PARALLEL-AND SERIES-REACTION MECHANISMS OF WOOD AND CHAR COMBUSTION

Thermogravimetric curves in air of beech wood and char, ob tained from con ven tional py rol y sis of beech wood at a lab o ra tory scale, have been re-ex am ined us ing dif fer ent ki netic mod els. Multi-step re ac tion mech a nisms, con sist ing of ei ther four (wood) or two (char) re ac tions are needed for ac cu rate pre dic tions of weight loss curves. In the case of wood, three re ac tions are lin ear in the re ac tant mass frac tion whereas the fourth step pres ents a power-law de pend ence. A lin ear re ac tion for devolatilization and a non-lin ear re ac tion for com bus tion are used for the weight loss curves of char. It has been found that ac ti va tion en er gies and pre-ex po nen tial fac tors are in vari ant with se riesor par al lel-re ac tions, pro vid ing changes in the stoichiometric co ef fi cients. Fur ther more, the ac ti va tion en er gies of the two re ac tions oc cur ring at higher tem per a tures in the four-step mech a nism (wood) and those of the two-step mech a nism (char) are the same. Thus, pre-ex po nen tial fac tors and re ac tion or der take into account variations in the char reactivity derived from different pyrolysis conditions.


Introduction
The de sign and op ti mi za tion of combustors and gasifiers of bio mass fu els is based on the knowl edge of re ac tion ki net ics.Com bus tion of bio mass con sists [1] of pyrol y sis, as so ci ated with the ho mo ge neous com bus tion of vol a tile prod ucts, and het er o geneous com bus tion/gasi fi ca tion of char.Hence in for ma tion is needed on both the devolatilization stage, that is, about the pos si ble in flu ences of ox y gen on the rates of vola tile re lease, and the re ac tiv ity of char, whose con ver sion is 10-100 times slower [2,3].How ever, com pared with in ert at mo spheres, only a few in ves ti ga tions have been car ried out on the ox i da tive de com po si tion of wood and bio mass which, among the most re cent, in clude [4,5,6].
More over, though the lit er a ture on the re ac tiv i ties of coal chars and their ki netic mod el ing is huge (see, for in stance, the re views [2,3,7]), bio mass/wood chars have been ex am ined only in a small num ber of stud ies.Most re cent pub li ca tions are [8,9,10,11] and a com plete re view of pre vi ous lit er a ture is re ported in [11].
Thermogravimetric curves of the de com po si tion of wood/bio mass in the presence of ox y gen have been shown to re tain, for the low tem per a ture zone, the same qual ita tive fea tures ob served in in ert en vi ron ments [12], fol lowed by com bus tion of the solid res i due.
Con se quently, it has been pointed out that a multi-step re ac tion mech a nism is needed, which should at least in clude a devolatilization and a com bus tion step.The most re cent re sults [6], ob tained with the com bined use of in te gral (TG) and dif fer en tial (DTG) data, in di cate that four re ac tions are re quired to take into ac count the pro cess de tails.As for char, de spite the widely used one-step re ac tion, DTG mea sure ments also show [10,11] that com bus tion is pre ceded by a devolatilization stage.Hence, a two-step re ac tion mech a nism should at least be used.
This work ex am ines sev eral is sues in the ki netic mod el ing of wood and char com bus tion not in ves ti gated in pre vi ous lit er a ture.It is not clear whether a par al lel-or a se ries-re ac tion mech a nism should be pre ferred and how ki netic con stants, re ac tion or ders and stoichiometric co ef fi cients vary from one as sump tion to an other.More over, the appli ca bil ity is not known of the ki net ics for the char com bus tion step, as de ter mined from the thermogravimetric anal y sis of wood, for chars pro duced from prac ti cal sys tems of bio mass py rol y sis.

Material
Thermogravimetric tests are re-ex am ined [6,11] of beech wood (Fagus sylvatica) and chars ob tained from beech py rol y sis at a lab o ra tory scale.The chem i cal com po si tion of beech wood [13] com prises 20% lignin, 78% holocellulose and 2% extract ives.Chars were pro duced from py rol y sis of thick (40 mm di am e ter) wood cyl in ders radiatively heated along the lat eral sur face.Re sults con cern ing tem per a ture dy nam ics, con ver sion times and prod uct yields were al ready pre sented else where [13,14].Con ditions cor re spond ing to an ex ter nal heat flux of 49 kW/m 2 with a steady py rol y sis tem per ature of 800 K and char yields equal to 24% of the ini tial dry mass of wood are ex am ined here.The el e men tal anal y sis of chars pro duced in this way re ports the fol low ing con tents: car bon 76.4%, hy dro gen 3.4%, and ni tro gen 0.16%.
Prior to thermogravimetric tests, both wood and char sam ples were milled to pow der (par ti cle sizes be low 80 µm) and pre-dried for 10 h at 373 K.

Method
The thermogravimetric sys tem has al ready been pre sented else where [15,16] and only the main char ac ter is tics are sum ma rized here.It con sists of a fur nace, a quartz re ac tor, a PID con trol ler, a gas feed ing sys tem, an ac qui si tion data set, and a pre ci sion bal ance.The fur nace is a ra di ant cham ber, which cre ates a uni formly heated zone, where a quartz re ac tor is lo cated.
The sam ple is ex posed to ther mal ra di a tion by means of a stain less steel mesh screen, whose sides are wrapped on two stain less steel rods con nected to a pre ci sion (0.1 mg) bal ance, which al lows the weight of the sam ple to be continously re corded.A gas flow (nomi nal ve loc ity of 0.5•10 -2 m/s for the tests dis cussed in this study) es tab lishes the proper re action en vi ron ment and re duces the res i dence time of va pors in side the re ac tor.
Solid con ver sion is made to oc cur un der known ther mal con di tions by means of feed back con trol of the sam ple tem per a ture (mea sured by a close-cou pled thin ther mocou ple), us ing the in ten sity of the ap plied ra di a tive heat flux as the ad just able vari able.The char ac ter is tic size of the pro cess is the thick ness of the sam ple layer.
For wood, it was ob served that sam ple thick nesses up to 120 mm al lowed a good tem per a ture con trol, given max i mum heat ing rates of 40 K/min.and a fi nal tem per a ture of 873 K. Also, the weight loss curve was the same as the wood layer thick ness was decreased be low 120 mm, in di cat ing that spa tial tem per a ture gra di ents were neg li gi ble and ox y gen dif fu sion was not the lim it ing pro cess.Hence, the tests were made for sam ple layers about 110 µm thick (5 mg dis trib uted over a sur face 25 ´5 mm 2 ) with heat ing rates of 5, 10, 20, and 40 K/min for a fi nal tem per a ture of 873 K.
For char, it was ob served that sam ple layer thick nesses up to 120 µm al lowed a good tem per a ture con trol, given max i mum heat ing rates of 15 K/min.and a fi nal tem pera ture of 873 K. Also, the weight loss curve was the same as the char layer thick ness was de creased be low 120 µm, in di cat ing that a ki netic con trol was es tab lished.Hence, the tests were made for sam ple lay ers about 110 µm thick (3.5 mg dis trib uted over a sur face 25 ´5 mm 2 ) with heat ing rates of 5, 10, and 15 K/min.for a fi nal tem per a ture of 873 K.

Kinetic mechanisms of wood combustion
As found in pre vi ous stud ies [6], deg ra da tion char ac ter is tics of wood in air are qual i ta tively sim i lar to those al ready ob served in ni tro gen.Once devolatilization be gins, a more or less pro nounced pla teau ap pears, usu ally as so ci ated with hemicellulose deg rada tion.The nar row range of tem per a tures where cel lu lose de com po si tion oc curs and the high amounts of volatiles gen er ated are re spon si ble for the at tain ment of the max i mum fol lowed by a rapid de cay.A com par i son be tween curves ob tained in air and in ert at mosphere, for slow heat ing rates, shows that the hemicellulose shoul der and the cel lu lose peak are an tic i pated by about 15 K and 25-35 K, re spec tively (also, cel lu lose peaks are about 1.5 times higher).In the ab sence of ox y gen, the peak rate is fol lowed by a wide region of very low val ues, es sen tially as a re sult of lignin de com po si tion [12].In the presence of ox y gen, given the rel a tively high tem per a tures, it is plau si ble that the ac tiv ity of the com bus tion re ac tions is al ready im por tant.
Then, com bus tion leads to the com plete con ver sion of the charred solid.The kinetic mod els are writ ten us ing lumped spe cies mass frac tions de fined in terms of the initial wood mass on ash free ba sis.The first model is the same pro posed by [6] and con sists of four se ries re ac tions: where A s is the virgin solid, B s , C s , and D s charred residues, V 1 , V 2 , V 3 , and V 4 the lumped species representative of volatile species, a, b, g, and d the amount of volatile species produced.
The sec ond model con sists of four par al lel re ac tions: where A v , B v , C v , and D v are the volatile groups, whose initial values are expressed as fractions of the initial wood mass and indicated as a, b, g, and d, and V 1 , V 2 , V 3 , and V 4 the lumped volatile species generated.
From the chem i cal point of view, the first two re ac tions can be as so ci ated mainly with hemicellulose and cel lu lose deg ra da tion, re spec tively.The third re ac tion is rep re sen ta tive of the fi nal part of the devolatilization pro cess (lignin de com po si tion) and the be gin ning of char com bus tion.The fourth re ac tion de scribes char com bus tion.
The rates of re ac tions (a1-a3) and (b1-b3) pres ent the usual Arrhenius de pendence (A pre-ex po nen tial fac tor and E ac ti va tion en ergy) on tem per a ture and are pro portional to the mass frac tions of re ac tants (ei ther in the solid or the gas/va por phase): For the char com bus tion rate, the rate of solid dis ap pear ance is gen er ally re lated to the par tial pres sure of ox y gen through an em pir i cal ex po nent and the pore sur face area avail able through the re ac tion vol ume.Given the rel a tively high air flow rate em ployed in the tests, it can as sumed that the ox y gen mass frac tion re mains con stant dur ing the reac tion pro cess.Con se quently, its con tri bu tion is in cor po rated in the pre-ex po nen tial factor.Also, a sim ple power law (n) ex pres sion of the solid mass frac tion [9] is ap plied to describe the evo lu tion of the pore sur face area dur ing the pro cess: The two mod els use twelve pa ram e ters: the ac ti va tion en er gies (E 1 , E 2 , E 3 , E 4 ), the pre-ex po nen tial fac tors (A 1 , A 2 , A 3 , A 4 ), the ex po nent n, and the vol a tile frac tions (indi cated in the fol low ing as stoichiometric co ef fi cients) (a, b, and g.).The fourth frac tion, d, is ob tained from the con ser va tion of the to tal mass:

Kinetic mechanisms of char combustion
Thermogravimetric curves of wood char show [11] a low-tem per a ture shoul der fol lowed by a peak which can be as so ci ated with devolatilization and com bus tion, respec tively.It has been shown [11] that a two-step re ac tion mech a nism pro vides ac cu rate de scrip tions of both in te gral and dif fer en tial curves of weight loss.Thus a two-step model is used here, again us ing lumped spe cies mass fractions defined in relation to the initial char mass on ash free basis.A series-reaction mechanism is considered first: where A s is the char, B s the devolatilized char, V 1 and V 2 lumped species representative of volatile species, e and f the amounts of volatile species generated.The sec ond [11] is a par al lel-re ac tion mech a nism: where A v and B v are two volatile groups, whose initial values are expressed as fractions of the initial char mass and indicated as e and f, V 1 and V 2 the lumped volatile species generated.
The rates of re ac tions (c1, d1) are as sumed to pres ent the usual Arrhenius depend ence on tem per a ture and to be pro por tional to the mass frac tion of com po nent A s or Sim i lar to wood, for the char com bus tion rate, a power law de pend ence on the mass frac tion of the re ac tant is as sumed: The two mod els use six pa ram e ters: the ac ti va tion en er gies (E 1 , E 2 ), the pre-expo nen tial fac tors (A 1 , A 2 ), the ex po nent n, and the vol a tile frac tion (in di cated in the follow ing as stoichiometric co ef fi cient) (e).The sec ond frac tion, f, is ob tained from the con ser va tion of the to tal mass: e + f =1.

Numerical method
Given the abil ity to de scribe both hard wood and soft wood de com po si tion in air for dif fer ent heat ing rates, the ac ti va tion en er gies, the pre-ex po nen tial fac tors and the expo nent n have been taken equal to those es ti mated in [6] (se ries re ac tions) for both models of wood com bus tion.The same pro ce dure is ap plied for the ki netic mod el ing of char com bus tion.That is, ac ti va tion en er gies, pre-ex po nen tial fac tors and ex po nent n have been taken equal to those es ti mated in [11] (par al lel re ac tions) for both mod els of char com bus tion.
The un known pa ram e ters (stoichiometric co ef fi cients) are es ti mated through the nu mer i cal so lu tion (im plicit Eu ler method) of the mass con ser va tion equa tions and the as so ci ated ini tial con di tions (the tem per a ture is a known func tion of time) and the ap plica tion of a di rect method for the minimization of the ob jec tive func tions, which con sider both TG and DTG data.The de tails of the method have been al ready de scribed by [16].
The fit be tween mea sured and cal cu lated curves is de fined as: where i represents the experimental (exp) or the simulated (sim) variable (y is the solid mass fraction, Y, or the devolatilization rate, -dY/dt) at the time t (N is the number of experimental points and the subscript peak indicates the maximum value).

Results
The re sults pro duced by the par al lel-and the se ries-re ac tion mech a nism for wood and char are dis cussed first.Then, a com par i son is made for the two ma te ri als ex am ined.

Wood combustion
The re sults of the ki netic anal y sis are sum ma rized in tab. 1. Good agree ment is ob tained be tween mea sure ments and pre dic tions, as shown in fig. 1 for the solid mass frac tions as func tions of time and fig. 2 for the devolatilization rates as func tions of the tem per a ture.The ac cu racy of the pre dic tions is slightly higher for the se ries re ac tions, as re ported by the fit be tween mea sured and cal cu lated curves (tab.1).The abil ity to take into ac count the dy nam ics of dif fer ent re ac tion net works by sim ply vary ing the stoichiometric co ef fi cients in di cate that the dif fer ences in the two cases are not ex ceedingly high.The high est amounts of volatiles are al ways re leased dur ing the first two re action stages (devolatilization of hemicellulose and cel lu lose com po nents).As the heat ing rate is in creased, the vol a tile amounts re leased dur ing the first stage be come suc ces sively higher and those in the sec ond stage lower.More over, for the se ries re ac tion mech a nism, the amounts of volatiles pro duced from hemicellulose de com po si tion are slightly higher   than those gen er ated from cel lu lose.The con trary oc curs for the par al lel re ac tion mech anism.The dif fer ences be tween the other two re ac tion stages are also rel a tively small, though the par al lel re ac tion model gives rise to barely higher amounts of char combusted in the fourth step.These re sults con firm that a large part of volatiles is re leased at rel atively low tem per a tures (amounts com prised be tween 72-75%) when het er o ge neous reac tions are not yet sig nif i cantly ac tive.
Ex am ples of the time his tory of the mass frac tions and the devolatilization rates of the re ac tants are shown in figs.3a and 3b for a heat ing rate of 5 K/min.and figs.4a and 4b for a heat ing rate of 40 K/min.For a mean ing ful com par i son be tween the mass fractions (figs.3a, 4a) it should be kept in mind that re ac tants re tain the en tire amount of volatiles re leased in se quence in the se ries re ac tion mech a nism.On the other hand, in the case of the par al lel re ac tion mech a nism, the volatiles are al ready lumped into four dif ferent groups.There fore, only the A com po nents pres ent dy nam ics qual i ta tively sim i lar, though the ac tual val ues are highly dif fer ent in the two cases.The com par i son in terms of devolatilization rates (figs.3b, 4b) is straight for ward.A sig nif i cant over lap, en hanced by high heat ing rates, be tween the times of vol a tile for ma tion ex ists, in de pend ently of the ki netic model.Also, the dif fer ences be tween the two mod els are small but slightly increas ing with the heat ing rate.

Char combustion
The re sults of the ki netic anal y sis for the weight loss curves of char com bus tion are sum ma rized in tab. 2 for the two mod els, whereas figs.5 and 6 pres ent a com par i son be tween pre dicted and mea sured curves (mass frac tions and devolatilization rates as func tions of time).The agree ment be tween mea sure ments and pre dic tions is very good in all cases, as con firmed by the val ues of the fit pa ram e ters re ported in tab. 2. The amounts of volatiles re leased dur ing the first re ac tion stage al ways de crease as the heat ing rate is in creased, but they are slightly lower in the case of par al lel re ac tions.In quan ti ta tive Ta ble 2. Ac ti va tion en er gies, pre-ex po nen tial fac tors, re ac tion or der (n), stoichiometric co ef fi cients and de vi a tions for in te gral (TG) and dif fer en tial (DTG) curves for char com bus tion, as es ti mated by the se ries-and parallel-reaction models  terms, the ef fects of the devolatilization re ac tions are rel a tively small, as they ac count only for about 15.5-18.5% of volatiles evolved.This find ing mo ti vate the as sump tion, often made in pre vi ous mod els, of a one-step global re ac tion for the de scrip tion of the en tire weight loss curve.How ever, as ex ten sively dis cussed by [11], the in clu sion of a devolatilization step is nec es sary for a cor rect eval u a tion of the ki netic pa ram e ters for the sec ond step ac tu ally de scrib ing the het er o ge neous com bus tion of char.In deed, the ac tiva tion en ergy var ies from about 114 (one-step re ac tion) to 183 kJ/mol (two-step re actions).In this way, in the en gi neer ing prac tice, such data can be safely used.
Ex am ples of the pro cess dy nam ics for slow (5 K/min.) and fast (15 K/min.)heat ing rates are shown in figs.7a and 7b, and figs.8a and 8b, re spec tively.Apart from the ob vi ous con sid er ation con cern ing the dif fer ent na ture of the re ac tants for the par al leland se ries-re ac tion mod els, it can be noted that the over lap be tween the devolatilization and com bus tion zone is prac ti cally un af fected and the change in the heat ing rate does not play a rel e vant role in this mat ter.Com pared with wood, the dif fer ences be tween the series-and the par al lel-re ac tion model are even lower.
A com par i son can also be made be tween the ki netic pa ram e ters of the two-step mech a nisms ap plied for char com bus tion (tab.2) and the last two re ac tions of the four-step mech a nism pro posed for wood (tab.1).The ac ti va tion en er gies are the same and it can be con cluded that the dif fer ent re ac tiv ity of char (caused by dif fer ent heat ing rates and tem per a tures ex pe ri enced by wood dur ing py rol y sis) can be well de scribed by a si mul ta neous vari a tion in the ex po nent n and pre-ex po nen tial fac tors.How ever, it should also be noted that, for both sets of ex per i ments, the ther mal con di tions of char for ma tion are those typ i cally en coun tered in con ven tional py rol y sis.There fore fur ther study is needed to de ter mine the mod i fi ca tions in the ki netic pa ram e ters needed to de scribe the be hav ior of chars gen er ated from fast py rol y sis.

Con clu sions
Weight loss curves of beech wood and chars, ob tained from con ven tional py roly sis of beech wood, have been re-ex am ined to eval u ate the ap pli ca bil ity of multi-step mech a nisms based on ei ther par al lel-or se ries-rection mech a nisms.
A four-step mech a nism is shown to de scribe with a good ac cu racy the dy nam ics of the ox i da tive de com po si tion of wood.Ac ti va tion en er gies, pre-ex po nen tial fac tors and re ac tion or der of the com bus tion rate for char ap pear to be in vari ant with the heat ing rate and the se lec tion of se ries or par al lel re ac tions.More over, rel a tively small vari a tions on the stoichiometric co ef fi cients are re quired to take into ac count the dif fer ent struc ture of the re ac tion net work.
A two-step re ac tion mech a nism de scribes with a good ac cu racy the thermogravimetric curves of both mass loss and rate of mass loss in air of con ven tional py rol y sis chars.Again, ac ti va tion en er gies, pre-ex po nen tial fac tors and re ac tion or der do not de pend on the heat ing rate and the ap pli ca tion of se ries or par al lel re ac tions.The varia tions in the stoichiometric co ef fi cients be tween the two mod els are even lower than those com puted for wood.Fi nally, ad just ments in the pre-ex po nen tial fac tors and re action or der are suf fi cient for tak ing into ac count the dif fer ent char re ac tiv i ties orig i nated from the py rol y sis con di tions.

No men cla ture
A -pre-ex po nen tial fac tor, [s -1 ] A i -re ac tant B i -re ac tant C i -re ac tant D i -re ac tant E -ac ti va tion en ergy, [kJ/mol] h -heat ing rate, [K/min.]n -re ac tion or der N -num ber of ex per i men tal points R i -rate of reaction t -time,

Figure 1 .
Figure 1.Solid mass fraction for beech wood as measured (symbols) and predicted (lines) for heating rates between 5-40 K/min.

Figure 2 .
Figure 2. Devolatilization rate for beech wood as measured (symbols) and predicted (lines) for heating rates between 5-40 K/min.

Fig ure 3 .Fig ure 4 .
Fig ure 3. Mass frac tion (a) and devolatilization rates (b) of re ac tants (beech wood) as pre dicted for a heat ing rate of 5 K/min.Fig ure 4. Mass frac tion (a) and devolatilization rates (b) of re ac tants (beech wood) as pre dicted for a heat ing rate of 40 K/min.

Fig ure 5 .Fig ure 6 .
Fig ure 5. Mass frac tions of con ven tional py rol y sis chars ver sus time for heat ing rates of 5-15 K/min.as mea sured (sym bols) and pre dicted (lines)

Fig ure 7 .Fig ure 8 .
Fig ure 7. Mass frac tion (a) and devolatization rates (b) of re ac tants (con ventional py rol y sis char) pre dicted for a heat ing rate of 5 K/min.
[s] T -tem per a ture, [K] V i -lumped vol a tile spe cies Y i -mass frac tion of re ac tant Greek letters a -stochiometric co ef fi cient b -stochiometric co ef fi cient g -stochiometric co ef fi cient d -stochiometric co ef fi cient e -stochiometric co ef fi cient f -stochiometric co ef fi cient y -solid mass frac tion or devolatilization rate Sub scripts DTG -dif fer en tial curves s -solid phase TG -in te gral curves v -gas/va por phase