AKTIEBOLAGET ATOMENERGI
STUDSVIK, NYKÖPING, SWEDEN 1974
AE-40K
THE DEPOSITION KINETICS OF CALCIUM HYDROXY APATITE
ON HEAT TRANSFER SURFACES AT BOILING
by
T Kelén, R Gustafsson
ABSTRACT
An experimental investigation was performed to study the deposition of calcium hydroxy apatite in boiler furnace tubes and on nuclear
steam generator tubing. The investigation was run in a high-pressure
loop at pressures up to 10 MPa. The heat transfer surface was run
at densities of heat flow rates up to 0. 9 MW- m"
and boiling. The
deposition rate constants thus recorded were in the range 0. 1-1 00
urn- s~ . Increments in the density of heat flow rate and in the water
temperature increased the deposition rate sharply. No clear
dependence of electrical conductivity or pH were traced. Sodium
polyacrylate had a marked inhibiting effect on the deposition. The deposition was recorded by measuring the gamma radiation from Ca-47,
which was used as a tracer isotope.
Printed and distributed in September 1 974
CONTENTS
page
1.
INTRODUCTION
3
2.
EXPERIMENTAL
3
2. 1
Loop construction
3
2.2
Determination of the deposition rate constant
4
2.3
Water chemistry control
5
3.
RESULTS
6
3.1
General remarks
6
3.2
Magnitude and reproducibility of the deposition rate
constants
6
3.3
Influence of steam quality
7
3.4
Influence of temperature
7
3. 5
Influence of density of heat flow rate
7
3.6
Influence of pH
7
3.7
Influence of electrical conductivity
8
3. 8
Influence of concentration of calcium- and silicaspecies
8
Influence of polyacrylate dosing
8
3. 9
4.
5.
DISCUSSION
8
4. 1
Range of the deposition rate constants
8
4. 2
Influence of density of heat flow rate
9
4.3
Influence of temperature
10
4. 4
Influence of chemistry
11
CONCLUSIONS
11
ACKNOWLEDGEMENTS
12
REFERENCES
13
TABLES
14
FIGURES
APPENDIX 1
- 3 -
1.
INTRODUCTION
The deposition of contaminants on heat transfer surfaces is a
well-known but disturbing phenomenon which may cause trouble in
conventional steam boilers as well as in nuclear reactor systems
if it is not properly controlled. Typical of the operational disturbances to which this phenomenon leads are rise of temperature, fall
in pressure» hide-out and, in nuclear primary systems, contamination with radioactive corrosion products.
Phosphate conditioning of the feed water involves special deposition problems, since in the presence of metal ions such as those
of the alkaline earths, phosphate precipitates may be formed. A
common contaminant in phosphate treated boilers and nuclear steam
generators is calcium hydroxy apatite, which is generally attributable
to calcium present in the make-up water. The aim of the present investigation was to study the deposition of this contaminant on heat
transfer surfaces under boiling conditions and to elucidate the parameters which determine the deposition rates.
2.
2.1
EXPERIMENTAL
Loop construction
The investigation was run in the high-pressure loop Maggan.
The loop consists of a primary circuit with pressure regulation,
a dosage section and a drainage section. Operational data are as
follows:
Pressure:
Temperature:
Circulation flow:
Dosage flow:
Power:
Density of heat flow rate:
Volume of water in the primary
circuit:
max 10 MPa (100 bars)
max 310°C (saturation temperature)
max 1 kg* s-1
2-20 g-s" 1
max 2-20kW
-2
max 1. 5 MW- m
5 dm"
A schematic diagram of the loop is presented in Fig 1.
The test section was electrically heated using an AC-source
operating between 0-10 V. The power supply was regulated in a
- 4 -
preheating section by an adjustable transformer and in the test section by a Variac transformer. The power in each part could be varied
between 0 and 20 kW corresponding to a range of density between 0-1.5
MW- m~
for the heat flow rate.
The calcium hydroxy apatite was obtained by mixing streams
of CaNO, and phosphate solutions using two piston pumps. The formation of the apatite was confirmed by X-ray diffraction analysis.
The feed water flow throughout the runs was held at a constant
rate of 2 g* s~
which gave an exchange constant for the loop water
of 4M0" 4 s ~ \
The steam quality in the test section was calculated from values
for the coolant flow and the subcooling, the latter being recorded
continuously on a pen-recorder during the experiments.
The pH and the electrical conductivity of the loop water were
recorded in the drain water.
2.2
Determination of the deposition rate constant
The amounts of calcium in the test section and in the water were
monitored by measuring the gamma radiation from Ca-47 (half life
4. 5 d, obtained from Risö, Denmark) which was added as an isotopic
tracer.
Two Nal scintillation detectors were used; one of which was
mounted at the test section to measure deposited calcium. The second measured the calcium concentration in the water, generally the
3
drainage water, which was sampled in 25 cm aliqots with a Vogel
pipet and transferred to a plastic vessel placed on the detector.
The detectors were fed by separate HV-units but were alternately switched to a common single channel analyzer connected to
a sealer.
The deposition rate constant was calculated from information
concerning the slope of the graph for deposited calcium vs time and
the calcium concentration in the water. The constant is defined as
follows:
dc,
-dT = k ' c w
where
0)
- 5 -
= mass of deposit per unit area, kg* m
t
= time, s
k
s rate constant, m* s
c
= concentration in the water, kg*m
w
-1
-3
The detector located at the test section and that used for the
water samples were calibrated against each other in such a way
that k could be calculated from the values for the relative counting
rate. A detailed description of the method is given in the appendix.
2.3
Water chemistry control
The investigation was based on a water chemistry designed to
simulate the normal chemistry of drum boilers at medium pressures;
the significant parameters being
pH
= 10
conductivity
~ 100 U-S- cm
CaO
= 1 0 g- m"
-1
(1 0 ppm)
Stepwise changes of this chemistry were made in some runs by
changing the pH, the conductivity or the calcium concentration.
The pH was kept at 1 0 by feeding a solution with a specific concentration of Na,PO.. Increments of the pH were made by simply
increasing the phosphate concentration. The pH was lowered by
changning from Na-PO, to mixtures of Na^HPO, and NaHLPO..
The conductivity was increased by dosing with Na.SO.-solutions.
Sudden changes between the various water chemistries were
made in order to obtain distinct transition points on the deposition
vs time plots. To achieve this, a special procedure was used as
follows. A 8mall volume of solution was fed into the loop in the space
of a few minutes. Although the volume concerned was too small to
displace any considerable part of the loop water, it contained chemicals that produced the desired change in water chemistry on
mixing with the loop water. The feed water system was then switched
over to new supply-tanks containing solutions satisfying the requirements of the newly imposed water chemistry. This procedure permitted adjustment of any chemical parameter to a new level within
- 6-
the space of i 0 to 20 minutes. Relying only on a direct change of
supply tanks to affect a transition several hours would have been required to establish a new equilibrium.
The feed water was degassed by bubbling a stream of nitrogen
through it.
3.
3.1
RESULTS
General remarks
The same test section of stainless steel SIS 2333 was used
throughout the investigation, the surfaces exposed to the water consisting initially of stainless steel oxides. These surfaces, however,
were covered with deposits of calcium hydroxy apatite during the preliminary running in of the loop. Accordingly the material of the test
section should be incapable of influencing the course of deposition
during the experimental runs.
The influences of the morphology, chemical condition and structural condition of the deposition surface were not investigated. It is
possible that if the test section had featured a different surface
roughness then a slight shift might have been observed for the set
of k-values. Furthermore a prolonged deposition run with constant
running data might have resulted in a deposit with a different surface
condition, which could in turn have influenced the deposition rates.
Although such long-term influences were not studied systematically
in this investigation, some preliminary runs of long duration indicate
that they are not very significant.
During each run the test section activity and the drain water
activity were plotted as a function of time. Examples of these plots
are given in Figs 2-5.
3.2
Magnitude and reproducibility of the deposition
rate constants
In Table 1 are gathered data concerning the operating conditions
and the resulting deposition rate constants. The values of the con-1
-1
stants range between zero (less than 0. 1 urn- s" ) and 80 unv s" .
The standard deviations of the constants obtained from independent runs under steady state conditions are presented in Table 2.
In general they do not exceed 50 % except in the runs at 224°C, where
the constants were rear the detection limit.
- 7 -
3. 3
Influence of the steam quality
In one run the steam quality in the test-section was varied byaltering the power supplied to the preheater section. The steam content at the inlet of the test section was kept initially at 1 . 2 % and at
the outlet at 2. 3 %. It was then increased to 3. 1 % at the inlet and
4. 2 % at the outlet by raising the preheating power from 1 0 to 1 7 kW.
The detector, which was placed half-way up the test section, recorded
the same deposition rate constant before and after the change. The
density of heat flow rate was held constant during the run.
The result indicates that the steam quality does not inflwence
the deposition rate within the range of steam contents used in this investigation.
3. 4
Influence of temperature
The deposition rate constant is plotted versus the temperature
in Figs 6 and 7. The plots show a strong positive dependence on temperature in the range investigated, namely 224-310 C.
3. 5
Influence of density of heat flow rate
Linear plots of the deposition rate constant vs the density of heat
flow rate are given in Fig 8, while log plots are shown in Fig 9. These
plots show that an increase in the heat flow rate leads to a sharp increase in the deposition rate.
The approximately linear relationship between deposition rate
constant and density of heat flow rate exhibited by the logarithmic
plot features slopes which lie between two and three for all the three
temperatures investigated. This demonstrates that the deposition rate
constant was approximately proportional to a value between the second
and the third power of the density of heat flow rate.
3. 6
Influence of pH
It was not possible to detect any definite influence of pH. Positive
changes were recorded after both reductions and increments of pH.
On the other hand sudden releases of deposit were recorded in some
cases. During one run no change was recorded of the deposition rate
although the pH was increased from 1 0 to 11.
- 8-
It is possible that during long runs a change in pH will lead to
a variation in the deposition rate since the deposition seems to be
sensitive to pH changes. It is, however, more probable that the r e corded changes were a direct result of disturbances of the water
chemistry itself rather than of changes in the actual value of the pH.
3.7
Influence of electrical conductivity
No significant influence was traced. In some cases an increase
in conductivity resulted in a sudden release of deposit. In other cases
nothing happened at all. There were no indications that the deposition
rate increased after dosing with Na^SO.-solution.
3.8
Influence of the concentration of calcium- and
silica-species
No significant influence was traced.
3. 9
Influence of polyacrylate dosing
Dosing with polyacrylate had a strong inhibiting influence on the
deposition. In the three runs in question a part of the deposit was r e leased to the water immediately after dosing was started. No deposition was recorded as long as the polyacrylate remained in the system.
In two of the runs the deposit actually continued to decrease after the
initial shock-release.
4.
DISCUSSION
The authors do not know of any literature data for the deposition kinetics of calcium hydroxy apatite on heat transfer surfaces under
conditions of high pressure boiling. The deposition of iron oxides is,
however, treated by several authors, of which Mankina et al [ i ] give
a good account for the deposition in fossil-fired boilers, while
Charlesworth [2] treats the deposition in nuclear boiling water systems.
4. 1
Range of the deposition rate constants
Deposition rate constants obtained in the present investigation
are compared with Mankind' s and Charlesworth' s in the table below.
- 9-
Source
Magnitude of
Density of
deposition r a t e
heat flow rate,
-2
MW • m
constant, t xm-s -1
Mankina
et al 1 )
l0
-1_1()
10 2 -1C ,
Charlesworth '
0. 03-0. 2
4
10"1-1C
This work
0. 26-1 . 4 0
0. 3 - 0 . 9
Temperature
Type of
deposition
iron oxides on
TP-1 70-boiler carbon steel
~ 285°C
-224-310°C
iron oxides
on zircaloy
apatite on
stainless steel
1)
Calculated from Mankinas data.
2)
Roughly estimated from Charlesworth' s data on the concentration of Fe in the water and the surface concentration of deposit
by assuming equilibrium between deposition and release and a
release probability of 1 • 1 0
4. 2
s
Influence of the density of heat flow rate
Both Mankina f1 "J and Charlesworth [2J report a strong dependence
of deposition on the density of heat flow rate, rp. Mankina proposes
an empirical proportionality to cp .
Charlesworth' s exponents range between 1 . 0 and 5. 5 When all
the data are considered, however, he estimates the best overall
value to be about 2.
In Fig 9 the slopes corresponding to the exponents 2 and 3 are
shown for comparison. The present data seem to fit in somewhere
between these two slopes.
Although the dependences on the density of heat flow rate obtained in this investigation are not strictly quadratic, the Mankina
constants have been calculated from the plots in Fig 9. The constant
is defined by
dt
M
w
«p
o-
where
= concentration of contaminant on the surface, kg-m
-2
5 -1
-2
= Mankinas constant, m -s -kW
w
= concentration of contaminant in the water, kg-m
-3
= density of heat flow rate, kW-m"
In the table below the Mankina constants obtained in this work
are compared with Mankinas own data.
Source
Mankinas constant,
5 -1 , w - 2
m • s «kW
Mankina et al
1 . 7 . ID" 10
Remarks
224°C
250°C
310°C
This work
It was mentioned earlier that alterations made to the steam content did not have any effect on deposition. This observation is in
good agreement with the results of other investigations.
4.3
Influence of temperature
The influence of temperature is appreciable, as can be seen from
Figs 6 and 7. The mechanism behind this is not known.
Kelén and Arvesen[3] report the value 1 . 0 m4-°C-kW~1 -kg"1 as
the thermal resistance number for a typical calcium hydroxy apatite
deposit obtained under boiling conditions. This value was used in combination with the mean values for the deposition rate constants given
in Table 2 to estimate rates of temperature rise on heat transfer surfaces at different pressures. The results are listed in the table below.
Pressure
MPa
i)
Density of heat
Rate of
flow rate, MW-m"2
temperature rise
2.5
0. 3
2 C* month"
4.0
0.4
5°C-week" 1
10.0
0.9
3°C«hour"1
assuming 10 rng-kg
calcium hydroxy apatite in
the water and no release of deposited material
.
11
.
The above values indicate the magnitude of the problem produced
by the rapid rise in temperature in steam generating equipment which
follows an increase in the pressure and in the density of heat flow
rate. The indications are that it becomes practically impossible to
run a unit at 10 MPa and 0.9 MW-m
with phosphate conditioning,
a fact which agrees well with normal water chemistry specifications.
4.4
Influence of chemistry
The calculation of deposition rate constants using the formula
(1) in section 2.2 presumes that the deposition rate is proportional
to the contaminant concentration, or in other words, that the deposition rate constant is independent of the contaminant concentration. To
check this, the concentration of apatite in the water was increased
during the course of a number of runs. Since no definite alteration
of the constant was detected, it was concluded that the equation, on
which the calculation was based, was valid in the ppm-range. It is,
however, probable that concentration effects will appear at low concentrations, where an appreciable part of the calcium is in solution.
Changes in pH and electrical conductivity or the addition of silica-species did not affect the deposition to a significant degree. The
only significant chemical influence which was observed was that produced by sodium polyacrylate, which acted as a deposition inhibitor.
This agrees with Ahrnbom' s L4J observations on a number of Swedish
drum boilers that have been conditioned with polyacrylate.
With the exception of the polyacrylate it seems as if the water
chemistry has played a secondary role in the deposition process
studied here. The determining parameters for the deposition rate
constant seem to be largely the temperature and the density of heat
flow rate.
5.
1.
The order of magnitude of the deposition rate constant was
0.1 -1 00 p,m» s"
2.
CONCLUSIONS
under the conditions investigated
The steam content did not influence the deposition rate in the
nucleate boiling regime.
3.
The deposition rate constant was roughly proportional to a function between the second and third power of the density of heat
flow rate.
4.
The deposition rate constant was appreciably larger at higher
temperatures.
5.
No clear dependence of pH and electrical conductivity was traced,
nor f^id the addition of silica influence the deposition rate.
6.
Sodium polyacrylate showed a strong inhibiting effect on the df osition.
7.
The results indicate that the deposition rate can be restricted
by limiting one or more of the parameters temperature, density
of heat flow rate and calcium hydroxy apatite concentration.
Another possibility is to add polyacrylate.
ACKNOWLEDGEMENTS
The authors gratefully acknowledge the advice and suggestions
offered by Lars Ahrnbom at the Swedish Steam Users Association.
We also wish to thank those of our colleagues at AB Atomenergi
who were involved in the investigation, and in particular Mr Mac
Arnell for his help with the experimental equipment and the evaluation of the data and Mr Marian de Pourbaix whose group was responsible for the construction and servicing of the Maggan-loop.
The investigation was carried out at the Section for Corrosion
and Reactor Chemistry, Aktiebolaget Atomenergi, Stud svik, and was
financed by grants from the Swedish Board of Technical Development.
REFERENCES
MANKINA, N.N. et al. ,
Teploenerg. 6 ( 1 ^ 9 ) ' 2 p . 79.
Transl. by J. Jackson:
Formation of iron deposits in recirculation steam boilers.
Brit. Power Eng. 2 (1 961 ):4 p. 60.
CHARLESWORTH, D.H. ,
The deposition of corrosion products in boiling-water systems.
Chem. Eng. Progr. Symp. Ser. 66 (197O):1O4 p. 21.
KELÉN, T. , andARVESEN, J . ,
Temperature increments from deposits on heat transfer surfaces: the thermal resistivity and thermal conductivity of deposits of magnitite, calcium hydroxy apatite, humus and copper
oxides. 1972.
(AE-459).
AHRNBOM, L. ,
Adding of polyacrylate for reduction of the phosphate content in
the boiler water and of the water side deposits in the tubes. 1 974.
(SVF-14) (in Swedish).
To be published in Svensk Papperstidn.
- 14 -
Table 1 Operating conditions
Run No
1
2
3
4
Date
7306 13
7306 14
7306 15
730618
Pressure, MPa
2.5
8.0
6.4
10.0
2.5
4.0
8.0
2.5
310
224
2. 1
Coolant flow, kg« s
0. 18
0. 17
224 250 294
0.17
Inlet steam content, %
2. 1
2. 1
2.1
Outlet steam content, %
3. 5
3.5
3.5
3.2
Density of heat flow
rate, MW.m" 2
0. 4
0.4
0.4
0.3 0.9 0
pH in drain
10 . 1
10. 1
10.1
10.0
n in drain, u-S* cm
110
110
120
110
Temperature,
C
224 294
4.0
250 280
Concentration of «
additives, mg- kg
CaO 10
Deposition rate
.
constant k, \irr\- s
0.2
Run No
5
7
8
Date
7:$0627
730629
730702
P r e s s u r e , MPa
2.2
CaO 10
1.3
1.9 13.1
CaO 10
0.7
0.7
10.0
10.0
224
310
310
Coolant flow, kg* s"
0. 18
0. 17
Inlet steam content, %
2. 1
2. 1
C
0. 17 0.17
5.5 0.8 0.3
0.21
2.1
Outlet steam content, %
3. 2 4.3
3.2
Density of heat flow
rate, MW-m" 2
0. 3 0.6
0.3 0 . 9 0
pH in drain
10.0
-10
10
11
11
H in drain, uS-cm"
Concentration of
additives, mg.kg"
100
100
100
500
500
CaO 10
CaO 10
Deposition rate
.
constant k, u,m« s
0. 6
4.4 73 r e l e a s e
1.4
5.3 2 . 1
3.5
3.5
3.2
0.4
CaO 10
11
5.3
2.1
CaC) 10
2.5
Temperature,
0. 18
11
15
0.9
- 1 5 -
Table 1 cont
Run No
9
10
12
Date
730703
730704
730808
Temperature,
4.0 6 . 4 6.4 6.4
250 280 280 280
2.5
P r e s s u r e , MPa
224
C
Coolant flow, kg* s
0.18 0.18 0.22
Inlet steam content, %
Outlet steam content, %
3.5
Density of heal flow
r a t e , MW-m
pH in drain
3.2
0.4
11
10
11
2 50
0 . 18
2.1
3.5
4.0
0.17
2. 1
1.2
3. 5
2.3 4.2
0. 4
0.3
10.1 10. 1
~7 - 1 0
3.1
10.0
K in drain, nS» cm"
100 450 450
100
Concentration of
additives, mg-kg"
CaO 10
CaO 10
Deposition r a t e
.
constant k, jim* s"
0.5
Run No
13
14
15
Date
730809
730810
730813
P r e s s u r e , MPa
0.4
release
100
120 350
85
CaO 10
0.9 3.0 7.7
18
0.5 0.5
2.5
10.0
10.0
224
310
310
Coolant flow, kg- s~
0.18
0. 17
0.17
Inlet steam content, %
2.1
2.1
2.1
Temperature,
C
Outlet steam content, %
3.2
4.3
Density of heat flow
r a t e , MW-m" 2
0.3 0.6
2.1 3.2
0
4.3
0.3 0.6
2.1 4.3
5.3
0
0.9
0.6
pH in drain
10.0
10.0
10,0
H in drain, nS» cm"
90
100
90-100
Concentration of .
additives, mg*kg"
CaO 10
CaO 10
Deposition r a t e
,
constant k, y,m» s~
0.3
0.8 6.0
0.9
CaO 10
50
0
52
82
- 16 -
Table 1 cont
Run No
16
17
18
19
Date
730814
730815
730816
730826
10.0
10.0
4.0
4.0
310
310
250
250
Coolant flow, kg* s
0. 17
0. 17
0. 17
0. 17
Inlet steam content, %
2.1
2.1
2.1
2. 1
Outlet steam content, %
4.3
4.3
4.3
3. 5
Density of heat flow
rate, MW-m"2
0.6
0.6
0.6
0.4
pH in drain
10.0
P r e s s u r e , MPa
Temperature,
C
c
95 550
90-100
CaO 10
CaO 5 - 1 0
3.5
1.6
Concentration of additives, mg-kg
CaO 10
CaO 10
56 5.3
36
11
3.5
1. 1
Run No
20
21
22
23
Date
730822
730823
730827
730828
4.0
4.0
4.0
4.0
250
250
250
250
Coolant flow, kg* s
0. 17
0. 17
0. 17
0. 17
Inlet steam content, %
2. 1
2. 1
2.1
2.1
Outlet steam content, %
3,5
3.5
3.5
3.5
Density of heat flow
rate, MW-m*2
0.4
0.4
0.4
0.4
pH in drain
10, 1
10.1
9.9
10.0
110 220
110 140
110
100
Concentration of
additives, mg-kg"
CaO 5 - 5 0
CaO 10
acrylate 600
CaO 10
acrylate 600
CaO 10
SiO2 50
Deposition rate
.
constant k, urn. s
3. 3
4. 4 release
2.2
3.1
C
H in drain, (j,S*cm
r
500
100
Temperature,
C
a
9.8
100 500
P r e s s u r e , MPa
I
r
9.7
H in drain, y,S* cm
Deposition rate
,
constant k, urn* s
9.8-10.0
9.7-10.0
0
release
2.9
- 17 -
Table 1 c ont
Run No
Date
24
25
26
730829
7 30904
730905
Pressure, MPa
Temperature, C
Coolant flow, kg»s~
Inlet steam content, %
Outlet steam content, %
Density of heat flow
rate, MW. m " 2
4.0
250
0. 17
2. 1
pH in drain
H in drain, u,S« cm
Concentration of
additives, mg« kg"
9.9
Deposition rate
,
constant k, |jim»s~
Run No
Date
P r e s s u r e , MPa
Temperature, C
Coolant flow, kg*s~
Inlet steam content, %
Outlet steam content, %
Density of heat flow
rate, MW.m' 2
pH in drain
H in drain, JAS* cm"
Concentration of
ajditives, mg-kg
Deposition rate <
constant k, ii,m«s"
27
8.0
2.5
2.5
224
224
0. 18
0. 18
2. 1
3.5
294
0. 17
2. 1
3. 5
2.1 3.2 5.3 2. 1 3.2 4 . 3
0.4
0.4
0
2.1
0.3 0.9 0
0.3
100 400
CaO 10
SiO2 50
10.0 10.5
120 300
CaO 10
SiO 2 50
CaO 1 0
3.1 2 . 9
7.3 8.2
0
28
29
30
31
730907
730910
730911
730912
2.5 6.4 10.0
224 280 310
0.18 0. 17 0. 17
2.1
0
10 . 0
120
7.8 0
4.0
4. 0
250
250
0. 17
0. 17
2.1
2.1
2. 1
3.2 4.3 2 . 1 3 . 3 5 . 3
0.4
0
0.3 0.6 0
0.6 0 . 9
10.0
10.0
10.0
100
150
130
1.0
110
CaO 10
CaO 10
0
0
4.0
250
0.17
2.1
5.1 22
135 140
CaO 10
3.5
CaO 10
0
10.0
i 00
U
0 .6
3. 1 4 . 3
0.3
0.6
10 . 0
120
100
150
CaO 10
release 4. 2 15 0.6 3.7
0.2
Table 2 Mean value and standard deviation of k at various
pressures and densities of heat flow rate
v, MW • m
T"
1
P
°c
MPa
224
2.5
250
280
295
310
4.0
6.4
8.0
10.0
0.3
0.4
0.6
0.9
No of values
5
4
3
2
Mean, urn* s
0. 3
0.4
0.8
4. 1
Dev, j^rrr s
0.3
0.3
0.6
5.3
Dev, %
100
75
75
130
No of values
2
10
3
1
Mean, urn- s
0.6
2. 1
3.8
15
Dev, p,m* s
0. 1
1.2
0.4
-
Dev, %
17
57
11
-
No of values
3
Mean, urn- s
3.3
Dev, |i,m* s
1.6
Dev, %
48
No of values
Mean, (im* s
3
5.0
Dev, y,m« s
2.6
Dev, %
52
No of values
2
3
4
2
Mean, u,m« s
5.2
15.4
48. 5
78
Dev, \in\' s
1. 1
5.8
8.7
6
Dev, %
21
38
6
8
Spray-condenser
'Feed
t
X
Test section
•mm
—->
.
. . . ^ ,^
water
;
I
, preheatfr
i
5
L_
J
ö
Preheating section
Drainage
I
i
. ._
Spray-flow
circuit
Primary circuit
B-
Y
Fig 1 Schematic diagram of the high-pressure loop Maggan
r i tc n i l
Feed w.i
i'i f c u i L
noo
1000
(O
900
a,
8
800
w
Q
O
H
700
D
O
600
224
I
500
310°C
280
I
0
I
I
8
10
8
10
TIME, h
OJ
W
H
15
W
10
2
O
H
<
oi
—
i—•
5
W
u
0
0
TIME, h
Fig 2
Deposition at various temperatures. Run 28
CONCENTRATION IN THE
WATER, cps
AMOUNT OF DEPOSIT, cps
O
O
tSJ
O
O
i—
o
o
T
o
o
O
c
CL
w
ET
3*
ex-
o
A
«
O
K
2
o
00
oo
3
o
o
00
o
o
r
o
o
o
o
o
o
o
1000
900
_
8
800
-
O
h
700
_
600
_
09
O<
O
h
W
Q
O
500
30
W
X
H
20
§
< , (Q
H
u
10 __
8
TIME, h
Fig 4
Influence of silica on deposition. Run 25
10
1150
1100 —
CA
04
U
1050
H
>-<
W
O
u
Q
1000 —
O
950
—
acrylate 600 ppm
900
8
0
10
TIME, h
W
Ä
100
n
50 —
8
TIME, h
Fig 5 Influence of poly aery Ute on deposition. Run 21
PRESSURE, MPa /non-linear scale)
2.5
4.0
6.4
8.0
90
80 1-
70
60
CD
•
50
X
H
40
u
w
30
§
20
8
W
Q
10
0
200
250
TEMPERATURE, °C
Fig 6 Influence of temperature
300
10.0
PRESSURE, MPa (non-linear scale
2.5
4.0
6.4
10"
8.0
10.0
T~~
I"
10
(0
10
<
H
CO
§
U
w
§
t-*
H
O
10
1
-1
200
i
i
i
250
TEMPERATURE, °C
yi
g 7
Influence of temperature, k in log-scale
i
i
300
i
90
80 _
70 _
60 U
(O
_
50
40
Z
O
30
-
20
-
w
8
W
10
Q
0
O
0.2
0.4
0.6
0.8
DENSITY OF HEAT FLOW RATE, M W - m " 2
Fig 8
Influence of density of heat flow rate
1.0
2.0
1.5
—
1.0
—
0.5
—
0.0
—
-0.5
-
(O
I
C
o
-1.0
-0.6
-0.4
-0.2
0.0
log cp (cp in MW* m~ )
Fig 9
Influence of density of heat flow rate, logarithmic scale
APPENDIX
CALIBRATING OF THE DETECTORS
The two detectors may be characterized by their respective
calibration constants kA and k , defined by
t
w
k = P/p and
kw = Q/q
'n
where
-3
P
p
Q
= specific activity in the test section, dps*m
= counting rate of the test section detector, cps
= specific activity measured on the water sample detectors,
dps* m~3
q
= counting rate of the water sample detector, cps
The deposition rate constant k is defined by
-srdt = k • cw
where
c , = surface concentration of deposit, dps-m
-1
k
= deposition rate constant, m* s
c
= concentration in the water, dps# m
r
w
k may then be expressed as
k =
dt
-2
0)
w
The surface concentration c , is obtained from the recording
d
made of p by assuming that the activity would give the same counting rate both homogenously dispersed in the solution and deposited
on the tube wall. This assumption is justified by the fact that the
detector sees the test section approximately as a straight line.
The counting rate p is transformed to specific volume activity
P by the calibration constant:
=P
APPENDIX i :Z
The transformation to specific surface activity, c , is then
achieved by multiplying by that volume of the test section seen by
the detector and dividing by the corresponding inner area:
(2)
c , = •=
—•
. • P =- • p •k
d Z *TT . r« 1
2
t
where
r
= inner radius of test section, m
1
= length of test section in view of the detector, m
The disappearance of the tube length " 1 " in the formula signifies
that the exact field of view of the detector need not be known.
c
is obtained from the recordings of q by
c
= Q =q
w
(3)
w
n
Substituting the expressions for c and c
k =
d
into (1) gives
fT
dT ( 2
dt
w
1 I
q
2
w
The determination of k from the counting rates of the respective
detectors thus leads to an acquisition of knowledge of the radius of the
test section and of the ratio kVk .
t' w
The values of r was 4 mm during all the runs.
The ratio k /k
was determined by filling the loop with a gamma
active solution and recording the counting rate p. The same solution
was then measured on the water sample detector, giving the counting
rate q. Since the specific activity was the same in both c?ses, k /k w
could be determined from the expressions
P'
w
w