belkacemi etal 1991

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2416 Ind. Eng. Chem. Res.1991,30, 2416-2425

temperature. This can be attributedto the loss of vo lat ilewith increasing temperature.

4. Effect of Impregnation Ratio and Reagent onYield. From Figure 12, one can observe that yield in-creases with impregnation ratio. However, this increasein yield is marginal beyond an im pregnation ra tio of25%.Th is is true for both reagents studied an d holds good forboth fluidized bed and static bed processes.

5. Effect of Gas Medium on Yield. Th e influence ofthe gas medium (nitrogen,air, and carbon dioxide) on yield

is shownin Figure13. It can be clearly seenthat the staticbed process gives a higher yield. Use of nitrogen an dcarbon dioxide results in a b etter yield compared to air a sth e medium. Phosphoric acid gives a slightly better yieldtha n ZnC12, when nitrogen an d carbon dioxide are em-ployed.

When air is used as he m edium, H3 P0 4 ives a low yieldcompared to ZnC1,. Th is may be due to the comb ustionreactions, which are more pronounced with H3 P0 4 ecauseof its lower temp erature stability (boiling point213 OC).

From the experimental data it may be concluded tha t airis unsuitableas he medium of activation since it gives lowactivation and also low yield compared to nitrogen andcarbon dioxide.

Conclusions

On the basis of the experimental study carried out, itc n be concludedthat the fluidizedbed process gives bette ractivation (high adsorption capacity of carbon) in less timeand at a lower temperature compared to th e static bedprocess. High activation and greater yield areboth possiblewith nitrogen a nd carbon dioxide compared to air as th emedium of activation.

Under the ex perimental conditions investigated for thechemical activation of coconut shells in the fluidized bed,a process time of2 h, a temperature of around500 Cwithzinc chlorideas he activating agent, and an im pregnationratio of 25% in the presence of nitrogen or carbon dioxide

may be taken as optimal parameters.

Nomenclature

= temperature,O C

t = time, minAbbreviationsI.R. = impregnation ratioMED = mediumof activationR = reagent for activation

37-9; Oz, 124-38-9; arbon,7440-44-0.Literature CitedEdwards,G. D.; Robert,Y.; Joseph T.; Loveday,P. E.; Williams,F.

D. Steam Activationof Charcoal: A systematicstudy of weightand volume losses. Proceedingsof the Fifth Carbon Conference;Pergamon Press: New York, 1963; Vol. 2, pp 265-285.

Hassler, J. W. Activated Carbon;Chemical: New York, 1977; p171-177.

Kirubakaran,C. J. Studies on ActivatedCarbonProductionfromCoconutshellsUsing a FluidizedBed Reactor. M.S.Thesis In-dian Institute of Technology,Madras,1990.

Kunii, D.; Levenspiel,0. FluidizationEngineering;Wiley: NewYork, 1969 pp 8-11.

Mantell,C. L. Carbonand Graphite Handbook; Interscience:NewYork, 1977; p 181-184.

Ruiz, Bevia, F.; Prats Rico, D.; MarcillaGomis,A. F. Activated

CarbonfromAlmond Shells.Chemical Activation.1. ActivatingReagent Selectionand Variables Influence. Znd. Eng. Chem.Prod. Res. Dev. 1984a, 23, 66-269.

Ruiz Bevia, F.; Prats Rico, D.; MarcillaGomis,A. F. ActivatedCarbon from Almond Shells. ChemicalActivation. 2. ZnC12ActivationTemperature Influence. Znd. Eng.Chem. Prod. Res.Dev. 1984b, 23, 269-271.

Snell, F. D., Ettre,L. S., Eds. Encyclopedia ofzndustrialChemicalAnalysis; Interscience: New York 1973; Vol. 17, pp 28-32.

Vogel, A. I. Text Book of Qua ntitativ e InorganicAnalysis,4th ed.;ELBS and Longman: London,1978; pp 370-379.

Wagner, N. J.; Jula, R. J. Activated Carbon Adsorption. InActi-vated CarbonAdsorption forWaste Water Treatment; Perrich,J. R., Ed.; CRC Press: London, 1981; Chapter 3.

Receivedfor reviewDecember6, 990Revisedmanuscript received May29,1991

Accepted June 20,1991

= average particle diameter, mm

Registry No. ZnC12,7646-85-7; 3PO4,7664-38-2; z, 727-

Phenomenological Kinetics of Complex Systems: MechanisticConsiderations in the Solubilization of Hemicelluloses followingAqueous/Steam Treatments

K. Belkacemi,? N. Abatzoglou,t R. P. Overend,+? nd E. Chornet*t+Departementde genie chimique, UnioersitBde Sherbrooke,Sherbrooke,Quebec,J l K 2 R1 , Canada,andDivisionof Biosciences,National Research Council of Canada, Ottawa, Ontario,K 1 A OR6, Canada

T he solubilization ofhemicelluloses from a lignocellulosic matrix is generally de scribed b y tw o parallel

fint-o rder reactions. Inths

paper we developa phenomenological descriptionthat relatesthe kineticparam eters associated w ith the hydrolysis of the glucosidic bon d t o linear free energy correlationof the Lefflertype. Sucha description has resulted in th e c orrect prediction of the acid hydrolysiskinetics ofa num ber of substrate s including th e publisheddata on Populus tremuloides and Betulapapyr i fe ra an d our own work on corn stalks an dStipa tenacissima. Th e key advan tage of ourapproach is tha t i t faci l i tates the obtention of kinet ic da ta for a given substrate with fewer experimental po ints than frequently used in isothermal experiments .

be modeled by combining the three main operationalvariables (i.e., residence time, temperature,and acid con-centration) within a single reaction coordina te, namedROH,which describes the severity of the thermochemicaltreatment. Theus of ROH eads to the derivation of threeparameters: th e energy-related parametersw and y havebeen interpretedas ndicators of the nonhomogeneity of

IntroductionIn a previous work, Abatzoglou et al.(1991), e have

shown th at th e kineticsof hemicellulose solubilization can

*Author to whom correspondenceshouldbe addressed.

t National Research Council of Canada.Universit6 deSherbrooke.

0888-5885/91/2630-2416$02.50/0 1991 American ChemicalSociety



Ind. Eng. Chem. Res., Vol.30, No. 11, 1991 2417

th e biomass substrates studied, while the param eterX islinkedto the catalytic role of th e acid.In the present paperwe develop alink between the reaction coordinateROH ndthe thermodynamic parameters (i.e., activation energy andentropy) that characterize the hydrolytically inducedglucosidic bond splitting.

The so-called prehydrolysis of lignocellulosic materialsleadingto th e hemicellulose solubilization will be th e focusof our analysis. In this type of trea tm ent the biomassundergoes significant structural and chemical changes,under appr opria te combinations of temperature, acidconcentration, an d reaction time,as described by Roudieran d Eberh ard (1967) and Casebier et al. (1969).

The polymeric carbohydrates treated with acids inaqueous media participate a t least in two distinct reactions:hydrolysis of th e glucosidic bonds; dehyd rations, as re-ported by Fe ather a nd Harris (1973). Th e mechanism ofthe hydrolysis and the reaction rates of both poly-saccharides and oligosaccharides have been extensivelystud ied (Capo n, 1967; Casebier e t al., 1969; Defaye, 1981;Harris, 1975). T he concept of the conformational mech-anism is generally accepted. Although there is some un-certainty on whether th e proton H + attacks th e oxygeninthe ring or the glucosidic bond preferentially, the con-formational mechanism remains the most accepted ex-plana tion of the hom ogeneous hydrolysis of glucosides inthe aqueous phase.

Wayman (1980,1983) reviewed the main reactions tak-ing place during the hemicellulose hydrolysis and studiedtheir kinetics. Since then a limited number of works havebeen published, proposing kinetic models for the hydrolysisof hemicelluloses. Maloney et al. (1984), Conner e t al.(19851, and Ha rris e tal. (1985) showed tha t the hemi-celluloses are solubilized following first-order kinetics a ndclaimed the existence of two distinct profiles of solubili-zation dueto th e coexistence of reactively different hem-icellulosic compon ents. On the other hand , Carrasco etal. (1987) claimed th at a single kinetic law is sufficient todescribe the same reaction system.

None of the se kinetic models has, however, been linkedto th e basic conforma tional mechanism. The reasonis thatthe mathematical calculations of the kinetic parametersof the overall reaction via optimization methods lead toresults lacking precise physical meaning. Th e termpseudokinetics is the n usedas in th e case of th e cellulosehydrolysis to signify a phenomenological approach. Th eobvious lack of a m odel linking classical thermodynamicconcepts, reaction mechanisms, and the kinetics of thecomplex carbohydrate solubilization ledus to the presentwork, which is based on th e severity factor concepts de-veloped by our g roup (Abatzoglou et al., 1991).

Hydrolysis of Lignocellulosic Materials:Rsactions and Mechanisms

Th e solubilization of hemicellulose is depen dent on bo ththe acid concentration of the aqueous medium and t hena ture of th e hemicellulosic material. Th e salient con-trolling parame ters according to Harris (1975), Defaye(19811, an d Fengel and Wegener (1984) are the acid type,th e concentrations, th e acid strength, th e temperature an dpressure, the phase in which the reaction takes place, thephysicochemical structure and the accessibility of thereactants, if the reaction is heterogeneous, the conforma-tion effects, and the electronic effects due to the chainsstructu re and their substitutes.

The process of f ragmenta t ion (a par t ia l de-polymerization)to yield soluble glucosides takes place bymeans of scission of th e glucosidic bonds (C-0-C). Twomechanism s are possible: (a) protona tion of the C-0-C

a . Hydrolysisvis the cyclic arbonium -oxonium on

HHPHCH,OH

H OH

H

b . ydrolysisvia the acyclic carbonium on

Figure 1. Mechanisms involved in scissionof glucosidicC-O-Cbonds.

glucosidic bond followed by form ation of a cyclic carbanionand the elimination of the aglycon part through scissionof the corresponding bond; (b) protonation of the anomericoxygen taking p art in th e glucosidic ring followed by anopening of the latter and formation of an acyclic carbanioncomplex. These two mechanisms are described in Figure

1. Th e most probable caseis th at both oxygen atoms areprotonated with the position of the scission dependingupon th e distribution of th e electronic density on the in-termediate carbanion (Harris, 1975).

It is generally adm itted th at in homogeneous reactionsthe mechanism through th e cyclic carbanion is the mostprobable (Capon, 1967). How ever, the ste p involving th ecyclic complex formation requires a n im portant modifi-cation of the conformation of the molecule whose activa-tion energy depends on the steric and electronic hindrancesencountered (Fengel and Wegener, 1984); in fact t heman datory half-chair conformation of th e cyclic car-banion is obtained through a slight rotation of the ringconstitutive (pendant) groups; thus the energy requiredfor this step depends on the steric and electronic inter-effects of the la tter a nd is likelyto be difficult in t he solidstate.

In t he case of a n heterogeneous reaction (i.e., th e acid-catalyzed depolymerization of the hemicellulosic poly-saccharides) the reaction m echanisms described above a restill likelyto be valid bu t the measured rateof the 243-42bonds cleavageis generally lower.Ross and Jurasek (1978)and Fengel and Wegener (1984) have proposedthat limitedaccessibility of th e oxygen atom s of th e C-0-C bonds isthe main reason; however, no means have beenso farproposedto satisfactorily quan tify these effects. Given thecomplexity of the overall reaction and theunknown natureof some of th e elementary steps taking place in the reac-tion, th e only positive wayto monitor the phenomenonisto follow the r ate of the polymer disappearance from th e



2418 Ind. Eng. Chem. Res., Vol.30, No. 11, 1991

solid phase (its solubilization in th e aqueous phase).

Kinetics of the Solubilization of theHemicelluloses

Veeraraghavan et al. (1982), Maloney et al. (19841,Conner et al. (1985), an d H arris et al. (1985) have showntha t the qua ntity of xylans remaining in the fibers fol-lowing th e prehydrolysis of lignocellulosic ma terial a sfunction of the tr eat me nt time follows two distinct solu-bilization profiles: an initial rapid solubilization process

an d a subsequent slow step. Both profiles are well fittedby first-order kinetics.Simmonds e t al. (1955), Kobayashi and Sakai (1956),

Springer et al. (1963), Brasch an d Free (19651, Springer(1966), Springer and Zoch (1968), Planes et al. (1981),Harris et al. (1985), Veeraraghavan (1982), Tri ck ett an dNeytzell de W ilde (1982a), Conner (1984), Maloney e tal.(1984), and Conner e t al. (1985) have estimate d th roughtheir experimental results th e pseudo-first-order reactionrate constantsk related t o both rapid an d slow solubili-zation steps for a variety of biomasses including wood,bagasse, an d annual p lants (Trick ett an d Neytzell deWilde, 1982b; Dutoit e t al., 1983). T he experimental d atagenerated by our work (to be described later) show thatth e hydrolysis of cornstalks and Sti pa tenacissima followsthe same pattern (two distinct solubilization profiles).

On th e basis of structu ral considerations as well as th eexperimen tal observations we can form ulate the followingset of assumptions which are th e basis for th e modelingapproach:

1. Th e mechanisms reported in the literature for thehomogeneous acid-catalyzed hydrolysis of th e glucosidicbonds are valid for the heterogeneous depolymerizationof the labile hemicellulosic polysaccharides present inlignocellulosics; however, we m ust consider th at th e ac-cessibility of the oxygen atoms of the different C-O-Cbonds present in th e macromolecules is not uniform, thusleading to reaction rates th at may vary with th e exten t ofthe overall solubilization. It is necessary to point o ut th at

when introducing the hypothesis of varying accessibilities,we do not consider the proton diffusion rates in thepolymeric matrix a s being a limiting step; the small sizeof th e hydrogen proton , the high a ctivation energies foracid hydrolysis reported in t he literature (higher tha n 126kJ/m ol), as well as th e reduced particle size of th e biom-asses used (<0.5 mm) and the relatively high tem peraturelevels of these treatments are such th at t he proton diffu-sion mechanism is much faster than the other chemicalsteps taking placein the reaction environment. Therefore,th e reaction kinetics will be consideredas governing thesolubilization process. Th is assumption is confirmed bythe work of Singh e t al. (1984), who reported no effect onhydrolysis for particles smaller than0.5 mm.

2. There are many hemicellulosic families; however, they

behave as two major groups. Th e existence of these twoforms leads to two distinct depolymerization profiles.3. Th e solubilization reaction for both hemicellulosic

groups follows an apparent first-order rate with respectto t he hemicelluloses remaining in th e solid (fiber) phase.Nonetheless, in all works published in the literature,aswell as in our experiments, th e monitored variable is th emass remaining and not the molar concentrationas clas-sical kinetics require.

4. Th e solubilization reactions arealso first order withrespect to the activity of the hydrogen proton in theaqueous phase. Since th e acidic solutionsused are diluted(less than 1% in the aqueous phase), we can assume th atth e hydrogen proton activity is equivalent to its concen-tration.

Le t us use th e following nomenclature:x , the fractionof initial hemicelluloses remaining in the fiber after a givenreaction time;xfl, th e initial fraction of the readily solu-bilizable hemicelluloses(this is a fmed quantity, depend ingonly upon the nature of the sub strate);x,, the fraction ofth e readily solubilizable hemicelluloses remaining in th efiber after a given reaction time;x B o ,he initial fraction ofth e hem icelluloses resistant to solubilization (also a fixedquantity, depend ing only upon the na ture of the substrate);and x, , the fraction of the hemicelluloses resistant to

solubilization a fter a given reaction time;x , = 1 - x,.The kinetic expressions are

Th e analytical solution of(1) and (2) givesX = X f i eXP[-k$~+t]+ (1 - X, eXp[-k,C~+t] (3)

Justification of the Kinetics Proposed for theAcid-Catalyzed Hydrolysis of the Glucosidic Bond

Th e elementary stepsto be considered are the following:1. equilibrium between t he polymer an d th e hydrogen

protonk

polymer + H+ & olymer-.H+k-1

(fast)

2. formation of th e cyclic carbanion

polymer.-H+- yclic carbanion complex+

3. formation of th e hydrolysis products

cyclic carbanion complex+ H 2 0==

k

aglycon (or saccharide) (slow)

ka

k-a

products + H t (fast)

Th e formation of the c arbanion is, accordingto the liter-ature , the slowest and consequently the rate-controllingste p of the process. Th e other two steps are essentiallyin equilibrium state.

Th is leads to th e following expression:

kl[polymer,] [H+ ]= k-l[polymer,.-H+] (4)

rr = k,[polymer,-H+] (5 )

rr = (klk2/k-l)[~olymer,lH+I (6)

Combining (4) and(5) ives

If we let

k , = k lkz /k - lthen

r , = kr[POlymer,l [H +l 7)

Th e expressions for the s-type hemicelluloses are analoguesto the previous ones. Th us

r, = ks[polymer,l [H+ l (8)

where[polymer,] = x ,

[polymer,] = x ,

[H+]= CH+



Ind. Eng. Chem. Res., Vol. 30,No. 11,1991 2419

Equations 7 and 8 are respectively(1) and (2) used in thepreceding section to model th e kinetics of solubilization.

Experimental Proof for the Existence of TwoForms of Hemicelluloses

Dutoit etal. (1984) have developed an experimentalmethod to extract in 24 h t he hemicelluloses contained inbagasse using a 4% w/v aqueous solution of NaOH. Oncethe final hemicellulose-rich liquid phase separated fromth e lignin-cellulose-rich solid, they proceeded to a seriesof precipitations from the filtrate using acetic acid andabsolute alcoholto obta in two types of precipita tes whichwere associated with the two different forms of hemi-celluloses.

In th e case of bagasse Dutoit e tal. (1984) obtained th efollowing results on a basis of 100 g of oven-dry biomass:17.75 g of typeA hemicelluloses (or 55.29% of the initialhemicelluloses) an d 14.35 gof type B hemicelluloses (or44.719% of th e initial hemicelluloses). T he hem icellulosesof type A correspond to the readily solubilized hemi-celluloses while those of ty peB correspond t o t he slowlysolubilized ones.To verify the claims of thi s method, wehave experimentally proceededto its application to thecase of the corn stalks and the results obtained areasfollows: 20.9 g of shredded oven-dry cornstalk yields 4.53g of typ e A hemicelluloses (or 74.18% of the initia l hem-icelluloses) and 1.58 g of typ eB hemicelluloses (or 25.82%of th e in itial hemicelluloses).

Moreover,as Dutoit etal. (1984) have show n, these twotypes of hemicellulosesalso show different hydrolysis rates.In fact, they have m easured t he a mo unt of monomericsugars released upon hydrolyzing the two substrates(hemicelluloses A a nd B) for2 h a t T = 96 C nd C H + =5% w/v H2 S04and found t ha t th e ratio of th e pseudo-fmt-ord er rate constants(k,/kJ is equal to 1.84. Subscriptr refers to A-type hemicelluloses while subscripts relatesto B-type hemicelluloses.

Definition of a Severity Factor Based on

Thermodynamic ConsiderationsWhen applying the transition-state theoryto elementary

ste p 2 describing the formation of t he activated carbanioncomplex, we can define the rate expression as

(10)

where # is th e activated complex in equilibrium with theactive center, polymer-H+, which we represent byF.

F2 = vC' = ( k B T / h ) C #

Since

K#eg2 = - exp[ 1 and = k T (11)C F

then

where

AG2,o = W , O TA S 2 , o (13)

The combination of(12) and (13) leads to

r2 = k Tex.[ % ] xp[ F ] C FW , 0 (14)h

Meanwhile, the equilibrium assumption for the elementarystep 1 gives

K, =CF

CpolymerCH+

ex.[- I-1RT

an d comb ination of (14) an d (15) yields

AS1,O + AS2,O

h

where r is the overall reaction rate describing the polymersolubilization.

The overall kinetic rate constantk can thenbe expressedas

1-.'P[B TASl,OR A S 2 P]P[ - ( M 1 , 0RT W , O

h

(17)

Since the activation energy is given by (see also Benson(1976) and Bamford and Tipper (1979))

an d from (17) we can deriveIn ( k ) =

we obtain8 In ( k ) 1 mi o + mz o-- - -

d T T R PWithin the tem perature ranges used one can assume tha t

RT << CHi,o = M I , O m 2 , 0

E = M 1 . 0 + m 2 , o

A S = AS1,o + A S 2 , o

H = M 1 , O + m 2 , o

According to (18)

(19)

(20)

(21)

Let us defineA S and AH as

Th e com bination of (17), (19), (201, an d(21) gives

In general, for organic reactions involvingsimilar transitionstates there appears to be a correlation betweenA S andA H sometimes called a compensation effect. In th e caseof the acid-catalyzed hydrolysis of glucosidic bonds inpolymers having different molecular size an d spatial ar-rangement of the monomer units (e.g., branching anddegree of substitu tion), th e Leffler (1955) relationship canbe assumed to ho ld

= a + BAS (23)wherea and 0 are characteristic constants.@is also knownas th e isokinetic temperature. I t represents a temper-



2420 Ind. Eng. Chem. Res., Vol.30, No. 11,1991

Ta b l e I. Kinet ic Param eters Der ivedfrom Publ i shed DataUsing O u r M o d e lsubstrate k@, s-l kd, s-l E,, J/mol E,, J /mol AS, J/(mol.K) AS, J/(mol.K) reference

birch 6.3313 3.6316 126.5303 156.3303 18.3 70.8 Maloney etal. (1986)red oakC 4.3307 4.6307 84.3 303 95.3303 -99.3 -98.7 Con ner etal. (1985)corn stover 1.3316 2.9323 142.030 3 176.030 3 62.5 202.5 Kim et al. (1987)southern red oakd 1.8309 1. 1E ll 84.3303 127.030 3 -68.3 -34.4 Conner et al. (1985)aspen 2.8312 1.7E16 117.OE03 154 .7303 -7.4 64.8 Grohmann et al. (1986)

Computational Resultstyp e of hemicellulose T h yK a, /mol roome D s-l

r: fast hydro lysis 340.3 120.6E03 0.994 1.8 E 4 6E: slow hydro lysis 262.9 131.1E03 0.964 3.7 3-14

OFrequency factor(8-l). AS In (k&/(kB T))R (J/(mol-ZQ) andT = 330 K. CHyd rolysiswith 5% w/w cetic acid. dAutohydrolysis.

This combined parameter will be used to correlate our

Application to the Solubilization of the

correlation coefficient.f D = (kBTh/h)exp(-a/(RTh)),

ature a t whichall reactions of a given type have th e samerate constant. experimental data.

Equation 23 can be expressed as

(24) HemicellulosesH - C Y E - C YP P

A S = - = -We have seenin the p revious mathem atical development

th at t he ex tent of the reaction of th e acid-catalyzed solu-bilization of th e hemicelluloses in aqueous p hase ca n be

Combining (22) and (26), we derive th e final expressionfor the reaction rate constant as

1R T

expressed by thes u m of t he so lubilization of the two typesof hemicelluloses. Thus

x = ~ f ixp[-k,C~+t]+ (1 - ~ f i ) xp[-k,C~+t](29)and , rearranging If we introd uce in this expression th e factor RB+ we have

Since 6 = Th we can define two new functions asT - Tb,

R T= OPB; (30)

DaT

T b ,k,CH+t= - Xp

D = - h exp[ eTh e experimental data found in th e literature concerning

T E T - T b th e acid hydrolysis of th e hemicelluloses have been usedto derive the different kinetic constants, shown in TableI. Th e application of (25)to both types of hemicellulosesis shown inFigurea 2 and 3, where the experimentalas wellas the optimization results are depicted. Th e severityfactors RB,+ andR , + are

Ti00

andk = D6

Th e overall hydrolysis rat e leading to solubilizationis

-dC,,ymer(26) RB,+= - exp[ , F ] c H + t- Thor (31)

- RB,+= - xp[ (32)

Tiao, R Tiso,

Cpolymer - Cpolymer 0) exp[-DaCH+t] Tiso, RTiso,

d t= kCplm,,CH+ =

If the p rocess is isothermal,T # T(t ), the n integration of(26) leads to T E, T - Tb ,

Hence, the fractionof residual hemicelluloses can beefining RB = at, we have

T E T - T b modeled introducing RB,+ andR B , +

asRB = 6 t = - x[

] t 27)

Tiso RTiso X = X f i exp[-D&~,'] + (1 - Xfi) exp[-D&~,+] (33)

Th e param eter RB allows us to estimate th e severity of agiven process since it is function of the time and tem-perature exposure. By introducing the acid concentration,we can defineR B + as

RB+ = R&H+

Concerning the units of the catalyst concentration t o beused in the kinetic expressions, we have opted for?%(weight of acidfweight of dry biomass). These units rep-resent th e acid loading with respect to t he d ry biomassused. Th is is consistent with the units used by mostworkers. Th e choice of these units renders th e acid con-centration dimensionless and consequently the constantD is expressed ins-l and RB+ n s. In th e case of auto-hydrolysis the acid concentration equals th e inheren tacidity of the substrate associated with the uronic andacetyl groups of th e hemicellulose althoughit is ratherdifficult to define it with accuracy.



Ind. Eng. Chem. Re s., Vol. 30, No. 1, 1991 2421

I 4

lwoooI I I I I

t

I

, Er 1 . 2 W E + 5 340.34'ASrornlation weificienl s 0.995

/

h Q U t

Measurable rcaction extent (x) -. 12 o - 2 0 a o

ASr (Jlmo1.K)Multiple non -linear regression analysis

Optimizations according to

Figure 2. Linearity observed between the activation energy andentropy for rapidly solubilized hemicelluloses.

184ooo

-z1

=a

W

@ooo.200 . l o o 0 1 0 0 2 0 0 3 0 0

ASS(Jlm1.K)

1 . onnu el d. (1985)

2 coma t d. lwa)

3 . rind . (1985)

4- rt d. (1986)

5 - Klmel d. (1887)

Figure 3. Linearity observed between the activation energy andentropy for slowly solubilized hemicelluloses.

To model the hydrolysis of the hemicelluloses, he sim-ulation routine shown in Figure 4 has been followed. Wehave then proceeded to the modeling of the results fromeight different biomasses: 1) corn stalks (our experimental

Measurable ndepeodent variables

Model

Results :Non -measurable parameters'1 : This parameter can also be measured

2) : F.B.G.S :

as explained in the text.

FLETCHER-BROYDEN-GOLDF'ELDTSHANNO

Figure 4. Kinetic modeling routine.

-1 0 ' 1 o s 1 0 ' 1 0 '

( 8 )

0,004 ' ' ~ ' ~ s ' ' ' ' ' ' ' ' -IO

R E * (s)

Figure 5. Modeling of hemicellulose solubilization. Populus t

Springer et al., 1963).

data); 2) red oak Harris et al., 1985); 3) Betula papy -rifera Maloney et al., 1985); 4) Populus tremuloides




Table 11. Simulat ion Resul tsbiomass iter E,, J/mol E,, J/mol Xm A x 0 reference

S t i m t . 1 85.5303 85.5303Pinus r . 1 101.6303 109.9303wheat stalks 2 123.5303 127.8303corn stalks 5 91.7303 109.8303Populus t . 6 149.3303 134.5E03Betula p . 14 117.6E03 129.3303aspen wood 2 126.3303 127.8303red oak 1 118.5303 128.7303

a Ax=

& ( x - x y / N y .

0.849 0.0590.210 0.1560.675 0.1110.698 0.0370.786 0.0560.652 0.0350.712 0.0590.800 0.015

this workBrasch and Free (1964)Grohmann et al. (1986)this workSpringer et al. (1963)Maloney et al. 1984)Grohmann et al. (1986)Harris et al. (1985)

Figure 6. Modeling of hemicellulose solubilization. Betula p .Maloney et al., 1985).

Michx. (Springer e t al., 1 963);(5) inus radiata of NewZealand (Brasch and F ree, 1964); (6) aspen wood (G roh-mann et al., 1986); (7) wheat stalks (Grohmann et al.,1986);(8) Stip a tenacissima (our experimental data). Th eresults of the modeling are reported in Table11. Figures5a, 6a, 7a and 8a show the fitting of the model to theexperimental da ta on four selected biomasses using th eseverity factorR g ; n th is fitting we can see the grouping

of th e experimental da ta for each particular acid concen-tration. If, however, instead of usingRB s the severityparameter we replace it by the new combined severityfactor RB+, which includes the acid effect, we obtain t hefittings depicted in Figures 5b-8b. One weakness of themodel when the experime ntal data a re fitted by means ofth e new combined severity parameterR B + s that th e au-tohydrolysis data are not very well modeled since theprecise acid concentrationof the aqueous media is notwell-defined and, moreover, it changes with time. In Figure8b we can recognize this lack of fitting; in th is particularcase we have found th at an acidity of0.05 w / w H2S04leads to the op timum fitting.

We should also point out th at t he proposed m odel hasbeen tried for all eight biomasses studied . Two optimi-

0,60

0,40Klnelkmodel -

0,zo

0 w1 0 ' 1 0 ' 1 0 '

I

0,201

0,W

, , , CA=?XH2SOI

, ,

II O ' 1 0 5 1 0 ' 1 0 ' 1 0 '

FIB+@)

Figure 7. Modeling of hemicellulose solubilization. Corn stalksthis work).

zation methods have been used to estimate the nonmea-surablexroand E , These two methods are (a) the steepestdescent method, by Marqu ardt (1963) and (b) th e methoddescribed by Dennis and Schnabel(1983) using th e Hes-sien update matrix following the Fletcher-Broyden-Goldfeldt-Shanno (FBGS ) approach.

Discussion

If we accept th at during th e heterogeneous reaction ofth e acid-catalyzed hydrolysis of the hemicelluloses leadingto the ir solubilization the form ation of t he cyclic carbanionis the rate-controlling step, we have shown tha t a rigorousderivation of th e rate expression can be m ade t o monitorth e extent of hemicellulose solubilization. Furthe rmore ,th e use of the ac tivated complex or transition-state theory,together with Leffler's relationship, has led us to thedefinitionof a seve rity factorR B having a thermodynamicfoundation. Several authors working in this field, amongthem Mehlberg and Tsao (1979) and D utoit etal. (1984),have claimed th at t he m odeling of th e hemicellulose sol-ubilization can be expressed by two pseudo-first-orderreactions with respect to the hemicelluloses remaining onth e lignocellulosic fiber network. On the basisof this



Ind. Eng. Chem. Res., Vol.30, No. 11, 1991 2423

Table 111. Estimation of the Pseudo-First-Order Rate Constantsbiomass E,, J/mol E,, J/mol ASr, J/ mol.K) AS,, J/ mol.K) kd, s-l k&, s-l k, 150 C), s-l k, 150 C), s l

Stim t . 85.5303 85.5303 -103.2 -173.3 2.8307 6.0304 0 . 7 3 4 3 1. 53 478.2309 4.2308 2.33-03 1. 13 45inus r. 101.6303 109.9303 -55.9

wheat stalks 123.5303 127.8303 8.4corn stalks 91.7303 109.8303 -85.1Populus t . 149.3303 134.5303 84.2

Kinet icmodel -C A d . O X H Z S 0 4

Experimenlr A C A d . 5 H 2 S 0 4

CA.1 .O X H2S04

- - ,E E

(.a

0,40.-

UKineticmodel -

;sK 0,20 - C A d 0 . 5 K H 2 S 0 4 o

, Erper imanls I A CA=l.O HZSCd

4x -

Kineticmodel -

Erper imanls I A CA=l.O HZSCdK C A d 0 . 5 K H 2 S 0 4 o

i CA=0.05Y H2S04 (Aulohydrolyr iacaw)

0,w ' ' ~ ~ ' ~ I ' I . ' " _ " ' I - . ' . '10 I O 1 0 ' 1 0 5 1 0 ' 10

RB*(s)Figure 8. Modeling of the hemicellulose solubilization. pa t .this work).

information and of the ma thematical formalism developedin a previous section, we have proposed a new pseudoki-netic model introducing th e use of th e severity factorRB+= RBCH+.Th is new model fits well th e variations of th eamountof nonsolubilized hemicelluloses remaining in t hefiber. It also estimates reasonably well th e readily solu-bilized fraction of hemicelluloses. Moreove r, th e modelhas shown tha t th ere are im porta nt differences betweenthe solubilization profiles obtained from the softwoodsPinus r. ) , he hardwoods, a nd graminae plants; in fact

higher severities ar e needed in t he case of the softwoodsto achieve t he same solubilization levels.The results obtained in our optimizations have alsoshown that th e amoun t of th e readily recoverable hemi-cellulosesin the aqueous phase varies between 60 and90w/w in thecase of hardwoods and gram inae plants. Torreset al. (1986), working on the thermomec hanical fraction-ation of Populus t . , reported a70% w/w readily solubilizedfraction of hemicelluloses. Maloney et al. (1984) andMaloney and Chapm an (1986) predicted a value of 68%w/ w, using the classical pseudo-first-order kinetic model,for the readily solubilized fractionof hemicelluloses derivedfrom Betula p . Our m odeling results a re in accord withthe results reported by these authors.

A comparison between the experimental values ofxdobtained by using the Dutoit e tal. (1984) method and t he

1.8E13 1.6312 1.OE-02 2.53-042.5308 4.OEO8 1 .13-03 1 .13451.7317 3.3313 6.13-02 7 . 9 3 4 4

RB (SIFigure 9. Fitting showing effect of optimizing xd starting from apreestablished value.

predictions ofour model in th e case of corns t a l k sis shownbelow.

xdpred) xdexp) error, %

69.8 74.2 ==6

Th e optimization has been conducted in two ways: (a)fixingxIo obtained experimentally an d estimating the op-timum activation energies; (b) estimating simultaneouslyx d and activation energies.

As we can see from the following tabu lated results, wehave not observed any significant variations on the op-

timized values of th e activation ene rgies, which proves thestatistical robustnessof the models.XrO E,, J/mol E,, J/mol

exp = 0.74 90.5303 108.9303opt = 0.70 91.7303 109.8303

In fact, a difference of 6% between the experimentallyobtained xd and the optimized one leads to a deviation of1 n the activation energies. In Figure 9 we presen t thedifferences observed for the two casesin terms of modeling.

The computationof the kIo and kBovalues has beenconducted using the a ctivation energies estimated by op-timization, Leffler's relationship, and the equation

In Table I11 we present the estimationof the pseudo-first-order rate constants.For the softwoods, representedby Pinus r. , the parameter xd is much lower than forhardwoods; in fact the optimization gave usa value of 21%.However, we should point o ut th at th e lackof extensiveda ta sets in softwood fractionation preven ts us from ad-vancing statistically consistent values. Nevertheless, theresults obtained seem coherent with what has been re-ported in the literature, especially in terms of activationenergies; in fact we have back calculated th e activationenergies th at lie in th e region between 80 and 150 kJ/mo l,which are similar to those reported in related works.

Th e observation that the amoun ts of rapidly solubilizedhemicelluloses are lower in softwoods than either in




CHZOH OH CH,OH

IOH COOH OH

Figure 10. Glucosidicchainshowing a substituent,C O O H ,nsteadof a regular hydroxyl,-OH, group.

hardwoods or in graminae plants shouldbe associated with

the existence of differences in the ultrastructure of thehemicellulosic families encountered in th e different sub-stra tes (Belkacemi, 1990). In fact, th e behavior of theglucosidic bonds during the ir hydrolysis is influenced bytwo effects which could be interdepen dent or not: th econformation of the m onomeric units of th e osidic poly-meric skeleton; the inductive effect of the substitutivegroups associated chemically with th e polymeric chain. Infact these different substituen ts (in Figure 10 we presentan example with carboxyl groups) create distinct distri-butions of electronic densities aroun d th e oxygen atom,thu s determining its reactivity.

T he global effect of th e carboxylic groupsas shown inFigure 10 is a stabiliza tion of the ringsand a lower prob-ability of hydrolytic reaction for the C-0-C bonds. Th isexplains the lower reactivity of highly branched xylanhaving 4-0-methylglucuronic groups. Since the softwoodsare com posed of uro nic acid rich hemicelluloses (Fengeland Wegener, 1984), it supp orts our interpr etation of theexperimental data collected and the modeling results.

Barnet (1984) studied t he fast au tohydrolysis ofPopulusand suggested that the hydrolysis of the hemicellulosesdoes not proceed randomly along the xylan polymericchains but proceeds deterministically preferring the de-acetylated positions. He concluded tha t th e acetylatedgroups stabilize th e glucosidic bond because their hydro-phobic behavior renders th e proton a ttac k more difficult.However, we should indicate t ha t th e acetyl groupsas wellas the uronic groups play a double role during the hy-drolysis; tha t is, they slow down the hydrolysis rates be-cause of the Stabilization hey bringto the glucosidic bondsand th ey speed up th e autohydrolysis rates because thedisengaged acetic acid can act as a catalyst. Th e samestabilization phen omenon is also reported in the work ofConner et al. (1984), and was previously proposed byMoelwyn-Hughes (1928) and Ingvar e t al. (1963).

Conclus ionsWe have proposed a kinetic model to simulate and

monitor the solubilization of polymeric carbohydrates (i.e.,hemicelluloses), based upon classical mechanistic consid-erations. Th is model leads to a severity factor which ex-presses the comm on effect of th e indepen dent variablesgrouped in a single reaction coordinate. Specific conclu-

sions ar e th e following:1. Th ere e xist two kinetic type s of hemicelluloses.2. The kinetics of the solubilization of the hemicelluloses

have been developed on the assumption that the con-trolling step is the formation of a cyclic carbanion aspredicted by the conform ational analysis; the successfulapplication of th e derived model to the experimental re-sults available in th e literature has shown the usefulnessof our choice.

3. Th e hydrolytic treatmen t can be represented by theseverity factor RB,whose thermodynam ic significance isassociated with the existence of an isokinetic temperatu reand a com pensation effect between th e enthalpy and en-tropy of the key elementary s teps of the hydrolysis reac-tion. Th is suggests th at the same mechanism of bond

rupture prevails inall the solubilization reactions despitethe possible structural diversity of the hemicelluloses be-longing to th e different ty pes of biomass.

4. Th e kinetic model developed in this work allowsusto have a good estim ation of th e rapidly solubilized fractionof the hemicelluloses,3cd, initially present in th e originalbiomass. Thexd parameter is an intrinsic characteristicof each particular biomass and is associated t o ita char-acteristic structure and chemical composition.

AcknowledgmentWe are indebted to th e Cen tre Quebecois de la Valori-

sation de la Biomasse and th e Gouvernement du Q uebec(FCA R) for funding relatedto this research program. Wealso gratefully acknowledge th e financial participation ofthe A lgerian Government for th e grant t ha t allowed K.B.to complete his Ph.D. program. M. M.J.-P. Lemonnier,G. Phaneuf,as well as M. T. S. Nguyen and the analyticalteam of the Laboratoire AssociB-Materiaux Ligno-cellulosiques of the University of Sherbrooke are alsogratefully acknowledged for the technical a nd analyticalsupp ort they provided.

Nomencla ture

A = constant (Arrhenius law preexp onential factor)B = constant(in equation expressing the compensation effed)C = concentrationD = D = kB*Tb/h* exp[-a/(R*/Ti,)]E = activation energy (in Arrhenius law)G = Gibbs free energyh = Planck constantH = enthalpy (factorH)k = rate constantkB = Boltzmann constantK = constantK, = equilibrium constantN = number of experimental pointsr = reaction rateRB+= severity factor based on mechanistic considerationsRB = severity factor corrected by the acid concentrationS = entropyt = timeT = temperatureT = mean temperatureTi, isokinetic temperaturex = fractionof hemicelluloses present in the fiberxro = fraction of hem icelluloses rapid ly solubilized initially

x s o = fraction of hemicelluloses slowly solubilized initially

A x = mean difference between the experimental and the

Greek Symbols= constant (in Leffler's relationship)

6 T ) = T/T,) exp[(E/RTb)((T- Tb)/2')]= characteristic

u = kBT/h= frequency factorIndexes and Abbreviations[ ] = concentrationeq = equilibriumexp = experimentalF = polymer.-H+is0 = isokineticmax = maximummod = modelr = fast reactiont = tabulated0 = reference state(25 OC, 101.3 kPa)1,2 = elementary step 1,2

present in the fiber

present in the fiber

theoretical values ofx

parameter



Ind. Eng. Chem. Res., Vol. 30, No. 11, 1991 2425

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Received for review November 19,1990Revised manuscript received June3, 1991

Accepted June 20, 1991

1202-1224.

431-444.

844-850.

551-555.

Registry No. Hemicellulose, 9034-32-6.

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