a model for primary and heterogeneous second

7/23/2019 A Model for Primary and Heterogeneous Second

1/11

272

Chem. Eng. Technol. 19 (1996) 272-282

A Mo del for Prima ry a nd Heterogeneous Secondary Reactions

of

Wood Pyrolysis

Pradeep Ahuja, Surendra Kumar and Prem Chand Singh*

A ch ain growth model for heterogeneous second ary reactions is developed for the pyrolysis

of la rge wood par t ic les and the parameters de termined by nonl inear op t imizat ion . The

model takes both the volati le retention time and cracking and repolymerization reactions

of

the vapours w ith the decomposing solid as well as autocatalysis into consideration. Th e

extent of the secondary reactions is s trongly influenced by the t ime and the ratio of the

autocatalytic (propagation) reaction rate to noncatalytic ( init iation) reaction rate. The

woo d which has a higher value of the autocatalytic/noncatalytic ratio also has a higher exo-

thermic heat of reaction and yields a higher amount of f inal char residue. T his fact con-

firms that the heterogeneous secondary reactions lead to carbon enrichment of the f inal

residue and are accompanied with an exothermic heat

of

reaction. The lower activation

energies of the in i t ia t ion and p ropagat ion reactions as compared to pr imary reactions (com-

petitive reaction model consisting of weight loss and char forming reactions ) confi rm a uto -

catalysis in large particles . The sealed reactor s tudies of small quantit ies of f ine wood

samples show that heterogeneous secondary reactions and not lower heating rates in large

particles are the main source of char formed dur ing the thermal decompos i t ion of la rge

woo d particles. The m odel predictions are in agreement with the weight loss an d tempera-

ture versus t ime curves over a wide range of particle s ize and furnace temperatures .

1 Introduction

Secondary vapour-solid interactions are the main source of

char form ed durin g biomass pyrolysis. I t has even been sug-

gested that char formation is not a primary s tep but is a

result of repolymerization of volati le m atter [I ] . Th e

vapo ur-solid in teraction s play a key role in the pyrolysis be-

haviour of macroscopic particles of biomass . The tempera-

ture profiles within

a

pyrolyzing solid particle are influenc-

ed not only by heat transfer phenomena but also by hetero-

geneous chemical reactions.

The least understood aspect of pyrolysis is the inte racti on of

the nascent, hot pyrolysis vapours with the decomposing

solid, which the va pours m ust transverse during their escape

to the environment [2] . Moreover, solid phase decomposi-

t ions are a challenging and poorly understood interdisci-

plinary field of inquiry. A ntal an d Varhegyi [2] conclude

that vapour-solid interactions (secondary reactions) are ef-

fectively the only source of char formed during the pyroly-

sis

of

pure cellulose. These reactions ar e key to the eff icient

(high yield) manufacture

of

charcoal f rom biomass . Mok

an d Antal [3] attr ibuted the increase in char yield a nd exo-

thermic heat

of

reaction at low purge gas f low rate to the

format ion

of

a volatile intermediate, which reacted by a

s t rong exotherm when i t was no t removed f rom the

DSC

cell by a high f low of purge gas .

*

P.

Ahuja, Prof. Dr. S. Kumar (to whom correspondence should be ad-

dressed), and Prof.

Dr.

P.C. Singh, Department of Chemical

Engineering and Technology, Institute

of

Technology, Banaras Hindu

University, Varanasi-221005, India.

Yields as high as 47% have been achieved by control

of

those conditions which affect the vapours born during py-

rolysis of the solid substrate [4] . High charcoal yields are

only ob ta ined when the vapours a re he ld in contac t wi th the

hot solid residue. Mok et al . [4] bserved that higher sam ple

loading increased charcoal yield and the associated exo-

thermic heat release an d lowered th e reaction onset temper-

a ture . The lower ing

of

reaction onset tempera ture may be

due t o the au tocata ly t ic ef fec t of the secondary reactions.

I t has been suggested by Akita [5] that th e primary decom -

position of wood has a very low heat of reaction an d tha t

the main cause of heat generation in decomposing wood is

secondary decomposition

of

volatile matter, possibly

catalysed by the solid residue. Th us, the heat of reaction in-

creases with increasing residence time of volati le matter in

the solid prior to evolution. Thus, under gentler heating

condition s as in the case of large particles , the expulsion of

volati le matter once formed would be less rapid and more

time would be available for secondary decomposition [6] .

Bradbury et al . [I] found that small sample s izes lead to

smaller char fractions. This indicated that the residence

time

of

volatiles in the cellulose during the pyrolysis reac-

tion largely influences the extent of char form at ion . Pyro ly-

sis

of

levoglucosan is known to give some residual char, an d

it has been suggested by Lewellen et al. [7] that char forma-

tion is not a primary s tep but is a result of repolymerization

of volati le matter . Arseneau [8] report that the depolymer-

ization reaction consists of two reactions contr ibu t ing to the

endothe rm, f irs t , the depolymerization of th e residual cellu-

lose followed by the volatilization

of

mo s t of the product ,

levoglucosan, thereafter . Thicker samples trap the levoglu-

CH Verlagsgesellschaft mbH, D-69451 Weinheim, 1996

0930-7516/96/0306-0272 $10.00+ .25/0


2/11

Chem . Eng . Technol. 19 (1996) 272-282

273

cosan, thereby eliminating the latter portion of the endo-

therm. The exotherm is not the result of the decompos i tion

of the anhydrocellulose but rather is the breakdown of

the product of the depolymerization reaction, presumed to

be levoglucosan. This was confirmed with the thermogram s

of the prepared levoglucosan. The f inal reaction varies

depending upon the conditions of th e experiment. I t may be

endothe rmic or exothermic. The levoglucosan formed m ay

be trapped by the overlay of cellulose an d decom posed ex-

othermally. Th e above results suggest that a crit ical param -

eter in cellulose pyrolysis is the residence time

of

volatiles

in the pyrolyzing cellulose matrix. The existence of an opt i -

mum residence t ime for obtaining a maximum rate of vola-

tilization is indicated. It is suggested that cracking, cross-

linking, and repolymerization reactions occur if this t ime is

substantially exceeded. Low temperatures or low heating

rate conditions, particularly involving large samples , wo uld

promote longer residence times of all pr imary products

within th e pyrolyzing ma trix and tha t repolymerization and

cross-linking leads to higher charcoal yields.

Tak amo to an d Pe t r i ch [9] in their s tudy on the effect of

heterogeneous secondary pyrolysis reactions on the therm al

decomposition of polyure thane scrap , concluded tha t b o th

act iva ted carbon and polyure thane char improve the l iqu id

product by promoting heterogeneous secondary pyrolysis

reactions. The polyurethane char provides the additional

benefit of increasing the amount of char produced . Char

yields as high as 40 were obtained when polyurethane

char was used as the carbon bed material , as compared to

15 t o 25 with other bed m aterial . They pyrolysed po lyure-

thane scrap in a batch laboratory-scale reactor and used a

packed bed t o influence the com position an d yield of pyrol-

ysis prod ucts . G lass beads and glass wool were also used as

inert packing materials . Cha r deposits on these m aterials in-

dicated that volati les a dsor b on the packing. T he reactions

of wood pyrolysis volati les with wood char and activated

carbon [ l o ] have also sho wn similar results . Crac king reac-

tions, leading t o lower molecular weight prod ucts , an d de-

position reactions, leading to increased char yields , have

been observed. T he pyrolysis volati les c an ad sorb , deposit ,

and react in the presence of a second carbon bed, altering

the composition and yields of the pyrolysis products .

Mazum dar and Chat terjee [ I I ] found th e d imens ions of the

coke charge

to

be quite significant in determining volatile

yields, while heating rate was

of

secondary impor tance .

Similar f indings are reported by Anth ony e t al . [12]. The ef -

fect of sample s ize is sometimes misconstructed a s a he ating

rate effect, s ince the t ime required to attain the f inal tem-

pera ture usually decreases with increasing sam ple size.

There is a broad support that these reactions are primarily

concerned with the ta r fraction of the volati les .

The ex ten t of the secondary reactions is s trongly influenced

by the residence t ime and concentration of reactive species

in contact with hot surfaces is also proved from the facts

that th e large beds accompany ing s low rate of heating yield

min imu m amo u n t s of volati les and devolati l ization at

higher pressures increases

the

secondary

decomposition

[12]. An th o n y an d Ho war d [I31 in fer tha t som e of the frag-

ments a re highly reactive free radicals subject to a variety

of secondary reactions such as cracking and repolymeriza-

t ion . Shaf izadeh and Bradbury [I41 also predict free radi-

cals in their work. The extent

of

secondary reactions can be

reduced by enhancing the transport of volatile fragments

away from the reactive environment, such as by operating

at redu ced pressures w ith smaller and m ore widely dispersed

particles . Th e free radical species would polymerize to coke

unless they could escape as tar at some intermediate s tage

of

polymerization and that the escaping tar might also

undergo cracking reactions producing coke and gas. Pre-

sumably, both cracking and polymerization are involved,

but their relative extents are une stablished.

Chen et al. [15] formula te a model for coal pyrolysis in

which the volati le tar can transport out of the char matrix

and u ndergoes cracking to yield m olecules with lower mo-

lecular weights. After the release of primary tar , active

char, which contains solid char and condensed tar , under-

goes relatively slow chemical decomposition and evapora-

tion, thereby generating additional tar molecules of dif-

ferent molecular weights. After leaving the char matrix, tar

molecules can recondense on the char surface followed by

interphase reactions. Moreover, the tar molecules with

lower molecular weights yield gaseous produc ts throug h py-

rolysis . Production of gaseous species can also take place

directly from char, for example, hydrogen evolves from

aromat iza t ion of char , and carbon d ioxide format ion

precedes tar release. Chan et al. [16] have also shown in-

crease char and gases yields and lower tar yields when the

particle sizes were increased.

Ram an e t a l .

[17]

report that th e f irs t s tep during pyrolysis

is devolati lization, which produce s volati le matter and char.

The second s tep consis ts of secondary reactions involving

the evolved volati les and the solid char. The f inal product

dis tr ibution for gasif ication is dictated by bo th th e devola-

ti lization an d the secondary reactions. T hus, the engineer-

ing design and de velopment of a process for the gasif ication

will require

a

basic knowledge

of

kinetic da ta o n the devola-

ti l ization as well as secondary reactions involved. This

becomes important considering the fact that in some reac-

tors (moving bed, rotary furnace) used in gasif ication and

pyrolysis processes, large particle sizes are processed. In

these cases , heat an d mass tra nsfer resistances m ay appe ar.

Signif icant temp erature profiles may be produced inside the

solid which influence the solid conversion and the amount

and compos i tion of the products ob ta ined .

Since the f irs t work by B amfo rd et al . [18], several models

have been proposed for the thermal decomposition of

wo o d . Mo s t of them [6, 19

-

31 was mod ified by Kung [24]

and Bilbao et al. [25] to incorpora te the ef fec ts of internal

convection; Kansa et

al.

[26] subsequently included the

momentum equation for the motion of the pyrolysis gases

within the solid and the influence of physical s tructure on

these phenom ena. Models which recognize therm al decom-

position as rate controlling appear mo re realis tic an d should

prove more f ru i t fu l in expIoring wider ranges of condi t ions .


3/11

274

Chem. Eng. Technol.

I9

(1996) 272-282

T he a im of the present work is to provide a rational model

for the purpose of describing the pyrolysis of a cylindrical

wood particle. The reaction at any point in the particle is

governed by the temperature at that point and consists

of

primary and heterogeneous secondary reactions. The pri-

mary reactions in the case of small particles are studied

through TG A an d isothermal heating. A model is described

which is found t o be applicable fo r both the modes of he at-

ing for small particles. The heating ra te used in TG A is 10,

20, and 40 K/min. The isothermal temperatures of the fur-

nace are 573, 623, 673, an d 723 K. The primary reaction

mod el consists of a weight loss and char forming reactions

which are compe titive in nature .

The propose d heterogeneous secondary reaction model con-

sists of chain growth mechanism including initiation and

propagat ion s teps and the rate parameters (act ivat ion

energy, preexponential factor, and deposition coefficient)

are determined by sim ulating the complete model (primary

and heterogeneous secondary) with the experimental residu-

al weight fraction and temperature versus time curves

of

large particles. The primary reaction p aramete rs were deter-

mined by simulating the primary reaction model with the

experimental weight fraction curves of small particles. The

secondary reactions also depend on the contact time be-

tween the volatiles an d the hot char a nd this factor is also

taken up in secondary react ion model . Apa r t f rom the ad -

sorpt ion of the volatiles o n the prim ary char, the chemical

reaction between the primary char and the volatiles takes

place and leads to the secondary char formation.

To

show that vapour-sol id in teractions are mo re impo rtant

than the lower heating rates which accompany large par-

ticles, stud ies

of

small and fine samples

of

the woods were

carried out in

a

specially designed sealed reactor in which

the volatiles a nd gases remain in contact with the dec ompos-

ing solid. The autocatalytic effects are described and the

heat of reaction, ratio of autocatalytic/noncatalytic reac-

tion rates, deposition coefficient, and the final ch ar yields

of large particles and those of small particles in sealed reac-

tor are determined to compare the physical and chemical

phenomena during pyrolysis of a large cylindrical wood

particle.

2

Model Description

2. Primary Reaction Kinetic Model

The primary reactions are described by the following

scheme:

ases +Volatiles

Biomass (B)

------()

Prim ary C h a r (C,)

It is assumed that the two reactions follow the Arrhenius

law. The mo del can predict the fin al char yield in different

heating conditions. Koufopanos et al. [27] and Dumpel-

mann et

al.

[28]

also attempted simplified m odels but with

added complications of intermediatehntermediates forma-

tion. Th e ordina ry differential equations which describe the

above kinetic schem e are:

_B

-

- A l e x p ) B n l - A 2 e x p s ) B n 2 (1)

d t

with the initial conditions: B =

1 ,

C,

=

0 at t = 0. B is the

educt wood f ract ion and is the f ract ion of virgin wood re-

maining in the solid residue, and

C1

is the primary char

weight frac tion. T he residual weight frac tion is given by the

sum:

W =

B + C In dynamic thermogravimetric analysis ,

the temperature may be a l inear function of time:

T=@T+TO.

The characteristics of a good model are that it should re-

quire the least number of parameters for the engineering

design

of

the reactor an d that it should be mechanistic. The

model which predicts the weight loss and char form ation a t

low temperatures and heating rates should be applicable at

high heating rates, because even at high heating rates and

tempera tures the sample has to pass through th e low heating

rates, where most of the devolatilization occurs. Our model

is able to f i t the data under dynamic a nd isothermal heat ing

conditions.

Under t he heating rates which are considered for the engi-

neering design of the equipments , the in termediate forma-

t ion does not occur as taken up in the model by B radbury

et al. [I]. Even for low heating rates, Varahegyi et al. [29]

has shown that in termediates formation does not take

place.

The two- or three-s tep model proposed by Lipska and

Park er [30] in the case

of

isothermal condit ions an d Tang

and Neil1 [31] for dy namic T G cond itions require a lot of

param eters, an d the lower steps govern the pyrolysis at very

low heating rates which are n ot required for the engineering

design of the gasifiers an d com bustors o r pyrolysis equip-

ments in which most of the tars or char formation takes

place. Therefore, a s tep model was not taken into con-

sideration to fit the experimental data for the various

heating rates and under isothermal conditions. Moreover,

the appearance of the single smooth curve during

nonisothermal

TG

study supports the fact that the transi-

t ion f rom char dom inat ing to tar dominat ing reactions is

gradual.

The model is consistent with a pyrolysis scheme in which

two competing sequences of cellulose pyrolysis reactions a re

initiated by (1) an intermolecular dehydration leading to

char form ation and (2)

a

depolymerization reaction.

Non-linear optimization procedure utilizing Marquardt

algorithm

[32]

an d Press et al.

[33]

were used for param eter

1

List of

symbols

at

the end

of

the

paper.


4/11

Chem. Eng. Technol.

19

(1996) 272-282

275

estimation (activation energy, pre-exponential factor , and

order of reaction). The best fitting was achieved by mini-

mizing the sum of the squares funct ion :

constants could not be used to give the rates as a funct ion

of temperature for the various isothermal conditions. So,

regression was used to f i t the rate constan ts as a function of

tempera ture .

2.2 Heterogeneous Secondary React ion Kinet ic Mo del

For s implicity, the o rder

of

the reaction 1 ) was set equal to

that of reaction (2) . In order to avoid poor parameter es ti-

mat ion due to improper sca l ing or parameter in terac t ion ,

the reparameterization recomm ended by Chen an d Aris [34]

was adopted:

In the large particles , along with the primary reactions,

heterogeneous secondary reactions also take place and the

model was expanded as:

Volatiles

+

Gases

ai

=

l n A i

ej =

Ei /

1200

R E )

W o o d ( B )

6

p

= T/1200

(3) (4)

Pr imary

-

Secondary - econdary + Gases

Therefore , tak ing the reparameter iza t ion and n , = n2= n ,

the ordinary differential equations become:

Reaction (3) is the init iation reaction a nd includes th e coef-

ficient of deposition 6, which depends o n the volati le con-

tact time inside the pyrolyzing particle. Reaction (4) is the

propagation reaction.

C1

s the pr imary char , C2 s the sec-

ondary char formed by the init iation reaction, and C22 s

the secondary char formed by the propagation reaction. C2

is the sum

of

C2, an d C2, and is the total secondary char.

%=t - [exp

(al

-:) + e x p

(a2-:)] B

(3)

(4)

To determine the parameters a , , e l , a2 , and e2 , the par t ia l

differential of the above two ordinary differential equations

with respect to these paramete rs is needful. A total of eight

more equations were obtained. The above two differential

equations along with the eight equations form a system

of

non-linear differential equations . The solution of the init ial

value problem can be obtained numerically by an explicit

algorithm. The ordinary differential equations were solved

by using a 4th-order Runge-Kutta algorithm. The optimum

step s ize was fo und t o be 1.5 s and the r ise in temperature

in each s tep was adjusted according to the heating rate.

Reaction ord ers tr ied were

.O

1.1,

1.3,

and 1 .5 . The order

of reactions of th e propos ed m odel, c onsidering the experi-

mental da ta an d residual curves, were established as being

equal to

1

. l .

The concepts

of

adsorption, deposition and reaction of tar

with char leading to cracking and repolymerization [I

-

,

8

I], residence time of volatiles

[6],

and presence of free

radica ls [12- 141 sup port o ur mod el and give a mechanistic

view

of

the same.

The ordinary differential equations of the overall kinetic

model become:

( K , + K 2 ) B n

B

d t

(7)

(9)

he same primary m odel was fou nd also applicable for iso-

thermal heating of small particle, at various furnace tem-

peratures . The primary reactions are:

d B

- =

- ( K I + K 2 ) B n

d t

with the init ial condition B = 1 , C1= 0, C2= 0 a t t = 0.

Th e residual weight fraction in the case of large particle is

given by the sum: W = B + C1+ C2.

Th e ordinary differential equations were again solved using

the R unge-Kutta 4th-ord er method as described previously

for the case of primary reactions. Also, in order to avoid

poor parameter es t imat ion due t o improper sca l ing or pa-

rameter interaction, the reparameterization recommended

by Chen and Aris [34] was adopted.

with s imilar initial conditions as above. Th e parame ters K ,

and K2 were determined fo r various isothermal conditions

by non-linear optimization as described above. T he plot

of

In K, versus

1

/ T an d In K2 versus 1/T did n ot give s traight

l ines and , therefore , the Arrhenius form for the ra te


5/11

276

Chem. Eng. Technol.

19

(1

996) 272

-

282

The rate cons tants K3 a n d K4 are assumed to be in Ar-

rhenius form . The temperature- t ime data of large samples

at various radii are needed to determine the kinetic p arame -

ters

of

the secondary reactions. The parameters A3 E3,A4,

E4 along with

6

were determined by simulating the model

with th e experimental weight loss curves of wood cylinders

by nonl ine ar opt imizat ion using the Marquardt method by

minimizing the sum

of

the squares funct ion

F .

2 . 3 Heat Transfer Model

Taking a differential control volume

of

a solid particle dur-

ing heating and neglecting the convective hea t transfer a nd

assuming the solid properties

e,

C p, ) inside the control

volume to remain constant, i t can be shown that the equa-

ae

ax

r>O

,

x = l

,

- = - H e

The weight loss kinetics a re used to solve the abov e partial

differential equation (PDE). The radius is divided into 14

s teps and temperature a t 15 points is determined a t increas-

ing values of t ime. The A t / A x 2 value is taken to be

1.0.

The Crank and Nicolson method was used for solving the

above PDE in to

15

algebraic equation s which were solved

using the initial condition as above. The heat

of

reaction

was determined by hit and trial method by simulating the

model with the experimental curve.

t ion for a cylind rical pellet is:

Rober ts [35] pointed out the tendency of volatiles to travel

along approximately isotherm al planes parallel to the wood

grains and int o cracks. The convective heat transfer c oeffi-

cient between the pyrolysis gas and the solid is unlikely to

be significant under these conditions. Pyle and Zaror [21]

also pointed o nto the unimportance of in ternal convect ion

in the model. Moreover, the migration of the volatiles

towards the cooler parts of the virgin wood may occur,

but the resistance to flow will invariably be greater in the

virgin wood tha n in the charcoa l region a nd , therefore, the

outward f low of volatiles is likely to be mo re sign ificant. In

the work of Bilbao et al.

[25],

when convective heat transfer

in the solid due to the volatiles is used, the temperatures

predicted show lower values tha n those ob tained experimen-

1

1 )

at

Initial condition:

t = 0, T(r,O)= To

Boundary condition:

t>O, r=O, -= 0

12)

(13)

a T

ar

14)

aT

ar

t>O, r

=

R , - k - = h ( T - T f ) + m ( T 4 -T:)

In the above formulation, external heat transfer is con-

sidered to occur by a combina tion of convective and radia -

tive m echanism.

Introducing the following groups:

k

r at

a=-

,

x = -

,

7 = -

ec,

R R 2

R

k

H

= -

h+ o ( T 3 T 2T f +TT:+ T:)]

- A H

QCp(To- T f )

Q =

The energy balance equation becomes:

_ = _e

i

- + - +Q

6 a20

ar x a x ax 2

- )

r

= 0 , 6 x , O )= 1

tally, especially when a significant weight loss is pioduced.

This delay in the temperature could be due to the assump-

tion that the volatiles formed leave the particle instan-

taneously, which overestimates the heat loss. On th e other

hand, the consideration that volatiles only flow radially

toward the solid surface an d without d iffusional resistance

is also questionable. Due to this anisotropy, preferential

paths for volatiles t o escape may exist in the woo d. There-

fore, it is difficult to establish the true p aths th at generated

volatiles follow. Taking into account these difficulties, it

has no t been cons idered appropr iate to include the assump-

tion of the convective heat transfer of

the volatiles.

With respect to the particle volume, previous experiments

were carried ou t with th e differen t particle sizes and were

stopped a t different temperatures an d solid conversions. An

appreciable particle shrinkage was only observed at high

solid conversions. In add ition, in oth er studies including the

particle shrinkage [21], a variation

of

the overall numerical

solution by less than

3

was obtained with this modifica-

tion. So,

a

constant pa rticle volume was used in our calcula-

tions.

3

Experimental

Section

Pyrolysis of acacia an d eucalyptus woods were investigated

in flowing nitrogen atmosphere in the thermogravimetric

analyser, gas-purged isothermal reactor, and a specially

(15)

16)


6/11

Chem . E ng. Technol. 19 (1996) 272-282

277

designed sealed reactor . The samples of various sizes were

stored in the laboratory under dry conditions.

A gas-purged isothermal reactor was employed to measure

the pyrolysis rate of large cylindrical an d small particles .

The tem perature variations inside a pyrolyzing woo d parti-

cle were also measured. A pipe of diameter 51 mm and

length 2.0 m was taken and kept in a n iner t a tmosphere by

passing nitrogen gas f rom below. T he lower half of the re-

actor was kept in

a

tubular electr ical furna ce to which

a

con-

troller was attached to main tain isothermal conditions. The

upper portion of the reactor was used for quenching and

rapid cooling of the hot sample. This was essential because

the hot sample had

to

be cooled in neutral atmosphere as

oxidation occurs in air leading to erroneou s weight loss

of

the samples .

The sample material (cylindrical pellets of diameter

15

m m

a n d l e ng th 9 0 m m , d i a 2 0 m m a n d l e ng th 1 2 0 m m , di a

25

mm and length 150 mm to s tudy the secondary reaction

kinetics , a nd f ine samples

of

0.3 to 0 .5 mm to s tudy the pr i-

mary reaction kinetics) of acacia a nd eucalyptus wood was

placed in a stainless steel wire mesh basket hu ng o n a metal-

lic rod , which c ould easily move vertically inside the reacto r

tube.

A

f low rate

of

2700 cm3 /min of nitrogen (a t 293 K

and 101.3 kPa) was chosen. I t was sufficiently high to ma in-

tain a uniform temperature zone, displace the oxygen from

the reactor , an d carry away the volati les a nd gaseous prod-

ucts. H eat was transmitted to the sample by means of con-

vection fro m the carrier gas an d radiation. Before entering

the reaction zone, the nitrogen s tream was passed through

a preheating coil.

Smal l samples

of

size 0.3 to

0.5

mm (0.2 g spread uniformly

over an area

of

14c m2 ) were kept between the folds of a

fine stainless steel wire mesh and the weight loss with time

was recorded at various temperatures . Similar weight loss

curves with 0.15 t o 0.3 mm particles were obtained to con-

firm that heat an d mass transfer resis tances d o not exist in

the study of small particles. For large particles, experiments

with different lengthldiam eter ratio of wood cylinders were

car ried out , and i t was found tha t a ra t io of 6 was safe for

the samples to act as of infinite length. Tem peratures

of

the

axis , at half radius from the axis , and just below the surfac e

of

the pellet were record ed w ith

a

f ine chromel/alumel ther-

mocouple . In some exper iments the ax is tempera ture a t d i f -

ferent lengths from the end

of

the pellet were recorded to

conf i rm that the heat ing was only rad ia l and tha t no tem-

perature variation exis ts along the length of the pellet.

To check the applicabili ty of the primary reaction model

under various heating conditions, dynam ic TG studies were

car r ied out on a Stan ton Redcrof t 780 STA. Small (6 to

7 mg) quantit ies of samples were investigated at heating

rates of 10, 20 , and 40K/min in n i t rogen f low ra tes of

50cm3/min . High f low ra te of purge gas were adopted to

remove the gaseous an d volati le pyrolysis pro ducts evolved

and, thus, minimize any secondary interactions between

them a nd the ho t so l id . Before carry ing out a run, th e varia-

tion in the base l ine were measured by performing a blank

run with an empty crucible. The samples were spread

uniformly o n the sam ple pan. S mall samples was a necessity

because the reaction was found endothermic, and large

mass loadings caused heat and mass transfer l imitations.

To s tudy the ef fec t of vapour-solid interactions on the py-

rolysis of wood, a specially designed cylindrical stainless

steel reactor

of

inside diameter 5

1

mm and height 124 mm

was used. T he lid of the reactor consisted of a circular plate

with a hole to which a pressure gauge was attached . A tef lon

ring and a stainless steel cover were used to seal the upper

part with the reactor . A fine chromel/alumel thermocouple

was inserted into the reactor to come in contact with the

sample. Small samples of size 0.3 to 0.5 mm (0.3 g spread

uniformly over a n area

of

20 cm2) were placed in th e reac-

tor a nd f lushed with nitrogen for 8 times under higher than

atmospheric pressure and thereafter the reactor was in-

serted in to the to p of the tubular furnace . The tempera ture

of the sam ple was recorded and came t o the furnace temper-

ature within 2 min. The pressure s tarted r is ing as gases and

volatiles were formed from the pyrolysis

of

the subs t ra te .

When the pressure reached a constant value, the reaction

was completed and the appara tus was removed f rom the

furnace and purged wi th n i t rogen to cool the sam ple and the

reactor . Precautions were taken that everytime a posit ive

pressure was maintained in the reactor so tha t the ou ts ide

air does not enter . The f inal weight of the char was re-

corded .

Elemental analysis

of

acacia and euc alyptus wood were de-

termined using Perkin Elmer 2400 CHN analyser . The

elemental analysis of acacia used is C = 45.13%, H

=

6.14070, ash = 0.8% and by difference = 47.93%. Euca-

lyptus contains C

=

46.21%, H

=

6.08%, ash

=

0 .7 % an d

by difference = 47.01 070 (dry weight basis).

4 Results and Discussion

Figs.

1

and 2 show the experimental points and theoretical

curves of the residual weight fractio n

of

acacia an d eucalyp-

tu s wo o d a t a heating rate of 20K/m in . Alongwith are

shown the theoretical char and virgin wood fractions ob-

tained by the primary reaction model. The residual weight

reported was norm alized as (residual - ash weight)/(initial

ash weight). T he activation energies , preexponential fac-

tors , and order

of

the reaction determined by nonlinear op-

t imization are repor ted in T ab . 1 . The isothermal residual

weight frac tion curves were obtain ed a t 573, 623, 673, an d

Table

1.

Primary reaction kinetic parameters for pyrolysis of acacia

and eucalyptus woods by TGA in nitrogen atmosphere.

~ ~~

Sample To Tf n A El A2

E2

[K] [K] [g-' '/s] [kJ/mol]

[g-'

'Is] [kJ/mol]

Acacia 413

833

1.1 5.87104 91.5 6.5710 3 85.9

wood

Eucalyptus 413

833

1 . 1 1.2810 5 93.1 1.16 lo4 86.7

wood


7/11

278

0.0.

:

. .

8

Educ t

residue ... .

I

I I

....__.

I

....-.-

.

C,:

Ch o r

/ ...c,

._....

I

l O F - y - - - - -.9

0 8

d

P

0.4

0.3

0.2

0.1

0 0

1.0

_ .

- Exp. Theo. Heot

rote

0

2OKlnnn

B E d u c t residue f r ac t i o n

C,- Char fraction

-

-

/...*.:

I_- .

__.

__.-

_..-

I I

I I

-4

_ - -

_ -

0.9

t

d

P

0.4

g

0.3

0.2

0.1

0 0

0 . 8L

-

-

-

__.

__.-

_..-

I I

I I

-4

_ - -

_ -

Exp. Theo. Heot rote

0

2OKlnnn

B E d u c t residue f r ac t i o n

C,- Char fraction

+ 0.6

3

0 . 5

I

w

TEMPERATURE

(CI

Figure

2. Thermogravimetry of eucalyptus wood. Experimental points

in comparison with the residual weight fraction, educt residue B and

char C curves predicted by the primary kinetic model for heating rate

of 20 K/min.

723K for acacia and eucalyptus wood and the rate

constants for the weight

loss

and char forming reactions are

reported in Tab.

2.

The same model

is

found applicable

under dynamic TG and isothermal studies. The order of the

reactions in the case of TG studies was found to be larger

than one but in isothermal studies the model was found fit

for an order equal to one.

Chem. Eng. Technol. 19

(1996)

272-282

The primary reaction kinetics of small particles is used in

the overall reaction model of pyrolysis of large particles to

determine the secondary reaction kinetic parameters.

Figs. 3 and 4 show the simulated and experimental residual

weight fraction curves and normalized temperatures of the

Table2. Values of rate constants of weight

loss

and char formation

reactions during isothermal pyrolysis

of

acacia and eucalyptus woods.

Sample Temperature [K]

K , [s -]

K2 [s-I

Acacia 573

wood 623

673

123

Eucalyptus 573

wood 623

673

723

1.31 1 0 - ~

7.74 1 0 - ~

1.36 I O - ~

2.04

6.07

1.07

2.52 lo-

6.85

lo-

1.36

1.47 I O - ~

4.73 1 0 - ~

1.21 1 0 - 2

5.20

3.49

4.84 1 0 - ~

1.05 lo-*

w 0.8

-

a

2

a

0.4

N

r

a

0.6-

I

w

W

-

2 0.2 -

0.0-

0 3 6

9

12

15

18 21

24

T IME (rnin.)

Figure 3. Experimental points and theoretical curves

of

residual weight

fraction and centre temperature during isothermal pyrolysis of acacia

wood cylinder (diameter 15mm and length 90 mm) at 623 K.

- 0 . 8

g

-

I

a

-0.6

I

I

-

0.4

?

-0 .2

2

- 0 . 0 L

I

e

ul

0 3 6

9

12 15

18

21 24

TIME min.1

Figure

4. Experimental points and theoretical curves of residual weight

fraction and centre temperature during isothermal pyrolysis of eucalyp-

tus wood cylinder (diameter 15 mm and length 90 mm) at 623 K.


8/11

Chem. Eng. Technol. 19 (1996) 272-282

279

axis of the 15 mm cylindrical pellet and length 90 mm at fur-

nace temperature of 623

K

for acacia and eucalyptus wood

respectively. The data for 20 mm dia and length 120 mm

wood cylinders are shown in Figs. 5 and 6 at furnace tem-

peratures of 673 and 723

K.

The temperature was normal-

ized as (temperature final temperature)/(initial

-

final

temperature).

The optimized parameters (deposition coefficient, preexpo-

nential factor, and activation energy) for the initiation and

propagation reactions of the chain growth mechanism,

alongwith the values of

autocatalytic/noncatalytic

reaction

rates within the temperature range which accompany the

pyrolysis of larger particles are given in Tab.

3

for the

acacia and eucalyptus woods. Reaction (3) is the initiation

rate constant and reaction (4) s the chain growth (or auto-

catalytic) rate constant and the ratio

K 4 / 6 K 3

epresents the

increase i? autocatalytic over noncatalytic rates of reaction

7 3

K

a

0.0

-

- 0 . 2

-

I

I

I

I I I

0

2

4 6

8 10 12 14 1 6

TIME min.1

Figure

5. Experimental points and theoretical curves of residual weight

fraction and centre temperature during isothermal pyrolysis of acacia

wood cylinder (diameter 20

m m

and length 120 mm) at 673 and 723

K.

I

a

a

g 0.0

- 0 . 2

I I I I I I I

0 2 4 6

8

1 0 1 2 1 4

TIME min

Figure 6. Experimental points and theoretical curves of residual weight

fraction and centre temperature during isothermal pyrolysis

of

eucalyp-

tus wood cylinder (diameter 20

m m

and length 120

mm

t 673 and

723 K.

Table 3.

Secondary reaction kinetic parameters for pyrolysis of acacia

and eucalyptus wood cylinders.

Sample 6 A

E3

A4

E4 K,/6K3

[s-'] [kJ/mol] [g -l s- '] [kJ/mol]

___

_____

_ _ _ _ ~

~~ ~~

Acacia 1.48 1.045.106 80.5 1.015.106 76.0 1.39- 1.69

wood

Eucalyptus 1.40 1.329. lo6 80.3 1.264. lo6 78.3 0.95- 1.03

wood

or the relative chain growth rate. The value varies from 1.39

to 1.69 for acacia wood in the temperature range 573 to

723

K

which being greater than one clearly reflects the im-

portance of the propagation reaction in the proposed chain

growth mechanism.

For the case of eucalyptus wood the relative chain growth

rate varies between 0.95 to 1.03 which shows that in this

case the propagation reaction is not as significant as in the

case of acacia wood and the major phenomena affecting the

pyrolysis

of

eucalyptus wood are the tar adsorption and de-

composition reactions.

Heterogeneous secondary reactions play an important part

at both low and high temperatures. At low temperatures

more residence time is available for vapour-solid interac-

tions and autocatalysis take place whereas at high tempera-

tures the tar decomposition reactions take place. Fraga et

al. [36] in their investigation of biomass pyrolysis tars show

that extensive modification of primary pyrolysis tars takes

place by means of intraparticle (heterogeneous) secondary

reactions, the reactions being intensified by increasing heat-

ing rates. The chain growth model takes both the volatiles

retention time and cracking and repolymerization reactions

of the vapours with the decomposing solid as well as auto-

catalysis into consideration.

The sealed reactor studies carried at 573, 623, 673, and

723

K

of small samples yield a final char residue of 36% and

32% for acacia and eucalyptus wood respectively. It is in-

teresting that the char formed from acacia and eucalyptus

wood in sealed reactor is in similar quantities as those ob-

tained for the two woods in gas-purged reactor for large

samples, although the heating rates in the sealed reactor are

much higher than the heating rates which accompany large

particles in the gas-purged reactor. This clearly shows that

the secondary reactions and not lower heating rates are the

source of secondary char formation in large particles. Ex-

periments carried out with higher initial nitrogen pressures

resulted in the similar amounts of final char residue which

predicts that vapour-solid interactions and not higher pres-

sure which accompany the inside of the large particles [37]

are the cause of higher char yields.

During the pyrolysis process the pores of the solid are

enlarged which offer many reaction sites and more second-

ary reactions take place which lead to the enrichment of

charcoal with carbon and reform the volatiles and gaseous

products. The volatiles generated from the inner virgin

wood pass through the outer charcoal regions and the pores


9/11

280

Chem. Eng. Technol.

19

(1996) 272-282

become smaller and smaller, thus, the retention time of the

tars increases, leading to again more of char, as more the

retention time of the volatiles, higher is the extent of sec-

ondary reactions. That autocatalysis observed

in

our experi-

ments is confirmed by the lower activation energies of reac-

tions (3) and (4) as compared to reactions (1) and (2). The

activation energies for acacia wood for reactions (3) and (4)

are 80.5 and 76.0 kJ/mol and are lesser than 91.5 and

85.9 kJ/mol for the primary reactions. Similar is the case

for eucalyptus wood in which the secondary reaction activa-

tion energies of 80.3 and 78.3 kJ/mol are lesser than 93.1

and 86.7 kJ/mol. Antal and Varhegyi [2] also comment that

vapour-solid interactions are accompanied with lower ac-

tivation energies. Murty and Blackshear [38] also observed

an increase in reaction rate constant at a particular tempera-

ture

on

passing from the surface to the center of the

specimen and Stamm [39] has described experiments in

which the rate of reaction was increased when products

were not free to escape, effects that could be called auto-

catalytic. Tabatabaie et al. [40] call attention to the fact that

their high temperature decomposition

of

cellulose in the

Fast-TGA sample boat may have been affected by autoca-

talysis (perhaps by the presence of organic acids such as for-

mic and acetic acids in the volatile pyrolysis products).

Autocatalysis is promoted by the presence of the lid which

hinders easy escape of the primary vapours from within the

sample boat into the inert carrier gas stream [41].

Alongwith the residual weight fraction the axis temperatures

are reported. The temperature in the pellet is simulated with

the energy balance model, and the theoretical curves and ex-

perimental points at half radius from the axis are shown in

Figs. 7 and 8 for acacia and eucalyptus wood respectively for

15

mm dia particles at 623

K.

The values of the properties

used in the model are taken as:

Wood specific heat = 2380.0 J/kg K

Char specific heat = 1600.0 J/kg

K

Wood thermal conductivity = 0.158 W/m

K

Char thermal conductivity = 0.107 W/m K

Solid emissivity = 0.95

Convective heat transfer

coefficient = 5.69+0.0098 TW/m2

K

[42].

It is considered that the local value of the property is a func-

tion of the conversion of wood. The local value of the heat

conduction coefficient, k and of the specific heat,

Cp,

of

the pyrolyzing solid were estimated as the sum of the two

values corresponding to the virgin material and of the char.

Each of the two values contributes to the sum in a way pro-

portional to the local conversion: property = (l-conver-

sion) (property),,,,, + (conversion) (property),ha,. The heat

of

reaction is determined as equal to 23 kJ/kg for acacia

wood and - 241 kJ/kg for eucalyptus wood. The tempera-

ture history of acacia and eucalyptus wood cylinders of dia

20 mm and length 120 mm at 723

K

as predicted by the

-0.2

T I ME r n i n . 1

Figure 7. Experimental ( - - ) and theoretical ( temperature

variation at a distance

R / 2

during pyrolysis

of

acacia wood cylinder

(diameter

15 mm

and length

90mm)

at

623 K.

1 *o

\

0 3 6 9 12 15 1 8 21 24

6

9 12 15

18

21

2

TIME

(rnin.1

Figure 8. Experimental ( - and theoretical

(

temperature

variation at a distance

R / 2

during pyrolysis of eucalyptus wood cylinder

(diameter

15

mm

and length

90mm)

at

623

K.

model are shown in Figs. 9 and 10 respectively. It is interest-

ing to note that acacia wood has a higher autocatalytic/

noncatalytic ratio and also has a higher exothermic heat of

reaction as compared to the eucalyptus wood and, more-

over, they yield higher char fractions in the sealed reactor

as well as for large particles in gas-purged reactor. Mok et

al. [4] observed that high sample loadings increased char

yield and the associated exothermic heat release and

lowered the reaction onset temperature. That the secondary

reactions and heat of reaction are linked, is in support of

our chain growth model of heterogeneous reactions during

wood pyrolysis.


10/11

Chem. Eng. Technol. 19 (1996) 272-282

550

I I

I

I

I I

0 2

6

8

10 12

T IME min . 1

Figure 9. Temperature history of acacia wood cylinder (diameter 20 mm

and length 120mm) during pyrolysis at 723 K as predicted by the model.

5

Conclusions

The chain growth model takes both the volatiles retention

time and cracking and repolymerization reactions of the

vapours with the decomposing solid as well as autocatalysis

into consideration. The secondary reaction activation ener-

gies determined are

80.5

and 76.0 kJ/mol for acacia, and

80.3 and 78.3 kJ/mol for eucalyptus wood for the initiation

and propagation reactions respectively, and deposition

coefficients larger than one are obtained for both the

woods. The activation energies of the heterogeneous reac-

tions are lesser than primary reactions which predict auto-

catalysis in large particles.

The vapour-solid interactions are an important pheno-

menon in biomass pyrolysis. Char yields of 36% for acacia

wood and 32% for eucalyptus wood have been obtained in

sealed reactor studies. Similar char yields are obtained for

pyrolysis of large particles which implies that the vapour-

solid interactions and not lower heating rates govern the

pyrolysis of large particles, since high heating rates accom-

pany sealed reactor studies.

The small samples in which the volatiles are immediately re-

moved are endothermic and those accompanied with sec-

ondary reactions in large particles are exothermic. The heat

of reaction

of

-

323 kJ/kg is determined for acacia wood,

550

I

I

I

I I

4

6 8 10 12

T I M E min.)

28

1

Figure

10.

Temperature history of eucalyptus wood cylinder (diameter

20

mm and length 120 mm) during pyrolysis at 723 K as predicted by the

model.

and of -241 kJ/kg for eucalyptus wood. Moreover, the

ratio of autocatalytic reaction to that of the noncatalytic

reaction in our chain growth model K 4 / 6 K 3 is higher for

acacia wood (1.39 to 1.69) than that of eucalyptus wood

(0.95 to 1.03) and also the deposition coefficient for acacia

wood is higher than that of eucalyptus wood, and acacia

yields more char. The positive correlation between the sec-

ondary reactions and exothermic heat of reaction proves the

applicability of the model.

Our model of secondary reactions is found to be satisfacto-

ry and can predict accurately the weight loss and char yield.

The secondary reactions are responsible for carbon enrich-

ment of the char residue and exothermic heat of reaction.

Received: July 19, 1994 [CET684]

Symbols used

preexponential factor for i

=

1,2, and 3

propagation reaction preexponential factor

transformed preexponential factor

educt (virgin) wood weight fraction

primary char weight fraction

secondary char weight fraction

specific heat capacity

activation energy


11/11

282

Chem. Eng. Technol.

19

1996)

272-282

ei [-I

F [-I

h [W/m2K]

A H

[kJ/kg]

H [-I

Ki

[s- 1

K4 [g-ls-']

k

[W/mK]

n j , n

[-I

P

[-I

Q

[-I

R , [J/molK]

r , R Iml

T [Kl

t [sl

w

[-I

x [-I

Greek letters

[-I

u

[W/m2K4]

Subscripts

transformed activation energy

sum of squares function

convective heat transfer coefficient

heat

of

reaction

dimensionless convective and radiative heat trans-

fer coefficient

rate constant for i = 1,2, nd

3

propagation reaction rate constant

thermal conductivity

reaction order

transformed absolute temperature

dimensionless heat of reaction

gas constant

radius of pellet

absolute temperature

time

residual weight fraction

dimensionless radius

deposition coefficient

dimensionless temperature

Prandtl number

density

dimensionless time

heating rate

solid emissivity

Stephan-Boltzmann constant

reaction number, i = 1,2,3,4

point employed in least square fitting

experimental

theoretical

initial

reactor

References

[l]Bradbury, A.G. W., Sakai, Y., Shafizadeh, F.,

J .

Ap p l . P o l ym.

[2]Antal, M.J., Jr., Varhegyi, G., Ind. Eng. C hem . Res. 34 (1995)

[3]Mok, W.S.-L., Antal, M.J., Jr ., Thermochim. Acta 68 (1983)

[4]Mok, W. S.-L., Antal, M. J. , Jr. , Szabo, P., Varhegyi, G., Zelei,

B., Znd. Eng. Chem. Res. 31 (1992) p. 1162-1166.

[5]Akita, K., Bull. Fire Prev. SOC. Jpn 5 (1956)pp. 43-44.

[6]Koufopanos, C. A., Papayannakos,

N. ,

Maschio, G., Lucchesi,

A., Can. J Chem . Eng. 69 (1991) pp.907-915.

[7]Lewellen, P.C., Peters, W.A., Howard, J.B., Sixteenth Znt.

S y m p . C o m b . , The Combustion Institute; Pittsburgh 1977,

Sci. 23 (1979) p. 3271 - 3280.

pp. 703-717.

pp.

165 186.

pp. 1471 1480.

[8]Arseneau, D.F., Can.

J .

Chem. 49 (1971) p. 632-638.

[9]Takamoto, D. Y., Petrich, M. A., Znd. Eng. Ch em . Res. 33 (1994)

pp. 3004

-

3009.

[lo]Boroson,

M.

., Howard, J. B., Longwell, J.P., Peters, W.A.,

[ll]Mazumdar, B.K., Chatterjee,

N.N. ,

Fuel 52 (1973) p. 11-19.

[12]Anthony, D. B., Howard, J . B., Hottel, H .C. , Meissner, H.P. ,

Fif teenth Int . Symp. Comb. , The Combustion Institute, Pitt-

sburgh 1975,pp. 1303- 1317.

[13]Anthony, D. B., Howard, J. B., AICh E

J .

22 (1976) p. 625 656.

[14]Shafizadeh, F., Bradbury, A.G.W.,

J .

Appl. Polym. Sci. 23

[15]

Chen, W.Y., Zhang, Z.P., Shen, B.C., Fan, L.T., Chem. Eng.

[16]Chan, W.C.R. , Kelbon, M., Krieger, B.B., Ind. Eng. Chem.

[17]Raman, P ., Walawender, W. P., Fan, L.T., Howell, J. A.,

Ind.

[I81 Bamford, C.H., Crank, J., Malan, D.H., Proc. Camb. Phil .

[19]Chan, W.C.R., Kelbon, M., Krieger, B.B., Fuel

64

(1985)

[20]Roberts, A.F., Clough, G . , Ninth ln t . Sym p. Comb. The Com-

[21]Pyle, D.L., Zaror, C.A., Chem. Eng. Sci. 39 (1984)

[22]Capart, R., Fagbemi, L., Gelus, M., in: Energyfrom Biomass,

(Palz, W., Coombs, J., Hall, Do.O., Eds.), Elsevier Appl. Sci.

Publ., Amsterdam 1986,pp. 842-846.

[23]Ahuja, P., Kumar,

S.,

Singh, P.C., in: Transport Phenomena in

Combustion (Chan, S. H., Ed.), Proc. Int. Symp. Transport Pro-

cesses (ISTP-8), Taylor and Francis Publ., 1995.

[24]Kung, H. C., Co mb . Flame 18 (1972) p. 185

-

195.

[25]Bilbao, R., Millera, A., Murillo, M.B.,

Ind.

Eng. Ch em. Res. 32

[26]Kansa, E.J., Perlee, H.E., Charken, R.F., Comb. Flame 29

[27]Koufopanos, C.A., Maschio, G., Lucchesi, A., Can.

J .

Ch em.

[28]Dumpelmann, R., Richarz, W., Stammbach, M.R., Can

J .

[29]Varhegyi, G., Szabo, P., Mok, W.S.-L., Antal, M.J., J r.,

J .

[30]Lipska, A. E., Parker, W. J.,

J .

Appl . Po lym. Sci . ,

10

(1966)

[31] Tang,W.K.,Neill,W.,J.Polym.Sci.PartC6 1964)pp.65-81.

[32]Marquardt, D.W.,

J.

SOC. ndust. Appl. Math.

I 1

(1963)

[33]Press, W.H., Flannery, B.P., Tenkolsky, S.A., Vetterling,

W.T., Numerical Recipes: The Art of Scientific Computing,

Cambridge Univ. Press, Cambridge 1986.

Energy Fuels 3 (1989)pp. 735

-

740.

(1979) p. 1431 1442.

Sci. 49 (1994)pp. 3687-3698.

Res. 27 (1988)pp. 2261 - 2275.

Eng. Chem . Process Res. Dev. 20 (1981) p. 630-636.

SOC. 2 (1946)

p.

166- 182.

pp. 1505- 1513.

bustion Institute, Pittsburgh 1963,pp. 158

-

166.

pp. 147

- 158.

(1993) p. 1811 1817.

(1977) p.311-324.

E n g .

67 (1989) p. 75 84.

Chem. Eng. 69 (1991) p. 953 -963.

Anal . Ap pl . Pyro lys is 26 (1993)pp. 159- 174.

pp. 1439- 1453.

pp. 431 -441.

[34]

Chen, N. ., Aris, R.,

AZChE

J .

38 (1992)

p.

626-628.

[35]Roberts, A. F., Thirteenth Int. Symp. Comb., The Combustion

[36]Fraga, A.R., Gaines, A.F., Kandiyoti, R., Fuel 70 (1991)

[37]Tinney, E. R., Tenth Znt. Sym p. C om b. , The Combustion In-

[38]Murty, K.A., Blackshear, P.L.,

Jr. ,

Pyrodynamics

4

(1966)

[39]

Stamm, A.J.,

Ind. Eng. Chem. 48 (1956)

p.

413-417.

[40]Tabatabaie-Raissi, A., Mok, W.S.-L., Antal, M. J.,

J r . ,

Ind .

[41]Varhegyi, G., Antal, M.J., Jr., Szekely, T., Till, F., Jakab, E.,

[42]

Alves, S.S. Figueiredo, J.L.,

Chem. Eng. Sci. 44 (1989)

Institute, Pittsburgh 1971,pp. 893 -903.

pp. 803 809.

stitute, Pittsburgh 1965, pp. 925

-

930.

pp. 285 - 298.

Eng. Chem . Res. 28 (1989) p. 856-865.

Energy Fuels 2 (1988) p. 267

-

272.

pp. 2861 - 2869.

a model for primary and heterogeneous second

Documents