Diffusion of sulfuric acid within lignocellulosic biomass particlesand its impact on dilute-acid pretreatment

Sung Bae Kim 1, Y.Y. Lee *

Department of Chemical Engineering, Auburn University, Auburn, AL 36849, USA

Received 20 June 2001; received in revised form 28 September 2001; accepted 14 October 2001

Abstract

Intra-particle diffusion of sulfuric acid into sugarcane bagasse, corn stover, rice straw and yellow poplar was investigated to

determine the effective diffusivity of sulfuric acid within the porous biomass structure. Diffusion experiments were conducted over

25–75 �C for two different biomass sizes using dynamic diffusion test cells. Diffusivities of sulfuric acid in agricultural residues weresignificantly higher than those of hard wood. Diffusivity data for each biomass were fitted into the Arrhenius equation for ex-

trapolation to higher temperatures. The diffusivity data were subsequently incorporated into a theoretical model to determine acid

profile within the biomass matrix. The modeling results indicate that intra-particle diffusion of acid influences the rate of dilute-acid

pretreatment if unground biomass feedstock is used under normal pretreatment conditions. A criterion was set up to determine the

critical biomass size at which the intra-particle acid diffusion becomes a rate-influencing factor for a given pretreatment condi-

tion. � 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Diffusivity; Sulfuric acid; Biomass; Pretreatment

1. Introduction

Treatment of biomass with dilute sulfuric acid iswidely used to pretreat and hydrolyze lignocellulosicmaterials (Kim and Lee, 1987; McMillan, 1992). Whenapplied to a continuous process such as a screw-fed co-current reactor, it requires a relatively short residencetime. Therefore, the penetration of acid catalyst into thebiomass, as well as acid dispersion in the reactor, cansignificantly affect the overall reaction, and consequentlythe reactor performance.Acid impregnation into wet biomass is a diffusion

process, which is more complex than homogeneoussystems because it occurs through a porous biomassstructure. The literature on this subject is very limited.Previous studies dealt with the diffusion of nonelectro-lytes (Fukuyama and Urakami, 1980, 1982, 1986), boricacid (Kumar and Jain, 1973), and sulfuric acid (Tillmanet al., 1990) through water-saturated wood. These

studies emphasized variation of diffusivity due to theasymmetry of the wood structure. They found that inwood, longitudinal diffusion dominates among the threediffusional directions (i.e., longitudinal, tangential andradial) in wood structure.In this work, the overall bulk transport properties of

sulfuric acid were investigated without considering dif-fusional directions. The primary purpose of this inves-tigation was to experimentally determine thefundamental transport properties of sulfuric acid, spe-cifically the effective diffusivity of sulfuric acid withinbiomass. The scope of the experimental involved fourdifferent substrates (sugarcane bagasse, corn stover, ricestraw, and yellow poplar), two different temperatures,and two different biomass sizes. The data were used todevelop a theoretical model that assesses the effect ofacid diffusion in dilute-acid pretreatment processes.

2. Methods

2.1. Materials

Bagasse and rice straw, and corn stover and yellowpoplar were obtained from BC International (Jen-nings, LA) and NREL (National Renewable Energy

Bioresource Technology 83 (2002) 165–171

*Corresponding author. Tel.: +1-334-844-2019; fax: +1-334-844-

2063.

E-mail addresses: sb_kim@nongae.gsnu.ac.kr (S.B. Kim), yylee@

eng.auburn.edu (Y.Y. Lee).1 On leave from Geongsang National University, Chinju, 660-701,

Korea.

0960-8524/02/$ - see front matter � 2002 Elsevier Science Ltd. All rights reserved.

PII: S0960-8524 (01 )00197-3

Laboratory), respectively. Each biomass was washedto remove dirt and extraneous materials and groundto desired sizes using a IKA Laboratory cutting mill(MF10) with a 3 mm sieve insert that was the largestone supplied by IKA. With this sieve insert, themaximum particle size attainable was 14 mesh. Aftersieve screening, the biomass was left for several daysat room temperature to equilibrate with moisture inthe air, and kept in a sealed container. Sulfuric acidsolution (0.1 N, Fisher Scientific) was used withoutdilution in the diffusion experiments.

2.2. Acid diffusivity

The diffusion apparatus used to determine the effec-tive diffusivity of sulfuric acid is shown in Fig. 1. Theexperimental setup consisted of a three-neck flask,constant-temperature water bath, conductivity meter(Suntex, SC-170), and computer-interfaced data acqui-sition system (Omega OMK-TDA4). The conductivitymeter was equipped with a glass cell (cell constant10 cm�1) and automatic temperature compensationprobe. The conductivity probe in the original design wasequipped with a protective glass shield around the metaltip that slowed the response. To reduce the time con-stant of the probe, the protective shield was removed.The linear range of the conductivity meter was cali-brated with respect to sulfuric acid concentration at 25,50 and 75 �C.In the diffusion experiment, 0.5 g of presoaked bio-

mass in 250 ml of deionized water was placed in the well-agitated flask. After attaining thermal equilibrium withthe water bath, a known amount of acid was injectedinto the flask. The variation of the bulk acid concen-tration due to diffusion into the biomass was traced withone-second intervals through digital transmission of

conductivity data into the data acquisition computer.The data acquisition was performed for 12 min. Theconcentration of acid measured at 30 min was taken asC1 in the theoretical analysis.

3. Unsteady-state diffusion model

Unsteady-state acid diffusion into a solid sphere in awell-agitated tank is a well-defined physical problem forwhich the mathematical solution is available from theliterature. To reduce complexity, the experiments wereconducted with highly agitated liquid so that the exter-nal film resistance was negligible. The modeling involvesan acid balance in the solid medium and in the bulkliquid.Diffusion into a spherical biomass particle is de-

scribed by the following PDE:

oCot

¼ Deo2Cor2

�þ 2

roCor

�: ð1Þ

The shape of ground biomass is assumed to be spherical.The particle diameter was assumed to be the same as thescreen opening. Eq. (1) can be solved using initial andboundary conditions.

t ¼ 0; 0 < r < R; C ¼ 0; ð2Þ

t > 0; r ¼ 0; oCor

¼ 0; ð3Þ

r ¼ R; C ¼ Cb; ð4Þ

where Cb is the concentration of acid in the solution.The acid balance in the liquid phase is expressed by

the following equation:

VdCbdt

¼ � ADeoCor

����r¼R

; ð5Þ

Fig. 1. Experimental apparatus for determination of acid diffusivity.

166 S.B. Kim, Y.Y. Lee / Bioresource Technology 83 (2002) 165–171

t ¼ 0; C ¼ Cb; ð6Þ

where V is the volume of solution and A is the totalsurface area of the particles.These equations can be solved by Laplace transforms.

The analytical solution of this classical problem is givenby Crank (1975) and expressed in terms of fractionaluptake, F, as follows:

F ðtÞ ¼ 1�X1n¼1

6a 1þ að Þ9þ 9a þ q2na2

exp

�� q2nDet

R2

�ð7Þ

where qn are the non-zero roots of tan qn ¼ 3qn=ð3þ aq2nÞ, a ¼ 3V =ð4pR3Þ is the ratio of the volumes ofliquid and solid spheres, F ¼ ðC0 � CðtÞÞ=ðC0 � C1Þ isthe fractional uptake, CðtÞ is the concentration at time tand C1 is the concentration at infinite time.For detailed solution procedure, readers may consult

Bird et al. (1960).

4. Results and discussion

The bulk acid concentrations in the diffusion experi-ments were held below 0.001 N, a concentration withinthe linear region of the conductivity probe. A typicalconductivity profile versus time in a diffusion experimentis shown in Fig. 2. The response curve indicates that themaximum conductivity was reached within 2 s after acidinjection, which is fast enough to ignore error due toprobe lag. There was substantial signal noise in theconductivity data, as indicated in Fig. 2. Unfortunately,it was unavoidable because most of it was primarily dueto liquid turbulence rather than the meter. The noiselevel was statistically reduced by regression curve-fittingsoftware available from Sigma Plot.

4.1. Effect of stirring speed and soaking time

The effects of the stirring speed and water soakingtime were investigated, as they are the major parameterspotentially affecting the diffusivity measurement. Theconductivity profiles were measured with various agita-tion speeds (Fig. 3). The results clearly indicate thatstirring speed does not affect the conductivity profilewithin 400–700 rpm. It also indicates that external filmresistance is negligible at this level of agitation. In a testwhere three levels of water presoaking were applied (10min, 2 h, and overnight), the conductivity profiles wereindistinguishable among the three cases (data notshown). From these observations, 600 rpm and 2 hsoaking time were applied throughout this work to en-sure complete mixing and a uniformly wet biomass.

4.2. Acid diffusivity

To determine diffusivity, the conductivity profileswere corrected for noise, as previously discussed forvarious biomass feedstocks. The experimental fractionaluptake F ðtÞ of sulfuric acid and the theoretical F ðtÞcalculated from Eq. (7) are compared in Fig. 4. The first10 terms of the infinite series in Eq. (7) were used, whichwas sufficient for convergence. Determination of thediffusivity was done using a parameter estimation pro-cess in SAS NLIN program (Freund and Littell, 1992).The best-fit diffusivity, the only parameter in Eq. (7),was estimated through a regression analysis of the ex-perimental F ðtÞ against Eq. (7). Fig. 4 verifies that theexperimental F ðtÞ agrees well with the theoretical pre-diction, which confirms that the proposed model is validfor the unsteady-state acid diffusion. In the figure it isalso shown that for all biomass species fractional uptakedoes not quite reach the saturation even after 600 s. At25 �C, approximate times to reach 70% of fractionaluptakes for bagasse, corn stover, rice straw and yellowpoplar were about 150, 220, 120, and 430 s, respectively.These data were taken from biomass samples of 14–20mesh size. The acid uptake profiles were also measuredfor unground bagasse. A random cut of the feedstocksinto 1–2 cm was applied to place them into the diffusioncell and keep them agitated. The times for 70% frac-tional uptakes measured for the unground substrate was420 s, which is about 3 times longer than that of 14–20mesh. This implies that intra-particle diffusion of acidcould indeed significantly affect the dilute-acid pre-treatment of this feedstock, especially for a pretreatmentprocesses shorter 420 s.The results of diffusivity measurements performed at

25, 50 and 75 �C are presented in Table 1. Diffusivitiesfor agricultural residues were much larger than yellowpoplar, reflecting that hardwood is more rigid and densethan agricultural residues. In most cases, except for cornstover at 50 and 75 �C, diffusivities for 14–20 mesh

Fig. 2. Typical conductivity profile obtained from a diffusion experi-

ment (bagasse, 14–20 mesh, 25 �CÞ.

S.B. Kim, Y.Y. Lee / Bioresource Technology 83 (2002) 165–171 167

biomass differ by 10–35% from those for 20–24 mesh.Theoretically diffusivity is independent of particle size.We believe this discrepancy is largely due to inaccuratesize designation we applied in this work. The mean ofmesh screen opening sizes used in modeling may not bethe true mean size of the particles. The size of the par-ticle affects the calculated diffusivity value quite sensi-tively. Our sample calculation shows that 30% differencein particle size (as in 14–20 mesh) causes about 40%difference in estimated diffusivity. Data listed in the tablewere fitted into the Arrhenius-type correlation such that:

D ¼ D0 expð�E=RT Þ; ð8Þwhere D is the diffusivity (cm2=s), D0 the pre-exponentialfactor for diffusivity (cm2=s), E the activation energy fordiffusion (cal=mol), T the absolute temperature (K) andR is the gas constant (cal=mol K).According to Eq. (8), a plot of lnD vs. 1=T should

yield a straight line with slope E=R. Arrhenius plotsprepared for bagasse, corn stover, rice straw and yellowpoplar are shown in Fig. 5. Using a linear regression, theArrhenius constants were determined as listed in Table2. Activation energy for rice straw was the highestamong them, giving it the highest sensitivity to tem-perature. Bagasse has the lowest activation energy. Ac-tivation energy for yellow poplar obtained from thisstudy was about 50% lower than that of Aspen wood(Tillman et al., 1990).In addition to the issue of particle size, another

problem occurred in diffusion experiments. Some com-

Fig. 3. Effect of stirring speed on conductivity profile (bagasse, 14–20 mesh, 25 �C).

Fig. 4. Fractional uptake of acid by various biomass feedstocks: (a)

bagasse (BG) and yellow poplar (YP), (b) rice straw (RS) and corn

stover (CS) (14–20 mesh, 25 �C, –: best fit for experimental data, - -:model prediction).

168 S.B. Kim, Y.Y. Lee / Bioresource Technology 83 (2002) 165–171

ponents extracted from solid biomass seemed to beneutralized with sulfuric acid because the maximumconductivity reached after injection varied with experi-mental condition; temperature, biomass species, andparticle size. The amount of acid neutralized increasedwith temperature. This amount also varied with biomassin the order of yellow poplar < bagasse < corn stover <rice straw. In the case of particle size, the 20–24 meshbiomass had a slightly higher neutralizing capacity thanthe 14–20 mesh biomass under the same condition. Theamount of acid neutralized was estimated from the dif-ference between maximum conductivity achieved and

the conductivity calculated from the calibration curve.The lowest neutralization capacity was observed with25 �C, 14–20 mesh of yellow poplar which showed zeroneutralization capacity; the highest was with 75 �C, 20–24 mesh of rice straw which showed approximately 38%neutralization of injected acid. The high neutralizationcapacity of rice straw raises a concern as to whether itinterferes with the measured diffusivity resulting in ahigher diffusivity than bagasse and corn stover. Neu-tralization, however, is a rapid process occurring withinthe first 3 s or so. The acid uptake process occurs afterthe neutralization over a much longer period. It was

(a) (b)

(c) (d)

Fig. 5. Arrhenius plots for acid diffusivity: (a) bagasse, (b) corn stover, (c) rice straw, (d) yellow poplar.

Table 1

Summary of acid diffusivity

Biomass Size (mesh) Diffusivity (cm2=s)

25 �C 50 �C 75 �C

Bagasse 14–20 3:59� 10�6 5:02� 10�6 7:25� 10�620–24 2:99� 10�6 4:02� 10�6 5:36� 10�6

Corn stover 14–20 3:25� 10�6 4:59� 10�6 7:13� 10�620–24 2:69� 10�6 4:48� 10�6 7:01� 10�6

Rice straw 14–20 5:79� 10�6 1:16� 10�5 2:01� 10�520–24 4:46� 10�6 9:62� 10�6 1:50� 10�5

Yellow poplar 14–20 1:73� 10�6 2:78� 10�6 4:34� 10�620–24 1:56� 10�6 2:29� 10�6 3:52� 10�6

S.B. Kim, Y.Y. Lee / Bioresource Technology 83 (2002) 165–171 169

therefore concluded that it would not interfere with thediffusion experiments. There is still a concern as to theeffect of neutralizing components remaining in the bio-mass. Whether it is significant enough to influence thediffusivity measurement in this work is unknown at thistime.

4.3. Acid profile within biomass

To verify the local acid concentration within solidbiomass, the unsteady state diffusion equation for flat-plate geometry was employed. This is a classical math-ematical problem with the following solution (Bird etal., 1960):

C � CbC0 � Cb

¼ 2X1n¼1

ð�1Þnþ1

n� 12

� �pexp

� n�

� 12

�2p2

DetL2

!

� cos n��

� 12

�pxL

�: ð9Þ

The reason for choosing a flat-plate geometry is jus-tified because the agricultural residues used in this work(sugarcane bagasse, rice straws, and corn stover) are inthe shape of a flat-plate. These substrates all have hardouter shells that comprise most of the total mass. Thecrushed feedstocks are mostly composed of thin crusts.In a commercial process, particle (or chip) sizes largerthan the one used in this experiment are likely to beused. A sample calculation of the local acid concentra-tion within the biomass matrix as a function of positionand time is shown in Fig. 6. In this example, the thick-ness of flat biomass was assumed to be 0.1 cm (or L (thecharacteristic length)¼ half-chip thickness¼ 0.05 cm). Itwas based on sugarcane bagasse, at 140 �C, with thecorresponding De of 1:12� 10�5 cm2=s. It describesthe gradual change of acid profile within the biomass.The figure shows that about 80% saturation of acid isachieved at the center point in 3 min. From the solutionof Eq. (9), we also find that the dimensionless diffusiontime, s ¼ Det=L2 ¼ 1, represents a critical value at whichthe acid profile starts to deviate from the fully saturatedlevel. One can thus define the critical diffusion time asL2=De. It is termed the critical diffusion time in the fol-lowing sense. If the biomass processing time is belowthis level, a discernible dip of acid profile in the centerregion of biomass is expected, therefore intra-particleacid diffusion becomes a significant factor in the overall

pretreatment process. To evaluate the critical diffusiontime one only needs to know the effective diffusivity (De)and the size of biomass (L). However, the critical dif-fusion time alone will not determine the significance ofthe acid diffusion. The pretreatment reaction time is alsoinvolved. For example, for a pretreatment process thatrequires 10 min of reaction, the acid diffusion process ofthe previous example will not be likely to affect theoverall process because most of the reaction will occurafter acid has fully saturated the biomass. On the otherhand, if the pretreatment process requires one minute ofreaction time, the overall process will be severely af-fected by acid diffusion because the pretreatment processoccurs during the early phase of the transient acidpenetration period. One may even find that the reactionoccurs only at the outer surface region.In conjunction with the above discussion, we now

propose the following general criterion for significanceof acid diffusion.Acid diffusion is unimportant, if

Thiele modulus ¼ / ¼ Lðk=DeÞ1=2 < 1;where k is the first-order rate constant of the pretreat-ment process (hemicellulose hydrolysis), and it is to bedetermined independently.This simple criterion covers both diffusion and pre-

treatment reaction simultaneously. It is offered as a toolto be utilized in pretreatment design and operation. Asan example application, we define the critical biomasssize as ðDe=kÞ1=2. For a given pretreatment process whereDe and k are predetermined, acid diffusion is an influ-encing factor only if the biomass size is above the criticalvalue, ðDe=kÞ1=2. It is to be noted again that L representsthe characteristic size of biomass, half-chip thickness forflat-plate shape, or one third of radius for a sphere. This

Fig. 6. Predicted acid concentration profile as a function of time and

position (bagasse, chip thickness¼ 0.1 cm or L ¼ 0:05 cm, 140 �C,Cb ¼ 1:0%Þ.

Table 2

Arrhenius constants for acid diffusion De ¼ D0 expð�E=RT Þ

Biomass D0 ðcm2=sÞ E (cal=mol)

Bagasse 2:69� 10�4 2610

Corn stover 1:16� 10�3 3540

Rice straw 2:46� 10�2 5000

Yellow poplar 6:08� 10�4 3500

170 S.B. Kim, Y.Y. Lee / Bioresource Technology 83 (2002) 165–171

is one example of a practical application of the funda-mental data we have provided in this work. Hopefullythe data and the methodology given in this work willfind broader application in biomass pretreatment pro-cesses.

Acknowledgements

This research was conducted as a part of a Cooper-ative Agreement with US Department of Energy (DE-FC36-99GO10475). The authors wish to thank BCI,Jennings, LA for providing sugarcane bagasse and ricestraw feedstocks, and NREL for corn stover feedstockand the Engineering Experiment Station of AuburnUniversity for providing additional financial assistancein the form of cost-share.

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