high pH. The solubility is low, approximately 5 g/kg as Co2+, butKD

=

0.3. For larger amounts of Co2+ in the water, the concentration in the steam will be

approximately constant at 1.5 g/kg and the value ofKDwill decrease. At lower pH, the total

concentration of the Co2+dissolved in the water is able to increase greatly as a result of the

higher solubility of the basic cobalt salts formed in this range, of the type CoOHCl.

Amphoteric compounds, such as Al2O3, show maxima in the relationship ofKDas a function

of pH.

If solubility of the ionic form in steam is negligible, then we can write for electrolytes

Dtedundissocia KClCv (3.37)

whereKDis a true distribution constant independent of concentration.

Ulmer and Klein,26in a series of tests in high pressure boilers, found somewhat lower values

of KD for sodium salts with concentrations in the water of the order of 10-4M, but better

agreement with the data of Styrikovich and Martynoval25 at higher concentrations. They

consider thatKDcan increase with concentration because of ion association and might expect

higher values ofKDat the higher concentrations.

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Figure 3.22 is a plot of the solubilities of some of the more important solutes at 255 atm, with

fluid enthalpy as the independent variable. Comparison of Figs. 3.21 and 3.22 demonstrates

the advantage of the enthalpy plot in spreading out the plots in the pseudocritical region. The

change in solubility with temperature in this region closely parallels the variation of density

with temperature, as shown on Fig. 3.23.

The data for iron as Fe3O4and copper as CuO are of major interest in these figures. Fe3O4data are not specifically referenced. The copper data are those of Pocock and Stewart 29and

Deeva.30Much of the Russian data were obtained in an experimental once-through boiler in

which the solute in the water was determined at the various parts of the cycle for various feed

concentrations. The feed concentration above which the point concentration did not increase

was taken as the solubility at that point. In the ferritic system employed, no effect of iron feed

was found at the high temperature parts of the cycle. At the mass velocities and heat transfer

rates employed, the system was therefore in equilibrium with magnetite in the absence of

additions.

The data in Figs. 3.21 and 3.22 permit an assessment of equilibrium processes in the heat

source region. The applicability to processes at high mass and heat transfer rates has beenquestioned.28

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Fig. 3.23, Density of water in supercritical region.

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However, tests in a supercritical loop16at high heat transfer rates (300,000 Btu (h ft2)] have

indicated that chemical processes proceed according to the slate of the bulk fluid, not

according to the state corresponding to the surface temperature.

Evaluation of processes in the turbine require, in addition to the data shown in Figs. 3.20 and

3.21, data in the superheat region as shown for NaCl and SiO2in Figs. 3.17 and 3.18. Similar

data for copper and its oxides are available only at a very limited range of temperatures andpressures. A compilation of data has been presented by Styrikovich et al.28and is shown in

Fig. 3.24 for the state line of a particular supercritical turbine cycle. The pressure and

temperalure curves for this turbine cycle are included in the diagram.

3-6 DEPOSITION IN STEAM-GENERATORS CARRY-OVER AND DEPOSITION

IN TURBINES

The data of the previous section can be utilized to consider a variety of problems pertinent to

nuclear steam generators, such as deposition in the heat source system, volatility, and

deposition in turbines. The magnitude of the problems varies considerably with the

parameters of the cycle, and whether it is a once-through or recirculating design. High

temperatures and pressures and once-through designs, although widely applied in

conventional power technology, are just now being considered for nuclear systems. The

problems treated will be restricted, therefore, to those associated with more immediate

applications.

3-6.1 Deposition on Heat Transfer Surfaces

Deposition has been investigated for supercritical systems by Dik et al. 31,32As noted earlier,

the simpler equilibrium approach to the deposition problem is a good approximation. The

pertinent relationships have been presented earlier in Eqs. (2.15) and (2.20) for boiling and

non-boiling systems, respectively.

The question of deposits in BWR's and PWR's will be considered in further detail in Chap. 9.

3-6.2 Entrainment

At low pressures and moderate temperatures, solute volatility is a minor source of transport

compared to physical carryover or entrainment. Consider a droplet of water, containing

sodium chloride, carried from the steam-generating to the superheating section of a reactor.

From Fig. 3.10 it is evident that solutions of NaCl are stable up to 590 F at 1000 psi.

The potential therefore exists for accelerated attack by chloride solutions, and carryover and

chlorides must be maintained at low values. To prevent the formation of concentrated

solutions, it would be necessary to maintain all surfaces above 590 F at all times. Droplets

carried in the steam without being deposited will dry out and the salt will ultimately volatilize

into the steam if the bulk concentration is less than the minimum solubility for the

superheater.

As previously noted, except for LiOH, caustic solutions will not dry out. These solutions are

aggressive to almost all desirable materials of construction so that free caustic in the steam

generating source should be avoided in superheat systems.

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Fig. 3.24. Variation in solubility of substances in passing through a turbine operating atsupercritical pressure (Ref. 28).

3-6.3 Turbine Deposits

In high pressure and supercritical cycles in nuclear systems, problems arising from the

volatile transport of solutes will be complicated by the radioactive nature of the solutes. It is

essential that this aspect of system operation be thoroughly explored prior to large-scale

nuclear undertakings of this type. Some idea of the potential problems can be provided from

the data in Fig. 3.24. The transport and retention of iron, for example, will probably be no less

than 0.1 ppb. For a 1000-MWe plant, the steam flow will be of the order of ten million pounds

of steam per hour or 8

10

10

pounds per year. Te iron transport will therefore be no less than8 pounds per year. This, and other material, will be radioactive and a potential nuisance in

turbine maintenance and repair.