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 of
water-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 various
oxides 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

F RT ln K
the activities or fugacities
Thus, for the reaction

(3.1)
of

the

phases

H2O H2 + O2
the equilibrium constant is

at

equilibrium

can

be

calculated.

Ke

f O12/ 2 f H 2
f H 2O

For the very small degrees of dissociation of pure water. which occur at the temperatures of
interest, we write
f H 2 PH2 2 f O2 2PO2

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 as f/P, me ratio of fugacity-to-partial
pressure for pure water.
Thus,

f H 2O PH2O

(3.2)

Broch2 has computed for saturated water vapor (and therefore the saturated liquid) up to the
critical point, and his data may be used in the calculations. He finds log (sat)-1 = 300P0.618,
with P in pounds per square inch.
Thus, Eq. (3.2) is written

PO2 2 PO2

Ke

(3.3)

Ke
PsatH2O
2

(3.4)

PsatH2O
or

PO22
3

and
K

PO2 e PsatH2O
2

(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

Ke

a Ni f O2
a NiO

(3.6)

PO2
(3.7)

since the solid phases have unit activity, and the fugacity of the gas maybe taken equal to its
partial pressure.
Thus,
2

PO2 K e2

(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. For
such 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 ( <200 F), is
stable even in water containing dissolved oxygen at 0.5 cm3/kg.*Copper is not
thermodynamically stable with respect to pure water, but is stable with respect to water
containing 25 cm3/kg; Ni is not stable io pure water but is stable in the hydrogenated water;
Fe is not stable, even in the hydrogenated water.

Fig. 3.1. Oxygen equilibrium pressures.

The chart is not applicable to situations where both hydrogen and oxygen exist in a
nonequilibrium state, as in the water or steam in a boiling water reactor resulting from the
dissociative process of reactor irradiation. Here, experience would seem to indicate that the
*

Volumes of gases will always refer to 0C, 1 atm, unless otherwise noted.

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 (10-4 M) 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 important
data 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
Acid

H+ + B
Proton Base

(3.9)

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

A1 B2 B1 A 2

(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
2H 2O H3O OH

(3.11)

with similar reaction for heavy water. The equilibrium for this reaction is written
aH O aOH
3
Kw
aH2 2O

(3.12)

For dilute solutions, up to 10-4 M, the activities are nearly equal to the molal concentrations m,
and the water activity is essentially constant. We may write, therefore.
4

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 of
data for the molal ion product of pure
Table 3.1
Molal Ion Product of Water

Temp., F

Kw 1014
Jones4

Temp., F

Kw 1014
Noyes et al.3

Kw 1014
Harned and
Owen5
0.57
54.6
222
403
308

75
0.90
64.4
0.64
200
43
212
55
300
208
313
268
400
500
424
645
480
645
583
340
540
628
water including a compilation from various sources by Jones4 and the data of Noyes et al.3
Harned and Owen5 present 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.

log K w

4470.99
6.0875 0.0170607T
T

The agreement between the various estimates is reasonably good.

(3.14)

Fig. 3.2. Molal ion product of water.

Some possibility exists that the experimental results of Noyes et al.3 may be in error. (See
comment by Wright et al.6)

The bases of interest in water reactor technology are KOH, LiOR, and NH4OH. 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 experimentally6 to be associated at high concentrations, and
the same is probably true for KOH at high temperatures. At the normal concentrations of
interest (10-4 M), however, only the dissociation of NH4OH need be taken into account in
computing solution pH. The dissociation constants for NH4OH and LiOH are presented in
Table 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 10-4 M solution of K2SO4 is more alkaline at
that temperature than a solution of NH3 which has a pH at 75F of 10.0{11.1 ppm NH3).
Table.3.2
Dissociation Constants: KB-NH4OH and LiOH; KA-HSO4-: Molal Units

NH4OH
LiOH
HSO4Temp., F
KB, Wright5
KB 106 Jones4
KB 106 Wright6
KA 106, a
75
17.9
120
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
10.0
520
0.84
0.0234
540
0.43
560
0.35
2.00
a
Data 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; also J. Phys. Chem,. 70, 12(December 1966).
The dissociation equilibria are calculated from the following equations:
[M+] + [H+] = [OH-]
(Condition of Electroneutrality)

(3.15)

[H+][OH-] = Kw
(Dissociation of Water)

(3.16)

[M+] + [MOB] = [B]

(Material Balance for Base)

(3.17)

M OH K

MOH

(3.18)

(Dissociation of Base)

The [ ] represent molal concentrations.

Fig. 3.3. Dissociation constants KB. for NH4OH and LiOH.

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,

Kw
Kw

H 1

H
K B H

(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, 13 Chap. 6).

3-3.2 Slightly Soluble Metal Oxides or Bases

Another group of dilute solutions of extreme importance in water reactor technology is that of
the saturated solutions of the corrosion product oxides. Jones7 has determined the
9

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 lefthand 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 for
1500 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 Cheng8 represent the temperature effect quite well, but include a
great 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 data7 for samples after about 1000 h of
constant-temperature operation. The pH is that of the solution at 550 F.
Table 3.3
Solubilities of Incoloy-600 Corrosion Producs, Corrosion, Ref. 8)

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

Water
Ammoniated
and
Hydrogen
Saturated at
Room
Temperature

pH
8.5
8.5
8.5
8.5
8.5

Element
ppb
Iron
Nickel
Chromium
Manganese
Cobalt

9.5
9.5
9.5
9.5
9.5

Water Temperature, F (C)

350(177) 450(232) 550(288)
20.5
9.5
2.7
10.9
9.0
4.5
<0.1
<0.1
<0.1
8.6
3.5
2.5
0.2
0.1
0.1
49.3
33.0
12.1

75(24)
1.0
14.4
<0.1
0.7
<0.1
16.3

200(93)
9.0
10.9
<0.1
2.6
0.3
22.9

Iron
Nickel
Chromium
Manganese
Cobalt

2.2
8.7
<0.1
0.4
0.1
11.5

2.9
4.2
<0.1
0.6
0.1
7.9

3.3
1.6
<0.1
0.7
<0.1
5.8

3.5
0.8
<0.1
0.6
<0.1
5.1

3.5
0.8
<0.1
0.3
<0.1
4.8

4.1
0.6
<0.1
0.3
<0.1
5.2

10.0
10.0
10.0
10.0
10.0

Iron
Nickel
Chromium
Manganese
Cobalt

0.8
0.2
<0.1
0.7
<0.1
1.9

1.1
0.4
<0.1
0.7
0.1
2.4

1.6
0.5
<0.1
0.8
0.1
3.1

1.0
0.7
<0.1
0.8
0.1
2.7

1.1
0.4
<0.1
0.7
0.1
2.4

2.2
0.3
<0.1
0.8
0.1
2.6

10.5
10.5
10.5
10.5
10.5

Iron
Nickel
Chromium
Manganese
Cobalt

1.8
0.6
0.1
0.2
<0.1
2.8

2.4
0.8
0.1
0.2
<0.1
3.6

2.7
0.9
0.1
0.4
<0.1
4.2

2.8
0.8
0.1
0.3
<0.1
4.1

3.0
0.7
0.1
0.2
<0.1
4.1

3.8
0.7
0.1
0.3
<0.1
5.0

10

650/343)
1.5
1.0
<0.1
1.3
0.2
4.1

Water
Lithiated
and
Hydrogen
Saturated at
Room
Temperature

pH
10.5
10.5
10.5
10.5
10.5

Element
ppb
Iron
Nickel
Chromium
Manganese
Cobalt

75(24)
0.6
3.6
<0.1
0.6
<0.1
5.0

200(93)
1.2
0.8
<0.1
0.6
<0.1
2.8

Water Temperature, F (C)

350(177) 450(232) 550(288)
1.5
1.1
1.2
1.4
4.2
1.6
<0.1
<0.1
<0.1
1.0
0.5
0.4
<0.1
<0.1
<0.1
4.1
6.0
3.4

650/343)
1.7
0.3
<0.1
0.2
<0.1
2.4

Table 3.4
Comparison of Solubilities of Incoloy-600 Corro,Ion Products
(Corrosion, Ref. 8)

[Hydrogen saturated and ammoniated water at room temperature, one-day run after
~1500 h al 340 F (171 C) Static water]
Solubility ppb Fe
pH 8.5
pH 10.0
21.4
1.8
27.7
2.0

Previous Autoclave Operation

1500 h at pH 8.5
1500 h at pH 10.0

Solubility ppb Ni
pH 8.5
pH 10.0
11.0
0.5
4.2
0.4

Table 3.5
Composition of Incoloy-600*

Element

Nickel
77.49
Chromium
15.14
Iron
6.78
Silicon
0.18
Manganese
0.22
Copper
0.10
Carbon
0.030
Sulfur
0.007
*Trademark, The International Nickel Co.
Although some scatter is still evident, the trends are reasonably clear. The solubilities of
nickel and manganese decrease substantially with increasing pH. The solubilities of iron and
chromium decrease with increasing pH but not as sharply as nickel and manganese. The
selective effect of the corrosion process is evident. The solution is enriched in iron and
manganese, and depleted in chromium and nickel, compared to the base metal.
A more classical approach to solubility measurements was taken by Mingulina et al.,9 in the
case of cobalt, which because of its longlived activity (60Co) is of extreme importance in
water reactor technology. The solubility of cobalt was studied in a boiling water apparatus at
185 atm (2720 psia, ~680F) as a function of room temperature pH and chloride content of the
water. The results of this investigation are shown in Fig. 3.6.

11

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

12

Fig. 3.6 Solubility of Co2+ in water at 680 F (saturated) (Ref. 9).

The apparatus was supplied with solutions of Co(OH)2 obtained 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 Co2+ + 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.9 at
680F, pH 10,0.008 ppm, are to be compared with those of Jones7 at 600F-pH 10 with LiOH,
less than 0.1 ppb.
Sweeton et al.10 have reported measurements of the solubility of Fe from Fe3O4 over a range
of temperatures in dilute acidic and basic solutions, saturated at room temperature with 1 atm
H2 pressure. They write, as the general dissolution reaction,

1
1
4
Fe3O 4 (s) (2 b)H H 2 (g) Fe(OH)(2b b) ( b)H 2O
3
3
3
They have interpreted their data in terms of three values of b corresponding to three soluble
forms for the iron; namely,
Fe2+
Fe(OH)+
Fe(OH)3-

b=0
b=1
b=3
13

for each of which a solubility product is defined

Kb

Fe(OH)
H P
2 b

2 b
b
1

H2

Writing Kb as a function of temperature as

log K

A / T B(ln T 1) D
2.303R

They have correlated all their data to these models.

The data and the correlations indicate the expected response of the solubility of Fe3O4 to the
pH of the solution. The following illustrative solubility data are calculated from the
correlations:
Solubility of Fe from Fe3O4
ppb
Temperature C/F
Base concentration
300/572
260/500
200/392
10-4 M
8.3
4.6
3.5
0M
16
32
89
In alkaline solution, 10-4 M, 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 conductance K, which is the conductance in reciprocal ohms of 1 cm) of
solution between parallel electrodes 1 cm apart.

14

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

1000

where C is the concentration of the solute in equivalents per liter. In all cases, the observed
conductance is corrected by subtracting the conductance of the pure solvent. Experimentally, it is
observed that the equivalent conductance is a function of concentration. The value of at infinite
dilution, termed 0 is 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

15

3.6 lists the ion conductances at infinite dilution at 25C (o+, o-) of a number of ions of interest, from
which 0 for a variety of salts can be obtained.

Table 3.6
Ion Conductance. at Infinite Dilution at 25 C, ohms-1, cm2 equiv-1
Cation

o+

Anion

o-

H+
Tl+
K+
NH4+
Na+
Li+
Ba2+
Ca2+
Sr2+
Mg2+

349.82
7.4.4
73.52
73.4
50.11
38.69
63.64
59.50
59.96
53.06

OHBrClNO3HCO3SO42-

197.6
78.4
76.8
71.44
44.5
79.8

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 temperature
is adequately represented by the Debye-Hckel-Onsager Equation

0 0 C

(3.19)

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

Table 3.7
Debye-Hckel-Onsager Conductivity Equation Parameters

0.2261
0.2289
0.2406
0.2549
0.2723
0.3016.
0.3139.
0.3318
0.4254
0.5272
0.6013
0.7269

Temperature, F
64.4
77.0
122.
167
212
262.4
284
312.8
424.4
500
537.8
582.8

50.50
60.10
99.75
146.5
201.0
266.6
298.0
340.0
523.5
650.8
737.3
870.0

Johnston11 showed that the variation of 0 with temperature was fairly well represented by the
equation

0 k n

(3.20)

16

where k and n are empirical constants and the solution (solvent) viscosity. Values for n for
some electrolytes in water are
NaCl
NH4OH
KCl
LiOH

= 0.94
= 0.71
= 0.86
= 0.75

In general, electrolytes with a high value of 0 at room temperature have lower values of n
than electrolytes with lower room temperature values of 0. Figure 3.7 shows the variation of
0 for a number of electrolytes over the temperature range of interest, including H-OH. These
data were obtained from the summary of Wright et al.6 and 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 3.8
Limiting Equivalent Conductances of Several Ions
at Temperatures to 400 C (Ref. 12)
ohms-1 cm2 equiv-1
Temperature, C

H+

Li+

Na+

K+

NH4+

OH-

Cl-

100 (1 atm)
200 (0.865 g/cm3)
300 (0.7125 g/cm3)
400 (0.8 g/cm3)

364
824
894
945

156
329
562

151
304
459
440

195
364
504
455

206
394
579

447
701
821

211
391
561
520

A useful application of these data is the calculation of the diffusion coefficient for the
infinitely dilute solution. From the Nernst Formula,

Z Z2
D (cm 2 /sec) 8.93 10-10T 1

Z1 Z2

0 0

0 0

For the dilute solutions normally of interest in reactor technology, the difference between
and 0 is 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
constant KDI defined by

K DI

C A
C A

(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

17

Table 3.9
Ion Association-KDI (Ref. 6)
Electrolyte
Temperature, C
NaCl
KCl
HCk
NaOH

281
306
281
306
260
306
218

KDI
0.22
0.093
0.49
0.12
0.12
0.035
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 region
below 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 surfaces
is 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,

P1 P10 N1

(3.22)

This equation can be rearranged to

P10 P1 P10 1 N1 P10 N 2

(3.23)
18

and

P10 P1
N2
P10

(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 temperature P1T is equal to the total applied pressure , assuming that T is greater
than the saturation temperature of the pure solvent at the pressure . The solution vaporpressure curve is limited by solubility or critical phenomena, of which the former is of
primary concern in current water reactors.

3-4.1 Strong Bases

The 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 low
solubility 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.
19

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

NaOH

LiOH

NaOH

LiOH

NaOH

Concentration
Grams per 100 Grams H2O
5
5
8.4
10
10
15.6
15b
15
25
Weight Percent
4.76
4.76
7.83
8.59
8.59
13.5
13.04
13.04
20.0
Molality
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
433
a
NaOH data calculated from vapor-pressure data in the International Critical Tables; LiOH data calculated from smooth curves in Figs. 3, 4 and
5 of Report BMI-1329.18
b
Saturated, approximately.

20

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.
21

Fig. 3.10. Vapor pressure of saturated solutions of some electrolytes.

3-4.2 Sodium Phosphates

Sodium phosphates are employed in boilers to precipitate alkaline earth phosphates and, in
part. to maintain an alkaline condition, while at the same time limiting the alkali concentration
during the evaporation of boiler water. Whirl and Purce1l20 have suggested the coordinated
phosphate control whereby the pH-phosphate relationship is maintained at, or slightly on, the
acid side of the curve for pure Na3PO4. The latter would precipitate on concentration of the
boiler water, and high levels of free caustic would be prevented. In addition to the difficulties
of defining an appropriate curve for pure Na3PO4, or allowing for the effects of other
buffering agents in the boiler water, it has been shown by Ravich and Shchcrbakova21 and
confirmed by Marcy and Halslead 22 that the solid phase separating from a solution of Na3PO4
at the temperatures of interest in high-pressure boilers is more acid than Na3PO4.
Marcy and Halstead22 found a congruent concentration at a ratio of 2.8 Na-to-l PO4 at
temperatures of 470,540, and 572F, whereas Ravich and Shcherbakova found congruent
composition ratios of 2.85 at 572 F and 2.65 at 689 F. To prevent the accumulation of free
caustic during precipitation of sodium phosphates, Marcy and Halstead recommend that the
Na/PO4 ratio be maintained at or slightly below 2.8, instead of the value of 3.0 as originally
recommended by Whirl and Purcell. Figure 3.11 shows pH vs phosphate curves for ratios of
sodium-to- phosphate of 2.0 to 3.0, taken from Marcy and Halstead's paper.

22

Fig. 3.11. pH of sodium orthophosphate solutions having various mol ratios of sodium-tophosphate (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 boiler
technology. 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 NH3 at various concentrations
and high temperatures.
The equilibrium is between un-ionized ammonia in the liquid and NH3 in the vapor. Thus,
[NH3]l [NH3]v

(3.25)

23

and

NH3 v
NH3 l

KD

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 NH3 and [NH4OH] as (1 -1) NH3. The relationship is

1
K
1 B H
KW

(3.26)

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

Various values of are assumed from which NH3 is calculated, and a curve of vs NH3
constructed. KD is then given by

NH3 v
K
1 - NH3 D

(3.27)

The apparent distribution coefficient is, therefore,

NH3 v

NH3

K D 1 - K D'

(3.28)

Figure 3.12 shows KD for NH3 as 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 fission
in 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 + H2O HI + HIO

(3.29)

Hypoiodous acid, in turn, can disproportionate to iodic acid and iodine. Thus,
5HIO HIO3 + 2I2 + 2H2O

(3.30)

The hydrolysis reaction increases with temperature and pH, and is inversely proportional to
the concentration of iodine. Dilute solutions, less than -10-5 M, are extensively hydrolyzed
even in neutral solution. Volatility is contributed by both I2 and HIO (a weak acid), since the
degree of dissociation of HIO will decrease with increasing pressure. The apparent KD
defined as

HIO I 2 v

HIO HI I 2 l
is a complex function of temperature and pH.
Styrikovich et al.24 have published the results of a series of determinations of the distribution
of iodine compounds between steam and water, as a function of pressure (temperature) and
low temperature pH (pH0), for saturated steam.
24

Fig. 3.12. Distribution coefficient KD of 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 10-4 M (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 the
increased volatilization from HIO. Figure 3.14 shows the apparent distribution coefficient KD
for HIO at 425 and 1000 psi. Here, the coefficients show maxima at a value of pH0 of 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 410-5 at a pH 10. Ordinarily, iodine derived from
high-temperature water reactors is present largely as iodide, which will have a very low
volatility except at very low pH values.
25

Fig. 3.13. KD values 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 of KD of the order of 10-4 or 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/cm2 pressure (o) and at
30 kg/cm2 pressure (0) (Ref. 24).

26

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 temperature
of 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 reducing
its 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. Line A-B is the composition of the saturated
liquid phase. Line C-D is the critical composition. Line E-F is the composition of the vapor in
27

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 isobars I-J are the vapors in equilibrium with the unsaturated solutions in the subcritical
(water) region. The isobars K-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-vapor
region.
It is advantageous to consider separately the data on volatilization from solutions, and of
solute solubility in steam.

28

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

29

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)
vapor
vapor

(3.31)

representing a solute molecule reacting with m water molecules to form a complex soluble in
the vapor phase. The equilibrium constant for this reaction is defined by the equations
F 0 H 0 TS 0

(3.32a)

F 0 RT ln Ke

(3.32b)

Ke

a xmH 2 O v

(3.33c)

a x amH 2O v

30

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

ln Cv m ln v

H v0
Constant
R

(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

ax

a xmH 2O

(3.34)

K e aHm2O

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

a xmH 2O a xmH 2O

K e aHm O K e aHm O
2
2

v
l

(3.35)

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

0
Cv
H l ,v S 0 (l , v)
m ln v

Cl
l
RT
R

(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
Cv v

Cl l

(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 the
weak electrolytes, and departures from strong electrolyte behavior.

31

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)2 at high pH. The solubility is low, approximately 5 g/kg as Co2+, but KD =
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 of KD will 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 of KD as a function
of pH.
If solubility of the ionic form in steam is negligible, then we can write for electrolytes
Cv
undissociated K D
Cl

(3.37)

where KD is a true distribution constant independent of concentration.

Ulmer and Klein,26 in 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 10-4 M, but better
agreement with the data of Styrikovich and Martynoval25 at higher concentrations. They
consider that KD can increase with concentration because of ion association and might expect
higher values of KD at the higher concentrations.

32

Fig. 3.20. Volatility of Co2+ in steam as a function of pH (Ref. 25).

At 2550 psi (~670F), NaCl is estimated from the data of Wright et al.6 to have an apparent
dissociation constant KDI of about 0.01.
From the data of Ulmer and Klein,26 the results listed in Table 3.11 are obtained. These data
can also be employed by simultaneous solution of the dissociation and distribution equations
[Eqs. (3.21) and (3.37)] to obtain the following:
KDI = 4.8 10-3
KD = 8.55 10-4
These parameters reproduce the curve of Ulmer and Klein26 over the entire range of the data.
This value for KD is less than the value shown in Fig. 3.19 for NaCl at 2550 psi,
approximately 2.0 10-3. There is probably no real discrepancy between the data of
Styrikovich and Martynova25 at intermediate concentrations, and Ulmer and Klein26 at low
concentrations. It is further evident that at the very low concentrations of solutes normally
found in nuclear reactors, the apparent distribution coefficient KD for electrolytes should be
quite low. Values of the order of 1 to 3 10-4 for radioisotopes have been reported by
Brutschy et al.27 for the Vallecitos Boiling Water Reactor (~1000 psi).
Table 3.11
True and Apparent Distribution Coefficients
NaCl
Na in Water, ppm
23
230
Na in Steam, ppb
3
100

-4
Apparent KD
1.3 10
4.3 10-4
(Degree of Dissociation of NaCl)
0.923
0.62
1-
0.077
0.38
Undissociated Na, ppm
1.88
87.5
-3
True KD
1.69 10
1.14 10-3
The other region of interest, that of solute solubility in steam from the saturated liquid to the
superheat and transcritical areas, is most readily examined over the whole temperature range
for constant pressure conditions. For supercritical pressures, the isobar represents a
continuum, with rapid but continuous variations in the pseudocritical region. Styrikovich et
al.28 have presented a set of solubility curves for some materials of interest at pressures of 255
and 300 atm. Figure 3.21 shows the solubility plotted as a function of temperatures for a
variety of materials.

33

Fig. 3.21. Dependence of the solubility of substances in water

on temperature, at P = 255 atm (Ref. 28).

Fig. 3.22. Dependence of the solubility of substances

in water on enthalpy, at P - 255 atm (Ref. 28).
34

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 Fe3O4 and copper as CuO are of major interest in these figures. Fe3O4
data are not specifically referenced. The copper data are those of Pocock and Stewart29 and
Deeva.30 Much 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 been
questioned.28

35

Fig. 3.23, Density of water in supercritical region.

36

However, tests in a supercritical loop16 at 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 SiO2 in Figs. 3.17 and 3.18. Similar
data for copper and its oxides are available only at a very limited range of temperatures and
pressures. A compilation of data has been presented by Styrikovich et al.28 and 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.31,32 As 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.

37

Fig. 3.24. Variation in solubility of substances in passing through a turbine operating at

supercritical 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 1010 pounds per year. Te iron transport will therefore be no less than
8 pounds per year. This, and other material, will be radioactive and a potential nuisance in
turbine maintenance and repair.

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