studies on pyrolysis of vegetable market wastes in presence of heat transfer resistance and...

INTERNATIONAL JOURNAL OF ENERGY RESEARCHInt. J. Energy Res. 2005; 29:811–828Published online 14 March 2005 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/er.1087

Studies on pyrolysis of vegetable market wastes in presence ofheat transfer resistance and deactivation

Ruby Ray, Ranjana Chowdhury and Pinaki Bhattacharyan,y

Chemical Engineering Department, Jadavpur University, Kolkata 700 032, India

SUMMARY

In the present investigation, the pyrolysis of predried vegetable market waste (dp=5.03mm)has been studied using a cylindrical pyrolyser having diameter of 250mm under both isothermaland non-isothermal conditions within the temperature range of 523–923K with an intention to investigatethe effective contribution of different heat transfer controlling regime namely intra-particle, externalalong with kinetically control regime on the overall global rate of pyrolysis. Thermogravimetricmethod of analysis was utilized to obtain experimental data for both isothermal and non-isothermalcases by coupling a digital balance with the pyrolyser. The pyrolysis of vegetable market waste hasbeen observed to exhibit deactivated concentration independent pyrolysis kinetics, analogous to catalyticpoisoning, throughout the entire range of study. The deactivation is of 1st order up to 723K and followsthe 3rd order in the temperature range of 7235T4923K. Starting from the mechanistic approach,a set of differential heat and mass balance equations has been developed and a general equationcontaining a specific parameter (dimensionless temperature, y) is presented which can conveniently beused to simulate concentration time histories of the participating components by assigning differentexpressions for y developed in the present investigation. A detailed procedure of simulation workunder different controlling regime has also been outlined. A comparison of experimental data withthe simulated values under isothermal conditions shows that the system is kinetically controlled atlower temperature region (T4723K). However, at higher temperature region (7235T5923K), thepyrolysis process is controlled by intra-particle heat transfer resistance. While studying the pyrolysisprocess under non-isothermal conditions, a segregated ramp function of furnace temperature risehas been used. The transient profiles of the reactant and products have been simulated following thesimilar procedure followed under isothermal conditions. When experimental data and simulatedvalues are compared, it is observed that unlike the case of isothermal condition, the globalpyrolysis rate is controlled by intra-particle heat transfer resistance. Copyright # 2005 John Wiley &Sons, Ltd.

KEY WORDS: pyrolysis kinetics; activity; heat transfer; deactivation; vegetable market waste

Received 25 March 2004Accepted 30 June 2004Copyright # 2005 John Wiley & Sons, Ltd.

yE-mail: pinaki [email protected]

Contract/grant sponsor: Council of Scientific and Industrial Research; contract/grant number: 9/96(330)/2000-EMR-IContract/grant sponsor: All India Council of Technical Education; contract/grant number: AICTE/Per/1-97

nCorrespondence to: Pinaki Bhattacharya, Head, Chemical Engineering Department, Jadavpur University, Kolkata700 032, India.

1. INTRODUCTION

Any pyrolysis process involving thermochemical decomposition of solid material undercontrolled condition presents a unique system for studying heterogeneous non-catalyticreaction behaviour under moderate to fairly high temperature environment. In such process,change of particle size may or may not occur depending on the system chosen. Like allheterogeneous reactions, during pyrolysis the global rate of reactions encounters a series ofresistances primarily from bulk diffusion and ash diffusion. Study of pyrolysis reaction is moreimportant in the sense that it provides an opportunity to understand how heat transfer either inthe bulk fluid phase or through the solid reactant material intrudes the overall global rate. Sincethe primary objective in any pyrolysis process is to obtain the maximum yield of desired volatilematers, an a priori knowledge on the extent of different resistances is absolutely necessary. Thusa thorough and comprehensive investigation is always desirable for any pyrolysis processwhen an unconventional or a new feedstock is used. Since pyrolysis process is basically athermochemical decomposition of reactants, a pedagogic consideration will always suggest thatcontribution of heat transfer resistance, both external and internal may be significantly highcompared to diffusional and chemical reaction resistances.

Previous investigations on pyrolysis of wood and other lignocellulosic materials have shownthe extremely complex network of hundreds of concurrent and consecutive reactions. The majorcomponents of lignocellulosic materials are lignin, cellulose and hemicellulose that are likely toreact independently. Due to this complex multiple reactions, the apparent rate constants andactivation energy of pyrolysis may change with reaction operating parameters.

Shafizadeh and Chin (1977) proposed that primary pyrolysis of wood occurs through threeparallel reactions producing gas, tar and char, while the tar decomposes following two parallelreactions yielding gas and char in the secondary pyrolysis step. The kinetics of reactionsinvolved in isothermal pyrolysis of cellulose has been widely reported by a three-reaction model(Agarwal, 1988; Bradbury et al., 1979; Arseneau, 1971). According to the model proposed byAgarwal (1988), cellulose decomposes to tar, char and gaseous products by three parallel first-order reactions. Thurner and Mann (1981) investigated the pyrolysing behaviour of wood intogas, tar and char and determined the kinetic parameters to predict the composition of thepyrolysis products. Pyle and Zaror (1984), Chan et al. (1985) and Antal (1985) considered theeffect of simultaneous heat-transfer on the observed rate of pyrolysis of wood and large biomassparticles. Balci et al. (1993) observed deactivation of pyrolysis reactions during their studies onpyrolysis of different types of wood and they proposed several models to incorporate the effectof deactivation in the global reaction kinetics. Bandyopadhyay et al. (1999) extensively studiedthe global pyrolysis kinetics of coconut shell and put forward different models to explain thedeactivation characteristics of the system.

In the present investigation, a comprehensive study on the pyrolysis of a highly heterogeneoussolid mass, vegetable market waste having volume surface mean diameter (dp) of 5.03mm, hasbeen carried out. In an early communication (Ray et al., 2004) it has been shown that thepyrolysis of the same feed material but having much smaller size (dp,old=3.26mm) encountersthe problem of deactivation as observed by noting the change of rate constant with progress oftime under isothermal condition. Such unusual behaviour (termed as deactivation) has also beenobserved by several research groups (Balci et al., 1993; Bandyopadhyay et al., 1999). Anelaborate discussion on such reaction engineering behaviour has also been made by the presentauthors (Ray et al., 2004). For smaller particle size (dp,old=3.26mm), the spatial temperature

Copyright # 2005 John Wiley & Sons, Ltd. Int. J. Energy Res. 2005; 29:811–828

R. RAY, R. CHOWDHURY AND P. BHATTACHARYA812

gradient was considered to be negligible and the sample was considered thermally thin; as aresult simultaneous heat transfer, both internal and external, did not have any significant effecton the pyrolysis characteristics.

In the present investigation, the particle size of the feed material has been selected significantlyhigh (dp/dp,old>1.5) from the standpoint of heat transfer study (the particle is no longerthermally thin) with the expectation that the effect of heat transfer should affect the globalreaction rate providing an opportunity to study the pyrolysis reaction engineering behaviourcontrolled by thermal resistances. A series of systematic and programmed experiments has beencarried out to investigate the effect of thermal resistances on the overall global rate of larger size(dp=5.03mm) vegetable market waste under both isothermal and non-isothermal conditions.During isothermal study, a set of temperatures ranging from 523 to 923K has been maintainedconstant and thermo gravimetric analysis has been carried out for each individual temperaturefor data acquisition. Under non-isothermal condition, pyrolysis temperature has been allowedto increase from the ambient value to final temperature of 923K following the pattern ofsegregated ramp function and the functionality constant has been varied in differenttemperature ranges according to the need of the time-temperature program of the presentheating system. Data obtained by measuring the weight loss at different instant have been usedto verify the prediction of the theoretical models developed by judiciously coupling mass andenergy balance equations incorporating the effect of simultaneously occurring heat transfer anddeactivated pyrolysis reactions.

2. EXPERIMENTAL WORK

2.1. Materials

The feedstock, vegetable market waste, was collected from the local city markets. First, thematerials were sun-dried for a considerable time period and then dried in an air-oven at 373Kfor 48 h. The waste material was irregular in shape. The volume surface mean diameter (dp) andthe specific surface area (ap) of the feed material were determined to be 5.03mm and 4254m�1,respectively, through cumulative screen analysis. Both proximate and ultimate analyses of thefeed material were carried out and the analytical results have been shown in Table I along withthe heating value and the bulk density of the feed material.

Table I. Characteristics of vegetable market waste.

Proximate Ultimate

Analysis Analysis(Dry basis) (Dry basis) Heating value Bulk density

Constituents (Weight %) Constituents (Weight %) (MJ kg�1) (kgm�3)

Fixed carbon 16.4 C 51.75Volatile matter 80.5 H 7.65 18.95 231.75Ash 3.1

O 36.8N 0.8Ash 3.1


PYROLYSIS OF VEGETABLE MARKET WASTES 813

2.2. Procedure

A set of experiments was carried out in a cylindrical reactor (Figures 1(a) and 1(b)) at differenttemperatures in the range of 523–923K under isothermal condition. The experimental systemconsisted of a cylindrical reactor of 250mm diameter inserted within a tubular furnace. A pieceof 200-mesh stainless steel (ss) screen was rolled and welded to form a cylindrical shaped holder.Biomass particles were placed inside this holder taking care that the desired bed density wasachieved. This ss-net holder had the length to diameter ratio 1:1 (10mm each). It was hung fromthe top of the reactor into the constant radiation zone with the help of a wire. This wire wasattached to a removable plug, which was also connected to a weighing balance. In order todetermine the temperature at different position of the reactor, thermocouples were insertedalong the length of the reactor. A downward nitrogen flow (4.16� 10�5mol/s) was maintainedin the reactor to ensure an inert environment.

To perform the experiment under isothermal condition, the empty reactor was heated up tothe desired final pyrolysis temperature (varying from 523 to 923K). As required by the existingheating element, ramping up of pyrolyser temperature from the ambient to the desired pyrolysis

Figure 1. (a) Experimental set-up (before entering the sample holder). 1. Reactor. 2. Sample holder.3. Thermocouples. 4. Digital balance. 5. Removable plug. 6. Gas outlet. 7. Temperature indicator.8. Nitrogen cylinder. 9. Adjustable stand. (b) Experimental set-up (after entering the sample holder).1. Reactor. 2. Sample holder. 3. Thermocouples. 4. Digital balance. 5. Removable plug. 6. Gas

outlet. 7. Temperature indicator. 8. Nitrogen cylinder. 9. Adjustable stand.



temperature was done using ramping constants of 0.2, 0.167, 0.15, 0.117 and 0.067K s�1 for0 ks4t41.2 ks, 1.2 ks5t41.8 ks, 1.8 ks5t43.0 ks, 3.0 ks5t43.6 ks and t>3.6 ks, respectively.Under these conditions no axial temperature profile was observed to exist. At each finaltemperature, the ss-holder containing material was introduced into the reactor and its weightwas noted from the digital balance at different time intervals. At each temperature, experimentwas carried out for a maximum time (tmax) of 10.8 ks.

Another set of experiments was carried out varying the furnace temperature with time i.e.under non-isothermal condition using same pattern of temperature programming as describedin case of temperature setting of isothermal experiments. In this case, the ss-net containingbiomass was introduced into the reactor before the furnace temperature was being raised. Theweight loss of the residual biomass was recorded at different time intervals. Under non-isothermal condition, experimental observation was pursued up to a maximum time period(tmax) of 10.8 ks. It was observed during experiment that at 4.2 ks, the maximum pyrolysistemperature selected for the present investigation of 923K was attained.

As observed by Balci et al. (1993) and the present group (Ray et al., 2004), the pyrolysisreaction was independent of nitrogen flow rate. Therefore, in the present investigation, the samenitrogen flow rate as in case of our previous study on reaction kinetics of ground vegetablewaste (dp=3.26mm) was maintained in the pyrolyser in all cases.

3. THEORETICAL ANALYSIS

As proposed by previous investigators (Shafizadeh and Chin, 1977; Bradbury et al., 1979;Thurner and Mann, 1981; Bandhopadhyay et al., 1999), the pyrolytic decomposition steps in thepresent investigation have been viewed as a combination of two parallel reactions}onegenerating different volatile compounds, lumped as volatiles and the other generating solidproduct, denoted as char. This representation of the reaction array has already been followed bythe present group (Ray et al., 2004) during their work on smaller vegetable waste materials(dp=3.26mm). Schematically the pyrolysis reaction may be represented as

Volatileskv

Predried vegetable waste

kc

Char

ð1Þ

The simulation has been carried out with the following data and assumptions:

1. Both the char and volatile forming reactions are of first order with respect to reactingbiomass (Shafizadeh and Chin, 1977; Thurner and Mann, 1981; Bandhyopadhyay et al.,1999; Ray et al., 2004).

2. The solid residue obtained at infinite reaction time is entirely made up of char (Thurnerand Mann, 1981). However, the residue at any time other than t!1 is comprised of bothchar and unreacted biomass.

3. Volatiles formed during the reaction diffuse through the reacted char at a faster ratetowards the outside furnace environment and thus the ash diffusion resistance may beneglected.



4. Anisotropy in the raw material may be neglected.5. The thermal and physicochemical properties like k, hc, e, cp, r, etc. of the solid are assumed

to be constant during the progress of pyrolysis.6. The enthalpy change associated with the set of selected reactions and physical changes is

taken to be zero (Balci et al., 1993).7. Mass transfer resistances, both external and internal are negligible.8. While reaction rate constants follow Arrhenius law, the deactivation rate constants follow

a modified form of Arrhenius law [defined in the latter section of the text].

An attempt has been made to incorporate the effect of simultaneous heat transfer (i.e. fluid filmheat transfer followed by intra-particle heat transfer) on the global rate with an intention todevelop model equations capable of predicting temperature distribution in both fluid phase andinside the solid particles. While doing such simulation work, model equations developed by Pyleand Zaror (1984) have been followed with necessary modification as discussed below.

3.1. Model A: intra-particle heat transfer control

In this situation, heat is viewed to transfer to solid surface from the surrounding gas bycombination of convection and radiation and the radial temperature profile within the sample issymmetrical about the central axis of the test piece stainless steel (ss) cylinder. The axial andangular gradient of temperature within the sample has been considered to be insignificantlysmall.

In order to develop a temperature distribution relationship within the particle, an energybalance has been made around a differential volume element of the sample. Further noting thatthe apparent enthalpy change associated with the set of selected reactions and physical changesmay be considered to be zero in the present case, the resulting differential equation indimensionless form is given by

@

@tðcpryÞ ¼

ktmax

R2

@2y

@b2þ

1

b@y@b

� �ð2Þ

which on simplification becomes

@y@t¼ Bcond

@2y

@b2þ

1

b@y@b

� �ð3Þ

As mentioned earlier, the variation of forcing function (furnace temperature in present case)under transient condition has been done following a segregated ramp function. Mathematicallythis may be expressed as

T0

tmax

dyfdt¼ m

m ¼ 0:2; 04t40:111

m ¼ 0:167; 0:1115t40:167

m ¼ 0:15; 0:1675t40:278

m ¼ 0:117; 0:2785t40:333

m ¼ 0:067; t > 0:333

2666666664

3777777775

ð4Þ

where functionality constant m=0 for isothermal condition.



The initial conditions for such intra-particle heat transfer may now be written as

y ¼ 1 att ¼ 0

05b51

( )ð5Þ

In order to solve Equation (3), the boundary conditions may be written as

k

R

@y@b¼ hcðyf � yÞ þ esT3

0ðy4f � y4Þ at

b ¼ 1

t > 0

( )ð6Þ

T0

R

@y@b¼ 0 at

b ¼ 0

t50

( )ð7Þ

It is immediately observed that Equation (3) becomes indeterminant under the boundarycondition (7). Thus in the present simulation, McLaurin’s expansion equation has been used tosolve Equation (3) as suggested by Pyle and Zaror (1984).

According to this expansion,

limb!0

1

b@y@b

� �¼@2y

@b2at fb ¼ 0g ð8Þ

which leads to the boundary condition at the centre of the solid as

@y@t¼ 2Bcond

@2y

@b2ð9Þ

The partial differential Equation (3) has now been converted to four ordinary differentialequations by the method of Lines. In this method the radius of the sample has been divided intothree equal parts (i.e. n=3). The partial derivatives with respect to radial position have beenreplaced by central finite difference expressions. Thus a set of four ordinary differentialequations with respect to time co-ordinate has been obtained as follows:

dyndt¼ Bcond

yn�1 � 2yn þ ynþ1Db2

þ1

bynþ1 � yn�1

2Db

� �for n ¼ nodal positions ð10Þ

3.2. Model B: external heat transfer control

In this case, the rate of heat transfer from the bulk gas to the surface of the particle is viewed tobe the slowest compared to the rate of heat transfer through the particle surface. As in theprevious case, a relationship for temperature distribution within the gas film has been obtainedby making an energy balance around a differential volume element of the gas film. Resultingequation is given below.

cprdydt¼

2tmax

Rb½hcðyf � yÞ þ esT3

0ðy4f � y4Þ� ð11Þ

The above equation can now conveniently be written as

dydt¼ 2½Bconvðyf � yÞ þ Bradðy

4f � y4Þ� ð12Þ

In this case also, the variation of forcing function (furnace temperature) has been consideredto follow the nature of ramp function as given by Equation (4).



In order to ascertain the partial contribution of external and internal heat transfer on theoverall reaction engineering behaviour of the present pyrolysis process, it is now necessary tocouple the heat sensitive terms in the overall global rate equation. In order to do such anexercise, a comprehensive mechanistic approach starting from the mass balance equation isnecessary.

The following section deals with the development of differential mass balance equations andincorporation of heat sensitive terms in those equations with an aim to achieve expressions for ywhich ultimately will indicate the partial contribution of thermal resistances to overall rateprocess. Simultaneously, it is necessary to study the reaction engineering behaviour in completeabsence of heat transfer effect, so that the effective contribution of thermal resistances eitherexternal or intra-particle on the global rate may be understood clearly. This can be achieved bysolving differential mass balance equations assuming the system to be unaffected by heattransfer effect. This in other word means, the system is then totally controlled by pyrolysiskinetics. While attempting to write the mass balance equations of the components involved inthe pyrolysis process, mechanism of the pyrolysis reaction outlined before has been followed.Intention of coupling y with the differential mass balance equations is to present a generalequation capable of describing reaction engineering behaviour of the present system. Suchunified approach is very much useful since by assigning suitable expressions of y in this generalequation, one can conveniently get an idea of effective contribution of different controllingresistances in the overall global pyrolysis rate.

3.3. Prediction of time histories of reactant, char and volatiles

Using differential mass balance, the formation of char and volatiles and the decomposition oflignocellulosic reactant may be written in dimensionless form as follows:

dV

dt¼ kvW ð13Þ

dC

dt¼ kcW ð14Þ

dW

dt¼ �kwW ð15Þ

wherekw ¼ kv þ kc ð16Þ

The initial conditions for isothermal pyrolysis runs are given by

W ¼W0 ¼ 1

V ¼ 0

C ¼ 0

2664

3775 at t ¼ 0 ð17Þ

Using Equation (17), Equations (13)–(15) have been solved analytically under isothermalconditions. This generates the following transient profiles of participating components:

WðtÞ ¼W0 expð�kwtÞ ð18Þ

VðtÞ ¼kvkw

W0½1� expð�kwtÞ� ð19Þ



CðtÞ ¼kckw

W0½1� expð�kwtÞ� ð20Þ

3.4. Determination of the experimental values of reacting components

Volatiles present at any time during isothermal pyrolysis can be obtained by the global massbalance,

VðtÞ ¼W0 � SðtÞ ð21Þ

where

SðtÞ ¼ CðtÞ þWðtÞ

The char to volatiles yield ratio at any time during isothermal pyrolysis is constant and may bepresented as,

dC

dV¼

kckv

ð22Þ

Therefore,

CðtÞVðtÞ

¼Cðt!1ÞVðt!1Þ

ð23Þ

According to Thurner and Mann (1981),

Sðt!1Þ ¼ Cðt!1Þ ð24Þ

Therefore,

Vðt!1Þ ¼W0 � Sðt!1Þ ð25Þ

From Equations (23) to (25), char and unreacted biomass present at any time may be evaluatedby the following equations:

CðtÞ ¼ VðtÞSðt!1Þ

W0 � Sðt!1Þ

� �ð26Þ

WðtÞ ¼W0 � CðtÞ � VðtÞ ð27Þ

By combining Equations (26) and (27), one gets

WðtÞ ¼W0 � VðtÞ 1þSðt!1Þ

W0 � Sðt!1Þ

� �ð28Þ

3.5. Deactivation phenomenon

It has already been reported (Ray et al., 2004) that for pyrolysis of thermally thin vegetablewaste (dp=3.26), deactivation phenomenon is observed and the activity, a, for such casedecreases with the increase in the conversion. It has also been pointed out that such deactivationphenomenon during non-catalytic pyrolysis of solid material is very much similar to catalystpoising (Levenspiel, 1972) observed during heterogeneous catalysis. Thus following the conceptof Levenspiel (1972), an expression for the observed rate constants incorporating the term ymaybe defined as

ki;obs ¼ aiki;true ¼ aik0i exp �%EEi

y

� �; i ¼ w; v; c ð29Þ



where ai are the activities of active materials (reacting biomass, volatiles and char) towardscorresponding reaction and ki,obs and ki,true are the observed and true reaction rate constantsrespectively.

The rates of different active materials undergoing deactivation may now be written in thedimensionless forms

dW

dt¼ �kw;obsW ð30Þ

dI

dt¼ ki;obsW I ¼ V;C and i ¼ v; c ð31Þ

It has been reported earlier (Ray et al., 2004) that a concentration independentmodel of deactivation can conveniently predict concentration time history of the partici-pating components of the present system. Since such model equation is independentof the concentrations of both reactant and product, the rate of change of activity, ai, isconsidered solely nth order function of activity itself (Levenspiel, 1972; Carberry, 1976). Inits dimensionless form, the concentration independent model equation may be representedas follows:

�daidt¼ kdiani ; i ¼ w; v; c ð32Þ

The temperature dependency of deactivation rate constants now needs to be suitablyrepresented for different controlling regime. This is given below.

kdi ¼ kd0i exp �%EEdi

y

� �; i ¼ w; v; c ð33Þ

From the knowledge of experimental values of kdi as a function of temperature, the parameterskd0i and Edi may be determined.

It has already been established (Ray et al., 2004) during the studies on thermally thinparticles that the present system follows a first order deactivation (n=1) up to temperature levelof 723K, above which a third order deactivation (n=3) is observed. Thus putting n=1 up toT=723K and n=3 for 7235T4923K, the concentration time histories of the concernedcomponents under different controlling regime can been predicted following the procedureoutlined below.

By assigning the expression for y given in Equation (3), in Equation (33) one can get the valueof kdi under intra-particle heat transfer controlling regime. Subsequently when this equation issubstituted in Equation (32), one can obtain ai as a function of t: Now using Equation (29) andthe values of ai obtained from Equation (32), ki,obs can be determined. The concentration timehistories of W, V and C under intra-particle heat transfer controlling regime can now bepredicted using Equations (30) and (31).

A similar approach for external heat transfer resistance controlling regime can be used bysubstituting the expression for y obtained from Equation (12) in Equation (33) and repeating thesimilar procedure mentioned above.

Prediction of time concentration history under kinetically controlled regime can be doneusing Equations (30)–(33) without assigning any special form of y; i.e. in Equation (33) ymay be



simply substituted as T/T0, the value of T being set depending on the operating conditions ( i.e.isothermal or non-isothermal).

All the mass balance and energy balance equations have been solved by 4th order RungeKutta equation using the software developed by the present authors.

4. RESULTS AND DISCUSSIONS

Values of activation energies and frequency factors from Arrhenius law have been taken fromliterature (Ray et al., 2004) and are shown in Table II. Similarly values of activation energiesand frequency factors for 1st order and 3rd order deactivation have also been taken from sameliterature and are given in Table III. In order to simulate model equations in Models A and B,thermal and physico-chemical data used are given in Table IV. The density of vegetable marketwaste was measured by gravimetric method. The values of thermal conductivity (k) and specificheat capacity (cp) were taken from the literature (Perry and Chilton, 1973). The values ofemissivity (e) of solid and convective heat transfer coefficient (hc) were obtained from Pyle andZaror (1984).

It has already been discussed under experimental section that the pyrolysis reactor wasoperated isothermally at different temperatures (viz. 523, 573, 623, 673, 723, 773, 823, 873 and923K) in the range of 523 to 923K. In order to understand rate control regime with respect toheat transfer, two representative temperatures, one in the lower region (623K) and other in thehigher region (923K) have been selected in the present presentation keeping parity with theprevious paper (Ray et al., 2004). Simulated values of concentrations of unreacted wastematerial, volatiles, char and solid residue at different dimensionless time for different heat

Table II. Calculated activation energies and frequency factors from Arrhenius law.

Reaction rateconstant

Frequencyfactor (min�1)

Activationenergy (kJmol�1)

Correlationcoefficient

Universal gas constant,(kJmol�1K�1)

ks,true 17.47 31.41 0.9452 0.0083kv,true 30.74 38.16 0.9321kc,true 0.37 16.30 0.9334

Table III. Calculated activation energies, frequency factors and order of deactivationas per deactivation model.

Temperaturerange

Reaction rateconstant

Frequencyfactor (s�1)

Activationenergy (kJmol�1)

Correlationcoefficient

Order ofdeactivation (d)

4723K kdw 3.77� 10�3 17.95 0.9982kdv 7.42� 10�3 23.12 0.9968 1kdc 1.25� 10�3 12.18 0.9975

>723K kdw 9.93 57.35 0.9954kdv 10.94 60.52 0.9998 3kdc 1.88 50.26 0.9998



transfer controlling regime i.e. intra-particle heat transfer control (Model A) and external heattransfer control (Model B) along with kinetically controlled mode, have been evaluatedfollowing the methods outlined earlier. The simulated values of W and S against dimensionlesstime for a constant furnace temperature of 623K are shown in Figure 2. In order to identify thespecific nature of controlling regime, experimental data have also been superimposed on thesame figure. Similarly simulated values of V and C along with experimental data at thistemperature have been plotted against dimensionless time. This is shown in Figure 3. The sameprocedures have been repeated for the higher temperature vale (923K). These data are shown inFigures 4–6.

An interesting observation is obtained when Figures 2–6 are studied simultaneously toidentify the specific controlling regime. It is evident from Figures 2 and 3 that at lowertemperature (i.e. 623K), no significant contribution of heat transfer resistance either external or

Table IV. Values of parameters used in the Models A and B.

Parameter Value

Thermal conductivity, k, kWm�1K�1 5.56� 10�5

Density, r, kg/m�3 0.232� 103

Specific heat capacity, cp, kJ kg�1K�1 1.67

Convective heat transfer coefficient, hc, kWm�2K�1 8.4� 10�3

Emissivity of the solid, e 0.95Radius of cylinder, r, m 0.5� 10�2

Initial temperature of the solid, T0, K 303Stephan–Boltzmann constant, s , kWm�2K�4 5.73� 10�11

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

W, S

W, S

τ

Figure 2. Comparison of experimental results (points) and simulated (lines) weight fraction histories forunreacted material (&) and residue (m) as per Model A (� � �), Model B (- - -) and kinetically controlled

model (}) using deactivation model at final temperature 623K.



0.0 0.2 0.4 0.6 0.8 1.00.0

0.1

0.2

0.3

0.4

0.5

0.6

V, C

τ

Figure 3. Comparison of experimental results (points) and simulated (lines) weight fraction histories forvolatiles (*) and char (^) as per Model A (� � �), Model B (- - -) and kinetically controlled model (}) using

deactivation model at final temperature 623K.

0.0

0.2

0.4

0.6

0.8

1.0

W, S

W, S

τ0.0 0.2 0.4 0.6 0.8 1.0

Figure 4. Comparison of experimental results (points) and simulated (lines) weight fraction histories forunreacted material (&) and residue (m) as per Model A (� � �), Model B (- - -) and kinetically controlled

model (}) using deactivation model at final temperature 923K.



τ

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

V

0.0 0.2 0.4 0.6 0.8 1.0

Figure 5. Comparison of experimental results (point) and simulated (lines) weight fraction histories forvolatiles (*) as per Model A (� � �), Model B (- - -) and kinetically controlled model (}) using deactivation

model at final temperature 923K.

ττ

0.00

0.05

0.10

0.15

0.20

0.25

C

0.0 0.2 0.4 0.6 0.8 1.0

Figure 6. Comparison of experimental results (points) and simulated (lines) weight fraction histories forchar (^) as per Model A (� � �), Model B (- - -) and kinetically controlled model (}) using deactivation

model at final temperature 923K.



intra-particle on the overall rate is observed and the system may be well represented byclassical kinetic control model without any significant error. This is possibly due to the factthat at lower temperature environment (T4723) both DTsurface i.e. (Tf�Tsurface) and DTparticle

i.e. (Tf�Tparticle) are insignificant to contribute any resistance to the overall global rate(Levenspiel, 1984). On the other hand, at higher temperature (923K), it is evident that thepyrolysis process is controlled by intra-particle heat transfer resistance since in this caseDTparticle is significantly high due to high environmental temperature. Thus in highertemperature region, there exists a radial temperature distribution (held in ss-cylinder), whichaffects the behaviour of the pyrolysing material under present investigation. The particle sizeselected in the present investigation (dp=5.03mm) cannot therefore be considered thermallythin under this situation.

In the present investigation, an attempt has also been made to identify the contribution ofheat transfer resistance in the pyrolysis process under non-isothermal conditions. It has beenfound from experiment that a length of time 1100 s was required for the system to reach 523K atwhich the pyrolysis in the present system initiates. This time has therefore been taken as initialtime in the present presentation. The furnace temperature was allowed to change with time from523 to 923K following the set-up conditions given in Equation (4). Simulated values of W, V, Cand S have been evaluated at each instant with the respective temperature at that instant. All thethree models i.e. Models A, B and kinetically controlled model have been used individually togenerate simulated data under non-isothermal conditions. These data along with theexperimental value have been plotted in Figure 7 against dimensionless time. The change offurnace temperature with dimensionless time is also shown in the same figure. It is evident from

0.10 0.15 0.20 0.25 0.30 0.350.0

0.2

0.4

0.6

0.8

1.0

τ

W, V

, C, S

500

600

700

800

900

1000

Tem

pera

ture

K

Figure 7. Comparison of simulated weight fraction history (lines) as per Model A (� � �), Model B (- - -)and Model C (}) using deactivation model during non-isothermal condition with the derived experimentalresults (points) for unreacted materials (&), volatiles (*), char (^) and residue (m) along with the

temperature history (- � - � -).



the figure that in such non-isothermal condition the system is totally controlled by intra-particleheat transfer resistance. This is, however, expected since under non-isothermal conditionDTparticle at a particular instant always remains high even at lower temperature region since theparticle remain at a particular temperature for a very short period of time.

NOMENCLATURE

a =activityap =surface area per unit volume of solid (m�1)Bcond =dimensionless number for conductionBconv =dimensionless number for convectionBrad =dimensionless number for radiationcp =specific heat capacity of solid (kJ kg�1K�1)C =normalized weight of char

(weight of char at any instant/weight of reactant at t=0)dp =volume surface mean diameter (mm)dp,old =volume surface mean diameter of thermally thin particle (mm)E =activation energy as per Arrhenius law (kJmol�1)%EE =dimensionless group related to activation energy (E/RT0)Ed =activation energy or temperature dependency of the deactivation%EEd =dimensionless group related to activation energy of the deactivation (Ed/RT0)hc =convective heat transfer coefficient (kWm�2K�1)k =thermal conductivity (kWm�1K�1)k =reaction rate constant (s�1)kd =deactivation rate constant (s�1)k0 =frequency factor as per Arrhenius law (s�1)kd0 =frequency factor of deactivation as per Arrhenius law (s�1)m =rate of change of furnace temperature (K s�1)R =radius of the cylinder (m)R =universal gas constant (kJmol�1K�1)S =normalized weight of residuet =(weight of reactant+weight of char at any instant/weight of reactant at t=0)

time (s,ks)T =temperature (K)Tparticle =temperature at any point in the interior of the particle (K)Tsurface =temperature at the surface of the particle (K)W =normalized weight of reactant

(weight of reactant at any instant/weight of reactant at t=0)V =normalized weight of volatiles

(weight of volatiles at any instant/weight of reactant at t=0)

Greek letters

b =dimensionless radius (r/R)y =dimensionless temperature (T/T0)



e =emissivity of the solidk =dimensionless rate constant (ktmax)s =Stephan–Boltzman constant (kWm�2K�4)t =dimensionless time (t/tmax)

Subscripts

c =chard =deactivationf =furnacei =species involved in pyrolysis reactionmax =maximumobs =observeds =residuetrue =Arrheniusv =volatilesw =reactive material0 =initial condition

Superscript

d =order of deactivation

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the financial support received from All India Council of TechnicalEducation (AICTE) and Council of Scientific and Industrial Research (CSIR).

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