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.

National Library I*I of Ca,, Bibliothèque nationale du Canada

Acquisitions and Acquisitions et Bibliographie Sewices services bibliographiques

395 Wellington Street 395, rue Wellington Ottawa ON K1A ON4 Ottawa ON K I A O N 4 Canada Canada

The author has granted a non- exclusive licence allowing the National Library of Canada to reproduce, loan, distribute or sel1 copies of this thesis in microform, paper or electronic formats.

The author retains ownership of the copyright in ths thesis. Neither the thesis nor substantial extracts f?om it may be printed or otherwise reproduced without the author's permission.

L'auteur a accordé une licence non exclusive permettant à la Bibliothèque nationale du Canada de reproduire, prêter, distribuer ou vendre des copies de cette thèse sous la forme de microfiche/film, de reproduction sur papier ou sur format électronique.

L'auteur conserve la propriété du droit d'auteur qui protège cette thèse. Ni la thèse ni des extraits substantiels de celle-ci ne doivent être imprimés ou autrement reproduits sans son autorisation.

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 :

Review of h i s t o r y , co r ros ion engineer ing a s p e c t s and factors

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

Corrosion Cracking of S t a i n l e s s S t e e l s i n High Temperature

Caustic Solut ions" , Corrosion Science, V o l . 39(6)1997, p.

1037-49,

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

S t a i n l e s s S t e e l To s t r e s s Corrosion Cracking i n 3 .5% Aqueous

Sodium Chloride", Corrosion, Vol 5 3 ( 8 ) 1997, p.612-16.

30. Spath, Helmuth, Spline Algori thrns f o r curves and s u r f a c e s ,

Utilitas Mathematics Publ ishing Inc, Manitoba, Winnipeg.

Canada, 1974 pp32-59.

31. Yeum, K . S . and Devereux, O. F. "An I t e r a t i o n Method f o r

F i t t i n g Complex E lec t rode P o l a r i z a t i o n Curves" Corrosion, 4 5

( 6 ) 1989, p . 478-87.

32. Crowe, D. C. and Troman, D."Caustic Cracking of Stainless

Steel" Canadian Metallurgical Q u a r t e r l y , V 23 (1) 1984, p . 99-

106.

3 3 . Bank, W. P . , Hutchison, M. and Hurd , R. M."Anodic

p r o t e c t i o n of Carbon S t e e l i n A l k a l i n e S u l f i d e Pulp

digesters" TAPPI, V 50 ( 2 ) 1967, p . 49-55

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