ageing of electroinsulating cellulosic materials

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Ageing of electroinsulating cellulosic materials.Part I. Chemistry, mechanisms and kinetics of decomposition of cellulose

Vadim G. Arakelian

All-Russia Electrotechnical institute, Moscow, Russia

Alan M. EmsleyGnosysUK Ltd, University of Surrey, Guildford, Surrey, GU2 7XH, UK

Abstract

Exact kinetic equations are developed to describe the degradation of cellulosic insulation in electrotechnical

equipment that include all environmental factors such that the equations can be used in an engineering environment to

model ageing under known conditions. The differing rates of ageing of crystalline and amorphous cellulose are consid-

ered, as well as external influences such as heat, moisture and oxygen.

Index Terms Transformer, Insulation, Condition, Cellulose, Degree of Polymerization, Ageing,

Life Assessment, Furan Compounds, Dissolved Gas, Water, Fault Diagnosis

Introduction

Modern transformers are insulated with cellulose-based materials impregnated with insulat-

ing oil. They degrade under operating conditions, due to the effects of heat, moisture and oxygen,

losing their initial properties, as the degree of polymerization of the cellulose is reduced. The first

part of this article considers theoretical aspects of the decomposition, providing definitive kinetic

equations for paper degradation as a function of operating conditions. The calculations are based on

two mechanisms of cellulose decomposition; one occurring in an amorphous fraction, accessible to

the oil, and the second in impervious crystalline cellulose. They include the effects of temperature,

humidity, initial degree of polymerization (DP), preliminary heat treatment, oxygen content of the

oil, antioxidant content, acid number and other factors such as the activation energy of scission of

glycosidic linkages. The formation of furfural, water and gaseous oxides of carbon and the distribu-

tion of all the components between the gas phase, oil and paper and effects of water and oxygen in a

transformer are considered in Part II.

The authors utilize the extensive literature of cellulose ageing [1] [39] to develop a set of

equations for engineers to use.

Chemistry of decomposition of cellulose

The paper and oil used to insulate transformers are known to decompose at rates that are

dependent on temperature and the presence of air and water. We know that ageing of paper results

from chemical changes in the cellulose, but the mechanism of decomposition is not well understood

and there is no strict representation of the chemistry of the process. However, the known depend-

ence of cellulose decomposition on a number of external conditions has established that the process

proceeds in one of the following ways.

Hydrolytic degradation

Water and acids attack the glycosidic linkage (the oxygen bridge) between glucose rings,

liminating one or more of them from the cellulose chain. At normal atmospheric humidity, papercontains 7 8 % of water by weight, but insulation paper is usually dried before use to minimize


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this type of decomposition. Nevertheless, the reaction becomes increasingly important as the

amount of water in the insulation system increases with time due to other processes.

Oxidative degradation

When cellulose is oxidized, the end-products depend on temperature, pH and the nature of

the oxidant. In all cases, hydroxymethyl groups in cellulose are oxidized to form carbonyl (alde-

hydes) and carboxyl (acid) groups. Water is also produced as a result of this chemical process. Thepresence of carboxyl or carbonyl groups weakens the glycosidic linkage and can lead to breakage of

the chain and further oxidation.

Thermal degradation

Heating cellulose in the absence of water or oxidant at temperatures up to 200 results in

severance of the glycosidic linkages and also opening of the glucosidic rings, to form mainly water

and oxides of carbon, but also glucose and organic acids.

The presence of water and oxygen also influences the further chemical transformation of

compounds formed from cellulose. In the presence of excess oxygen, carbon dioxide is the basic

oxide of carbon formed. Where the hydrolytic mechanism dominates some glucose product (or,

more exactly, its dehydrated form 1,6-anhydro--D-glucopyranose, levoglucosan) is transformedinto furan-based compounds due to further dehydration, with the release of more carbon dioxide

and water.

Formation of furan compounds

The amount of glucose produced could be used as an indicator of the degree of paper de-

composition, but its solubility in mineral oil is very low and it mainly remains within the paper.

Under the influence of moisture and acids the glucose transforms to derivatives of furan such as:

2-furaldehyde (furfural), 5-hydroxymethylfurfural, 2-furfurylalcohol, 5-methyl-furfural, 2-acetyl-

furan and 2-furancarbonic acid, depending on the local chemical conditions. Detailed chroma-

tographic analysis [14] using high performance liquid chromatography has also shown the presence

of 3-furancarbonic acid, methanol, a monomethyl ether of hydroquinone and benzaldehyde. A sec-

ond source of furfural is hemicellulose, which accounts for up to 67 % of the dry weight of Kraft

paper*).As the chemical polarity of furan compounds increases their solubility in mineral insulation

oil decreases. The most soluble in mineral oil are furfural and methylfurfural, whereas furan car-

bonic acid is practically insoluble in both oil and water. Adsorption of water-soluble furanic com-

pounds (all the above mentioned except acetylfuran and furan carbonic acid) on to paper increases

with increasing water content of the paper. The solubility of furanic compounds in oil influences the

formation of end-products, driving the chemical reactions towards the formation of compounds

more soluble in oil, by removing them from the reaction zone. The more insoluble products of reac-

tion remain in the paper until external factors convert them into more soluble compounds. Researchhas shown that furfural is the dominant furan product.

The general description of cellulosedecomposition

It is known, that the basic structural formations of cellulose are crystalline cellulose (up to

70 % by weight, a compacted structure accessible to diffusing molecules, but inaccessible to oil)

and amorphous cellulose (rather open structure, more accessible to oil). The decomposition of cellu-

lose, as an element of insulation of oil-filled equipment, proceeds simultaneously by two independ-

ent processes. One takes place production of furfural. in the oil-impregnated amorphous phase and

the other in the bulk of the cellulose inaccessible to the oil.

*) Hemicellulose (pentozane(584) n) is an initial product for industrial production of furfural.


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Severance of a cellulose chain occurs at the glycosidic link between glucose units and re-

sults in the formation of levoglucosan. Where the cellulose molecule is in the amorphous phase sur-

rounded by mineral oil and the levoglucosan remains in this comparatively dry, oxygenloaded envi-

ronment, it will degrade to oxides of carbon and water. In addition, oxidizing processes will form

carboxyl groups, which promote decomposition to oxides of carbon, water and low molecular

weight aldehydes and acids. The amorphous phase is the most vulnerable to decomposition, because

of its exposure to the oil environment. Within it, ends of glycoside chains (the so-called fringe),floating in the oil environment, are particularly vulnerable to the effects of heat and oxygen. They

are most likely to form low molecular weight products such as water and gases oxides of carbon,

hydrogen and light hydrocarbons 1 and 2 (except acetylene). However, the contribution of such

vulnerable parts of cellulose is insignificant, except in the early stages of ageing and decreases with

time as the fringe is consumed.

If degradation occurs in the crystalline cellulose where access of oil is restricted, but water

can diffuse freely, the products (glucose or levoglucosan rings) are surrounded by adsorbed water.

They are vulnerable to ring opening processes and transformation to furan compounds by consecu-

tive dehydration reactions and some will diffuse out and dissolve in the mineral oil. Approximately,

one third of levoglucosan products contribute to furan formation, the remainder degrades to oxides

of carbon, water, other gases and simple compounds.There is a continuous competition between decomposition reactions that form gases (mainly,

2 and CO, and also 2 with the participation of oxygen) and hydrolysis reactions that result

in the formation of2, 2 and furan compounds (mainly, furfural). The latter process dominates

in the crystalline phase where the cellulose is heavily impregnated with water and the former in the

amorphous fringes. The type of reaction occurring is not specifically determined by the cellulose

structure, but is solely due to the environment. For convenience, we shall refer to the first process as

that occurring in the fringe and the second as that occurring in the crystalline cellulose.

The concept of bond splits in the crystalline cellulose

The concept has been described as follows [25]. It is supposed, that fresh, non-degraded cel-

lulose is an absolute monodisperse polymer, so an initial degree of polymerization DPo = 1000, for

example, means that all cellulose chains have 1000 glucose rings. Thermal degradation of a mole-

cule of cellulose results in the formation of two chains with a lower degree of polymerization, one

of which is unstable and loses one unit of levoglucosan. Chemically:

DP DP1 + DP2 + Levoglucosan ()

As soon as thermal degradation starts, cellulose loses its monodisperse property and becomes a

mixture of chains of different length: DP, DP1 and DP2. If the molecule fragments remain in the

bulk of the cellulose, the degree of polymerization becomes

x DP +y (DP1 + DP2)DP =

x + 2y

wherex is the number of undegraded molecules and 2y is the number of degraded fragments. SinceDP1 + DP2 = DP (strictly DP 1, but DP is large enough to ignore 1), then

(x +y) DPDP = (1)

x + 2y


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The initial number of molecules of cellulose is

M=x +y (2)

andM can be calculated from the molecular weight as

M= 106Gp/ (162 DP) (3)

whereGp is the mass of paper (in tonnes), 162 is the molecular mass of the anhydroglucosidic ring.Substituting x =My from equation (2) in the equation 1 gives

MDPDP = (4)

M+yso

M(DP DP)y = (5)DP

and after substituting equation (3)

y = 106

(Gp/ 162)(1/ DP 1/ DP) (6)

The value ofy represents the number of cellulose chains that have undergone degradation atany moment in time with the formation of molecules of levoglucosan. Thus, the weight of the de-

composed paper (mp) in grams, is given by

mp = 106Gp(1/DP 1/DP) (7)

where Gp is in tonnes. According to this equation, the mass of decomposed paper corresponding toa change of degree of polymerization of 1000 to 250 is 3 mg per gram. Thus a comparatively small

loss of cellulose mass results in a drastic drop in degree of polymerization.

The main feature of this mechanism is that it is independent of the position of scission of the

cellulose molecule, provided that all the formed fragments remain in the main bulk of the cellulose.

The majority of cellulose decomposes in this way.

The concept of separation of end-rings in the insulating oil environment

Whereas rupture within a chain results in a sharp decrease in the degree of polymerization,

separation of a terminal ring or several links and subsequent decomposition to gases and water does

not cause an appreciable change in the degree of polymerization. Such a process can occur to cellu-

lose chains with free ends floating in the aggressive environment of the mineral oil mainly in the

amorphous fringe, but with some small contribution from crystalline cellulose. The ruptured end-

rings, surrounded by molecules of oil, remain in the mineral oil until the action of oxidants and free

radicals decomposes them to water and gases.

This mechanism probably operates continuously, but its contribution is likely to be most im-

portant in the initial stages of equipment operation, during the early stages of ageing of the paper

insulation, in that small fringe area in the amorphous cellulose region. Although this mechanismgenerates cellulose decomposition products, the main decrease in the degree of polymerization

arises from central chain scission.


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When rupture occurs at the extreme ends of a chain, the degree of polymerization of the

given molecule will decrease by the number of ruptured rings. The average degree of polymeriza-

tion of paper will therefore be given by

xDP +y(DP n)DP = (8)

x +y

where x is the number of the molecules not decomposed, y is thenumber of the molecules that have

undergone decomposition, n is the number of ruptured end-rings. The total number of molecules ofcellulose remains

M=x +y

After substitution of equation (2) into equation (8) the following formula is derived:

yn =M(DP DP) (9)

The product yn is the number of moles of levoglucosan formed as a result of the given process. If

yn is multiplied by molecular weight of levoglucosan,the mass of levoglucosan can be calculatedand is equivalent to the amount of paper lost, mp, which will eventually be transformed into gases

and water. After substitution ofM(from equation (3))

DP DP

mp = 162 yn = 106Gp (10)

DP

This equation shows the relationship between the mass of levoglucosan formed and thechange of degree of polymerization due to rupture of end-rings. Consequently, if the process of de-

composition of paper proceeded only by this mechanism then, at DP = 250 (from DP = 1000) three

quarters of all the mass of cellulose would be decomposed. That is a rather large loss of weight for a

minor change in degree of polymerization and is not observed in practice. Only the very small part

of amorphous cellulose with terminal linkages, mainly in the fringe, is subject to this mechanism.

Kinetics of decomposition of cellulose

The rate of chemical reaction for the decomposition of crystalline cellulose to furan com-pounds is constant and mainly depends on temperature, humidity and other external factors. It is

independent of the initial cellulose concentration, since the stock of available paper is effectively

unlimited and only an insignificant fraction is consumed during decomposition, i.e. the reaction can

be treated as monomolecular of zero order reaction. Thus

dc/dt= k (11)

where k is the rate constant of cellulose decomposition, c is the concentration of cellulose in

moles. Provided that Gp is the mass of paper, in tones,


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c = Gp /(162 DP)*)

and equation (11) becomes

d(1/DP)/dt= kDP

wherekDP is the rate constant for change of degree of polymerization. The equation integrated to:

1/DP 1/DP = kDPt (12)

Emsley [23], [24] has come to the same equation from empirical considerations and has

demonstrated it can be applied to the historical data of Fabre and Pichon [13] and others. Accepting

the concept of a zero order of reaction has now allowed it to be derived by theory. Emsleys subse-

quent interpretation [26] of the pre-exponential factor in terms of the temperature dependence of a

decreasing rate of reaction improved the fit to experimental data. Calvinis interpretation [28] in

terms of Limit Of DP (LODP) adds theoretical credence. We can now further improve the interpre-

tation by considering the following factors that influence the values [23] of the pre-exponential fac-

tor for Kraft and cotton paper.Viz:

humidity of the paper,

concentration of oxygen,

amount of antioxidant or acidity of the oil,

the 2.5-fold increase in the yield of furan compounds (hence decomposition of paper) in air

compared to in vacuo [25], [31],

independence from oxygen concentration at high humidity [27],

2 acceleration of ageing in old non-inhibited oils compared to new non-inhibited oils [36], 2.7 acceleration of ageing in new non-inhibited oil compared to new inhibited oil [36], 1.3 acceleration of ageing in old inhibited oil compared to new inhibited oil [36].

We can express the degree of ageing in inhibited oils in terms of the concentration of anti-

oxidant ant (%) and the degree of ageing of non-inhibited oils through the acid number AN (mg in 1 g oil) as follows:

(ant antallow) AN ANnor for inhibited oils = 0.5 0.11 +

(antnorant

allow) ANallow ANnor (13)

AN ANnor

for non-inhibited oils = 1 + ANallow ANnor

where ANallow, ANnorare the acid numbers, allowable for old insulation oil and normative for new

insulation oil and antallow andant

nor are allowable and normative values of the concentration of an-

tioxidant respectively.Then the equation to calculate the rate constant of change of degree of po-

lymerization is

kDP= 0.5(3WmW)2 kb10

8 + 0.38 WeEA /(RT) (14)

*) Formally, the mole concentration of paper increases as the degree of polymerization decreases (therefore there is no

minus sign in equation (11)).


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where 2 is the relative contents of oxygen (0.21 in air), Wis the humidity of the paper (in %)within the limits of three molecular adsorption layers

*)(that is forW3Wm),kb is determined by

the basis of the paper: for Kraft it equals 1, for cotton 0.3, EA is the energy of activation in kJ/mol,

Tis the absolute temperature. The humidity of a monomolecular layer can be calculated and thedata resulted in the Table 1.

Table 1. The initial data, equation and factors for calculation of humidity of a monolayer for three

types of paper [16]

Humidity of a monolayer, Wm, %Temperature, Cable paper K-120 Cardboard Capacitor paper

-2

23

26

29

45

70

4.38

4.25

3.86

3.44

4.6

4.44

3.92

3.30

4.22

4.08

3.25Wm = 2.7547+2114.7/ 5.1544+2893.8/ 3.1154+2184.3/

Thus, the change of degree ofpolymerization can be calculated in terms of time and the pa-

rameters of ageing experience (or operating condition, if it is considered to be constant) from equa-

tions (12), (13) and (14). The amount of decomposed cellulose in the bulk of crystallite according to

the equations (7) and (12) is:

mp = 106Gp(1/DP 1/DP) = 10

6GpkDPt (15)

The differential equation for end-ring scission is:

dmp / dt= kpm-p

so the mass of the decomposed cellulose will be expressed by the equation

mp = mp, [1 exp (kp t)] (16)

where mp, is the initial amount of fringe cellulose affected by mineral oil and available to decom-

pose, kp is the rate constant of cellulose decomposition by this mechanism and tis time. Decompo-sition proceeds much faster by this mechanism, than in crystalline cellulose and would ultimately

reduce the DP of participating molecules to unity. In the same time frame the change of DP in crys-talline cellulose will be insignificant, due to the inaccessible nature of the material.

The mechanism of decomposition of crystalline cellulose with formation of levoglucosan is

described by equations (7) and (15), where the product of rate constant and time is related to 1/DP

1/DP, equaling kDPt(equation (12)). However, the rupture of end-links in mineral oil leads to a re-

lationship described in terms of (DPDP)/DP (equation (10)) equal to kpt. Thus

kpt= (DPDP)/DP = 1 DP/DP = DP(1/DP 1/DP) = DP k'DP t= DP k kDP t

*) The fourth layer of adsorbate has insignificant influence on the adsorbent and partial pressure of the adsorbate ap-proaches saturation pressure. This approach relates to the fact that the speed of decomposition of a paper is proportional

to its water content approximately up to 7 % of humidity [21].


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where k'DP is the rate constant for an equivalent change in degree of polymerization due decompo-sition in crystalline material and k is a conversion factor to the rate constant in crystalline cellulose

(kDP). Substituting for DP from equation (12) DP = 1/(kDPt+1/DP), the final expression forfringe decomposition becomes

k

kpt= (17)1 + 1

DP kDP t

and the kinetic equation (16) for the mechanism of end-link rupture in oil is

mp = mp, [1 exp (k /(1/(DP kDP t) + 1))] (18)

The small amount of fringe cellulose affected by mineral oil and undergoing end-link deg-

radation (mp, in grams) can be expressed as a fraction* of the total:

mp,=*106Gp (19)

where Gp is the mass of paper in tonnes. The kinetic equation of paper decomposition for end-linkscission, expressed in terms of the parameters of crystalline decomposition, becomes

mp = *106Gp [1 exp (k /(1/(DP kDP t) + 1))] (20)

Summing up, two independents processes of paper degradation can be described through

one rate constant for change in degree of polymerization and time:

process I(in the oil interface) mp = *106Gp [1 exp (k/(1/(DP kDP t) + 1))] (equation 20)

process II(in the (crystalline) bulk cellulose) mp = 106GpkDP t (equation 15)

and the mechanism of decomposition of cellulose is determined not by the presence of the so-called

"weak links", but by the environment.

Effect of moisture and degree of polymerization on long term ageing

Because there is a substantial growth in water content of the oil-filled electric equipment in

service, and water content of papers strongly influences the speed of its thermal decomposition, it

becomes clear that its actually wrong to consider a rate constant of paper decomposition as a con-

stant. According to equation (14) the increase in humidity should result in an increase in the rate

constant. However, Emsley [27] has come to the conclusion, that decomposition process gradually

decreases and introduced a correction to take this phenomenon into account. He showed that the

equation

d(1/DP)

= k1 exp(k2t) (21)dt


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correctly described a slowing down of decomposition at the final stage upon achievement at low

values of degree of polymerization. The equation (21) integrates to

1 1 k1

= (1 ek2t

) (22)

DP DP k2Clearly, the conclusion can be drawn that there is some physical phenomenon which com-

pensates for the accelerating action of increasing humidity.

It is obvious, that time, i.e. duration of degradationprocess, is not the reason for the decrease

in the rate constant, as it follows from the equation (21), but the decrease in a degree of polymeriza-

tion. If we write the rate constant as a linear function of reciprocal degree of polymerization

d(1/DP) / dt = k1 k2/DP (23)

then the integrated solution can be completely equivalent to equation (22)

1/DP 1/DP = (1/DPmin 1/DP)(1 ek2t

) (24)

where k1/k2 in equation (22) equals (1/DPmin 1/DP), provided t and DPmin is a limit to whichthe degree of polymerization will approach at the given temperature. Both equations (22) and (24)

imply that the decomposition will reach a certain degree of polymerization and then stop. This con-

cept is highly improbable. The process can considerably slow down, but not stop, and will proceed

until total destruction of the cellulose material.

The true reason for the decrease in rate is increasing activation energy of glycosidic linkage

scission as the degree of polymerization decreases. The structure of cellulose in paper, an artificially

prepared product, is non-uniform and so are the energy levels of molecules. Rising temperature re-sults in a mechanical tension in the molecules due to the increasing amplitude of fluctuation of at-

oms. Steric (spatial) factors in the solid result in a range of activation energies for linkage scission.

The lower activation energy linkages break first so that the energy required for further scission

gradually increases to that of a non-sterically hindered structure i.e. that of a dimer or trimer.

Equation (14) defines the influence of humidity and energy of activation on the rate con-

stant. An increase in humidity from 0.2 to 2% accelerates the process by 4 5 times. An increase in

energy of activation from 110 to 115 kJ/mol reduces the rate by a factor of 4 6 and would thus

compensate for the change in humidity.

Decomposition of the paper is the main source of water and the second part of this article

will define specifically the amount of water produced. Here we give a general view only:

W= N + Mt (25)

where N and M areconstants determined by conditions of experimental or operational conditions.Steric factors dictate that the activation energy is at a minimum, when the degree of polym-

erization is highest. When the degree of polymerization is reduced due to destruction of the most

strongly affected molecules, the energy of activation increases to a level, typical of more compact,

less sterically hindered molecules in the limit up to dimer.

As with all solid material, change of paper temperature results in internal pressures due to

thermal change in volume. The greater the temperature rise, the more the internal pressure and the

greater the deformation pressure on the glycosidic bond. This reduces the durability of the bondand, hence, less energy is required to break it. We can represent this effect, for any particular work-


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ing range of temperature, through a factorL = e

. Then the final equation for calculation of en-

ergy of activation for DP 200 (say as a lower limit) will become

200

EA = (EA,o + EA ) e

(26)

DP

Using data published in [27], equation 26 can be written:

200

EA = (147 + 9.7 ) e0.0008

(in kJ/mol)DP

We can substitute equations (25) and (26) into equation (14) to calculate the rate constant as

a function of humidity, energy of activation, degree of polymerization and time

kDP= e0.5(3Wm NMt)2kb10

8 + 0.38(N + Mt)e

L(EA,o + 200 EA/DP)/(RT) (27)

Equation (27) can be generalized as:

kDP=A eBt

eb/DP

(28)

where:

A = e0.5(3Wm NMt)2

kb108 + 0.38N

eEA,oL/(RT) ,

B = (0.875 0.52 )M,

b = 200EAL / (RT),L = e

0.0008T,

2 is the relative content of oxygen in the gas space above the oil (0.21 in air),N and M in (25) are determined by humidity analysis of the oil (see Part II),

comes from equation (13),Wm is determined from the equations in Table 1,

kb is 1 for Kraft and 0.3 for cotton,

EA,oandEA are 147 and 9.7, accordingly,

tis time in hours,

R = 8.3144 kJ/(molK).The kinetic equation in the differential form is:

d(1/DP) / dt = kDP=A eBt

eb/DP

which integrates to:

eb/DP

eb/DPo A

= (eBt

1) (29)b B

forW 3Wm, (designations are given above).


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Equation (29) defines the change in degree of polymerization of paper up to the point of for-

mation of the fourth molecular adsorption layer of water. The time required to attain the humidity of

this condition (in hours) is determined from equation (25)

tmax = (3Wm N)/ M

Further increases in humidity do not affect the process of paper degradation, because thepartial pressure of water approaches that of saturation. In this case, the rate constant (27) can be de-

fined as

kDP= e0.5(3Wm 3Wm)2kb10

8 + 0.383Wme

EA,oL/(RT)e (200 EAL/DP))/(RT) =

= kb108 + 1.14Wm

eEA,oL/(RT)e

(200 EAL/DP))/(RT)

or

kDP=Ae

b/DP

where A =kb108 + 1.14Wm

eEA,oL/ (RT) and b = 200EAL/(RT),

The kinetic equation can be written in the differential form as:

d(1/DP) / dt = kDP=A eb/DP

and the final equation becomes

e

b/DP

e

b/DPo

= At for W> 3Wm (30)

b

(i.e. for t (3Wm N)/M or initial humidityW 3Wm),

where A =kb108 + 1.14Wm

eEA,oL/(RT) and other designations are the same as in equation

(28).

Equations (29) and (30) provide an exact representation of the dependence of change in de-

gree of polymerization of cellulose under the combined effects of temperature, humidity, changing

energy of activation (from the viewpoint of rate constant increase), concentration of oxygen, influ-ence of the cellulose material structure, etc.

As humidity of paperW> 3W is improbable for the high-voltage equipment, and time ofachievement of such condition exceeds a life of paper, the equation (29) for a prediction of a degree

of polymerization of a paper it is possible to use for all practical and theoretical calculations

bDP = (31)

ln[(Ab/B)(et 1) + e b/DP]

: = e 0,5(3W N)2 kb 10 8 + 0,38N e 17680 exp( 0,0008)/(T) ,

= (0,875 0,52) M,


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b = 1940 0,0008

/(RT) = 223330 0,0008/T

NMin (25) are determined by humidity analysis of the oil (see Part II), comes from equation (13),Wm is determined from the equations in Table 1,

kb is 1 for Kraft and 0.3 for cotton,

t is time in hours.

The second part of this article presents kinetic equations for the calculation of the amount of

furfural, carbon oxide gases and water formed under the influence of oxygen concentration, pre-

liminary thermal processing and the distribution of the products between the gas phase, oil and pa-

per, using data available from the literature and other sources.

Conclusion

1. Exact kinetic equations are presented for the decrease in degree of polymerization of cel-lulose-based insulation during ageing, taking into account the working environment of equipment or

of laboratory experiments.

2. The equations take into account the different mechanisms of chain scission, and subse-

quent chemical transformation of the two macroscopic forms of cellulose that exist in paper - the

crystalline and amorphous phases.

3. They account for interactions with the oil environment, in which amorphous cellulose

primarily undergoes end-link scission and consider the relatively oil-free environment of the bulk

crystalline cellulose. Here chain scission occurs more slowly and more centrally in the molecule

and so has more effect on DP.

4. The equations also account for the slowdown in the ageing process that occurs over the

course of time, despite the increasing humidification of the paper. It is proposed that this arises fromreduced steric factors in the smaller molecules that demand a higher activation energy for breakage

of the glycosidic linkage.

References

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[3] W.G.Lawson, M.A.Simmons, P.S.Gale, "Thermal ageing of cellulose paper insulation",IEEE Trans., EI-12, No. 1,p. 61 66, 1977.[4] V.M.Montsinger, "Loading transformer by temperature". Trans. Amer. Elect. Engrs., Vol. 49, p. 776 790, 1930.[5] D.H.Shroff, A.V.Stannet, "A review of paper aging in power transformers".IEE Proceedings, Vol. 132, Part C,

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Vadim Gareginovich Arakelian is a leading research worker of All-Russian ElectrotechnicalInstitute, Moscow. In 1961 he graduated from Moscow Institute of Fine Chemical Technology(M.V.Lomonosov). In 1969 he defended the candidate thesis dealing with the theory and practiceof gas chromatography. Once he started working for All-Russian Electrotechnical Institute in

1969, his scientific interests were reoriented from analytical chemistry to the area of electricalengineering, in particular to the development of bases of creation of SF6 electrotechnical

equipment and to the application of gas chromatography for diagnostics of damage to oil-filledelectrotechnical equipment. Dr. Arakelian has pioneered a new branch in electrical engineering,which was the basis of his doctoral dissertation titled Physical chemistry of electrotechnical de-vices, which he defended in 1995. This was the first dissertation to be composed touching upon

the physical chemistry of electrotechnical equipment. He is the author of 120 published articles, 100 of them concerningelectrical engineering. He is also the author of the monograph Physical chemistry of SF6 electrotechnical equipment,

Moscow, 2002 (in Russian). Address for contact: [email protected]

Alan Michael Emsley is a senior research worker with GnosysUK Ltd at the University of

Surrey, Guildford, UK. He graduated from the University of Edinburgh in 1968 with an honors de-gree in chemistry and started work for the nationalized electrical power industry at their central re-search laboratories in Leatherhead, Surrey. Over 23 years in the industry, he researched various top-ics related to the degradation of materials including oxidation of stainless steel in high temperature,high pressure carbon dioxide, formation of carbon on metal surfaces by decomposition of carbon

monoxide and methane, for which he was awarded a PhD by the University of Edinburgh and, mostrecently, the ageing of cellulosic materials in power transformers a topic for which he is regardedas an international expert. He has published over 50 peer reviewed papers in journals and confer-

ences and is coauthor of a book on polymer recycling and sustainable development. Address for contact:[email protected]

ageing of electroinsulating cellulosic materials

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