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Numerical Simulation of the Anodic P r o t e c t i o n f o r a Continuous
Digester
Said AbdiRahman Mohamed
A thesis submitted in conformity w i t h the requirements for the Master of Applied Science
Graduate Department of Chexnical Engineering and Applied C h e m i s try
University of Toronto
@ Copyright by Said AbdiRahman Mohamed 1999.
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Numerical Simulation of the Anodic Protect ion for a Continuous
Digester
Master O£ Applied Science 1999
w Said Abdirahman Mohamed
Chemical Engineering and Applied Chernis try
University of Toronto
In this study a mathematical mode1 was developed to understand
anodic protection of the Kraft digester. Several polarization
curve cases, for stainless steel and carbon steel, were
studied.
The results showed that, a system wi th low critical c u r r e n t
density, such as the cooking zoner was the easiest to protect
with only 0.358 V applied potential. However, a system with
high c r i t i ca l current densi ty , such as the impregnation,
showed t h a t one small cathode is insufficient to initiate the
anodic protection process. In this case, an applied potential
as high as 26 V was required, which may lead to high rate
hydrogen gas production at the cathode.
It was found that the large concetric cathode case and the
four ca thodes w i t h 2 .54 c m r a d i u s case p rov ided a good
protection.
1 would like to thank my supervisor Prof. Don E. Co-mack f o r his
support while doing my thesis work. Also 1 would like to extend
an additional spec ia l thanks to Prof. D. W. Krik for using his
lab to obta in the polarization curves, t o Prof. S. J. Thorpe for
using his lab polishing equipment to polish the metal samples,
and t o Rami and D r . J. Graydon for their he lp .
1 a lso apprec ia te the valuable discussions about anodic
protection with Winston Shim and Derek Mawhinney. Finally 1
would like to thank rny family f o r their he lp .
TABLE OF CONTlENTS
Abstract .................................................. ii ........................................... Acknowledqement iv
List of Figures .......................................... . v i
List of Tables ............................................ xii Nomenclature ............................................ xiii
1. INTRODUCTION ...........................o..............,. ..l
......................................... 2, LITERATURE SURVEY 4
2.1 The Pulping Process ................................. 4
............ 2 . 2 . Corrosion in the Kraft Liquors Digester 7
2-2.1. Stress Corrosion Cracking (scc) ............. 8 2.2.2. Passivity .................................. IO
2.2.2.1 Polarization Curves and the
Potentiostat ................................. 12 2.2.2.2 Reactions On Carbon Steel Metal in
........................ Alkaline Solution 16
......... 2.2.2.3. Effects of Chernical Additions 20
........................... 2.2.3. Anodic Protection - 22
.................... 3. POLARIZATION and EXPERIMENTAL RESULTS 26
........... 4. MATHEMATICAL MODELING of the CONTINüûUS DIGESTER 37
4.1. Mathematical Representaion of the Polarization
Curves .............................................. 37
......................... 4.2. The Boundary Element Method 48
....................... 4.3. Applied Potential Calculation 50
4.4. Program description ................................ - 5 2
5 . DISCUSSION and RESULTS ................................... 55
........................................ 5.1.Cooking Zone - 5 6
.................................... 5.2.Impregnation Zone 58
5.3.Lab Low Concentration Electrolyte .................... 61 ................... 5.4.Lab High Concentration Electrolyte 69
................................................ 6. CONCLUSIONS 88
......................................... 7 . RECOMMENDATIONS - 9 0
8 . REFERENCES ............................................... 91
.............................................. 9 . APPENDICES - 9 6
List OF Figures
Fig.2.1.The Kamyr continuous d i g e s t e r ............................ 6
Fig.2.2. Anodic po la r i za t ion curve with the illustration of the
.................. three zones i t is nonnally divided to 2 3
Fig .2 .3 . The p o l a r i z a t i o n curves for the anode and the cathode
.................. when oxidizers ( i n h i b i t o r s ) are used - 1 5
Fig.3.l . The three electrode ce11 used in obtaining polarization
........ curves for carbon and s t a i n l e s s s t e e l s i n the lab 27
Fig.3.2. P o l a r i z a t i o n curves for carbon steel, which were
obtained in the u n i v e r s i t y l ab ........................ .28
Fig.3.3. Polarization curves for carbon s teelr s forward and
backward scans in the low concentration electrolyte ... 30
Fig.3.4. Polarization curves for s t a i n l e s s steel 316L, which
was obtained in the university lab ..................o.* 32
Fig.3.5. Polarization curves f o r stainless s t e e l 316L f o r the
high concentration Comparing fresh and old
e l e c t r o d e s . . . . . . . . . . . . .* . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 2
Fig.3.6 Polarization curves obtained by a Company inside the
.............................................. digester - 3 3
Fig.3.7. The cathode polarization curve for the carbon and
stainless steel obtained for the low concentration
electrolyte ............................................ 36
Fig.4. 1. Carbon steel polarization curve for the high
concentration electrolyte, using the normal
electrochemical equations ....................-......... 43
Fig.4.2. Carbon steel polarization curve for the low
concentration electrolyte, using the normal
electrochemical equations ............................. - 4 3
Fig.4.3. Low concentration backward scan, using the electro-
chemistry curve fit ................................... - 4 4
Fig.4.4. Polarization curve for the stainless steel in the
high concentration electrolyte, and its curve
fit using the electrochernistry equations ............... 44 Fig.4.5. Polarization curve for stainless steel in the low
concentration electrolyte, and its curve fit
using the electrochemistry equations ........... . . . . . . . . f i
Fig.4.6. Polarization cuve for an old stainless steel in the
low concentration electrolyte, and its curve fit
using the electrochemistry equations ................-O - 4 5
Fig.4.7. P o l a r i z a t i o n curve for t he cooking zone obta ined by
a Company inside the continuous d i g e s t e r
w i th t h e s p l i n e f i t .................................... 47
Fig.4.8. P o l a r i z a t ion curve for t h e impregnat i o n zone obtained
by a Company inside t h e continuous d i g e s t e r
with t h e s p l i n e f i t ................................... - 4 7
Fig.4.9. The p o l a r i z a t i o n curve f o r the 304 s t a i n l e s s s t e e l
........................... and the its s p l i n e curve f i t 48
The program flow
Fig.5.1. P o l a r i z a t i o n curves for the cooking zone and t h e model
r e s u l t ................0......*0............0...........57
Fig.5.2. P o l a r i z a t i o n curves f o r t h e impregnation zone w i t h
the mode1 r e s u l t f o r one cathode case .................. 59
Fig.5.3. Polarization curves f o r t h e impregnation zone with
t h e mode1 r e s u l t f o r two cathodes case. ................ 59
Fig.5.4. P o l a r i z a t i o n curves for t h e low concen t ra t ion case,
.............................. when one cathode was used 63
Fig.5.5. P o l a r i z a t i o n curves for the low concentration case,
............................ when two cathodes was used - 6 3
Fig .5 .6 . Current density distribution around the geometry used
...................... in the mode1 for one cathode case 64
Fig .5 .7 . Current density distribution around the geometry used
in the mode1 for two cathodes case ..................... 64
Fig.5.8. Potential distribution around the stainless steel
surface while reducing the current applied on the
................................................ cathode 66
Fig.5.9. Current density distribution while reducing the current
applied on the cathode ..................*........... -66
Fig.5. IO. The mode1 result when the system was backed using t h e
backward curve, when the carbon steel start to
.............................................. passivate 68
Fig.5. 11. The model result when the system was backed using the
backward curve, when the carbon steel is in the middle of
........................................... passive zone 68
Fig.S.12. The model result when the systern was backed using the
backward curve, when the carbon steel is in a point after
............. which the system passes to the active zone 68
Fig.5.13. Carbon steel polarization curve with the model result,
.......................... for the concentric geometry - 7 0
Fig.S.14. The result for 20 V on the cathode side, when old
stainless steel was used ............................... 7 2
Fig .5 .15 . The result for 20 V on the cathode side, when fresh
stainless steel was use ..........,.....,............... 7 2
Fig.5.16. The result for the carbon steel for 26 V on t h e
cathode side, when the o l d stainless steel was used ... - 7 3
Fig.5.17. The result for the carbon steel for 26 V on the
cathode side, when the fresh stainless steel was used..73
Fig.5. 18. The mode1 result f o r one cathode at 1224 mV.. . . . . . . . 7 5
Fig.5.19. The model result f o r one cathode a t 1112 mV.. . . . . . . . 7 5
Fig.5.20. The model result for one cathode when a l 1 p o i n t pass
back t o the active region ............................. - 7 6
Fig.5.21. Model result for two cathodes case, when the
polarization curves for high concentration was used .... 7 6
Fig.5.22. Model result for three cathodes case when the
polarization curves for high concentration was used .... 78
Fig.5.23. Model result for fou r cathodes case when the
polarization curves for high concentration was used .... 7 8
Fig.5.24. This graph shows the effect of changing the number of
cathodes on the applied potential ...................... 80
Fig.5.25. Comparing the current density dis tribution around the
carbon steel when the number of cathode was varied ..... 80 Fig.5.26. Cürrx i t dcisity distritütiûu a r v ü ~ c ! t h e c r thcd- :.hile
............... cornparing different numbers of cathodes 81
Fig.5.27. Model result for a cathode placed 100 cm away from the
................................................. centre 82
Fig.5.28. Model result f o r a cathode placed 140 cm away from the
centre ................................................. 82
Fig.5.29. Current density distribution around the carbon steel
in the passive area .............................o.....-..... 84
Fig.5.30. Current density distribution around the stainless
.......... steel, when the carbon is in the passive area 84
Fig.5.31. Current density distribution around the carbon steel
.............. while changing the sizes of four cathodes 84
Fig.5.32.Carbon steel polarization curve with the mode1 result,
......................... for the concentric geometry ..8 5
LIST OF TABmS
Table -3.1. Potential ranges for the active and passive zones,
with the critical and passive current densities for the
r t z U i e d czcoc ..............,............................. 34
Table.4.1. The curve fit Parameters for carbon steel in the
h igh concentration electrolyte ........................... 41 Table.5.1. Summary of the applied potential and the current
density for the studied cases .......................... . .87
Tab1e.A. 1 The curve f i t parameters for the forward scan for
carbon steel in the low concentration case ............. 97
Tab1e.A. 2. The curve fit parameters for the backward scan for
carbon steel in the low concentration electrolyte ...... 98
Tab1e.A. 3 The curve fit parameters for the backward scan f o r
carbon steel in the low concentration electrolyte ...... 99 Tab1e.A. 4. The curve fit parameters for the forward scan f o r
the high concentration case for the s t a i n l e s s steel ... 1 0 0
Tab1e.A. 5. The curve f i t parameters for the forward scan for
an old the stainless steel in the concentration
........................................... electrolyte 101
TableB. 1. Conductive for the lab and Corrosion Service L t d
...................................... electrolyte solutions 102
1. INTRODUCTION
Due to t h e presence of highly c o r r o s i v e chemicals such as, NaOH
and Na2S, i n p u l p production, many p ieces of equipment i n t he
pulp and paper i n d u s t r y face a s e v e r e corrosion problem. This i n
turn led t o a search for means t o confront this c o s t l y problem.
To prevent c o r r o s i o n i n the continuous d iges te r , which is built
from an ou te r s h e l l of carbon s tee l with an i n t e r i o r concentr ic
s t a i n l e s s s t e e l pipe, d i f f e r e n t techniques have been used.
Anodic p r o t e c t i o n is one of t he p r o t e c t i o n methods t h a t has been
demonstrated t o ef fectively reduce corrosion a t tack . I t has been
successful against s t r e s s co r ros ion cracking (SCC) , which i s the
major corrosion type tha t a t t a c k s t h e upper p a r t (irnpregnation
zone) o f cont inuous diges t e r s .
The main idea of anodic p ro t ec t ion i s t o force t h e p o t e n t i a l of
the corroding surface t o pass t h e p o t e n t i a l range a t which SCC
normally t akes place to a s e t p o t e n t i a l i n t he pas s ive region.
This is achieved by applying a high cur ren t dens i ty t o force the
surface p o t e n t i a l t o pass the c r i t i c a l c u r r e n t dens i ty
po ten t i a l . Then the current is reduced u n t i l it reaches the
passive zone where a passive film c o n s i s t of an imer l aye r of
Fe30c and an o u t e r l aye r of yFe203 is formed on t h e su r f ace . This
leads t o a decrease in the rate of SCC and o t h e r corrosion
types.
There are two configuration setups applied in the anodic
protection system. In one case, the cathode is placed concentric
with the central stainless steel pipes, and in the other
configuration the cathode ( s ) is mounted to the outer wall
(digester) or the central pipe wall. It was found that, with
time, cathodes fastened to the digester wall failed to protect
the digester, and led to more rapid corrosion." In this study
the effect of cathode position, size, and the number of cathodes
used will be studied.
A mathematical model was developed using the boundary element
method (B.E) , to gain a better understanding of the continuous
digester corrosion problem and anodic protection. The
polarization curves utilized in the boundary element rnethod for
the carbon steel and the stainless steel studied, were generated
in the university lab and some were generated inside an
operating degester.
The model results showed that a digester with a low current
density polarization curve will be easily protected with only
one or two cathodes, when the cathode(s) are placed on the
stainless steel wall. Since stainless steel also consumes some
of the applied current density, it is important to consider both
metals when irnplementing anod ic p ro tec t ion . P lac ing t he cathode
concen t r i c a l l y around t h e central pipe solves this problem and
reduces t h e r e q u i r e d app l i ed p o t e n t i a l and c u r r e n t dens i t y . Also
it was f o n d tha t it is d i f f i c u l t t o protect t h e upper p a r t of
t h e digester, where the concen t ra t ion is high, wi th on ly one
cathode. This i s due t o the f a c t tha t t h e h igh cu r r en t d e n s i t y
needed t o f o r c e t h e systern t o pass the c r i t i c a l cu r r en t d e n s i t y
may be l a r g e r t han what the cathode could p r a c t i c a l l y d e l i v e r .
A t t h a t high c u r r e n t density and p o t e n t i a l range hydrogen gas
may be produced in a high r a t e , and t h i s may lirnit the c u r r e n t
needed t o p a s s t o the anode. However, four cathodes placed
closer t o the s t a i n l e s s s t e e l p ro tec ted both metal su r f ace s wi th
minimum i n i t i a l and f i n a l current d e n s i t i e s .
2 . LITERATURE SURVEY.
2.1 The Pulping Process:
Pulp production is
production . Pulping
following processes :
one of the important steps in paper
is normally performed by one of the
chemical, semichemical and mechanka1
pulping. By one of these three
two, the hardwood or softwood is
the lignin is dissolved causing
processes or a combination of
digested. In chemical pulping,
the wood to decompose into its
fibers components. Also this can be done mechanically by
grinding the wood using a large revolvi~g grindingstone. With
this process the longest - f ibered
semichemical case, both processes
quality pulp.
pulp is obtained. In the
are combined to get high
The pulping process is achieved by using batch or continuous
digester. E a r l y pulp production was performed by using the batch
designer. However, in 1930 the f irst continuous pulping process
was introduced as the Ashland defibrillator for mechanical
pulping. The first chemical pulping continuous digester, a 50
t/d unit, was introduced by Kamyr in Sweden in 1948. There are
different chemical process applied in the pulp and paper
industry to produce pulp. Soda process which was the first
chemical process used, is no longer produced in the big
industries i n North America, but çtill produced in some mal1
production industries. Kraft pulping has become the most
dominant pulping process in North America.
While trying to improve the quality of the pu lp product, many
other processes were introduced, such as Neutra1 Sulfite
Semichemical NSSC, polysulifide-type kraft pulping, Soda AQ, and
s u l f i t e . Also with the increase of environmental concern, sodium carbonate or soda-oxygen have been installed.
This study is directed a t studying corrosion prevention by
anodic protection of continuous digesters. Therefore, i n the
following more explanation and description of the continuous
digester w i l l be given.
Fig.2.1 shows the Kamyr continuous digester with impregnation
and chip immersion, which is built of carbon steel A516 grad 70
to maintain the high pressure. It consists of a rotary pocket
ieeder with stem balancing and emptying, concentric
t e s t epa c i and DL(~P>
Recycled L q u o r i
Fig.2. 1 The Kamyr continuous digester.
l iquor i n l e t s pipes and s t r a i n e r s f o r ex t r ac t ion of t h e l i quor .
T h e d i g e s t e r is divided i n t o t h r e e zones, impregnation zone,
cooking zone, and washing zone. The performance of t h i s type of
d iges te r has been improved by int roducing a mechanical o u t l e t i n
the lower p a r t t o discharge the pulp. This i n t u r n improves t h e
mechanical p rope r t i e s of t h e pulp, which a re a l s o enhanced by
recycling cool weak l i quor . The washing sec t ion is an add i t iona l
improvement t o remove the ch ips and any mater ia l s on t h e wal l ,
2 . 2 . Corrosion in the Kraft and Soda Liquors Digester:
Corrosion Fs a tough problem t o be faced i n the pulp and paper
industry. Most of the equipment i n t h i s i ndus t ry s u f f e r s a
severe and rapid corrosion r a t e , which leads t o a very c o s t l y
problem. The corrosion types taking place i n the pulp and paper
industry are mostly, stress cor ros ion cracking, corrosion
thinning, and p i t t i n g corrosion. S t r e s s cor ros ion cracking
normally occurs a t the upper p a r t of the d i g e s t e r i n t h e
v i c i n i t y of the welds, and it l e d t o t h e c a t a s t r o p h i c f a i l u r e of
a d iges t e r i n 1980. I t w i l l be discussed i n d e t a i l i n t h e
following s e c t i o n . 5 ~ 8 r 2 0 e "
Corrosion th inn ing is a r ap id t h i m i n g which tends t o occur
toward t h e bottom p a r t of t h e d iges ter , where the p o t e n t i a l is
low. Because of the wide fluctuation in the potential with tirne
in that zone, anodic protection may n o t be completely effective.
Carbon steel weld buildup is used for many digesters which
experience thinning . However, such buildup can be considered as
a temporary solution, since the digester continues to experience
thinning at a rapid or more rapid rate than it did before. An
alternative to the carbon steel weld buildup, is the application
of steel weld overlay.
Pitting corrosion is a result of muriatic acid washing at high
temperature or poor circulation. Cleaning caused pits are
hemispherical in shape and have a rough appearance. Also pits
rnay be due to digester liquor. This type of pit has an irregular
shape.
In the f ollowing sections stress corrosion cracking, passivity
and developrnent of the polarization curves, and anodic
protection will be discussed in more detail.
2.2.1. Stress Corrosion Cracking (SCC)
With the failure of the Pine Hill digester, Alabama in 1980,
stress corrosion cracking of the welds became one of the major
problems fac ing kraft d i g e s t e r s . T h e upper p a r t of t h e d i g e s t e r
is the most suscept ib le s ec t ion t o such cor ros ion . T h i s i s due
t o the high concentrat ion of t h e caustic and Na2S i n t h a t
section. A survey revealed t ha t more than ha l f of t h e continuous
d iges t e r s i n North America were cracked . 2 4 t 2 5 t 2 Î I n f a c t ,
corrosion cracking (SCC) was de tec ted t o be occurr ing
v i c i n i t y of welds. I t is a r e s u l t of s t r e s s over the
l i m i t of t h e metal, which exposed simultaneously
concentrated a lka l ine so lu t ion . F i r s t , i t was c a l l e d
embrittlement, because alkal ies were one of t h e causes
stress
a t t h e
e l a s t i c
t o ho t
c a u s t i c
leading
t o SCC. S tud ie s of anodic p o l a r i z a t i o n of carbon s t e e l showed
that SCC i s most l i k e l y t o happen near the t r a n s i t i o n between
ac t ive and passive regions. To s t u d y SCC, a slow s t r a i n ra te was
used because of i t s a b i l i t y t o produce SCC i n specimens i n a
r e l a t i v e l y s h o r t time. 'A."
Yeske and Guzi [26 ] , us ing a S i l v e d s i l v e r - s u l f i d e e l ec t rode as
reference e lec t rode , found t h a t the p o t e n t i a l requi red f o r SCC
t o occur w i th in the range of -870 to -830 mV vs SCE i n summer.
I n winter, t h e lower limit was no t change. However, the upper
1 s t w a s above -830 mV v s SCE. They also observed that at -790
mV vs SCE, there was no cracking.
Singbiel and Garner [22,23], came to almost the same conclusion
in their studies. They saw that A516 grade 70 and A285 type C
specimens cracked. A secondary crack was seen at potentials
between -970 and -870 mV vs SCE at temperature of 90 O C for a
solution of 90 g/l NaOH + 35 g / l Na& and at -900 mV vs SCE f o r
a temperature of 110 OC. At a potential of -1200 mV vs SCE, a
transguranular cracking occurred. They detected two d i f f e r e n t
active-passive regions for the dif ferent concentrations of NaOH
and Na& One near -900 mV vs SCE as a result of the presence of
Na& and -1100 rnV vs SCE with the presence of NaOH.
Studies found that on the surface of some metals and alloys a
thin corrosion resistant layer is formed, on which most
commercially available resistant alloys depend on to resist
corrosion, which is known as the passive film. At f i rs t , it was
believed that the passive film was a monolayer. However, it has
been observed that the passive film current density decreases
with time, which means that the passive film thickens with tirne.
Evans was one of the early people who worked on the chemistry of
the passive film formation. The f i l m consists of an inner l a y e r
of Fe304 and an outer layer of yFez03. Uhlig and CO-workers gave
an explanation for the chemisorption of oxygen on the surface of
the transition metals. They found that oxygen is adsorbed in the
presence of uncoupled d-electrons . Optical measurements found the thickness of the film to be between 1 O 10 m. Other
studies have shown in some cases that also OH- is adsorbed on the
; -, surface of the metal to form the passive fiim.-*-
For a metal or alloy to reach passivity, it needs to show
active-passive behaviour in its polarization curve . Also to
maintain passivity, the passive region should be broad. With the
understanding of the passivity theory, better rneans of corrosion
protection were developed. Protection of the corroding material
with the help of passivation could be achieved by adding
oxidizers ( inhibi tors) or using anodic protection. Anodic
protection will be explained in d e t a i l later
However, to achieve protection by using
equilibrium potential of the oxidizers should
system should be in the passive region.
in this chap
oxidizers,
be high, and
Hence with
er.
the
the
any
disturbance the passive film will not breakdown. However, adding
oxidizers may lead to a fluctuation of the potential with time
leading to pitting and localized corrosion. Passive f i l m
breakdown could take place, if H S and/or Cl' are present in the
electrolyte. But at high temperature Crowe and Troman [12]
reached a conclusion that the passive film will be very stable
and will not breakdown easily.
More explanation of t h e r e a c t i o n mechanism t o produce t h e
pass ive f i L m and t he e f f e c t of the a d d i t i o n o f chemicals t o the
s o l u t i o n w i l l be given i n the fo l lowing s e c t i o n s .
2.2.2.1 Polarization Cumes and the Potentiostat:
P o l a r i z a t i o n curves are a good rnap o f the co r ro s ion behaviour of
the metals and a l l o y s . To develop t h e p o l a r i z a t i o n curves a
p o t e n t i o s t a t is used t o measure t h e c u r r e n t de l ive red t o t h e
surface. The e lec t rochemical ce11 c o n s i s t s of an anode wnich is
the meta l t o be studied, a r e f e r ence e l e c t r o d e , and a counter
e l e c t r o d e (ca thode) . I t starts w i t h a s tepwise inc rease of t h e
p o t e n t i a l o f the anode from the co r ro s ion p o t e n t i a l t o more
noble p o t e n t i a l , and a t each p o t e n t i a l t h e cu r r en t w i l l be
recorded. T o understand i f a meta l o r a l l o y is going t o form a
passive f i l m , a p o l a r i z a t i o n curve should be a v a i l a b l e a t hand.
Most anodic p o l a r i z a t i o n curves, as i n Fig.2.2., show t h r e e
zones: active, pass ive , and t r a n s p a s s i v e regions. The active
zone is the zone i n which co r ro s ion t akes place, The passive
zone is where a passive film is f o m e d on the metal su r f ace .
This film reduces the r a t e of corrosion and increases the
service life of the equipment. In the transpassive zone, it is
believed t h a t the passive film breaks down and initiation of
localized co r ro s ion starts. To have a stable passive
surface of the metal and effective anodic protection
zone should be broad.
f i l m on the
the passive
1
Active 1 Passive
-400 400 -700 -600 -500 -400 -300 -zoo -tw O
Potanlal mv vs HmgO r i t
Fig.2. 2 . Anodic polarization c u v e with the illustration of the three zones it is normally divided to.
Fig.2.3 shows the polarization of carbon steel as the anode, and
the polarization line of the cathodic reaction taking place on
the carbon steel surface. The figure is a representation of the
case when inhibitor are used to protect the systern. Ip and Ic
are the passive and critical current densities respectively. The
two curves intersect at two main points; one is in the passive
region and the other is in the active region. In the passive
zone the current is almost constant and ewal to ip, which is the
passive current density at which the system could be protected.
In the active zone where the two l i n e s intersect, corrosion
takes place, where Eccrr stands for corrosion potential. The
current for this potential is the lirniting current, which is the
maximum current density that reaction rate can not exceed This
is due to a limited diffusion rate of the oxidizing ions, it is
called concentration polarization. The limiting current density
can be calculated using the following equation:
Where n is the number of charge transfered in the reaction, F is
Faraday's constant, C is the bulk concentration of the
electrolyte, 6 is the thickness of the diffusion layer, and D2 is
the diffusivity of the species. To obtain a better lasting
protection with the inhibitor, ir should be greater than the
maximum current density of the active region, which is known as
the critical current Ic. iL is increased by higher solution * .
concentration, higher temperature, and higher solution rnixing. "-
corrosion
i L
L -- . . . -- 1 1
1 i Ezorz
Fig.2. 3. The polarization curves for the anode and the cathode when oxidizers (inhibitors) are used.
Whereas in the case of the anodic protection the carbon steel
surface potential is moved to a set potential in the passive
zone, and kept there while applying the passive current density.
With no current disturbance, the film was found to be difficult
to break?
The polarization curves are sensitive to the rate of
polarization, electrolyte composition, alloy composition, and
from lab to lab. The polarization curves are not reproducible,
since the passive current
polarization curves given
steel digester, show sorne
density changes with time. The anodic
by the previous studies for the carbon
lab to lab variations.
In the mathematical model t w o different groups of polarization
curves where used, depending on the location at which they were
collected. One group was obtained by Corrosion Service Ltd.
inside the digester. The other group was obtained in the our
laboratory using synthetic white liquor . There are three curves obtained by Corrosion Service Ltd., one for each stainless steel
and carbon steel in the impregnation zoner and one for carbon
steel in the cooking zone. The lab collected curves are grouped
as low concentration and hiqh concentration curvêsr depending on
the concentration of the electrolyte used. Each se t was
consisted of one polarization curve for each carbon steel and
stainless steel. To study the anodic protection both curves were
used together in the mathematical model.
2 2.2.2 Reactions On Carbon S t e e l Metal in A l k a l i n e Solution:
In the pulp and paper industry an alkaline solution is used to
digest the woodchips. To be able to reduce the corrosion rate of
Carbon Steel Digesters in such environment, it is necessary to
understand the chemical reactions taking place on its surface.
One of the major reactions i n the solution is dissolution of the
su l f ide as given by Crowe and Troman [12],
Na$ + H20 + 2 ~ a + +OH- + HS-
O H and
surface
surface
HS- are formed and start t o cornpete for adsorption on the
of the digester. Depending on which anion is on the
of the alloy, one of two processes may occur in that
area. F i r s t , when the OH' is
to be formed by the anodic
Charlton [Glas
adsorbed, a passive film is l i k e l y
oxidation proposed by Wensley and
The above reaction is believed to take place at E.=,,,, which is
the potential at the cr i t ica l current density. After that point
the system reaches passivity and the passive film is produced.
Other studies have shown that Fe204 is believed to be the inner
part of the film, which continues to oxidize by producing Fe103
or FeOOH as follows
d
Fe,O, + 2H.O -+ 3FeOOH + H+ + e or
This leads to the thickening of the passive film. Though there
are different mechanism for the formation of the passive film,
in general, the above iron oxides are believed t o form the
passive film.
I n the case t h e HS- i s adsorbed, the following r e a c t i o n s take
place.
- Fe+HSd -+ FeS+H' + 2 e - ( 2 . 7 )
FeS+HS- + FeS, + H' + 2 e (2 . 8 )
However, both of the Fes and FeS- w i l l d issolve producinq Fe203
and FeOOH.
The oxide formation r a t e slows wi th the increase o f the r a t i o of
HS- t o OH-, which support t h e adsorpt ion compet i t ion. A s t h e
po ten t i a l increases toward the t ranspass ive reg ion the OH- i s
displaced by HS' and the adsorption r eac t ion becomes
HS;, + HS,
Therefore, p a r t of the metal s u r f a c e s t a r t s t o be covered with
HS-. The HS- may deprotonated producing S O ~ which is more
reac t ive with ~e'' o r ~ e " leading t o faster breakdown of the
passive film, and with the d i s so lv ing of the passive f i l m the
surface becornes unprotected r e s u l t i n g with p i t t i n g .
It was determined tha t repass iva t ion of p i t is poss ib l e by
reducing t h e p o t e n t i a l of the cathode until the current s t a r t s
3 t o decrease. However, most of the s t u d i e s were lab based and
there is no evidence i f it would work in the f i e l d appl ica t ion .
To maintain a p a s s i v e f i l m being on the su r f ace o f the metal,
t h e ra te of HS- t h a t d i s so lves t h e film should be equa l t o o r
less than t h e r a t e of OH- t h a t forms t h e new p a s s i v e film.
Otherwise, w i t h t i m e the pass ive f i l m w i l l breakdown leaving the
rnetal unprotected. Therefore, i t i s important t o main ta in the
cur ren t d e n s i t y i n the passive zone. This shows how important it
is t o c o n t r o l the t o t a l cur ren t t h a t w i l l maintain p a s s i v i t y .
On t h e ca thode side i n anodic p ro t ec t i on , t h e fol lowing
reac t ions rnay take place. F i r s t , i t w i l l s t a r t w i t h the
adsorption of hydrogen atoms on t h e i r o n a l l oy , known a s the
Volmer r eac t i on ,
Hydrogen t hen starts t o be produced by one of t h e following
reac t ions steps .
Heyrovs ky reaction,
The production of Hz gas at a high rate may reduce the current
density that produced by the cathode to pass to the anode.
Another possible problem is that excess hydrogen may lead to
hydrogen embrittlernent in the stainless steel surface close to
cathode,
2.2.2.3 Effects of C h d c a l Additions.
In this section, t h e effect of several chemical additives on the
corrosion rate are discussed. In fact, in some cases the
digester corrosion was brought to rest unprotected, by chemical
addition .
Some of the practical results achieved by Mueller [IO] are, that
addition of 1 g / l of s u l f u r to white liquor containing 3.2 g/l
sodium thiosulfate passivated the steel tube even without anodic
current. The addition of 1 g/l sulfur to 5.2 g/l NaSOl leads to
the borderline at which a specimen may not become passive. With
the addition of 1.5 g/l of sulfur to white liquor anodic
protection is needed.
Wensley and Charlton [6] observed the effects of different
chemical solution on the current and potential of the anodically
protected digester. They found that the cur ren t dens i ty maximum
was increased w i t h t h e increase of Na7S a t c o n s t a n t NaOH, NaOH a t
constant Na& and temperature from 25 t o 85 OC. Dimethydislfide,
pyrogallol , ox id ized black l iquor , and hydrogen peroxide a l s o
increased the c u r r e n t dens i ty maximum, which i n turn increased
t h e corrosion ra te of the mild s t e e l .
Addition of g r e a t e r than 0 .8 g / l sodium polysulfide a t 80 O C ,
0.5 t o 3.25 g/l of sodium polysu l f ide t o half s t rength w h i t e
l iquor a t 75 O C , and unoxidized black l i q u o r , resul ted i n a
decrease i n t h e anodic c r i t i c a l c u r r e n t dens i ty . Also an
increase i n t h e temperature from 96 t o 177 O C showed the sarne
r e s u l t . However, t h e c r i t i c a l anodic current was unchanged w i t h
t he addi t ion of 5 g/l sodium t h i o s u l f a t e a t 30 OC, sodium
chloride, sodium carbonate, and sodium s u l f a t e a t 35 O C . This
shows a l s o that t hey are not promoters o r i n h i b i t o r s of t h e
corrosion i n mild s t e e l i n w h i t e liquor.
A caus t ic concent ra t ion between 20 and 200 g/l and temperature
between 25 t o 90 O C produced an increase i n the magnitude of the
c r i t i c a l current dens i ty which reflects the greater d i f f i c u l t y
i n a t t a i n i n g p a s s i v i t y i n t h e s e s o l u t i o n s . In the case of
th iosu l f a t e , i t w a s observed t ha t t he magnitude of c r i t i c a l
anodic cu r ren t was rnaximized, which i n d i c a t e s that it is a
corrosion a c t i v a t o r . Its presence makes it d i f f i c u l t f o r the
mild s t e e l t o pas s iva t e . For NazS concentra t ion i n the range
found i n the t y p i c a l k r a f t l i quor , increas ing t h e NazS caused an
increase i n t he magnitude of t h e maximum c u r r e n t which led to an
increase i n t h e cor ros ion r a t e .
Wensley [7 ] i n her s tudy p l o t t e d the low and high c o r r o s i v i t y on
map of t h i o s u l f a t e concentra t ion versus Na2S concentra t ion. She
found t h a t high c o r r o s i v i t y white l i quor occurs a t a high
concentrat ion of bo th compounds. She also reached the conclusion
t h a t under 32 g/l of NapS and 5 g / l t h i o s u l f a t e no cracking
occurred, but a t 4 0 g/l Na2S and 10 g/l t h i o s u l f a t e severe
cracking was observed.
2.2.3, Anodic protection
Many Pulp and Paper plants are using anodic p ro t ec t ion t o
prevent rap id cor ros ion i n the d iges te r , clarifier, s torage
tankage, and o t h e r untis. To pro tec t any equipment from
corroding by anodic pro tec t ion , the environment should be
aggressive, and the act ive-passive a l l o y should have a broad
passive region t o maintain pass iv i ty . Since t he current
maintaining p a s s i v i t y i s low i n such alloys, anodic p ro t ec t ion
is economical. It consumes much less power than ca thodic
pro tec t ion would need. '*'O
It was observed that anodic protection is superior to cathodic
protection in kraft liquor under al1 conditions. Anodic
protection requires a fraction of the current density needed for
cathodic protection. In fact, cathodic protection current
density may be too high to be applied practically. On the other
hand, anodic protection is still possible in the presence of
thiosulfate, and it is strongly prornoted by the presence of
ploysufide. However, the electrical equipment used in anodic
protection is cornplex, and with loss of control corrosion will
attack rapidly . Therefore, the system must be rnonitored with *i, ü, 7,10,11
The high cost of a new digester and the dom-time losses
associated with its maintenance is another problem, Thus it is
practical to use anodic protection, since it reduces the
corrosion rate in the kraft digester with a lower operating
cost. Besides, the kraft digester is a good candidate for anodic
protection, because of the aggressive solution in the
impregnation zone, where the concentration of the solution is
high and most darnage occurs. The installation of the anodic
protection system solves the problem of SCC which may lead to
catastrophic failure.
The procedure for anodic protection can be summarized as
follows. At the beginning, to achieve the passive potential,
high current needs to be applied to increase the potential from
the active region to the passive region. Then the current is
dropped gradually until the set passive potential is reached. In
Yeskes study[26], anodic protection of a clarifier was not
successful in the first attempt, since the current applied was
lower than the critical current, Thus the systern stayed in the
active region. In the second attempt, he added chemical oxidant,
an emulsified sulfur to the white liquor, since polysulfides are
known to passivate the system. This did not work either. In the
third attempt a total current of 2000 mA increased the potential
from -961 mV vs SCE to the targeted potential of -700 mV vs SCE
in less than 24 hours.
He indicated that passivation is not lost immediately during a
power failure,
continued for
protection the
of protecting
corrosion.
but it would be lost
more than one hour.
current density should be
the digester, it will
if the loss of power
For practical anodic
very stable, or instead
increase the rate of
Bank [ 3 3 ] , concluded that if a field anodic protection system is
sufficiently large to obtain passivity at the start of the cook
(200 OF), it will be sufficiently large to do so at any higher
temperature. He showed that anodic protection can control
digester corrosion at al1 temperatures up to 350 O F . At high
temperature the current is normally consumed in the oxidization
of the sulfide .
Though anodic protection was identified as the best way to
protect the digester, there have been a few problerns to
consider. In some cases, where anodic protection failed, t h e
stitch welds keeping the cathode attached to the wall of the
digester simply disappeared leaving damaged area on the shell
where they once were attached. Thus anodic p r o t e c t i o n should be
used with caution. Acid wash to clean the digester in between
shutdowns can remove the passive film created by the anodic
protection. Therefore, the current density setting should be
checked and monitored to ensure that it is at the desired
3. POLARIZATION and EXeERIMENTAL RESULTS.
The three electrode configuration system was used in the
development of the polarization curve for stainless steel and
carbon steel coupons. The ce11 consists of working electrode,
counter electrode, reference electrode and electrolyte solution.
One side of the working electrode was polished to 600 grit, and
cleaned with acetone and distilled water. The back of the
electrode was welded to a copper wire, and coated with three
layers Aremcoating leaving a big part of the polished side
uncovered. The area of the uncovered portion was determined
using image analysis software. The electrolyte solution was
prepared only from the corrosive inorganic components of the
white liquor, 2.25 M (90 g/L) NaOH, 0.44 M (35 g/L) Na2S for the
high concentration, and 1 M ( 4 0 g/L) NaOH, 0.32 M (25 g / L ) NarS
for the low concentration case. The solution was heated to 90 * 3 OC, and kept at that temperature before starting to collect
any data.
The reference electrode, made of Hg/HgO, was kept in a separate
tube a t 25 OC, i n an electrolyte solution made of NaOH with a
concentration of the cell solution, throughout the experirnent,
It was linked to the main ce11 by a salt bridge, as illustrated
in Fig.3.1.
Salt bridge K
reference electrode+
l Water Bath l
Fig.3.1. The electrochemical ce l l .
The
and
200
three electrodes were connected to HAB-151 potentiostate,
the potential of the anode was increased from -1000 mV t o
mV f o r the stainless steel and -1000 t o -200 mV for the
carbon steel , with a step rate increase of 0.2 mV/s. At the same
t h e the p o t e n t i a l vç c u r e n t data is collected and stored in
the cornputer.
Fig.3.2. compares the high and the low concentration
polarization curves for t h e carbon steels. Both curves showed a
Fig.3.2. P o l a r i z a t i o n curves f o r the carbon s t e e l , which was obtained i n the u n i v e r s i t y lab.
similar r e s u l t s to most given curves in the l i t e r a tu re . The high
concentration curve is having two obvious peaks, whereas the low
concentration f i r s t peak i s a l i t t l e suppressed. Previous
studies detennined t h a t SCC range s t a r t s w i t h the s t a r t of the
second peak and ends with the s t a r t of the passive f i l m
formation. However, the passive zone showed what is expected,
the s t a r t of the f i l m formation and then the decrease of current
density which is an ind ica t ion of the thickening o f the f i l m i n
both curves. Though it is more obvious i n the case of the high
concentration. M t e r that point the transpassive region s t a r t s
t o form w i t h a sharp increase, and looks like it w i l l l e v e l o f f .
However, s ince th2 data were col lected up to -300 mV, the
level ing o f f of the t ranspass ive region is c lea r only i n the
high concentration case. T h e potent ial range fo r the c r i t i c a l
current density was almost the same, and was between -800 and -
700 mV vs Hg/HgO reference, -970 and -870 mV vs SCE reference.
This is the range most of the previous studies obtained, and it
was found to be the l i m i t s at which SCC takes place. The passive
area is extended from -700 to -523 mV vs Hg/HgO reference in
the case of the high concentration case. In the case of the low
concentration it was extended t o -629 mV vs Hg/HgO ref.
The transpassive region started t o level off a t -450 RV and -350
mV vs Hg/HgO reference for the high and low concentrations
respectively. In the lower concentration the t ranspass ive region
seems t o have smoother s lope . An electrode which was polarized
to a high potential, showed c l e a r l y that the current density in
transpassive region levels off. There are different opinions on
what is occurring in the transpassive region, some b e l i e v e that
pitting starts to take place, and others are of the opinion that
jus t oxidation takes place. While performing the experiment it
was observed that an electrode which scanned just with the
forward scan and ended at the high potential of the transpassive
region has some corrosion products on its surface. This is an
indication of corrosion taking place in the transpassive region.
The higher concentration curve looks a little more noble. this
was due to the fact tha t the data were collected for a second
run using the same electrode. The first run data were having
current densi ty f luc tua t ion problem i n the passive zone. To
avoid that problem t h e data were recorded manually.
Fig.3.3. is a good representat ion o f a f u l l scan cycle, in which
the carbon steel was scanned forward and backward. The change i n
- LALE: L - CJ L - + pu C ~ A A L ~ ~ ~ 3 --ru- i n d i r a t o c -- - -- +ha+ a ~ i n q electrode was mare
noble than the f r e sh electrode. Also since the area to be
protected is less, due t o some p a r t of t h e surface is covered
w i t h the passive f i l m from the forward scan, a drop i n the
current densi ty is observed i n the transpassive and the passive
zones. However, t he re is a big increase in the c r i t i c a l current
density, which is an evidence t h a t the passive f i l m d isso lu t ion
requires high current dens i ty .
Potentiil mV vs HgMgO rcf.
F i g . 3 . 3 . Polarization curves f o r carbon steel's forward and backward scans i n the low concentration electrolyte,
This may prove what Yeskes [SG J observed, that passivation will
not be lost immediately after power f ailure.
Fig.3.4. shows t h e polarization curves f o r stainless steel in
LI- - L~~~ h i j h a;zY l ~ w c x c c ~ t r r t i r r : e l o c t r c l y t o r.-ses. In the high
concentration case the stainless steel showed a similar trend
like the one given by Crowe and Troman[32] . The active, passive, and transpassive regions are well identifiable, however in the
low concentration case there is no drop in the current which is
normally an indication for oxide formation. But it was assumed
that the f l a t portion of the curve is the passive area for t h i s
rnetal. Fig.3.5 shows the polarization curves for two s t a i n l e s s
steel electrodes in the high concentration electrolyte solution.
One is for a fresh electrode, and the other one is f o r an old
electrode . They showed sirnilarities for the entire anode curve . Except for the last section, a potential range from O to 200 mV
vs Hg/HgO reference, t h e current density almost jumped to a
value five times that of the fresh electrode. This difference in
the current densities will be used later to investigate the
effect of the stainless steel on the anodic protection.
Fig. 3.6. shows the three polarization curveç obtained for an
operating commercial digester, one for the carbon steel in the
potmttd mV vs H m 0 rd.
Fig.3.4. Polarization curves for stainless steel 316L, which was obtained in the university lab.
-- -- W. ,
Pot- mV vs HgtHgO rd.
Fig. 3.5. Polarization curves for stainless steel 316L, comparing new and old electrode obtained in the university lab .
Fig.3.6. P o l a r i z a t i o n curves obtained by a Company i n s i d e t h e d i g e s t e r .
impregnation zone, one f o r carbon s t e e l i n the cooking zone, and
one f o r s t a i n l e s s s t e e l i n the impregnation zone. Unfortunately
there is no information regarding the metal surface preparat ion
f o r these curves, except that they were c o l l e c t e d i n s i d e t h e
d iges t e r by being mounted on the wall of t he d i g e s t e r . Cornparing
the two carbon steel curves, it was observed t h a t wi th the
increase of concentra t ion t h e current dens i ty increases .
Therefore, the impregnation zone will need higher cu r ren t t o be
passivated. The carbon s t e e l i n this zone showed a
s imi la r t o the low concentra t ion case, though it has
passive area and low c r i t i c a l cu r r en t dens i ty .
behaviour
a broader
Table 3.1 summarizes the carbon steel polarization curves'
potential ranges and the cr i t i ca l and the pass ive cur ren t
densities, to change from Hg/HgO to SCE ref . deduct 172 from the
given potential. It shows that the passive current density is
low for the cooking zone, and almost the same for the
Table 3.1. The potential ranges vs Hg/HgO ref . and the critical
and passive current densities f o r the studied cases,
Coo king
Impregnation
Low-Conc
f orward
Low-Conc
Bac k w a r d
High Conc
Act ive
Potential
r a n g e mV
- -- -
Passive
potent ia l
range mV
-679 -590
-655 -486
-679 -558
-
res t
potential
rnv
-750
-845
Cr i t i ca l
CD u ~ / c m '
Passive
CD u~/cm'
impregnation and the lab l o w concentration cases. The high
concentration has the highest critical and passive current
densities. However, for al1 of the studied cases the passive
zone seems to lay in the same range.
The stainless steel showed a lower current density with no good
clear passive zone. This may be due to the material used, SS304,
or the difference in the concentration of the white liquor.
Crowe and Troman[32] gave in their study a clear presentation
for the active, passive and transpassive zone for SS316 in high
concentration of
similar shape,
difference in the
NaOH. The 1a.b
but different
concentrations
collected data resulted with a
current density due to the
To understand the behaviour of the cathode used normally in
pulp and paper anodic protection, SS316 ( S S 3 0 4 ) was polarized
cathodically to a high potential. At a high current density
above 2 * l o 5 u~/cm', the current density starts to level off. At
that point, it is believed that the hydrogen production rate
increases rap id ly . A system which needs a current density
greater than the limiting current density of the cathode will
be difficult t o protect. Also the production of hydrogen may
affect in a direct way the stainless steel, which is close to
the cathode, causing hydrogen embrittlement of the stainless
steel.
Fig.3.7. shows that even the cathodic polarization curve for
the carbon steel behaves in the same way in that region of the
curve. This means that metal unrelated reactions are taking
place in that portion of the curve. In the calculation of the
applied potential l a t e r in this work the stainless s t ee l curve
was used,
A l s o the electrolyte s o l u t i o n conduc t iv i ty which was obtained
i n both t h e lab and in side the d iges te r f o r t h e whi te liquor
are given in appendix C.
4 l
-1600 -1400 -1200 -1000 -800 -600 -400 -200 O
Potential mV vs HgiHg0 ref.
Fig.3.7. The ca thod ic polarization c u v e for the carbon and stainless steels, Collected f o r the low concentration electrolyte.
4 . MATHEMATICAL MûDELLING of the CONTINUOUS DIGESTER,
In the modeling of anodic protection of the Kamyr digester,
which built of carbon steel outer shell and a central pipes of
stainless steel, the Boundary Element Method (BE) is used with
non-linear boundary condition. The carbon steel and the
stainless steel polarization curves data were collected at 90 f3
O C . The electrolyte solution was prepared from the most corrosive
inorganic components of the white liquor, NaOH and Na2S. Then the
polarization data was cuve fitted to produce an equation which
gives the current density as a function of the potential.
The following sections of this chapter will start with analyzing
the curve fitting method used, then the Boundary Element Method
and its application in the case of anodic protection of the
Kamyr digester will be illustrated. Finally the applied
potential calculation will be given followed by a brief
description of how the progrm works.
4 . 1 . Mathematical Representation of the Polarization Cumes:
To produce a continuously differentiable equation to fit the
polarization data, a mal1 FORTRAN program was developed using
the algorithm given by Yeum and Devereux [3l] . They proposed
that an eiectrochemical relationship between the current density
and the potential is given for any reaction in the form of one
of the follow equations:
where i; is the current density for the j reaction, i3: is the
limiting diffusion current density, V the potential, R. is the
resistance of the electrolyte, and V* is parameter containing in
it the equilibrium potential or the rest potential V' and iO is
t he exchange current density as follows,
where Ç j is negative for the cathodic reaction and positive for
the anodic reaction, b, is the Tafel slope of reaction j.
Equation 4.3 was not used, y e t it was included in the program
l ist . This equation needs to be solved numerically each time it
will be used in boundary element method for the non-linear case,
which in turn added more difficulty to the mode1 for the anodic
protection of the digester .
To fit the data of the carbon steel polarization curve in the
high concentration electrolyte, nine reactions were assumed to
be controlling the corrosion rate of the carbon steel. For this
case, al1 the reactions were assumed to be of the type of
equation 4 - 2 . Therefore, there are 27 unknowns to be calculated,
three for each equation. The program is very sensitive to small
change in the parameters, since the electrochemistry formula
relating the current density and the potential is logarithmic
which can result in large changes with a small change in the
parameters. To avoid such problem a good guess of the parameters
is required as an initial guess. The irregularity in the curve
made it difficult to fit with regular fitting procedures. The
spline f itting procedure suggested by Hermann f its the curve,
but it is not continuous over the entire curve. This led to a
d i f f i c u l t y when calculating any point that falls outside the
given data range. Since the normal procedure to solve the non-
linear B. E. problem will be by iteration procedure, the point
could be in any place at the start. So for that reason, it is
important that the curve fit representing the polarization data
to be continuous and differentiable over the whole domain.
The parameter estimation procedure starts with inputting the
potential/current data by dividing the curve into nine zones,
where each reaction is dominantly controlling one zone. Then
first g u e s s for each individual zone parameters are entered,
depending on which equation will be used for that particular
reaction. If equation 4.1 is used there are only two parameters
to find, in equation 4.2 there are three parameters need to be
calculated. With changing one parameter and keeping al1 the
others constant the total current density is calculated by
Where i'j is the sum of the current density of al1 the reactions
other than the j" reaction. If the current density calculated is
equal to the current density given for that portion of the curve
then the parameters will be stored, and the program will
continue calculating the other parameters in the same way until
al1 parameters fit the curve with a reasonable error.
Tab1e.l gives a summary of the calculated pârameters which were
used in the boundary element method calculat ion for the carbon
steel in the high concentration electrolyte, which was obtained
in university lab. The parameters for the other polarization
curves a r e given i n appendix A. Now t he t o t a l current density
f o r any point on the curve can be calculated by equation ( 4 . 6 ) .
in the Table.4.l. The curve fit Parameters f o r carbon steel high concentration electrolyte.
reaction Parameters
Fig.4. l . t o 4 . 6 show the Lab obtained curves and their fit. The
e r r o r i n the curve f i t v a r i e d from - 2 % t o 9 . 8 . However, rnost of
the po in t s , as can be observed from t h e curves were well f i t .
Due to t he effect of some r e a c t i o n equations on each o t h e r some
points were d i f f i c u l t to fit with error less than 5 % . I n general
t h e smoother curve fo r t h e low concentra t ion data , Fig.4.2, was
b e t t e r f i t t e d than t h e o t h e r s . The po in t s of t h e high
concentra t ion e l e c t r o l y t e curve which lays between t h e two
peaks, Fig.4.1, where d i f f i c u l t t o fit and t h e e r r o r was high i n
t ha t po r t i on o f the curve. However, the passive zone e r r o r was
kept low, below 5%, since i t i s an important zone where most of
t h e f i n a l result of the mode1 reaches and needed t o be kept i n .
The t r anspas s ive region of the carbon s t e e l was fit well a l so ,
with e r r o r less then 1%.
In the case o f Fig.4.4. and 4 .5 . the anode side of the curve
was the main cons idera t ion i n ob ta in ing t h e f i t t i n g equat ions
for t he s t a i n l e s s s t e e l . Since, i f t h e s t a i n l e s s is a cathode,
there w i l l be no corrosion problern t o worry about. In f a c t , i n
most o f the r e s u l t s obtained t he stainless steel was behaving as
an anode. However, the o l d s t a i n l e s s steel, Fig.4.6, w a s fitted
well i n both sides of t h e p o l a r i z a t i o n curve, t h e cathode and
the anode.
Fig.4. 1 Carbon s tee l p o l a r i z a t i o n curve f o r t h e high c o n c e n t r a t i o n electrolyte, us ing t h e normal electrochemical equations.
Fig.4. 2 Carbon steel p o l a r i z a t i o n curve for the low c o n c e n t r a t i o n electrol yte, us ing the normal electrochemical e q u a t i o n s .
-900 -800 -700 -600 400 -400 -300 -200 -100 O
Potential mV vs HgWgO ref-
Fig.4. 3 Low concentration backward scan, using the electro- chemistry curve fit.
- - - Poteml mV vs HglHgO nt.
Cig.4. 4 . Polarization curve f o r stainless steel in the low concentration e lec t ro ly te , and its curve fit using the electrochemistry equations.
t
r SS316 Pol. data C u r v e fit
-400 -2 00 O 2 n 4 -. .
Potential mV vs HgMgO rd.
Fig.4. 5. Polarization c u v e for the stainless s t e e l i n t h e high concent ra t ion electrolyte, and i t s c u v e f i t using t h e electrochernistry equations.
-1 000 600 -600 -400 -200 O 200 400
Potential rnV vs HgMgO ref.
Fig.4. 6. Polarization curve for an old stainless steel electrode i n t h e h igh concentrat ion e l e c t r o l y t e , and its curve f i t us ing the electrochernical equat ions.
To reduce the error in the curve fit for the curves obtained
inside an operating digester, the spline curve fit method was
used. Since it is well know method in fitting curved geometries.
A small FORTRAN program was developed from an algorithm by
Spath[28], which generates the cubic spline parameters A, B, C
and D, the equation was in the f o m of.
where Y is the current density and AX is the potential
difference, The cuve to be fitted was divided into several
parts, and the pararneters for each section were calculated. The
potential intervals and their parameters were fed to the main
program for the anodic protection. There is one problern with
this curve fit method, there is no solution for any points
laying before or after the end points for a given curve. To
solve the end point problern, a straight line with a slight slope
was assumed for the points before and after the end points.
Fig.4.7 to 4.9 show how well the spline fit the polarization
curves for the carbon and the 304 stainless steel. Though the
spline fitted the curves obtained in the lab, they were not used
in this study .
Patentfal mV vs SCE rd.
Fig.4. 7. Polarization curve for the cooking zone obtained by a company inside the continuous digester with the spline fit.
PormtW mV vs HgWgO r d .
Fig.4. 8. Polarization c u v e for the cooking zone obtained by a company ins ide the continuous digester with the spline fit.
I 1-exp.
b ( . C w o fit j
Potenüal mV vs SCE ref.
Fig.4. 9 . Polarization curve for 304 s t a i n l e s s s t e e l and t he i t s s p l i n e curve fit.
The s p l i n e f i t worked well f o r the commercially operat ing
d iges t e r cu rves . However, i n the case of t h e lab generated
curves it w a s d i f f i c u l t t o get a reasonable resu l t with the
spl ine f i t . Th is was due t o t h e high cu r r en t d e n s i t y i n the
t ranspass ive region f o r the s t a i n l e s s s teel .
4 . 2 . The Boundary Element Method:
Since t h e boundary elernent rnethod (B.E.) is
books by Brebbia [16,17], i n t h i s thesis
boundary cond i t i ons re levant t o the anodic
d e s c r i b e d i n many
on ly the s p e c i f i c
protection
and t h e s o l u t i o n procedure w i l l be descr ibed b r i e f l y .
dimensional s u r f a c e of t he carbon steel, stainless steel
problem
A two
and the
cathode is divided into N equal spaced nodes. The quadratic
elernent method is used to define the nodes, where each three
adjacent nodes formed an elernent. In the B.E. the following
linear system of equation for the Lapacers equation will be
solved for the problem studied.
Gq= Hqî .
Where H and G are matrices for the geometry coefficients for the
system. H is a matrix of the NIN and G a rnatrix of a Nf2N. 4
and q are vectors of potential and potential gradient
respectively of length N where N is the number of the nodes. As
a boundary condition for the digester and the cathode system,
the following boundary condition are given:
Cathode : @ = # * Anode : = f(#)
34 4=z
In electrochemistry the current density is given as a function
of the potential gradient and the conductivity, as follows:
so equations (4.11, 4.12) can be rearranged as
Where i is the c u r r e n t d e n s i t y which will be solve by using the
equation for the polarization curve fit. Since the procedure t o
solve t h e boundary condition is by iteration, an error vector F
is defined as follow
F=Gq- H4 ( 4 . 1 4 )
Since in the first iteration a l 1 of the right hand side of
equation (4.14) is known, the error is calculated, and checked
if it is less than a pre-set error value. If the error is large
the calculation continues by adding 6 to the p r e v i o u s unknown
potential and current dens i ty , which is ca lcu la ted from t h e
following equation,
JS= F ( 4 . 1 5 )
where J is t he Jacobian of equation (4 . 14) . The above equation
was solved by the Cholesk's method.
4 . 3 Applied Potential Calculation:
The potentials obtained from t h e boundary element so lu t i on are
the solution po t en t i a l s near metal surface, To calculate the
applied potential the following adjustment were made :
The anode o v e r p o t e n t i a l is given as
7 = 4 : - 4 :
The applied potential is the difference between the
cathode metal potentials,
45=9::-4:
( 4 . 16)
anode and
To simplify the calculations the anode rnetal p o t e n t i a l $ay was
taken as a reference. Therefore, the above equations can be
rewri t ten as
V d = -4:
The cathode rnetal p o t e n t i a l can a lso be calculated frorn the
overpotential of the cathode and the solution p o t e n t i a l near
the cathode as,
Finally t h e applied potential can be c a l c u l a t e d as ,
4 - 4 . Program description :
The program for modeling the Kamyr digester mainly consists of
four main sections; input section and geornetry calculation, H
and G rnatrix calculation, iteration section for solving the non-
linear condition, and output section. In the input section
geometry of the anode, one cathode at the center, and the
central pipe data are given. Then the location of the cathode (s)
at any point different than the center is calculated. In this
section also, with varying t h e numbers of the cathodes, new data
for the e x t r a cathodes are calculated, and if the central pipe
will be used or not is determined.
After that the H , and the G matrices for the given geometry are
calculated. In this section the only problem that can arise from
the point which will be repeated due to the connection of any
two circles. This leads to the wrong definition of the end of
each surface's boundary in the give geometry. This was solved by
using the last node's coordinate of each surface, which is
normally different than the others starting node. When al1 the
H and G matrices are calculated they will be stored and used in
the next section. In which the potentials and the current
densities of the anode and the cathodes will be calculated.
With the use of a code def ining each surface, the F matrix is
calculated f o r the f ollowing equat ion
F =Gq-H#
The i t e r a t i o n cont inues by adding a d e l t a , which is obtained
from equation ( 4 . i 5 j , co ne anoae p o t e n t i a l and the câthûde
current d e n s i t y . The ca lcu la t ion continues until F is small
enough. Then the p o t e n t i a l and t h e current d e n s i t y of the anode
are given as an output . By using t he above method, a t what area
of the p o l a r i z a t i o n curve t h e system w i l l fa11 a f t e r a l 1 points
pass the c r i t i c a l current dens i ty is determined f o r both carbon
steel and t h e s t a i n l e s s s t e e l . The system w i l l then be backed
from t h a t p o i n t t o the passive zone where the system w i l l be
protected. A f l o w chart of the program is give i n Fig.4.10.
Input Geometry w and first assumptions
Calculate G and H
d4
Calculate F
Print out the results of 4 and i
Fig.4.10. T h e progarm flow chart
5. DISCUSSION:
In this chapter the results obtained from the mathematical mode1
will be discussed. The discussion is divided into four sections
starting with the case for the lowest critical curent density,
the cooking zone, followed by the impregnation zone, then the
lab low concentration, and finally the lab high concentration.
A horizontal two dimensional cut from the Kamyr digester
geornetry, for a concentric carbon steel and stainless steel with
270 un and 19 cm radius respectively, in which the ca thode(s )
was placed between the two metals, was simulated. In rnost cases
the cathode was 10 un away from the staileçs steel wall, and a
cathode (s) with 2.54 cm radius was used. However, for the cases
when the cathode was place near the carbon steel, at 140 cm from
the centre, the effect of changing the cathode radius was
s t u d i e d for four cathodes case. In the case when the cathode was
concentric with the stainless steel, the carbon steel dimension
was kept constant and a cathode with 29.485 cm radius was used.
Only the lab collected polarization cuves were used for this
case.
When the cooking zone was studied, only one cathode was used.
This is due to the uniform distribution around the carbon steel
and the central stainless steel pipe. In the cases of the
55
impregnation zone and the low concentration up to two cathodes
were studied. However, in the case of the high concentration up
to four cathodes w e r e used. In this case also, the location and
the sizes of the cathodes were varied for four cathodes case to
observe their effect on the passivation and the distribution
around the carbon steel and the stainless steel.
5.1, Cooking Zone:
The polarization curves used in the mathematical mode1 for this
case were obtained inside the digester at a level of 147 ft.
However, the stainless steel polarization curves used here was
collected in the impregnation zone, which is normally at a
higher concentration. That w a s due to the lack of data for the
polarization curve for the stainless steel for the white liquor
in that section of the digester.
Fig.5.1 shows the polarization curves for the stainless steel
and the carbon steel with the mode1 resul t for the cooking zone,
Both carbon steel and stainless steel have a uniform current
density and potential distribution, and the potential is almost
the same near each metal surface. This is an indication of a
small variation in the potential i n the solution, meaning t h a t
a rnocieiresuits Il cs 51 6 p l . in the cooking zone 1
I - - SS304 pot. I
I 1
potential mV vs SCE ref.
Fig.5.1. P o l a r i z a t i o n curves f o r the cook ing zone and t h e mode1 r e s u l t obtained f o r them.
the system has a good throwing power. However, since the
polarization curve for the stainless steel used here is for the
impregnation zone, the result may be different for the case when
the s t a i n l e s s steel polarization curve for the cooking zone is
used,
The current density needed in this case to be applied to pass
the critical current density is less than the other studied
cases. This is clear from t h e polarization curve, which shows a
critical current density of just 13 rnA/cm2. Therefore, it seems
that for a system having such low critical current density, it
will easily be protected with only one cathode. Thus resulting
with a well uniform current density and potential distributions
around the anode. This also indicates that the stainless steel
also has a good current density distribution.
5.2, Impregnation Zcne:
As it is apparent from Fig.5.2. and 5.3 the potential and the
current density distribution around the anode and the stainless
steel were improved with increasing the number of cathodes to
two. Even in the case of one cathode, al1 of the anode's surface
is in the passive region and there is a little variation in the
/ -CS 51 6 Pol. i Model resuits. /
Fig. 5 . 2 . P o l a r i z a t i o n curves for t h e impregnation zone w i t h the model r e s u l t for one cathode case.
1 -CS 516 Pol. m Modal resuits. ; 4 ï
Fig. 5.3. P o l a r i z a t i o n curves for t h e irnpregnation zone with t h e model r e s u l t for t w o cathodes case.
potential around the surface . However, the variation in the
potential and the current density increases on the stainless
steel surface, where the current density for the closest surface
to the cathode was around 100 r n ~ / c m ~ and drops to around 8 r n ~ / c r n '
at the far end. This is the expected r e su l t , since the cathode
was just 4" away from the stainless steel wall. Besides, in this
case the critical current density and the passive current
density are higher than those for the cooking zone. Therefore, a
higher current density must be applied to protect the systern,
which led to the observed variation, It can be seen in Fig. 5.2.
that the potential varied between -600 t e -792 mV vs SCE ref. On
the other hand, the potential d i f ference in the cooking zone was
just around 8 mV.
Also from Fig.5.3. the difference between the maximum and the
minimum potentials of the stainless steel decreased when the
number of cathodes was increased to two, and the cu r ren t density
and the potential distributions around the anode becarne uni fo m.
Though the re is no clear definition of the active, passive, and
transpassive regions on this stainless steel polarization curve,
it seems, as it was in the cooking zone, that the potential of
the stainless steel is in a region closer to the a c t i v e region.
A further study to mapping the p o t e n t i a l zones for the ÇS304
polarization curve will be needed, to mark exactly the passive,
active, and transpassive zones.
5.3. Lab Low Concentration Electrolyte:
As explained before, the lab collected polarization data were
f o r an electrolyte containing only the two main compounds
believed to be involved in causing corrosion in the digester,
NaOH and Na-S. However, the shape of the polarization curve seems
to be almost the same as the impregnation zone polarization
curve developed from a coupon inside the real digester with 1/8
critical current density of the lab generated value. This rnay be
an indication that these two compounds a r e the most likely to
control the polarization of the carbon steel. Though thiosulfate
N G 0 3 is believed to be one of the factors that may lead to
corrosion in such system, it was neglected since only a small
amount of it is present in the white liquor.
A close look at the polarization of the stainless steels given
in the experixnent and polarization curves section Fig.3.5 and
3 . 3 for the lab low concentration case and the one obtained in
an operating digester, shows that there is sorne difference in
the shape of the polarization curves. This may be due to the
presence of other neglected compounds such asr Na2S203r NaClr
Na2Sf13, NaCl, NaS04, and NaS03. Moreover, the organic compounds
of the white liquor may have small influence on the shape of the
polarization curve, which has not been studied yet.
Fig.S.4. and 5.5 show the same trend a s in the impregnation
zone, with the increase in the number of the cathodes, the
uniformity of the current density and the potential distribution
around both materials was improved. However, d i f f erence in the
current density between the highest and the lowest potential for
the stainless steel in the case of one electrode was much larger
than that for the impregnation zone. This is due to the higher
current density required to force the system to pass to the
passive region, which has a direct effect on the stainless steel
which is closer to the cathode.
Fig.5.6 and 5.7 show how the current density distribution around
the stainless and the carbon steel is changing with the location
of the surface from the cathode. The carbon steel is uniforrn in
both case. However, the stainless steelf s current density is
high near the cathode and low in the area f a r away from it. From
Fig.5.6 it is clear that the surface which is closer to the
cathode has the highest current density while the current
density drops on surface which lays at a far distance from it.
ALso it was observed t h a t with the increase of the number of the
Potential mV vs H g / H g O ref.
Fig. 5.4, Polarziation curves for the l o w concentration case, when one cathode was used,
Potential Mv vsHg/HgO ref.
Fig.5.5. Polarziation curves for the high concentration case, when two cathodes was used.
-meW density
Fig.5.6. Current density distribution around the geometry used in the model for one cathode case-
Fig.5.7. Current density distribution around the geornetry used in the model for two cathodes case-
cathodes to two, Fig.5.7, the maximum current density dropped by
four from that of the one cathode case.
As expla ined in the anodic protection section 2.2.3, a high
current density will be applied to force the system over the
critical current density and pass to the transpassive region,
and then i t is necessary to reduce the applied potential
gradua l ly until the system reaches the passive zone. Fig.5.8
shows how the potential of the stainless steel becomes uniform
while the cathode potential and current density are decreased to
force the carbon steel to reach passivity. This is a result of
the higher applied current density and potential on the cathode,
when the system is passing from the critical c u r r e n t to the
transpassive region. The potential gets lower and more uniform
when it reaches the passive zone. The change between the passive
and the transpassive zones is more obvious in the case of t h e
current density as show in Fig.5.9. There is a s h a r p d i f ference
between the s u r f a c e which is closer to the cathode and that far
away when the system is in the high transpassive region, and it
becornes more uniform in the passive region. This means the
applied current density should be reduced quickly, otherwise the
surface of the stainless steel which is closest to the cathode
may corrode faster than might be expected. Also since
+ at high transppasive * at IOW transpassive
Fig. 5 .8 . P o t e n t i a l d i s t r i b u t i o n around the s t a i n l e s s steel while reducing the current app l i ed on t h e cathode.
+in the passive zone -rt Before passivation 4 at low transpassive region +At high transpassive.
Fig .5 .9 . Current density d i s t r i b u t i o n around the stainless s t e e l while reducing the cu r ren t app l i ed on the cathode.
the cathode c u r r e n t density and t he po ten t i a l needed for the
system t o pass t o the transpassive region is very high, H? gas is
produced a t a very rapid r a t e i n t h a t p o t e n t i a l range. So
holding the syçtem long i n the transpassive zone may lead t o
hydrogen embrittlement a t those port ions of s t a i n l e s s s t e e l
surface c l o s e s t t o the cathode.
Since the system must be backed from the t ranspass ive region t o
the passive region, the e f f e c t of using the backward
polar izat ion curve f o r t he carbon s t e e l was s tud ied . In Fig.5.10
t o 3.12 f o r one cathode, the potent ia l d i s t r i b u t i o n on the
carbon s t e e l became more uniforrn than the c a s e of us ing the
forward p o l a r i z a t i o n curve. Even t h e s t a i n l e s s s t e e l dif ference
between the lowest potent ial and the highest potent ia l was
reduced. A s the potential of the carbon s t e e l was decreased i n
the passive region, the s t a i n l e s s s t e e l a lso showed a decrease
i n t h e p o t e n t i a l . I n Fig.5.10 most of the surface potent ial
stayed i n a location higher than t h e corros ion p o t e n t i a l .
However, when the potent ial of the carbon s t e e l was moved to the
middle s e c t i o n of the passive zone, as i n Fig.5.11, the
potent ial a t the surface f a r away frorn the cathode s t a r t ed to
drop t o a p o t e n t i a l c loser t o the corrosion potent ia l . In
Fig.5.12 where the potent ial of the carbon s t e e l i s a t the end
point immediately before i ts p o t e n t i a l jumps back t o the active
Potential mV vs HgRlgO ref.
Fig.S.10. The model result when the system was backed u s i n g the backward curve, when the carbon steel s t a r t to passivate.
Potential mV vs HgiHgO ref.
Fig.5.11. The model resu l t u s i n g the backward curve, when t h e carbon steel i n t h e middle of passive zone.
Potential mV vs HgMgO ref.
Fig.5.12. The model result using the backward curve, when the carbon s tee l is in a point after which the sys tem passes to the act ive zone.
region, it was observed t ha t some sec t ions of t h e s t a i n l e s s
s t e e l have passed t o the cathode side of the po lo r i za t ion curve.
This may r e s u l t w i t h a galvanic coupling effect on the s t a i n l e s s
steel, which may r e s u l t with a loca l ized corrosion. Thus i t
seems t h a t the choice of the passive p o t e n t i a l a t which the
carbon steel w i l l be kept protected depends on the s t a i n l e s s
steel . A p o t e n t i a l a t which both metals w i l l be protected should
be chosen.
Fig.5.13, shows the r e s u l t fo r a cathode which i s concentr ic
with the s t a i n l e s s s t e e l geometry. In t h i s geometry on ly the
carbon steel i s needed t o be pro tec ted . Since the cathode is a t
t he centre a u n i f o m d i s t r ibu t ion of cur ren t dens i ty on the
carbon steel was observed. In t h i s t he t o t a l cu r ren t and the
applied p o t e n t i a l a r e rnuch less than what was needed i n the case
when s t a i n l e s s steel was included. Obviously wi th no s t a i n l e s s
s t e e l i n the p i c t u r e , the current de l ivered by the cathode w i l l
drop. With t h i s advantage, t h i s geometry seems t o be preferab le .
5 . 4 . Lab High Concentration :
In the high concentration case a s explained i n t h e po la r i za t ion
and the experimental r e s u l t , the concentrat ion of t h e NaOH was
n
Potentfal mV vs HgMgO ref.
Fig.5.13 The carbon s tee l polarization c u v e with the mode1 result, f o r the concentric geometry.
increased
increased
stainless
stainless
from 40 g/L to 90 g/L, while the NazS concentration was
from 25 g/L to 35 g/L. To understand the effect of
s t e e l on the required current densi ty, two dif ferent
steel polarization curves were used. One was for a
fresh SS316L electrode used for the first tirne, and the other
was for an old electrode used for a second time.
Fig.5.14 to 5.17 show the change in the carbon steel current
density and potential distribution while varying the stainless
steel polarization curves. Fig.5.14. and 5-15 show results for a
potential of 20 V on the cathode side. In Fig.5.14 the
polarization curve for the new stainless steel was used, and it
is obvious that large section of the carbon steel surface passes
to the transpassive region. This is not the case with the old
stainless steel, since it utilized higher current it seems that
most of the applied current was used by stainless s tee l rather
than the carbon steel. That may be why few points pass to the
transpassive region. With the increase of the p o t e n t i a l at the
cathode to 26 V, as in Fig.5.16 and 5.17, the number of poin ts
t h a t have passed over the Flade potential increases and the same
trend was observed with each increase in the potential. In
addition, for the higher potential, the surface current density
became more uniform though the potential on the surface varies.
-1000 -900 8 W -700 -600 -500 -400 -300 -200 -1 W O
Potentail mV vs HgMgO ref
Fig.5.14 The result f o r 2 0 V on t h e cathode side, when o l d s t a i n l e s s steel was used.
-1000 -900 aoo -7 00 -600 -500 400 -300 -200 -1 00 O
POtcntial rnV vs HgMgO ref.
Fig.5.15. The result f o r 20 V on the cathode side, when fresh stainless steel was used.
-rm -9~0 go0 -700 -600 500 -400 300 -200 -1 00
Potential mV vs HgMgO ref.
Fig.5.16. The resu l t f o r the carbon s tee l f o r 26 V on the cathode side, when the high current density stainless steel was used.
4 % 1
4 i
-1U)o -go0 800 -700 -600 500 -400 300 -200 -100 O
Potenti al mV vs HgMgO ref.
Fig.5.17. The result for the carbon steel for 2 6 V on the cathode side, when the fresh stainless steel was used.
From these graphs i t i s c l ea r t h a t one cathode is i n s u f f i c i e n t
t o pro tec t t h e system.
Looking a t the cathodic po la r i za t ion c u v e f o r t h e s t a i n l e s s
s t ee l 316, Fig. 3. IO., t h i s high cur rent d e n s i t y shows t h a t Hz gas
is produced a t very high ra t e . Thus t h i s may lead, as discussed
before, t o hydrogen embrittlement . Moerover, the high cu r ren t
needed i n some case may not be r ea l i zab le i n r e a l l i f e .
Fig.5.18 and 5.19. show the r e s u l t s , for the one electrode case,
a t the passive region. They show tha t the current dens i ty
d i s t r ibu t ion on t h e carbon s t e e l surface has a srnall v a r i a t i o n
when compared with the low concentration case. However, the
variat ion i n the po ten t i a l was very high on the s t a i n l e s s s t e e l
surface. I n Fig.5.19 when the potential on the cathode was
dropped by 100 mV, the d i f fe rence between the lowest and the
highest p o t e n t i a l on the s t a i n l e s s steel surface was reduced a
l i t t l e . However, decreasing the po ten t i a l f u r t h e r t o 552 mV a s
i n Fig.5.20., cuased t h e e n t i r e surface of the carbon s t e e l t o
pass back t o the a c t i v e region. This agrees w i t h what w i l l be
expected t o take p lace i n t h e real i ndus t ry where a drop i n the
applied current may result w i t h t h e corrosion of the d igeç te r .
The d i s t r i b u t i o n around the s t a i n l e s s s t e e l also shows t ha t the
surface f a r away from the cathode iç c lose r t o i t s corrosion
Fig.5.18. The model result f o r one cathode at 1224 mV.
Potential mV vs HgNgO ref.
Fig.5.19. The model r e su l t f o r one cathode at 1112 mV.
Fig.5.20. The mode1 result for one cathode when a l 1 p o i n t pass back t o the ac t ive reg ion .
Potential mV vs HgMgO ref.
Fig.5.21. Mode1 r e s u l t for the two cathodes case, when polarization curves for high concentration was used.
po ten t i a l . Therefore, t h a t s ec t ion may corrode f a s t e r than a l 1
of the o t h e r po in t s .
When two cathodes were used, which is the case i n Fig.5.21, t he
current d e n s i t y around the s t a i n l e s s s t e e l dropped. Also t h e
po ten t i a l and the current d e n s i t y d i s t r i b u t i o n s were uniforrn. I n
addit ion, the po t e n t i a l needed
passive zone alrnost reduced t o
of one e l e c t r o d e . In t he c a s e
po ten t i a l d i s t r i b u t i o n around
and the d i f f e r e n c e between t h e
t o hold t h e carbon s t e e l i n t h e
half of t h a t needed f o r t h e case
of t h r e e cathodes, Fig. 5 - 2 2 , the
the s t a i n l e s s s t e e l go t b e t t e r ,
lowest and the h ighes t p o t e n t i a l
became s m a l l e r . However, t h e appl ied cur ren t d e n s i t y and
po ten t i a l b a r e l y decreased.
Fig. 5 - 2 3 i l l u s t r a t e s how f o u r cathodes r e s u l t e d with a p o t e n t i a l
d i s t r i b u t i o n s imi l a r t o the th ree cathodes around the carbon
steel, and a l i t t l e d i f f e r e n c e between end t o end p o t e n t i a l
around t h e s t a i n l e s s steel. Though the applied c u r r e n t dens i ty
was reduced by about 20%, the applied p o t e n t i a l dropped on ly 103
from the case of th ree cathodes . This r e s u l t i n d i c a t e s that a t
some po in t an increaçe i n t h e number of cathodes will not add
much t o the improvernent of t he anodic pro tec t ion . Fig.5.24
i l l u s t r a t e s the change in the applied p o t e n t i a l , and proves that
w i t h the increase of the number of cathodes no b i g change will
SS3l6 for 0.008 V
I
Poteritial rnV vs HgMgO ref.
Fig.5.22. Model result f o r t h e three cathodes case.
r
Modal Resilb S S 3 1 6 pot. /
-- -
. t 00 400 400 -200 0 2
81 1 Potentiat mV vs HgMgO ref.
Fig. 5.23. Model result for the f o u r cathodes case.
be detected in either the applied potential or the applied
current. This is due to the fact that increasing the number of
cathodes has a direct influence on the area, so adding more
cathodes caused a decrease in the added area fraction, In
Fig.5.25 it is clear that increasing the nurnber of cathodes
irnproves the uniformity of the potential and the current density
around the carbon steel. However, no b i g change was observed
while increasing the number of cathodes from three to four. Even
the initial current density on the cathode is reduced with
increasing the number of the cathodes used as observed from
Fig.5.26. ALso the gap between the initial current densities
gets srnaller with the increase of the number of cathodes.
To improve the current density and the potential distribution
around the stainless steel central pipe, the effect of moving
the cathodes away from centre was investigated. In this case,
four cathodes were moved 100 and 140 cm away from the centre of
the digester. The result showed a very uniform potential and
current density distribution around both the stainless steel and
the carbon steel as shown in Fig.5.27 and 5.28. There was only a
srnall decrease in the potential on the stainless steel for the
140 cm spacing compared to that of the 100 cm spacing. However,
following the mapping of the zones given by Crowe and Troman
[32], it is clear that the stainless steel is in its active
region. This may result in corrosion attack on the surface.
' -8u.m ber 67 enthode&
Fig. 5.24.This graph shows the e i f ect of changing cathodes on the applied potential.
3.5 4
t h e number
Nodr #
Fig.5.25 Comparing t he current d e n s i t y distribution around the carbon steel when the number of cathode was varied.
' 1 cathode / 1 1 I ; + 2 cathodes i
* 3 cathodes i
++ 4 cathodes ( l
Fig.5.26. Current distribution around t h e cathode while comparing different numbers of cathodes.
- "cs 516 W Result for cs516 1 i
Potential mV vs HgCHg0 ref.
Fig. 5 . 2 7 . Model result f o r t h e case when t h e cathode was placed 1 0 0 cm away from t h e center.
a Resdt lbr cs516 l
-SS316 pal. 1 1
c 1
Potential mV vs HgMgO ref.
Fig.5.28. Model result f o r t h e case when the cathode was placed 140 cm away from the center.
Since t h e d i s t r i b u t i o n of the p o t e n t i a l i s uniform the co r ros ion
rnay be uniform a l s o . Due t o t h e low appl ied c u r r e n t dens i ty , no
hydrogen embrittlement is expected while keeping the system a t
t h i s condi t ion . Although i n Fig. 5.29 t h e cur ren t d e n s i t y
d i s t r i b u t i o n around the carbon s t e e l (anode) became more v a r i e d
while the cathodes were moved c l o s e r t o it, t h e r e was no e f f e c t
on the p a s s i v i t y of t h e metal su r f ace . This can be c lea r ly seen
i n Fig.5.27 and 5.28, where t h e da ta a r e p l o t t e d on the
po la r i za t ion curve. When the s i z e s of the fou r cathodes were
changed, as i n Fig.5.30 and 5.31, they were loca ted a t 140 an
from the cen t r e . No b i g change was detected i n the c u r r e n t
dens i t y d i s t r i b u t i o n .
A s Fig.5.30. shows the s t a i n l e s s s t e e l c u r r e n t d e n s i t y iç
uniform, s i m i l a r t o what was observed f o r t h e 2.5 u n cathode a t
1 0 0 cm and 1 4 0 cm away from the cente r . Fig. 5.31 confirms t h a t
as the cathodes are moved away from the anode, t he c u r r e n t
d e n s i t y around t h e anode becomes more unif orm. Therefore,
increasing the s i z e of t he cathode will have b e t t e r r e s u l t f o r
cathodes placed f u r t h e r away from the carbon s t e e l , near the
s t a i n l e s s steel.
Fig.S.32 shows the mode1 resul t for t h e c o n c e n t r i c geometry. The
same dimensions as t h e low concent ra t ion case were used. I t is
observed t h a t the concent r ic geometry highly improves and
Fig .5 .29 The c u r r e n t denisty d i s t r i b u t i o n around t h e carbon s t ee l i n t h e pass ive area.
Fig.5.30 The c u r r e n t d e n s i t y distribution around the s t a i n l e s s steel, while t h e carbon i s in t h e passive area, and t h e radius of t h e cathode i s changing.
Fig. 5.31 The c u r r e n t denisty distribtuion around the carbon steel for changing the sizes of four cathodes.
-Io00 -900 8QO -700 -600 -500 4 0 -300 -200 -1 00 O
Potential mV vs Hg/HgO ref.
Fig.S.32. The carbon s teel polarization curve and the mode1 r e s u l t when concentric geometry was used.
reduces t h e initial required current density. In addition, the
current density required to maintain passivity was approximately
1/9 of that for the four cathodes case.
Table.5.1. summaries the applied potential and the current for
the systems discussed above. The cooking zone has the lowest
applied potential to keep the system in the passive region.
Whereas the high concentration one cathode case will need a
potential as high as 2.5 V vs Hg/HgO r e f . to keep the system in
the protected zone. Though moving t he cathodes closer t o the
anode did not result in a change in the current density
distribution around the carbon steel, but it resulted with a
drop in the applied potential and the cathode3 c u r r e n t density.
This will result in a lower protection cost, since the power
needed to p r o t e c t the system w i l l also decrease. However, as
discussed above these cases a r e not good for t h e stainless
steel, which ni11 be in the active zone in both cases.
Table. 5.1. The applied potential r e s u l t for the dif ferent
studied cases.
High
concentration
-
Low
Concentrat ion
Cooking
Impregnation
Concentric Low
Conc
Concentric High
Conc,
Number of Solution I cathodes Pot. V
1 -1 , 112
2 -.216
3 ,008
4 . 008
4 a t 100 .232
Cath. Cd in the
pass ive UA/ cm'
-100000
-38325.7
Applied
6 . CONCLUSIONS
As a result of this study the following conclusions were
reached :
1. The mathematical mode1 qualitatively represented
protection for the given polarization curves in
dimensional geometry.
2.A carbon steel with a low critical current
polarization curve will be easily protected by
protection, with only one or two cathodes.
anodic
a two
density
anodic
3. In the high concentration case {impregnation zone) , one srnall
cathode is insufficient to protect the system. This is due to
the high current needed to maintain the carbon steel in the
passive region. It rnay also lead to hydrogen production at the
cathode, which in turn may lead to hydrogen embrittlement of
the stainless steel which is the closest to the cathode.
4. Increasing the number of the cathodes, which means increasing
the cathode's area, leads to a more uniform distribution of
the current density and the potential around the carbon steel
and stainless steel surfaces. In this study, four cathodes
resulted with a good anodic protection for both metals.
5.Concentric cathode geometry showed i n the numerical
simulation, that the required current densi ty and the applied
potent ia l are reduced dramatically.
6. I t is important t o be sure not t o lower the cur rent t o a very
low value where the systern may jump back t o the a c t i v e region,
as it is the case in Fig.5.20.
7. Moving the cathodes c loser t o the carbon s t ee l improves the
potential distribution around the stainless s t e e l , but reduces
its potential to the active zone where corrosion may take
place.
8 . I t is important t o try t o protect both materials i f t he
cathode uill not be placed concentric with the stainless
steel. Otherwise, while trying to protect the carbon steel,
t he s t a i n l e s s steel may corrode.
T o o b t a i n a b e t t e r achievement from anod ic p r o t e c t i o n system,
f u r t h e r s t u d i e s a r e needed as fo l lows :
1. More s t u d i e s should be done t o unders tand t h e chernical
kinetics r e l a t e d t o t h e pass ive and active behaviour of the
s t a i n l e s s s t e e l i n white l i q u o r .
2 . More s t u d i e s concerning t h e ca thode ' s e f f e c t on the
s t a i n l e s s s t e e l should be done. It w i l l be v a l u a b l e t o know
a t what hydrogen gas c o n c e n t r a t i o n hydrogen damage t o the
s t a i n l e s s s t e e l will occur .
3 . A numerical s imu la t i on of anodic p r o t e c t i o n should be
perforrned, before it i s a p p l i e d t o a real d i g e s t e r .
4 . Though normal ly t he carbon s t ee l i s the major focus o f
anodic p r o t e c t i o n , t h e s t a i n l e s s s tee l shou ld also be
considered, if the cathodes are going t o be p l a c e d c l o s e t o
the wall of the stainless s t ee l c e n t r e p i p e .
l.Riggs, Olen L. and Locke Carl E.,Anodic Protection Theory
and Practice in the Prevention of Corrosion, Plenum Press,
New York, 1980, p 3-123.
2 . Denny A. Jones, Principles and Prevention of Corrosion,
Prentice-Hall, NJ, 1992, pll6-138.
3. T. Hakkarainen ,"Repassivation Potential of Corrosion pits in
stainless steel" Passivity of Metal and Semiconductors, New
York, 1981, p367.
4. James P. Casey, Pulp and Paper Chemistry and Chernical
Technology, John wiley and sons. Inc, Canada, 1980, p161-
219.
5. Insruber, 0. V., Kocurek, M. J., and Wong, A., Pulp and
Paper Manfacture, Joint Text book committee of the paper
industry, V 4 . , 1983, P97-128.
6. Wensley, D. A., Charlton, R. S., "Corrosion Studies in Kraft
White Liquor: Potentiûstatic Polarization of Mild Steel in
Caustic Solutions Containing Sulfur Speciestf, Corrosion , 36
(8) 385- 389 (1980)
7 . Wensley, D. A., "Corrosion Studies in Kraft White Liquor
Tankage", Corrosion symposium, 1986. P 15-22.
8. Wensley, D. A., " Corrosion and Protection of Kraft
Digesters", TAPPI Journal. Vol. 79 (10) 1996. p 153-160.
9. Wensley, D. A., " Corrosion of Batch and Continuous
Digesters", International Symposium on Corrosion in the
Pulp and Paper Industry. Ottawa 1998. p 27-37.
lO-Mueller, W. A., " Corrosion Rates of Carbon Steel Tubes in
Kraft Liquor With an Without Anodic or Cathodic Protection"
Pulp and Paper Industry Corrosion Problems, V 2, 1977, p
140-146
11 .Bennett, D. C., Anodic Protection for corrosion prevention
in a Soda process Continuous Digester" Third International
Symposium Corrosion, 1980, p322-328.
12 .Crowe, C. and Tromnas, D. " High-temperature polarization
Behaviour of Carbon Steel in Alkaline Sulphide Solution"
Corrosion, 44 (3) 142-148 (1987) . 13. Crowe, C., " On-line Corrosion monitoring in Kraft White
Liquor Cla r i f i e r su , TAPPI Journal. Vol. 79 (6) 1996. p.166-172.
14. Protch Orest, " Preventing Anodic protection Failures on
Pulp Digesters", Welding Journal. 1994 Jan., p . 83-85.
15. Yeske, Ronald A., Hill, E., " Anodic Protection of white
Liquor Clarifier", Corrosion Symposium, 1985, p. 219-225.
6 . A. Brebbia, J. Dominguez," Boundary Element an
Introductory course" McGraw Hill, Great Britain, 1989.
17. W. Partidge, C. A. Brebbia, ' The Dual Reciprocity
Boundary Element Method" McGraw Hill, New York, 1992, p24-
18.V. Ingruber, M. J. Kocurek, and A. Wong, " Pulp and Paper
Manufacture" Joint text book committee of the paper
industry, 1983, p97-128.
19. E. Varela, Y. Kurata, N. Sanada, " The Influence of
Temperature on the galvanic corrosion of a Cost Iron-
Stainless Steel Couple" Corrosion-Science, V 39 ( 4 ) 1997,
20. F. Yan, S. N. R. Pakalapati, T. V. Nguyen, and R. E.
White, \' Mathematical Modeling of Cathodic protection Using
the Boundary Elernent Method with a Nonlinear Polarization
curve" J. Electrochem. Soc V 139(7) 1992 p.1932-36.
21. Singbeil, D. L. and Trornans, D. " Stress Corrosion
Cracking of mild Steel in Alkaline Sulfide Solution" Third
international symposium on corrosion in pulp and paper
industry, Sweden V 4, 1980, p40-46.
22. Singbeil, D. L. and Garner, A., ' Electrochemical and
Stress Corrosion Cracking behavior of Digester Steel in
Kraft White Liquors", Corrosion- NACE 1985 p. 634-39.
23. Singbeil, D. L. and Garner, A. , \' Potential-dependent
Cracking of Kraft Continuous Digesters" r TAPPI Vol 6 8 ( 4 )
1985. p . 112-16.
24. Wensley, D. Angela. " Cracking of Continuous Digesters: an
Uptodated Survey", TAPPI., V 71(8) 1989. p. 211-15.
25 . Bennet, David C . " Cracking i n Continuos Diges t e r s :
His tory of t h e problem and the search f o r p reven t ive
measure", TAPPI., V 65 ( 1 2 ) 1982, p.43-45.
2 6 . Yeske, Ronald A . , Guzi, Charles E, " I n - s i t u Studies of
s t r e s s Corrosion Cracking i n Continuous Digester" Tappi
Journal , V 6 9 ( 5 ) 1986, p . 104-08.
27 . Bennet, David C . . " Cracking of Continuous Diges t e r s :
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a f f e c t i n g cracking", Fourth i n t e r n a t i o n a l symposium on
co r ros ion in pulp and paper indus t ry , Sweden V 4 , 1983
28 . Rondel l i , G . , V i c e n t i n i , B . , and Sivieri, E . , " S t r e s s
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29. Ashour, E . A. , Abd E l Meguid, E . A. , and Ateya, B . G . , \\
Effects of Th iosu l f a t e on S u s c e p t i b i l i t y of Type 316
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( 6 ) 1989, p . 478-87.
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9. APPENDIX A,
Tab1e.A. 1 The c u v e fit parameters fox the forward scan f o r carbon steel in the l o w concentration case.
Parmeters
Tab1e.A. 2 T h e curve f i t parameters f o r the backward scan for carbon steel in the low concentration case.
Paramet ers
Tab1e.A. 3 The curve fit parameters f o r the stainless s tee l in t he low concentration case.
Parameters
Sj b j v4 (mV) i'j
Tab1e.A. 4 . The curve fit parameters f o r the forward scan for t he high concentration case f o r t h e s t a i n l e s s s t e e l .
Tab1e.A. 5. The curve fit p a r m e t e r s for the forward scan f o r an old stainless s tee l in the high concentration e l e c t r o l y t e case.
Parameters
4 v' (mV)
Appendix B.
Table B. 1. Conductivity (mS/cm) for the lab and i n s ide the
digester electrolyte solutions
High Concentration
Low concentration
Inside the digseter 254